SUMMARY REPORT ON FATIGUE RESPONSE OF ASPHALT MIXTURES TM-UCB-A-003A-89-3 Prepared for Strategic Highway Research Program Project A-003-A by S. C. S. Rao Tangella, Assistant Research Engineer J. Craus, Professor of Civil Engineering J. A. Deacon, Professor of Civil Engineering C. L. Monismith, Professor of Civil Engineering Institute of Transportation Studies University of California Berkeley, California February 1990
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SUMMARY REPORT ONFATIGUE RESPONSE OF ASPHALT MIXTURES
TM-UCB-A-003A-89-3
Prepared for Strategic Highway Research ProgramProject A-003-A
by
S. C. S. Rao Tangella, Assistant Research EngineerJ. Craus, Professor of Civil Engineering
J. A. Deacon, Professor of Civil EngineeringC. L. Monismith, Professor of Civil Engineering
Institute of Transportation StudiesUniversity of California
Berkeley, California
February 1990
ABSTRACT
The purpose of this summary report is to evaluate test procedures for measuring the
fatigue response of asphalt paving mixtures and to summarize what is known about the
factors that influence fatigue response.
Available test methods are conveniently classified into the following categories:
simple flexure, supported flexure, direct axial, diametral, triaxial, fracture mechanics, and
wheel-track testing. Criteria used to evaluate each method for its potential use as a
laboratory standard included: (1) ability to simulate field conditions, (2) applicability of test
results for use in modelling pavement performance, (3) simplicity, and (4) correlation of
results with performance of in-service pavements. The three most promising methods are
considered to be simple flexure, diametral fatigue, and tests based on fracture mechanics
principles. Although not a fatigue test in itself, direct tension testing offers considerable
potential as a simple surrogate for more complex fatigue tests: French researchers have
achieved quite good correlations between direct tension and fatigue test results.
Factors affecting fatigue response include specimen fabrication, mode of loading,
mixture variables, and loading and environmental variables. Among the various fabrication
or compaction methods, rolling-wheel, kneading, and gyratory methods seem to best
duplicate field compaction. Although fatigue response is not expected to differ among
specimens compacted by these three methods, an evaluation of the possible effects of
compaction method on fatigue response is in order since prior compaction research has
focused on other engineering properties.
Mode of loading, typically either controlled-stress or controlled-strain for laboratory
testing, is one of the primary factors affecting fatigue response. Controlled-stress tests
essentially measure the loading necessary for crack initiation: longer fatigue lives are
recorded in controlled-strain tests because crack propagation is included as well.
Air void content and temperature--both affecting mixture stiffness--may have more
significant influence on fatigue response than any other variable(s). However, many mixture,
load, and environmental factors also influence fatigue response and must be considered both
in the development of test protocols and in the determination of asphalt and mixture
properties that are essential for fatigue-resistant pavements.
Finally, in most prior work, the maximum principal tensile strain has been used as
the cause or determinant of fatigue damage, and the linear summation of cycle ratios
hypothesis has been used to accumulate this damage under mixed traffic loading. Other
damage determinants, such as work strain as well as cumulative failure laws, such as
constancy of dissipated energy, offer possible alternatives.
ii
ACKNOWLEDGEMENTS
The work reported herein has been conducted as a part of project A-003A of the
Strategic Highway Research Program (SHRP). SHRP is a unit of the National Research
Council that was authorized by section 128 of the Surface Transportation and Uniform
Relocation Assistance Act of 1987. This project is entitled, "Performance Related Testing
and Measuring of Asphalt-Aggregate Interactions and Mixtures," and is being conducted by
the Institute of Transportation Studies, University of California, Berkeley, with Carl L.
Monismsith as Principal Investigator. The support and encouragement of Dr. Ian Jamieson,
SHRP Contract Manager, is gratefully acknowledged.
The draft of this report was reviewed by an Expert Task Group (ETG) which
includes the following members:
Ernest Bastian Eric E. Harm
Federal Highway Administration Illinois Department of Transportation
Campbell Crawford Charles S. HughesNational Asphalt PavingAssocation Virginia Highway and Transportation
Research Council
William Dearasaugh Dallas N. LittleTransportation Research Board Texas A&M University
Francis Fee Kevin Stuart
ELF Asphalt Federal Highway Administration
Douglas I. Hanson Roger L. YarbroughNew Mexico State Highway Department University Asphalt Company
Other reviewers included: Dr. R.G. Hicks, Dr. S.F. Brown, and Dr. P.S. Pell. Ms.
Joanne Birdsall prepared the final manuscript.
oo.
111
DISCLAIMER
The contents of this report reflect the views of the authors, who are solely responsible
for the facts and accuracy of the data presented. The contents do not necessarily reflect the
official view or policies of the Strategic Highway Research Program (SHRP) or SHRP's
sponsors. The results reported here are not necessarily in agreement with the results of
other SHRP research activities. They are reported to stimulate review and discussion within
the research community. This report does not constitute a standard, specification, or
regulation.
iv
TABLE OF CONTENTS
ABSTRACT ....................................................... i
ACKNOWLEDGEMENTS ............................................ iii
DISCLAIMER ..................................................... iv
TABLE OF CONTENTS .............................................. v
LIST OF TABLES .................................................. vii
LIST OF FIGURES ................................................. viii
3.6 Bending Fatigue Test Machine (Bonnot, 1986) ........................ 46
3.7 Fatigue Test Apparatus (Barksdale, 1977) ............................ 50
3.8 Schematic Representation of Direct Axial Fatigue Test(Raithby and Sterling, 1972) ...................................... 53
3.9 Effect of Strain Reversal on Fatigue Life(Raithby arid Sterling, 1972) ...................................... 54
3.10 Loading Configuration and Failure in Diametral Test(Kennedy, 1977) ............................................... 58
oo°
VIII
3.11 Relative Stress Distributions and Element Showing Biaxial State of Stress for theDiametral Test (Kennedy, 1977) ................................... 59
3.21 Operational Layout of the ALF (Metcalf et al., 1985) ................... 78
3.22 Circular Track Facility for Fatigue Testing (LCPC) ..................... 79
4.1 Results of Fatigue Tests at Various Temperatures and Speeds(Saal and Pell, 1960) ........................................... 88
4.2 Strain-Life Fatigue Results for a Range of Mixes(Pell and Taylor, 1969) .......................................... 89
4.3 Typical Stress Difference-Fatigue Life Relationships for VariousTest Methods (Porter and Kennedy, 1975) ........................... 90
4.4 Relation of Energy Ratio and Mix Stiffness for an AsphalticConcrete (van Dijk, 1975) ....................................... 97
ix
4.5 Phase Angle, Energy Ratio, and Dissipated Energy Charts Showingthe Limits for the Base Course and Wearing Course and WearingCourse Mixes Tested (van Dijk et al., 1977) .......................... 98
4.6 Distortion Energy (Garretsen et al., 1987) .......................... 103
5.1 Direct Tension Testing Apparatus (Epps, 1969) ...................... 106
5.2 Typical Window Formed by Boundary Curves (Little and Richey, 1983) .... 111
6.1 Asphalt-Concrete Thickness vs. Tensile Stress for a TypicalFull-Depth Pavement .......................................... 120
6.2 Asphalt-Concrete Thickness vs. Tensile Stress for a TypicalPavement with Granular Base ................................... 121
6.3 Distortion Energy (Related to Work Strain) and Horizontal StrainDue to a Ve.rtical Load (Kunst, 1989) .............................. 127
A.1 Stress vs. Applications to Failure ................................. 142
A.2 Strain vs. Applications to Failure ................................. 142
X
1.0 INTRODUCTION
This summary report, focussing on the fatigue response of asphalt mixtures, is one
of a series prepared as a part of SHRP Project A-003A, "Performance Related Testing and
Measuring of Asphalt-Aggregate Interactions and Mixtures," to evaluate available
information on the fatigue, permanent deformation, thermal cracking, aging, and water
sensitivity characteristics of asphalt mixtures.
