The purposes of this research are to apply numerical modelling to prediction of the pore water pressure response induced by helical pile installation into fine-grained soil and to gain better understanding of the pore pressure behaviour observed during the field study of helical pile - soil interaction, performed at the Colebrook test site at Surrey, B.C. by Weech (2002). The critical state NorSand soil model coupled with the Biot formulation were chosen to represent the behaviour of saturated fine-grained soil. Their finite element implementation into NorSandBiot code was adopted as a modelling framework. Thorough verification of the finite element implementation of NorSandBiot code was conducted. Within the NorSandBiot code framework a special procedure for modelling helical pile installation in 1-D using a cylindrical cavity analogy was developed. A comprehensive parametric study of the NorSandBiot code was conducted. It was found that computed pore water pressure response is very sensitive to variation of the soil OCR and its hydraulic conductivity kr. Helical pile installation was modelled in two stages. At the first stage expansion of a single cavity, corresponding to the helical pile shaft, was analysed and on the second stage additional cavity expansion/contraction cycles, representing the helices, were added. The pore pressure predictions were compared and contrasted with the pore pressure measurements performed by Weech (2002) and other sources. The modelling showed that simulation of helical pile installation using a single cavity expansion within NorSandBiot framework provided reasonable predictions of the pore pressure response observed in the field. More realistic simulation using series of cavity expansion/contraction cycles improves the predictions. The modelling confirmed many of the field observations made by Weech (2004) and proved that a fully coupled NorSandBiot modelling framework provides a realistic environment for simulation of the fine-grained soil behaviour. The proposed modelling approach to simulation of helical pile installation provided a simplified technique that allows reasonable predictions of stresses and pore pressures variation during and after helical pile installation.
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Transcript
NUMERICAL MODELLING OF TIME DEPENDENT PORE PRESSURE
RESPONSE INDUCED BY HELICAL PILE INSTALLATION
by
ALEXANDER M. VYAZMENSKY
Diploma Specialist in Civil Engineering (B.Hons. equivalent)
St. Petersburg State University of Civil Engineering and Architecture, 1997
2.0. OVERVIEW OF FIELD STUDY OF HELICAL PILE PERFORMANCE IN SOFT SENSITIVE SOIL ..............................................................................................................8
3.0 LITERATURE REVIEW ..................................................................................................30 3.1. INTRODUCTION. ...............................................................................................................30
iii
Table of contents.
3.2. PORE PRESSURE RESPONSE INDUCED BY PILE INSTALLATION INTO FINE GRAINED SOIL AND ITS INFLUENCE ON PILE CAPACITY ...........................................................................30
3.2.1. FIELD GENERATION OF EXCESS PORE PRESSURE. ......................................................30
3.2.2. FIELD DISSIPATION OF EXCESS PORE PRESSURE. .......................................................31
3.2.3. OBSERVED AXIAL PILE CAPACITY AS FUNCTION OF DISSIPATION OF EXCESS PORE PRESSURE..................................................................................................................33
3.3. PREDICTION OF TIME-DEPENDENT PORE PRESSURE RESPONSE ........................................34
4.0. FORMULATION OF MODELLING APPROACH ....................................................49 4.1. INTRODUCTION. ..............................................................................................................49
4.2. MODELLING APPROACH TO SIMULATION OF HELICAL PILE INSTALLATION INTO FINE GRAINED SOIL .................................................................................................................49
7.0. MODELLING OF PORE PRESSURE CHANGES INDUCED BY PILE INSTALLATION IN 1-D ..............................................................................................138
7.2.1. STAGE I. MODELLING OF HELICAL PILE INSTALLATION AS SINGLE CAVITY EXPANSION..............................................................................................................139
7.2.1.1. COMPARISON OF MODELED AND FIELD PORE PRESSURE RESPONSES .........139
7.2.1.2. NORSANDBIOT “BEST FIT” WITH FIELD DATA..........................................141
7.2.2. STAGE II. MODELLING OF HELICAL PILE AS SERIES OF CAVITY EXPANSIONS ..146
7.2.2.1. DETAILS OF HELIX MODELLING .................................................................146
7.2.2.2. EFFECT OF CAVITY EXPANSION/CONTRACTION CYCLING ON PORE PRESSURE RESPONSE................................................................................................................147
7.3. IMPLICATIONS FROM 1-D MODELLING. .........................................................................153
7.3.1. PREDICTED VERSUS MEASURED/INTERPRETED PORE PRESSURE RESPONSE.......153
7.3.2. FROM PORE PRESSURE RESPONSE PREDICTIONS TO PILE BEARING CAPACITY ..155
8.0. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY ..........175 8.1. SUMMARY AND CONCLUSIONS. ...................................................................................175
8.2. RECOMMENDATIONS FOR FURTHER RESEARCH. ..........................................................177
8.2.1. LABORATORY STUDY .........................................................................................177
APPENDIX A. SOURCES OF SUBSURFACE INFORMATION FOR COLEBROOK SITE .....................189
APPENDIX B. PIEZOMETERS RESPONSE ...................................................................................191
APPENDIX C. VALIDATION OF NORSAND MODEL AGAINST BONNIE SILT.................................193
APPENDIX D. NORSAND-BIOT COUPLING ..............................................................................197
APPENDIX E. NORSAND-BIOT CODE VERIFICATION. ..............................................................200
APPENDIX F. COUPLED MODELLING OF OBSERVED PORE PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION (PAPER) ...............................................................209
vi
List of tables.
LIST OF TABLES TABLE PAGE
2.1. Average index properties of clayey silt/silty clay layer ..................................................... 11
3.1. Solutions for prediction of pore response induced by penetration of piles and piezocones.. 36
4.1. NorSand model formulation ............................................................................................... 55
5.1. List of correlations used to estimate K0 from CPT test data .............................................. 70
5.2. Calculation of radial hydraulic conductivity, kr ................................................................ 74
5.3. Estimation of slope of critical state line, λ, based on laboratory derived values of Cc reported by Crawford & Campanella (1991)...................................................................... 77
5.4. Summary of NorSand parameters for Colebrook silty clay ............................................... 79
5.5. Undrained shear strength and sensitivity estimated from field measurements and NorSand simulation of triaxial test ................................................................................................... 79
5.6. NorSand-Biot input parameters for Colebrook silty clay................................................... 80
6.1. List of scenarios for NorSandBiot code sensitivity analysis .............................................. 99
6.2. Parametric study results.................................................................................................... 101
6.3. Ranking of NorSandBiot formulation input parameters .................................................. 111
7.1. Modelling parameters for “base case” and “best fit” simulations.................................... 142
7.2. Undrained shear strength and sensitivity estimated from simulation of triaxial test with “base case” and “best fit” set of parameters ..................................................................... 142
7.3. Pore pressure response for “base case”, “best fit” and field data (Weech, 2002) ............ 143
7.4. Variation of effective stresses with time for “base case” and “best fit” simulations........ 144
7.5. Piezometers considered for the analysis .......................................................................... 148
7.6. Final stress state for “base case”, “best fit” and Case A simulation with 5 helices ......... 152
2.9. Variation of excess pore pressure with pile tip depth, S/D=1.5 ......................................... 24
2.10. Variation of excess pore pressure with pile tip depth, S/D=3 ............................................ 25
2.11. Radial distribution of excess pore pressure generated by penetration of pile shaft .......... 26
2.12. Radial distribution of maximum excess pore pressure after penetration of helices .......... 27
2.13. Radial distribution of excess pore pressure around helical piles (above level of bottom helix) during dissipation process ....................................................................................... 28
2.14. Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process ............................................................................................................. 28
2.15. Average dissipation trends for different radial distances from pile .................................. 29
2.16. Dissipation curves from piezometers/piezo-ports located at different radial distances from pile ................................................................................................................................ 29
3.1. Effect of pile installation on soil conditions ...................................................................... 44
3.2. Measured excess pore pressures due to installation of piles ............................................. 44
3.4. Increase in pile bearing capacity with time ....................................................................... 46
3.5. Increase in pile bearing capacity and pore pressure dissipation ........................................ 46
3.6. Comparison of variation of pile bearing capacity with time and theoretical decay of excess pore pressure .......................................................................................................... 47
3.7. Idealized schematics of soil set-up phases ........................................................................ 47
3.8. Cavity expansion zones along pile .................................................................................... 48
3.9. Comparison of measured and theoretical soil displacements due to pile penetration ....... 48
4.1. Schematic representation of 2-D modelling approach ...................................................... 60
viii
List of figures.
4.2. Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 2-D .................................................................................................... 61
4.3. Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 1-D .................................................................................................... 61
4.4. Normal compression lines from isotropic compression tests on Erksak sand ................... 62
4.5. Definition of NorSand parameters Γ, λ, ψ, and R ........................................................... 62
4.6. Definitions of internal cap, pi, pc, Mtc, Mi and ηL on yield surface for a very loose sand .. 63
4.7. Conventional and NorSand representation of overconsolidation ratio for soil initially at p′ = 500 kPa subject to decreasing mean stress ..................................................................... 63
4.8. NorSand fit to Bothkennar Soft clay in CK0U triaxial shear ............................................ 64
4.9. NorSand simulation fit to constant p=80kPa drained triaxial test on Bonnie silt ............. 65
4.10. Flow chart for large strain numerical code ........................................................................ 66
5.1. Typical shear modulus reduction with strain level for plasticity index between 10% and 20% 81
5.2. Level of shear strain for various geotechnical measurements ........................................... 81
5.3. Variation of small strain shear modulus Gmax with elevation ............................................ 82
5.4. Inferred variation of rigidity index with depth .................................................................. 83
5.5. Variation of shear modulus G with elevation .................................................................... 84
5.6. Range of overconsolidation ratio OCR with elevation ...................................................... 85
5.7. Variation of coefficient of earth pressure K0 with elevation ............................................. 86
5.8. Variation in estimated coefficient of horizontal consolidation with depth ....................... 87
5.9. Variation in estimated coefficient of horizontal consolidation with elevation with corrected CPTU derived values ........................................................................................ 88
5.10. Variation of vertical effective stress with elevation .......................................................... 89
5.11. Variation of equilibrium pore water pressure with elevation ............................................ 90
5.12. Probable range of slope of critical state line, λ .................................................................. 91
5.13. Variation of void ratio with mean effective stress based on data reported by Crawford & Campanella (1988) ............................................................................................................ 92
5.14. Variation of state parameter and overconsolidation ratio with mean effective stress ....... 92
5.15. Simulation of drained triaxial test with NorSand model, using “base case” set of input parameters .......................................................................................................................... 93
5.16. Simulation of undrained triaxial test with NorSand model, using “base case” set of parameters .......................................................................................................................... 94
6.1. FE Mesh for Parametric Study ........................................................................................ 114
6.2. Cylindrical cavity expansion from non-zero radius ........................................................ 114
6.3. Radial distribution of generated excess pore water pressure at the end of cavity expansion for “base case” scenario ................................................................................................... 115
ix
List of figures.
6.4. Time dependent pore pressure response at cavity wall for “base case” scenario ........... 115
6.5. Stress path for “base case” scenario ................................................................................ 116
6.6. Variation of void ratio, e, with mean effective stress, p΄ for “base case” simulation ..... 116
6.7. Variation of e with p΄ for “base case”, 20 & 21 scenarios ............................................... 117
6.8. Effect of K0 on radial distribution of generated excess pore pressure at the end of cavity expansion ......................................................................................................................... 117
6.9. Effect of K0 on time dependent pore water pressure response at cavity wall .................. 118
6.11. Effect of coupled R & ψ on radial distribution of excess pore pressure response at the end of cavity expansion .......................................................................................................... 119
6.12. Effect of coupled R & ψ on time dependent pore water pressure response at cavity wall 119
6.13. Effect of uncoupling R & ψ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with positive ψ ...................................... 120
6.14. Effect of uncoupling R & ψ on time dependent pore water pressure response at the cavity wall, for simulations with positive ψ ............................................................................... 120
6.15. Effect of uncoupling R & ψ on time dependent pore pressure response at the cavity wall, for simulations with negative ψ. ...................................................................................... 121
6.16. Generation of excess pore pressure during cavity expansion for the first mesh element adjacent to the cavity, presented in terms of pore pressure components ......................... 121
6.17. Effect of uncoupling R & ψ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with negative ψ. .................................... 122
6.18. Radial distribution of different excess pore pressure components for scenario 5a ......... 122
6.19. Radial distribution of generated pore pressure, for scenario 5a, at different levels cavity expansion ......................................................................................................................... 123
6.20. Initial conditions in e-ln (p΄) space for scenarios 3..6 and base case .............................. 123
6.21. Stress paths for scenarios 3…6 and base case .................................................................. 124
6.22. Variation of e with p΄ for scenarios 3…6 and base case ................................................... 124
6.23. Effect of G on radial distribution of excess pore pressure at the end of cavity expansion .125
6.24. Effect of G on time dependent pore pressure response at cavity wall ............................. 125
6.29. Effect of Γ on radial distribution of excess pore water pressure at the end of cavity expansion ......................................................................................................................... 128
6.30. Effect of Γ on time dependent pore water pressure response at cavity wall .................... 128
6.32. Effect of Γ & λ on radial distribution of excess pore pressure at the end of cavity expansion.......................................................................................................................... 129
6.33. Effect of Γ & λ on time dependent pore water pressure response at cavity wall ............. 130
6.41. Effect of χ on radial distribution of excess pore pressure at the end of cavity expansion...134
6.42. Effect of χ on time dependent pore water pressure response at cavity wall .................... 134
6.43. Stress paths for simulations with “base case”, scenario 18 & 19 set of input parameters .. 135
6.44. Effect of permeability, k, on radial distribution of excess pore pressure at the end of cavity expansion.......................................................................................................................... 135
6.45. Effect of permeability, k, on time dependent pore pressure response at cavity wall ........ 136
6.47. Location of final stress state in q-p΄ space, at the end of pore pressure dissipation, in relation to critical state line ............................................................................................................ 137
7.1. Radial pore pressure distribution at the end of pile installation reported by Levadoux & Baligh (1980), measured by Weech (2002) and simulated with “base case” parameters .. 158
7.2. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with “base case” parameters.......................................................... 158
7.3. Comparison of modelled undrained triaxial response for ”best fit” and “base case” sets of NorSandBiot input parameters ........................................................................................ 159
7.4. Radial pore pressure distribution at the end of pile installation reported by Levadoux & Baligh (1980), measured by Weech (2002) and simulated with “best fit” parameters .... 160
7.5. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with “best fit” parameters.............................................................. 160
7.6. Comparison of ∆u/σ′v0 and σ′v/σ′v0 vs. time for “best fit” and “base case” simulation and the field measurements ........................................................................................................... 161
7.7. Stress path plot for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation of helical pile shaft installation with “best fit” parameters. 161
7.8. Void ratio versus mean stress (e-ln(p΄)) plot for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation with “best fit” parameters ........................................................................................................................ 162
xi
List of figures.
7.9. Modelling cases considered in the analysis of the effect of the helices ........................... 163
7.10. Modelling algorithm of helical piles installation in 1-D ................................................. 163
7.11. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case A). ............ 164
7.12. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case B). ............. 165
7.13. Comparison of radial pore distribution for simulations with and without helices and the field measurements........................................................................................................... 166
7.14. Radial pore pressure distribution during first helix expansion (Case A).......................... 166
7.15. Radial pore pressure distribution during first helix contraction (Case B)........................ 167
7.16. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A).................................................................................. 167
7.17. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case A).................................................................................. 168
7.18. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case B). ................................................................................. 168
7.19. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case B). ................................................................................. 169
7.20. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case A)..................................................................................................... 170
7.21. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case A). ................................................................................................... 170
7.22. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case B)..................................................................................................... 171
7.23. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case B)..................................................................................................... 171
7.24. Stress path plot for mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation of helical pile shaft installation....................................................................... 172
7.25. Void ratio versus mean stress (e – ln(p΄)) plot for mesh element adjacent to the cavity wall (r/Rshaft = 1.08).................................................................................................................. 172
7.26. Comparison of stress paths for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulations with different set of input parameters and modelling schemes ............................................................................................................ 173
7.27. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A. Assumption 2)......................................................... 174
xii
Acknowledgements.
ACKNOWLEDGEMENTS.
I wish to thank my scientific supervisors, Dr. Dawn Shuttle and Dr. John Howie for their
invaluable guidance throughout this project.
Dr. Shuttle was always willing to assist with solving the most challenging problems and had
always been a source of brilliant ideas. Her ability to explain complex concepts with clarity and
ease and her truly endless patience are greatly appreciated. Dr. Shuttle’s enthusiasm for this
project had never run out and her pressure, in a good sense, kept me going.
My study at the University of British Columbia was a great learning experience. I would like to
thank Dr. Howie for taking me into the UBC Geotechnical Group. It was always a great
pleasure to work with him. Thoughtful contributions of Dr. Howie to many discussions related
to this project are sincerely appreciated.
I would like to express my gratitude to Dr. Michael Jefferies for shearing the code and for his
valuable suggestions.
Special thanks for the ideas and helpful information belongs to my fellow graduate students:
Sung Sik Park, Mavi Sanin, Ali Amini and Somasundaram Sriskandakumar.
My deep appreciation goes to my fiancé Valeria and my stepson Vadim, who inspired me all the
way through. Their patience and moral support are greatly acknowledged.
Most of all, I would like to thank my parents Sofia & Mikhail, and my elder brother Alexei.
Their unconditional love has always been there for me. I am indebt for their steadfast backing
of my intellectual and spiritual growth. This thesis is one of the fruits of their dedication and
love. There will be many more to come.
I dedicate this work to my beloved family.
PER ASPERA AD ASTRA
xiii
Chapter 1. Introduction.
