การทดสอบจุดกดแบบปรับเปลี่ยนของหินผนังบอ ที่เหมืองแรทองคําชาตรี นายชาติชาย อินทรประสิทธิ์ วิทยานิพนธนี้เปนสวนหนึ่งของการศึกษาตามหลักสูตรปริญญาวิศวกรรมศาสตรมหาบัณฑิต สาขาวิชาเทคโนโลยีธรณี มหาวิทยาลัยเทคโนโลยีสุรนารี ปการศึกษา 2552
การทดสอบจดกดแบบปรบเปลยนของหนผนงบอ ทเหมองแรทองคาชาตร
นายเดโช เผอกภม
นายชาตชาย อนทรประสทธ
วทยานพนธนเปนสวนหนงของการศกษาตามหลกสตรปรญญาวศวกรรมศาสตรมหาบณฑต
สาขาวชาเทคโนโลยธรณ
มหาวทยาลยเทคโนโลยสรนาร
ปการศกษา 2552
MODIFIED POINT LOAD TESTS OF PIT WALL
ROCK AT CHATREE GOLD MINE
Chatchai Intaraprasit
A Thesis Submitted in Partial Fulfillment of the Requirements for the
Degree of Master of Engineering in Geotechnology
Suranaree University of Technology
Academic Year 2009
MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT
CHATREE GOLD MINE
Suranaree University of Technology has approved this thesis submitted in
partial fulfillment of the requirements for a Masterrsquos Degree
Thesis Examining Committee
_________________________________
(Asst Prof Thara Lekuthai)
Chairperson
_________________________________
(Assoc Prof Dr Kittitep Fuenkajorn)
Member (Thesis Advisor)
_________________________________
(Dr Prachya Tepnarong)
Member
_______________________________ _________________________________
(Prof Dr Pairote Sattayatham) (Assoc Prof Dr Vorapot Khompis)
Acting Vice Rector for Academic Affairs Dean of Institute of Engineering
ชาตชาย อนทรประสทธ การทดสอบจดกดแบบปรบเปลยนของหนผนงบอทเหมองแรทองคาชาตร (MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT CHATREE GOLD MINE ) อาจารยทปรกษา รองศาสตราจารย ดร กตตเทพ เฟองขจร 191 หนา
การทดสอบจดกดแบบปรบเปลยนไดถกนามาใชในการหาคาความเคนกด แรงดง และคาความยดหยนของหนตวอยางในหองปฏบตการทดสอบ มาเปนเวลาเกอบสบปแลว วธการทดสอบนไดถกประดษฐ และจดทะเบยนลขสทธโดยมหาวทยาลยเทคโนโลยสรนาร เครองมอ และวธการทดสอบถกออกแบบใหมราคาถกและงาย เมอเปรยบเทยบกบวธการทดสอบเพอหาคณสมบตเชงกลของหนแบบดงเดม เชน วธการทดสอบตามมาตรฐาน ISRM และ ASTM ในอดตการทดสอบจดกดแบบปรบเปลยนสวนใหญมกทดสอบในแทงตวอยางหนทเปนรปวงกลม และรปสเหลยมมมฉาก ในขณะทมการอางวาการทดสอบแบบจดกดแบบปรบเปลยนนสามารถใชไดกบหนทกรปราง แตผลทดสอบวธนกบหนทมรปรางไมเปนทรงเรขาคณตยงมนอยมาก เนองจากเหตนจงยงไมมการยนยนอยางเพยงพอวา วธการทดสอบจดกดแบบปรบเปลยนสามารถใชไดจรงและมความสมาเสมอเพยงพอในการตรวจหาคณสมบตทางกลศาสตรพนฐานของหนในภาคสนามซงไมสามารถจดหาเครองเจาะและเครองตดหนได วตถประสงคของงานวจยนคอ เพอประเมนศกยภาพของการทดสอบของวธการทดสอบแบบจดกดแบบปรบเปลยนในหนตวอยางทมรปรางไมเปนทรงเรขาคณต ตวอยางหนสามชนด จานวน 150 ตวอยางเปนอยางนอย ไดแก porphyritic andesite silicified-tuffaceous sandstone และ tuffaceous sandstone ซงเกบรวบรวมมาจากผนงบอทางดานทศเหนอของเขาหมอทเหมองแรทองคาชาตร จะถกนามาใชในการทดสอบน อตราสวนระหวางความหนาของหนตวอยางตอเสนผาศนยกลางของหวกด แปรผนระหวาง 2 ถง3 และ อตราสวนระหวางเสนผาศนยกลางของตวอยางหนกบเสนผาศนยกลางของหวกดแปรผนระหวาง 5 ถง 10 การสญเสยรปรางและการแตกหกของหนจะถกนามาใชในการคานวณหาคาความยดหยนและความแขงแรงของหน และจะมการทดสอบแรงกดในแกนเดยวและแรงกดในสามแกน การทดสอบแรงดง และการทดสอบจดกดแบบด ง เด มในหนท งสามชนดดวยเช นกนเพ อนาผลการทดสอบท ได มาใชในการเปรยบเทยบกบผลทไดจากการทดสอบจดกดแบบปรบเปลยน แบบจาลองโดยใชโปรแกรมคอมพวเตอรจะถกนามาใชในการศกษาการกระจายตวของแรงเคนในกอนตวอยางหนของการทดสอบจดกดแบบปรบเปล ยนภายใต อ ตราสวนระหวางความหนาของหนต วอย างต อเสนผาศนยกลางของหวกดทตางๆกน และจะมการประเมนเชงปรมาณของผลกระทบของความมรปรางทไมเปนรปทรงทางเรขาคณตของหนตวอยาง ความเหมอนและความแตกตางของผล
II
สาขาวชา เทคโนโลยธรณ ลายมอชอนกศกษา ปการศกษา 2552 ลายมอชออาจารยทปรกษา
การทดสอบจดกดแบบปรบเปลยนและการทดสอบจดกดแบบดงเดมจะถกนามาพจารณา อาจมการประยกตการคานวณทเปนแบบแผนของการทดสอบจดกดแบบปรบเปล ยน เพ อเพ มความสามารถในการคาดคะเนคณสมบตทางกลศาสตรของหนตวอยางทมรปรางไมเปนรปทรงทางเรขาคณตไดดยงขน
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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ASTM D7012-07 Standard test method for compressive strength and elastic moduli
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Conshohocken American Society for Testing and Materials
ASTM D3967-81 Standard test method for splitting tensile strength of intact rock
core specimens In Annual Book of ASTM Standards (Vol 0408)
Philadelphia American Society for Testing and Materials
ASTM D4543-85 Standard test method for preparing rock core specimens and
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Materials
ASTM D5731-95 Standard test method for determination of point load strength
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Philadelphia American Society for Testing and Materials
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Bieniawski Z T (1975) The point-load test in geotechnical practice Engng
Geol 9 1-11
89
Bieniawski Z T and Bernede M J (1979) Suggested methods for determining the
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Mech Min Sci 16 (2)xxxx (page no)
Bray J W (1987) Some applications of elastic theory In E T Brown (ed)
Analytical and Computational Methods in Engineering Rock
Mechanics (pp 32-94) Allen amp Unwin London
Broch E and Franklin J A (1972) The point-load test Int J Rock Mech Min
Sci 9 669-697
Book N (1977) The use of irregular specimens for rock strength tests Int J
Rock Mech Min Sci amp Geomech Abstr 14 193-202
Book N (1979) Estimating the triaxial strength of rocks Int J Rock Mech Min
Sci amp Geomech Abstr 16 261-264
Book N (1980) Size correction for point load testing Int J Rock Mech Min
Sci 17231-235 [Technical note]
Book N (1985) The equivalent core diameter method of size and shape correction
in point load testing Int J Rock Mech Min Sci amp Geomech Abstr
22 61-70
Brown E T (1981) Rock characterization Testing and Monitoring ISRM
Suggestion Methods New York International Society for Rock
Mechanics Pergamon Press
Butenuth C (1997) Comparison of tensile strength values of rocks determined by
point load and direct tensile tests Rock Mech Rock Engng 30 65-72
90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
the uniaxial compressive strength Int J Rock Mech Min Sci 27 495-503
Chau KT (1997) Youngrsquos modulus interpreted from compression tests with end
friction J Engng Mech January 1-7 plat Ann Inst Tech Trav Publics
58 967-971
Chau KT and Wei X X (1999) A new analytic solution for the diametral point
load strength test on finite solid circular cylinders Int J Solids and
Structures 38(9) 1459-1481
Chau KT and Wong R HC (1996) Uniaxial compressive strength and point
load strength Int J Rock Mech Min Sci 33183-188
Davis R O and Selvadurai APS (1996) Elasticity and Geomechanics New
York Cambridge University Press 198 p
Deere DU and Miller R P (1966) Engineering Classification and Index
Properties for Intact Rock US Air Force Weapons Lab Rep AFWL-
TR-65-116
Durelli A J and Parks V (1962) Relationship of size and stress gradient to brittle
failure stress In Proceeding of the 4th US National Cong Of Appl
Mech (pp 931-938)
Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
In Proceeding of the 4th Symp Rock Mech (pp 105-118) Penn State
University
Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
strength of intact rock In Proceeding of 5th North American Rock
Mechanics Symposium and the 17th Tunneling Association of Canada
Conference (NARMS-TAC 2002) (pp ) Toronto
Fuenkajorn K and Daemen J J K (1986) Shape effect on ring test tensile
strength In Key to Energy Production Proceeding of the 27th US
Symposium on Rock Mechanics (pp 155-163) Tuscaloosa University of
Alabama
Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
modified point load strength of Saraburi Marble In the 6th Mining
Metallurgical and Petroleum Engineering Conference Bangkok
Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
Apache Leap tuff investigation for scale effects In Proceeding of the 35th
US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
size and shape effects in point-load testing Int J Rock Mech Min Sci
19 241-246
Gunsallus K L and Kulhawy F H (1984) A comparative evaluation of rock
strength measures Int J Rock Mech Min Sci 21 233-248
Hassani F P Scoble M J and Whittaker B N (1980) Application of point load
index test to strength determination of rock and proposals for new size-
correction chart (pp 543-564) Rolla
Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
compression test of irregular test piece Int J Rock Mech Min Sci 3
89-99
Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the
Hoek-Brown falure criterion-Technical note Int J Rock Mech Min Sci
amp Geomech Abstr 27 227-229
Hoek E and Brown E T (1980a) Empirical strength criterion for rock masses J
Geotech Eng Div 106 (GT9) 1013-1035
Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
low tensile resistance by the Brazilian (indirect tensile) test with particular
reference to concrete Aust J Appl Sci 10 243-264
Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
brittle solids axial splitting and shear failure J Geophts Res 90 3105-
3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
strain curve for rock In Proceeding of the 13th US Symp Rock Mech (pp
773-795) Urbana
ISRM (1985) Suggested method for determining point load strength Int J Rock
Mech Min Sci amp Geomech Abstr 22 53-60
ISRM (1985) Suggested methods for deformability determination using a flexible
dilatometer Int J Rock Mech Min Sci amp Geomech Abstr 24 123-134
Jaeger J C and Cook N G W (1979) Fundamentals of Rock Mechanics
London Chapman and Hall 593 p
Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
Lama R D and Vutukuri V S (1978) Testing techniques and results In
Handbook on Mechanical Properties of Rock Vol III No 2 Trans
Tech Publications (International Standard Book Number 0-87849-022-1
Clausthal Germany)
Lonborg N (1967) The strength-size relation of granite Int J Rock Mech Min
Sci 4 269-272
Miller R P (1965) Engineering Classification and Index Properties for Intact
Rock PhD Dissertation Univ Of Illinois Urbana III 92 p
Nimick F B (1988) Empirical relations between porosity and the mechanical
properties of tuff In Key Questions in Rock Mechanics (pp 741-742)
Balkema Rotterdam
Obert L and Stephenson D E (1965) Stress conditions under which core disking
occurs Trans Soc Min Eng AIME 232 227-235
94
Panek L A and Fannon T A (1992) Size and shape effects in point load tests
of irregular rock fragments J Rock Mechanics and Rock Engineering
25 109-140
Pells P J N (1975) The use of point load test in predicting the compressive
strength of rock material Aust Geotech (pp 54-56) G5(N1)
Reichmuth D R (1968) Point-load testing of brittle materials to determine the
tensile strength and relative brittleness In Proceeding of the 9th US Symp
Rock Mech (pp 134-159) University of Colorado
Sammis C G and Ashby M F (1986) The failure of brittle porous solid under
compressive stress state Acta Metall 34 511-526
Serata S and Fuenkajorn K (1992a) Finite element progam lsquoGEOrsquo for modeling
brittle-ductile deterioration of aging earth structures In SMRI Paper
Presented at the Solution Mining Research Institute Fall Meeting
October 19-22 Houston Texas 24p
Sheorey P R Biswas A K and Choubey V D (1989) An empirical failure
criterion of rocks and jointed rock masses Eng Geol 26 141-159
Stowe R L (1969) Strength and deformation properties of granite basalt
limestone and tuff US Army Corps of Engineers WES Misc Paper C-69-1
Taliercio A and Sacchi Landrianni G (1988) Failure criterion for layered rock
Int J Rock Mech Min Sci amp Geomech Abstr 25 299-305
Tepnarong P (2001) Theoretical and experimental studies to determine
compressive and tensile strengths of rocks using modified point load
testing M Eng Thesis Suranaree University of Technology Thailand
95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
modulus and triaxial compressive strength of intact rocks by modified
point load testing PhD Eng Thesis Suranaree University of
Technology Thailand
Tepnarong P and Fuenkajorn K (2004) Determining of elasticity and strengths
of intact rocks using modified point load test In Proceeding of the ISRM
International Symposium 3rd ASRM Vol 2 (pp 397-392)
Timoshenko S (1958) Strength of materials I Element Theory and Problems
(3rd ed) Princeton N J D Van Nostard
Timoshenko S and Goodier J N (1951) Theory of Elasticity (2nd ed) New
York McGraw-Hill
Truk N and Dearman W R (1985) Improvements in the determination of point
load strength Bull Int Assoc Eng Geol 31 137-142
Truk N and Dearman W R (1986) A correction equation on the influence of
length-to-diameter ratio on uniaxial compressive strength of rocks J Eng
Geol 22 293-300
Wei X X and Chau K T (2002) Analytic solution for finite transversely
isotropic circular cylinder under the axial point load test J Eng Mech
(pp 209-219)Vol
Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
axial point load strength test on solid circular cylinders J Eng Mech (pp
1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
tensile strength of rocks Int J Rock Mech Min Sci amp Geomech
Abstr 15 149-160
Wijk G (1980) The point load test for the tensile strength of rock Geotech Test
ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
MODIFIED POINT LOAD TESTS OF PIT WALL
ROCK AT CHATREE GOLD MINE
Chatchai Intaraprasit
A Thesis Submitted in Partial Fulfillment of the Requirements for the
Degree of Master of Engineering in Geotechnology
Suranaree University of Technology
Academic Year 2009
MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT
CHATREE GOLD MINE
Suranaree University of Technology has approved this thesis submitted in
partial fulfillment of the requirements for a Masterrsquos Degree
Thesis Examining Committee
_________________________________
(Asst Prof Thara Lekuthai)
Chairperson
_________________________________
(Assoc Prof Dr Kittitep Fuenkajorn)
Member (Thesis Advisor)
_________________________________
(Dr Prachya Tepnarong)
Member
_______________________________ _________________________________
(Prof Dr Pairote Sattayatham) (Assoc Prof Dr Vorapot Khompis)
Acting Vice Rector for Academic Affairs Dean of Institute of Engineering
ชาตชาย อนทรประสทธ การทดสอบจดกดแบบปรบเปลยนของหนผนงบอทเหมองแรทองคาชาตร (MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT CHATREE GOLD MINE ) อาจารยทปรกษา รองศาสตราจารย ดร กตตเทพ เฟองขจร 191 หนา
การทดสอบจดกดแบบปรบเปลยนไดถกนามาใชในการหาคาความเคนกด แรงดง และคาความยดหยนของหนตวอยางในหองปฏบตการทดสอบ มาเปนเวลาเกอบสบปแลว วธการทดสอบนไดถกประดษฐ และจดทะเบยนลขสทธโดยมหาวทยาลยเทคโนโลยสรนาร เครองมอ และวธการทดสอบถกออกแบบใหมราคาถกและงาย เมอเปรยบเทยบกบวธการทดสอบเพอหาคณสมบตเชงกลของหนแบบดงเดม เชน วธการทดสอบตามมาตรฐาน ISRM และ ASTM ในอดตการทดสอบจดกดแบบปรบเปลยนสวนใหญมกทดสอบในแทงตวอยางหนทเปนรปวงกลม และรปสเหลยมมมฉาก ในขณะทมการอางวาการทดสอบแบบจดกดแบบปรบเปลยนนสามารถใชไดกบหนทกรปราง แตผลทดสอบวธนกบหนทมรปรางไมเปนทรงเรขาคณตยงมนอยมาก เนองจากเหตนจงยงไมมการยนยนอยางเพยงพอวา วธการทดสอบจดกดแบบปรบเปลยนสามารถใชไดจรงและมความสมาเสมอเพยงพอในการตรวจหาคณสมบตทางกลศาสตรพนฐานของหนในภาคสนามซงไมสามารถจดหาเครองเจาะและเครองตดหนได วตถประสงคของงานวจยนคอ เพอประเมนศกยภาพของการทดสอบของวธการทดสอบแบบจดกดแบบปรบเปลยนในหนตวอยางทมรปรางไมเปนทรงเรขาคณต ตวอยางหนสามชนด จานวน 150 ตวอยางเปนอยางนอย ไดแก porphyritic andesite silicified-tuffaceous sandstone และ tuffaceous sandstone ซงเกบรวบรวมมาจากผนงบอทางดานทศเหนอของเขาหมอทเหมองแรทองคาชาตร จะถกนามาใชในการทดสอบน อตราสวนระหวางความหนาของหนตวอยางตอเสนผาศนยกลางของหวกด แปรผนระหวาง 2 ถง3 และ อตราสวนระหวางเสนผาศนยกลางของตวอยางหนกบเสนผาศนยกลางของหวกดแปรผนระหวาง 5 ถง 10 การสญเสยรปรางและการแตกหกของหนจะถกนามาใชในการคานวณหาคาความยดหยนและความแขงแรงของหน และจะมการทดสอบแรงกดในแกนเดยวและแรงกดในสามแกน การทดสอบแรงดง และการทดสอบจดกดแบบด ง เด มในหนท งสามชนดดวยเช นกนเพ อนาผลการทดสอบท ได มาใชในการเปรยบเทยบกบผลทไดจากการทดสอบจดกดแบบปรบเปลยน แบบจาลองโดยใชโปรแกรมคอมพวเตอรจะถกนามาใชในการศกษาการกระจายตวของแรงเคนในกอนตวอยางหนของการทดสอบจดกดแบบปรบเปล ยนภายใต อ ตราสวนระหวางความหนาของหนต วอย างต อเสนผาศนยกลางของหวกดทตางๆกน และจะมการประเมนเชงปรมาณของผลกระทบของความมรปรางทไมเปนรปทรงทางเรขาคณตของหนตวอยาง ความเหมอนและความแตกตางของผล
II
สาขาวชา เทคโนโลยธรณ ลายมอชอนกศกษา ปการศกษา 2552 ลายมอชออาจารยทปรกษา
การทดสอบจดกดแบบปรบเปลยนและการทดสอบจดกดแบบดงเดมจะถกนามาพจารณา อาจมการประยกตการคานวณทเปนแบบแผนของการทดสอบจดกดแบบปรบเปล ยน เพ อเพ มความสามารถในการคาดคะเนคณสมบตทางกลศาสตรของหนตวอยางทมรปรางไมเปนรปทรงทางเรขาคณตไดดยงขน
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
REFERENCES
ASTM D2664-86 Standard test method for triaxial compressive strength of
undrained rock core specimens without pore pressure measurements In
Annual Book of ASTM Standards (Vol 0408) Philadelphia American
Society for Testing and Materials
ASTM D7012-07 Standard test method for compressive strength and elastic moduli
of intact rock core specimens under varying states of stress and
temperatures In Annual Book of ASTM Standards (Vol 0408) West
Conshohocken American Society for Testing and Materials
ASTM D3967-81 Standard test method for splitting tensile strength of intact rock
core specimens In Annual Book of ASTM Standards (Vol 0408)
Philadelphia American Society for Testing and Materials
ASTM D4543-85 Standard test method for preparing rock core specimens and
determining dimensional and shape tolerances In Annual Book of ASTM
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Materials
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Geol 9 1-11
89
Bieniawski Z T and Bernede M J (1979) Suggested methods for determining the
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Mech Min Sci 16 (2)xxxx (page no)
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Analytical and Computational Methods in Engineering Rock
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Sci 9 669-697
Book N (1977) The use of irregular specimens for rock strength tests Int J
Rock Mech Min Sci amp Geomech Abstr 14 193-202
Book N (1979) Estimating the triaxial strength of rocks Int J Rock Mech Min
Sci amp Geomech Abstr 16 261-264
Book N (1980) Size correction for point load testing Int J Rock Mech Min
Sci 17231-235 [Technical note]
Book N (1985) The equivalent core diameter method of size and shape correction
in point load testing Int J Rock Mech Min Sci amp Geomech Abstr
22 61-70
Brown E T (1981) Rock characterization Testing and Monitoring ISRM
Suggestion Methods New York International Society for Rock
Mechanics Pergamon Press
Butenuth C (1997) Comparison of tensile strength values of rocks determined by
point load and direct tensile tests Rock Mech Rock Engng 30 65-72
90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
the uniaxial compressive strength Int J Rock Mech Min Sci 27 495-503
Chau KT (1997) Youngrsquos modulus interpreted from compression tests with end
friction J Engng Mech January 1-7 plat Ann Inst Tech Trav Publics
58 967-971
Chau KT and Wei X X (1999) A new analytic solution for the diametral point
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Structures 38(9) 1459-1481
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load strength Int J Rock Mech Min Sci 33183-188
Davis R O and Selvadurai APS (1996) Elasticity and Geomechanics New
York Cambridge University Press 198 p
Deere DU and Miller R P (1966) Engineering Classification and Index
Properties for Intact Rock US Air Force Weapons Lab Rep AFWL-
TR-65-116
Durelli A J and Parks V (1962) Relationship of size and stress gradient to brittle
failure stress In Proceeding of the 4th US National Cong Of Appl
Mech (pp 931-938)
Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
In Proceeding of the 4th Symp Rock Mech (pp 105-118) Penn State
University
Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
strength of intact rock In Proceeding of 5th North American Rock
Mechanics Symposium and the 17th Tunneling Association of Canada
Conference (NARMS-TAC 2002) (pp ) Toronto
Fuenkajorn K and Daemen J J K (1986) Shape effect on ring test tensile
strength In Key to Energy Production Proceeding of the 27th US
Symposium on Rock Mechanics (pp 155-163) Tuscaloosa University of
Alabama
Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
modified point load strength of Saraburi Marble In the 6th Mining
Metallurgical and Petroleum Engineering Conference Bangkok
Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
Apache Leap tuff investigation for scale effects In Proceeding of the 35th
US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
size and shape effects in point-load testing Int J Rock Mech Min Sci
19 241-246
Gunsallus K L and Kulhawy F H (1984) A comparative evaluation of rock
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Hassani F P Scoble M J and Whittaker B N (1980) Application of point load
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Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
compression test of irregular test piece Int J Rock Mech Min Sci 3
89-99
Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the
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amp Geomech Abstr 27 227-229
Hoek E and Brown E T (1980a) Empirical strength criterion for rock masses J
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Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
low tensile resistance by the Brazilian (indirect tensile) test with particular
reference to concrete Aust J Appl Sci 10 243-264
Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
brittle solids axial splitting and shear failure J Geophts Res 90 3105-
3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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773-795) Urbana
ISRM (1985) Suggested method for determining point load strength Int J Rock
Mech Min Sci amp Geomech Abstr 22 53-60
ISRM (1985) Suggested methods for deformability determination using a flexible
dilatometer Int J Rock Mech Min Sci amp Geomech Abstr 24 123-134
Jaeger J C and Cook N G W (1979) Fundamentals of Rock Mechanics
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Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
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Obert L and Stephenson D E (1965) Stress conditions under which core disking
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94
Panek L A and Fannon T A (1992) Size and shape effects in point load tests
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25 109-140
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Int J Rock Mech Min Sci amp Geomech Abstr 25 299-305
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95
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1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
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Abstr 15 149-160
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT
CHATREE GOLD MINE
Suranaree University of Technology has approved this thesis submitted in
partial fulfillment of the requirements for a Masterrsquos Degree
Thesis Examining Committee
_________________________________
(Asst Prof Thara Lekuthai)
Chairperson
_________________________________
(Assoc Prof Dr Kittitep Fuenkajorn)
Member (Thesis Advisor)
_________________________________
(Dr Prachya Tepnarong)
Member
_______________________________ _________________________________
(Prof Dr Pairote Sattayatham) (Assoc Prof Dr Vorapot Khompis)
Acting Vice Rector for Academic Affairs Dean of Institute of Engineering