1.1 Problem Definition
Pavement distress resulting from repeated bending or fatigue of asphalt-concrete
pavements has been a well-recognized problem in the United States since 1948 (Hveem and
Carmany, 1948). In order to address fatigue distress in mixture and pavement design
procedures, it is necessary to describe the behavior of asphalt-concrete mixtures under
repeated stressing of the type encountered in situ. To this end, it is useful to evaluate
various laboratory fatigue tests with the objective of recommending a relatively simple test
(or tests) which can best simulate field conditions.
1.2 Purpose
The primary purpose of this research report is to review various fatigue test methods
and to recommend the most appropriate method for defining the fatigue response of
asphalt-concrete mixtures and for ultimate incorporation into an asphalt-aggregate mixture
analysis system.
1.3 Obiective_
This report includes an evaluation of factors affecting the fatigue characteristics of
dense-graded asphalt concrete together with an assessment of test methodologies used to
measure these characteristics.
Fatigue, as considered herein, is a form of cracking resulting from repeated traffic
loading. Cracking resulting from thermal stresses (non traffic associated) is described in
another summary report in this series.
From an evaluation of available information, it is evident that there are many
procedures, including both laboratory and field testing, to define the fatigue response of
asphalt-concrete mixtures. These procedures involve a variety of test techniques, equipment
types, specimen configurations, types and modes of loading, test conditions (for example,
frequency of loading, temperature, etc.), and analysis procedures.
Thus, the objectives of this study are to:
1. Review the factors affecting the fatigue performance of dense-graded
asphalt-concrete mixtures,
2. Summarize the steps necessary to measure fatigue lives and related
parameters which are useful in the structural analysis and design of
asphalt-concrete pavements,
3. Provide a listing of both the advantages and disadvantages of each test
method, and
4. Evaluate and list, in order of preference, the methods used to measure fatigue
response for mixture evaluation and design as well as for prediction of
pavement life in situ.
The methods which have been analyzed in this summary report include:
1. Simple flexure testing,
2
2. Supported flexure testing,
3. Direct axial testing,
4. Diametral testing,
5. Triaxial testing,
6. Fracture mechanics testing, and
7. Wheel-track testing.
Two additional considerations relative to fatigue are included. One is associated with
an indirect determination of an appropriate asphalt content for reasonable fatigue response
based on failure envelope defined for thermal cracking and permanent deformation. The
other is concerned with the phenomenon of load associated cracking which originates at or
near the surface of asphalt-concrete pavements.
This summary report is organized into seven sections. Section 1 contains the
introduction. Factors affecting the fatigue response of asphalt concrete, based on a review
of available information, are summarized in Section 2. Section 3 includes a summary of the
various methods to define fatigue, including a listing of their advantages and disadvantages.
It also provides the basis for evaluating alternate test methods in order to arrive at an initial
ranking for the laboratory studies to be conducted as a part of this project. Section 4
examines several fundamental concepts that may prove useful in developing a better
understanding of fatigue response of both laboratory specimens and in-situ materials.
Section 5 discusses alternate procedures having the potential for easing the burden of
laboratory fatigue testing and simplifying the analysis of pavement structures. Section 6
presents a discussion of the relationship(s) of test results to field performance. Finally,
3
Section 7 provides conclusions based on this detailed evaluation, a ranking of the existing
test methods, and an identification of some areas which may require additional investigation.
Appended to the report is the recommended laboratory study plan to evaluate the
various tests methodologies which have evolved as the candidate procedures.
4
2.0 BACKGROUND
The purpose of this section is to provide background information regarding the
fatigue response of asphalt mixtures. First, a summary is presented of the various factors
affecting fatigue response including the method of specimen fabrication (compaction), the
mode of loading, mixture variables, and, finally, traffic and environmental variables. Next,
the limitations of available information are briefly highlighted. The section concludes with
an overview of fatigue test methods and their development.
2.1 Factors Affecting Fatigue Response
Included herein is a brief summary of available information on factors affecting the
fatigue response of those types of asphalt paving mixtures that are comprised of asphalt
cements and of aggregates which produce dense mixtures when properly compacted.
Included are discussions of (1) methods of specimen fabrication, (2) mode of loading
considerations, (3) the influence of mixture variables on fatigue performance, and (4) the
influence of loading and environmental variables on fatigue response.
2.1.1 Specimen Fabrication
The primary objective of specimen fabrication or compaction is to produce "realistic"
test specimens, that is, specimens that reasonably duplicate the corresponding in-situ asphalt
paving in all major respects including composition, density, and engineering properties. The
effect of method of testing is examined more thoroughly in the following section.