1. INTRODUCTION.
1.1. CHALLENGES IN AXIAL PILE CAPACITY PREDICTIONS IN SOFT FINE-GRAINED SOILS. Piles are relatively long and normally slender structural foundation units that transfer
superstructure loads to underlying soil strata. Presently there are more than 100 different types
of piles. The major share in piling foundations belongs to driven or jacked piles of various
shapes, which are often referred to as traditional piles.
In geotechnical practice, piles are usually employed when soil conditions are not suitable for use
of shallow foundations, i.e. when the upper soil layers are too weak to support heavy vertical
loads from the superstructure.
Piles transfer vertical loads by friction along their surface and/or by direct bearing on the
compressed soil at, or near, the pile tip. Given that the pile material is not over-stressed, the
ultimate axial load capacity of a pile is equal to the sum of end bearing and side friction. The
amount of resistance contributed by each component varies according to the nature of load
support, soil properties and pile dimensions.
Prediction of pile capacity is complicated by the fact that during installation the soil surrounding
the pile is severely altered. This is particularly relevant for piles installed in thick deposits of
soft fine-grained soils, where the friction along the shaft is usually a prime factor governing the
pile capacity.
Soft-fine grained soils are known for their tendency to lose strength when disturbed, and their
slow rate of strength recovery following disturbance. Gradual gain of pile capacity with time
after pile installation is a well-known occurrence. Although factors such as thixotropy and
aging contribute to this phenomenon, the most significant cause for gain of capacity with time is
associated with the dissipation of the excess pore water pressure generated during pile
installation.
The processes occurring during and after pile installation has a very limited analytical
treatment and pile design is still largely relies on empirical correlations. At a recent
symposium on pile design (Ground Engineering, 1999) the participants were asked to provide
a prediction of the capacity of a single driven steel pile. The general success rate was very
poor with only 2 of 16 teams getting within 25% of the correct capacity. The best prediction
of the pile’s capacity was obtained from compensating errors; a too low side friction capacity
1
Chapter 1. Introduction.
was balanced by a too high end bearing. Randolph in his Rankine lecture (2003) also
recognized the lack of accuracy in pile design. Due to shortcomings in pile capacity
predictions geotechnical engineers have to rely on pile load tests to refine final piling
foundation design.
The ability to accurately predict the variation of stresses and pore pressures in fine-grained soil
due to pile installation is a key to improving pile capacity prediction capabilities.
The problem of predicting the variation of pile capacity in fine-grained soils is one of predicting
the excess pore pressure and associated stresses at the pile shaft as a function of time. It appears
that development of a robust technique for evaluation of pore pressure changes due to pile
installation will provide a basis from which a method accounting for capacity gain with time in
design and testing can be developed.
This study is concerned with modelling the time-dependent pore pressure response due to helical
pile installation in soft fine-grained soil.
1.2. HELICAL PILES.
A helical pile is an assembly of mechanically connected steel shafts with a series of steel helical
plates welded at particular locations on the lead section, as shown in Fig. 1.1.a.
Historically helical piles have evolved from early foundations known as screw piles. The screw
piles have been in use since the early 19th century. Early applications of these piles were based
on hand installation. The first power installed screw piles were employed during construction of
a series of lighthouses in England in 1833 (Wilson & Guthlac, 1950). Generally, the screw
piles had a very limited use until the 1960’s; when reliable truck mounted hydraulic torque
motors became readily available.
Nowadays the major helical piles manufacturer is a USA based company - AB Chance Ltd.
They manufacture piles with the shaft Ø 3.8 – 25 cm and helical plates Ø 15 - 36 cm. The
diameter of manufactured piles is quite small and their application is currently restricted to
relatively small jobs. It appears that the potential of helical piles is not fully exploited to date.
A new boost in helical pile’s application is expected from recent development of high capacity
torque units, which will make possible installation of helical piles with larger diameters,
installed to greater depths.
2
Chapter 1. Introduction.
Generally, helical piles can be employed in any application where driven and jacketed piles are
used, except for the cases where penetration of competent rock is required. Currently helical
piles found application in the following areas:
• foundation repairs, upgrades & retrofits;
• pump-jacks and compressor stations for oil and gas industry (large diameter piles);
• pipelines support;
• foundations for temporary and mobile structures.
Experience with conventional (small diameter) helical piles in soft soils in British Columbia
revealed a tendency for buckling of the slender steel shaft during loading. Aiming to reduce the
buckling effect, placement of grout around the shaft was proposed and patented by Vickars
Developments Co. Ltd, as grouted, or PULLDOWNTM, pile, shown in Fig. 1.1.b.
Normally, helical piles are installed by sections. The leading section, also called a screw
anchor, is placed into the soil by rotation of the pile shaft using a hydraulic torque unit. The pile
is screwed into the ground in the same method a wood screw is driven. Helical plates of the
leading section create a significant pulling force that makes the shaft advance downwards.
Following the screw anchor installation, extension sections are bolted to the top of the screw
anchor shaft. Installation continues by resumed rotation, and further extension sections are
added until the project depth of the pile is reached. For the grouted helical piles, at each
section’s connection, displacement plates are attached to the shaft. During pile installation they
create a cylindrical void, which is filled by the flowable grout.
Helical piles have several distinctive advantages over traditional driven and jacketed piles:
• mobilize soil resistance both in compression and uplift;
• quick and easy to install: vibration free, no heavy equipment required, possible to install
inside buildings (for small diameter piles);
• reusable.
Helical piles are typically installed in soils that permit the compressive capacity of the pile to be
developed through end-bearing below each of the helices at the bottom of the pile. Where the
thickness of soft cohesive strata is too extensive to make it practical to advance helical piles to a
competent bearing stratum, it may be necessary to develop the capacity of the piles in friction
within the soft cohesive soil. However, experience using helical piles in such soils is limited at
this time, as is the understanding of the complex sensitive fine-grained soil-helical pile interaction.
3
Chapter 1. Introduction.
1.3. PURPOSES AND OBJECTIVES OF RESEARCH.
Helical piles are gaining popularity in North America as an alternative foundation solution to
traditional driven and jacked piles. To date the major research efforts in the field of helical piles
have concentrated on their lateral and uplift capacity. However, limited knowledge of the time-
dependent effect of helical pile installation on soil behaviour remains a significant drawback to
their widespread application in soft fine-grained soils.
Pore pressure response due to helical pile installation has not been studied until very recently.
Field studies of helical pile performance in soft silty clay, carried out by Weech (2002) in Surrey,
British Columbia, provide quality data on the pore pressure regime during and after helical pile
installation. Given natural constraints of the field studies, such as a limited number of measuring
points and measurements accuracy, numerical simulation provides an effective tool for improving
our understanding of complex response of soft fine-grained soil due to helical pile installation.
The main objectives of this research are:
• Develop a modelling approach that will realistically simulate the pore pressure response during
helical pile installation and the subsequent excess pore water pressure dissipation with time.
• Numerically model helical pile installation into the soft fine-grained soil at the
Colebrook helical pile research site and investigate pore water pressure response
during and after helical pile installation. Compare and contrast the modelled response
with the field measurements and the field interpretations performed by Weech (2002).
The ability to understanding and predict the impact of pile installation on soft fine-grained soil
will contribute to improving existing pile bearing capacity calculation methods.
In addition the conducted research will be a major step towards development of an independent
geotechnical software tool, that will be able to help practicing engineers to estimate variation of
bearing capacity with time after pile installation.
The developed numerical approach should be extendable to other than helical types of piles,
which is to be confirmed by additional research.
1.4. SCOPE AND LIMITATION OF STUDY.
The conducted study is mainly focused on soil pore water pressure response due to pile
penetration, as it is believed to be an important factor affecting the variation of pile bearing
4
Chapter 1. Introduction.
capacity with time. Adequate simulation of the pore water pressure response in the soft fine-
grained soil requires a realistic soil model and a fully coupled modelling approach.
NorSandBiot formulation adopted in the current study incorporates the NorSand soil model
(Jefferies, 1993; Jefferies & Shuttle, 2002) to represent the fine-grained soil stress-strain behaviour
and the Biot (Biot, 1941) consolidation theory to account for the effect of coupling the pore
pressure response to behaviour to the soil stress-strain behaviour.
All numerical simulations conducted in the current study were based on the finite element
implementation of the NorSandBiot formulation developed by Shuttle (2003). Pore pressure and
stress predictions of the NorSandBiot code were successfully verified against a number of
available analytical solutions.
Given the complexity of helical pile installation process, numerical simulation of excess pore
pressure generated due to helical pile installation poses many challenges. It appears that the most
realistic simulation of helical pile installation will require a 3-D approach, which is hard to
implement and widely apply. The focus of the current research was on developing simple, yet
realistic representation of pore pressure response. It was necessary to neglect some features of
helical pile-soil interaction while simplifying the analysis. In the present study helical pile
installation was analyzed in 1-D employing the cylindrical cavity expansion analogue.
A better insight in pore pressure response induced due to helical pile installation may be achieved
when the effect of soil remoulding and 2-D effects of soil response are considered. Due to the
large volume of the conducted study these issues were left for future research.
Laboratory study was also beyond the scope of this work. Modelling input parameters were
derived from three previous investigations of Colebrook silty clay properties. They explicitly
provided many, but not all, of the input parameters required for the NorSandBiot formulation.
Some of the input parameters were taken as a best estimate, believed and shown to be
reasonable based on all information available. Another challenge in establishing input
parameters resulted from differences between laboratory and in-situ derived values of soil
properties. This is not unusual in a silty site where soil disturbance during sampling is a major
issue. Local spatial property variation, as seen in the in situ measurements, added to parameter
uncertainty. It appears that detailed laboratory study is required to refine the modelling input
parameters taken in the current study.
5
Chapter 1. Introduction.
1.5. THESIS ORGANIZATION.
In Chapter 1 of this thesis helical piles are introduced, research purposes and objectives are stated,
along with the scope and limitations of the conducted study.
An overview of the study of helical pile performance in soft fine-grained soils, carried out by
Weech (2002), is given in Chapter 2. This comprises a description of the scope of the work,
information on site stratigraphy and basic soil properties, geometry of the tested piles and
measuring equipment. A brief outline of the results of the Weech’s study relevant to the current
research is also presented.
Chapter 3 reviews the literature to provide information leading to the formulation of the modelling
approach.
Modelling approach adopted in this study is formulated in Chapter 4. NorSand critical state soil
model and Biot consolidation theory are presented along with their finite-element implementation.
Formulation input parameters are explained.
Chapter 5 describes the selection of site-specific soil parameters for modelling. Overview of all
available subsurface information is given. Selection process for all model input parameters is
individually analyzed. Best estimates of the soil properties for modelling are presented.
In Chapter 6, the description and results of the NorSand-Biot formulation parametric study are
presented. An accent is put on highlighting the input parameters that have the most profound
influence on the modelling results.
Chapter 7 presents modelling results and their analysis. A comparison of modelling with the
available field data, including Weech (2002) measurements, is provided and discussed. Effects of
the pile shaft and the helices on pore pressure response are separately analysed. Implications
from the modelling are presented.
Chapter 8 provides conclusions from the current study and recommendations for further research.
6
Chapter 1. Introduction.
a b
Fig. 1.1. Helical piles: a – conventional pile; b – grouted (PULLDOWNTM) pile.
7
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
2.0 OVERVIEW OF FIELD STUDY OF HELICAL PILE PERFORMANCE IN SOFT
SENSITIVE SOIL.
2.1. INTRODUCTION.
This study develops a numerical formulation to analyze pore pressure response due to helical pile
installation. As a basis for development of a robust numerical approach to modelling of time
dependent pore pressure response, induced by helical pile installation, high quality field data is
essential. Information obtained in the field provides an initial framework of expected soil
response and can serve as a reference point for modelling results verification.
A comprehensive field study of helical pile performance in sensitive fine-grained soils,
conducted at Surrey, British Columbia, by Weech (2002), was chosen as a source of necessary
background information for numerical analysis in a current research.
Weech’s study was mainly oriented towards improving understanding of the effects that the
installation of helical piles has on the strength characteristics of sensitive fine-grained soils.
Current research is focused on time-dependent pore water pressure response due to helical pile
installation. In this chapter a brief overview of Weech’s work is given and Weech’s key findings
relevant to the current study are presented. In addition a review of available information on site
subsurface conditions is provided.
2.2. SCOPE OF WEECH’S STUDY.
Six instrumented full-scale helical piles were installed in soft sensitive marine deposits. Prior to
pile installation, an in-situ testing program was carried out, that consisted of:
• two profiles of vane shear tests;
• five piezocone penetration soundings, with pore pressure dissipation tests carried out at
two soundings and shear wave measurements at three soundings.
The excess pore pressures within the soil surrounding the piles were monitored during and after
pile installation by means of piezometers located at various depths and radial distances from the
pile shaft, and using piezo-ports, which were mounted on the pile shaft.
After allowing a recovery period following installation, which varied between 19 hours, 7 days
and 6 weeks, piles with two different helix plate spacing were loaded to failure under axial
8
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
compressive loads. Strain gauges mounted on the pile shaft were monitored during load testing
to determine the distribution of loading throughout the pile at the various load levels up to and
including failure. Load-settlement curves were generated for different pile sections at different
times after installation. The piezometers and piezo-ports were also monitored during load testing
and the distribution of excess pore pressures
2.3. SITE SUBSURFACE CONDITIONS.
The test site, also referred to as the Colebrook site, is located under the King George Highway
(99A) overpass over Colebrook Road and the adjacent BC Railway line, South Surrey, BC;
approximately 25 km southwest of downtown Vancouver, as shown in Fig. 2.1.
2.3.1. SITE STRATIGRAPHY.
The subsoils found in this area belong to so called Salish Sediments. According to Armstrong
(1984): “Salish sediments include all postglacial terrestrial sediments and postglacial marine
sediments that were deposited when the sea was within 15 m of present sea level”. These deposits
were likely laid down during the Quaternary period between 10,000 and 5,000 years ago.
Cross-section of site stratigraphy is shown on Fig. 2.2. From the surface there is a layer of fill,
about 0.6 m thick, which was placed during 99A Highway construction. The fill is underlain by
a layer of firm to stiff peat, possibly bog and swamp deposit, that formed the original ground
surface; the thickness of this peat layer is about 0.3 m. Below the peat there is a layer of firm
clayey silt of deltaic origin, with some sand inclusions. The thickness of this layer is about 1 m.
The layer of clayey silt is underlain by layer of soft silty clay with organic inclusions (peat, plant
stalks). Given the proximity of the Serpentine river, this deposit likely has a tidal origin: it was
deposited within the inter-tidal zone between the Serpentine river delta and Semiahmoo Bay.
Below the silty clay layer there is a thick (around 27 m) layer of soft clayey silt to silty clay of
marine origin. The marine deposits are underlain by a stiff layer of sand and gravels of glacial
origin.
Crawford & Campanella (1991) reported slight artesian pressure at the interface of the silty clay
layer and glacial deposits. Weech (2002) indicated that the groundwater table can be found at
–2 m elevation (0.7m from the surface), with an upward hydraulic gradient of 5 to 10 %, which
is possibly explained by the groundwater recharge from the upland area north of the site.
9
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
2.3.2. SOIL PROPERTIES.
Three subsurface investigations were performed at, or close to, the helical piles performance
research site. Site plan and locations of all subsurface investigations are presented in Fig. 2.3. A
brief description of each investigation and their reviews reported in the literature are presented
below in chronological order.
2.3.2.1. FIELD INVESTIGATION BY MINISTRY OF TRANSPORTATION AND HIGHWAYS.
Prior to construction of the Colebrook Road overpass (Highway 99), the Ministry of
Transportation and Highways (MoTH) performed an extensive geotechnical study of the soil
conditions along the alignment of a planned overpass (in 1969). The MoTH investigation
included dynamic cone penetration tests and drilling with diamond drill to establish the depth
and profile of the competent stratum underlying the soft sediments. Field vane shear tests were
performed at selected depths. “Undisturbed” samples of the soft soils were recovered with a
Shelby tube sampler. A number of laboratory tests were carried out on the MoTH samples,
including index tests, consolidated and unconsolidated triaxial tests and laboratory vane shear
tests.
Crawford & deBoer (1987) studied the long-term consolidation settlements underneath the
approach embankments, located in the vicinity of the helical piles performance research site.
They reported some of the data obtained during the MoTH investigation - typical for the
Colebrook site soil properties and results of three unidirectional consolidation tests performed in
a triaxial cell, with radial drainage. Crawford & deBoer (1987) report, based on laboratory
testing, an average coefficient of consolidation in the horizontal direction, ch = 1.5·10-3 cm2/s, an
average coefficient of secondary consolidation, Cα = 0.014 and an initial void ratio, for all three
tests, e0 = 1.25. A summary of typical soil properties from MoTH investigation given by
Crawford & deBoer (1987) are presented in Table A.1 (Appendix A).
2.3.2.2. RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (1).
Crawford & Campanella (1991) reported the results of a study of the deformation characteristics
of the subsoil, using a range of in-situ methods and laboratory tests to predict soil settlements
underneath the embankment, and compare them with the actual settlements. In-situ tests
included field vane shear tests, piezocone penetration test (CPTU) and a flat dilatometer test
(DMT). Laboratory tests were limited to constant rate of strain odometer consolidation tests on
10
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
specimens obtained with a piston sampler. Results of a series of the CRS consolidation tests are
presented in Table A.2 (Appendix A).
As a continuation of previous works by Crawford & deBoer (1987) and Crawford & Campanella
(1991), Crawford et al. (1994) studied the possible reasons for the difference between predicted
and measured consolidation settlements underneath the embankment using the finite-element
consolidation analysis with CONOIL computer program (by Byrne & Srithar, 1989). The soil
properties employed in the numerical analysis are shown in Table A.3 (Appendix A).
2.3.2.3. RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (2).
As a part of his study of helical pile performance in soft soils, a comprehensive investigation of
site soil conditions was carried out by Dolan (2001) and Weech (2002).