ชาตชาย อนทรประสทธ การทดสอบจดกดแบบปรบเปลยนของหนผนงบอทเหมองแรทองคาชาตร (MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT CHATREE GOLD MINE ) อาจารยทปรกษา รองศาสตราจารย ดร กตตเทพ เฟองขจร 191 หนา
การทดสอบจดกดแบบปรบเปลยนไดถกนามาใชในการหาคาความเคนกด แรงดง และคาความยดหยนของหนตวอยางในหองปฏบตการทดสอบ มาเปนเวลาเกอบสบปแลว วธการทดสอบนไดถกประดษฐ และจดทะเบยนลขสทธโดยมหาวทยาลยเทคโนโลยสรนาร เครองมอ และวธการทดสอบถกออกแบบใหมราคาถกและงาย เมอเปรยบเทยบกบวธการทดสอบเพอหาคณสมบตเชงกลของหนแบบดงเดม เชน วธการทดสอบตามมาตรฐาน ISRM และ ASTM ในอดตการทดสอบจดกดแบบปรบเปลยนสวนใหญมกทดสอบในแทงตวอยางหนทเปนรปวงกลม และรปสเหลยมมมฉาก ในขณะทมการอางวาการทดสอบแบบจดกดแบบปรบเปลยนนสามารถใชไดกบหนทกรปราง แตผลทดสอบวธนกบหนทมรปรางไมเปนทรงเรขาคณตยงมนอยมาก เนองจากเหตนจงยงไมมการยนยนอยางเพยงพอวา วธการทดสอบจดกดแบบปรบเปลยนสามารถใชไดจรงและมความสมาเสมอเพยงพอในการตรวจหาคณสมบตทางกลศาสตรพนฐานของหนในภาคสนามซงไมสามารถจดหาเครองเจาะและเครองตดหนได วตถประสงคของงานวจยนคอ เพอประเมนศกยภาพของการทดสอบของวธการทดสอบแบบจดกดแบบปรบเปลยนในหนตวอยางทมรปรางไมเปนทรงเรขาคณต ตวอยางหนสามชนด จานวน 150 ตวอยางเปนอยางนอย ไดแก porphyritic andesite silicified-tuffaceous sandstone และ tuffaceous sandstone ซงเกบรวบรวมมาจากผนงบอทางดานทศเหนอของเขาหมอทเหมองแรทองคาชาตร จะถกนามาใชในการทดสอบน อตราสวนระหวางความหนาของหนตวอยางตอเสนผาศนยกลางของหวกด แปรผนระหวาง 2 ถง3 และ อตราสวนระหวางเสนผาศนยกลางของตวอยางหนกบเสนผาศนยกลางของหวกดแปรผนระหวาง 5 ถง 10 การสญเสยรปรางและการแตกหกของหนจะถกนามาใชในการคานวณหาคาความยดหยนและความแขงแรงของหน และจะมการทดสอบแรงกดในแกนเดยวและแรงกดในสามแกน การทดสอบแรงดง และการทดสอบจดกดแบบด ง เด มในหนท งสามชนดดวยเช นกนเพ อนาผลการทดสอบท ได มาใชในการเปรยบเทยบกบผลทไดจากการทดสอบจดกดแบบปรบเปลยน แบบจาลองโดยใชโปรแกรมคอมพวเตอรจะถกนามาใชในการศกษาการกระจายตวของแรงเคนในกอนตวอยางหนของการทดสอบจดกดแบบปรบเปล ยนภายใต อ ตราสวนระหวางความหนาของหนต วอย างต อเสนผาศนยกลางของหวกดทตางๆกน และจะมการประเมนเชงปรมาณของผลกระทบของความมรปรางทไมเปนรปทรงทางเรขาคณตของหนตวอยาง ความเหมอนและความแตกตางของผล
II
สาขาวชา เทคโนโลยธรณ ลายมอชอนกศกษา ปการศกษา 2552 ลายมอชออาจารยทปรกษา
การทดสอบจดกดแบบปรบเปลยนและการทดสอบจดกดแบบดงเดมจะถกนามาพจารณา อาจมการประยกตการคานวณทเปนแบบแผนของการทดสอบจดกดแบบปรบเปล ยน เพ อเพ มความสามารถในการคาดคะเนคณสมบตทางกลศาสตรของหนตวอยางทมรปรางไมเปนรปทรงทางเรขาคณตไดดยงขน
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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point load testing PhD Eng Thesis Suranaree University of
Technology Thailand
Tepnarong P and Fuenkajorn K (2004) Determining of elasticity and strengths
of intact rocks using modified point load test In Proceeding of the ISRM
International Symposium 3rd ASRM Vol 2 (pp 397-392)
Timoshenko S (1958) Strength of materials I Element Theory and Problems
(3rd ed) Princeton N J D Van Nostard
Timoshenko S and Goodier J N (1951) Theory of Elasticity (2nd ed) New
York McGraw-Hill
Truk N and Dearman W R (1985) Improvements in the determination of point
load strength Bull Int Assoc Eng Geol 31 137-142
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length-to-diameter ratio on uniaxial compressive strength of rocks J Eng
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(pp 209-219)Vol
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96
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Abstr 15 149-160
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
ชาตชาย อนทรประสทธ การทดสอบจดกดแบบปรบเปลยนของหนผนงบอทเหมองแรทองคาชาตร (MODIFIED POINT LOAD TESTS OF PIT WALL ROCK AT CHATREE GOLD MINE ) อาจารยทปรกษา รองศาสตราจารย ดร กตตเทพ เฟองขจร 191 หนา
การทดสอบจดกดแบบปรบเปลยนไดถกนามาใชในการหาคาความเคนกด แรงดง และคาความยดหยนของหนตวอยางในหองปฏบตการทดสอบ มาเปนเวลาเกอบสบปแลว วธการทดสอบนไดถกประดษฐ และจดทะเบยนลขสทธโดยมหาวทยาลยเทคโนโลยสรนาร เครองมอ และวธการทดสอบถกออกแบบใหมราคาถกและงาย เมอเปรยบเทยบกบวธการทดสอบเพอหาคณสมบตเชงกลของหนแบบดงเดม เชน วธการทดสอบตามมาตรฐาน ISRM และ ASTM ในอดตการทดสอบจดกดแบบปรบเปลยนสวนใหญมกทดสอบในแทงตวอยางหนทเปนรปวงกลม และรปสเหลยมมมฉาก ในขณะทมการอางวาการทดสอบแบบจดกดแบบปรบเปลยนนสามารถใชไดกบหนทกรปราง แตผลทดสอบวธนกบหนทมรปรางไมเปนทรงเรขาคณตยงมนอยมาก เนองจากเหตนจงยงไมมการยนยนอยางเพยงพอวา วธการทดสอบจดกดแบบปรบเปลยนสามารถใชไดจรงและมความสมาเสมอเพยงพอในการตรวจหาคณสมบตทางกลศาสตรพนฐานของหนในภาคสนามซงไมสามารถจดหาเครองเจาะและเครองตดหนได วตถประสงคของงานวจยนคอ เพอประเมนศกยภาพของการทดสอบของวธการทดสอบแบบจดกดแบบปรบเปลยนในหนตวอยางทมรปรางไมเปนทรงเรขาคณต ตวอยางหนสามชนด จานวน 150 ตวอยางเปนอยางนอย ไดแก porphyritic andesite silicified-tuffaceous sandstone และ tuffaceous sandstone ซงเกบรวบรวมมาจากผนงบอทางดานทศเหนอของเขาหมอทเหมองแรทองคาชาตร จะถกนามาใชในการทดสอบน อตราสวนระหวางความหนาของหนตวอยางตอเสนผาศนยกลางของหวกด แปรผนระหวาง 2 ถง3 และ อตราสวนระหวางเสนผาศนยกลางของตวอยางหนกบเสนผาศนยกลางของหวกดแปรผนระหวาง 5 ถง 10 การสญเสยรปรางและการแตกหกของหนจะถกนามาใชในการคานวณหาคาความยดหยนและความแขงแรงของหน และจะมการทดสอบแรงกดในแกนเดยวและแรงกดในสามแกน การทดสอบแรงดง และการทดสอบจดกดแบบด ง เด มในหนท งสามชนดดวยเช นกนเพ อนาผลการทดสอบท ได มาใชในการเปรยบเทยบกบผลทไดจากการทดสอบจดกดแบบปรบเปลยน แบบจาลองโดยใชโปรแกรมคอมพวเตอรจะถกนามาใชในการศกษาการกระจายตวของแรงเคนในกอนตวอยางหนของการทดสอบจดกดแบบปรบเปล ยนภายใต อ ตราสวนระหวางความหนาของหนต วอย างต อเสนผาศนยกลางของหวกดทตางๆกน และจะมการประเมนเชงปรมาณของผลกระทบของความมรปรางทไมเปนรปทรงทางเรขาคณตของหนตวอยาง ความเหมอนและความแตกตางของผล
II
สาขาวชา เทคโนโลยธรณ ลายมอชอนกศกษา ปการศกษา 2552 ลายมอชออาจารยทปรกษา
การทดสอบจดกดแบบปรบเปลยนและการทดสอบจดกดแบบดงเดมจะถกนามาพจารณา อาจมการประยกตการคานวณทเปนแบบแผนของการทดสอบจดกดแบบปรบเปล ยน เพ อเพ มความสามารถในการคาดคะเนคณสมบตทางกลศาสตรของหนตวอยางทมรปรางไมเปนรปทรงทางเรขาคณตไดดยงขน
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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22 61-70
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Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
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Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
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Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
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Biomechanics Summer Conference Columbus Ohio University
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heterogeneous tuff Int J Engineering Geology 32 209-223
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Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
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US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
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19 241-246
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3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
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1349-1357) Vol
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Wijk G (1978) Some new theoretical aspects of indirect measurements of the
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
II
สาขาวชา เทคโนโลยธรณ ลายมอชอนกศกษา ปการศกษา 2552 ลายมอชออาจารยทปรกษา
การทดสอบจดกดแบบปรบเปลยนและการทดสอบจดกดแบบดงเดมจะถกนามาพจารณา อาจมการประยกตการคานวณทเปนแบบแผนของการทดสอบจดกดแบบปรบเปล ยน เพ อเพ มความสามารถในการคาดคะเนคณสมบตทางกลศาสตรของหนตวอยางทมรปรางไมเปนรปทรงทางเรขาคณตไดดยงขน
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
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Forster I R (1983) The influence of core sample geometry on axial load test Int
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Greminger M (1982) Experimental studies of the influence of rock anisotropy on
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Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
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93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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Jaeger J C and Cook N G W (1979) Fundamentals of Rock Mechanics
London Chapman and Hall 593 p
Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
Lama R D and Vutukuri V S (1978) Testing techniques and results In
Handbook on Mechanical Properties of Rock Vol III No 2 Trans
Tech Publications (International Standard Book Number 0-87849-022-1
Clausthal Germany)
Lonborg N (1967) The strength-size relation of granite Int J Rock Mech Min
Sci 4 269-272
Miller R P (1965) Engineering Classification and Index Properties for Intact
Rock PhD Dissertation Univ Of Illinois Urbana III 92 p
Nimick F B (1988) Empirical relations between porosity and the mechanical
properties of tuff In Key Questions in Rock Mechanics (pp 741-742)
Balkema Rotterdam
Obert L and Stephenson D E (1965) Stress conditions under which core disking
occurs Trans Soc Min Eng AIME 232 227-235
94
Panek L A and Fannon T A (1992) Size and shape effects in point load tests
of irregular rock fragments J Rock Mechanics and Rock Engineering
25 109-140
Pells P J N (1975) The use of point load test in predicting the compressive
strength of rock material Aust Geotech (pp 54-56) G5(N1)
Reichmuth D R (1968) Point-load testing of brittle materials to determine the
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Rock Mech (pp 134-159) University of Colorado
Sammis C G and Ashby M F (1986) The failure of brittle porous solid under
compressive stress state Acta Metall 34 511-526
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brittle-ductile deterioration of aging earth structures In SMRI Paper
Presented at the Solution Mining Research Institute Fall Meeting
October 19-22 Houston Texas 24p
Sheorey P R Biswas A K and Choubey V D (1989) An empirical failure
criterion of rocks and jointed rock masses Eng Geol 26 141-159
Stowe R L (1969) Strength and deformation properties of granite basalt
limestone and tuff US Army Corps of Engineers WES Misc Paper C-69-1
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Int J Rock Mech Min Sci amp Geomech Abstr 25 299-305
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
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Abstr 15 149-160
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
CHATCHAI INTARAPRASIT MODIFIED POINT LOAD TESTS OF PIT
WALL ROCK AT CHATREE GOLD MINE THESIS ADVISOR ASSOC PROF
KITTITEP FUENKAJORN Ph D PE 191 PP
TRIAXIAL COMPRESSIVE STRENGTHUNIAXIAL COMPRESSIVE
STRENGTH ELASIC MODULUS POINT LOADTENSILE STRENGTH
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strengths and elastic modulus of intact rock
specimens in the laboratory This method was invented and patented by Suranaree
University of Technology The test apparatus and procedure are intended to be
inexpensive and easy compared to the relevant conventional methods of determining
the mechanical properties of intact rock eg those given by the International Society
for Rock Mechanics (ISRM) and the American Society for Testing and materials
(ASTM) In the past much of the MPL testing practices have been concentrated on
circular and rectangular disk specimens While it has been claimed that MPL method
is applicable to all rock shapes the test results from irregular lumps of rock have been
rare and hence are not sufficient to confirm that the MPL testing technique is truly
valid or even adequate to determine the basic rock mechanical properties in the field
where rock drilling and cutting devices are not available
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine will be used
as rock samples A minimum of 150 samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone will be collected from the site The
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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Book N (1977) The use of irregular specimens for rock strength tests Int J
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Book N (1980) Size correction for point load testing Int J Rock Mech Min
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Book N (1985) The equivalent core diameter method of size and shape correction
in point load testing Int J Rock Mech Min Sci amp Geomech Abstr
22 61-70
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Mechanics Pergamon Press
Butenuth C (1997) Comparison of tensile strength values of rocks determined by
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90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Durelli A J and Parks V (1962) Relationship of size and stress gradient to brittle
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Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
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Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
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Conference (NARMS-TAC 2002) (pp ) Toronto
Fuenkajorn K and Daemen J J K (1986) Shape effect on ring test tensile
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Symposium on Rock Mechanics (pp 155-163) Tuscaloosa University of
Alabama
Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
modified point load strength of Saraburi Marble In the 6th Mining
Metallurgical and Petroleum Engineering Conference Bangkok
Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
Apache Leap tuff investigation for scale effects In Proceeding of the 35th
US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
size and shape effects in point-load testing Int J Rock Mech Min Sci
19 241-246
Gunsallus K L and Kulhawy F H (1984) A comparative evaluation of rock
strength measures Int J Rock Mech Min Sci 21 233-248
Hassani F P Scoble M J and Whittaker B N (1980) Application of point load
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Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
compression test of irregular test piece Int J Rock Mech Min Sci 3
89-99
Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the
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amp Geomech Abstr 27 227-229
Hoek E and Brown E T (1980a) Empirical strength criterion for rock masses J
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Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
low tensile resistance by the Brazilian (indirect tensile) test with particular
reference to concrete Aust J Appl Sci 10 243-264
Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
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3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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ISRM (1985) Suggested method for determining point load strength Int J Rock
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ISRM (1985) Suggested methods for deformability determination using a flexible
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Jaeger J C and Cook N G W (1979) Fundamentals of Rock Mechanics
London Chapman and Hall 593 p
Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
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94
Panek L A and Fannon T A (1992) Size and shape effects in point load tests
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Rock Mech (pp 134-159) University of Colorado
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Int J Rock Mech Min Sci amp Geomech Abstr 25 299-305
Tepnarong P (2001) Theoretical and experimental studies to determine
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testing M Eng Thesis Suranaree University of Technology Thailand
95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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(pp 209-219)Vol
Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
axial point load strength test on solid circular cylinders J Eng Mech (pp
1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
tensile strength of rocks Int J Rock Mech Min Sci amp Geomech
Abstr 15 149-160
Wijk G (1980) The point load test for the tensile strength of rock Geotech Test
ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
IV
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure will be used to calculate the elastic modulus and strengths of the rocks
Uniaxial and triaxial compression tests Brazilian tension test and conventional point
load test will also be conducted on the three rock types to obtain data basis for
comparing with those from the MPL testing Finite difference analysis will be
performed to obtain stress distribution within the MPL samples under different td and
Dd ratios The effects of the sample irregularity will be quantitatively assessed
Similarity and discrepancy of the test results from the MPL method and from the
conventional methods will be examined Modification of the MPL calculation
scheme may be made to enhance its predictive capability for the mechanical
properties of irregular shaped specimens
School of Geotechnology Students Signature
Academic Year 2009 Advisors Signature
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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Forster I R (1983) The influence of core sample geometry on axial load test Int
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Greminger M (1982) Experimental studies of the influence of rock anisotropy on
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Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
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1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
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Wijk G (1980) The point load test for the tensile strength of rock Geotech Test
ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
ACKNOWLEDGMENTS
I wish to acknowledge the funding support of Suranaree University of
Technology (SUT) and Akara Mining Company Limited
I would like to express my sincere thanks to Assoc Prof Dr Kittitep
Fuenkajorn thesis advisor who gave a critical review and constant encouragement
throughout the course of this research Further appreciation is extended to Asst Prof
Thara Lekuthai chairman school of Geotechnology and Dr Prachya Tepnarong
Suranaree University of Technology who are member of my examination committee
Grateful thanks are given to all staffs of Geomechanics Research Unit Institute of
Engineering who supported my work
Chatchai Intaraprasit
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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undrained rock core specimens without pore pressure measurements In
Annual Book of ASTM Standards (Vol 0408) Philadelphia American
Society for Testing and Materials
ASTM D7012-07 Standard test method for compressive strength and elastic moduli
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temperatures In Annual Book of ASTM Standards (Vol 0408) West
Conshohocken American Society for Testing and Materials
ASTM D3967-81 Standard test method for splitting tensile strength of intact rock
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Philadelphia American Society for Testing and Materials
ASTM D4543-85 Standard test method for preparing rock core specimens and
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ASTM D5731-95 Standard test method for determination of point load strength
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Bieniawski Z T (1974) Estimating of the strength of rock materials J Inst
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Bieniawski Z T (1975) The point-load test in geotechnical practice Engng
Geol 9 1-11
89
Bieniawski Z T and Bernede M J (1979) Suggested methods for determining the
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Bray J W (1987) Some applications of elastic theory In E T Brown (ed)
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Broch E and Franklin J A (1972) The point-load test Int J Rock Mech Min
Sci 9 669-697
Book N (1977) The use of irregular specimens for rock strength tests Int J
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Book N (1979) Estimating the triaxial strength of rocks Int J Rock Mech Min
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Book N (1980) Size correction for point load testing Int J Rock Mech Min
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Book N (1985) The equivalent core diameter method of size and shape correction
in point load testing Int J Rock Mech Min Sci amp Geomech Abstr
22 61-70
Brown E T (1981) Rock characterization Testing and Monitoring ISRM
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Mechanics Pergamon Press
Butenuth C (1997) Comparison of tensile strength values of rocks determined by
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90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Chau KT (1997) Youngrsquos modulus interpreted from compression tests with end
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Chau KT and Wei X X (1999) A new analytic solution for the diametral point
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Structures 38(9) 1459-1481
Chau KT and Wong R HC (1996) Uniaxial compressive strength and point
load strength Int J Rock Mech Min Sci 33183-188
Davis R O and Selvadurai APS (1996) Elasticity and Geomechanics New
York Cambridge University Press 198 p
Deere DU and Miller R P (1966) Engineering Classification and Index
Properties for Intact Rock US Air Force Weapons Lab Rep AFWL-
TR-65-116
Durelli A J and Parks V (1962) Relationship of size and stress gradient to brittle
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Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
In Proceeding of the 4th Symp Rock Mech (pp 105-118) Penn State
University
Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
strength of intact rock In Proceeding of 5th North American Rock
Mechanics Symposium and the 17th Tunneling Association of Canada
Conference (NARMS-TAC 2002) (pp ) Toronto
Fuenkajorn K and Daemen J J K (1986) Shape effect on ring test tensile
strength In Key to Energy Production Proceeding of the 27th US
Symposium on Rock Mechanics (pp 155-163) Tuscaloosa University of
Alabama
Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
modified point load strength of Saraburi Marble In the 6th Mining
Metallurgical and Petroleum Engineering Conference Bangkok
Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
Apache Leap tuff investigation for scale effects In Proceeding of the 35th
US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
size and shape effects in point-load testing Int J Rock Mech Min Sci
19 241-246
Gunsallus K L and Kulhawy F H (1984) A comparative evaluation of rock
strength measures Int J Rock Mech Min Sci 21 233-248
Hassani F P Scoble M J and Whittaker B N (1980) Application of point load
index test to strength determination of rock and proposals for new size-
correction chart (pp 543-564) Rolla
Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
compression test of irregular test piece Int J Rock Mech Min Sci 3
89-99
Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the
Hoek-Brown falure criterion-Technical note Int J Rock Mech Min Sci
amp Geomech Abstr 27 227-229
Hoek E and Brown E T (1980a) Empirical strength criterion for rock masses J
Geotech Eng Div 106 (GT9) 1013-1035
Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
low tensile resistance by the Brazilian (indirect tensile) test with particular
reference to concrete Aust J Appl Sci 10 243-264
Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
brittle solids axial splitting and shear failure J Geophts Res 90 3105-
3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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ISRM (1985) Suggested method for determining point load strength Int J Rock
Mech Min Sci amp Geomech Abstr 22 53-60
ISRM (1985) Suggested methods for deformability determination using a flexible
dilatometer Int J Rock Mech Min Sci amp Geomech Abstr 24 123-134
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Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
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94
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95
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1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
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Abstr 15 149-160
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
TABLE OF CONTENTS
Page
ABSTRACT (THAI) I
ABSTRACT (ENGLISH) III
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VI
LIST OF TABLES IX
LIST OF FIGURES XIII
LIST OF SYMBOLS AND ABBREVIATIONS XVII
CHAPTER
I INTRODUCTION 1
11 Background and rationale 1
12 Research objectives 2
13 Research concept 3
14 Research methodology 3
141 Literature review 3
142 Sample collection and preparation 5
143 Theoretical study of the rock failure
mechanism 5
144 Laboratory testing 5
1441 Characterization tests 5
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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22 61-70
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Mechanics Pergamon Press
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90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
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Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
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91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
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Fuenkajorn K and Daemen J J K (1986) Shape effect on ring test tensile
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Symposium on Rock Mechanics (pp 155-163) Tuscaloosa University of
Alabama
Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
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Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
Apache Leap tuff investigation for scale effects In Proceeding of the 35th
US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
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19 241-246
Gunsallus K L and Kulhawy F H (1984) A comparative evaluation of rock
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Hassani F P Scoble M J and Whittaker B N (1980) Application of point load
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Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
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89-99
Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the
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amp Geomech Abstr 27 227-229
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Hondros G (1959) The evaluation of Poissonrsquos ratio and modulus of material of a
low tensile resistance by the Brazilian (indirect tensile) test with particular
reference to concrete Aust J Appl Sci 10 243-264
Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
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3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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ISRM (1985) Suggested method for determining point load strength Int J Rock
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ISRM (1985) Suggested methods for deformability determination using a flexible
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Jaeger J C and Cook N G W (1979) Fundamentals of Rock Mechanics
London Chapman and Hall 593 p
Kaczynski R R (1986) Scale effect during compressive strength of rocks In
Proceeding of 5th Int Assoc Eng Geol Congr p 371-373
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94
Panek L A and Fannon T A (1992) Size and shape effects in point load tests
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Int J Rock Mech Min Sci amp Geomech Abstr 25 299-305
Tepnarong P (2001) Theoretical and experimental studies to determine
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
axial point load strength test on solid circular cylinders J Eng Mech (pp
1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
tensile strength of rocks Int J Rock Mech Min Sci amp Geomech
Abstr 15 149-160
Wijk G (1980) The point load test for the tensile strength of rock Geotech Test
ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
VII
TABLE OF CONTENTS (Continued)
Page
1442 Modified point load tests 6
145 Analysis 6
146 Thesis Writing and Presentation 6
15 Scope and Limitations 7
16 Thesis Contents 7
II LITERATURE REVIEW 8
21 Introduction 8
22 Conventional point load tests 8
23 Modified point load tests 11
24 Characterization tests 14
241 Uniaxial compressive strength tests 14
242 Triaxial compressive strength tests 15
243 Brazilian tensile strength tests 16
25 Size effects on compressive strength 16
III SAMPLE COLLECTION AND PREPARATION 17
31 Sample collection 17
32 Rock descriptions 17
33 Sample preparation 20
IV LABORATORY TESTS 22
41 Literature reviews 22
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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89
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Rock Mech Min Sci amp Geomech Abstr 14 193-202
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22 61-70
Brown E T (1981) Rock characterization Testing and Monitoring ISRM
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Butenuth C (1997) Comparison of tensile strength values of rocks determined by
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90
Cargill J S and Shakoor A (1992) Evaluation of empirical methods for measuring
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Chau KT and Wei X X (1999) A new analytic solution for the diametral point
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Chau KT and Wong R HC (1996) Uniaxial compressive strength and point
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Durelli A J and Parks V (1962) Relationship of size and stress gradient to brittle
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Evans I (1961) The tensile strength of coal Colliery Eng 38 428-434
Fairhurst C (1961) Laboratory measurement of some physical properties of rock
In Proceeding of the 4th Symp Rock Mech (pp 105-118) Penn State
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Farmer I (1983) Engineering Behavior of Rocks New York Chapman and Hall
208 p
91
Forster I R (1983) The influence of core sample geometry on axial load test Int
J Rock Mech Min Sci 20 291-295
Fuenkajorn K (2002) Modified point load test determining uniaxial compressive
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Fuenkajorn K and Daemen J J K (1991b) An empirical strength criterion for
heterogeneous welded tuff In ASME Applied Mechanics and
Biomechanics Summer Conference Columbus Ohio University
Fuenkajorn K and Daemen J J K (1992) An empirical strength criterion for
heterogeneous tuff Int J Engineering Geology 32 209-223
Fuenkajorn K and Tepnarong P (2001) Size and stress gradient effects on the
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Thailand(pp)
Ghosh A Fuenkajorn K and Daemen J J K (1995) Tensile strength of welded
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US Rock Mech Symposium (pp 459-646) University of Navada Reno
Goodman R E (1980) Methods of Geological Engineering in Discontinuous
Rock New York Wiley and Sons
92
Greminger M (1982) Experimental studies of the influence of rock anisotropy on
size and shape effects in point-load testing Int J Rock Mech Min Sci
19 241-246
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Hiramatsu Y and Oka Y (1966) Determination of tensile strength of rock by a
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Horii H and Nemat-Nasser S (1985) Compression-induced microcrack growth in
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3125
93
Hudson J A Brown E T and Fairhurst C (1971) Shape of the complete stress-
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Panek L A and Fannon T A (1992) Size and shape effects in point load tests
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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Wei X X and Chau K T and Wong R H C (1999) Analytic solution for
axial point load strength test on solid circular cylinders J Eng Mech (pp
1349-1357) Vol
96
Wijk G (1978) Some new theoretical aspects of indirect measurements of the
tensile strength of rocks Int J Rock Mech Min Sci amp Geomech
Abstr 15 149-160
Wijk G (1980) The point load test for the tensile strength of rock Geotech Test
ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand
VIII
TABLE OF CONTENTS (Continued)
Page
411 Displacement Function 22
42 Basic Characterization Tests 23
421 Uniaxial Compressive Strength Tests
and Elastic Modulus Measurements 23
422 Triaxial Compressive Strength Tests 31
423 Brazilian Tensile Strength Tests 38
424 Conventional Point Load Index (CPL) Tests 39
43 Modified Point Load (MPL) Tests 46
431 Modified Point Load Tests for Elastic
Modulus Measurement 54
432 Modified Point Load Tests predicting
Uniaxial Compressive Strength 61
433 Modified Point Load Tests for Tensile
Strength Predictions 63
434 Modified Point Load Tests for Triaxial
Compressive Strength Predictions 69
V FINITE DIFFERENCE ANALYSIS 79
51 Objectives 79
52 Model Characteristics 79
53 Results of finite difference analyses 79
IX
TABLE OF CONTENTS (Continued)
Page
VI DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS 83
61 Discussions 83
62 Conclusions 85
63 Recommendations 86
REFERENCES 87
APPENDICES
APPENDIX A CHARACTERIZATION TEST RESULTS 96
APPENDIX B MODIFIED POINT LOAD TEST RESULTS FOR
ELASTIC MODULUS PREDICTION 104
BIOGRAPHY 180
LIST OF TABLES
Table Page
31 The nominal sizes of specimens following the ASTM standard
practices for the characterization tests 20
41 Testing results of porphyritic andesite 30
42 Testing results of tuffaceous sandstone 30
43 Testing results of silicified tuffaceous sandstone 30
44 Uniaxial compressive strength and tangent elastic modulus
measurement results of three rock types 31
45 Triaxial compressive strength testing results of porphyritic andesite 35
46 Triaxial compressive strength testing results of
tuffaceous sandstone 35
47 Triaxial compressive strength testing results of silicified
tuffaceous sandstone 36
48 Results of triaxial compressive strength tests on three rock types 38
49 The results of Brazilian tensile strength tests of three rock types 41
410 Results of conventional point load strength index tests of
three rock types 44
411 Results of modified point load tests on porphyritic andesite 49
412 Results of modified point load tests on tuffaceous sandstone 51
413 Results of modified point load tests on silicified tuffaceous sandstone 52
X
LIST OF TABLE (Continued)
Table Page
414 Results of elastic modulus calculation from MPL tests on porphyritic andesite57
415 Results of elastic modulus calculation from MPL tests on
silicified tuffaceous sandstone 58
416 Results of elastic modulus calculation from MPL tests on
tuffaceous sandstone 60
417 Comparisons of elastic modulus results obtained from
uniaxial compressive strength tests and those from modified
point load tests 61
418 Comparison the test results between UCS CPL Brazilian
tensile strength and MPL tests 63
419 Results of tensile strengths of porphyritic andesite predicted from MPL tests 64
420 Results of tensile strengths of silicified tuffaceous sandstone
predicted from MPL tests 66
421 Results of tensile strengths of tuffaceous sandstone
predicted from MPL tests 68
422 Results of triaxial strengths of porphyritic andesite predicted from MPL tests 71
423 Results of triaxial strengths of silicified tuffaceous sandstone
predicted from MPL tests 72
424 Results of triaxial strengths of tuffaceous sandstone
predicted from MPL tests 74
XI
LIST OF TABLE (Continued)
Table Page
425 Comparisons of the internal friction angle and cohesion
between MPL predictions and triaxial compressive strength tests 78
51 Summary of the results from numerical simulations 82
A1 Results of conventional point load strength index test on porphyritic andesite 97
A2 Results of conventional point load strength index test on
silicified tuffaceous sandstone 98
A3 Results of conventional point load strength index test on
tuffaceous sandstone 99
A4 Results of uniaxial compressive strength tests and elastic
modulus measurement on porphyritic andesite 100
A5 Results of uniaxial compressive strength tests and elastic
modulus measurement on silicified tuffaceous sandstone 100
A6 Results of uniaxial compressive strength tests and elastic
modulus measurement on tuffaceous sandstone 100
A7 Results of Brazilian tensile strength tests on porphyritic andesite 101
A8 Results of Brazilian tensile strength tests on silicified
tuffaceous sandstone 101
A9 Results of Brazilian tensile strength tests on
tuffaceous sandstone 102
A10 Results of triaxial compressive strength tests on porphyritic andesite 102
XII
LIST OF TABLE (Continued)
Table Page
A11 Results of triaxial compressive strength tests on
silicified tuffaceous Sandstone 102
A12 Results of Brazilian tensile strength tests on
tuffaceous sandstone 103
LIST OF FIGURES
Figure Page
11 Research plan 4
21 Loading system of the conventional point load (CPL) 10
22 Standard loading platen shape for the conventional point
load testing 10
31 The location of rock samples collected area 19
32 Some prepared rock specimens of porphyritic andesite for MPL Tests 21
33 The concept of specimen preparation for MPL testing 21
41 Pre-test samples of porphyritic andesite for UCS test 25
42 Pre-test samples of tuffaceous sandstone for UCS test 25
43 Pre-test samples of silicified tuffaceous sandstone for UCS test 26
44 Preparation of testing apparatus of porphyritic andesite for UCS test 26
45 Post-test rock samples of porphyritic andesite from UCS test 27
46 Post-test rock samples of tuffaceous sandstone
from UCS test 27
47 Post-test rock samples of tuffaceous sandstone from UCS 28
48 Results of uniaxial compressive strength tests and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted
as a function of axial strains 28
XIV
LIST OF FIGURES (Continued)
Figure Page
49 Results of uniaxial compressive strength tests and elastic
modulus measurements of tuffaceous sandstone (Top)
and silicified tuffaceous sandstone (Bottom) The axial
stresses are plotted as a function of axial strains 29
410 Pre-test samples for triaxial compressive strength test the
top is porphyritic andesite and the bottom is tuffaceous sandstone 32
411 Pre-test sample of silicified tuffaceous sandstone for triaxial
compressive strength test 33
412 Triaxial testing apparatus 33
413 Post-test rock samples from triaxial compressive strength tests
The top is porphyritic andesite and the bottom is tuffaceous sandstone 34
414 Post-test rock samples of silicified tuffaceous sandstone from
triaxial compressive strength test 35
415 Mohr-Coulomb diagram for porphyritic andesite 37
416 Mohr-Coulomb diagram for tuffaceous sandstone 37
417 Mohr-Coulomb diagram for silicified tuffaceous sandstone 38
418 Pre-test samples for Brazilian tensile strength test (a) porphyritic andesite
(b) tuffaceous sandstone and
(c) silicified tuffaceous sandstone 40
419 Brazilian tensile strength test arrangement 41
XV
LIST OF FIGURES (Continued)
Figure Page
420 Post-test specimens (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 42
421 Pre-test samples of porphyritic andesite for conventional point load
strength index test 43
422 Conventional point load strength index test arrangement 43
423 Post-test specimens from conventional point load
strength index tests (a) porphyritic andesite (b) tuffaceous
sandstone and (c) silicified tuffaceous sandstone 45
424 Conventional and modified loading points 47
425 MPL testing arrangement 47
426 Post-test specimen the tension-induced crack commonly
found across the specimen and shear cone usually formed
underneath the loading platens 48
427 Example of P-δ curve for porphyritic andesite specimen The ratio
of ∆P∆δ is used to predict the elastic modulus of MPL
specimen (Empl) 56
428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests 62
429 Uniaxial compressive strength predicted for silicified
tuffaceous sandstone from MPL tests 62
XVI
LIST OF FIGURES (Continued)
Figure Page
430 Uniaxial compressive strength predicted for tuffaceous
sandstone from MPL tests 63
431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and
modified point load test 75
432 Comparisons of triaxial compressive strength criterion of
silicified tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 76
433 Comparisons of triaxial compressive strength criterion of
tuffaceous sandstone between the triaxial compressive
strength test and modified point load test 77
51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm 80
52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm 80
53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm 81
54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm 81
55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm 82
LIST OF SYMBOLS AND ABBREVIATIONS
A = Original cross-section Area
c = cohesive strength
CP = Conventional Point Load
D = Diameter of Rock Specimen
D = Diameter of Loading Point
De = Equivalent Diameter
E = Youngrsquos Modulus
Empl = Elastic Modulus by MPL Test
Et = Tangent Elastic Modulus
IS = Point Load Strength Index
L = Original Specimen Length
LD = Length-to-Diameter Ratio
MPL = Modified Point Load
Pf = Failure Load
Pmpl = Modified Point Load Strength
t = Specimen Thickness
α = Coefficient of Stress
αE = Displacement Function
β = Coefficient of the Shape
∆L = Axial Deformation
XVIII
LIST OF SYMBOLS AND ABBREVIATIONS (Continued)
∆P = Change in Applied Stress
∆δ = Change in Vertical of Point Load Platens
εaxial = Axial Strain
ν = Poissonrsquos Ratio
ρ = Rock Density
σ = Normal Stress
σ1 = Maximum Principal Stress (Vertical Stress)
σ3 = Minimum Principal Stress (Horizontal Stress)
σB = Brazilian Tensile Stress
σc = Uniaxial Compressive Strength (UCS)
σm = Mean Stress
τ = Shear Stress
τoct = Octahedral Shear Stress
φi = angle of Internal friction
CHAPTER I
INTRODUCTION
11 Background and rationale
In geological exploration mechanical rock properties are one of the most
important parameters that will be used in the analysis and design of engineering
structures in rock mass To obtain these properties the rock from the site is extracted
normally by mean of core drilling and then transported the cores to the laboratory
where the mechanical testing can be conducted Laboratory testing machine is
normally huge and can not be transported to the site On site testing of the rocks may
be carried out by some techniques but only on a very limited scale This method is
called for point load strength Index testing However this test provides unreliable
results and lacks theoretical supports Its results may imply to other important
properties (eg compressive and tensile strength) but only based on an empirical
formula which usually poses a high degree of uncertainty
For nearly a decade modified point load (MPL) testing has been used to
estimate the compressive and tensile strength and elastic modulus of intact rock
specimens in the laboratory (Tepnarong 2001) This method was invented and
patented by Suranaree University of Technology The test apparatus and procedure
are intended to be in expensive and easy compared to the relevant conventional
methods of determining the mechanical properties of intact rock eg those given by
the International Society for Rock Mechanics (ISRM) and the American Society for
2
Testing and Materials (ASTM) In the past much of the MPL testing practices has
been concentrated on circular and disk specimens While it has been claimed that
MPL method is applicable to all rock shapes the test results from irregular lumps of
rock have been rare and hence are not sufficient to confirm that the MPL testing
technique is truly valid or even adequate to determine the basic rock mechanical
properties in the field where rock drilling and cutting devices are not available
12 Research objectives
The objective of this research is to experimentally assess the performance of
the modified point load testing on rock samples with irregular shapes Three rock
types obtained from the north pit-wall of Khao Moh at Chatree gold mine are used as
rock samples A minimum of 150 rock samples of porphyritic andesite silicified-
tuffaceous sandstone and tuffaceous sandstone are collected from the site The
sample thickness-to-loading diameter ratio (td) is varied from 2 to 3 and the sample
diameter-to-loading diameter ratio (Dd) from 5 to 10 The sample deformation and
failure are used to calculate the elastic modulus and strengths of rocks Uniaxial and
triaxial compression tests Brazilian tension test and conventional point load test are
conducted on the three rock types to obtain data basis for comparing with those from
MPL testing Finite difference analysis is performed to obtain stress distribution
within the MPL samples under different td and Dd ratios The effect of the
irregularity is quantitatively assessed Similarity and discrepancy of the test results
from the MPL method and from the conventional method are examined
Modification of the MPL calculation scheme may be made to enhance its predictive
capability for the mechanical properties of irregular shaped specimens
3
13 Research concept
A modified point load (MPL) testing technique was proposed by Fuenkajorn
and Tepnarong (2001) and Fuenkajorn (2002) The objectives of this testing are to
determine the elastic modulus uniaxial compressive strength and tensile strength of
intact rocks The application of testing apparatus is modified from the loading
platens of the conventional point load (CPL) testing to the cylindrical shapes that
have the circular cross-section while they are half-spherical shapes in CPL
The modes of failure for the MPL specimens are governed by the ratio of
specimen diameter to loading platen diameter (Dd) and the ratio of specimen
thickness to loading platen diameter (td) This research involves using the MPL
results to estimate the triaxial compressive strength of specimens which various Dd
and td ratios and compare to the conventional compressive strength test
14 Research methodology
This research consists of six main tasks literature review sample collection
and preparation laboratory testing finite difference analysis comparison discussions
and conclusions The work plan is illustrated in the Figure 11
141 Literature review