Compaction methods presently being utilized to fabricate test specimens include the
Definition of failure; Well-defined since specimen fractures Arbitrary in the sense that the test isnumber of cycles discontinued when the load level has been
reduced to some proportion of its initial
value; for example, to 50 percent of theinitial level
Scatter in fatigue test data Less scatter More scatter
Required number of Smaller Largerspecimens
Simulation of long-term Long-term influences such as aging lead to Long-term influences leading to stiffness
influences increased stiffness and presumably increased increase will lead to reduced fatigue lifefatigue life
Magnitude of fatigue life, Generally shorter life Generally longer lifeN
Effect of mixture variables More sensitive Less sensitive
Rate of energy dissipation Faster Slower
Rate of crack propagation Faster than occurs in situ More representative of in-situ conditions
Beneficial effects of rest Greater beneficial effect Lesser beneficial effect
periods
17
Table 2.2 Factors Affecting the Stiffness and Fatigue Response
of Asphalt Paving Mixtures a
Effect of Change in Factor
Factor Change in Factor On Stiffness On Fatigue Life in On Fatigue Life inControlled-Stress Mode Controlled-Stress Mode
1983 Little. and Richey Diametral Controlled stress andfailure envelopeconcept
1982 Bonnaure, Gravois, and Center-point flexure Controlled strainUdron
1982 Mahoney and Terrel Suppported beam Intermediate mode of5th Intl (rectangular, rubber) with loadingConf on Str roiling-wheel loadingDes of AsphPavements
1981 Whitcomb, Hicks, and Diametral Controlled stressAAPT Boonders
1981 Monismith Third-point flexureAAPT
1980 Bonnaure, Gravois, and Statistical regression for 146 Controlled stress andUdron fatigue lines covering several controlled strain
major test methods andmixture variables of variousauthors
1977 Classen, Edwards, Sommer, Dissipated energy method Limiting tensile strain4th Intl and Uge which is independent of test criteriaConf on Str conditions
Des of AsphPavements
30
YEAR INVESTIGATOR(S) TEST METHODS EVALUATION
AND CONDITIONS METHOD
Same Shell method Dissipated energy method Limiting tensile strainwhich is independent of test criteriaconditions
Same Finn, Sara, Kulkarni, Nair, AASHO Road Test results Limiting tensile strainSmith, and Abduilah and computer programs criteria
1977 Van Dijk Cantilever (trapezoidal) and Controlled stress,AAPT centerpoint (rectangular) controlled strain, and
flexure dissipated energytheory
Same Ruth, Gary, and Oslan Flexure (77* F, 41" F, and Controlled stress and23* F) and diametral (41" F) controlled strain
Same Barksdale and Hicks Repeated load plate tests Numericalcharacterization
(layered theory andfinite elementapproaches)
Same Pell Rotating flexure Controlled stress withcomparison tocontrolled strain
Same Deacon State-of-the-art survey Suggested controlledstress, controlledstrain, and numericalmethods
Same Finn Serviceability index Numerical correlationbetween degree ofcracking and presentserviceability index
Same Terrel Examples of work from Controlled stress andMonismith, King,ham, and controlled strainKallas
Same Witczak Analysis of AASHO Road Allowable strainTest data criteria for a given
number of load
repetitions
Same The Asphalt Institute Same Same
Same Majidzadeh and Ramsamooj Supported beams (elastic Intermediate mode offoundation) loading and fracture
mechanics
Same Freeme and Marais Cantilever (rectangular and Controlled straintrapezoidal) flexure, 5 Hz, halfsinewave pulses
32
YEAR INVESTIGATOR(S) TEST METHODS EVALUATION
AND CONDITIONS METHOD
1972 Moore and Kennedy Diametral Controlled stress3rd IntlConf on Str
Des of AsphPavements
Same Pell and Brown Uniaxial tension-compression Controlled strainfatigue
Same Bennot Cantilever flexure Controlled stress andcontrolled strain
Same Kirk Third-point flexure Controlled strain
1972 Witczak Kingham's results of strain vs Allowable tensile3rd Intl fatigue life relationships for strain criteriaConf on Str full-depth asphalt concreteDes of Asph pavements of the AASHOPavements Road Test
Same Kingham and Kallas Center-point flexure Controlled stress andcontrolled strain
Same Van Dijk and Moreaud, Cantilever and center-point Controlled stress andQuedeville and Uge flexure controlled strain
Same Verstraeten Cantilever (trapezoidal) Controlled stressflexure
1972 Raithby and Sterling Cyclic axial tensile tests Controlled stress
RRL LR496 (prismatic samples)
1972 Monismith and Salam Third-point flexure Controlled stressAAPT
33
YEAR INVESTIGATOR(S) TE_T METHODS EVALUATION
AND CONDITIONS METHOD
1971 Salana Third-point flexure Controlled stress and
Ph.D., UC fracture mechanicsBerkeley
1971 Majidzadeh, Kauffman, and Center-point flexure Fracture mechanicsAAPT Ramsamooj
1971 Freeme Cantilever (trapezoidal) Controlled stress and
Ph.D., Univ flexure controlled strainof Natal
1969 Pell and Taylor Rotating cantilever flexure Controlled stressAAPT
L- rernorque de / inlermediair_ principolmolorilollon e-.a nncau e.
b_lon
Figure 3.22 - Circular Track Facility for Fatigue Testing (LCPC)
79
4. The number of parameters to be measured for further application in mixture
and structural design.
5. If the needed parameters could be measured by the same equipment or by
different equipment.
Application of test results refers to the possibility of using the test results to design
a mixture or a pavement structure with fatigue as the major concern.
The summary table (Table 3.1) lists the advantages, disadvantages, and limitations
of each method considered in this report. These methods are evaluated based on simplicity,
ability to simulate the field conditions, and applicability of the test results to design the
pavement for fatigue adequacy. Necessary data on field correlations are not available;
hence, it was not possible to take this factor into consideration in the evaluation.
No attempt has been made to apply a weighting to the individual criteria listed
above. Rather, they were collectively considered and evaluated against the overall
objectives of the task to develop a test method to define fatigue response. Simply stated,
these objectives are to develop a test which properly reflects the influence on the asphalt
binder on the fatigue performance of in-service pavements and which can be used ih an
asphalt aggregate mixture analysis system (AAMAS). The final ratings shown in Table 3.1
represent the combined judgment of the authors of the report.
In arriving at the final rankings, it should be noted that some consideration was given
to the following as well. It is possible in the ranking process that a method which had not
been placed near the top of the ranking might utilize equipment and methodology
associated with a test method already highly ranked. For example, the dissipated energy
80
method includes similar methodology to that used to define fatigue response in flexural
fatigue which was considered to have good potential. Thus once the flexural fatigue test had
been ranked, it would seem reasonable to consider the dissipated energy as a candidate
procedure at a level near the flexural fatigue test methodology. Similarly, while the flexural
fatigue tests provide a better simulation of field conditions than the direct tension test, this
test is simpler, less costly, and requires less time than a flexure test. It is possible, as the
LCPC has demonstrated, to use the direct tension test results to predict fatigue response.
Hence, the two tests might be ranked together as shown in Table 3.1.
81
Table 3.1 - Comparison of Test Methods
Method Applicationo( Advanta_z Disadvantages ,_mulatioa ,_mplkiWTest Results and d lr_cld P.mfldng
I Jmltatiol_ ColldliilioQII
Repeated Yes 1.Well known, Costly, time 4 4 Iflexure test widespread, consuming,
ab or eb,Smix 2. Basic technique specializedcan be used for equipment needed.different concepts.3. Results can beused directly indesign.4. Options ofcontrolled stress orstrain.
Direct tension Yes (through 1. Need for In the LCPC 9 1 Itest correlation) conducting fatigue methodology:
e b or eb, Smix tests is eliminated, a. The correlations2. Correlations exist based on one million
with fatigue test repetitionsresults, b. Temperature only
at 10*C.c. Use of EQI(thickness ofbituminous layer) forone millionrepetitions only.