Dolan (2001) obtained continuous piston tube samples from ground level to 8.6 m depth and
performed index testing to determine natural moisture content, Atterberg limits, grain-size
distribution, organic and salt content.
Results of index tests carried out by Dolan (2001) on samples obtained with the piston tube
sampler are summarized in Table 2.1
Table 2.1. Average index properties of clayey silt/silty clay layer (elevation -4.1 m and below).
Soil Property Average Value Comments
natural moisture content (wn) 42%+/-3% -
liquid limit (wL) 40%+/-4% -
plasticity index (PI) 13.5%+/-4.5%, below –8m in elevation PI is up to 21%
unit weight (γ) 17.8+/-0.3 kN/m3 -
in-situ void ratio (eo) 1.16+/-0.09 derived from moisture content data, assuming specific gravity of 2.75
Weech (2002) carried out a detailed in-situ site characterization program, which included field
vane shear tests; cone penetration tests with pore pressure (CPTU) and shear wave travel time
measurements (SCPT).
Locations of sampling and in-situ soundings are presented in Fig. 2.4. A summary of
engineering parameters for the silty clay layer, estimated from in-situ tests by Weech, are
presented in Table A.4 (Appendix A).
11
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
Field vane shear strength profiles for the Colebrook site measured by Weech (2002) and
Crawford & Campanella (1991) are shown in Fig. 2.5.
In Fig. 2.5a the peak undrained shear strength is plotted with depth. For the clayey silt/silty clay
layer it varies from 15 to 30 kPa. The profile of the remoulded shear strengths, (su)rem, is also
plotted on Fig. 2.5a, showing a variation from 2 to 0.7 kPa within the clayey silt/silty clay layer.
Due to such low remoulded strengths, the sensitivity, St = (su)peak/(su)rem, determined from the
field vane measurements is very high. Profiles of sensitivity are shown on Fig. 2.5b. The
sensitivity appears to increase approximately linearly with depth from a minimum of 6 at surface
to about 40 at –12 m elevation. Even higher sensitivity, in the range of 50 to 75, was measured
by Crawford & Campanella (1991) between –12 and –17 m, who state that the high sensitivity of
the marine deposits is likely caused by leaching of pore-water salts due to the slight artesian
conditions, particularly at the lower depth.
The ratio of su to the effective overburden pressure, σ΄vo, is presented in Fig. 2.5c. In the upper
part of the marine deposits (from –4.1 to –4.4 m in elevation) the su/σ΄vo ratio is quite high –
around 0.7, which indicates moderately overconsolidated soil. At lower depths the deposit is
lightly overconsolidated, with the su/σ΄vo ratio around 0.4.
A typical CPT cone test result for Colebrook site, including profiles of corrected tip resistance,
qT, sleeve friction, fs, and excess penetration pore pressure, ∆u, measured behind the shoulder of
the cone (u2 filter position), are presented on Fig. 2.6.
A detailed overview of the soil properties, relevant to the current study, is given in Chapter 5.
2.4. HELICAL PILES AND PORE PRESSURE MEASURING EQUIPMENT.
2.4.1. TEST PILES GEOMETRY AND INSTALLATION DETAILS.
For the purpose of studying different failure mechanisms, piles with two different lead sections
were used. The largest helical piles manufacturer, Chance Anchors, commonly uses helical
plates attached to the lead section such that the distance between successive plates (S) is 3 times
the diameter (D) of the lower plate. In this case, current thinking based on small scale model
tests (Narasimho Rao et al., 1991) is that during loading to failure, failure occurs at individual
helices. For the closer spacing of the helical plates, the failure mechanism is believed to be
different - all helices fail simultaneously, so that a cylindrical failure surface is generated
12
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
coinciding with the outside edge of the helical plates. To investigate such a possibility the
testing was carried out on piles which had either 3 plates at S/D = 3, or 5 plates at S/D = 1.5, so
that the total length from the top to bottom helix was equal for the two pile types (2.1 m). The
pitch of the helix plates was 7.5 to 8 cm, which is the standard pitch on helical piles manufactured
by Chance Anchors. The geometry of both types of lead sections is shown in the Fig. 2.7.
In total six helical piles - three for each leading section type were installed, their locations are
shown in Fig. 2.8. Two piles, TP-1 - with three helices (S/D = 3) and TP-2 with five helices
(S/D = 1.5), were chosen for the detailed monitoring. The other piles served as a source of
additional information.
All piles were installed to a tip depth of 8.5 m (-9.8 in elevation). Installation of a single pile, including
breaks for section mounting and adjustments to maintain pile verticality, usually took about 2 hours.
Deducting interruptions, the average rate of soil penetration by helical pile was about 1.5 cm/s.
2.4.2. MEASURING EQUIPMENT.
A total of 26 UBC push-in piezometers were installed at different depths and radial distances
from the 6 test piles, and a total of 10 piezo-ports were located at 3 different positions on the
shaft of the piles, as indicated in Table B.1 (Appendix B). Piezo-ports, which contained an
electric pore pressure transducer with a porous filter, were installed within the wall of the pile
shaft on the lead sections. The piezometers were pushed into the soil at least one week prior to
pile installation so that full dissipation of the excess pore pressures generated during piezometer
installation could occur. These piezometers were then used to monitor the variation in pore
pressures caused by pile installation and their subsequent dissipation.
During pile installation piezometers were continuously monitored using the multi-channel data
acquisition system. After the end of pile installation piezoports located on the pile shaft were also
connected to the data acquisition system and were continuously monitored in conjunction with the
piezometers. Two types of electronic pore pressure transducers were employed for the piezometers and
the piezoports, with measuring capacity 345 and 690 kPa. The resolution of the automatic acquisition
system used to monitor the piezometers was 0.035 to 0.07 kPa (for 345 and 690 kPa transducers,
respectively). The rated accuracy of the pressure transducer measurements was ±0.1% of full scale.
Even though every attempt was made to carefully assemble and install measuring equipment, the
response of many piezometers and piezoports was less than perfect, as shown in Table B.1.
13
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
2.5. SUMMARY OF WEECH’S STUDY RESULTS.
This summary is based on Weech’s interpretations of pore pressure response measured during
and after helical pile installation. Only key points are presented here, more details can be found
in Weech (2002).
2.5.1. PORE WATER PRESSURE RESPONSE DURING HELICAL PILE INSTALLATION.
Pore pressure profiles measured at different radial distances during installation for piles TP-1 and
TP-2 are shown in Fig. 2.9 and Fig. 2.10. In these figures profiles of normalized peak pore
pressure ∆ui/σ΄vo are plotted against the depth of the pile tip below the elevation of the
piezometer filter (zpile – zpiezo). For reference, the locations of the different parts of the pile
relative to the tip are also shown on the right side of these figures. Based on Fig. 2.9 and 2.10
Weech (2002) made the following observations:
• There is a very sudden increase in ∆ui as the tip of the pile shaft approaches and then
passes the elevation of the piezometer filters. This increase is particularly abrupt at the
piezometers located closer to the pile.
• The magnitude of excess pore pressure generated within the soil by the pile installation
decreases with radial distance from the pile.
• Negative pore pressures were observed just before the pile tip passes the piezometers
locations. Baligh & Levadoux (1980) linked such behaviour with vertical displacement of
soil in advance of a penetrating pile or probe, which is initially downward. According to
Weech (2002), downward soil movement relative to the static piezo-cell induces a short
lived tensile pore pressure response which is observed just before the response becomes
compressive with a primarily radial displacement vector.
• Each helical plate passing the piezometers generates a “pulse” in pore pressure. The first
“pulse” generated by a leading helical plate is the strongest, all subsequent helical plates
generate less definitive pore pressure “pulses”. Such an effect is noticeable only at
piezometers located within one helix radius from the helix edge (r/Rshaft1 = 7 and 8) .
• Only the soil located very close to the outside edge of the helix plates (within about 10 to
12 times the helix plate thickness - thx) appears to respond directly to the penetration of 1 In this overview, radial distance is represented by the r/Rshaft ratio, where Rshaft is the radius of the pile shaft (in the current study, identical for all piles), r – radial distance from the pile centre.
14
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
the helix plates. Within this zone, distinctly different responses are observed for the
S/D = 1.5 and S/D = 3 piles.
• At radial distances larger than about 10-12 thx beyond the edge of the helices, the pore
pressure response to the penetration of the S/D = 1.5 and S/D = 3 piles is very similar.
Weech (2002) attempted to quantify separately pore pressures generated by pile shaft and the helices,
where the pore pressures generated by the pile shaft were inferred from the piezometers response
to penetration of the pile tip.
In Fig. 2.11 is shown a radial distribution of normalized pore pressures induced by the pile tips
of all test piles. According to Fig. 2.11, for r/Rshaft = 5 to 17, ∆ushaft/σ′vo decreases steeply and
almost linearly. After r/Rshaft = 17, ∆ushaft becomes quite small (< 0.1σ′vo) and the slope of the
pore pressure decay with distance flattens. For r/Rshaft ≥ 60 generated pore pressures are
practically negligible.
In Fig. 2.12 is shown radial distribution of peak pore pressures generated, during installation, by
helical pile shaft and the helices, and, the best estimate of pore pressures generated by helical
pile shaft alone, so that the effect of the helical plates can be studied. Weech (2002) made the
following observations from this figure:
• The contribution of the helical plates to the magnitude of generated pore pressures,
during helical pile installation, appears to be quite significant. At distances up to r/Rshaft
= 6, the pore pressures generated by the helices make up to 20% of the total pore
pressures and at distances greater than r/Rshaft = 17 make up to 75% .
• Penetration of the helices extends the radial distance of generated pore pressures from
r/Rshaft about 60, estimated for penetration of pile shaft alone, to r/Rshaft about 90.
Weech (2002) argued that there appears to be a gradual outward propagation of the pore pressure
induced by the helices, during continuing pile penetration, attributed to total stress redistribution
caused by soil destructuring.
2.5.2. PORE WATER PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION.
Weech (2002) compiled a combined dataset of all (for piles with both S/D = 1.5 and 3)
normalized piezometric measurements, taken at different times, at the locations above the bottom
helical plate as presented in Fig. 2.13. Despite some scatter in the data there is a trend in the
observed pore pressure dissipation behaviour, represented by the fitted curves. According to Fig.
15
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
2.13, excess pore pressure, ∆u, decreases monotonically throughout the soil around the pile, out
to a radial distance of at least 30 shaft radii. The rate of dissipation at different radial distances
appears to vary such that the ∆u(r)/σ′vo-log(r) curve becomes more and more linear as the
dissipation process progresses.
Fig. 2.14 shows curves fitted to all the available data of normalized excess pore pressure
measured at the location above and below the level of the bottom helical plate (where the
influence of plate penetration is minimal). Weech (2002) made the following observations from
this figure:
• No residual ∆uhx is observed in the soil (from r/Rshaft = 5 to at least 17) below the level of
the bottom helix within 10 minutes after stopping penetration
• Dissipation of ∆u within the soil close to the helices (r/Rshaft < about 10) is much more
rapid below the level of the bottom helix than above, at least during the first 17 - 20 hours
of dissipation.
• The elevated pore pressures at the tail of the distribution (r/Rshaft > 17), which are due to
the penetration of the helix plates, remain above the initial level generated by the pile
shaft until about 20 hours.
Average dissipation curves at different radial distances from the piles are shown in Fig. 2.15.
Shown dissipation curves do not exhibit a unified dissipation trend at bigger times,
Weech (2002) attributed this to the higher rate of dissipation at larger radial distances.
In Fig. 2.16 shows the dissipation curves based on ∆u(t)/σ΄vo data from individual
piezometers/piezo-ports located at different radial distances from the test piles (above the bottom
helix). Based on this figure Weech (2002) made the following observations:
• The dissipation occurs much more quickly below the bottom helix than above, at radial
distances close to the pile.
• Even though greater proportions of dissipation occur sooner at larger radial distances, all
of the curves tend to converge at the end of the dissipation process. For all monitored
piles 100% dissipation occurred at about 7 days for most locations around the piles.
• The dissipation process appears to be essentially independent of the number or spacing of
the helix plates.
16
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
2.6. SUMMARY.
A comprehensive study of helical pile performance carried out by Weech (2002) was an
important step towards better understanding of a complex helical pile – fine-grained soil
interaction. Weech reported details of the pore pressure response observed during and after
installation of helical piles at the Colebrook site and attempted to interpret them. However, the
presented problem analysis cannot be considered complete. The applicability of the observations
made during Weech’s study on sites with different soil conditions and different helical piles
geometries is questionable.
According to Terzaghi2: “Theory is the language by means of which lessons of experience can be
clearly expressed”. It appears that the lessons of experience gained during Weech’s study may
be effectively utilized using numerical modelling.
In the current study the field measurement of the pore water pressure response measured by
Weech (2002) is employed as a reference point for analysing the results of numerical modelling.
2 Quote from Karl Terzaghi biography by Goodman (1999).
17
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
Test Site
N
Fig. 2.1. Helical pile performance research site location.
Surrey, BC
18
Fig. 2.2. Site subsurface conditions at the research site (modified after Weech, 2002).
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil.
scale - metres
Fig. 2.3. Approximate locations of subsurface investigations at the Colebrook site (modified after Crawford & Campanella, 1991).
Fig. 2.4. Location of CPT tests and solid-stem auger holes (after Weech, 2002)
19
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-30 10 20 30 40
Field Vane Shear Strength(su)FV (kPa)
Elev
atio
n (m
)
Peak Strength (VH-1&2)
Remoulded Strength (VH-1&2)
Peak (from Craw ford & Campanella, 1991)
Rem (from Craw ford & Campanella, 1991)
Possibly affected by
sandy silt
a)
0.0 0.2 0.4 0.6 0.8
Strength Ratiosu/σ'vo
0 10 20 30 40 50
SensitivitySt = (su)peak/(su)rem
VH-1&2
Craw ford & Campanella(1991)
c) b)
Fig. 2.5. Variation of field vane shear strength test results with elevation (after Weech, 2002).
20
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
Fig. 2.6. Example of cone penetration test results (CPT-7) (after Weech, 2002). -12
-11
-10
-9
-8
-7
-6
-5
-4
-30 1 2 3 4 5 6 7
Tip ResistanceQT (bar)
Elev
atio
n (m
)
a)
0 1 2 3 4 5 6
Sleeve Frictionfs (kPa)
b)
-50 0 50 100 150 200 250
Excess Pore Pressureat U2 - ∆u (kPa)
c)
Note:Breaks in profile correspond to data recorded upon resuming penetration after seismic tests
21
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
Fig. 2.7. Helical piles geometry (modified after Weech, 2002).
22
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
pile cap
300 mm widehexagonal
RC piles
3rd bridge pier from South abutment
2nd bridge pier from South abutment
Fig. 2.8. Heli
Helical piles
cal piles locations (modified after Weech, 2002).
23
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
-2
-1
0
1
2
3
4
5-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Excess Pore Pressure during Pile Installation - ∆ui/σ'vo
Dep
th o
f Pile
Tip
Bel
ow P
iezo
Filt
er E
lev.
(m)
PZ-TP4-1 (r/R = 4.8)
PZ-TP2-5 (r/R = 7.3)
PZ-TP2-1 (r/R = 8.0)
PZ-TP2-7 (r/R = 11)
PZ-TP2-3 (r/R = 17)
PZ-TP2-4 (r/R = 30)
Note:Dissipation during breaks in installation removed.
HelixPlates
Grout Disc
Grout Column
Line of Max Pore Pressure
r = radial distance from pile centerR = radius of pile shaft
Fig. 2.9. Variation of excess pore pressure with pile tip depth, S/D=1.5. (after Weech, 2002)
24
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
-2
-1
0
1
2
3
4
5-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Excess Pore Pressure during Pile Installation - ∆ui/σ'vo
Dep
th o
f Pile
Tip
Bel
ow P
iezo
Filt
er E
lev.
(m)
PZ-TP3-1 (r/R = 5.8)
PZ-TP3-2 (r/R = 8.1)
PZ-TP1-7 (r/R = 12)
PZ-TP1-3 (r/R = 14)
PZ-TP1-4 (r/R = 25)
Note:Dissipation during breaks in installation removed.
HelixPlates
Grout Disc
Grout Column
Line of Max Pore Pressure
r = radial distance from pile centerR = radius of pile shaft
Fig. 2.10. Variation of excess pore pressure with pile tip depth, S/D=3. (after Weech, 2002).
25
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
TP1-4
TP2-4
TP5-1
TP1-3
TP1-6
TP2-3
TP1-5
TP2-7
TP6-2
TP2-2TP2-5
TP2-6
TP1-9TP4-2
TP4-1TP3-1
TP6-1
TP3-2
TP2-1
TP1-7
TP2-9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1 10
Radial Distance from Pile Center (shaft radii) - r/Rshaft
Exce
ss P
ore
Pres
sure
dur
ing
Inst
alla
tion
- ∆u i
/ σ' vo
Pile Piezos (due to pile tip penetration)
Pile Piezo-Ports (End of Installation)
Edge
of H
elic
es
Logarithmic Trend Line
Linear Trend Line
Linear Trend Line
100
Fig. 2.11. Radial distribution of excess pore pressure generated by penetration of pile shaft (modified after Weech, 2002).
26
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1 10Radial Distance from Pile Center (shaft radii) - r/Rshaft
∆u/
σ' vo
Peak u at Piezos after Passing of Pile Tip
Max u at Piezo-Ports (End of Installation)
Shaft Penetration (best fit of data from Fig. 2.11)
Shaft Penetration (best estimate for r < 5R)
Edg
e of
Hel
ices
∆uhx (best estimate)
∆uhx
100
Fig. 2.12. Radial distribution of maximum excess pore pressure after penetration of helices (after Weech, 2002).
