Summary & Conclusion 6. SUMMARY AND CONCLUSION 6.1. Summary Although analysis of a pile is a three-dimensional case, the vertically loaded pile in horizontally bedded soil can be analyzed by simplifying as a problem of the axi- symmetry. The numerical results presented in this report were obtained by using axi- symmetric elements. The meshes were prepared such that in the regions of higher stress concentration the element sizes were smaller. It is known that when the element sizes become smaller (i.e. mesh becomes finer) the result obtained using-the finite element method approaches the analytical result (Zienkiewicz, 1977). The analytical solutions have been derived by considering the influence of the surface loads on a semi-infinite soil medium (i.e. boundaries of the influence region are at the infinity). But in the case of finite element analysis, boundary has to be fixed at a known distance away from the pile. Considering smaller elements and a lager influence region will minimize deviations in the numerical solution. As mentioned, in Chapter four, analysis here was limited to linear elastic materials, and effects of consolidation, secondary creep, etc are not included. However the results are a good indicator for the initial stress distribution and its consequences in the soil medium. As long as a good estimate of secant modules can be made for the pile materials and soils, the predicted results here could be used in a wider perspective. Only a limited parametric study was undertaken in this work, due to limitation of time and length of report, in order to demonstrate the trend of interface shear behavior of the specimen considered. Also, materials are considered as linear isotropic elastic. A more detailed investigation involving a wider range of material parameters is preferable as a further study of'the behavior of piles in layered media. In this aspect, comparison with some available test results is also preferable in order to predict a good representative value for the constitutive parameter used in the interface elements to represent the interface adhesion and friction. University of Moratuwa 6-1
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Summary & Conclusion
6 . S U M M A R Y A N D C O N C L U S I O N
6.1. Summary
Although analysis of a pile is a three-dimensional case, the vertically loaded pile in
horizontally bedded soil can be analyzed by simplifying as a problem of the axi-
symmetry. The numerical results presented in this report were obtained by using axi-
symmetric elements. The meshes were prepared such that in the regions of higher
stress concentration the element sizes were smaller.
It is known that when the element sizes become smaller (i.e. mesh becomes finer) the
result obtained using-the finite element method approaches the analytical result
(Zienkiewicz, 1977).
The analytical solutions have been derived by considering the influence of the surface
loads on a semi-infinite soil medium (i.e. boundaries of the influence region are at the
infinity). But in the case of finite element analysis, boundary has to be fixed at a
known distance away from the pile. Considering smaller elements and a lager
influence region will minimize deviations in the numerical solution.
As mentioned, in Chapter four, analysis here was limited to linear elastic materials,
and effects of consolidation, secondary creep, etc are not included. However the
results are a good indicator for the initial stress distribution and its consequences in
the soil medium. As long as a good estimate of secant modules can be made for the
pile materials and soils, the predicted results here could be used in a wider
perspective.
Only a limited parametric study was undertaken in this work, due to limitation of time
and length of report, in order to demonstrate the trend of interface shear behavior of
the specimen considered. Also, materials are considered as linear isotropic elastic. A
more detailed investigation involving a wider range of material parameters is
preferable as a further study of'the behavior of piles in layered media. In this aspect,
comparison with some available test results is also preferable in order to predict a
good representative value for the constitutive parameter used in the interface elements
to represent the interface adhesion and friction.
University of Moratuwa 6 - 1
Summary & Conclusion
The reduction of negative friction by applying coatings to the pile has been
investigated under several field conditions by Bjerrum et al. (1969). The coating can
be bitumen; bentonite slurry or bitumen covered with bentonite slurry can be applied
for driving piles with enlarged base. These coating techniques also can be modelled in
FEAP with interface element and good representative values of interface bond
strength can be found.
6.2. Implementation in Real Situations and Verification
For the implementation of this method in real situations, various relations are
available in the literature for the evaluation of Young's Modulus and Poisson's Ratio
(e.g. Selvadurai, 1979, Tomlinson, 1986). V^
The representative value for the constitutive parameter used in the interface elements
to model the interface adhesion 'arid friction (Cs) actually depends on the
constructional practices such as the method of installation and quality control at the
site. The interface behavior may be totally different than that assumed by the
designer. It can behave like soil, bentonite, concrete or combination of any of the
above and the behavior may differ according to site situations.
The present work focuses on a parametric study to cover the possible range of
behaviour in layered soil as compared to the often-difficult task of evaluating exact
parameters to simulate the real situations.