Literature review is carried out to study the state-of-the-art of CPL and MPL
techniques including theories test procedure results analysis and applications The
sources of information are from journals technical reports and conference papers A
summary of literature review is given in this thesis Discussions have been also been
made on the advantages and disadvantages of the testing the validity of the test results
4
Preparation
Literature Review
Sample Collection and Preparation
Theoretical Study
Laboratory Ex
Figure 11 Research methodology
periments
MPL Tests Characterization Tests
Comparisons
Discussions
Laboratory Testing
Various Dd UCS Tests
Various td Brazilian Tension Tests
Triaxial Compressive Strength Tests
CPL Tests
Conclusions
5
when correlating with the uniaxial compressive strength of rocks and on the failure
mechanism the specimens
142 Sample collection and preparation
Rock samples are collected from the north pit-wall of Khao
Moh at Chatree gold mine Three rock types are tested with a minimum of 50
samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable Sample preparation is carried out in the laboratory at Suranaree
University of Technology
143 Theoretical study of the rock failure mechanism
The theoretical work primarily involves numerical analyses on
the MPL specimens under various shapes Failure mechanism of the modified point
load test specimens is analyzed in terms of stress distributions along loaded axis The
finite difference code FLAC is used in the simulation The mathematical solutions
are derived to correlate the MPL strengths of irregular-shaped samples with the
uniaxial and traiaxial compressive strengths tensile strength and elastic modulus of
rock specimens
144 Laboratory testing
Three prepared rock type samples are tested in laboratory
which are divided into two main groups as follows
1441 Characterization tests
The characterization tests include uniaxial compressive
strength tests (ASTM D7012-07) Brazilian tensile strength tests (ASTM D3967
1981) triaxial compressive strength tests (ASTM D7012-07) and conventional point
6
load index tests (ASTM D5731 1995) The characterization testing results are used
in verifications of the proposed MPL concept
1442 Modified point load tests
Three rock types of rock from the north pit-wall of
Khao Moh at Chatree gold mine are used as rock samples A minimum of 150 rock
samples of porphyritic andesite silicified-tuffaceous sandstone and tuffaceous
sandstone are used in the MPL testing The sample thickness-to-loading diameter
ratio (td) is varied from 2 to 3 and the sample diameter-to-loading diameter ratio
(Dd) from 5 to 10 The sample deformation and failure are used to calculate the
elastic modulus and strengths of rocks The MPL testing results are compared with
the standard tests and correlated the relations in terms of mathematic formulas
145 Analysis
Finite difference analysis is performed to obtain stress
distribution within the MPL samples under various shapes with different td and Dd
ratios The effect of the irregularity is quantitatively assessed Similarity and
discrepancy of the test results from the MPL method and from the conventional
method are examined Modification of the MPL calculation scheme may be made to
enhance its predictive capability for the mechanical properties of irregular shaped
specimens
146 Thesis writing and presentation
All aspects of the theoretical and experimental studies
mentioned are documented and incorporated into the thesis The thesis discusses the
validity and potential applications of the results
7
15 Scope and limitations
The scope and limitations of the research include as follows
1 Three rock types of rock from the pit wall of Chatree gold mine are
selected as a prime candidate for use in the experiment
2 The analytical and experimental work assumes linearly elastic
homogeneous and isotropic conditions
3 The effects of loading rate and temperature are not considered All tests
are conducted at room temperature
4 MPL tests are conducted on a minimum of 50 samples
5 The investigation of failure mode is on macroscopic scale Macroscopic
phenomena during failure are not considered
6 The finite difference analysis is made in axis symmetric and assumed
elastic homogeneous and isotropic conditions
7 Comparison of the results from MPL tests and conventional method is
made
16 Thesis contents
The first chapter includes six sections It introduces the thesis by briefly
describing the background and rationale and identifying the research objectives that
are describes in the first and second section The third section describes the proposed
concept of the new testing technique The fourth section describes the research
methodology The fifth section identifies the scope and limitation of the research and
the description of the overview of contents in this thesis are in the sixth section
CHAPTER II
LITERATURE REVIEW
21 Introduction
This chapter summarizes the results of literature review carried out to improve an
understanding of the applications of modified point load testing to predict the strengths and
elastic modulus of the intact rock The topics reviewed here include conventional point
load test modified point load test characterization tests and size effects
22 Conventional point load tests
Conventional point load (CPL) testing is intended as an index test for the strength
classification of rock material It has long been practiced to obtain an indicator of the
uniaxial compressive strength (UCS) of intact rocks The testing equipment (Figure 21)
is essentially a loading system comprising a loading flame hydraulic oil pump ram and
loading platens The geometry of the loading platen is standardized (Figure 22) having
60 degrees angle of the cone with 5 mm radius of curvature at the cone tip It is made of
hardened steel The CPL test method has been widely employed because the test
procedure and sample preparation are simple quick and inexpensive as compared with
conventional tests as the unconfined compressive strength test Starting with a simple
method to obtain a rock properties index the International Society for Rock Mechanics
(ISRM) commissions on testing methods have issued a recommended procedure for the
point load testing (ISRM 1985) the test has also been established as a standard test
method by the American Society for Testing and Materials in 1995 (ASTM 1995)
9
Although the point load test has been studied extensively (eg Broch and Franklin
1972 Bieniawski 1974 and 1975 Wijk 1980 Brook 1985) the theoretical solutions
for the test result remain rare Several attempts have been made to truly understand
the failure mechanism and the impact of the specimen size on the point load strength
results It is commonly agreed that tensile failure is induced along the axis between
loading points (Evans 1961 Hiramutsu 1976 Wijk 1978 1980) The most
commonly accepted formula relating the CPL index and the UCS is proposed by
Broch and Franklin (1972) The UCS (or σc) can be estimated as about 24 times of
the point load strength index (Is) of rock specimens with the diameter-to-length ratio
of 05 The IS value should also be corrected to a value equivalent to the specimen
diameter of 50 mm The factor of 24 can sometimes load to an error in the prediction
of the UCS Most previous studied have been done experimentally but rare
theoretical attempt has been made to study the validity of Broch and Franklin
formula
The CPL testing has been performed using a variety of sizes and shapes of
rock specimen (Wijk 1980 Foster 1983 Panek and Fannon 1992 Chau and Wong
1996 Butenuth 1997) This is to determine the most suitable specimen sizes These
investigations have proposed empirical relations between the IS and σc to be
universally applicable to various rock types However some uncertainly of these
relations remains
Panek and Fannon (1992) show the results of the CPL tests UCS tests and
Brazilian tension tests that are performed on three hard rocks (iron-formation
metadiabase and ophitic basalt) The CPL strength is analyzed in terms of the
10
Figure 21 Loading system of the conventional point load (CPL) (Tepnarong 2001)
Figure 22 Standard loading platen shape for the conventional point load testing
(ISRM suggested method and ASTM D5731-95)
11
size and shape effects More than 500 an irregular lumps were tested in the field
The shape effect exponents for compression have been found to be varied with rock
types The shape effect exponents in CPL tests are constant for the three rocks
Panek and Fannon (1992) recommended that the monitoring of the compressive and
tensile strengths should have various sizes and shapes of specimen to obtain the
certain properties
Chau and Wong (1996) study analytically the conversion factor relating
between σc and IS A wide range of the ratios of the uniaxial compressive strength to
the point load index has been observed among various rock types It has been found
that the uniaxial compressive strength of rocks can vary from 62 (Nevada test site
tuff) to 105 (Flaming Gorge shale) times the IS depending on rock type The
conversion factor relating σc to be Is depends on compressive and tensile strengths
the Poissonrsquos ratio and the length and diameter of specimen The conversion factor
of 24 (Broch and Franklin 1972) falls within this range but it is no by meaning
universal
23 Modified point load tests
Tepnarong (2001) proposed a modified point load testing method to correlate
the results with the uniaxial compressive strength (UCS) and tensile strength of intact
rocks The primary objective of the research is to develop the inexpensive and
reliable rock testing method for use in field and laboratory The test apparatus is
similar to the conventional point load (CPL) except that the loading points are cut
flat to have a circular cross-section area instead of using a half-spherical shape To
derive a new solution finite element analyses and laboratory experiments were
12
carried out The simulation results suggested that the applied stress required failing
the MPL specimen increased logarithmically as the specimen thickness or diameter
increased The MPL tests CPL tests UCS tests and Brazilian tension tests were
performed on Saraburi marble under a variety of sizes and shapes The UCS test
results indicated that the strengths decreased with increased the length-to-diameter
ratio The test results can be postulated that the MPL strength can be correlated with
the compressive strength when the MPL specimens are relatively thin and should be
an indicator of the tensile strength when the specimens are significantly larger than
the diameter of the loading points Predictive capability of the MPL and CPL
techniques were assessed Extrapolation of the test results suggested that the MPL
results predicted the UCS of the rock specimens better than the CPL testing The
tensile strength predicted by the MPL also agreed reasonably well with the Brazilian
tensile strength of the rock
Tepnarong (2006) proposed the modified point load testing technique to
determine the elastic modulus and triaxial compressive strength of intact rocks The
loading platens are made of harden steel and have diameter (d) varying from 5 10
15 20 25 to 30 mm The rock specimens tested were marble basalt sandstone
granite and rock salt Basic characterization tests were first performed to obtain
elastic and strength properties of the rock specimen under standard testing methods
(ASTM) The MPL specimens were prepared to have nominal diameters (D) ranging
from 38 mm to 100 mm with thickness varying from 18 mm to 63 mm Testing on
these circular disk specimens was a precursory step to the application on irregular-
shaped specimens The load was applied along the specimen axis while monitoring
the increased of the load and vertical displacement until failure Finite element
13
analyses were performed to determine the stress and deformation of the MPL
specimens under various Dd and td ratios The numerical results were also used to
develop the relationship between the load increases (∆P) and the rock deformation
(∆δ) between the loading platens The MPL testing predicts the intact rock elastic
modulus (Empl) by using an equation Empl = (tαE) (∆P∆δ) where t represents the
specimen thickness and αE is the displacement function derived from numerical
simulation The elastic modulus predicted by MPL testing agrees reasonably well
with those obtained from the standard uniaxial compressive tests The predicted Empl
values show significantly high standard deviation caused by high intrinsic variability
of the rock fabric This effect is enhanced by the small size of the loading area of the
MPL specimens as compared to the specimen size used in standard test methods
The results of the numerical simulation were used to determine the minimum
principal stress (σ3) at failure corresponding to the maximum applied principal stress
(σ1) A simple relation can therefore be developed between σ1 σ3 ratio Poissonrsquos ratio
(ν) and diameter ratio (Dd) to estimate the triaxial compressive strengths of the rock
specimens σ1 σ3 = 2[(ν(1-ν))(1-(dD)2)]-1 The MPL test results from specimens with
various Dd ratios can provide σ1 and σ3 at failure by assuming that ν = 025 and that
failure mode follows Coulomb criterion The MPL predicted triaxial strengths agree
very well with the triaxial strength obtained from the standard triaxial testing (ASTM)
The discrepancy is about 2-3 which may be due to the assumed Poissonrsquos ratio of 25
and due to the assumption used in the determination of σ3 at failure In summary even
through slight discrepancies remain in the application of MPL results to determine the
elastic modulus and triaxial compressive strength of intact rocks this approach of
14
predicting the rock properties shows a good potential and seems promising considering
the low cost of testing technique and ease of sample preparation
24 Characterization tests
241 Uniaxial compressive strength tests
The uniaxial compressive strength test is the most common laboratory
test undertaken for rock mechanics studies In 1972 the International Society of Rock
Mechanics (ISRM) published a suggested method for performing UCS tests (Brown
1981) Bieniawski and Bernede (1979) proposed the procedures in American Society
for Testing and Materials (ASTM) designation D2938
The tests are also the most used tests for estimating the elastic
modulus of rock (ASTM D7012) The axial strain can be measured with strain gages
mounted on the specimen or with the Linear Variable Differential Tranformers
(LVDTs) attached parallel to the length of the specimen The lateral strain can be
measured using strain gages around the circumference or using the LVDTs across
the specimen diameter
The UCS (σc) is expressed as the ratio of the peak load (P) to the
initial cross-section area (A)
σc= PA (21)
And the Youngrsquos modulus (E) can be calculated by
E= ΔσΔε (22)
Where Δσ is the change in stress and Δε is the change in strain
15
The ratio of lateral strain and axial strain magnitudes (εlatεax) determines the value of
Poissonrsquo ratio (ν)
ν = - (εlatεax) (23)
242 Triaxial compressive strength tests
Hoek and Brown (1980b) and Elliott and Brown (1986) used the
triaxaial compressive strength tests to gain an understanding of rock behavior under a
three-dimensions state of stress and to verify and even validate mathematical
expressions that have been derived to represent rock behavior in analytical and
numerical models
The common procedures are described in ASTM designation D7012 to
determine the triaxial strengths and D7012 to determine the elastic moduli and in
ISRM suggested methods (Brown 1981)
The axial strain can be measured with strain gages mounted on the
specimen or with the LVTDs attached parallel to the length of the specimen The
lateral strain can be measured using strain gages around the circumstance within the
jacket rubber
At the peak load the stress conditions are σ1 = PA σ3=p where P is
the maximum load parallel to the cylinder axis A is the initial cross-section area and
p is the pressure in the confining medium
The Youngrsquos modulus (E) and Poissonrsquos ratio (ν) can be calculated by
E = Δ(σ1-σ3)Δ εax (24)
and
16
ν = (slope of axial curve) (slope of lateral curve) (25)
where Δ(σ1-σ3) is the change in differential stress and Δ εax is the change in axial strain
243 Brazilian tensile strength tests
Caneiro (1974) and Akazawa (1953) proposed the Brazilian tensile
strength test of intact rocks Specifications of Brazilian tensile strength test have been
established by ASTM D3967 and suggested approach is provided by ISRM (Brown 1981)
Jaeger and Cook (1979) proposed the equation for calculate the
Brazilian tensile strength as
σB = (2P) ( πDt) (26)
where P is the failure load D is the disk diameter and t is the disk thickness
25 Size effects on compressive strength
The uniaxial compressive strength normally tested on cylindrical-shaped
specimens The length-to-diameter (LD) ratio of the specimen influences the
measured strength Typically the strength decreases with increasing the LD ratio
but it tends to become constant or ratios in the order of 21 to 31 (Hudson et al 1971
Obert and Duvall 1967) For higher ratios the specimen strength may be influenced
by bulking
The size of specimen may influence the strength of rock Weibull (1951)
proposed that a large specimen contains more flaws than a small one The large
specimen therefore also has flaws with critical orientation relative to the applied
shear stresses than the small specimen A large specimen with a given shape is
17
therefore likely to fail and exhibit lower strength than a small specimen with the same
shape (Bieniawski 1968 Jaeker and Cook 1979 Kaczynski 1986)
Tepnarong (2001) investigated the results of uniaxial compressive strength
test on Saraburi marble and found that the strengths decrease with increase the
length-to-diameter (LD) ratio And this relationship can be described by the power
law The size effects on uniaxial compressive strength are obscured by the intrinsic
variability of the marble The Brazilian tensile strengths also decreased as the
specimen diameter increased
CHAPTER III
SAMPLE COLLECTION AND PREAPATION
This chapter describes the sample collection and sample preparation
procedure to be used in the characterization and modified point load testing The
rock types to be used including porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone Locations of sample collection rock description are
described
31 Sample collection
Three rock types include porphyritic andesite silicified-tuffaceous sandstone
and tuffaceous sandstone collected from Chatree Gold Mine Akara Mining Company
Limited Phichit Thailand are used in this research The rock samples are collected
from the north pit-wall of Khao Moh Three rock types are tested with a minimum of
50 samples for each rock type The selection criteria are that the rock should be
homogeneous as much as possible and that sample collection should be convenient
and repeatable The collected location is shown in Figure 31
32 Rock descriptions
Three rock types are used in this research there are porphyritic andesite
silicified tuffaceous sandstone and tuffaceous sandstone Tuffaceous sandstone is
medium brownish grey the clasts are andesite rhyolite andesitic tuff and quartz
fragments and sub-rounded to sub-angular matrix sand andesitic tuff rock fragment
19
19
Figure 31 The location of rock samples collected area
lt 10 quartz 3 pyrite and litho-facies massive ungraded clast supported
moderately sorted Silicified tuffaceous sandstone is medium brown clasts are fine to
medium sand and silt sub-rounded shape quartz rich with siliceous matrix massive
non-graded well sorted moderately Silicified Porphyritic andesite is grayish green
medium-coarse euhedral evenly distributed phenocrysts are abundant most
conspicuous are hornblende phenocrysts fine-grained groundmass Those samples
are collected from Chatree Gold Mine Akara mining Co Ltd Phichit Thailand
20
33 Sample preparation
Sample preparation has been carried out to obtain different sizes and shapes
for testing It is conducted in the laboratory facility at Suranaree University of
Technology For characterization testing the process includes coring and grinding
Preparation of rock samples for characterization test follows the ASTM standard
(ASTM D4543-85) The nominal sizes of specimen that following the ASTM
standard practices for the characterization tests are shown in table 31 And grinding
surface at the top and bottom of specimens at the position of loading platens for
unsure that the loading platens are attach to the specimen surfaces and perpendicular
each others as shown in Figure 32 The shapes of specimens are irregularity-shaped
The ratio of specimen thickness to platen diameter (td) is around 20-30 and the
specimen diameter to platen diameter (Dd) varies from 5 to 10
Table 31 The nominal sizes of specimens following the ASTM standard practices
for the characterization tests
Testing Methods
LD Ratio
Nominal Diameter
(mm)
Nominal Length (mm)
Number of Specimens
1UniaxialCompressive Strength Test and Elastic Modulus Measurement (ASTM D7012)
25 54 135 10
2 Triaxial Compressive Strength Test (ASTM D7012) 20 54 108 10
3 Brazilian Tensile Strength Test (ASTM D3967) 05 54 27 10
4 Point Load Strength Index Test (ASTM D 5731) 10 54 54 10
21
Figure 32 Some prepared rock specimens of porphyritic andesite for MPL Tests
td asymp20 to 30
Figure 33 The concept of specimen preparation for MPL testing
CHAPTER IV
LABORATORY TESTS
Laboratory testing is divided into two main tasks including the
characterization tests and the modified point load tests Three rock types porphyritic
andesite silicified-tuffaceous sandstone and tuffaceous sandstone are used in this
research
41 Literature reviews
411 Displacement function
Tepnarong (2006) proposed a method to compute the vertical
displacement of the loading point as affected by the specimen diameter and thickness
(Dd and td ratios) by used the series of finite element analyses To accomplish this
a displacement function (αE) is introduced as (∆P∆δ)middot(tE) where ∆P is the change in
applied stress ∆δ is the change in vertical displacement of point load platens t is the
specimen thickness and E is elastic modulus of rock specimen The displacement
function is plotted as a function of Dd And found that the αE is dimensionless and
independent of rock elastic modulus αE trend to be independent of Dd when Dd is
beyond 15 The αE is sensitive to ν particularly when υ is between 025 and 05 This
agrees with the assumption that as the Poissonrsquos ratio increases the αE value will
increase because under higher ν the ∆δ will be reduced This is due to the large
confinement resulting from the higher Poissonrsquos ratio Nevertheless most rocks have
Poissonrsquos ratio within a range between 020 and 030 particularly for moderate to
23