Diametral Yes 1.Simple in nature. 1. Biaxial stress state. 6 2 IIrepeated load 4ab and Smix 2. Same equipment 2. Underestimatestest can be used for other fatigue life.
tests.
3. Tool to predictcracking.
Dissipated O, *, Sraixand 1. Based on a 1.Accurate 5 5 IIIenergy method ob or _t, physical prediction requires
phenomenon, extensive fatigue test2. Unique relation data.between dissipated 2. Simplifiedenergy and N. procedures provides
only a generalindication of the
magnitude of thefatigue life.
82
Method Applicationof Advantages Disadvantages S_ation S_p_ty Ovc_Test _lt_ and o_ Field lhnlrin .u
llmilaliOIS Conditions
Fracture Yes 1. Strong theory for 1. At high temp., Kt 7 8 IVmechanics tests Kn, Sm_ curve low temperature, is not a material
(a/h - N); 2. In principle the constant.calibration need for conducting 2. Large amount of
function (also fatigue tests experimental dataKn) eliminated, needed.
3. Ku (shear mode)data needed. Link
between K! and KIt
to predict fatigue lifeto be established.
4. Only stable crack
propagation state isaccounted for.
Repeated Yes 1. Need for flexural 1. Comparedto 8 3tension or ob or e b, Smix fatigue tests direct tension test,tension and eliminated, this is time
compression consuming, costly,
test and specialequipment required.
Triaxial Yes 1. Relatively better 1. Costly, time 2 6
repeated O'd,a c, Smix simulation of field consuming, andtension and conditions, special equipmentcompression needed.
test 2. Imposition ofshear strains
required.
Repeated Yes 1. Relatively better 1. Costly, time 3 7
flexure test on ob or e b, Smix simulation of field consuming, and
elastic conditions, special equipmentfoundation 2. Tests can be required.
conducted at higher
temperatures sincespecimens are fullysupported.
Wheel track Yes 1. Good simulation 1. For low Smix 1 9
test o b or Eb of field conditions, fatigue is affected by(laboratory) rutting due to lack of
lateral wanderingeffects.
2. Special equipmentrequired.
Wheel track Yes 1. Direct 1. Expensive, time 1 10
test (field) a b or _b determination of consuming.fatigue response 2. Relatively fewunder actual wheel materials can be
loads, evaluated at onetime.
3. Special equipmentrequired.
83
NOTES:
ob = breaking stress (in fatigue or direct tension)
oa = deviator st:tess
Triaxial testsoc = confining stress
eb = breaking strain (in fatigue or direct tension)
S,._,= mix stiffness
= phase angle
= energy factor
84
4.0 FAILURE CONCEPTS
Fatigue cracking is considered to be a tensile phenomenon. It is the repetitive
application of tensile forces, at levels considerably below that required to induce immediate
fracture, that is responsible for the initiation and propagation of fatigue cracks. Early
fatigue research found that fatigue life was often better correlated with tensile strains than
with tensile stresses, and that the basic failure relationship could be characterized as follows:
N! = a(1) b (4.1)e t
where Nf is the fatigue life, et is the applied tensile strain, and a and b are constants,
determined from laboratory testing.
So that Equation 4.1 might be used in the analysis and design of pavement structures,
Et, the damage determinant, was assumed to be the maximum principal tensile strain, a
quantity identical to the maximum applied strain in uniaxial laboratory tests and determined
from the complex, multidimensional stress state imposed by traffic on pavements in service.
In an attempt to account for differences sometimes observed in the fatigue life-strain
relationship as loading frequency and temperature vary, a mixture stiffness term can be
added to Equation 4.1 as follows:
Nf = a(l) b (Smt_)c (4.2)e t
where Smix is the stiffness modulus of the asphalt mixture and c is a third calibration
constant.
85
Equation 4.2 is applicable for a specific value of the repetitively applied strain level,
Et. For pavements in service, strains induced in the structure vary widely as a result of
variations in the types of axles, their loaded weights, tire pressures, lateral placement, etc.
Accordingly, some means for accumulating the damaging effects of mixed loading is
required. The most common means is the linear summation of cycle ratios, described as
follows:
n 1 II2 nit n m+ + ... + + ... + (4.3)
82:
where i is the ith level of applied strain at a critical point within the pavement structure, ni
is the actual number of applications of strain i that is anticipated, and Nif is the number of
applications of strain i expected to cause fatigue failure if applied in a non-mixed loading
environment. Failure in the pavement under mixed loading is expected when the linear
summation of cycle ratios reaches one.
The primary purpose of this section is to review research developments directed
toward better understanding the cause or determinant of fatigue distress and the
accumulation of damage under mixed loading.
4.1 Unique Strain
Based on results of controlled-stress testing, Saal and Pell (1960) postulated a single,
unique relationship between strain and fatigue life independent of test temperature and
loading frequency (Figure 4.1). Tests to establish this relationship were conducted at low
temperatures within a relatively small range, that is, from -13.5 °C to 7 °C. Pell later showed
86
that unique strain relationships applied for different mixes over a temperature range 0*C
to + 20" C. There was some evidence that longer lives were obtained at higher temperatures
of + 30°C where some crack propagation occurred and non-linear stiffness behavior became
apparent (Figure 4.2).
According to Witczak (1976), all researchers reporting the existence of a unique
strain criterion applied continuous, sinusoidal loading. On the other hand, those who used
pulse loading with rest periods obtained a different fatigue life-strain relationship for each
combination of temperature and loading frequency. When loading conditions were such that
mixture response in the fatigue test was nonlinear, the fatigue relationships were not parallel
if the strains had been either measured directly with gauges or calculated using a stiffness
from deflection measurements. On the other hand, parallel curves were observed if strains
had been calculated using stiffnesses which ignored the actual nonlinearity, such as those
determined from the Shell nomographs or those measured under low stress levels typical of
dynamic-modulus testing.