Tomlinson (1986) illustrated the behaviour of a single pile in a uniform soil when
subjected to vertical loading by Figures 6.1a and 6.1b. These figures show that the
end-bearing component as well as the skin friction component (load carried by the
shaft) increases as the load on the pile is increased. Figure 6.1b shows the expected
shapes of the curves of the axial load carried by the pile versus depth. The curves are
plotted based on readings taken from strain gauges embedded along the length of the
pile. The Figure 5.1b in Chapter 5 of this work shows the numerically predicted
behaviour of the axial load carried by the pile with depth in homogeneous media.
Curves of Figure 5.1b are in general agreement with the behaviour of those in Figure
University of Moratuwa 6 - 2
Summary & Conclusion
end-bearing Figure 6.1a Load-settlement curve for a pile Figure^, lb. Strain gauge readings on pile
Figure 6.1 Behaviour of a pile in a uniform soil under vertical load, after Tomlinson (1986)
Verification of the behaviour predicted numerically in this work can be performed by
embedding strain gauges along the pile length as indicated by Tomlinson (1986). In
real situations the parameter Cs will increase with settlement, as shown in Figure
6.1b. The present work provides a method to estimate the load transfer from pile to
soil at a given instant in the loading history.
6.3. CONCLUSION
Elastic finite element analysis of piles in layered soil media along with the
incorporation of elastic interface element enables the simulation of the stress-transfer
behaviour of such piles. This work concentrated mainly on the effect of layer
thickness and the properties of a weak layer sandwiched between two competent
layers at the top and bottom of the pile. The load transfer due to shear stress
developed at the interface was also studied by introducing theory - based estimates for
interface elements under drained and undrained conditions. The effect of angle of
friction and cohesion of the weak layer under drained condition for bored piles is
investigated with range of parameters.
Exact parameters applicable for a particular field condition would be difficult to
obtain, and finite element analysis such as presented here enables a parametric
analysis of the problem, by varying the interface roughness, geometry and material
University of Moratuwa 6 - 3
6.1b. This resemblance with Figure 6.1b can be observed even for curves predicted
for layered media, such as those in figures in section 5.3.
Summary! & Conclusion
properties. The possible ranges of constitutive parameters for the interface elements
were considered.
According to the numerical results for smooth wall conditions, the interface shear
stress increases linearly with depth and does not depend on the thickness of weak
layer. As the wall roughness increases the shear stress developed becomes non-linear
with depth and the properties and the thickness of the weak layer becomes significant.
When the Young's Modulus of weak layer is very low (one hundredth of the stronger
media) the shear stress developed on the pile-soil interface were observed as negative
at the outer most depth of the weak layer. This is the negative skin friction developed
on the pile-soil interface due to the relative settlement of the weaker soil. The sudden
change in modulus value at the boundaries of the weak layer causes the change in
direction of interface shear.
According to the numerical results, the drained capacity of the skin friction is
somewhat higher for driven piles and lower for bored piles when compared to the
undrained capacity. Percentage of applied load transferred by skin friction for driven
pile is approximately half than that for bored pile. Angle of friction of a weak layer
has only a small effect on the drained skin factional resistance for the range of
drained parameters whereas it shows a higher effect when cohesion introduced.
The numerically predicted results show some agreement with the test data reported by
Tomlinson (1986), and successfully confirm the generally expected trend of shear
stress distribution along the interface and axial load transmission through pile shaft.
6.4. RECOMMENDATIONS
The analysis is limited to horizontally oriented layered soil homogenous in nature and
of uniform diameter of pile. Further studies can be suggested for tapered pile analysis
and layered homogenous soils with inclined orientations.
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References
REFERENCES
1. Balaam N.P., Poulos H.G. and Booker J.R. (1975) "Finite Element Analysis of the effect of Installation on Piles Load-Settlement Behaviour" Geotechnical Engineering. 6(1), 33-48.
2. Balakirshnan E.G., Balasubramaniam A.S. and Noppadol Phein-wej (1999) "Load Deformation of Analysis of Bored Piles in Residual Weathered Formation" J. Geotech. Engng. ASCE, 125(2), 121-131.
3. Banerjee P.K. (1978); "Analysis of Axially and Laterally Loaded Pile Groups" In Development in Soil Mechanics. Ed. C. Scott, Ch 9, London. Applied Science Publishers.
4. Banerjee P.K. and Davis T.G. (1977); "The Behaviour of Axially and Laterally Loaded Single Pile Embedded in Non-homogeneous Soils", Geotechnigue, 28, No.3, 309-326.
5. Bowles J.E. (1997); "Foundation Analysis and Design", Mc-Graw Hill publications, Fifth Edition, 313-316.
6. Butterfield R. and Banarjee P.K. (1971); "The Elastic Analysis of Compressible Piles and Pile Groups" Geotechnigue, 21, No. l , 43-60.