hard rocks As a result the Poissonrsquos ratio of 025 will provide a reasonable
prediction of the value of αE values
Figure 51 plots αE or (∆P∆δ)middot(tE) as a function of td for the ratios of Dd ge
10 The displacement function increase as the td increases which can be expressed
by a power equation
αE = (∆P∆δ)middot(tE) = 150 (td)064 (51)
by using the least square fitting The curve fit gives good correlation (R2=0998)
These curves can be used to estimate the elastic modulus of rock from MPL results
By measuring the MPL specimen thickness t and the increment of applied stress (∆P)
and displacement (∆δ)
42 Basic characterization tests
The objectives of the basic characterization tests are to determine the
mechanical properties of each rock type to compare their results with those from the
modified point load tests (MPL) The basic characterization tests include uniaxial
compressive strength (UCS) tests with elastic modulus measurements triaxial
compressive strength tests Brazilian tensile strength tests and conventional point load
strength index tests
421 Uniaxial compressive strength tests and elastic modulus
measurements
The uniaxial compressive strength tests are conducted on the three
rock types Sample preparation and test procedure are followed the ASTM standards
(ASTM D7012) and the ISRM suggested methods (Brown 1981) The core size is
24
54 mm in diameter (NX size) and the ratio of the length to diameter is 25 A total of
10 specimens are tested for each rock type
A constant loading rate of 05 to 10 MPas is applied to the specimens
until failure occurs Tangent elastic modulus is measured at stress level equal to 50
of the uniaxial compressive strength Post-failure characteristics are observed
The uniaxial compressive strength (σc) is calculated by dividing the
maximum load by the original cross-section area of loading platen
σc= pf A (41)
where pf is the maximum failure load and A is the original cross-section area of
loading platen The tangent elastic modulus (Et) is calculated by the following
equation
Et = (Δσaxial) (Δε axial) (42)
And the axial strain can be calculated from
ε axial = ΔLL (43)
where the ΔL is the axial deformation and L is the original length of specimen
The average uniaxial compressive strength and tangent elastic
modulus of each rock types are shown in Tables 41 through 44
25
Figure 41 Pre-test samples of porphyritic andesite for UCS test
Figure 42 Pre-test samples of tuffaceous sandstone for UCS test
26
Figure 43 Pre-test samples of silicified tuffaceous sandstone for UCS test
Figure 44 Preparation of testing apparatus for UCS test
27
Figure 45 Post-test rock samples of porphyritic andesite from UCS test
Figure 46 Post-test rock samples of tuffaceous sandstone from UCS test
28
Figure 47 Post-test rock samples of silicified-tuffaceous sandstone from UCS
0
50
100
150
0 0001 0002 0003 0004 0005Axial Strain
Axi
al S
tres
s (M
Pa)
Andesite04
03
01
05
02
Andesite
Figure 48 Results of uniaxial compressive strength test and elastic modulus
measurements of porphyritic andesite The axial stresses are plotted as
a function of axial strain
29
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Strain
Axi
al S
tres
s (M
Pa)
Pebbly Tuffacious Sandstone
04
03
05
01
02
Tuffaceous Sandstone
0
50
100
150
0 0001 0002 0003 0004 0005
Axial Stain
Axi
al S
tres
s (M
Pa)
Silicified Tuffacious Sandstone
0103
05
0402
Silicified Tuffaceous Sandstone
Figure 49 Results of uniaxial compressive strength test and elastic modulus
measurements of tuffaceous sandstone (top) and silicified tuffaceous
sandstone (bottom) The axial stresses are plotted as a function of axial
strain
30
Table 41 Testing results of porphyritic andesite
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 5366 13486 282 1327 451 And-06-03-UCS-02 5366 13494 283 1106 397 And-02-01-UCS-03 5366 13485 280 1061 470 And-08-03-UCS-04 5366 13417 284 1282 392 And-04-04-UCS-05 5366 13564 285 973 438
Average 1150 plusmn 150 430 34 plusmn
Table 42 Testing results of tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 5366 13810 266 1017 538 TST-01-02-UCS-02 5366 13236 268 1238 545 TST-02-04-UCS-03 5366 13558 264 973 441 TST-06-09-UCS-04 5366 13515 267 1459 475 TST-02-02-UCS-05 5366 13745 263 884 566
Average 1114 plusmn 233 513 53 plusmn
Table 43 Testing results of silicified tuffaceous sandstone
Sample No Diameter (mm)
Length (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 5366 13309 271 1194 656 SST-07-01-UCS-02 5366 13547 267 930 632 SST-07-03-UCS-03 5366 13095 268 1194 503 SST-02-06-UCS-04 5366 13475 269 1614 661 SST-06-02-UCS-05 5366 13577 270 1106 713
Average 1207 plusmn 252 633 80 plusmn
31
Table 44 Uniaxial compressive strength and tangent elastic modulus measurement
results of three rock types
Rock Type
Number of Test
Samples
Uniaxial Compressive Strength σc (MPa)
Tangential Elastic Modulus
Et (GPa)
Porphyritic andesite 50 1150plusmn150 430plusmn34 Silicified-tuffaceous sandstone 50 1207plusmn252 633plusmn80
Tuffaceous sandstone 50 1114plusmn233 513plusmn53
422 Triaxial compressive strength tests
The objective of the triaxial compressive strength test is to determine
the compressive strength of rock specimens under various confining pressures The
sample preparation and test procedure are followed the ASTM standard (ASTM
D7012-07) and the ISRM suggested method (Brown 1981) A total of 16 rock
specimens are tested under various confining pressures 6 specimens of porphyritic
andesite 5 specimens of silicified-tuffaceous sandstone and 5 specimens of
tuffaceous sandstone The applied load onto the specimens is at constant rate until
failure occurred within 5 to 10 minutes of loading under each confining pressure
The constant confining pressures used in this experiment are ranged from 0345 067
138 276 and 414 MPa (50 100 200 400 and 600 psi) in andesite 0345 069
276 414 and 552 MPa (50 100 400 600 and 800 psi) in silicified-tuffaceous
sandstone and 0345 069 138 207 and 276 MPa (50 100 200 300 and 400 psi)
in pebbly tuffaceous sandstone Post-failure characteristics are observed
32
Figure 410 Pre-test samples for triaxial compressive strength test the top is
porphyritic andesite and the bottom is tuffaceous sandstone
33
Figure 411 Pre-test samples of silicified tuffaceous sandstone for triaxial
compressive strength test
Hook cell
Figure 412 Triaxial testing apparatus
34
Figure 413 Post-test rock samples from triaxial compressive strength tests The top
is porphyritic andesite and the bottom is tuffaceous sandstone
35
Figure 414 Post-test rock samples of silicified tuffaceous sandstone from triaxial
compressive strength test
Table 45 Triaxial compressive strength testing results of porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
And-04-02-TR-01 10803 5366 285 04 1459 And-06-04-TR-03 10806 5366 284 07 1526 And-06-02-TR-02 10806 5366 283 14 1636 And-08-01-TR-04 10665 5366 284 28 2034 And-08-02-TR-05 10948 5366 283 41 2520
Table 46 Triaxial compressive strength testing results of tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
TST-01-01-TR-04 10989 5366 266 04 1061 TST 02-01-TR-01 10852 5366 262 07 1238 TST-06-01-TR-02 10889 5366 264 138 1415 TST-06-03-TR-03 10755 5366 264 201 1813 TST-06-08-TR-05 11025 5366 267 28 2056
36
Table 47 Triaxial compressive strength testing results of silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa)
SST-05-01-TR-01 10875 5366 266 04 1305 SST-07-02-TR-02 10790 5366 266 14 1371 SST-01-04-TR-03 11022 5366 267 28 1592 SST-01-03-TR-04 10713 5366 267 41 1901 SST-01-01-TR-05 10530 5366 265 55 2255
The results of triaxial tests are shown in Table 42 Figures 413 and 414
show the shear failure by triaxial loading at various confining pressures (σ3) for the
three rock types The relationship between σ1 and σ3 can be represented by the
Coulomb criterion (Hoek 1990)
τ = c + σ tan φi (44)
where τ is the shear stress c is the cohesion σ is the normal stress and φi is the
internal friction angle The parameters c and φi are determined by Mohr-Coulomb
diagram as shown in Figures 415 through 417
37
φi =54˚ Andesite
Figure 415 Mohr-Coulomb diagram for andesite
φi = 55˚
Tuffaceous Sandstone
Figure 416 Mohr-Coulomb diagram for pebbly tuffaceous sandstone
38
Silicified tuffaceous sandstone
φi = 49˚
Figure 417 Mohr-Coulomb diagram for silicified tuffaceous sandstone
Table 48 Results of triaxial compressive strength tests on three rock types
Rock Type
Number of
Samples
Average Density (gcc)
Cohesion c (MPa)
Internal Friction Angle φi (degrees)
Porphyritic Andesite 5 283 33 54
Tuffaceous Sandstone 5 265 28 55 Silicified Tuffaceous Sandstone 5 267 36 49
423 Brazilian Tensile Strength Tests
The objectives of the Brazilian tensile strength test are to determine
the tensile strength of rock The Brazilian tensile strength tests are performed on all
rock types Sample preparation and test procedure are followed the ASTM standard
(ASTM D3967-81) and the
39
ISRM suggested method (Brown 1981) Ten specimens for each rock
type have been tested The specimens have the diameter of 55 mm with 25 mm thick
The Brazilian tensile strength of rock can be calculated by the following
equation (Jaeger and Cook 1979)
σB = (2pf) (πDt) (45)
where σB is the Brazilian tensile strength pf is the failure load D is the diameter
of disk specimen and t is the thickness of disk specimen All of specimens failed
along the loading diameter (Figure 420) The results of Brazilian tensile strengths
are shown in Table 49 The tensile strength trends to decrease as the specimen size
(diameter) increase and can be expressed by a power equation (Evans 1961)
σB = A (D)-B (46)
where A and B are constants depending upon the nature of rock
424 Conventional point load index (CPL) tests
The objectives of CPL tests are to determine the point load strength index for
use in the estimation of the compressive strength of the rocks The sample
preparation test procedure and calculation are followed the standard practices
(ASTM D 5731-02) and the ISRM suggested method (Brown 1981) Twenty
specimens of each rock types are tested The length-to-diameter (LD) ratio of the
specimen is constant at 10 The specimen diameter and thickness are maintained
constant at 54 mm (Figure 421) The core specimen is loaded along its axis as
shown in Figure 422 Each specimen is loaded to failure at a constant rate such that
40
(a)
(b)
(c)
Figure 418 Pre-test samples for Brazilian tensile strength test (a) porphyritic
andesite (b) tuffaceous sandstone and (c) silicified tuffaceous
sandstone
41
Figure 419 Brazilian tensile strength test arrangement
Table 49 Results of Brazilian tensile strength tests of three rock types
Rock Type
Average Diameter
(mm)
Average Length (mm)
Average Density (gcc)
Number of
Samples
Brazilian Tensile
Strength σB (MPa)
Porphyritic andesite 5366 2672 283 10 170plusmn16
Tuffaceous sandstone 5366 2737 265 10 131plusmn33
Silicified tuffaceous sandstone
5366 2670 267 10 191plusmn32
42
(a)
(b)
(c)
Figure 420 Post-test specimens (a) porphyritic andesite (b) tuffaceous sandstone
and (c) silicified tuffaceous sandstone
43
Figure 421 Pre-test samples of porphyritic andesite for conventional point load
strength index test
Figure 422 Conventional point load strength index test arrangement
44
failures occur within 5-10 minutes Post-failure characteristics are observed
The point load strength index for axial loading (Is) is calculated by the
equation
Is = pf De2 (47)
where pf is the load at failure De is the equivalent core diameter (for axial loading
De2 = 4Aπ and A=WD) A is the minimum cross-sectional area of a plane through
the platen contact points W is the specimen width (thickness of core) and D is the
specimen diameter The post-test specimens are shown in Figure 423
The testing results of all three rock types are shown in Table 410 The
point load strength index of andesite pebbly tuffaceous sandstone and silicified
tuffaceous sandstone are average as 81 plusmn 12 102 plusmn 20 and 108 plusmn 22 MPa
Table 410 Results of conventional point load strength index tests of three rock types
Rock Types Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index
Is (MPa) Porphyritic Andesite 5493 5366 283 81plusmn12 Tuffaceous Sandstone 5545 5366 265 102plusmn20 Silicified Tuffaceous Sandstone 5491 5366 268 108plusmn22
45
Figure 423 Post-Test rock specimens from conventional point load strength index
tests (a) porphyritic andesite (b) tuffaceous sandstone and (c)
silicified tuffaceous sandstone
46
43 Modified point load (MPL) tests
The objectives of the modified point load (MPL) tests are to measure the
strength of rock between the loading points and to produce failure stress results for
various specimen sizes and shapes The results are complied and evaluated to
determine the mathematical relationship between the strengths and specimen
dimensions which are used to predict the elastic modulus and uniaxial and triaxial
compressive strengths and Brazilian tensile strength of the rocks
The testing apparatus for the proposed MPL testing are similar to those of the
conventional point load (CPL) test except that the loading points are cylindrical
shape and cut flat with the circular cross-sectional area instead of using half-spherical
shape (Tepnarong 2001) The loading platens used in this research are 7 10 and 15
mm in diameter and the thickness-to-loading point diameter ratio (td) of about 25
The specimen diameter-to-loading point diameter is varying from 5 to 100 The load
is applied at the rate of 200 Ns Fifty specimens are prepared and tested for each
rock type The vertical deformations (δ) are monitored One cycle of unloading and
reloading is made at about 40 failure load Then the load is increased to failure
The MPL strength (PMPL) is calculated by
PMPL = pf ((π4)(d2)) (48)
where pf is the applied load at failure and d is the diameter of loading point Figure
26 shows the example of post-test specimen shear cone are usually formed
underneath the loading points and two or three tension-induced cracks are commonly
found across the specimens
47
The MPL testing method is divided into 4 schemes based on its objective
elastic modulus uniaxial and triaxial compressive strengths and Brazilian tensile
strength determination
Figure 424 Conventional and modified loading points(Tepnarong 2006)
Figure 425 MPL testing arrangement
48
Tension-induced crack Shear cone
Shear cone
Tension-induced crack
Figure 426 Post-test specimen the tension-induced crack commonly found across
the specimen and shear cone usually formed underneath the loading
platens
49
Table 411 Results of modified point load tests on porphyritic andesite
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-01 246 543 280 125 159 And-MPL-02 351 632 370 180 471 And-MPL-03 236 634 150 170 191 And-MPL-04 266 960 250 234 319 And-MPL-05 284 903 370 369 471 And-MPL-06 245 793 280 182 357 And-MPL-07 263 874 260 234 331 And-MPL-08 261 980 210 171 268 And-MPL-09 280 777 270 056 344 And-MPL-10 244 569 280 124 159 And-MPL-11 251 613 650 138 368 And-MPL-12 226 631 600 189 340 And-MPL-13 233 1126 180 151 468 And-MPL-14 279 1203 220 165 572 And-MPL-15 239 503 400 011 227 And-MPL-16 281 474 300 012 170 And-MPL-17 305 861 390 021 497 And-MPL-18 233 653 500 008 283 And-MPL-19 294 1386 380 200 484 And-MPL-20 265 860 410 017 522 And-MPL-21 238 425 550 087 311 And-MPL-22 230 417 450 087 255 And-MPL-23 223 557 500 231 283 And-MPL-24 250 760 550 112 311 And-MPL-25 259 1243 180 585 468 And-MPL-26 303 560 310 143 395 And-MPL-27 273 1640 390 156 497 And-MPL-28 282 906 220 200 280 And-MPL-29 311 934 290 156 369 And-MPL-30 246 1314 250 650 650 And-MPL-31 262 982 200 175 255 And-MPL-32 260 1147 180 156 468 And-MPL-33 240 700 450 101 255 And-MPL-34 304 800 240 135 306 And-MPL-35 250 455 220 127 280 And-MPL-36 243 1697 120 292 312 And-MPL-37 333 1520 310 156 395 And-MPL-38 238 661 170 260 442
50
Table 411 Results of modified point load tests on porphyritic andesite (Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
And-MPL-39 318 347 130 186 338 And-MPL-40 245 551 150 260 390 And-MPL-41 207 561 150 325 390 And-MPL-42 223 425 500 231 283 And-MPL-43 207 561 150 346 390 And-MPL-44 324 340 310 234 395 And-MPL-45 275 426 240 169 306 And-MPL-46 302 397 130 175 166 And-MPL-47 255 314 100 170 127 And-MPL-48 257 220 250 094 142 And-MPL-49 256 214 130 057 74 And-MPL-50 243 166 180 078 102
51
Table 412 Results of modified point load tests on tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-01 270 546 220 212 293 TST -MPL-02 258 787 230 326 293 TST -MPL-03 275 730 200 143 255 TST -MPL-04 282 715 400 143 510 TST -MPL-05 254 1345 220 264 280 TST -MPL-06 292 893 200 143 255 TST -MPL-07 243 853 550 112 311 TST -MPL-08 287 1047 210 319 268 TST -MPL-09 230 787 370 212 471 TST -MPL-10 230 427 260 132 147 TST -MPL-11 282 1243 450 319 573 TST -MPL-12 254 604 200 127 255 TST -MPL-13 288 1180 290 159 369 TST -MPL-14 251 631 410 170 232 TST -MPL-15 214 1104 120 260 312 TST -MPL-16 229 486 380 102 215 TST -MPL-17 259 715 110 650 286 TST -MPL-18 243 285 180 073 102 TST -MPL-19 285 316 130 128 130 TST -MPL-20 241 295 180 170 102 TST -MPL-21 298 417 300 100 170 TST -MPL-22 265 642 300 088 170 TST -MPL-23 314 611 450 101 255 TST -MPL-24 303 481 650 124 368 TST -MPL-25 223 223 260 126 331 TST -MPL-26 273 652 260 178 331 TST -MPL-27 216 887 420 170 535 TST -MPL-28 319 718 290 164 369 TST -MPL-29 231 516 200 128 255 TST -MPL-30 260 641 380 280 484 TST -MPL-31 287 496 330 158 420 TST -MPL-32 264 368 230 170 293 TST -MPL-33 238 415 230 130 293 TST -MPL-34 271 824 140 260 364 TST -MPL-35 283 800 220 325 572 TST -MPL-36 242 1013 180 325 468 TST -MPL-37 254 715 90 217 234 TST -MPL-38 210 755 150 520 390
52
Table 412 Results of modified point load tests on tuffaceous sandstone
(Continued)
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
TST -MPL-39 293 508 110 260 286 TST -MPL-40 273 410 100 347 260 TST -MPL-41 234 628 80 260 208 TST -MPL-42 259 433 130 260 338 TST -MPL-43 265 546 220 435 280 TST -MPL-44 255 829 260 222 147 TST -MPL-45 254 368 240 315 306 TST -MPL-46 293 695 370 222 210 TST -MPL-47 247 297 180 128 102 TST -MPL-48 310 611 300 237 170 TST -MPL-49 225 337 160 371 416 TST -MPL-50 259 410 120 394 312
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
Specimen Number td Ded Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-01 300 782 170 280 442 SST-MPL-02 250 480 220 307 572 SST-MPL-03 314 424 340 356 433 SST-MPL-04 292 809 220 450 572 SST-MPL-05 275 1142 300 532 780 SST -MPL-06 308 490 190 273 494 SST -MPL-07 317 611 280 418 728 SST -MPL-08 233 684 240 414 624 SST -MPL-09 255 480 230 371 598 SST -MPL-10 217 772 120 958 312 SST -MPL-11 312 903 270 400 702 SST -MPL-12 255 1094 150 272 390 SST -MPL-13 286 742 400 408 510 SST -MPL-14 248 615 350 296 198 SST -MPL-15 253 805 210 282 546 SST -MPL-16 243 1094 150 260 390
53
Table 413 Results of modified point load tests on silicified tuffaceous sandstone
(Continued)
Specimen Number td Dd Failure Load pf
(kN)
∆P∆δ (GPamm)
Pmpl (MPa)
SST-MPL-17 234 1090 250 416 650 SST -MPL-18 253 1371 240 473 624 SST -MPL-19 327 434 320 330 408 SST -MPL-20 270 310 390 278 497 SST -MPL-21 269 691 410 185 522 SST -MPL-22 312 504 380 182 484 SST -MPL-23 319 627 260 150 331 SST -MPL-24 281 689 330 295 420 SST -MPL-25 210 720 390 259 497 SST -MPL-26 303 775 370 221 471 SST -MPL-27 272 714 310 274 395 SST -MPL-28 292 855 600 209 764 SST -MPL-29 310 742 400 176 510 SST -MPL-30 284 847 410 158 522 SST -MPL-31 320 891 650 464 828 SST -MPL-32 261 256 400 178 226 SST -MPL-33 224 405 550 131 311 SST -MPL-34 231 379 450 215 255 SST -MPL-35 290 442 1050 190 594 SST -MPL-36 241 521 500 102 283 SST -MPL-37 275 605 600 067 340 SST -MPL-38 263 616 650 127 368 SST -MPL-39 227 615 350 229 198 SST -MPL-40 236 508 550 090 311 SST -MPL-41 318 1142 300 498 780 SST -MPL-42 303 809 210 392 546 SST -MPL-43 228 805 210 244 546 SST -MPL-44 283 1142 300 571 780 SST -MPL-45 277 772 120 780 312 SST -MPL-46 288 1206 280 411 728 SST -MPL-47 250 508 570 309 323 SST -MPL-48 275 442 1050 338 594 SST -MPL-49 272 605 650 254 368 SST -MPL-50 260 805 200 360 520
54
431 Modified point load tests for elastic modulus measurement
The MPL tests are carried out with the measurement of axial
deformation for use in elastic modulus estimation Fifty irregular specimens for each
rock type are tested The specimen thickness-to-loading diameter (td) is about 25
and the specimen diameter -to-loading diameter (Dd) is varied from 25 to 50 Cyclic
loading is performed while monitoring displacement (δ)
The testing apparatus used in this experiment includes the point load
tester model SBEL PLT-75 and the modified point load platens The displacement
digital gages with a precision up to 0001 mm are used to monitor the axial
deformation of rock between the loading points as loading decreases The cyclic
load is applied along the specimen axis and is performed by systematically increasing
and decreasing loads on the test specimen After unloading the axial load is
increased until the failure occurs Cyclic loading is performed on the specimens in
an attempt at determining the elastic deformation The ratio of change of stress to
displacement (∆P∆δ) is measured from unloading curve Post-failure characteristics
are observed and recorded Photographs are taken of the failed specimens
The results of the deformation measurement by MPL tests are shown
in Tables411 through 413 The stresses (P) are plotted as a function of axial
displacement (δ) and shown in Figures B1 through B150 (Appendix B) The results
of ∆P∆δ are used to estimate the elastic modulus of the specimen
The elastic modulus predictions from MPL results can be made by
using the value of αE plotted as a function of Ded for various td ratios as shown in
Figure 427 and the MPL elastic modulus can be expressed as
55
⎟⎠⎞
⎜⎝⎛
ΔΔ
⎟⎟⎠
⎞⎜⎜⎝
⎛=
δαPtE
Empl (Tepnarong 2006) (49)
where Empl is the elastic modulus predicted from MPL results αE is displacement
function value from numerical analysis and ∆P∆δ is the ratio of change of stress to
displacement which is measured from unloading curve of MPL tests and t is the
specimen thickness The value of αE used in the calculation is 260 for td ratio equal
to 25-30 (Tepnarong 2006) The results of elastic modulus predictions from MPL
tests are tabulated in Tables 414 through 416 Table 417 compares the elastic
modulus obtained from standard uniaxial compressive strength test (ASTM D3148-
96) with those predicted by MPL test
The values of Empl for each specimen with P-δ curve are shown in
Appendix B The MPL method under-estimates the elastic modulus of all tested
rocks This is the primarily because the actual loaded area may be smaller than that
used in the calculation due to the roughness of the specimen surfaces As a result the
contact area used to calculate PMPL is larger than the actual In addition the EMPL
tends to show a high intrinsic variation (high standard deviation) This is because the
loading areas of MPL specimens are small This phenomenon conforms by the test