4.2 Deviator Stress
Fatigue lives measured by diametral tests are smaller than those obtained by other
methods. Porter and Kennedy (1975) have suggested that these differences can be
attributed in part to the fact that specimens in the diametral test are subjected to a biaxial
stress state. Fatigue curves obtained by the diametral test more closely approximate those
obtained by other tests if the applied tensile stress, at, is replaced by a stress difference, a t -
crc (Figure 4.3). Accordingly, a combined stress theory should be used for a better
prediction of fatigue response. Kennedy et al. used a combined stress theory based on
87
/lO• lO_ lOe iOr lOa
CyclestoFailure(n)
Figure 4.1 - Results of Fatigue Tests at Various Temperatures
and Speeds (Saal and Pell, 1960)
88
Cyctcs to failure -Ns
TI_ Series G I Test 5,ri_s
T¢_. ="_" _ .... /rain
[Symbot [Symbot
Figure 4.2 - Strain-Life Fatigue Results for
a Range of Mixes (Pell and Taylor, 1969)
89
IO S1rels 011feren¢/o_N/cm2
ioe ,,I i I i , i , , i I i , 1 .L_..J__L LJ }
_'2 | I_ I_11_ _ N/_ z ) ' (14_*"I _
,o,. ,,. o)OMe,,,s,'-,_h et o0'_ \O _.....--- P_ e_ ae
Figure 6.3 - Distortion Energy (Related to Work Strain)
and Horizontal Strain Due to a Vertical Load (Kunst, 1989)
127
7.0 CONCLUSIONS AND RECOMMENDATIONS
Conclusions obtained from this evaluation are presented in three parts: (1) specimen
fabrication; (2) factors which influence the fatigue response of asphalt paving mixtures; and
(3) evaluation of test methods.
7.1 Specimen Fabrication
For the SHRP program, it is considered important to examine the influence of
method of compaction on the response characteristics of laboratory prepared specimens.
Accordingly, a fatigue testing program will be conducted on specimens prepared by the three
most promising compaction techniques; kneading, gyratory, and rolling wheel.
7.2 Factors Affecting Fatigue Response
1. The controlled-stress mode of loading appears to represent the response of
thick asphalt pavements to repetitive loading while the controlled-strain
approach is suitable for thin pavements. The controlled-strain mode of testing
results in a greater fatigue life for the same mixture than controlled-stress
testing.
2. Air void content is an important factor which affects fatigue life of an asphalt
mixture and which should be as small as possible (but not less than the
minimum limit of 3.0 percent) to obtain the greatest fatigue life.
3. Another variable that can be controlled by the engineer and which has a
significant effect on the fatigue life is asphalt content. The optimum asphalt
content to obtain a maximum fatigue life is generally higher than the design
required for rutting considerations. Therefore, the asphalt content should be
128
as high as possible with due consideration to stability.
4. Asphalts should be quite stiff for thick asphalt pavements but relatively more
flexible for thin ones. For asphalt pavements of intermediate thickness,
asphalts of about 100 penetration (25 °C, 100 gr, 5 sec) are recommended.
5. Mixes containing dense-graded aggregates are recommended for use in
pavements containing thick asphalt layers while a more-open graded aggregate
(less fines) is recommended for pavements containing thin asphalt layers.
6. Higher temperature lowers fatigue life in the case of thick asphalt pavements
but increases fatigue life for thin pavements.
7.3 Test Methods
The various methods considered herein have been evaluated using the criteria
described earlier. This evaluation is summarized in Table 3.1. It will be noted that the
repeated flexure test received the highest ranking. The direct tension test was also included
in this category because of the possibility of using it to define fatigue response, following the
LCPC approach. The diametral test received a relatively high ranking, in part because of
its simplicity and in spite of the complex stress state which may exist, particularly at higher
temperatures. Also included in the first four categories are considerations of dissipated
energy and fracture mechanics.
7.4 Recommendations
This evaluation of existing information on the fatigue response of asphalt concrete
has suggested a set of competing alternatives which must be developed to establish a
suitable methodology for defining the fatigue response of asphalt-aggregate mixtures. This
129
program will involve the use of the tests and methodologies evaluated in Table 3.1 and rated
I to IV. In addition, as noted earlier, a study will be undertaken to assess the influence of
compaction method on fatigue response. The hypotheses to be tested and the associated
program are included as Appendix A.
This evaluation of existing information has also suggested other areas which require
additional investigation, some of which are beyond the scope of the SHRP research
endeavor. However, it is important to at least briefly describe them herein.
1. It is extremely important that the results of fatigue tests performed on
laboratory specimens be related to the fatigue performance of the same
materials in pavements in service. One approach to this problem is the use of
correlation (shift) factors.
2. The phenomenon of surface cracking should be investigated. This form of
distress may be related to high shear stresses developed near the pavement
surface. Accordingly, it is desirable to investigate the response of asphalt
concrete subjected to repeated shear stresses. While such an investigation will
not be conducted as a part of this program, there are sufficient examples of
pavements in which this distress has manifested itself to warrant further
investigation. Repeated shear tests can also take more effective account of the
types of load to which thin surface courses and interlayers are subjected.
3. According to van Dijk, loading mode, temperature, loading frequency, and
occurrence of rest periods do not have a significant influence on the cumulative
amount of energy dissipated before fatigue failure. As of this date, energy
130
considerations have been applied only to flexural fatigue tests. Further study
is needed (1) to apply energy considerations to other types of fatigue tests, like
diametral, direct axial, and supported flexure; (2) to determine the exact effects
of temperature and rest periods on the relationship between dissipated energy
and fatigue load, and (3) to apply energy considerations to the structural design
of asphalt pavements.
131
8.0 REFERENCES
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4. Anagnos, J. N. and Kennedy, T. W. (1972). Practical Methods of Conducting theIndirect Tensile Test, Research Report 98-10, Center for Highway Research, TheUniversity of Texas at Austin.
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10. Bazin, P., and Saunier, J. (1967). "Deformability, Fatigue and Healing Propertiesof Asphalt Mixes." Proceedings, Second International Conference on the StructuralDesign of Asphalt Pavements, University of Michigan.
11. Bonnaure, F., Huibbers, A.H.J.J., and Booders, A. (1982) "A Laboratory Investigationof the Influence of Rest Periods on Fatigue Characteristics of Bituminous Mixes."Proceedings, The Association of Asphalt Paving Technologists, Vol. 51, 104.
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132
13. Bonnot, J. (1972). "Assessing the Properties of Materials for the Structural Designof Pavements." Proceedings, Third International Conference on the Structural Design ofAsphalt Pavements, London, 200-213.
14. Brown, S.F., Bell, C.A., and Brodrick, V.B. (1977). Permanent deformations offlexible pavements. Final Technical Report, University of Nottingham, U.K.
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20. de Boissoudy, A., le Bechec, J., Lucas, J., and Rouques, G. (1973). Etudes deFaisabilite d'un Manege de Fatigue des Structures Routieres. Laboratoire Central desPonts et Chausees (in French).
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23. Epps, J.A., and Monismith, C.L. (1972). Fatigue of Asphalt Concrete Mixtures -Summary of Existing Information, in STP 508, ASTM, 19-45.
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133
25. Gerritsen, A. H., van Gurp, C.A.P.M., van der Heide, J.P.J., Molenaar, A.A.A., andPronk, A. C. (1987). "Prediction and Prevention of Surface Cracking in AsphaltPavements," Proceedings, 6th International Conference on the Structural Design ofAsphalt Pavements, University of Michigan, Ann Arbor, 378-391.