27
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1 10 100Radial Distance from Pile Center (shaft radii) - r/Rshaft
∆u/
σ'vo
0.1 min after stopping10 min after stopping1 hr after stopping5 hrs after installation17-20 hrs after installation2 days after installationInitial Shaft Penetration
Edge ofHelices
Fig. 2.13. Radial distribution of excess pore pressure around helical piles (above level of bottom helix) during dissipation process (after Weech, 2002).
10 min (Ushaft = 4%)
10 min
1 hr
5 hrs
17-20 hrs
2 days
1 hr(Ushaft = 16%)
5 hrs(Ushaft = 35%)
17-20 hrs(Ushaft = 57%)
2 days(Ushaft = 76%)
0.1 min (Ushaft = 0%)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1 10Radial Distance from Pile Center (shaft radii) - r/Rshaft
∆u/
σ'vo
10 min (Below Helices)1 hr (Below Helices)5 hrs (Below Helices)17-20 hrs (Below Helices)2 days (Below Helices)10 min (Above Bottom Helix)1 hr (Above Bottom Helix)5 hrs (Above Bottom Helix)17-20 hrs (Above Bottom Helix)2 days (Above Bottom Helix)
Edge of Helices
100
Fig. 2.14. Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process (after Weech, 2002).
Fig. 2.14. Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process (after Weech, 2002).
28
Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000Time after Stopping Installation (min)
∆u(
t)/∆
u o
r/R = 1(Pile Shaft)
r/R = 4 (Edge of Helices)
r/R = 6
r/R = 8
r/R = 12
r/R = 16.5
r/R = 25
∆uo = ∆u at 0.1 min after stopping installation
Fig. 2.15. Average dissipation trends for different radial distances from pile (after Weech, 2002)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1 10 100 1000 10000Time (min) from End of Installation
Fig. 3.4. Increase in pile bearing capacity with time (after Seed & Reese, 1957).
Fig. 3.5. Increase in pile bearing capacity and pore pressure dissipation (modified after Konrad Roy, 1987). &
46
Chapter 3. Literature review.
Fig. 3.6. Comparison of variation of pile bearing capacity with time and theoretical decay of excess pore pressure (after Randolph & Wroth, 1979).
zed schematics of soil set up phases (modified after Komurka et al., 2003).
Phase 1: Nonlinear rate of excess pore pressure dissipation and set-up
Phase 2: Linear rate of excess pore pressure dissipation and set-up
Phase 3: Aging
Fig. 3.7. Ideali
47
Chapter 3. Literature review.
Fig. 3.8. Cavity expansion zones along pile (modified after Klar & Einav, 2003). Zone I – displaced soil moves at sides and slightly upwards; Zone II – displaced soil moves primarily radially (cylindrical cavity analogue). Zone III – displaced soil moves at sides and downwards (spherical cavity analogue).
Fig. 3.9. Comparison of measured and theoretical soil displacements due to pile penetration (after Randolph et al, 1979).
48
Chapter 4. Formulation of modelling approach.
4. FORMULATION OF MODELLING APPROACH.
4.1. INTRODUCTION.
A number of researchers addressed prediction of the pore water pressure response due to pile, or
cone penetration into fine-grained soils, as discussed in Chapter 3. The existing pore pressure
prediction solutions were specifically developed for conventional piles and piezocones. These
solutions are able to predict pore pressure generated by the pile, or cone, shaft. A helical pile
consists of the shaft and the helical plates attached to the shaft. As discussed in Chapter 2,
Weech (2002) argued that the helices had a significant effect on the generated excess pore
pressure. Therefore, existing pore pressure prediction solutions are not directly applicable to the
problem of helical pile installation.
The objective of this chapter is development of a simple modelling procedure for simulation of
helical pile installation within a framework realistically representing the behaviour of fine-
grained soil.
4.2. MODELLING APPROACH TO SIMULATION OF HELICAL PILE INSTALLATION INTO FINE-
GRAINED SOIL.
4.2.1. MODELLING FRAMEWORK.
There is a consensus of opinions in the reviewed literature: accurate prediction of pore pressure
response due to pile installation requires coupled analysis where a realistic soil model is
employed.
The volume changes in the silty-clay during and following pile installation influence the
magnitude and distribution of time-dependent pore pressure and effective stress. Therefore, it is
important that the chosen soil model generate realistic volume changes during shearing. A
generalized critical state based soil model, NorSand (Jefferies, 1993; Jefferies & Shuttle, 2002),
was adopted here to represent fine-grained soil stress-strain behaviour. In order to predict the
changes in stresses and pore pressure under partially drained conditions, an analysis that
accounts for the coupling between the rate of loading and the generation of fluid pressures is
required. The Biot consolidation theory (Biot, 1941) was used to incorporate the effect of the
coupling the pore pressure behaviour to the soil response.
49
Chapter 4. Formulation of modelling approach.
4.2.2. MODELLING PROCEDURE FOR SIMULATION OF HELICAL PILE INSTALLATION.
The following major aspects of pore water pressure response due to helical pile installation are
of interest in this study:
• excess pore pressure induced by helical pile installation;
• dissipation process of the induced excess pore pressure.
In the coupled numerical analysis dissipation of the excess pore water pressure is typically
automatically handled within the formulation. At the same time generation of the realistic excess
pore water pressure requires a special modelling procedure for simulation of the helical pile
installation. Conventional procedures for helical pile installation are outlined in Section 1.2.
Helical piles consist of the pile shaft and the helices attached to the leading section of the pile.
The mechanism of pore pressure generation induced by the helical pile shaft penetration is
similar to the one for conventional piles, discussed in Section 3.2. The mechanism of pore
pressure generation induced by the helical pile shaft penetration is much more complex. The
helices cut through the soil by a spiral trajectory generating a significant pulling force that
advances the helical pile shaft. As the helical plates move downward by one flight they displace
and release the volume of the soil equal to the volume of the plate. It should be noted that the
volume of the soil displaced by the helical plate is quite small in comparison to the volume
displaced by the pile shaft. Generally the pore pressures induced by the helices will be a
complex combination of the pore pressures generated by soil displacement, soil shearing and the
impact of the pulling force.
Due to such complexities a detailed simulation of helical pile penetration would require a 3-D
modelling approach, where the interaction between the rigid helical pile and deformable soil,
and the effect of the pulling force can be comprehensively addressed. This is theoretically
possible by employing a 3-D large strain Lagrangian finite difference analysis (e.g. FLAC 3-D).
This method may realistically represent the process of pile installation accounting for changes in
soil properties with depth and influence of the free soil surface. However, there are numerous
numerical difficulties involved in this process, including problems of formulation of the non-
linear contact interfaces between the pile tip and the soil (Klar & Einav, 2003). Additionally,
the problem of formulating the interface between soil and advancing helical plates, would make
the modelling process especially challenging.
50
Chapter 4. Formulation of modelling approach.
In this study we are primarily interested in the magnitude and trends of the generated excess pore
water pressure, rather than reproducing the exact mechanism of pore pressure generation. This
allows us to simplify the modelling of helical pile installation and ignore the 3-D effect.
Similarly to conventional piles, simulation of the helical pile shaft installation can be modelled using
the cylindrical cavity expansion analogy, described in Section 3.3.2.1. Penetration of the individual
helical plates can be modelled as an expansion of a cylindrical cavity over one flight, where the
expanded cavity volume is equivalent to the volume of the displaced soil, as shown in Fig. 4.1.
If such an approach is employed, considering the circular cross-section of the helical pile shaft,
cylindrical modelling of helical pile installation can be simplified to a 2-D axisymmetric problem.
For 2-D analysis the mesh could be set up so that the size of the elements in a vertical direction
is equal to one flight of the helical plate. In this case helical pile installation can be modelled as
shown in Fig. 4.2. This figure presents the helical pile shaft, modelled as expansion of a
cylindrical cavity, advancing each step downwards by the distance equal to one flight, at the
same time at the locations of the helices local cylindrical cavities are expanded. Each
consequent step as pile and helical plates move downwards by one flight, previously expanded
cavities, that correspond to the helices, are contracted up to pile shaft surface and the next set of
local cavities, corresponding to a new location of the helical plates and the shaft is expanded.
This procedure is executed until pile tip reaches its final position.
A 2-D simulation procedure can be further simplified if it is assumed that only radial
deformations and water flow have any significance. As discussed in Section 3.3.2.1 the
assumption of predominantly radial deformation is reasonable for modelling of conventional
piles penetration, hence the same assumption is valid for simulation of helical pile shaft. At the
same time penetration of helical plates may cause some vertical soil movement due to the
pulling force. The effect of the pulling force on the pore pressure magnitude is largely unknown
and could only be addressed within a full 3-D analysis.
In 1-D axisymmetric analysis the helical pile installation can be simulated with one row of finite
elements. Assuming that the left boundary of this row is adjacent to the central axis of helical
pile shaft and that the row is located within the pile penetration path (so that the pile tip and all
pile helices are passing through this location) helical pile installation can be modelled according
to the scheme shown in Fig. 4.3. In this figure the modelling location remains constant through
51
Chapter 4. Formulation of modelling approach.
out the simulation. Helical pile installation is simulated as helical pile shaft and helices passing
through the modelling location. First, penetration of a helical pile shaft is modelled. After a
pause equal to the time required for the first helix to reach the modelling location, a cavity
corresponding to the first helix is expanded and contracted. Following a pause necessary for the
second helix to reach the modelling location, a cavity corresponding to the second helix is
expanded and contracted. This cycle is repeated for each subsequent helix. Knowing the
geometry of the pile and the rate of pile penetration, the time spans for each modelling stage,
shown in Fig. 4.3, can be readily computed.
Overall, it appears that the main features of the pore pressure response induced by the helical pile
installation may be captured with the 1-D axisymmetric analysis, which offers a simple modelling
set up and fast computation times. Adding additional levels of complexity will likely refine the
modelling predictions, although significantly increasing the time necessary for the computation
and modelling set up. Considering these facts and following the logical progression rule “from
simple to complex”, a 1-D modelling approach was adopted for the current study.
4.3. NORSANDBIOT FORMULATION.
4.3.1. NORSAND CRITICAL STATE SOIL MODEL.
4.3.1.1. MODEL DESCRIPTION.
NorSand is a generalized Cambridge-type constitutive model developed from the fundamental
axioms of critical state theory and experimental data on sands. A description of the NorSand soil
model was published by Jefferies (1993), Shuttle & Jefferies (1998) and Jefferies & Shuttle (2005).
The brief outline of the NorSand model given here is largely based on these published accounts.
The work of Roscoe, Schofield & Wroth (1958) at Cambridge defined what was understood by
the term ‘critical state’, which led to the development of the framework of soil behaviour known
as ‘critical state soil mechanics’ (Schofield & Wroth, 1968). In critical state soil mechanics
(CSSM), the coupling of yield surface size to void ratio explains why and how soil behaviour
changes with density. Based on the CSSM framework several critical state soil constitutive
(Burland, 1965) and GrantaGravel (Schofield & Wroth, 1968). The term “constitutive model”
here implies an idealized mathematical relationship that represents the real soil behaviour.
These CSSM models were rarely applied for modelling sand behaviour, because of their
52
Chapter 4. Formulation of modelling approach.
inability to reproduce the softening and dilatancy observed in sands. This lead to the
development of CSSM models based on the state parameter ψ that accurately capture the effect
of dilatancy. NorSand was the first of these models.
Jefferies (1993) described the two fundamental critical state soil mechanics axioms and soil
idealizations taken as a basis for the NorSand model development.
Axiom 1: A unique locus exists in q, p, e space such that soil can be deformed without limit at
constant stress and constant void ratio; this locus is called the critical state locus (CSL).
Axiom 2: The CSL forms the ultimate condition of all distortional processes in soil, so that all
monotonic distortional stress state paths tend to this locus.
Basis assumptions of soil behaviour:
• a single yield surface exists in stress space at any instant;
• intrinsic cohesion between soil particles is absent;
• stress is coaxial with strain increment;
• associated flow, i.e. strain increment is normal to the yield surface.
The critical state axioms have been used to develop a general soil model that complies with the
axioms under all choices of initial conditions and with specific application to sand.
Many critical state soil models, such as CamClay, Modified CamClay and GrantaGravel, are
based on the assumption that any yield surface intersects the CSL. This provides the ability to
link the yield surface size with void ratio. However, this assumption is not necessarily valid for
real soils, which may exhibit infinity of normal consolidation lines (NCL), not parallel to the
CSL, as shown on the example of Erksak sand (Been & Jefferies, 1986) in Fig. 4.4. An infinity
of normal consolidation lines prevents the direct coupling between yield surface size and void
ratio, so that a separation between the state of the soil and overconsolidation ratio is required.
Generally, it is accepted that soil may exist in a number of states. Casagrande (1975) found that
during shear, soils experience volume change – they may exhibit either contractive or dilative
behaviour, until a critical state is reached at which point the soil continues to deform with no
volume change under constant stress and void ratio. State parameter ψ is a measure of the
current soil state, defined as the difference between the void ratio at the current state and the
void ratio at critical state at the same mean stress. Overconsolidation ratio, R, within NorSand
53
Chapter 4. Formulation of modelling approach.
represents the proximity of a stress state to its yield surface, when measured along the mean
effective stress axis. Conceptually this is demonstrated in Fig. 4.5.
NorSand has an internal cap, required for self-consistency of the model, so that the soil cannot
unload to very low mean stress without yielding. The internal cap is taken as a flat plane, and its
location depends on the soil’s current state parameter. Fig. 4.6 shows the NorSand yield surface
for a very loose sand. The location of the internal cap is dependent on the limiting effective
stress ratio ηL that the soil can withhold.
It should be noted that the presence of the internal cap means that once unloading has reached
about R ≈ 3, then the yield surface shrinks in size. However, the soil can remain dense and
ψ becomes more negative. This indicates that the one cannot directly compare NorSand with
standard views of the effect of overconsolidation without varying ψ. Broadly, for unloading a
normally consolidated soil to R ≈ 3, overconsolidation ratio R in NorSand is the same as R as
conventionally viewed. Thereafter, NorSand holds to R ≈ 3 and just becomes more negative in
ψ. This idea can be demonstrated by simulation soil unloading and computing variation of R
and ψ with changing mean effective stress. To simulate this is to compute two things: first, to
compute the void ratio change for a reduced mean stress via the swelling line from which the
new state parameter can be determined; second, allow the overconsolidation ratio to increase to
its limiting value (R ≈ 3) and then hold it at that. The example of soil unloading from p´=500
kPa shown in Fig. 4.7.
Considering the infinity of NCL, in accordance with the second critical state mechanic’s axiom,
the problem of coupling the yield surface size to void ratio is solved within NorSand by
introducing an incremental hardening rule - by defining an image of the critical state on the yield
surface and requiring that the image state become critical with shear strain. The idea of an
image state is based on the fact that, in general, yield surfaces do not intersect the critical state.
The critical state is achieved when dilatancy and rate of change of dilatancy is zero. Soil is at
the image state when former condition is satisfied and latter is not satisfied. The concepts of
image and critical stress are demonstrated in Fig. 4.6.
There is no closed form solution available for the NorSand model. The stress-strain relationship
is established by integrating stresses and strains increments. Mathematical representation of the
NorSand model is summarized in Table 4.1.
54
Chapter 4. Formulation of modelling approach.
Table 4.1. NorSand model formulation (all stresses are effective).
Internal Model Parameters
)ln( ppii λψψ += , where cee−=ψ
ii MM ψ−=
Critical State
( )pec lnλ−Γ= 2/)( MNMCc MMM +==η
where ( ) ( )( )θθ sin3/61cos/33 −+= tcMC MM
and ( ) ( )( ) 32
2
232
2
923
327sin4
3sin983
327
tctc
tc
MNMN
MN
MMM
MMM
+−
−=
−+−
−
θθ
Flow Rule η−= ip MD
Yield Surface & Internal Cap ⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
ii pp
Mln1η with ( )tciitc
i Mpp
,max
exp ψχ−=⎟⎟⎠
⎞⎜⎜⎝
⎛
Hardening Rule qii
i
ii
i
pp
MppH
pp
εχψ
&&
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −⎟⎟⎠
⎞⎜⎜⎝
⎛= 1expmod
Elasticity G, ν - constant (input parameters)
4.3.1.2. MODEL PARAMETERS.
The NorSand soil model requires 11 input parameters, shown in Table 4.2.
Table 4.2. NorSand code input parameters.
Material Properties Description
General G shear modulus ν Poisson ratio OCR ( R )1 overconsolidation ratio K0 coefficient of lateral earth pressure at rest σ′v0 vertical effective stress NorSand Mcrit critical state coefficient χ state dilatancy parameter ψ state parameter λ slope of CSL in e-ln(p) space Γ intercept of the CSL at 1 KPa stress Hmod hardening coefficient
1 – overconsolidation ratio is often referred to as OCR = σv max/σv which is not the same as R = pmax/p. The relation between them depends on K0, which tends to increase with OCR, however assuming that K0 is constant, both definition produce numerically identical results.
55
Chapter 4. Formulation of modelling approach.
The “general” set of parameters in Table 4.2 includes parameters common for geotechnical
analysis that require no additional introduction. Only parameters that are related to the variant
of NorSand soil model employed in the current analysis, are explained here:
• Critical state coefficient, Mcrit , describes the ratio between stresses at critical state and is
a function of Lode angle. For triaxial compression conditions, critical state coefficient is
directly related to friction angle at constant volume φ΄cv:
Mcrit(tc) = 6sin φ΄cv/(3-sin φcv) (4.3)
where φcv is usually determined from triaxial tests on loose samples.
• Parameters describing critical state line: λ - slope of CSL in e-ln(p) space; Γ - intercept
of the CSL at 1 KPa stress. Their definition is graphically shown in Fig. 4.5. Critical
state line is normally determined by a series of undrained triaxial compression tests.