results obtained by Fuenkajorn and Deamen (1992) They conclude that smaller test
specimens not only exhibit a higher strength than larger one (size effect) but also
show a high intrinsic variability due to the heterogeneity of rock fabric particularly at
small sizes This implied that to obtain a good prediction (accurate result) of the rock
elasticity a large amount of MPL specimens are desirable This drawback may be
compensated by the ease of testing and the low cost of sample preparation
56
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (MPa)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure 427 Example of P-δ curve for porphyritic andesite specimen The ratio of
∆P∆δ is used to predict the elastic modulus of MPL specimen (Empl)
57
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-01 246 543 125 260 1776 And-MPL-02 351 632 180 260 2430 And-MPL-03 236 634 170 260 1546 And-MPL-04 266 960 234 260 2390 And-MPL-05 284 903 369 260 4031 And-MPL-06 245 793 182 260 1712 And-MPL-07 263 874 234 260 2367 And-MPL-08 261 980 171 260 1717 And-MPL-09 280 777 056 260 603 And-MPL-10 244 569 124 260 1748 And-MPL-11 251 613 138 260 2001 And-MPL-12 226 631 189 260 2464 And-MPL-13 233 1126 151 260 947 And-MPL-14 279 1203 165 260 1239 And-MPL-15 239 503 011 260 151 And-MPL-16 281 474 012 260 195 And-MPL-17 305 861 021 260 247 And-MPL-18 233 653 008 260 108 And-MPL-19 294 1386 200 260 2263 And-MPL-20 265 860 017 260 173 And-MPL-21 238 425 087 260 1195 And-MPL-22 230 417 087 260 1154 And-MPL-23 223 557 231 260 2976 And-MPL-24 250 760 112 260 1615 And-MPL-25 259 1243 585 260 4073 And-MPL-26 303 560 143 260 1667 And-MPL-27 273 1640 156 260 1639 And-MPL-28 282 906 200 260 2172 And-MPL-29 311 934 156 260 1868 And-MPL-30 246 1314 650 260 4310 And-MPL-31 262 982 175 260 1766 And-MPL-32 260 1147 156 260 1093 And-MPL-33 240 700 101 260 1398 And-MPL-34 304 800 135 260 1576 And-MPL-35 250 455 127 260 1221 And-MPL-36 243 1697 292 260 1909 And-MPL-37 333 1520 156 260 2000 And-MPL-38 238 661 260 260 1665 And-MPL-39 318 347 186 260 1592 And-MPL-40 245 551 260 260 1712
58
And-MPL-41 207 561 325 260 1815
59
Table 414 Results of elastic modulus calculation from MPL tests on porphyritic
andesite (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
And-MPL-42 223 425 231 260 2976 And-MPL-43 207 561 346 260 1932 And-MPL-44 324 340 234 260 2912 And-MPL-45 275 426 169 260 1785 And-MPL-46 302 397 175 260 2033 And-MPL-47 255 314 170 260 1667 And-MPL-48 257 220 094 260 1393 And-MPL-49 256 214 057 260 843 And-MPL-50 243 166 078 260 1094 Average 1743 Standard Deviation 910
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-01 300 782 280 260 2262 SST -MPL-02 250 480 307 260 2066 SST -MPL-03 314 424 356 260 4302 SST -MPL-04 292 809 450 260 3533 SST -MPL-05 275 1142 532 260 3939 SST -MPL-06 308 490 273 260 2266 SST -MPL-07 317 611 418 260 3572 SST -MPL-08 233 684 414 260 2595 SST -MPL-09 255 480 371 260 2546 SST -MPL-10 217 772 958 260 5593 SST -MPL-11 312 903 400 260 3360 SST -MPL-12 255 1094 272 260 1864 SST -MPL-13 286 742 408 260 4435 SST -MPL-14 248 615 296 260 4235 SST -MPL-15 253 805 282 260 1918 SST -MPL-16 243 1094 260 260 1698 SST -MPL-17 234 1090 416 260 2621 SST -MPL-18 253 1371 473 260 3224 SST -MPL-19 327 434 330 260 4153 SST -MPL-20 270 310 278 260 2863
60
Table 415 Results of elastic modulus calculation from MPL tests on silicified
tuffaceous sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
SST -MPL-21 269 691 185 260 1914 SST -MPL-22 312 504 182 260 2183 SST -MPL-23 319 627 150 260 1839 SST -MPL-24 281 689 295 260 3193 SST -MPL-25 210 720 259 260 2090 SST -MPL-26 303 775 221 260 2577 SST -MPL-27 272 714 274 260 2862 SST -MPL-28 292 855 209 260 2350 SST -MPL-29 310 742 176 260 2097 SST -MPL-30 284 847 158 260 1728 SST -MPL-31 320 891 464 260 5707 SST -MPL-32 261 256 178 260 2678 SST -MPL-33 224 405 131 260 1690 SST -MPL-34 231 379 215 260 2863 SST -MPL-35 290 442 190 260 3174 SST -MPL-36 241 521 102 260 1416 SST -MPL-37 275 605 067 260 1064 SST -MPL-38 263 616 127 260 1926 SST -MPL-39 227 615 229 260 3005 SST -MPL-40 236 508 090 260 1226 SST -MPL-41 318 1142 498 260 4264 SST -MPL-42 303 809 392 260 3196 SST -MPL-43 228 805 244 260 1500 SST -MPL-44 283 1142 571 260 4348 SST -MPL-45 277 772 780 260 5826 SST -MPL-46 288 1206 411 260 3184 SST -MPL-47 250 508 309 260 4464 SST -MPL-48 275 442 338 260 5364 SST -MPL-49 272 605 254 260 3981 SST -MPL-50 260 805 360 260 2523 Average 2986 Standard Deviation 1190
61
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-01 270 546 212 260 2202 TST -MPL-02 258 787 326 260 3232 TST -MPL-03 275 730 143 260 1513 TST -MPL-04 282 715 143 260 1551 TST -MPL-05 254 1345 264 260 2579 TST -MPL-06 292 893 143 260 1606 TST -MPL-07 243 853 112 260 2273 TST -MPL-08 287 1047 319 260 3521 TST -MPL-09 230 787 212 260 1875 TST -MPL-10 230 427 132 260 1752 TST -MPL-11 282 1243 319 260 3455 TST -MPL-12 254 604 127 260 1241 TST -MPL-13 288 1180 159 260 1764 TST -MPL-14 251 631 170 260 2465 TST -MPL-15 214 1104 260 260 1500 TST -MPL-16 229 486 102 260 1345 TST -MPL-17 259 715 650 260 4530 TST -MPL-18 243 285 073 260 1025 TST -MPL-19 285 316 128 260 2105 TST -MPL-20 241 295 170 260 2360 TST -MPL-21 298 417 100 260 1722 TST -MPL-22 265 642 088 260 896 TST -MPL-23 314 611 101 260 1830 TST -MPL-24 303 481 124 260 2166 TST -MPL-25 223 223 126 260 1083 TST -MPL-26 273 652 178 260 1869 TST -MPL-27 216 887 170 260 2065 TST -MPL-28 319 718 164 260 2011 TST -MPL-29 310 742 128 260 1136 TST -MPL-30 260 641 280 260 2800 TST -MPL-31 287 496 158 260 1742 TST -MPL-32 264 368 170 260 1725 TST -MPL-33 238 415 130 260 1192 TST -MPL-34 271 824 260 260 1942 TST -MPL-35 283 800 325 260 2478 TST -MPL-36 242 1013 325 260 2115 TST -MPL-37 254 715 217 260 1484 TST -MPL-38 210 755 520 260 2944 TST -MPL-39 293 508 260 260 2052 TST -MPL-40 273 410 347 260 2552
62
Table 416 Results of elastic modulus calculation from MPL tests on tuffaceous
sandstone (continued)
Specimen Number td Ded ∆P∆δ (GPamm) αE Empl (GPa)
TST -MPL-41 234 628 260 260 1638 TST -MPL-42 259 433 260 260 1814 TST -MPL-43 265 546 435 260 4440 TST -MPL-44 255 829 222 260 3265 TST -MPL-45 254 368 315 260 3075 TST -MPL-46 293 695 222 260 2502 TST -MPL-47 247 297 128 260 1827 TST -MPL-48 310 611 237 260 4240 TST -MPL-49 225 337 371 260 2252 TST -MPL-50 259 410 394 260 2746 Average 2190 Standard Deviation 830
Table 417 Comparisons of elastic modulus results obtained from uniaxial
compressive strength tests and those from modified point load tests
Rock Type Tangential Elastic Modulus from UCS
tests Et (GPa)
Elastic Modulus from MPL tests
Empl (GPa) Porphyritic andesite 430plusmn34 174plusmn91
Silicified tuffaceous sandstone 633plusmn80 299plusmn119
tuffaceous sandstone 513plusmn53 219plusmn83
432 Modified point load tests predicting uniaxial compressive strength
The uniaxial compressive strength of MPL specimens can be predicted
by plotting Pmpl as a function of diameter ratio Ded as shown in Figures 428 through
430 At diameter ratio equal to unity the Pmpl represents the uniaxial compressive
strength of rock The uniaxial compressive strength predicted from MPL tests
compared with those from CPL test and UCS standard test is shown in Table 418
63
UCS PREDICTION OF PORPHYRITIC ANDESITE FROM MPL TESTS
Pmpl = 11844(Ded)05489
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Ded Ratio
MPL
Stre
ngth
(MPa
)
Figure 428 Uniaxial compressive strength predicted for porphyritic andesite from
MPL tests
64
UCS PREDICTION OF SILICIFIED TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 11463(Ded)07447
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Ded Ratio
MPL
-Str
engt
h (M
Pa)
Figure 429 Uniaxial compressive strength predicted for silicified tuffaceous
sandstone from MPL tests
65
UCS PREDICTION OF TUFFACEOUS SANDSTONE FROM MPL TESTS
Pmpl = 10222(Ded)05457
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ded Ratio
MPL
-Stre
ngth
(MPa
)
Figure 430 Uniaxial compressive strength predicted for tuffaceous sandstone from
MPL tests
Table 418 Comparison the test results between UCS CPL Brazilian tensile
strength and MPL tests
Uniaxial Compressive Strength (MPa)
Tensile Strength (MPa) Rock Type UCS
Testing CPL
Prediction MPL
PredictionBrazilian Testing
MPL Prediction
And 1150 1944 plusmn12 1005 170plusmn16 139plusmn43 TST 1114 2448plusmn20 1308 131plusmn33 121plusmn73 SST 1207 2592plusmn22 1022 191plusmn32 171plusmn126
433 Modified Point Load Tests for Tensile Strength Predictions
The MPL results determine the rock tensile strength by using the
relationship of the failure stresses (Pmpl) as a function of specimen thickness to
66
loading diameter ratio (td) The tensile strength from MPL prediction can be
expressed as an empirical equation (Tepnarong 2001)
σt mpl = Pmpl (αT ln (td)+βT) (410)
where αT = 133 ln (Ded)-756 and βT= -70 ln (Ded)+ 1952
The results of tensile strengths of all rock types are shown in Tables
419through 421 The predicted tensile strengths are compared with the Brazilian
tensile strengths for the three rock types in Table 418 A close agreement of the
results obtained between two methods The discrepancies of the results are less than
the standard deviation of the results
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa)
And-MPL-01 246 543 159 1495 767 750 And-MPL-02 351 632 471 1697 661 1688 And-MPL-03 236 634 191 1701 659 900 And-MPL-04 266 960 319 2252 369 1240 And-MPL-05 284 903 471 2170 412 1761 And-MPL-06 245 793 357 1999 502 1558 And-MPL-07 263 874 331 2127 435 1330 And-MPL-08 261 980 268 2279 355 1053 And-MPL-09 280 777 344 1971 517 1351 And-MPL-10 244 569 159 1557 734 746 And-MPL-11 251 613 368 1656 683 1666 And-MPL-12 226 631 340 1695 662 1662 And-MPL-13 233 1126 468 2464 257 2000 And-MPL-14 279 1203 572 2552 211 2022 And-MPL-15 239 503 227 1392 822 1114 And-MPL-16 281 474 170 1314 863 765 And-MPL-17 305 861 497 2108 445 1776 And-MPL-18 233 653 283 1740 638 1340 And-MPL-19 294 1386 484 2741 112 1577 And-MPL-20 265 860 522 2106 446 2091
67
And-MPL-21 238 425 311 1169 939 1595 And-MPL-22 230 417 255 1142 953 1338 And-MPL-23 223 557 283 1529 749 1431 And-MPL-24 250 760 311 1941 532 1347 And-MPL-25 259 1243 468 2596 188 1763 And-MPL-26 303 560 395 1535 746 1613
68
Table 419 Results of tensile strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) And-MPL-27 273 1640 497 2964 -006 1671 And-MPL-28 282 906 280 2252 369 1035 And-MPL-29 311 934 369 2216 388 1272 And-MPL-30 246 1314 650 2670 149 2543 And-MPL-31 262 982 255 2282 353 997 And-MPL-32 260 1147 468 2488 244 1783 And-MPL-33 240 700 255 1832 590 1161 And-MPL-34 304 800 306 2010 496 1121 And-MPL-35 250 455 280 1259 891 1370 And-MPL-36 243 1697 312 3010 -030 1181 And-MPL-37 333 1520 395 2863 047 1130 And-MPL-38 238 661 442 1755 630 2054 And-MPL-39 318 347 338 897 1082 1594 And-MPL-40 245 551 390 1513 758 1847 And-MPL-41 207 561 390 1537 745 2089 And-MPL-42 223 425 283 1169 939 1507 And-MPL-43 207 561 390 1537 745 2089 And-MPL-44 324 340 395 871 1096 1864 And-MPL-45 275 426 306 1172 937 1441 And-MPL-46 302 397 166 1079 986 760 And-MPL-47 255 314 127 766 1151 1159 And-MPL-48 257 220 142 291 1401 845 And-MPL-49 256 214 74 257 1419 443 And-MPL-50 243 166 102 -078 1595 928 Average 1427 Standard Deviation 44
69
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) SST -MPL-01 300 782 442 1336 851 2018 SST -MPL-02 250 480 572 1331 853 2759 SST -MPL-03 314 424 433 1196 924 1888 SST -MPL-04 292 809 572 2024 489 2155 SST -MPL-05 275 1142 780 2483 247 2827 SST -MPL-06 308 490 494 1357 840 2086 SST -MPL-07 317 611 728 1651 685 2808 SST -MPL-08 233 684 624 1800 606 2932 SST -MPL-09 255 480 598 1331 853 2849 SST -MPL-10 217 772 312 1962 522 1529 SST -MPL-11 312 903 702 2170 412 2436 SST -MPL-12 255 1094 390 2426 277 1533 SST -MPL-13 286 742 510 1910 549 2011 SST -MPL-14 248 615 198 1661 680 905 SST -MPL-15 253 805 546 2017 492 2312 SST -MPL-16 243 1094 390 2426 277 1607 SST -MPL-17 234 1090 650 2421 280 2780 SST -MPL-18 253 1371 624 2726 120 2354 SST -MPL-19 327 434 408 1196 924 1740 SST -MPL-20 270 310 497 748 1160 2618 SST -MPL-21 269 691 522 1816 599 2181 SST -MPL-22 312 504 484 1394 821 2012 SST -MPL-23 319 627 331 1686 667 1263 SST -MPL-24 281 689 420 1812 601 1699 SST -MPL-25 210 720 497 1869 570 2541 SST -MPL-26 303 775 471 1968 519 1745 SST -MPL-27 272 714 395 1859 576 1623 SST -MPL-28 292 855 764 2098 450 2830 SST -MPL-29 310 742 510 1910 549 1881 SST -MPL-30 284 847 522 2087 456 1981 SST -MPL-31 320 891 828 2153 421 2832 SST -MPL-32 261 256 226 492 1295 1282 SST -MPL-33 224 405 311 1106 972 1672 SST -MPL-34 231 379 255 1017 1019 1363 SST -MPL-35 290 442 594 1221 912 2690 SST -MPL-36 241 521 283 1439 797 1374 SST -MPL-37 275 605 340 1639 692 1445 SST -MPL-38 263 616 368 1661 680 1611
70
Table 420 Results of tensile strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded Pmpl (MPa)
αT βT σt mpl (MPa)
SST -MPL-39 227 615 198 1661 680 969 SST -MPL-40 236 508 311 1406 814 1540 SST -MPL-41 318 1142 780 2483 247 2500 SST -MPL-42 303 809 546 2024 489 1999 SST -MPL-43 228 805 546 2017 492 2530 SST -MPL-44 283 1142 780 2483 247 2757 SST -MPL-45 277 772 312 1962 522 1236 SST -MPL-46 288 1206 728 2555 209 2502 SST -MPL-47 250 508 323 1406 814 1533 SST -MPL-48 275 442 594 1221 912 2769 SST -MPL-49 272 605 368 1639 692 1580 SST -MPL-50 260 805 520 2017 492 2147 Average 2045 Standard Deviation 56
71
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-01 270 546 293 1502 763 1299 TST -MPL-02 258 787 293 1988 508 1226 TST -MPL-03 275 730 255 1888 560 1031 TST -MPL-04 282 715 510 1860 575 2035 TST -MPL-05 254 1345 280 2701 133 1058 TST -MPL-06 292 893 255 2156 420 933 TST -MPL-07 243 853 311 2095 451 1346 TST -MPL-08 287 1047 268 2279 355 970 TST -MPL-09 230 787 471 1988 508 2179 TST -MPL-10 230 427 147 1176 935 769 TST -MPL-11 282 1243 573 2596 188 1994 TST -MPL-12 254 604 255 1636 693 1149 TST -MPL-13 288 1180 369 2527 224 1274 TST -MPL-14 251 631 232 1695 662 1044 TST -MPL-15 214 1104 312 2438 271 1465 TST -MPL-16 229 486 215 1347 845 1098 TST -MPL-17 259 715 286 1861 575 1220 TST -MPL-18 243 285 102 637 1219 571 TST -MPL-19 285 316 130 776 1146 665 TST -MPL-20 241 295 102 685 1194 568 TST -MPL-21 298 417 170 1143 952 771 TST -MPL-22 265 642 170 1178 934 1059 TST -MPL-23 314 611 255 1652 685 989 TST -MPL-24 303 481 368 1423 805 1545 TST -MPL-25 223 223 331 313 1389 2018 TST -MPL-26 273 652 331 1738 640 1389 TST -MPL-27 216 887 535 2146 424 1850 TST -MPL-28 319 718 369 1866 572 1350 TST -MPL-29 231 516 255 1425 804 1276 TST -MPL-30 260 641 484 1715 651 2114 TST -MPL-31 287 496 420 1373 832 1846 TST -MPL-32 264 368 293 976 1041 1475 TST -MPL-33 238 415 293 1151 948 1504 TST -MPL-34 271 824 364 2049 476 1418 TST -MPL-35 283 800 572 2010 496 2210 TST -MPL-36 242 1013 468 2324 331 1965 TST -MPL-37 254 715 234 1861 575 1013 TST -MPL-38 210 755 390 1932 537 1976
72
Table 421 Results of tensile strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded Pmpl (MPa) αT βT σt mpl
(MPa) TST -MPL-39 293 508 286 1406 814 1229 TST -MPL-40 273 410 260 1124 963 1243 TST -MPL-41 234 628 208 1688 666 990 TST -MPL-42 259 433 338 1194 926 1639 TST -MPL-43 265 546 280 1502 763 1257 TST -MPL-44 255 829 147 2057 472 614 TST -MPL-45 254 368 306 976 1041 1568 TST -MPL-46 293 695 210 1822 595 1846 TST -MPL-47 247 297 102 691 1190 561 TST -MPL-48 310 611 170 1652 685 665 TST -MPL-49 225 337 416 1939 533 1972 TST -MPL-50 259 410 312 1120 965 1537 Average 1336 Standard Deviation 56
434 Modified point load tests for triaxial compressive strength predictions
The objective of this section is to predict the triaxial compressive strength
of intact rock specimens by using the MPL results (modified point load strength Pmpl) It
is speculated that increase of applied load (σ1) will invoke a confining pressure (σ3) on
the imaginary cylindrical profile between the two loading points This is due to the
effect of Poissonrsquos ratio (ν) which causing a potential expansion of rock in this cylinder
The greater the σ1 the greater the σ3 in addition Poissonrsquos ratios also affect the
magnitude of σ3 The magnitude of σ3 also depends on the specimen shape particularly
the Ded ratio In principle σ3 will equal zero for Ded ratio equal to unity But when
Ded ratio is very large approaching infinity σ3 will reach its maximum This maximum
value of σ3 will also depend on the rock Poissonrsquos ratio From computer simulation of
td =25 the variation of σ1 σ3 ratio can be simply expressed by Tepnarong (2006) as
73
(σ1 σ3) = 2 ((ν (1ndashν) (1-(dDe) 2)) (411)
where ν is the Poissonrsquos ratio of rock specimen d is the modified point load diameter
and De is the equivalent diameter of the specimen The Poissonrsquos ratio of rock
specimen used in equation 411 can be assumed to be 25 The σ1 σ3 ratio tends to be
independent of Ded for Ded greater than 10 This implies that when MPL specimen
diameter is more than 10 times of the loading point diameter the magnitude of σ3 is
approaching its maximum value (Tepnarong 2006)
It should be pointed out that approach used here to determine σ3
assumes that there is no shear stress (τrz) along the imagination cylinder As a result
the magnitude of σ3 determined here would be higher than the actual σ3 applied in the
true triaxial test specimen This mean that the σ1 σ3 ratios at failure obtained from
MPL tests will be lower than the actual failure stress ratio from the true triaxial tests
From the concept of σ1 σ3-Ded relation proposed the major and
minor principal stresses at failure (σ1 σ3) can be predicted from the measured MPL
failure stress Pmpl and Ded ratio The Poissonrsquos ratio used here is equal to 025
Comparison between the failure stress (σ1 σ3) obtained from the
standard triaxial compressive strength testing (ASTM D7012-07) and those predicted
from MPL test results are made graphically in Figures 431 through 433 for ν =025
The figures are plotted the maximum shear stress (frac12(σ1-σ3)) as a function of mean
shear stress (frac12(σ1+σ3)) indicating that the predicted failure stresses under-estimate
the value obtained from the standard testing This is because of the assumption of no
shear stresses developed on the surface of the imaginary cylinder The under
prediction may be due to the intrinsic variability of the rocks The predictions are
also sensitive to assumed Poissonrsquos ratio The Poissonrsquos ratio of the tested specimens
74
may be lower than the assumed value of 025 This comparison implies that the
triaxial strength predicted from MPL test will be more conservative than those from
the standard testing method
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests
Specimen Number
td Ded σ1
(MPa)σ3
(MPa)Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-01 246 543 159 2527 6663 9190 And-MPL-02 351 632 471 7583 19776 27358 And-MPL-03 236 634 191 3075 8017 11091 And-MPL-04 266 960 319 5198 13325 18522 And-MPL-05 284 903 471 7682 19726 27408 And-MPL-06 245 793 357 5792 14938 20730 And-MPL-07 263 874 331 5393 13864 19257 And-MPL-08 261 980 268 4368 11192 15560 And-MPL-09 280 777 344 5581 14407 19988 And-MPL-10 244 569 159 2535 6659 9194 And-MPL-11 251 613 368 5911 15445 21356 And-MPL-12 226 631 340 5465 14253 19717 And-MPL-13 233 1126 468 7660 19568 27228 And-MPL-14 279 1203 572 9372 23911 33283 And-MPL-15 239 503 227 3589 9529 13118 And-MPL-16 281 474 170 2678 7154 9831 And-MPL-17 305 861 497 8087 20797 28884 And-MPL-18 233 653 283 4561 11874 16435 And-MPL-19 294 1386 484 7946 20231 28177 And-MPL-20 265 860 522 8501 21864 30365 And-MPL-21 238 425 311 4854 13143 17997 And-MPL-22 230 417 255 3962 10758 14720 And-MPL-23 223 557 283 4521 11894 16415 And-MPL-24 250 760 311 5049 13045 18094 And-MPL-25 259 1243 468 7671 19562 27234 And-MPL-26 303 560 395 6308 16591 22899 And-MPL-27 273 1640 497 8167 20757 28924 And-MPL-28 282 906 280 4574 11726 16300 And-MPL-29 311 934 369 6026 15459 21484 And-MPL-30 246 1314 650 1066 27166 37828 And-MPL-31 262 982 255 4160 10659 14819 And-MPL-32 260 1147 468 7663 19567 27229
75
And-MPL-33 240 700 255 4118 10680 14798 And-MPL-34 304 800 306 4966 12804 17770
76
Table 422 Results of triaxial strengths of porphyritic andesite predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
And-MPL-35 250 455 280 4401 11812 16213 And-MPL-36 243 1697 312 5130 13034 18163 And-MPL-37 333 1520 395 6488 16501 22989 And-MPL-38 238 661 442 7125 18535 25661 And-MPL-39 318 347 338 5112 14342 19455 And-MPL-40 245 551 390 6222 16387 22609 And-MPL-41 207 561 390 6230 16383 22613 And-MPL-42 223 425 283 4413 11948 16361 And-MPL-43 207 561 390 6230 16383 22613 And-MPL-44 324 340 395 5952 16769 22721 And-MPL-45 275 426 306 4767 12903 17670 And-MPL-46 302 397 166 2559 7001 9560 And-MPL-47 255 314 127 3211 9223 12433 And-MPL-48 257 220 142 1852 6151 8003 And-MPL-49 256 214 74 950 3205 4155 And-MPL-50 243 166 102 1493 6331 7823
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-01 300 782 442 7389 19703 27092 SST -MPL-02 250 480 572 9028 24083 33112 SST -MPL-03 314 424 433 6767 18273 25040 SST -MPL-04 292 809 572 9293 23951 33244 SST -MPL-05 275 1142 780 1277 32611 45382 SST -MPL-06 308 490 494 7811 20792 28603 SST -MPL-07 317 611 728 1169 30552 42241 SST -MPL-08 233 684 624 1008 26160 36235 SST -MPL-09 255 480 598 9439 25178 34617 SST -MPL-10 217 772 312 5061 13068 18129 SST -MPL-11 312 903 702 1144 29377 40817 SST -MPL-12 255 1094 390 6381 16308 22689 SST -MPL-13 286 742 510 8255 21350 29605 SST -MPL-14 248 615 198 3183 8316 11500
77
Table 423 Results of triaxial strengths of silicified tuffaceous sandstone predicted
from MPL tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
SST -MPL-15 253 805 546 8869 22863 31732 SST -MPL-16 243 1094 390 6381 16308 22689 SST -MPL-17 234 1090 650 1063 27180 37814 SST -MPL-18 253 1371 624 1024 26077 36317 SST -MPL-19 327 434 408 6369 17198 23567 SST -MPL-20 270 310 497 7344 21169 28513 SST -MPL-21 269 691 522 8438 21896 30333 SST -MPL-22 312 504 484 7672 20368 28040 SST -MPL-23 319 627 331 5626 13897 19224 SST -MPL-24 281 689 420 6790 17624 24414 SST -MPL-25 210 720 497 8039 20821 28860 SST -MPL-26 303 775 471 7648 19743 27391 SST -MPL-27 272 714 395 6388 16551 22939 SST -MPL-28 292 855 764 1244 31997 44436 SST -MPL-29 310 742 510 8255 21350 29605 SST -MPL-30 284 847 522 8498 21866 30364 SST -MPL-31 320 891 828 1349 34656 48146 SST -MPL-32 261 256 226 3165 9741 12906 SST -MPL-33 224 405 311 4825 13157 17982 SST -MPL-34 231 379 255 3912 10783 14695 SST -MPL-35 290 442 594 9307 25071 34377 SST -MPL-36 241 521 283 4499 11905 16404 SST -MPL-37 275 605 340 5452 14259 19711 SST -MPL-38 263 616 368 5912 15445 21357 SST -MPL-39 227 615 198 3183 8316 11500 SST -MPL-40 236 508 311 4939 13100 18039 SST -MPL-41 318 1142 780 1277 32611 45382 SST -MPL-42 303 809 546 8870 22862 31733 SST -MPL-43 228 805 546 8869 22863 31732 SST -MPL-44 283 1142 780 1277 32611 45382 SST -MPL-45 277 772 312 5061 13068 18129 SST -MPL-46 288 1206 728 1193 30433 42361 SST -MPL-47 250 508 323 5119 13577 18695 SST -MPL-48 275 442 594 9307 25071 34377 SST -MPL-49 272 605 368 5906 15447 21354 SST -MPL-50 260 805 520 8447 21774 30221