7. Coyle H.M. and Reese L.C. (1966) "Load Transfer for Axially Loaded Piles in Clays" J. Soil Mechs Fdn Engng, ASCE, 92, No.SM2, 1-26.
8. Desai C S . (1974) "Numerical Design-Analysis for Piles in Sands" J. Geotech. Engng. ASCE, 100(6), 613-635.
9. Desai C S . and Chiristian J.T. (1977) "Numerical Methods in Geotechnical Engineering", Mc Grow-Hill.
10. Ellision R.D. et al. (1971) "Load-Deformation Mechanism of Bored Piles" J. Geotech. Engrg. ASCE, 97(4), 661-678.
11. Guo W.D. (2000) "Vertical Loaded Single Piles in Gibson Soil" J. Geotech. Engng. ASCE, 126(2), 189-193.
12. Guo W.D. and Randolph M.F. (1997) "Vertically Loaded Piles in homogeneous Media" J. Geotech. Engrg. ASCE, 21(8), 507-532.
13. Kodagoda S.S.I and Puswewala U.G.A.P (2001) "Numerical Modelling of Pile-Rock Interface In Rock Socketed Piles", Proc 7th Annual Symposium, ERU, University of Moratuwa.
14. Kraft L.M., Ray R.P. and Kagawa T. (1981) "Theoretical t-z Curves" J. Geotech. Engng. ASCE, 107(11), No. GT11, 1543-1561.
15. Lee C.Y. and Small J .C (1991) "Finite Layer Analysis of Axially Loaded Piles" J. Geotech. Engng. ASCE, 117(11), 1706-1722.
University of Moratuwa 1
References
16. Leland M. Kraft Jr. (1999) "Performance of Axially Loaded Piles in Sand" J. Geotech. Engng. ASCE, 117(2), 272-296.
17. Mabsout E.M., Reese L.C. and Tassoulas J.L. (1995) "Study of Pile Driving by Finite Element Method" J. Geotech. Engng. ASCE, 121(7), 535-543.
18. Ottaviani M. (1975) "Three-Dimensional Finite Element Analysis of Vertically Loaded Pile Groups" Geotechnigue, 25, No.2, 159-174.
19. Poulos H.G. (1989) "Pile Behaviour - Theory & Application", Journal of Geotech. Engng. ASCE, 39(3), 365-415.
20. Poulos H.G. and Davis E.H. (1980) "Pile Foundation Analysis and Design" john Willy and Sons, New York. N. Y.
21. Puswewala U.G.A.P (2003) "Lecture Notes on Computer Application", P.G. Dip/M.Eng in Foundation Engineering, University of Moratuwa.
22. Rajashree S.S. and Sitharam T.G. (2001) "Non-linear Finite Element Modeling of Batter Piles under Lateral Load"./ Geotech. Engng. ASCE, 127(7), 604-612.
23. Randolph M.F. and Wroth (1978) "Analysis Deformation of Vertically Loaded Piles" J. Geotech. Engng. ASCE, 104(12), 1465-1488.
24. Selvaduarai, A.P.S. (1979) "Elastic Analysis of Soil Foundation Interaction", Amsterdam: Geotechnical Engineering Vol 17.
25. Tomlinson, M J . (1986) "Foundation Design and Construction" Fifth Ed., ELBS, Longman Group, UK.
26. Thilakasiri H.S. (2003) "Lecture Notes on Design and Construction of Deep Foundation", P.G. Dip/M.Eng in Foundation Engineering, University of Moratuwa.
27. Trochanis A.M., (1991) "Numerical Methods in Geotechnical Engineering", 3rd
Edition, ELBS London.
28. Trochanis A.M., Bielack J. and Christiano P. (1991a) "Three-Dimensional Non-Linear Study of Piles" J. Geotech. Engng. ASCE, 117(3), 429-447.
29. Trochanis A.M., Bielack J. and Christiano P. '(1991b) "Simplified Model Analysis of for One or Two Piles" J. Geotech. Engrg. ASCE, 117(3), 448-466.
30. Wyllie D.C. (1992) "Foundation on Rock" First Edition E& FN Spon London.
31. Zehong Yuan and Koon Meng Chua (1992) "Exact Formulation of Axisymmetric interface Element Stiffness Matrix", J. Geotech. Engng. ASCE, 118(8), 1264-1271.