• State Parameter, ψ, defines the state of the soil. It relates normal compression line with
the critical state line, as shown in Fig. 4.5. A positive state parameter indicates a loose
state (looser than critical state), or contractive soil; a negative state parameter indicates a
dense state (denser than critical state), or dilative soil.
• Hardening coefficient, Hmod , is a NorSand specific parameter that has similar meaning to
the rigidity index Ir, but for plastic strains. Generally, all hardening/softening models
have an equivalent to Hmod. In NorSand, the hardening coefficient is required because of
decoupling of the yield surface from the critical state line; it defines the extent of the
yield surface. Hmod is a function of the state parameter, usually derived by calibration of
the NorSand model to experimental data.
• State dilatancy parameter, χ, is also unique to NorSand, and is a function of soil structure
and fabric. Parameter χ is a proportionality coefficient between soil state and minimum
dilatancy:
Dmin = χ ψ i (4.6)
Usually, it is taken within a range 2.5 … 4.5, where the exact value can be found by
fitting the experimental data.
4.3.1.3. BEYOND SAND.
It is a misconception to associate the NorSand model explicitly with sands. Even though its name
suggests sand, NorSand model has no intrinsic limitations for application to fine-grained soils.
56
Chapter 4. Formulation of modelling approach.
Studying the effect of pore water pressure dissipation on pressuremeter test results, Shuttle
(2003) modelled a pressuremeter test in soft Bothkennar clay, employing the NorSand model
coupled with the Biot consolidation formulation. Input parameters for numerical simulation
were obtained by calibrating the model to the Bothkennar triaxial test data, as shown in Fig. 4.8.
Results of that study show that the NorSand model can be applied to fine-grained soils, showing
good agreement with the experimental data.
In the current study, validity of application of NorSand model to fine-grained soils was analysed
by modelling a series of drained constant p triaxial tests on Bonnie silt, carried out for the
VELACS1 project. An example of a NorSand model fit to the Bonnie silt data is shown in
Fig. 4.9. More NorSand fits along with the input parameters used in the analysis are provided in
Appendix C. All conducted simulations showed a very good agreement with the laboratory
triaxial data. It appears that NorSand model can represent fine-grained soil triaxial behaviour
very well, which is in agreement with the conclusions of Shuttle (2003).
gradually dissipate in time. During the dissipation process there is a link between changes in
pore pressure and soil stresses and vice versa. Realistic pore pressure dissipation prediction
methods should account for this relationship; such a theory was developed by Biot (1941).
Biot’s theory accounts for “solid to fluid” and “fluid to solid” coupling.
For the radial symmetry assumed in the current analysis, the Biot governing equation is given by:
tp
tu
ru
rk
rukK ww
rw
rw ∂
∂∂∂
∂∂
∂∂
γ−=⎥
⎦
⎤⎢⎣
⎡+
1'2
2
(4.7)
where: K′ - bulk modulus of the soil [kN/m2]; γw - unit weight of water [kN/m3]; uw - pore pressure [kN/m2]; kr - radial hydraulic conductivity [m/s] ; p - mean total stress [kN/m2]. r - radial distance [m]
Implementation of the NorSand model in conjunction with Biot consolidation requires two
additional parameters:
1 VELACS – Verification of Liquefaction Analysis with Centrifuge Studies
57
Chapter 4. Formulation of modelling approach.
- uo – initial pore pressure (the code is actually using the change in pore pressure);
- kr – hydraulic conductivity in radial direction.
4.3.3. FINITE ELEMENT IMPLEMENTATION OF NORSANDBIOT FORMULATION.
The current study employs a one-dimensional version of the large strain NorSandBiot code
developed by Shuttle (Shuttle & Jefferies, 1998; Shuttle, 2003).
The NorSand model was implemented within a 1-D finite element code using an incremental
viscoplastic formulation. Viscoplasticity (Zienkiewicz & Cormeau, 1974) is an approach for
representing plastic behaviour and its irrecoverable strains within the finite element method.
Accurate representation of plasticity is essential because irrecoverable strains are a fundamental
aspect of soil behaviour. This is particularly relevant to the problem of helical pile installation,
where existence of large irrecoverable volumetric strains is apparent. Although not typically
used with more complex soil models, the viscoplastic approach has the advantages of being both
simple and fast to converge (Shuttle, 2004).
The incremental viscoplastic formulation by Zienkiewicz & Cormeau (1974) was implemented
according to the general approach described by Smith & Griffith (1998). Description of the
code is given by Shuttle & Jefferies (1998). Flow chart illustrating the solution methodology is
presented in Fig. 4.10. Biot’s coupling was implemented using the structured approach
described in Smith & Griffiths (1998). The particulars of this implementation are presented in
Appendix D.
Finite-element mesh discretization was based on four node rectangular elements with linear
shape functions. It was necessary to include the vertical dimension in the finite element mesh
for self-consistency of the code, although no vertical stresses or deformations were allowed. In
addition to NorSand, the code also allows the analysis to be run with the Mohr-Coulomb and
Tresca soil models.
4.3.4. FINITE ELEMENT CODE VERIFICATION.
There are no analytical solutions available for cavity expansion within the NorSand soil model.
Therefore prediction of stresses and pore pressure by NorSandBiot code cannot be verified
directly. However correctness of particular aspects of the finite element code implementation
and predictions can be checked, as described below.
58
Chapter 4. Formulation of modelling approach.
Finite element implementation of the NorSand soil model was verified against direct integration
of the NorSand equations (see Section E.1, Appendix E). Simulation of cavity expansion was
verified using Mohr-Coulomb analysis in contrast with analytical solutions by Gibson &
Anderson (1961), Carter et al. (1986) and Houlsby & Withers (1988) (see Section E.2,
Appendix E).
Pore pressure dissipation prediction of the NorSandBiot code were verified against Schiffman’s
(1960) solution for 1-D consolidation with construction loading, (see Section E.3, Appendix E);
Overall, the verifications performed showed that NorSandBiot code produces correct stresses
and strains during cylindrical cavity expansion and is able to simulate pore water pressure
generation and dissipation process very well.
4.4. SUMMARY.
A realistic simulation of fine-grained soil requires partially drained analysis with both a fully
coupled modelling approach and a realistic soil model. NorSand critical state soil model was
chosen to represent the soil medium, the coupling between changes in stress-strain conditions
and the pore water pressure response is provided by Biot equations. A special modelling
procedure was developed to simulate helical pile installation using a cylindrical cavity
expansion analogue. The conducted verification of the finite element code showed excellent
agreement with existing analytical solutions.
59
Chapter 4. Formulation of modelling approach.
a).
b).
one flight (9.5 cm)
helical pile shaft
helical plate
Fig. 4.1. Schematic representation of 2-D modelling approach.
a). helix is represented as helical plate, with the volume equivalent to the v helix.
b). helical plate penetration is modelled as cylindrical cavity expansion, wh expanded volume is equivalent to the volume of the helical plate. For ax conditions - it is one half of the volume (Volume A on the figure).
60
Volume A
Volume A
olu
ereisy
1.54 cm
13.35 cm
0.9 cm
8.9 cm
me of the
mmetric
Chapter 4. Formulation of modelling approach. initial state 1st penetration step 2nd step 3nd step
Fig. 4.2. Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 2-D.
Fig. 4.3. Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 1-D.
Time
61
Chapter 4. Formulation of modelling approach.
Fig. 4.4. Normal compression lines from isotropic compression tests on Erksak sand (after Been & Jefferies, 1986).
Fig. 4.5. Definition of NorSand parameters Γ, λ, ψ, and R (modified after Jefferies, 1993).
62
Chapter 4. Formulation of modelling approach.
internal cap
CSL
Fig. 4.6. Definitions of internal cap, pi, pc, Mtc, Mi and ηL on yield surface (modified after Jefferies & Shuttle, 2005).
R = 3
0
5
10
15
20
25
30
0 50 100 150 200 250 300 350 400
mean effective stress: kPa
Ove
rcon
solid
atio
n ra
tio, R
NorSand state parameter
conventional representation of density by overconsolidation ratio
NorSand overconsolidation ratio
Fig. 4.7. Conventional and NorSand representation of overconsolidation rap′ = 500 kPa subject to decreasing mean stress.
63
for a very loose sand
450 500-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
stat
e pa
ram
eter
tio for soil initially at
Chapter 4. Formulation of modelling approach.
Fig. 4.8. NorSand fit to Bothkennar Soft clay in CK0U triaxial shear (after Shuttle, 2003).
64
Chapter 4. Formulation of modelling approach.
-2
-1
0
1
2
3
0 5 10 15 20axial strain: %
volu
met
ric s
train
: %
NorSand
Bonnie Silt CD BS-25
0
25
50
75
100
125
150
0 5 10 15 20axial strain: %
devi
ator
stre
ss, q
: kPa
NorSand
Bonnie Silt CD BS-25
0
20
40
60
80
100
120
0 20 40 60 80 1p, kPa
q, k
Pa
NorSand
Bonnie Silt CD BS-25
00
Fig. 4.9. NorSand simulation fit to constant p=80kPa drained triaxial test on Bonnie silt.
65
Chapter 4. Formulation of modelling approach.
* Read in material properties * Initialize original state * Define geometry & number of time steps * Define elastic stress-strain matrix, D * Set initial element stresses Loop number of steps * Iterations=0 * Null loads, excess loads (bodyloads), incremental strain ∆ε, incremental plastic strain ∆εp, stiffness matrix * Assemble BK stiffness matrix, using current coordinates * Add convected term to global matrix BK. * Fix nodal displacement at cavity wall to incremental displacement in BK * Invert stiffness matrix Loop Iterations * Fix displacement at cavity wall & outer boundary * Compute nodal displacements and pore pressures from {δ}=[K]-1{f} * Check whether yield criterion is reached Loop Elements * dε = B da total strain increment * dεe = dε - dεp elastic strain increment * ∆σ = D ∆εe elastic stress increment * σ = σstep-1 + ∆σ “new” stress * Update new yield surface Does element stress state exceed yield? No * continue to next element Yes
* calculate d vpε , increment viscoplastic strain rate .
* d d increment of viscoplastic strain this iteration dtvp vpε ε=.
Next Element Is there any elements on yield surface this iteration ? Yes * Continue to next iteration No * Recover element stresses and strains for all elements * Project stresses to cavity wall * Update radius in each element
* Update nodal coordinates * Output element stresses, strains, void ratio, etc. Next displacement increment (step)
Fig. 4.10. Flow chart for large strain numerical code (after Shuttle & Jefferies, 1998).
66
Chapter 5. Selection of site specific soil parameters for modelling.
5.0. SELECTION OF SITE SPECIFIC SOIL PARAMETERS FOR MODELLING.
5.1. INTRODUCTION.
In this study the numerical formulation developed in Chapter 4 is verified by modelling the field
experimental data obtained by Weech (2002) at the Colebrook helical pile performance research
site. Therefore the modelling input parameters should correspond to the Colebrook site soil
properties. We are interested in the properties within a region where the pore pressures were
monitored during helical pile installation. At the Colebrook site, pore pressure monitoring
equipment was located within a silty clay layer at elevations -4.57 … -9.92 m, see Fig. 2.2.
Hence, for the current analysis only the properties of silty clay for these elevations are analyzed.
Section 2.3 presented a brief overview of the site investigations by MoTH (reported by
Chapter 5. Selection of site specific soil parameters for modelling.
Fig. 5.1. Typical shear modulus reduction with strain level for plasticity index between 10% and 20% (after Sun et al., 1988) with the estimate for Colebrook silty clay (after Weech, 2002).
Fig. 5.2. Level of shear strain for various geotechnical measurements (after Ishihara, 1996).
81
Chapter 5. Selection of site specific soil parameters for modelling.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 5 10 15 20Small Strain Shear Mod
Elev
atio
n (m
)
SCPT-5 (Weech, 2002)
SCPT-7 (Weech, 2002)
Fig. 5.3. Variation of small strain shear modulus G2002).
82
MARINE CLAYEY SILT TO SILTY CLAY
Gmax= - 2.36(Elevation) + 1.9
25 30 35 40ulus - Gmax (MPa)
SCPT-6 (Weech, 2002)
Linear (Average Gmax)
max with elevation (modified after Weech,
Chapter 5. Selection of site specific soil parameters for modelling.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 100 200 300 400 500 600
Rigidity Index - Ir = G/su
Elev
atio
n (m
)
G(CPT-5)/Su(CPT-2)
G(CPT-6)/Su(CPT-1)
G/Su (CPT-7)
MARINE CLAYEY SILT TO SILTY CLAY
Fig. 5.4. Inferred variation of rigidity index with depth (after Weech, 2002).
83
Chapter 5. Selection of site specific soil parameters for modelling.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 5Shear
Elev
atio
n (m
)
SCPT-5 (Weech, 2002
SCPT-7 (Weech, 2002
Fig. 5.5. Variation of shear modulus G with
MARINE CLAYEY SILT TO SILTY CLAY
10Modulus -
)
)
elevation.
84
G = - 0.75(Elevation) + 2.375
15 20 G (MPa)
SCPT-6 (Weech, 2002)
Linear (Average G)
Chapter 5. Selection of site specific soil parameters for modelling.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
1 2 3 4 5 6 7 8Overconsolidation Ratio - OCR
Elev
atio
n (m
)
CPT-1 data. (Weech 2002)CPT-7 data. (Weech 2002)CPT-2 data. (Weech 2002)Lab Data (Crawford and Campanella 1988)Lab data (MoTH 1969)
zone 1OCR 3…7avg. OCR = 5
zone 2OCR 1.7…3avg. OCR = 2.35
zone 3OCR 1.2…2.2avg. OCR = 1.7
MARINE CLAYEY SILT TO SILTY CLAY
Fig. 5.6. Range of overconsolidation ratio OCR with elevation (modified after Weech, 2002).
85
Chapter 5. Selection of site specific soil parameters for modelling.
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 0.2 0.4 0.6
Coefficient of Later
Ele
vatio
n (m
)
MARINE CLAYEY SILT TO SILTY CLAY
Fig. 5.7. Variation of coefficient of earth pressure
OCR - CPT7, (Weech, 2002)OCR - lab data (Crawford & Campanella, 1991)OCR - lab data (MoTH, 1969)
K0 with elevation (modified after Weech, 2002).
Chapter 5. Selection of site specific soil parameters for modelling.
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
0.0001 0.001 0.01 0.1 1
Coefficient of Horizontal Consolidation - ch (cm2/s)
Elev
atio
n (m
)
CPTU - U2 (log T - T&H) - (Weech, 2002)CPTU - U2 (root T - T&H) - (Weech, 2002)CPTU - U3 (log T - T&H) - (Weech, 2002)CPTU - U3 (root T - T&H) - (Weech, 2002)CPTU U2 (root T - L&B) - (Crawford & Campanella, 1991)Lab Data - (MoTH, 1969)Lab Data -(Crawford & Campanella, 1991)
root T = "root Time" correction of Colebrook dissip. curveslog T = "log Time" correction of Colebrook dissipation curvesT&H = Teh & Houlsby (1991) solution for dist'n from SPML&B = Levadoux & Baligh (1986) solution for dist'n from SPM
MARINE CLAYEY SILT TO SILTY CLAY
Fig. 5.8. Variation in estimated coefficient of horizontal consolidation with depth (modified after Weech, 2002).
87
Chapter 5. Selection of site specific soil parameters for modelling.
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
0.0001 0.001 0.01 0.1 1
Coefficient of Horizontal Consolidation - ch (cm2/s)
Elev
atio
n (m
)
cor. CPTU - U2 (log T - T&H) - (Weech, 2002)cor. CPTU - U2 (log T - L&B) - (Weech, 2002)cor. CPTU - U2 (root T - T&H) - (Weech, 2002)cor. CPTU U2 (root T - L&B) - (Crawford & Campanella, 1991)Lab Data - (MoTH, 1969)Lab Data -(Crawford & Campanella, 1991)
root T = "root Time" correction of Colebrook dissip. curveslog T = "log Time" correction of Colebrook dissipation curvesT&H = Teh & Houlsby (1991) solution for dist'n from SPML&B = Levadoux & Baligh (1986) solution for dist'n from SPM
Fig. 5.9. Variation in estimated coefficient of horizontal consolidation with elevation with corrected CPTU derived values.
88
Chapter 5. Selection of site specific soil parameters for modelling.
Fig. 5.10. Variation of vertical effective stres
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 50
Vertical effect
Ele
vatio
n (m
)
MARINE CLAYEY SILT TO SILTY CLAY
σ′vo (kPa)= -8.0(Elevation) – 3.7
s with elevation.
89
100 150 200
ive stress σ 'v0 (kPa)σ΄vo (kPa)
Chapter 5. Selection of site specific soil parameters for modelling.
Fig. 5.11. Variation of equilibrium pore water pressure with elevation.
90
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
0 50 100 150 200
Equilibrium pore pressure u0 (kPa)
Ele
vatio
n (m
)
MARINE CLAYEY SILT TO SILTY CLAY
uo (kPa) = -10.2(Elevation) - 7.1
Chapter 5. Selection of site specific soil parameters for modelling.
-10
-9
-8
-7
-6
-5
-4
-3
0 0.2 0.4 0.6 0.8Slope of critical state line, λ
Elev
atio
n (m
)
based on Schofield & Wroth (1968) correlationapproximated from Cc reported by Crawford & Campanella (1991)
MARINE CLAYEY SILT TO SILTY CLAY
Fig. 5.12. Probable range of slope of critical state line, λ.
91
Chapter 5. Selection of site specific soil parameters for modelling.
0.000
0.500
1.000
1.500
2.000
2.500
3.000
1 10ln p' KPa
e
Lab data after Crawford and Campanella (1988)
densest state
average
loosest state
λ = 0.165
100
Fig. 5.13. Variation of void ratio with mean effective stress based on data reported by Crawford & Campanella (1991).