78
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-01 270 546 293 4672 12313 16986 TST -MPL-02 258 787 293 4756 12272 17028 TST -MPL-03 275 730 255 4125 10676 14801 TST -MPL-04 282 715 510 8243 21356 29599 TST -MPL-05 254 1345 280 4599 11713 16312 TST -MPL-06 292 893 255 4151 10663 14814 TST -MPL-07 243 853 311 5067 13036 18103 TST -MPL-08 287 1047 268 4368 11192 15560 TST -MPL-09 230 787 471 7651 19741 27393 TST -MPL-10 230 427 147 2296 6212 8508 TST -MPL-11 282 1243 573 9397 23964 33361 TST -MPL-12 254 604 255 4089 10695 14783 TST -MPL-13 288 1180 369 6052 15445 21497 TST -MPL-14 251 631 232 3734 9739 13474 TST -MPL-15 214 1104 312 5105 13046 18151 TST -MPL-16 229 486 215 3400 9057 12457 TST -MPL-17 259 715 286 4626 11986 16612 TST -MPL-18 243 285 102 1474 4358 5833 TST -MPL-19 285 316 130 1934 5544 7478 TST -MPL-20 241 295 102 1489 4351 5840 TST -MPL-21 298 417 170 2641 7172 9813 TST -MPL-22 265 642 170 2650 7168 9817 TST -MPL-23 314 611 255 4091 10693 14784 TST -MPL-24 303 481 368 5843 15476 21322 TST -MPL-25 223 223 331 4370 14376 18745 TST -MPL-26 273 652 331 5336 13892 19229 TST -MPL-27 216 887 535 8716 22394 31109 TST -MPL-28 319 718 369 5977 15483 21460 TST -MPL-29 231 516 255 4046 10716 14762 TST -MPL-30 260 641 484 7793 20307 28100 TST -MPL-31 287 496 420 6654 17692 24346 TST -MPL-32 264 368 293 4477 12411 16888 TST -MPL-33 238 415 293 4560 12370 16930 TST -MPL-34 271 824 364 5917 15240 21157 TST -MPL-35 283 800 572 9290 23953 33242 TST -MPL-36 242 1013 468 7646 19575 27221 TST -MPL-37 254 715 234 3785 9806 13592 TST -MPL-38 210 755 390 6321 16338 22659
79
Table 424 Results of triaxial strengths of tuffaceous sandstone predicted from MPL
tests (continued)
Specimen Number td Ded σ1
(MPa)σ3
(MPa)
Maximum shear stress
(MPa)
Mean stress(MPa)
TST -MPL-39 293 508 286 4536 12031 16567 TST -MPL-40 273 410 260 4036 10981 15017 TST -MPL-41 234 628 208 3345 8727 12071 TST -MPL-42 259 433 338 5279 14259 19538 TST -MPL-43 265 546 280 4469 11778 16247 TST -MPL-44 255 829 147 2394 6163 8557 TST -MPL-45 254 368 306 4671 12951 17622 TST -MPL-46 293 695 210 7616 19759 27375 TST -MPL-47 247 297 102 1491 4359 5841 TST -MPL-48 310 611 170 2728 7129 9870 TST -MPL-49 225 337 416 6744 17426 24170 TST -MPL-50 259 410 312 4841 13178 18019
ANDESITE
τm= 07103σm + 26
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=
((σ
1-σ
3)2
) (M
Pa)
MPL PredictionTriaxial Compressive
Figure 431 Comparisons of triaxial compressive strength criterion of porphyritic
andesite between the triaxial compressive strength test and MPL test
80
SILICIFIED TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Mean stressσm= ((σ1+σ3)2) (MPa)
Max
imum
shea
r stre
ss
τm=(
( σ1minus
σ3)
2)
(MPa
)MPL Prediction
Triaxial Compressive Strength test
Figure 432 Comparisons of triaxial compressive strength criterion of silicified
tuffaceous sandstone between the triaxial compressive strength test
and MPL test
81
TUFFACEOUS SANDSTONE
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Mean stress σm=((σ1+σ3)2) (MPa)
Max
imum
shea
r st
res
τ m=(
( σ1-
σ3)
2)
(MPa
)
MPL Prediction
Triaxial Compressive Strength test
Figure 433 Comparisons of triaxial compressive strength criterion of tuffaceous
sandstone between the triaxial compressive strength test and MPL
test
Table 425 compares the triaxial test results in terms of the cohesion c
and internal friction angle φi by assuming the failure mode follows the Coulombrsquos
criterion The c and φi values are calculated from the test results and the predicted
results by the assumption of Coulombrsquos criterion (Jaeger and Cook 1978) Table
425 shows that the strengths predicted by MPL testing of all rock types under-
estimate those obtained from the standard triaxial testing This is probably the actual
Poissonrsquos ratio of the rock specimens are probably lower than those assumed in the
model simulation which is assumed the Poissonrsquos ratio as 025
82
Table 425 Comparisons of the internal friction angle and cohesion between MPL
predictions and triaxial compressive strength tests
Triaxial Compressive Strength Test
MPL Predictions (ν=025) Rock Type
c (MPa) φi (degrees) c (MPa) φi (degrees)
Porphyritic Andesite 12 69 4 45
Silicified Tuffaceous Sandstone 13 65 3 46
Tuffaceous Sandstone 7 73 2 46
CHAPTER V
FINITE DIFFERENCE ANALYSES
51 Objectives
The objective of the finite difference analyses is to verify that the equivalent
diameter of rock specimens used in the MPL strength prediction is appropriate The
finite difference analyses using FLAC software is made to determine the MPL
strength for various specimen diameters (D) with a constant cross-sectional area
52 Model characteristics
The analyses are made in axis symmetry Four specimen models with the
constant thickness of 318 cm are loaded with 10 cm diameter loading point The
diameter of the specimen (D) models is varied from 508 cm to 762 cm Each
specimen has a constant cross-sectional area of 1613 cm2 as shown in Figure 51
through 55 The load is applied to the specimens until failure occurs and then the
failure loads (P) are recorded
53 Results of finite difference analyses
The results of numerical simulation are shown in Table 51 The results
suggest that the MPL strength remains roughly constant when the same equivalent
diameter (De) is used It can be concluded that the equivalent diameter used in this
research is appropriate to predict the MPL strength
80
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 51 Simulation model No1 t= 318 cm D= 508 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 52 Simulation model No2 t= 318 cm D= 572 cm d=10 mm
81
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 53 Simulation model No3 t= 318 cm D= 635 cm d=10 mm
CL
Point Load Platen
D2
318
cm
d2
P (Load)
Figure 54 Simulation model No4 t= 318 cm D= 698 cm d=10 mm
82
P (Load)
d2
318
cm
D2
Point Load Platen
LC
Figure 55 Simulation model No5 t= 318 cm D= 762 cm d=10 mm
Table 51 Summary of the results from numerical simulations
Model Number
Specimen Thickness
t (cm)
Specimen Diameter
D (cm)
Cross-Sectional
Are of Specimen
A (cm2)
Equivalent Diameter
De (cm)
Failure Load P
(kN)
1 318 508 1613 508 4485 2 318 572 1613 508 4630 3 318 635 1613 508 4614 4 318 698 1613 508 4627 5 318 762 1613 508 4590
CHAPTER VI
DISCUSSIONS CONCLUSIONS AND
RECOMMENDATIONS
This chapter discusses various aspects of the proposed MPL testing technique
for determining the elastic modulus uniaxial and triaxial compressive strengths and
tensile strength of intact rock specimens The discussed issues include reliability of
the testing results validity scope and limitations of the proposed method of
calculations and accuracy of the predicted rock properties
61 Discussions
1) For selection of rock specimens for MPL testing in this research an
attempt has been made to select the specimens particularly in obtaining a high degree
of uniformity of rock matrix so as to reduce the intrinsic variability of the mechanical
test results and hence clearly reveals of the relation between the standard test results
with the MPL test results Nevertheless a high degree of intrinsic variability
remains as evidenced from the results of the characterization testing For all tested
rock types here the igneous rocks are normally heterogeneous The high intrinsic
variability is caused by the degree of weathering among specimens and the
distribution of rock fragments in the groundmass which promotes the different
orientations of cleavage planes and pore spaces to become a weak plane in rock
specimens Silicified tuffaceous sandstone the high standard deviation may be
caused by the silicified degree in rock specimens
84
2) For prediction of elastic modulus of rock specimens the effects of the
heterogeneity that cause the selective weak planes are enhanced during the MPL
testing This is because the applied loading areas are much smaller than those under
standard uniaxial compressive strength testing This load condition yields a high
degree of intrinsic variability of the MPL testing results The standard deviation of
the elastic modulus predicted from MPL results are in the range between 35-50
This means that in order to obtain the accurate prediction a large number of rock
specimens is necessary for each rock types and that the MPL testing is more
applicable in fine-grained rocks than coarse-grained rocks Another factor is the
uneven contacts between the loading platens and the rock surfaces which caused the
elastic modulus of all rock types that predicted from MPL testing to be lower
compared with those from the uniaxial compressive strength
3) Equivalent diameter used to define the rock specimen width (perpendicular
to the loading direction) seems adequate for use in MPL predictions of rock
compressive and tensile strengths
4) Determination of σ3 at failure for the MPL testing is the empirical In fact
results from the numerical simulation indicate that σ3 distribution along the imaginary
cylinder between the loading points is not uniform particularly for low td ratio
(lower than 25) Along this cylinder σ3 is tension near the loading point and
becomes compression in the mid-length of the MPL specimen There are also shear
stresses along the imaginary cylinder The induced stress states along the assume
cylinder in MPL specimen are therefore different from those the actual triaxial
strength testing specimen The MPL method can not satisfactorily predict the triaxial
compressive strength of all tested rock types primarily due to the heterogeneity of
85
rock specimens that is the different sizes of phenocrysts in igneous rock in lateral and
horizontal directions This promotes the different failure formations
62 Conclusions
The objective of this research is to determine the elastic modulus uniaxial
compressive strength tensile strength and triaxial compressive strength of rock
specimens by using the modified point load (MPL) test method Three rock types
used in this research are porphyritic andesite silicified tuffaceous sandstone and
tuffaceous sandstone Prior to performing the modified point load testing the
standard characterization testing is carried out on these rock types to obtain the data
basis for use to compare the results from MPL testing The MPL specimens are
irregular-shaped with the specimen thickness to loading platen diameter (td) varies
from 25-35 and the equivalent diameter of specimen to loading platen diameter
(Ded) varies from 15 to 20 Loading platen diameters used in this research are 7 10
and 15 mm Finite different analysis is used to verify the equivalent diameter that use
to calculate rock properties from MPL tests
The research results illustrate that the elastic modulus estimated from MPL tests
under-estimates those obtained from the ASTM standard test with the standard
deviation of 40 for porphyritic andesite 48 for silicified tuffaceous sandstone and
43 for tuffaceous sandstone The MPL test method can satisfactorily predict the
uniaxial compressive strength and tensile strength of all rock types tested here The
conventional point load test method over-predicts the actual strength results by much as
100 The MPL method however can not predict the triaxial compressive strengths
for three rock types tested here primarily due to heterogeneous and different
86
weathering degree of rock specimens and uneven surface of rock specimens This
suggests that the smooth and parallel contact surfaces on opposite side of the loading
points are important for determining the strength of rock specimens for MPL method
63 Recommendations
The assessment of predictive capability of the proposed MPL testing technique
has been limited to three rock types More testing is needed to confirm the applicability
and limitations of the proposed method Some obvious future research needs are
summarized as follows
1) More testing is required for elastic modulus and triaxial compressive strength
on different rock types Smooth and parallel of rock specimen surfaces in the opposite
sides should be prepared for all rock types The results may also reveal the impacts of
grain size on elasticity and strength of obtained under different loading areas And the
effects of size of the areas underneath the applied load should be further investigated
2) To truly confirm the validity of MPL predictions for the elastic modulus and
strength of rocks may be desirable to obtain the actual Poissonrsquos ratio of all rock types
The results could reveal the accuracy of the predicted elastic modulus under the assumed
Poissonrsquos ratio of 025 Comparison between the elastic modulus obtained from the
actual Poissonrsquos ratio may show the validity of assumption of the Poissonrsquos ratio posed
here
3) All tests made in this research are on dry specimens the results of pore
pressure and degree of saturation have not been investigated It is desirable to learn also
the proposed MPL testing technique can yield the intact rock properties under
different degree of saturation
88
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95
Tepnarong P (2006) Theoretical and experimental studies to determine elastic
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point load testing PhD Eng Thesis Suranaree University of
Technology Thailand
Tepnarong P and Fuenkajorn K (2004) Determining of elasticity and strengths
of intact rocks using modified point load test In Proceeding of the ISRM
International Symposium 3rd ASRM Vol 2 (pp 397-392)
Timoshenko S (1958) Strength of materials I Element Theory and Problems
(3rd ed) Princeton N J D Van Nostard
Timoshenko S and Goodier J N (1951) Theory of Elasticity (2nd ed) New
York McGraw-Hill
Truk N and Dearman W R (1985) Improvements in the determination of point
load strength Bull Int Assoc Eng Geol 31 137-142
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length-to-diameter ratio on uniaxial compressive strength of rocks J Eng
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(pp 209-219)Vol
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96
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Abstr 15 149-160
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ASTM 3 49-54
APPENDIX A
CHARACTERIZATION TEST RESULTS
97
Table A-1 Results of conventional point load strength index test on porphyritic
andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
And-06-05-CPL-01 5397 5366 284 52 And-06-05-CPL-02 5332 5366 283 78 And-08-04-CPL-03 5432 5366 284 90 And-08-04-CPL-04 5482 5366 286 87 And-06-01-CPL-05 5330 5366 285 76 And-06-01-CPL-06 5613 5366 284 76 And-04-04-CPL-07 5617 5366 281 75 And-04-05-CPL-08 5525 5366 282 75 And-03-02-CPL-09 5595 5366 280 85 And-03-02-CPL-10 5535 5366 283 85 And-06-06-CPL-11 5475 5366 283 75 And-09-01-CPL-12 5552 5366 286 90 And-09-01-CPL-13 5503 5366 283 90 And-02-04-CPL-14 5542 5366 282 85 And-09-03-CPL-15 5607 5366 282 85 And-09-03-CPL-16 5452 5366 285 96 And-01-03-CPL-17 5530 5366 283 87 And-01-03-CPL-18 5313 5366 283 90 And-01-04-CPL-19 5465 5366 284 56 And-01-04-CPL-20 5572 5366 283 97
Average 81plusmn12
98
Table A-2 Results of conventional point load strength index test on silicified
tuffaceous sand stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
SST-02-03-CPL-01 5373 5366 268 125 SST-06-04-CPL-02 5469 5366 268 70 SST-02-07-CPL-03 5505 5366 269 70 SST-02-06-CPL-04 5518 5366 267 130 SST-02-04-CPL-05 5626 5366 267 125 SST-02-03-CPL-06 5139 5366 270 132 SST-02-03-CPL-07 5483 5366 271 71 SST-02-05-CPL-08 5340 5366 266 125 SST-02-05-CPL-09 5399 5366 265 70 SST-07-05-CPL-10 5643 5366 263 99 SST-07-05-CPL-11 5381 5366 266 106 SST-05-02-CPL-12 5439 5366 274 104 SST-05-02-CPL-13 5491 5366 271 104 SST-03-04-CPL-14 5430 5366 263 113 SST-03-04-CPL-15 5556 5366 263 106 SST-09-03-CPL-16 5491 5366 272 125 SST-09-03-CPL-17 5703 5366 271 125 SST-01-01-CPL-18 5705 5366 267 132 SST-02-07-CPL-19 5596 5366 269 111 SST-02-07-CPL-20 5527 5366 271 118
Average 108plusmn22
99
Table A-3 Results of conventional point load strength index test on tuffaceous sand
stone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
Point Load Strength Index Test Is (MPa)
TST-06-05-CPL-01 5657 5366 263 125 TST-06-05-CPL-02 5781 5366 264 109 TST-02-05-CPL-03 5686 5366 263 106 TST-02-05-CPL-04 5747 5366 264 80 TST-08-03-CPL-05 5606 5366 268 115 TST-08-03-CPL-06 5574 5366 266 118 TST-08-01-CPL-07 5491 5366 268 111 TST-08-01-CPL-08 5478 5366 268 115 TST-04-02-CPL-09 5422 5366 263 103 TST-04-02-CPL-10 5387 5366 264 111 TST-08-04-CPL-11 5371 5366 267 115 TST-08-04-CPL-12 5463 5366 267 113 TST-06-07-CPL-13 5545 5366 267 108 TST-04-01-CPL-14 5729 5366 261 59 TST-06-06-CPL-15 5457 5366 261 99 TST-06-06-CPL-16 5469 5366 263 109 TST-06-06-CPL-17 5497 5366 266 122 TST-04-03-CPL-18 5550 5366 261 87 TST-04-03-CPL-19 5521 5366 262 52 TST-04-05-CPL-20 5477 5366 264 87
Average 102plusmn20
100
Table A-4 Results of uniaxial compressive strength tests and elastic modulus
measurements on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-5 Results of uniaxial compressive strength tests and elastic modulus
measurements on silicified tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
Table A-6 Results of uniaxial compressive strength tests and elastic modulus
measurements on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σc (MPa)
E (GPa)
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
101
Table A-7 Results of Brazilian tensile strength tests on porphyritic andesite
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
And-04-03-BZ-01 2628 5366 281 395 178 And-04-03-BZ-02 2551 5366 279 350 163 And-04-03-BZ-03 2755 5366 285 380 164 And-04-03-BZ-04 2669 5366 279 415 184 And-04-06-BZ-05 2686 5366 280 320 141 And-04-06-BZ-06 2699 5366 286 415 182 And-04-06-BZ-07 2649 5366 282 395 177 And-04-06-BZ-08 2642 5366 286 340 153 And-06-01-BZ-09 2678 5366 286 435 193 And-06-01-BZ-10 2758 5366 285 385 166
Average 170plusmn16
Table A-8 Results of Brazilian tensile strength tests on silicified tuffaceous
sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
SST-02-02-BZ-01 2507 5366 265 450 213 SST-01-06-BZ-02 2664 5366 264 520 232 SST-01-02-BZ-03 2595 5366 262 400 183 SST-01-02-BZ-04 2593 5366 261 320 146 SST-01-02-BZ-05 2608 5366 266 500 228 SST-02-01-BZ-06 2710 5366 266 500 220 SST-02-01-BZ-07 2654 5366 262 450 201 SST-01-05-BZ-08 2778 5366 268 350 150 SST-01-05-BZ-09 2793 5366 266 400 170 SST-01-05-BZ-10 2795 5366 266 400 170
Average 191plusmn32
102
Table A-9 esults of Brazilian tensile strength tests on tuffaceous sandstone
Sample No Thickness (mm)
Diameter (mm)
Density (gcc)
Failure Load (kN)
σB (MPa)
TST-02-03-BZ-01 2811 5366 260 360 152 TST-02-03-BZ-02 2757 5366 260 255 110 TST-02-03-BZ-03 2739 5366 262 325 141 TST-02-03-BZ-04 2688 5366 263 175 77 TST-06-04-BZ-05 2765 5366 266 450 193 TST-06-04-BZ-06 2729 5366 264 280 122 TST-06-04-BZ-07 2730 5366 260 230 100 TST-06-02-BZ-08 2748 5366 264 285 123 TST-06-02-BZ-09 2743 5366 261 290 125 TST-06-02-BZ-10 2658 5366 265 370 165
Average 131plusmn33
Table A-10 esults of triaxial compressive strength tests on porphyritic andesite
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
And-02-02-UCS-01 13486 5366 282 1327 451 And -06-03-UCS-02 13494 5366 283 1106 397 And -02-01-UCS-03 13485 5366 280 1061 470 And -08-03-UCS-04 13417 5366 284 1282 392 And -04-04-UCS-05 13464 5366 285 973 438
Average 115plusmn150 430plusmn34
Table A-11 Results of triaxial compressive strength tests on silicified tuffaceous
sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
SST-02-01-UCS-01 13309 5366 271 1194 6569 SST-07-01-UCS-02 13547 5366 267 930 632 SST-07-03-UCS-03 13095 5366 268 1194 503 SST-02-06-UCS-04 13475 5366 269 1614 661 SST-06-02-UCS-05 13577 5366 270 1106 713
Average 1207plusmn252 633plusmn80
103
Table A-12 Results of triaxial compressive strength tests on tuffaceous sandstone
Sample No Length (mm)
Diameter (mm)
Density (gcc)
σ3 (MPa)
σ1 (MPa
TST-08-02-UCS-01 13810 5366 266 1017 538 TST-01-02-UCS-02 13236 5366 268 1238 545 TST-02-04-UCS-03 13558 5366 264 973 441 TST-06-09-UCS-04 13515 5366 267 1459 475 TST-02-02-UCS-05 13745 5366 263 884 566
Average 1114plusmn233 513plusmn53
APPENDIX B
MODIFIED POINT LOAD TEST RESULTS FOR ELASTIC
MODULUS PREDICTION
116
AND-MPL-01
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 125 GPamm
Figure B1 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-01
And-MPL-02
00500
100015002000250030003500400045005000
0 005 01 015 02 025 03 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 180 GPamm
Figure B2 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-02
117
And-MPL-03
00200400600800
100012001400160018002000
000 002 004 006 008 010 012 014
Diplacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B3 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-03
And-MPL-04
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B4 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-04
118
And-MPL-05
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 369 GPamm
Figure B5 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-05
And-MPL-06
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B6 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-06
119
And-MPL-07
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss (
MPa
)
ΔPΔδ = 234 GPamm
Figure B7 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-07
And-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 171 GPamm
Figure B8 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-08
120
And-MPL-09
00
500
1000
1500
2000
2500
3000
3500
000 020 040 060 080 100 120 140Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 056 GPamm
Figure B9 Applied stress (P) as a function of displacement (δ) for specimen no And-
MPL-09
And-MPL-10
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 124 GPamm
Figure B10 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-10
121
And-MPL-11
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030 035 040Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 138 GPamm
Figure B11 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-11
And-MPL-12
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 189 GPamm
Figure B12 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-12
122
And-MPL-13
00500
100015002000250030003500400045005000
000 010 020 030 040 050 060
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 151 GPamm
Figure B13 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-13
And-MPL-14
00
1000
2000
3000
4000
5000
6000
7000
000 010 020 030 040 050 060Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 165 GPamm
Figure B14 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-14
123
And-MPL-15
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120 140 160Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 011 GPamm
Figure B15 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-15
And-MPL-16
00
200
400
600
800