26. Gonzales, G., Kennedy, T. W., and Anagnos, J. N. (1975). Evaluation of the ResilientElastic Characteristics of Asphalt Mixtures Using the Indirect Tensile Test. ResearchReport 183-6, Center for Highway Research, The University of Texas at Austin.
27. Grainger, G.D. (1964). The Reconstruction of No. 3 Road Machine for PavementDesign Studies. Transport and Road Research Laboratory, Lab Note LN/506/GDG.
28. Hadley, W. O. and Vahida, H. (1983). "Fundamental Comparison of the Flexural andIndirect Tensile Tests," Transportation Research Record 911, Transportation ResearchBoard, Waslhington, D. C., 42.
29. Hicks, R. G. (1970). Factors Influencing the Resilient Properties of Granular Materials.Ph.D. Thesis, University of California, Berkeley.
30. Hicks, R.G. and Monismith, C.L. (1971). "Factors Influencing the ResilientResponse of Granular Materials," Highway Research Record 345, Highway ResearchBoard, Washington, D. C.
31. International Conference on the Structural Design of Pavements, Fourth, Universityof Michigan, Ann Arbor. (1977). Proceedings, Vol. I.
32. Jimenez, R..A., and Gallaway, B.M. (1962). "Behavior of Asphaltic ConcreteDiaphragms to Repetitive Loadings." International Conference on the StructuralDesign of Asphalt Pavements. 339.
33. Kennedy, T. W. (1977). "Characterization of Asphalt Pavement Materials Using theIndirect Tensile Test," Proceedings, The Association of Asphalt Paving Technologists,Vol. 56.
34. Kennedy, T. W. and Anagnos, J. N. (1983). Procedures for the Static and Repeated-Load Indirect Tensile Tests. Research Record 183-14, Center for TransportationResearch, University of Texas at Austin.
35. Kennedy, T. W. and Hudson, W. R. (1968). "Application of the Indirect Tensile Testto Stabilized Materials," Highway Research Record 235, Highway Research Board,Washington, D. C.
134
36. Khosla, N. P. and Omer, M. S. (1985). "Characterization of Asphaltic Mixtures forPrediction of Pavement Performance," Transportation Research Record 1034,Transportation Research Board, Washington, D. C., 47-55.
37. Kim, Y.R., Little, D.N., and Benson, F.C. (1990). "Chemical and MechanicalEvaluation on Healing of Asphalt Concrete." Proceedings, Association of AsphaltPaving Technologists, Vol. 59.
38. Kirk, J.M. (1967). "Results of Fatigue Tests on Different Types of BituminousMixtures." Proceedings, Second International Conference on the Structural Design ofAsphalt Pavements, University of Michigan.
39. Kunst, P.A.J.C. (1989). Surface Cracking on Asphalt Layers, Working Committee B12,Hoevelaken, Holland.
40. Little, N. Dallas and Richey, B. L. (1983). "A Mixture Design Procedures Based onthe Failure Envelope Concept," Proceedings, Association of Asphalt PavingTechnologists, 379-415.
41. Majidzadeh, K., Kauffmann, E. M., and Ramsamooj, D. V. (1971). "Application ofFracture Mechanics in the Analysis of Pavement Fatigue," Proceedings, Associationof Asphalt Paving Technologists, 227-246.
42. Majidzadeh, K., Kauffmann, E. M., and Saraf, C. L. (1972). "Analysis of Fatigue ofPaving Mixtures from Fracture Mechanics View Point," ASTM STP 508, 67-83.
43. Maupin, G. W. (1980). Investigation of Fatigue Failure in Bituminous Base Mixes,Virginia Highway and Transportation Research Council, Charlottesville.
44. McLean, D. B. (1974). Permanent Deformation Characteristics of Asphalt Concrete.Ph.D. Thesis, University of California, Berkeley.
45. Metcalf, J.B., McLean, J.R., and Kadar, P. (1985). "The Development andImplementation of the Australian Accelerated Loading Facility (ALF) Program," inAccelerated Testing of Pavements, Annual Transportation Convention, Pretoria, SouthAfrica, 27 pp.
46. Monismith, C. L. (1981). "Fatigue Characteristics of Asphalt Paving Mixtures andTheir Use in Pavement Design," Proceedings, 18th Paving Conference, University ofNew Mexico, Albuquerque.
47. Monismith, C. L. (1966). Asphalt Mixture Behavior in Repeated Flexure, Report No.TE 66-66, ITIE, to California Division of Highways, University of California.
135
48. Monismith, C. L. and Deacon, J. A., (1969). "Fatigue of Asphalt Paving Mixtures,"ASCE Tramportation Engineering Journal, Vol. 95:2, 317-346.
49. Monismith, C.L., Epps, J. A., and Finn, F.N. (1985). "Improved Asphalt MixDesign," Proceedings, Association of Asphalt Paving Technologists.
50. Monismith, C.L., Epps, J.A., Kasianchuk, and McLean, D.B. (1971). AsphaltMixture Behavior on Repeated Flexure. Report No. TE 70-5, University of California,Berkeley, 303.
51. Monismith, C. L., Finn, F. N., and Vallerga, B. A. (1987). A Comprehens&eAsphaltConcrete Mixture Design System. Paper prepared for presentation at ASTMSymposium on "Development of More Rational Approaches to Asphalt Concrete MixDesign Procedures," Bal Harbor, Florida.
52. Monismith, C. L., Inkabi, K., McLean, D. B., and Freeme, C. R. (1977). DesignConsiderations forAsphalt Pavements, Report No. TE 77-1, University of California,Berkeley, March, 131.
53. Monismith, C. L. and Salam, Y. M. (1973). "Distress Characteristics of AsphaltConcrete Mixes," Proceedings, Association of Asphalt Paving Technologists. 320-350.
54. Monismith, C. L., Seed, H. B., Mitry, F. G., and Chan, C. K. (1967). "Predictions ofPavement Deflections for Laboratory Tests," Proceedings, Second InternationalConference on the Structural Design of Asphalt Pavements, University of Michigan,Ann Arbor.
55. Owen, D. B. (as corrected by Painter, L. J. of Statistics PLUS, San Rafael, CA)(1962). Handbook of Statistical Tables. Addison-Wesley.
56. Paris, P. C. and Erdogan, F. A. (1963). "Critical Analysis of Crack PropagationLaws," Transactions of ASME, Journal of Basic Engineering, Series, D, Vol. 85, No.3.
57. Paterson, W.D.O. (1972). "Deformations in Asphalt Concrete Wearing CoursesCaused by Traffic." Proceedings, Third International Conference on Structural Designof Asphalt Pavements, VoL 1, 317-325.
58. Pell, P.S. (1967). "Fatigue Characteristics of Bitumen and Bituminous Mixes,"Proceedings, International Conference on the Structural Design of Asphalt Pavements,Ann Arbor, University of Michigan, 310.