2.2
0.026
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
0 10 20 30 40 50 60 70 80 90 100
Mean effective stress, p, kPa
Ove
rcon
solid
atio
n ra
tio
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Stat
e pa
ram
eter
NorSand state parameter
NorSand overconsolidation ratio
p' = 42 kPa - average for elevations -4.57 … -9.92 m
Overconsolidation ratio for p' = 42 kPa
State parameter for p' = 42 kPa
Fig. 5.14. Variation of state parameter and overconsolidation ratio with mean effective stress.
92
Chapter 5. Selection of site specific soil parameters for modelling.
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35 40axial strain: %
devi
ator
stre
ss, q
: kPa
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30 35 40axial strain: %
volu
met
ric s
trai
n, %
Fig. 5.15. Simulation of drained triaxial test with NorSand model, using “base case” set of input parameters.
93
Chapter 5. Selection of site specific soil parameters for modelling.
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10axial strain: %
devi
ator
stre
ss, q
: kPa
12
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 6p, kPa
q, k
Pa
Stress PathCSL
0
Fig. 5.16. Simulation of undrained triaxial test with NorSand model, using “base case” set of parameters.
94
Chapter 6. NorSandBiot code parametric study.
6. NORSANDBIOT CODE PARAMETRIC STUDY.
6.1. INTRODUCTION.
In Chapter 4 a numerical NorSand-Biot formulation was introduced. An acceptable range of
site-specific soil parameters for modelling was established in Chapter 5. In this chapter a
parametric study using the NorSand-Biot finite element code is presented.
A parametric study is one of the essential components of a numerical analysis. Generally, a
parametric study may serve to:
• validate a formulation;
• indicate unrealistic simulated behaviour;
• evaluate sensitivity of parameter variation on modelled behaviour;
• detect critical criteria;
• suggest accuracy for calculating parameters;
• guide future data collection efforts.
In the current research, the NorSand-Biot code was validated against well-known closed form
solutions, as described in Section 4.3.4. Therefore, the focus of the parametric analysis
presented here is mainly to evaluate the sensitivity of the modelling results to the range of input
parameters previously given. Being more specific, in this chapter, sensitivity of the computed
pore water pressure response, including the magnitude of the generated pore pressure, radial
distribution and dissipation time, to the variation of values of the NorSand-Biot input parameters
is evaluated.
6.2. MODELLING PARTICULARS.
The 1-D parametric study was carried out by running NorSand-Biot on a one-row mesh of 50
elements, shown in Fig. 6.1. The boundary conditions of the analysis were as follows:
• displacements were allowed only in a radial direction;
• inner, top and bottom boundaries were set impermeable, so that there is no vertical flow
or gradient. The outer boundary was set permeable to allow radial flow.
• outer boundary was placed far enough from the inner boundary so that it had negligible
effect on the pore water pressure response.
95
Chapter 6. NorSandBiot code parametric study.
To examine the effect of variation of NorSandBiot input parameters on pore pressure response,
the pile penetration was modelled as a single cylindrical cavity expansion up to the helical pile
shaft radius. Simulation of the helices was omitted to simplify the analysis.
For realistic simulation, a cavity corresponding to the helical pile shaft, must be created from
zero initial radius. However, numerical modelling of a cavity with zero radius creates a problem
of infinite circumferential strain that would occur for an initial cavity radius of zero. Carter et
al. (1979) found that expanding a cavity from initial radius a0 to 2a0 can give the adequate
approximation to what happens in a soil when cavity is expanded from zero radius to r0, as
shown on Fig. 6.2. If both types of deformation occur at constant volume then relation between
r0 and a0:
00 a3 r = (6.1)
At the helical pile research site all helical piles had identical pile shaft radius Rshaft (r0) = 0.0445
m. From Eq. 6.1 the helical pile shaft can be modelled as a cylindrical cavity expanded to a
doubled initial radius, where the initial radius a0 = 0.0257 m.
For all simulations:
• cavity expansion was displacement controlled, where cavity was expanded up to 0.0257 m;
• cavity was expanded up to the final radius in 3.85 seconds (based on expansion rate 1.5 cm/s);
• simulations were continued until full dissipation of the induced pore water pressures;
• the length of the time steps was identical for all simulations;
• the change in pore pressure in the central gaussian point of the element closest to the pile
shaft (at r/Rshaft = 1.08) was studied.
6.3. REFERENCE RESPONSE.
Generally, the reference response is a response simulated with a set of parameters representing
average, or typical, behaviour. Such response is required in a parametric study to provide a
reference line of typical behaviour. The magnitude of deviation from this response may serve as
a measure of the influence of changing modelling conditions.
For the current analysis the reference response was obtained using the best estimate of
Colebrook silty clay properties established in Chapter 5, Table 5.4, also shown in Table 6.1 as a
“base case” scenario.
96
Chapter 6. NorSandBiot code parametric study.
The pore pressure response due to pile, or cone, installation is normally represented by pore
pressure distribution with distance and time. The same approach was adopted in the current
study. Pore pressure response, due to helical pile shaft penetration, simulated for the base case
input parameters, is presented in Fig. 6.3 and 6.4.
Fig. 6.3 shows excess pore pressure distribution with radial distance away from the expanded
cavity wall. On this plot, as on all following plots showing simulated pore pressure response,
the generated excess pore pressure was normalized by the vertical effective stress (vertical axis
∆u/σ′vo). This makes possible a direct comparison of numerical simulations with the field data.
All accounts found in the literature, related to studying of pore pressure response due to pile or
cone penetration, use normalized scale for representation of radial distance, where radial
distance is normalized by the radius of the penetrating body. Such representation allows direct
comparison of studies where different diameters of penetrating bodies are involved. The same
approach was adopted to represent radial distance in the current study (horizontal axis r/Rshaft).
From Fig. 6.3 it can be seen that the field of generated excess pore pressure at the end of cavity
expansion extended up to r/Rshaft = 20 and the maximum magnitude of normalized excess pore
pressure ∆u/σ′vo = 2.36. The shape of radial pore pressure distribution exhibits almost a linear
trend in a log scale.
Fig. 6.4 shows time dependent pore pressure response, where time is counted from the start of
cavity expansion. It should be noted that cavity expansion stage (first 3.85 seconds) are omitted
in this figure and only the pore pressure dissipation stage is shown. As follows in Fig. 6.4, the
generated excess pore pressure induced by cavity expansion fully dissipates after 11000 minutes
(~183 hours).
Fig. 6.5 and Fig. 6.6 show the stress path and variation of void ratio with mean normal effective
stress of the element adjacent to the cavity wall (identical abbreviations were used for both
figures). These figures provide a valuable insight into the complex stress-strain behaviour of the
medium during and after cavity expansion.
For the period of the initial stage of cavity expansion, deformations are elastic and the deviator
stress, q, increases with no change in mean normal stress (region AB, Fig. 6.5). As the cavity
expansion progresses the soil yields and deformations become irreversible. Because the soil is
soft and of low OCR, shear causes the soil to contract. This generates an increase in pore
97
Chapter 6. NorSandBiot code parametric study.
pressure, and as such, the mean normal effective stress decreases as the deviator stress increases.
This pattern continues until the stress path reaches the critical state line, where deformation
occurs under constant ratio of deviator to normal stress (region BC, Fig. 6.5). The soil yields to
failure at constant void ratio, indicating an absence of any volumetric strains, or fully undrained
behaviour (regions AB and BC, Fig. 6.6).
Interestingly, after failure is reached, an initial dilative response is observed (region CD, Fig. 6.5)
and then, at some point, the rate of dilation slows and eventually the response becomes contractive
(region DE, Fig. 6.5). This effect can be explained by the effect of partial drainage. For
simulations with higher hydraulic conductivity, where partial drainage is larger, such effect is
more significant, and is almost negligible when a lower hydraulic conductivity is assumed, as
demonstrated in Fig. 6.7. It should be noted that the overall effect of partial drainage on the
reference, or, base case pore pressure response is very insignificant.
At the end of cavity expansion, the pore pressure dissipates; it triggers a consolidation process in
the medium, when the void ratio is decreasing with dissipating pore pressure (region EF, Fig.
6.6). During the dissipation period, shear stress is diminishing, and then gradually rises with
decreasing pore pressure (region EF, Fig. 6.4).
The position of the critical state line shown in figures Fig. 6.5 and Fig. 6.6 (as in all other figures
in this chapter) is inferred. The actual slope of critical state line, Mcrit, depends on the Lode
angle and varies from triaxial expansion to triaxial compression.
6.4. PARAMETRIC STUDY SCENARIOS.
To study the sensitivity of the modelling results to variation of the input parameters, 23
scenarios were developed, as shown in Table 6.1, where shaded cells indicate parameters varied
in the particular scenario. The following parameters were varied in the sensitivity analysis:
• coefficient of earth pressure, K0;
• overconsolidation ratio, OCR;
• shear modulus, G;
• state parameter, ψ;
• intercept of the critical state line (CSL) at 1 kPa stress, Γ;
• slope of CSL in e-ln(p΄) space, λ;
• hardening modulus, Hmod;
98
Chapter 6. NorSandBiot code parametric study.
• critical state coefficient in triaxial compression, Mcrit;
• model parameter, χ;
• hydraulic conductivity in the radial direction, kr;
• Poisson ratio, ν.
Table 6.1. List of scenarios for NorSand-Biot formulation sensitivity analysis. Input Parameters
Varied Constant σ΄vo u0
1Scenarios K0
OCR
G MPa
ν
ψ
Γ
λ
Hmod
Mcrit
χ kr
m/s kPa base case 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0
For consistency, simulation scenarios 4, 5, 5a and 9, where input parameters were varied outside
the acceptable range for Colebrook silty clay, were not included in this rating. The NorSandBiot
parameter ranking presented here is site specific and strongly dependent on the assumed range
of parameters varied. It may represent only general trends applicable to other sites, where
position of particular parameters within the ranking may be slightly different.
111
Chapter 6. NorSandBiot code parametric study.
If we assume as significant, a change in pore pressure response in excess of ±10 percent of a
base case value, the variation of the following input parameters (shaded cells in Table 6.3) have
significant effect on pore pressure response:
• Measures of soil state (ψ & OCR) have predominant influence on the magnitude of pore
pressure response and the radial pore pressure distribution, and also, significantly affect
pore pressure dissipation time. This is consistent with the pore pressure response
observed in natural soils, where degree of soil overconsolidation is one of the governing
factors.
• Influence of hydraulic conductivity (kr) on pore pressure dissipation time is the most
significant among other parameters; even small variation in hydraulic conductivity
considerably effects the dissipation time.
• Ratio of lateral and vertical stress (K0) has major effect on both pore pressure magnitude
and the radial pore pressure distribution.
• Elastic properties also have an important influence on pore pressure response. Varying
the shear modulus (G) affects the extent of generated excess pore pressure and varying
the Poisson’s ratio (ν) influences pore pressure dissipation time.
In addition to the ranking of the NorSandBiot input parameters results of the parametric study
have another important implication – the variation of input parameters affects not only the pore
pressure response, but also the level of stress at the end of pore pressure dissipation.
Fig. 6.47 shows the locations of the final stress in q – p′ space, reached by the end of pore
pressure dissipation, in relation to the critical state line for parametric study simulations where
parameters were varied within the range acceptable for Colebrook silty clay, except for
scenarios 16 and 17, where the critical state line had a different slope in comparison to the other
studied cases. As follows from this figure, final stress values for the majority of simulations fall
within the small region C. Taking as a reference level of stress for the base case (located in the
centre of region C) the following observations of the influence of varying the model input
parameters on the level of final stress can be made:
• Variation of hydraulic conductivity (kr) , stress dilatancy parameter (χ) and slope of the
critical state line (Γ), in a studied range, have an insignificant affect on soil stress state at
the end of pore pressure dissipation;
112
Chapter 6. NorSandBiot code parametric study.
• Lowering elastic parameters (ν and G), horizontal stress (K0) and position of the critical
state line in e-log (p΄) space (Γ & λ) brings the final stress level closer to the critical state
line.
• The maximum variation in the final stress level is achieved by changing soil state
characteristics (ψ & OCR);
• Standalone variation of hardening modulus (Hmod) affects the level of deviator stress the
most.
Numerical modelling provides a valuable insight into the complex stress-strain response of a soil
and allows the separating out of the effects of change of different soil properties on the final
level of stress. The importance of this knowledge will be further elaborated in Section 7.3.2.
6.7. SUMMARY.
The conducted parametric study of the NorSand-Biot formulation shows that for majority of the
input parameters, variations within an acceptable range for the Colebrook site, established in
Chapter 5, does not have a significant affect on the calculated pore water pressure response. At
the same time, the computed pore water pressure response is very sensitive to the soil state
(represented in the NorSandBiot formulation by the state parameter, ψ, and overconsolidation
ratio, OCR) and its flow characteristic (represented by the hydraulic conductivity k). Also, such
parameters as lateral stress (represented by the coefficient of lateral earth pressure at rest, K0)
and soil elasticity (represented by shear modulus, G, and Poisson ratio, ν) have a major
influence on pore pressure response.
Results of the parametric study will be used in Chapter 7 as a guide to match modelled pore
pressure response, with the field measurements by Weech (2002).
113
Chapter 6. NorSandBiot code parametric study.
Fig. 6.1. FE Mesh for Parametric Study.
Fig. 6.2. Cylindrical cavity expansion from non-zero radius (after Carter et al., 1979).
114
Chapter 6. NorSandBiot code parametric study.
0
0.5
1
1.5
2
2.5
3
1 10r/Rshaft
∆u/
σ' v
o Edge of Helices Edge of Pile
100
Fig. 6.3. Radial distribution of generated excess pore water pressure at the end of cavity expansion for “base case” scenario.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.1 1 10 100 1000 10000 100000
Time (min)
∆u/
σ' vo
dissipation stage starts at ~0.064 min
Fig. 6.4. Time dependent pore pressure response at cavity wall for “base case” scenario.
115
Chapter 6. NorSandBiot code parametric study.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 1
p', kPa
q, k
Pa
AAE - cavity expansion AB - region of elastic deformations BC - yielding up to failure CD - failure corresp. to dilative response DE - failure corresp. to contractive responseEF - consolidation
E
D
B
F
C
CSL
20
Fig. 6.5. Stress path for “base case” scenario.
1.245
1.25
1.255
1.26
1.265
1.27
1.275
10 100p', kPa
e
A
E
D
B
F
CCSL
Fig. 6.6. Variation of void ratio, e, with mean effective stress, p′ for “base case” simulation.
116
Chapter 6. NorSandBiot code parametric study.
Fig. 6.7. Variation of e with p′ for “base case”, 20 & 21 scenarios.
0
0.5
1
1.5
2
2.5
3
1 10r/Rshaft
∆u/
σ' vo
Edge of Helices
Edge of Pile
A - Base Case. Ko = 0.66B - Sc.1 Ko = 0.56C - Sc.2 Ko = 0.76
BB
C
A
CA
C A
B
1.245
1.25
1.255
1.26
1.265
1.27
1.275
10 100p, kPa
e
A - Base case: k = 2.1e-9 m/sB - Sc. 20: k = 2.1e-10 m/sC - Sc. 21: k = 3.1e-9 m/s
A
C
B
C
A
B
100
Fig. 6.8. Effect of K0 on radial distribution of generated excess pore pressure at the end of cavity expansion. Fig. 6.8. Effect of K0 on radial distribution of generated excess pore pressure at the end of cavity expansion.
117
Chapter 6. NorSandBiot code parametric study.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.1 1 10 100 1000 10000 100000Time (min)
∆u/
σ' vo
A - Base Case. Ko = 0.66B - Sc.1 Ko = 0.56C - Sc.2 Ko = 0.76
95 % dissipation lines
B
C
A
AB C
95 % dissipation lines B A C
95 % dissipation time
Fig. 6.9. Effect of K0 on time dependent pore water pressure response at cavity wall.
120 Fig. 6.47. Location of final stress state in q-p′ space, at the end of pore pressure dissipation, in relation to critical state line. (AB - line parallel to the critical state line, crossing final stress state
Fig. 7.11 compares the pore pressure responses measured in the field during installation of helical
piles with 3 and 5 helices, and the responses obtained from simulation of helical pile installation as
a series of cavity expansions/contractions cycles for Case A (see Fig. 7.9). The mismatch between
the magnitude of measured and modelled responses observed in this figure is quite significant.
Cavity contraction causes an effect similar to suction, with the excess pore pressure dropping by
about 300% compared to the value reached during helix expansion. This is a major exaggeration
in comparison with the field data, where the measured pore pressure decrease after helical plate
penetration never exceeded 100% of a previously generated value.
However, although the magnitude of the simulated and observed pore pressures shown in Fig. 7.11
are not a good match, the trends in pore pressures are more similar. Fig. 7.11 exhibits a clear trend
of gradual pore pressure build up during cavity expansion/contraction cycling, which is in agreement
with the pore pressure response observed in the field. Field data shows that penetration of the first
(bottom) helix induces a major pulse in pore pressure response, whereas penetration of the
subsequent helices causes only a gradual pore pressure increase. These effects were not
reproduced, likely due to the excessive pore pressure drop during cavity contractions.
Simulation of the helical pile installation, where expansions/contractions of the cavities
corresponding to the helices were based on Case B (see Fig. 7.9), is shown in Fig. 7.12 and
generally mirrors the effects described for Case A, but on a smaller scale.
Overall, the simulation of helical plate penetration using cavity/expansion contraction cycles is
able to capture the general trend of pore pressure response. However, the proposed scheme of
helical plate penetration modelling tends to overestimate the effect of unloading, and as a result
148
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
there is a significant mismatch between predicted and measured pore pressures near the cavity
wall at the end of helical pile installation. This limitation should be considered when analyzing
the modelling results. The fact that the purpose of the modelling presented here is not the exact
fitting of the pore pressure at the pile wall, but rather capturing general trends observed in the
field and producing reasonable response predictions also should be considered.