32. Zienkiewicz O.C. (1977) "The Finite Element Method", 3rd Edition Mc. Graw-Hill Co., London, U.K.
University of Moratuwa 2
ABBREVIATIONS
A Cross sectional area of the cylinder
a Half the length of a rectangular element
b Half the width of a rectangular element
C Pile perimeter
c„ Adhesion
Cs A bond modulus for the adhesive strength
D, ri Diameter of pile
ds Relative displacement parallel to the bond interface
E Young's modulus
E s Soil modulus
F Total applied force
F w Correction factor for tapered pile
H Thickness of the weak layer
Ko Lateral earth pressure coefficient
K n , K s Interface element stiffness
L Length of pile shaft
N Shape function
P Vector of Transformed stresses
P1.P2 • Force acting on node number 1, 2
Ultimate shaft resistance
Ultimate base resistance
Q Load on head of pile
q Effective overburden pressure at depth Zj
Q s - skin friction on pile
Qb - Base resistant on pile
Q P - Failure load on pile
s - Surface of a finite element
- Strain energy of an elastic body
V - Volume of a finite element
W ] W2 - Weight factors
~ Weight of the pile
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Abbreviations
Work done by surface tractions
~ Work done by body forces
- Ordinates in X-Axis (i=l,2,3 etc)
Yi - Ordinates in X-Axis (i=1,2,3 etc)
a A Coefficient
Constants for shape function (i=l,2,3 etc)
P - A Coefficient
<l> - Angle of friction of soil
M „ - Angle of friction between pile and soil
A. - A Coefficient
r„ - Shear resistance at the pile so iUnter face
_ Normal stress between pile and soil
- Poisson's ratio
- Normalized co-ordinates along X-Axis
- Normalized co-ordinates along Y-Axis
e - Strain vector
~ Potential energy
w ~ Shape function matrix
- Modulus vector
{f} - Body forces vector
w - Derivation vector
M - Displacement matrix
{a} - Stress vector
{T} - Applied traction vector
W - Nodal Displacement vector
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Appendix A
APPENDIX A: - COMPUTER PROCEDURE FOR FINITE ELEMENT ANALYSIS PROGRAM
Finte element program can be seperated in to two basic parts as follows:
(a) Data input module and preprocessor, and
(b) Solution and output module to carry out the actual analysis. (See Figure A.lfor
simplified schematic)
The data input module shown in Figure A.l must transmit sufficient information to the
other modules so that each problem can be solved. The data input module is used to read
from an input file the necessary geometric, material, and loading data so that all
subsequent finite element arrays can be established. In the program a set of dimensioned
arrays are established which store nodal coordinates, element connections, material
properties, boundary restrains codes, prescribed nodal forces and displacements, nodal
temperature, etc. Table A.l list the array names (and their dimensions) which are used to
store these quantities.
Figure A. 1 Simplified schematic of finite element program
A single array is partitioned to store all the data arrays, as well as some global arrays, e.g.
residuals, displacements, loads, etc. each array indicated in Table A.l is dynamically
Data input Module (Preprocessor)
Solution and Output Module (Postprocessor)
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Appendix A
dimensioned to the size and precision required for each problem by using a set of pointers
established in the control program.
Table A. J FORTRAN Variable names used for data storage
Variable names (dimensions) Description
Material property data sets, limited to i8 words per set
Nodal forces and displacements
Boundary restrains conditions after input of data changed to equation numbers in global arrays
Element type for each material set
Element nodal connections and Material set numbers
Nodal temperature
Nodal coordinates
Maximum numbers of degree of freedom at any node (Maximum 6) Spatial dimension of problem (Maximum is 3)
Maximum numbers of nodes connected to any element
NEN+3
Numbers of elements
Numbers of material sets
Numbers of nodes
Once a mesh for a problem has been established data can be prepared for finite element
analysis computer program. The first steps in preparation of input data for the program is
consist of specifying problem title and control information given in Table A.2, which is
used during subsequent data input and also is used to allocate memory in the program.
In addition to the input data formats, Table A.2 gives the variable names used in the
program. The variables NDF,NEN, and NAD are used to calculate the size of the element
arrays, NST. Normally for displacement formulations NDFxNEN is the size of the
element array.
Once the control data is supplied the program expects the data record for the mesh
description, e.g. nodal coordinates, element connections, etc.
D (18, NUMMAT)
F (NDF, NUMNP)
ID (NDF,NUMNP)
IE (8, NUMMAT)
DC (NEN1, NUMEL)
T(^UMNP)
X (NDM, NUMNP)
NDF
NDM
NEN NEN1 NUMEL NUMEL NUMNP
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Appendix A
Table A. 2 Title and control information format
Title-Format (20A4) The title also serves as a start of problem record. The first four (4) columns must contain the start word FEAP.