59. Pell, P.S. (1965). "Fatigue of Bituminous Materials in Flexible Pavements,"Proceedings, Institution of Civil Engineers, Vol. 31.
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60. Pell, P. S. and Brown, S. F. (1972), "The Characteristics of Materials for the Designof Flexible Pavement Structures," Proceedings, Third International Conference on theStructural Design of Asphalt Pavements, London, 326.
61. Pell, P. S. (1973). "Characterization of Fatigue Behavior," in Structural Design ofAsphalt Concrete Pavements to Prevent Fatigue Cracking. Special Report 140,Highway Research Board, 49-64.
62. Pell, P. S. and Cooper, K. E. (1975). 'q'he Effect of Testing and Mix Variables on theFatigue Performance of Bituminous Materials," Proceedings, The Association ofAsphalt Paving Technologists, Vol. 44.
63. Pell, P. S. and Hanson, J. M. (1973). "Behavior of Bituminous Road Base Materialsunder Repeated Loading," Proceedings, Association of Asphalt Paving Technologists,201, 229.
64. Pell, P. S. and Taylor, I. F. (1969) "Asphaltic Road Materials in Fatigue," Proceedings,The Association of Asphalt Paving Technologists, Vol. 38.
65. Porter, B. P. and Kennedy, T. W. (1975). Comparison of Fatigue Test Methods forAsphaltic Materials. Research Report 183-4, Center for Highway Research, TheUniversity of Texas at Austin.
66. Raithby, K. D. and Ramshaw, J. T. (1972). Effect of Secondary Compaction on theFatigue Performance of a Hot-Rolled Asphalt, TRRL-LR 471, Crowthorne, England.
67. Raithby, K. D. and Sterling, A. B. (1972). Some Effects of Loading History on thePerformance of Rolled Asphalt, TRRL-LR 496, Crowthorne, England.
68. Rao Tangella, S.C.S. (1989). Development of an Asphalt-Aggregate Mixture AnalysisSystem (AAMAS), Doctor of Engineering Dissertation, Department of CivilEngineering, University of California, Berkeley.
69. Ruth, B. E. and Schaub, J. H. (1966). "Gyratory Testing Machine Simulation of FieldCompaction of Asphaltic Concrete," Proceedings, Association of Asphalt PavingTechnologists, 451-484.
70. Saal, R.N.J. and Pell, P. S. (1960). "Fatigue of Bituminous Road Mixes," KolloidZeitschrift (Darmstadt), Vol. 171.
71. Said, S. F. (1988). "Fatigue Characteristics of Asphalt Concrete Mixtures," VT1meddelande 583A, Vag-6ch Trafic Institutet (Swedish).
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72. Salam, Y. lVI.(1971). Characteristicsof Deformation and Fracture of Asphalt Concrete,Ph.D. Dissertation, University of California, Berkeley.
73. Santucci, L. E. (1977). Thickness Design Procedure for Asphalt and EmulsifiedAsphalt Mixes. Vol. 1 Proceedings, Fourth International Conference on the StructuralDesign of A6phalt Pavements, University of Michigan, Ann Arbor, 424-456.
74. Schmidt, R. J. (1971) "A Practical Method for Measuring the Resilient Modulus ofAsphalt-Treated Mixes," Highway Research Record 404, Highway Research Board,Washington, D. C.
75. Scholz, T., Hicks, R. G., and Scholl, L. (1989). Repeatability of Testing Proceduresfor Resilient Modulus and Fatigue. Report to Materials and Research Section, OregonDOT, Oregon State University.
79. Terrel, R. L. and Krukar, M. (1970). "Evaluation of Test Tracking Pavements,"Proceedings, The Association of Asphalt Paving Technologists, 272.
80. Vallerga, B. A. (1951). "Recent Laboratory Compaction Studies of BituminousPaving Mixttlres." Proceedings, Association of Asphalt Paving Technologists, Vol. 20,117-153.
81. Van Dijk, W. (1975). "Practical Fatigue Characterization of Bituminous Mixes,"Proceedings, 'TheAssociation of Asphalt Paving Technologists, 38.
82. Van Dijk, W., Moreaud, H., Quedeville, A, and Uge, P. (1972). 'q"he Fatigue ofBitumen and Bituminous Mixes," Proceedings, The Association of Asphalt PavingTechnologists, 38.
83. Van Dijk, W. and Visser, W. (1977). "The Energy Approach to Fatigue for PavementDesign," Proceedings, The Association of Asphalt Paving Technologists, Vol. 46, 1.
84. Verstraeten, J. (1972). "Moduli and Critical Strains in Repeated Bending ofBituminous Mixes, Application to Pavement Design," Proceedings, Third InternationalConference on the Structural Design of Asphalt Pavements, l.xmdon, 729.
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85. Verstraeten, J., Veverka, V., and Franken, L. (1982). "Rational and Practical Designof Asphalt Pavements to Avoid Cracking and Rutting," Proceedings,Fifth InternationalConference on the Structural Design of Asphalt Pavements, 45.
86. Von Quintus, H. L., Scherocman, T. A., Hughes, C. S., and Kennedy, T. W. (1988).Development of Asphalt-Aggregate Mixture Analysis System: AAMAS. Brent RauhutEngineering, Inc., Austin.
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139
APPENDIX A
HYPOTHESES AND RECOMMENDED TEST PROGRAM
A.1 Hypotheses
Based on this evaluation of the fatigue response of asphalt-aggregate mixtures, the
following hypotheses have been postulated relative to their fatigue response characteristics:
1. Cracking results from a tensile stress or strain (less than the fracture stress or
strain-at-break under one load application) at a specific number of stress (or
strain) applications, the number of load applications being larger as the
magnitude of the stress or strain is smaller, i.e.:
N = A(1/_t) t_ or N = C(1/at) a
The relationships are dependent on the temperature and mode-of-loading
[coefficients (A and b) and (C and d)] and must be established by some form
of repetitive load testing; or
2. Cracking results from repetitive stress (strain) applications when either the total
ener_ or the strain energy, of di_t0rtion reaches some limiting value regardless
of the mode of loading to which the specimen is subjected; or
3. A direct correlation can be established between the stiffness and fracture
characteristics of a mix and its fatigue response (e.g., similar to that established
by the LCPC of France); or
4. Results of fracture tests on notched specimens can be used to predict the
fatigue: response of asphalt concrete mixtures over a range in temperatures.
140
From experimental evidence such as that illustrated in Figures A1 and A2, the
magnitude of tensile stress or strain repeatedly applied appears to be a reasonable
determinant of the cracking which occurs in asphalt-bound layers subjected to repetitive
trafficking. Since actual pavements are subjected to bending stresses, this model of loading
appears most reasonable to define fatigue response using laboratory test equipment.
While bending stresses are representative of in-situ conditions, other modes of
loading will also be utilized and include diametral and direct tension testing.