1000
1200
1400
1600
1800
000 050 100 150 200Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 012 GPamm
Figure B16 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-16
124
And-MPL-17
00
500
1000
1500
2000
2500
000 020 040 060 080 100 120
Displacement (mm)
Stre
ss P
(MPa
) ΔPΔδ = 021 GPamm
Figure B17 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-17
And-MPL-18
00
500
1000
1500
2000
2500
3000
000 050 100 150 200 250 300 350Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 008 GPamm
Figure B18 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-18
125
And-MPL-19
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B19 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-19
And-MPL-20
00
1000
2000
3000
4000
5000
6000
000 050 100 150 200 250 300
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 017 GPamm
Figure B20 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-20
126
And-MPL-21
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B21 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-21
And-MPL-22
00
500
1000
1500
2000
2500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 087 GPamm
Figure B22 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-22
127
And-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B23 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-23
And-MPL-24
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =112 GPamm
Figure B24 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-24
128
And-MPL-25
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 585 GPamm
Figure B25 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-25
And-MPL-26
00500
10001500200025003000350040004500
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 143 GPamm
Figure B26 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-26
129
And-MPL-27
00500
10001500200025003000350040004500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B27 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-27
And-MPL-28
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 200 GPamm
Figure B28 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-28
130
And-MPL-29
00500
1000150020002500300035004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B29 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-29
And-MPL-30
00
1000
2000
3000
4000
5000
6000
7000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B30 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-30
131
And-MPL-31
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B31 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-31
And-MPL-32
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B32 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-32
132
And-MPL-33
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 101 GPamm
Figure B33 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-33
And-MPL-34
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 135 GPamm
Figure B34 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-34
133
And-MPL-35
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 127 GPamm
Figure B35 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-35
And-MPL-36
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 292 GPamm
Figure B36 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-36
134
And-MPL-37
050
100150200250300350400450
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 156 GPamm
Figure B37 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-37
And-MPL-38
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B38 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-38
135
And-MPL-39
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 186 GPamm
Figure B39 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-39
And-MPL-40
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 20 GPamm
Figure B40 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-40
136
And-MPL-41
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B41 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-41
And-MPL-42
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ =231 GPamm
Figure B42 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-42
137
And-MPL-43
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 346 GPamm
Figure B43 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-43
And-MPL-44
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 234 GPamm
Figure B44 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-44
138
And-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 169 GPamm
Figure B45 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-45
And-MPL-46
00
200
400
600
800
1000
1200
1400
1600
1800
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 175 GPamm
Figure B46 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-46
139
And-MPL-47
00
200
400
600
800
1000
1200
1400
1600
1800
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B47 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-47
And-MPL-48
00
200
400
600
800
1000
1200
1400
1600
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 094 GPamm
Figure B48 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-48
140
And-MPL-49
00
100
200
300
400
500
600
700
800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 057 GPamm
Figure B49 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-49
And-MPL-50
00
200
400
600
800
1000
1200
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 078 GPamm
Figure B50 Applied stress (P) as a function of displacement (δ) for specimen no
And-MPL-50
141
SST-MPL-01
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 280 GPamm
Figure B51 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-01
SST-MPL-02
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 307 GPamm
Figure B52 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-02
142
SST-MPL-03
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 356 GPamm
Figure B53 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-03
SST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 450 GPamm
Figure B54 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-04
143
SST-MPL-05
00100020003000400050006000700080009000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 532 GPamm
Figure B55 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-05
SST-MPL-06
00500
100015002000250030003500400045005000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 273 GPamm
Figure B56 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-06
144
SST-MPL-07
0010002000300040005000600070008000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 418 GPamm
Figure B57 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-07
SST-MPL-08
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 414 GPamm
Figure B58 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-08
145
SST-MPL-09
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B59 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-09
SST-MPL-10
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 958 GPamm
Figure B60 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-10
146
SST-MPL-11
00
10002000
300040005000
60007000
8000
000 005 010 015 020 025 030Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 400 GPamm
Figure B61 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-11
SST-MPL-12
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 272 GPamm
Figure B62 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-12
147
SST-MPL-13
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 408 GPamm
Figure B63 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-13
SST-MPL-14
00
500
1000
1500
2000
2500
000 002 004 006 008 010Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 296 GPamm
Figure B64 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-14
148
SST-MPL-15
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 282 GPamm
Figure B65 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-15
SST-MPL-16
00500
1000150020002500300035004000
000 005 010 015 020
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 26 GPamm
Figure B66 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-16
149
SST-MPL-17
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 416 GPamm
Figure B67 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-17
SST-MPL-18
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 473 GPamm
Figure B68 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-18
150
SST-MPL-19
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ngth
P (M
Pa)
ΔPΔδ = 330 GPamm
Figure B69 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-19
SST-MPL-20
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 278 GPamm
Figure B70 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-20
151
SST-MPL-21
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 185 GPamm
Figure B71 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-21
SST-MPL-22
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 182 GPamm
Figure B72 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-22
152
SST-MPL-23
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 15 GPamm
Figure B73 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-23
SST-MPL-24
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 295 GPamm
Figure B74 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-24
153
SST-MPL-25
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 259 GPamm
Figure B75 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-25
SST-MPL-26
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030 035 040
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 221 GPamm
Figure B76 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-26
154
SST-MPL-27
00500
10001500200025003000350040004500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 274 GPamm
Figure B77 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-27
SST-MPL-28
0010002000300040005000600070008000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 209 GPamm
Figure B78 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-28
155
SST-MPL-29
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 176 GPamm
Figure B79 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-29
SST-MPL-30
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B80 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-30
156
SST-MPL-31
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 464 GPamm
Figure B81 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-31
SST-MPL-32
00
500
1000
1500
2000
2500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 178 GPamm
Figure B82 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-32
157
SST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 131 GPamm
Figure B83 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-33
SST-MPL-34
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 215 GPamm
Figure B84 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-34
158
SST-MPL-35
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 190 GPamm
Figure B85 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-35
SST-MPL-36
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B86 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-36
159
SST-MPL-37
00500
1000150020002500300035004000
000 010 020 030 040 050
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 067 GPamm
Figure B87 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-37
AND-MPL-38
00
500
10001500
2000
2500
3000
35004000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ssP
(MPa
)
ΔPΔδ = 127 GPamm
Figure B88 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-38
160
SST-MPL-39
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 229 GPamm
Figure B89 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-39
SST-MPL-40
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 090 GPamm
Figure B90 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-40
161
SST-MPL-41
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 498 GPamm
Figure B91 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-41
SST-MPL-42
00
1000
2000
3000
4000
5000
6000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 392 GPamm
Figure B92 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-42
162
SST-MPL-43
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 244 GPamm
Figure B93 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-43
SST-MPL-44
00100020003000400050006000700080009000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 571 GPamm
Figure B94 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-44
163
SST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 001 002 003 004 005 006 007 008
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 780 GPamm
Figure B95 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-45
SST-MPL-46
0010002000300040005000600070008000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 411 GPamm
Figure B96 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-46
164
SST-MPL-47
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 309 GPamm
Figure B97 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-47
SST-MPL-48
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 338 GPamm
Figure B98 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-48
165
SST-MPL-49
00500
1000150020002500300035004000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 254 GPamm
Figure B99 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-49
SST-MPL-50
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 360 GPamm
Figure B100 Applied stress (P) as a function of displacement (δ) for specimen no
SST-MPL-50
166
TST-MPL -01
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 212GPamm
Figure B101 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-01
TST-MPL-02
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=326 GPamm
Figure B102 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-02
167
TST-MPL-03
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacememt (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B103 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-03
TST-MPL-04
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B104 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-04
168
TST-MPL-05
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 264 GPamm
Figure B105 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-05
TST-MPL-06
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025
Displacment (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 143 GPamm
Figure B106 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-06
169
TST-MPL-07
00
500
1000
1500
2000
2500
3000
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 162 GPamm
Figure B107 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-07
TST-MPL-08
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=319 GPamm
Figure B108 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-08
170
TST-MPL-09
00500
100015002000250030003500400045005000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =212 GPamm
Figure B109 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-09
TST-MPL-10
00200400600800
1000120014001600
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 132GPamm
Figure B110 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-10
171
TST-MPL-11
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =319 GPamm
Figure B111 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-11
TST-MPL-12
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 127 GPamm
Figure B112 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-12
172
TST-MPL-13
00500
1000150020002500300035004000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 159 GPamm
Figure B113 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-13
TST-MPL-14
00
500
1000
1500
2000
2500
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =170 GPamm
Figure B114 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-14
173
TST-MPL-15
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 260 GPamm
Figure B115 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-15
TST-MPL-16
00500
100015002000250030003500400045005000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 102 GPamm
Figure B116 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-16
174
TST-MPL-17
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 650 GPamm
Figure B117 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-17
TST-MPL-18
00
200
400
600
800
1000
1200
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=073 GPamm
Figure B118 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-18
175
TST-MPL-19
00
200
400
600
800
1000
1200
1400
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B119 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-19
TST-MPL-20
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=170 GPamm
Figure B120 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-20
176
TST-MPL-21
00200400600800
10001200140016001800
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=100 GPamm
Figure B121 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-21
TST-MPL-22
00200400600800
10001200140016001800
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 088 GPamm
Figure B122 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-22
177
TST-MPL-23
00
500
1000
1500
2000
2500
3000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 101 GPamm
Figure B123 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-23
TST-MPL-24
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 124 GPamm
Figure B124 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-24
178
TST-MPL-25
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 126 GPamm
Figure B125 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-25
TST-MPL-26
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 178 GPamm
Figure B126 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-26
179
TST-MPL-27
00
1000
2000
3000
4000
5000
6000
000 005 010 015 020 025 030 035
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B127 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-27
TST-MPL-28
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020 025 030
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 164 GPamm
Figure B128 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-28
180
TST-MPL-29
00
500
1000
1500
2000
2500
3000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 128 GPamm
Figure B129 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-29
TST-MPL-30
00500
100015002000250030003500400045005000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔP Δδ =280 GPamm
Figure B130 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-30
181
TST-MPL-31
00500
10001500200025003000350040004500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 158 GPamm
Figure B131 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-31
TST-MPL-32
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 170 GPamm
Figure B132 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-32
182
TST-MPL-33
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 130 GPa mm
Figure B133 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-33
TST-MPL-34
00
500
1000
1500
2000
2500
3000
3500
4000
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B134 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-34
183
TST-MPL-35
00
1000
2000
3000
4000
5000
6000
7000
000 005 010 015 020 025
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B135 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-35
TST-MPL-36
00500
100015002000250030003500400045005000
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 325 GPamm
Figure B136 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-36
184
TST-MPL-37
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014 016
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 217 GPamm
Figure B137 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-37
TST-MPL-38
00500
10001500200025003000350040004500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 52 GPamm
Figure B138 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-38
185
TST-MPL-39
00
500
1000
1500
2000
2500
3000
3500
000 005 010 015 020
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B139 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-39
TST-MPL-40
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 347 GPamm
Figure B140 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-40
186
TST-MPL-41
00
500
1000
1500
2000
2500
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B141 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-41
TST-MPL-42
00
500
1000
1500
2000
2500
3000
3500
4000
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 260 GPamm
Figure B142 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-42
187
TST-MPL -43
00
500
1000
1500
2000
2500
3000
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 435 GPamm
Figure B143 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-43
TST-MPL-44
00
200
400
600
800
1000
1200
1400
1600
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B144 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-44
188
TST-MPL-45
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 315 GPamm
Figure B145 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-45
TST-MPL-46
00
500
1000
1500
2000
2500
000 002 004 006 008 010 012 014Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 222 GPamm
Figure B146 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-46
189
TST-MPL-47
00
200
400
600
800
1000
1200
000 005 010 015 020Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ=128 GPamm
Figure B147 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-47
TST-MPL-48
00200400600800
10001200140016001800
000 002 004 006 008 010
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ= 237GPamm
Figure B148 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-48
190
TST-MPL-49
00
500
1000
1500
2000
2500
3000
3500
4000
4500
000 002 004 006 008 010 012 014 016Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 371 GPamm
Figure B149 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-49
TST-MPL-50
00
500
1000
1500
2000
2500
3000
3500
000 002 004 006 008 010 012 014
Displacement (mm)
Stre
ss P
(MPa
)
ΔPΔδ = 394 GPamm
Figure B150 Applied stress (P) as a function of displacement (δ) for specimen no
TST-MPL-50
BIOGRAPHY
Mr Chatchai Intaraprasit was born on July 30 1973 in Khon Kaen province
Thailand He received his Bachelorrsquos Degree in Science (Geotechnology) from Khon
Kaen University in 1996 He worked with the construction company for ten years
after graduated the Bachelorrsquos Degree For his post-graduate he continued to study
with a Masterrsquos Degree in the Geological Engineering Program Institute of
Engineering Suranaree University of Technology He has published a technical
papers related to rock mechanics as in 2009 ldquoModified point load testing of volcanic
rocks from Chatree gold minerdquo in the proceeding of the second Thailand symposium
on rock mechanics Chonburi Thailand For his work he is working as a
geotechnical engineer at Akara mining company limited Phichit province Thailand