Columns Description Variables
1 to 4 Must contain FEAP TITL(l)
Alphanumeric information for header _ T „ T / , 1 N . _ _ A 5 to 50 . _ , c TITL(l) i=2,20 in output fie
Control Data-Format (715) The title also serves as a start of problem record. The first four (4) columns must contain the start word FEAP. Columns Description Variables
1 to 5 Numbers of nodes NUMEL
6 to 10 Numbers of elements NUMEL
11 to 15 Numbers of material sets NUMNP
16 to 20 Spatial dimensions (<3) NDM
21 to 25 Numbers of unknown per node (<3) NDF
26 to 30 Numbers of nodes/ elements NEN
31 to 35 Added size to elements matrices, in NAD 31 to 35 excess of NDFxNEN NAD
An analysis will require at least:
(a) Coordinate data which follows the macro command COOR and is prepared
according to Table A.3
Table A.3 Coordinate Data
Coordinate Data-Format (2110, 6F10.0) - must immediately follow a COOR macro.
Columns Description Variables
1 to 10 Node number N
10 to 20 Generator increment NG
21 to 30 XI coordinate XL(1)->X(1,N)
31 to 40 X2 coordinate XL(2)->X(2,N)
41 to 50 - X3 coordinate XL(3)->X(3,N)
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UPJI!/&R§ITY OF M0BATW17A. SB! LAMM M O R A T U W A Appendix A
(b) Element data which follows the macro command ELEM and is prepared according to
Table A.4; and
Table A.4 Element Data
Element Data -Format (1615) - must immediately follow an ELEM macro.
Columns Description Variables
I to 5 Material number L
• 6 to 10 Material set number LX(NEN1,L)
II to 15 Node 1 number K(1,L)
16 to 20 Node 2 number- IX(2,L)
etc.
etc. Node NEN number LX^NEN.L)
etc. Generator increment LX
(c) Material data which follows the macro command MATE and is prepared as described
in Table A.4 and the data required for each particular element
Table A.5 Material Property Data
Material property Data -Format (8110) must immediately follow a MATE macro.
Columns Description Variables
I to 10 Property set number MA
II to 20 Element type (lto4) IEL
21 to 30 Global DOF number for local DOF 1 IDL(l)
31 to 40 Node 1 number IDL(2)
Etc to NDF
In addition most analysis will require specification of nodal boundary restrained
conditions, macro BOUN, and the corresponding nodal force or displacement value,
macro FORC, which are specified according to Table A.6 and A.7 respectively.
8 5 7 9 3
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Appendix A
Table A. 6 Boundary Restraint Data
Element Data -Format (1615) -must immediately follow a BOUN macro.
Columns
I to 5
6 to 10
II to 15
16 to 20
etc.
etc.
Description
Node number
Generation increment
DOF 1 boundary code
DOF 2 boundary code
Variables
N
NX IDL(l)->- rDL(l,N)
roL(2)->.IDL(2,N)
DOF NDF boundary code IDL(NDF)—> TDL(NDF,N)
Table A. 7 Nodal Forced Boundary 'Value Data
Material property Data -Format (8110) must immediately follow a MATE macro.
Columns
I to 10
II to 20
21 to 30
31 to 40
etc.
etc.
Description
Node number
Generation increment
DOF 1 Force (Displ.)
DOF 2 Force (Displ.)
Variables
N
NX XL(l)-> XL(1,N)
XL(2)-> XL(2,N)
DOF NDF Force (Displ.) XL(NDF)—>• XL(NDF,N)
Macro commands for solution of a linear elastostatic problem
The following contains list of macroinstruction commands, which may be used to
construct solution algorithms. In batch mode the command MACR must be inserted after
the mesh data. The other macro commands follow immediately and terminate with an
END. macro.
Output can be obtained using the instructions DISP for displacements and STRE for
element variable such as strains and stresses.
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Appendix A
Table A. 8 list of macro programming commands
1-4 16-19 31-45 46-60 61-75 Description
TANG VI V2 Compute and factor tangent matrix (IS W=6)*
FORM Form right side of the equations
SOLV Solve for new displacements (after FORM)
DISP All , - N l N2 N3 Out put displacements for node Nl to N2 at increments of N3: ALL prints all
STRE Node Nl N2 N3 Out put variable (Stress,, etc.) for node Nl to N2 at increments of N3 (ISW=8)
Operations are performed in each element sub-program for specified ISW value.