Fig. 7.13 shows a comparison between the radial pore pressure distribution at the end of helical
pile installation, for simulations with and without helices, and the field measurements. Based on
this figure the following observations related to the effect of the simulated helices on radial pore
pressure distribution can be made:
1). The presence of the helices (cavity expansion/contraction cycles) extends the zone of excess
pore pressure generated during shaft penetration (expansion of a single cavity). The amount of
this increase is dependent on the length of the helix at its maximum extent (the magnitude of the
cavity expansion). It can be seen that cavity expansion/contraction cycles with smaller
magnitudes (Case B) have practically no influence on the maximum extent or radial pore pressure
distribution r/Rshaft = 38, whereas cavity expansion/contraction cycles with greater magnitudes
(Case A) extend the zone of generated excess pore pressure up to r/Rshaft = 70, which is very close
to the observed in the field r/Rshaft = 65. For both cases, the maximum extent of the generated
excess pore pressure is reached during the first helix expansion and is not altered by the
subsequent cycling.
2). The magnitude of radial pore pressure distribution at the end of cavity expansion/
contraction cycles is significantly diminished in the immediate vicinity of the shaft. The larger
the length of the expanded/contracted cavities the bigger the drop in pore pressure (see Cases A
and B in Fig. 7.10). Also, it appears that the pore pressure decrease in this area is dependent on
the number of expansion/contraction cycles, so that a higher number of cycles is associated with
a larger drop in pore pressure (see Case A with 3 and 5 helices).
3). Both Case A and Case B simulations show distinctive peaks in generated excess pore
pressure at some distance from the cavity wall (for Case A - r/Rshaft = 21; for Case B - r/Rshaft =
6.6). Beyond these peaks the trend of pore pressure distribution appears to be in good
agreement with the pore pressure response simulated by expansion of a single cavity and the
field measurements.
149
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
Further understanding of the pore pressure changes induced by the helices may be gained by
examining the process of pore pressure response during cavity expansion/contraction cycling.
Fig. 7.14 shows the mechanism of pore pressure generation during expansion of the cavity
corresponding to the first helix, for Case A. It can be seen that gradual pore pressure increase is
observed during the whole period of expansion of the cavity corresponding to the first (bottom
helix). At the end of helix cavity expansion, the pore pressure is increased both in magnitude
and radial extent. The new shape of the pore pressure distribution is nearly parallel to the
response simulated with a single cavity expansion and provides a reasonably good agreement
with the field measurements. After the expanded cavity has reached its full extent, it is
contracted back to the pile shaft boundary. The mechanism of pore pressure response during
this process is shown in Fig. 7.15. As cavity contraction progresses, pore pressures are
significantly diminished, reaching at 100% contraction a distribution similar to the one shown in
Fig. 7.13. It should be noted that more than 80% of the pore pressure drop was observed before
50% of the cavity contraction was reached. The effect of continuing expansion/contraction
cycling for simulation of installation of helical pile with 5 helices is shown in Fig. 7.16. As
follows from this figure, at the end of each subsequent expansion or contraction, the pore
pressure magnitude is gradually increasing. There appears to be a threshold at r/Rshaft = 21
beyond which subsequent cavity expansion/contractions cycles have no substantial impact on
the pore pressure generated during the expansion of the cavity, corresponding to the first helix.
The zone of influence of cavity contraction is three times smaller than the area affected by
cavity expansion (maximum extent of generated excess pore pressure is observed at
r/Rshaft = 70). Fig. 7.17 shows that a reduction in the number of cycles given the same cavity
expansion/contraction magnitude does not change the trends observed in Fig. 7.16. The pore
pressure response for smaller expansion/contraction magnitudes (Case B), shown in Figs. 7.18
and 7.19, confirms the overall trends observed for Case A.
Time dependent pore pressure responses at the cavity wall for Case A and Case B simulations
with 3 and 5 helices are shown in Fig. 7.20 - 7.23. From these figures we can infer the following:
1). Cavity expansion/contraction cycling significantly alters the pore pressure magnitude in the
close vicinity of the cavity wall. Pore pressure magnitude at the end of the cycling is a function
of the number of cycles and the length of the expanded cavity, so that maximum pore pressure
150
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
alteration is observed for simulation with the lengthiest cavity expansion and the fewer number
of expansion/contraction cycles (Case A with 3 helices, shown in Fig. 7.21).
2). After the end of the expansion/contraction cycling some recovery of altered pore pressure is
observed, so that an additional peak in pore pressure response is clearly visible. The magnitude
of “recovered” pore pressure is the largest for the simulation with the fewer expansion
contraction cycles and smaller length of cavity expansion (Case B with 3 helices, Fig. 7.23). It
appears that that the observed pore pressure recovery is related to the pore pressure
redistribution after the end of cycling.
3). Interestingly, despite significant pore pressure alteration after expansion/contraction cycling
all simulations showed reasonable dissipation time predictions. However, none of them improve
prediction of the pore pressure dissipation time obtained from simulation of the helical pile shaft
installation (marked as “shaft only on the figures). Dissipation trends for both Case B
simulations (see Fig. 7.22, 7.23) join with the “shaft only” trend at about 1000 minutes. For
Case A simulations (see Fig. 7.20, 7.21) dissipation time for 95 % dissipation is slightly longer
than for the “shaft only” case.
The effect of cycling on stress level and void ratio variation, for the Case A with 5 cavity
expansion/contraction cycles, is shown in Figs. 7.24 and Fig. 7.25. It can be seen that during cycling
(region C in both figures) the stress path is moving along the critical state line, as schematically
shown for the first expansion/contraction cycle in Fig. 7.24. Cavity expansion corresponding to the
first helix causes yielding of the medium and contractive response (corresponding to decrease in
void ratio in Fig. 7.25) is observed. As the cavity is contracted it causes dilation (corresponding to
increase in void ratio in Fig. 7.25) and the stress path moving back towards and even slightly beyond
the point where the cavity expansion had started, which eventually leads to some stress level
increase (see point B and D on the figure). During a pause between cycling pore pressure begins
to dissipate and the stress path is moving away from the critical state line exhibiting some decrease
in shear stress. As the next cavity expansion begins, yielding of the medium quickly brings the
stress path to the critical state line and the pattern described for the first expansion/contraction
cycle is repeated. After the end of cycling, as pore pressures dissipate (region DE), shear stress
decreases and eventually begins to increase close to the end of the dissipation process.
Comparison of the stress paths for simulations of single cavity expansion with “base case” and
“best fit” input parameters, and Case A simulation with 5 cavity expansion/contraction cycles is
151
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
shown in Fig. 7.26. The quantitive comparison of the final level of stress for this simulation is
provided in Table 7.6.
Table 7.6. Final stress state for “base case”, “best fit” and Case A simulation with 5 helices.
Stress, kPa Simulation with “base case” parameters
Simulation with “best fit” parameters
Case A simulation with 5 helices
q 45.2 17.3 7.5 p′ 102 57.2 30.9
The following observation can be made from Fig. 7.26 and Table 7.6:
• Given the same initial conditions the final level of stress appears to be very different
depending on a choice of input parameters and simulation particulars. Generally for
simulations with the sensitive set of parameters (“best fit” and Case A), the final stress
level is much lower than for the simulation with non-sensitive parameters (“base case”).
The maximum reduction is observed for the shear stress q.
• Expansion/contraction cycling significantly reduces the mean normal effective stress, so
that after five such cycles q is reduced by 57% and p′ by 46%.
• In terms of proximity to the critical state line, the simulation with the cycling resulted
final stresses closest to the critical state line and the lowest p′.
The modelling described so far was based on the Assumption 1. Simulations based on this
assumption provided reasonably good pore pressure response predictions and were able to
capture general trends of the field behaviour. The major limitations of this assumption,
discovered during the modelling, lies in its inability to produce a reasonable simulation of helix
unloading, resulting in poor predictions of the pore pressure magnitude at the pile wall.
In Section 7.2.2.1 an alternative assumption (Assumption 2) that allowed the formation of a gap
between the pile wall and soil was discussed. Due to the anomalously low pore pressure generated
at the pile wall, Assumption 2 is investigated further. Fig. 7.27 shows a comparison of the pore
pressure generated due to the first helix penetration (expansion/contraction cycle) for Case A with
5 helices simulation based on different assumptions of soil/cavity interface boundary conditions
during unloading and the corresponding field measurements. As follows from this figure, fixed
soil/cavity interface (Assumption 1) significantly diminishes the pore pressure generated during
the helix expansion. This is likely related to the stress relief in the zone adjacent to the cavity
wall, which is triggering suction, resulting in the pore pressure drop. Simulation based on this
152
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
assumption correspond to the general trend of pore pressure drop during unloading observed in the
field, although exaggerates this effect severely. At the same time no substantial changes in the
pore pressure during cavity contraction is shown by the simulation where the soil was left to
rebound freely (Assumption 2). This indicates absence of any plastic deformations.
In reality when the penetrating helical plate releases the displaced volume of the soil some
plastic yielding, stress relief and some pore pressure suction are likely to occur. Assumption 2 is
unable to replicate these effects, whereas Assumption 1 exaggerates them. It appears that the
field pore pressure response can potentially be fitted by assuming smaller degree of unloading
for Assumption 1. As the purpose of the analysis was not to achieve an exact fit to the field
data, this approach was not pursued since it will not yield any additional insights into the
complex pore pressure response induced by the helices.
Summarizing the section’s findings we should emphasize the following:
• introduction of the helices extends the zone of generated excess pore pressure;
• assumption of a fixed soil/cavity interface exaggerates the effect of helices unloading
leading to underprediction of the pore pressure magnitude at the cavity wall;
• NorSandBiot code is able to capture observed field trends of the pore pressure response
induced by the helices
• conducted simulations provided an interesting insight into the complex pore pressure and
stress response of the fine-grained soil;
7.3. IMPLICATIONS FROM 1-D MODELLING.
7.3.1. PREDICTED VERSUS MEASURED/INTERPRETED PORE PRESSURE RESPONSE.
A comprehensive field study of helical pile performance in sensitive fine-grained soils,
conducted at Surrey, British Columbia, by Weech (2002) provided an initial framework of
expected soil response and served as a reference point for the current numerical study. Having
completed the modelling, we may now specifically address some of the observations and
propositions made during the field study:
Weech (2002) observed that excess pore pressures generated by the penetration of the helical
pile shaft appear to be significant (∆u > 0.1σ΄vo) out to a radial distance of at least 17 shaft radii
153
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
from the centre of the pile, which is in a close agreement with the modelling carried out at
Stage I of the current analysis. The simulation of expansion of a single cavity predicted the
generation of significant (∆u > 0.1σ΄vo) excess pore pressure for the “base case” set of input
parameters out to a radial distance of 15 shaft radii. The simulation with the “best fit” set of
parameters showed a similar effect to a radial distance of 18 shaft radii (see Fig. 7.4).
It was also observed during the field study that at the end of helical pile installation, elevated
pore pressures are generated out to radial distance of 65 shaft radii or greater. This is in good
agreement with the results of the Stage II modelling where simulation of the helical pile
installation as a series of cavity expansions predicted the generation of pore pressures out to 70
shaft radii (see Fig. 7.13).
Field observations indicated that the number of penetrating helical plates does not have a major
impact on the pore pressure magnitude at the shaft. The first penetrating helix produces the
maximum impact on this magnitude. The modelling partially supports this, as shown in Fig.
7.16 and Fig. 7.17 with each subsequent cavity expansion slightly increasing the pore pressure
magnitude. However, the increase in the magnitudes of excess pore pressure from each
subsequent cavity expansion is nearly identical. The modelling does not consider the effect of
altering soil properties during penetration of the helices; therefore the distinguishable effect of
the first helix cannot be reproduced.
Based on the field observations Weech (2002) argued that there appears to be a gradual outward
propagation of pore pressures induced by the helices during continuing pile penetration, which is
attributed to the total stress redistribution effects. 1-D modelling results partially confirm this
hypothesis, as can be seen in Fig. 7.16 near the edge of the helices (at r/Rshaft = 8 … 20) where a
pore pressure build up and gradual radial propagation with each subsequent
expansion/contraction cycle is observed. At the same time the maximum extent of the radial
pore pressure distribution appears to be unaffected by the cycling. Pore pressures reach their
maximum extent during the first cycle and penetration of the subsequent helices does not
advance or alter the extent of the pore pressure distribution zone.
It appears that the vertical component neglected in 1-D modelling may be a significant factor
affecting the mechanism of pore pressure distribution due to penetration of the helical plates. 2-
D modelling is required to confirm this idea.
154
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
7.3.2. FROM PORE PRESSURE RESPONSE PREDICTIONS TO PILE BEARING CAPACITY.
To date, the ability of current geotechnical practice to accurately predict pile capacity for all pile
types is limited. According to the recent Rankine Lecture presented by Randolph (2003):
“… despite continuous advances in approaches to pile design, estimation of (axial) pile
capacity - relies heavily upon empirical correlations. Improvements have been made in
identifying the processes that occur within the critical zone of soil immediately
surrounding the pile, but quantification of the changes in stress and fabric is not
straightforward”.
It appears that numerical solutions may offer the necessary means to overcome these problems.
As shown in Chapter 6 and in the current chapter, fully coupled NorSandBiot formulation
provides a valuable insight in the pore pressure and stress response during and after helical pile
installation.
One important factor controlling the pile’s capacity is the long-term effective stress at the pile-soil
interface and around the helices. This stress is controlled by the evolution of pore pressures and
effective stress during pile installation and subsequent pore pressure dissipation. For all piles, and
particularly helical piles where less case history data exists, an ability to accurately predict and
understand the evolution of effective stress and pore pressures at the pile wall would provide a basis
for accurate pile design. As shown in Section 7.2.1.2, the variation of effective stresses with pore
pressure dissipation can be readily estimated using the NorSandBiot formulation. No measurements
of total stress during and after helical pile installation were taken at the Colebrook site, so direct
comparison of the modelling results and the fields measurements is not possible. However,
comparison of simulations with sensitive and non-sensitive sets of input parameters showed a good
agreement with the trend observed at the other sites by Lehane & Jardine (1994).
The modelling process is not without challenges: depending on the choice of the modelling input
parameters, the predicted response varies significantly. As shown in the parametric study, even
a small variation of some of the input parameters may have a large impact on the modelling
predictions. Even if the pore pressure at the cavity wall following pile installation was correctly
estimated, the time-dependent magnitude of the lateral stresses and pore pressures over time can
be very different, as discussed in the paper by Vyazmensky et al (2004) given in Appendix F.
This highlights the importance of good engineering judgement while establishing input
parameters for modelling and interpreting the numerical simulation results.
155
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
7.4. SUMMARY.
Within a framework of the NorSandBiot formulation two conceptual approaches to the
modelling of the helical pile in 1-D were considered in the present study:
I. Modelling of the helical pile as a single cylindrical cavity expansion;
II. Modelling of the helical pile as a combination of a single cylindrical cavity
expansion and series of additional cylindrical cavity expansion/contraction cycles.
It has been shown that, provided a careful selection of input parameter values applicable to the
Colebrook site, single cavity expansion produced quite accurate prediction of the pore pressure
dissipation time and satisfactory estimate of pore pressure distribution at the end of helical pile
installation observed by Weech (2004).
Introduction of the expansion/contraction cycles (helices) on top of a single cavity expansion
helped to improve prediction of the maximum extent or the radial pore pressure distribution and
the pore pressure dissipation time. Assumption of a fixed soil/cavity interface during cycling,
exaggerated the effect of helices unloading leading to underprediction of the pore pressure
magnitude at the cavity wall and its immediate vicinity. Although, at greater distances the
modelling was able to capture effectively general trends of pore pressure behaviour measured in
the field, including gradual pore pressure build up and outward propagation during penetration
of the helices.
Largely, given the complexity of the modelled process and taking into account the major
simplifications involved in the analysis, overall results of the Stage I and Stage II modelling
were more than satisfactory.
The conducted modelling proved that as a fully coupled formulation, NorSandBiot is able to
provide a realistic framework for studying complex response of fine-grained soils. Applying
numerical methods to the analyse of the soil behaviour observed at the Colebrook site allowed
for valuable insights to be gained into the nature of changes of pore pressures during and after
helical pile installation.
The modelling confirmed many of the field observations and propositions made by Weech
(2004). At the same time some of them may not be fully confirmed or dismissed until additional
levels of complexity to the modelling are added, in particular the effect of soil remoulding and
the effect of deformations and drainage in the vertical direction.
156
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
In addition the modelling showed that sensitivity has a large effect on the equalized lateral
effective stress ratio σ′h/σ′v0, which is in agreement with findings of Lehane & Jardine (1994).
This is an important step towards ability to predict lateral stress and pile capacity with
reasonable degree of accuracy.
157
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1 .2
1 .4
1 .6
1 .8
2
2 .2
2 .4
2 .6
Weech (2002) average field data S t = 6…24
NorSandBiot simulation withbase case parameters, S t = 1
Fig. 7.1. Radial pore pressure distribution at the end of pile installation reported by Levadoux & Baligh (1980), measured by Weech (2002) and simulated with “base case” parameters.
0.0
0.5
1.0
1.5
2.0
2.5
1 10 100 1000 10000 100000Time (min)
∆u/
σ' vo
Weech (2002) average field data (from piezoelements located below helices)
95 % dissipation lines
Weech (2002)
NorSandBiot simulation with base case input parameters
base case
Fig. 7.2. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with “base case” parameters.