At the University of California at Berkeley, the bending fatigue tests will be
conducted at a rate of 100 repetitions per minute, a comparatively slow rate and one in
which the influence of rest periods has been shown to be negligible. Since it may be
desirable, should this method of testing be selected, to conduct a bending test at a faster
rate of loading, controlled-stress fatigue tests on pyramidal shaped specimens will be
conducted at SWK/Nottingham University at a rate approximately ten times as fast.
Since the bending mode of loading requires taht specimens be sawed to prismatic or
pyramid shapes, it was considered desirable to test specimens not requiring sawing; hence
the direct tension tests at SWK/Nottingham performed on cylindrical specimens.
When testing to define fatigue behavior, the mode of loading influences response
with specimens of comparatively low stiffness performing well in the controlled-strain mode
and specimens of high stiffness performing well in the controlled-stress mode. Since both
controlled-stress and controlled-strain tests will be performed at UCB, consideration will be
given to the determination of the total strain energy and the strain energy of distortion in
141
/0,000_ I I f t I i I I I I I i I i I I I i _ I I_
I/000
- l _Nf--/.55x/0_6(i/o_)_T _
- /-_ ___ -
IOC ._- _-_"_---- _ - ..... I_ _"-_ _
_ _-- Nf-3.97, I0,4 _-"'_-__(//__)5.36_ 7 68°F --
! I I I II0 I I I li I I r t i I I I I I I I
I02 i0_ 104 105 I06 I0z
Stress _ppl/cot/ons-Nf
Figure A1. Stress vs. Applications to Failure
#A.v'p,_ _ i i , ! [ i _ i I i I I i i i i
•_ --68"F
103 _ . ]i '"_, _ 4o2£ • I.-"-_,
_',_ - #:e35,,o_','d" "; _..o&_.
a,o, ..
_ _ _
/0 I I II I I I[ I I tl [ I II I I flI02 I03 I0 _ I0 5 I0 6 IC z
Stress ,_pplicotions- Nf
Figure A2. Strain vs. Applications to Failure
142
an attempt to eliminate the mode-of-loading variable. Such analyses will require a measure
of the complex modulus and phase angle for each mixture corresponding to the time of
loading and temperature of the fatigue test together with the stress/strain vs. number of
load applications to failure. While this approach still requires the conduct of fatigue tests,
it may have the potential to sort out mode-of-loading effects.
To reduce the amount of testing required to define fatigue response in the laboratory,
consideration will be given to the correlation developed by the LCPC between the fracture
characteristics of a mix in uniaxial loading and its fatigue response. In the LCPC
methodology, measurement of the stiffness characteristics of the specific mix at different
strain levels and temperatures are also required. An evaluation of the LCPC approach will
be made to determine its efficacy since the use of a direct tension test has the potential to
reduce considerably the time required to define fatigue response of asphalt-aggregate
mixtures as compared to repetitive load testing.
The use of fracture mechani¢_ principles has the potential to shorten the time
required in the laboratory to define fatigue response. Rather than conduct repetitive
loading fatigue tests, direct loading tests on notched specimens permit the determination of
specific material parameters from which the fatigue response can be estimated. Depending
on the size of the non-elastic zone at the crack tip, different interpretations are required.
If the majority of the material behaves elastically, the stress intensity factor, K, governs the
response. On the other hand, if the non-elastic zone is large, either the J-integral or the C'-
line integral may be required to define crack propagation. It is anticipated that the stress
intensity factor will be suitable to define fatigue response at low temperatures (i.e. 32"F).
143
At high temperatures, however, it may be necessary to consider either the J integral or the
C'-line integral; both will be evaluated.
By conducting the conventional fatigue tests together with the additional tests
described herein, sufficient data will have been obtained to permit the evaluation of all of
the above hypotheses permitting the selection of an appropriate methodology for further
development and evaluation.
A.2. Test Program
Tests. As outlined in the work plan (and modified based on the literature review),
the following tests will be evaluated:
AGENCY TEST
University of California Beams - controlled stress and controlledstrain
Direct tension - correlation with fatigue
University of Nottingham (SWK) Trapezoidal specimens - sinusoidalloading (controlled stress)Direct tension - sinusoidal loading(controlled stress)
North Carolina State University Diametral - pulsed loading (controlledstress and controlled strain)
It is now expected that each laboratory will prepare its own test specimens. In
addition, a limited test program will be conducted at Berkeley to evaluate the fracture
mechanics methodology. This program has not been defined at this time to the degree that
the repeated load test program has been and is described in the figllowing section.
144
Variables Considered. Table A-1 summarizes the significant variables for the fatigue
study. A total of ten variables were considered. Of these, four will be fixed (aggregate
gradation, grade of asphalt, aging, and moisture conditioning). Each of the others will be
evaluated at two levels. This results in a total number of combinations of 2 6 (or 64 cells)
for each test method.
Using principles of experimental design, it was determined that a 1/2
fraction of the complete factorial (i.e., 32 cells) would be necessary to estimate both main
effects and all two-factor interactions. To obtain estimates of purely experimental error,
these 32 factorial combinations will be replicated three times, for a total of 96 tests for the
beam testing, and twice (64 tests) for the other fatigue tests. The beam tests require greater
replication because of the larger variation expected as compared to the other tests.
The total number of samples contained in this testing program is 512. This testing
program is expected to be completed by June 1990. A summary of sample requirements is
shown in Table A.2.
Expected Results, The results of this study will provide insight as to which of the
fatigue test systems is most promising for implementation using the criteria stated at the
beginning of this chapter. The selected equipment will be used in the subsequent plans of
the project study.
145
Table A.1. Significant Mixture and Test Variables for Fatigue Study
Level of TreatmentVariable No of
Levels
1 2 3
Aggregate
Stripping potential Low High (2)
Gradation Medium (1)
Asphalt
Temperature susceptibility Low High (2)
Grade Medium (1)
Content Optimum High (2)
Compaction
Air voids 4 +_1/2% 8 + 1/2 % (2)
Test conditions
Temperature 32* F 68* F (2)
Stress Low ttigh (2)
Conditioning
Aging None (1)
Moisture None (1)
2_
146
Table A.2. Number of Samples for Fatigue Factorial Design
Number of SamplesTest Total
1/2 Fractional Repficates
University of California
• Flexural Beam, Controlled Stress 32 64 96
• Flexural Beam, Controlled Strain 32 64 96
• Direct Tension, Static 32 32 64
North Carolina State University
• Diametral, Controlled Stress 32 32 64
• Diametral, Controlled Strain 32 32 64
University of Nottingham (SWK)
• Direct Stress, Controlled Stress 32 32 64
• Trapezoidal Beam, Controlled Stress 32 32 64
Grand Total 512
Complete Factorial 26 = 641/2 Fractional = 32Total Number of Samples = 512Estimated Time for Testing = 6-9 months