•
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Appendix B
APPENDIX B: - MATERIAL PARAMETERS
Typical range values for Poisson ratio v (Bowles, 1968)
Type of soil v -value
Clay, Saturated ' 0.4 - 0.5
Clay, Unsaturated 0.1-0.3
Sandy Clay 0.2 - 0.3
Silt 0.3-0.35
Sand (dense) 0.2 - 0.4
Coarse (e=0.4-0.7) 0.15
Fine grained (e=0.4 - 0.7) 0.25
Rock 0 .1 -0 .4
(Depends somewhat on type of rock)
Range values for modulus of Elasticity Es for selected soils (Bowles, 1968)
Type of soil E-value (kN/m 2)
Very soft Clay 3 5 0 - 2,800
Soft Clay 1,750 -4,200
Medium Clay 4,200 - 8,400
Hard Clay 7,000 --17,500
Sandy Clay 28,000 - 42,000
Silty Sand 7,000 --21,000
Loose Sand 10,500 -24,500
Dense Sand 50,000 - 84,000
Dense Sand & Gravel 100,000 - 200,000
Loess 100,000 - 125,000
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APPENDIX C: - TYPICAL DATA INPUT FILE
FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
END MACR TANG,FORM 0 . 0 . SOLV 0 . 0 . D I S P 0 . 0 . STRE 0 . 0 . END 0 . 0 . STOP
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Appendix D
APPENDIX D: - TYPICAL OUTPUT FILE
FINITE E L E M E N T ANALYSIS P R O G R A M (FEA 81)
*****************************************
FEAP IS A GENERAL PURPOSE FINITE ELEMENT PROGRAM DEVELOPED AS A RESEARCH AND EDUCATIONAL TOOL AT U.C.BERKELEY BY R.L.TAYLOR. REFERENCE CAN BE MADE TO FEM TEXT BOOK BY O.C.ZIENKIEWITZ (3RD EDITION) CHAPTER 24. THE 1981 VERSION WAS PREPARED AT AIT IN 1981 BY W.KANOK-NUKULCHAI, AND IS FULLY COMPATIBLE WITH THE BOOK VERSION, ALTHOUGH MANY ADDITIONAL CAPABILITIES ARE INCORPORATED.
M E S H G E N E R A T I O N OFEAP * finite modelling of piles * Axi-symmetric analysis of pile * 07/08/03*
NUMBER OF NODAL POINTS = 255 NUMBER OF ELEMENTS = 224 NUMBER OF MATERIAL SETS = 6 DIMENSION OF COORDINATE SPACE = 2 DEGREE OF FREEDOMS/NODE = 2 NODES PER ELEMENT (MAXIMUM) = 4 EXTRA D.O.F. TO ELEMENT = 0
R-STORAGE = 2006 M-STORAGE = 2155
OFEAP * finite modelling of piles * Axi-symmetric analysis of pile * 07/08/03* NODAL COORDINATES NODE 1 COORD 2 COORD
OFEAP * finite modelling of piles * Axi-symmetric analysis of pile * 07/08/03*
MATERIAL PROPERTIES
MATERIAL SET 1 FOR ELEMENT TYPE 15
AXISYMMETRIC LINEAR ELASTIC ELEMENT/ MODULUS = 0.21000E+05 POISSON RATIO = 0.200 ALPHA = 0.00000E+00 MATERIAL TEMPERATURE = 0.0000E+00 LAMBDA = 0.58333E+04 MU = 0.87500E+04 LB = 2 LS = 2
MATERIAL SET 2 FOR ELEMENT TYPE 15
AXISYMMETRIC LINEAR ELASTIC ELEMENT/ MODULUS = 0.21000E+03 POISSON RATIO = 0.250 ALPHA = O.OO000E+0O MATERIAL TEMPERATURE = 0.0000E+00 LAMBDA = 0.84000E+02 MU = 0.84000E+02 LB = 2 LS = 2
MATERIAL SET 3 FOR ELEMENT TYPE 15
AXISYMMETRIC LINEAR ELASTIC ELEMENT/ MODULUS = 0.21000E+02 POISSON RATIO = 0.450 ALPHA = 0.00000E+00 MATERIAL TEMPERATURE = 0.0000E+00 LAMBDA = 0.65172E+02 MU = 0.72414E+01 LB = 2 LS = 2
MATERIAL SET 4 FOR ELEMENT TYPE 17
INTERFACE/BOND ELEMENT FOR 2-D ANALYSES MODULASC-s = 0.10000 MODULASC-t = 0.12000E+06 NO. OF GAUSS POINTS
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Appendix D
INTERFACE ELEMENT FOR AXISYMMETRIC ANALYSIS GAUSS QUADRATURE FOR ADFREEZE ELEMENTS
MATERIAL SET 5 FOR ELEMENT TYPE 17
INTERFACE/BOND ELEMENT FOR 2-D ANALYSES MODULASC-s = 0.10000E+06 MODULASC-t = 0.12000E+06 NO. OF GAUSS POINTS INTERFACE ELEMENT FOR AXISYMMETRIC ANALYSIS GAUSS QUADRATURE FOR ADFREEZE ELEMENTS
MATERIAL SET 6 FOR ELEMENT TYPE 17
INTERFACE/BOND ELEMENT FOR 2-D ANALYSES MODULASC-s = 0.10000E-01 MODULASC-t = 0.12000E+06 NO. OF GAUSS POINTS INTERFACE ELEMENT FOR AXISYMMETRIC ANALYSIS GAUSS QUADRATURE FOR ADFREEZE ELEMENTS
OFEAP * finite modelling of piles * Axi-symmetric analysis of pile * 07/08/03* NODAL B.C.
** 0 / 0 / 0 / 0 M 4 STRE VI = 0 . 0 0 0 0 E + 0 0 , V2 = O.OOOOE+00 0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
ELEMENT MAT 1-COORD 2-COORD 1 1 1 1
S - 1 2 E - 1 2
S - 2 2 E - 2 2
S - 3 3 E - 3 3
STRESS STRAIN
2 - STRESS 2 - S T R A I N
ANGLE ANGLE
SHEAR SHEAR
5 0 . 0 0 0 0
1 5 0 . 0 0 0 0
- 2 5 0 . 0 0 0 0
- 2 5 0 . 0 0 0 0
0 . 2 0 7 3 E - 0 1 - 0 . 8 1 1 3 E - 0 5
0 . 2 2 2 8 E - 0 1 - 0 . 8 2 6 4 E - 0 5
0 . 1 3 8 3 E - 0 1 0 . 1 5 8 0 E - 0 5
- 0 . 8 0 4 9 E - 0 2 - 0 . 9 1 9 9 E - 0 6
0 -0 0
0 . 4 5 0 4 E - 0 4 - 0 0 7 / 0 8 / 0 3 *
9 3 4 8 E + 0 0 4 4 1 2 E - 0 4 9 5 5 1 E + 0 0
2 0 7 3 E - 0 1 8 1 1 3 E - 0 5 2 4 0 4 E - 0 1 8 1 6 3 E - 0 5
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
0 . 9 3 5 0 E + 0 0 0 . 4 4 1 3 E - 0 4 0 . 9 5 5 1 E + 0 0
4 5 0 4 E - 0 4 0
. 2 0 5 2 E - 0 1 8 1 2 5 E - 0 5 2 2 2 1 E - 0 1 8 2 6 8 E - 0 5
8 9 . 1 3 89 . 1 3
- 8 9 . 5 1 - 8 9 . 5 1
0 . 4 5 7 2 E + 0 0 0 . 5 2 2 6 E - 0 4 0 . 4 6 6 5 E + 0 0 0 . 5 3 3 1 E - 0 4
AXISYMMETRIC STRESSES
ELEMENT MAT 1 - COORD 2 - COORD s - 1 1 S- 12 S- 22 S- 33 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E- 1 1 E- 12 E- 2 2 E- 33 1 - S T R A I N 2 - S T R A I N ANGLE SHEAR
- 0 8 6 0 6 E - 05 - 0 1 4 5 1 E - 05 0 4 1 2 1 E - 0 4 - 0 8 6 1 8 E - 05 0 4 1 2 2 E - 0 4 - 0 8 6 1 6 E - 0 5 - 8 9 17 0 4 9 8 4 E - 0 4 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
ENT MAT 1 - COORD 2 - COORD s - 11 s - 12 S- 2 2 s - 33 1 - STRESS 2 - S T R E S S ANGLE SHEAR E- 11 E- 12 E- 2 2 E- 33 1 -STRAIN 2 -STRAIN ANGLE SHEAR
- 0 8 0 5 1 E - 05 - 0 3 5 5 6 E - 06 0 3 8 9 8 E - 0 4 - 0 8 1 0 6 E - 05 0 3 8 9 8 E - 0 4 - 0 8 0 5 2 E - 0 5 - 8 9 7 8 0 4 7 0 3 E - 0 4 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f . . p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
ENT MAT 1 - COORD 2 - COORD s-- 1 1 S- 12 s- 22 s - 3 3 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E- 1 1 E- 12 E- 22 E- 33 1 - STRAIN 2 - S T R A I N ANGLE SHEAR
- 0 . 7 3 2 9 E - 05 - 0 . 3 9 1 7 E - 06 0 3 8 2 4 E - 0 4 - 0 7 2 8 9 E - 05 0 3 8 2 4 E - 0 4 - 0 7 3 3 0 E - 0 5 - 8 9 7 5 0 4 5 5 7 E - 0 4 f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * OFEAP
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
ENT MAT 1 - COORD 2 - COORD s - 1 1 s- 12 s - 22 s - 33 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E- 11 E- 12 E- 22 E- 33 1 -STRAIN 2 - S T R A I N ANGLE SHEAR
- 0 6 8 5 3 E - 0 5 - 0 1 1 8 4 E - 05 0 3 5 9 7 E - 0 4 - 0 6 8 2 2 E - 05 0 3 5 9 7 E - 0 4 - 0 6 8 6 1 E - 0 5 - 8 9 2 1 0 4 2 8 4 E - 0 4 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
ENT MAT 1 - COORD 2 - COORD s-• 1 1 s- 12 s - 2 2 s - 33 1 -STRESS 2 - S T R E S S ANGLE SHEAR E- 11 E- 12 E- 2 2 E- 33 1 -STRAIN 2 - S T R A I N ANGLE SHEAR
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
- 0 . 5 6 5 7 E - 0 5 - 0 . 1 3 4 8 E - 0 5 0 . 2 8 5 6 E - 0 4 - 0 . 5 6 3 3 E - 0 5 0 . 2 8 5 8 E - O 4 - 0 . 5 6 7 1 E - 0 5 - 8 8 . 8 7 0 . 3 4 2 5 E - 0 4 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
MENT MAT 1 - COORD 2 - COORD S-• 1 1 s-•12 s - •22 S-•33 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E-• 1 1 E-•12 E-•22 E- 33 1 -STRAIN 2 - S T R A I N ANGLE SHEAR
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
0 FEAP * f i n i t e m o d e l l i n g o f p i l e s *
. 1 3 2 2 E - 0 1 - 0 . 1 0 4 5 E - 0 1
. 1 3 5 7 E - 0 1 - 0 . 1 4 7 2 E - 0 2 A x i - s y m m e t r i c a n a l y s i s o f ' p i l e * 0 7 / 0 8 / 0
AXISYMMETRIC STRESSES
MENT MAT 1 - COORD 2 - COORD s--11 s-- 1 2 s- 2 2 s - 3 3 ' ^ 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E- 1 1 E- 12 E- 2 2 E- 3 3 1 -STRAIN 2 -STRAIN ANGLE SHEAR
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
ELEMENT MAT 1 - COORD 2 - COORD S- 1 1 s - 12 s - 2 2 s - 3 3 1 - S T R E S S 2 - S T R E S S ANGLE SHEAR E- 1 1 E- 12 E- 22 E- 3 3 1 -STRAIN 2 - S T R A I N ANGLE SHEAR
- 0 . 8 2 6 7 E - 05 0 . 2 5 4 0 E - 0 5 0 3 9 0 2 E - 04 - 0 1 0 4 3 E - 04 0 . 3 9 0 6 E - 04 - 0 . 8 3 0 1 E - 0 5 8 8 . 4 6 0 4 7 3 6 E - 04 OFEAP * f i n i t e m o d e l l i n g o f p i l e s i " A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
• /•
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS
1 7 1 5 2 0 0 . 0 0 0 0 - 6 3 9 4 . 3 3 7 6 - 0 1 7 1 5 2 0 0 . 0 0 0 0 - 6 1 0 5 . 6 6 2 4 - 0 FEAP * f i n i t e m o d e l l i n g o f p i l e s *
AXISYMMETRIC STRESSES
1 4 9 6 E - 0 2 0 . 2 3 8 5 E - 0 3 1 1 0 6 E - 0 1 0 . 4 4 1 0 E - 0 3 A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0
OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 * INTERFACE STRESSES AT GAUSS POINTS (TIME = 0)
- 0 . 1 7 2 4 E - 05 - 0 . 4 2 2 8 E - 0 6 0 . 1 3 3 8 E - 04 - 0 . 1 8 7 9 E - 05 0 . 1 3 3 8 E - 04 - 0 . 1 7 2 7 E - 05 - 8 9 2 0 0 1 5 1 1 E - 04 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-C00RD TANGT-STRESS NORML-STRESS
- 0 . 4 4 8 0 E - 06 - 0 . 1 7 8 9 E - 0 6 0 1 0 0 6 E - 04 - 0 4 0 9 4 E - 06 0 1 0 0 6 E - 04 - 0 4 4 8 8 E - 06 - 8 9 5 1 0 1 0 5 1 E - 04 OFEAP * f i n i t e m o d e l l i n g o f p i l e s * A x i - s y m m e t r i c a n a l y s i s o f p i l e * 0 7 / 0 8 / 0 3 *
INTERFACE STRESSES AT GAUSS POINTS (TIME = 0) ELEMENT TYPE 1-COORD 2-COORD TANGT-STRESS NORML-STRESS