158
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
A
0
20
40
60
0 2 4 6 8 10 12axial strain: %
q, k
Pa
b
best fit parameters (St = 2.4)best fit (St = 2.4; su = 15.1 kPa)
ase case parameters (St = 1)base case (St = 1; su = 22.6 kPa)
B
0
20
40
60
80
0 10 20 30 40 50 60p', kPa
q, k
Pa
best fit parameters (St = 2.4)
base caseparameters (St = 1)
critical state lineMcrit = 1.33
critical state lineMcrit = 1.243
Fig. 7.3. Comparison of modelled undrained triaxial response for ”best fit” and “base case” sets of NorSandBiot input parameters.
A – Variation of deviator stress with axial strain. B – Stress paths.
159
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1 .2
1 .4
1 .6
1 .8
2
2 .2
2 .4
2 .6
Weech (2002) average field data S t = 6…24
NorSandBiot simulation withbase case parameters, S t = 1
NorSandBiot simulation with best fit parameters, S t = 2.4
Fig. 7.4. Radial pore pressure distribution at the end of pile installation reported by Levadoux & Baligh (1980), measured by Weech (2002) and simulated with “best fit” parameters.
0.0
0.5
1.0
1.5
2.0
2.5
1 10 100 1000 10000 100000Time (min)
∆u/
σ' vo
NorSandBiot simulation with best fit parameters
Weech (2002) average field data (from piezoelements located below helices) 95 % dissipation lines
Weech (2002)
NorSandBiot simulation with base case input parameters
best fit base case
Fig. 7.5. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with “best fit” parameters.
160
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
1.68
1.99
1.171.11
0.30
2.09
0.0
0.5
1.0
1.5
2.0
2.5
1 10 100 1000 10000Time (min)
∆u/σ 'vo
& σ 'h/σ 'vο
Best fitBase Case
Pore Pressure
Lateral Effective Stress
Fig. 7.6. Comparison of ∆u/σ′v0 and σ′v/σ′v0 vs. time for “best fit” and “base case” simulation and the field measurements.
0
5
10
15
20
25
30
0 10 20 30 40 50 60 7p', kPa
q, k
Pa
AC - cavity expansion AB - failure towards critical state line BC - failure along critical state lineCD - pore pressure dissipation
A
B
CD
initial state
end of cavity expansion
0
Fig. 7.7. Stress path plot for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation of helical pile shaft installation with “best fit” parameters.
161
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
1.358
1.36
1.362
1.364
1.366
1.368
1.37
1.372
1.374
10 100p', kPa
einitial state
end ofcavityexpansion
A
B C
D
AC - cavity expansion AB - failure towards critical state line BC - failure along critical state lineCD - pore pressure dissipation
Fig. 7.8. Void ratio versus mean stress (e – ln(p΄)) plot for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation with “best fit” parameters.
162
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
Case A pile shaft helix
Case B pile shaft helix
1.54 cm
2.57 cm 4.74 cm
Fig. 7.9. Modelling cases considered in the analysis of the effect of the helices.
Shaft + 3 Helices Shaft + 5 Helices
A B A Btime
3.85 3.85 3.85 3.85
6.3 6.3 P P 6.3 6.3
3.16 1.03 3.16 1.03
3.16 1.03 3.16 1.03
P 30.3 30.3
3.16 1.03
3.16 1.03
P 30.3 30.3
3.16 1.03 3.16 1.03
3.16 1.03 3.16 1.03
P 30.3 30.3
3.16 1.03
3.16 1.03
P 30.3 30.3
3.16 1.03 3.16 1.03
3.16 1.03 3.16 1.03
Legend: pile shaft expansion
pile shaft contraction
P pause in installation
helix expansion
helix contraction
time, sec
P
case case
62.766.9
66.9 62.7
time, sec
P
Fig. 7.10. Modelling algorithm of helical pile installation in 1-D.
163
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 50 100 150 200 250 300
Time (sec) after pile tip passed piezometer location
Simulated response:Case A. Shaft + 5 helices (r/Rshaft = 4.8)
a
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 50 100 150 200 250 300
Time (sec) after pile tip passed piezometer location
∆u/σ
' vo Measured response:
piezometer PZ-TP3-1(r/Rshaft = 5.8)
Simulated response: Case A. Shaft + 3 helices (r/Rshaft = 5.8)
b
Fig. 7.11. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case A).
(a) – for helical pile with five helices; (b) – for helical pile with three helices.
164
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 50 100 150 200 250 300
Time (sec) after pile tip passed piezometer location
Simulated response:Case B. Shaft + 3 helices (r/Rshaft = 5.8)
b
Fig. 7.12. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case B).
(a) – for helical pile with five helices; (b) - for helical pile with three helices.
165
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 10 100r/Rshaft
∆u/σ
' voaverage field data (fitted curve)shaft onlyshaft + 5 helices (Case A)shaft + 3 helices (Case A)shaft + 5 helices (Case B)shaft + 3 helices (Case B)
Edge of Pile
Edge of Helicesfor Case B
Edge of Helicesfor field data
r/Rshaft = 21
r/Rshaft = 6.6
Edge of Helicesfor Case A
Fig. 7.13. Comparison of radial pore distribution for simulations with and without helices and the field measurements.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 10r/Rshaft
∆u/σ
' vo
average field data - end of pile installation
shaft only - end of expansion
5% of 1st helix expansion
20% of 1st helix expansion
50% of 1st helix expansion
100% of 1st helix expansion
direction of pore pressure riseduring expansion of first helix
Edge of Helicesfor field data
Edge of Helicesfor Case Asimulations
Edge of Pile
100
Fig. 7.14. Radial pore pressure distribution during first helix expansion (Case A).
166
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
Fig. 7.15. Radial pore pressure distribution during first helix contraction (Case A). Fig. 7.15. Radial pore pressure distribution during first helix contraction (Case A).
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1 10
r/Rshaft
∆u/σ
' vo
end of 1st helix expansionend of 1st helix contractionend of 2nd helix expansionend of 2nd helix contractionend of 3rd helix expansionend of 3rd helix contractionend of 4th helix expansionend of 4th helix contractionend of 5th (last) helix expansion end of 5th (last) helix contr.shaft only - end of expansion
Edge of Helicesfor field data
Edge of Pile
Edge of Helicesfor Case Asimulations
-0.5
0
0.5
1
1.5
2
1 10 100
r/Rshaft
∆u/σ
'vo
average field data - end of pile instal.
shaft only - end of expansion
100% of 1st helix expansion
5% of 1st helix contraction20% of 1st helix contraction
50% of 1st helix contraction
100% of 1st helix contraction
Edge of Helicesfor field data
Edge of Helices for Case A simulations
Edge of Pile
Fig. 7.16. Radial pore pressure distribution during expansion/contractof helical pile with 5 helices (Case A). Fig. 7.16. Radial pore pressure distribution during expansion/contractof helical pile with 5 helices (Case A).
167
r/Rshaft = 21
100
ion cycles for simulation ion cycles for simulation
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
Fig. 7.17. Radial pore pressure distribution during expansion/contractof helical pile with 3 helices (Case A).
-0.5
0
0.5
1
1.5
2
1 10
r/Rshaft
∆u/σ
' vo
average field data - end of pile inst.shaft only - end of expansionend of 1st helix expansionend of 1st contractionend of 2nd helix expansionend of 2nd helix contractionend of 3rd (last) helix expansionend of 3rd (last) helix contraction
Edge of Helicesfor field data
Edge of Helices for Case A simulations
Edge of Pile
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 10r/Rshaft
∆u/σ
' vo
average field shaft only - enend of 1st helend of 1st helend of 2nd heend of 2nd heend of 3rd heend of 3rd heend of 4th helend of 4th helend of 5th (lasend of 5th (las
Edge of Helices for Case B simulations
Edge of Pile
Edge of Helices for field data
r/Rshaft = 7.6
Fig. 7.18. Radial pore pressure distribution during expansion/contractof helical pile with 5 helices (Case B).
168
r/Rshaft = 21
ion cycles for simulation
100
100
data - end of pile inst.d of expansionix expansionix contractionlix expansionlix contractionlix expansionlix contractionix expansionix contractiont) helix expansiont) helix contraction
ion cycles for simulation
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 10r/Rshaft
∆u/σ
' vo
average field data: end of pile inst.shaft only: end of expansionend of 1st helix expansionend of 1st contractionend of 2nd helix expansionend of 2nd helix contractionend of 3rd (last) helix expansionend of 3rd (last) helix contraction
Edge of Helicesfor case B simulations
Edge of Pile
Edge of Helicesfor field data
r/Rshaft = 7.6
100
Fig. 7.19. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case B).
169
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
-0.3
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000
Time (min)
∆u/σ
' vo
Weech (2002) typical field data - below helices
shaft only
shaft + 5 helices
Weech (2002) typical field data - between helices
shaft only
end of installationshaft + 5 helices
end of installationshaft only
Fig. 7.20. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case A).
-0.3
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000
Time (min)
∆u/σ
' vo
Weech (2002) field data - between helices
Weech (2002) field data - below helices
shaft only
shaft + 3 helices
shaft only
Fig. 7.21. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case A).
170
Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.
0.0
0.5
1.0
1.5
2.0
0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000
Time (min)
∆u/σ
' vo
Weech (2002) field data - between helices
Weech (2002) field data - below helices
shaft only
shaft + 5 helices
shaft only
Fig. 7.22. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case B).
Fig. 7.23. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case B).
171
Chapter 7. Modelling of pore pressure changes induced by pile installation in 1-D.
172
Fig. 7.24. Stress path plot for mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation of helical pile shaft installation.
Fig. 7.25. Void ratio versus mean stress (e – ln(p΄)) plot for mesh element adjacent to the cavity wall (r/Rshaft = 1.08).
Chapter 7. Modelling of pore pressure changes induced by pile installation in 1-D.
173
Fig. 7.26. Comparison of stress paths for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulations with different set of input parameters and modelling schemes.
Chapter 7. Modelling of pore pressure changes induced by pile installation in 1-D.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 5 10 15 20 25 30 35 40 45Time (sec) after pile tip passed piezometer location
Fig. 7.27. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A. Assumption 2).
174
Chapter 8. Summary, conclusions and recommendations for further study.
8. SUMMARY, CONCLUSIONS & RECOMMENDATIONS FOR FURTHER STUDY.
8.1. SUMMARY AND CONCLUSIONS.
Predictions of the pore pressure response induced by traditional piles and CPT piezocones has
been analysed in a number of studies. However, the pore pressure response due to installation of
helical piles has not been addressed until very recently. Weech (2002), during a field study of
helical pile performance in soft fine-grained soil, measured pore pressures during and after
helical pile installation.
According to Terzaghi: “Theory is the language by means of which lessons of experience can be
clearly expressed”. Following this view the current study is a theoretical attempt to reproduce
the pore pressure response observed in the field by applying numerical methods. The field
experimental data obtained during Weech’s study provided the necessary background
information for the numerical analysis.
There is a consensus of opinions in the reviewed literature – realistic simulation of the time
dependent pore pressure response induced by pile installation requires a framework that utilizes
advanced soil models coupled with consolidation analysis. Simulation of the pile installation
process within this framework can be achieved using either cavity expansion or a strain path
analogue. In the present study, the critical state model NorSand, coupled with Biot’s
consolidation equations, was chosen as the framework for a cavity expansion analysis. Even
though its name suggests sand, the NorSand model has no intrinsic limitations for application to
fine-grained soils. Modelling of the triaxial tests on Bonnie silt carried out during the present
study, further reaffirmed this idea. The finite element implementation of the coupled
NorSandBiot formulation developed by Shuttle (e.g. 2003) was adopted in this study. Thorough
verification of the NorSandBiot code has shown that its numerical predictions fully match
available theoretical solutions.
The NorSandBiot code requires 13 input parameters. The extensive dataset of available
information on Colebrook silty clay properties provided information on many, but not all, of the
input parameters. Some of the parameters required for NorSandBiot code were not directly
measured during previous investigations, thus in a present study their values were derived based
on the information available. Despite the difficulties, reasonable acceptable ranges for all
175
Chapter 8. Summary, conclusions and recommendations for further study.
NorSandBiot input parameters were established and a best estimate set of input parameters for
modelling was proposed.
A comprehensive parametric study of the NorSandBiot code has shown that several of the input
parameters, varied within the range acceptable for the Colebrook site, do not have a significant
effect on the calculated pore water pressure response. The computed pore water pressure
response was however very sensitive to the soil OCR (in the NorSandBiot formulation
represented by the state parameter, ψ, and overconsolidation ratio, R) and its flow characteristic
(represented by the hydraulic conductivity kr). Also, the lateral stress (represented by the
coefficient of lateral earth pressure at rest, K0) and soil elasticity (represented by shear modulus,
G, and Poisson’s ratio, ν) have a major influence on the pore pressure response.
The study was conducted in 1-D, so a special simplified procedure was developed to simulate
helical pile installation using a series of cylindrical cavity expansion/contraction cycles. The
modelling of the helical pile installation into Colebrook silty clay was conducted in two stages:
I. Modelling of the helical pile as a single cylindrical cavity expansion;
II. Modelling of the helical pile as a combination of a single cylindrical cavity
expansion and series of additional cylindrical cavity expansion/contraction cycles.
It has been shown that, provided a careful selection is made of input parameter values applicable
to the Colebrook site, single cavity expansion produced quite accurate prediction of the pore
pressure dissipation time and a satisfactory estimate of the pore pressure distribution at the end
of helical pile installation observed by Weech (2004).
Introduction of the expansion/contraction cycles (helices) on top of a single cavity expansion helped
improve prediction of the maximum extent of the radial pore pressure distribution and the pore
pressure dissipation time. Assumption of a fixed soil/cavity interface during cycling, exaggerated
the effect of unloading after passage of the helices leading to underprediction of the pore pressure
magnitude at the cavity wall and its immediate vicinity. Nevertheless, at greater distances the
modelling was able to capture effectively the general trends of pore pressure behaviour measured
in the field, including gradual pore pressure build up and outward propagation during penetration
of the helices.
Largely, given the complexity of the modelled process and taking into account the major
simplifications involved in the analysis, the overall results of the Stage I and Stage II modelling
were encouraging.
176
Chapter 8. Summary, conclusions and recommendations for further study.
The following major conclusions can be drawn from the study:
• A fully coupled NorSandBiot modelling framework provides a realistic environment for
simulation of the fine-grained soil behaviour.
• The proposed modelling approach of simulating helical pile installation provides a
simplified technique that allows reasonable predictions of stresses and pore pressure
variations during and after helical pile installation;
• The modelling highlighted the importance of careful input parameter selection and
significance of modelling assumptions.
• The modelling showed a generally good agreement with the pore water pressure response
trends observed at the Colebrook site by Weech (2004).
• The modelling demonstrated that soil sensitivity has a large effect on the equalized
lateral effective stress ratio σ′h/σ′v0, which is in agreement with findings of Lehane &
Jardine (1994).
It appears that the modelling approach developed in this study has a great potential for
application in geotechnical practice:
• NorSand-Biot code can be integrated into independent geotechnical software tools that
will be capable of estimating variation of bearing capacity with time after pile
installation.
• Simulation of a single cavity expansion in the NorSandBiot framework can be readily
applied for studying pore pressures and stress predictions induced by traditional piles and
piezocones.
However, before these tasks are undertaken further research is needed.
8.2. RECOMMENDATIONS FOR FURTHER RESEARCH.
8.2.1. LABORATORY TESTING.
The Colebrook site investigations performed by MoTH, Crawford & Campanella (1991) and
Weech (2002) provided a good basis for establishing many, but not all, of the input parameters
required for the NorSand-Biot formulation.
177
Chapter 8. Summary, conclusions and recommendations for further study.
Limited knowledge of triaxial behaviour of Colebrook silty clay made it difficult to establish
accurately NorSand model parameters, including:
• critical stress ratio, Mcrit;
• slope of the critical state line, λ;
• intercept of the CSL at 1 kPa stress, Γ;
• hardening coefficient, Hmod;
• state parameter, ψ;
• state dilatancy parameter, χ.
Also, none of the previous investigations provided direct measurements of hydraulic
conductivity k, for the Colebrook site. Establishing this parameter was complicated by the
differences between laboratory and in situ derived values. Similar to the other NorSand
parameters, a broad range of hydraulic conductivity values was assumed.
Considering sensitivity of modelling outcome to variation of mentioned above parameters,
modelling results presented can be refined if the above mentioned parameters are adjusted
through additional laboratory testing.
It is recommended to select several sampling location within a 10 meter vicinity from the helical
pile research site, recover a number of samples of Colebrook silty clay between elevations
-4.6 … -9.9 m, using either a Laval or Sherbrooke sampler to minimize sample disturbance, and
perform a series of drained (Mcrit; Hmod; χ) and undrained (Γ; λ) triaxial tests to establish
NorSand parameters and falling head permeability tests to evaluate hydraulic conductivity, k.
8.2.2. 2-D NUMERICAL MODELLING.
It appears that 2-D modelling may provide additional insights into the complex pore pressure
response of fine-grained soils due to helical pile installation.
Effect of Vertical Drainage.
2-D effects on pore pressure response are largely unknown. Quite often it is assumed that pore
water migrates only in the radial direction away from the pile and vertical dissipation is
negligible. Apparently this approach is only a crude approximation of real conditions.
Baligh & Levadoux (1980) proposed a range kh/kv of 2 to 5 for the layered clays with silt
inclusions, Gillespie & Campanella (1981) recommended use of kh/kv = 2.5 for the silty clays
178
Chapter 8. Summary, conclusions and recommendations for further study.
found in the Fraser river delta. It would be particularly interesting to model helical pile
installation in 2-D with the “best fit” set of parameters established in Chapter 7, assuming
different ratios for horizontal and vertical permeability and taking kh/kv = 2.5 as a reference.
Modelling results can be contrasted and compared to the 1-D simulation and field measurements
by Weech (2002).
Effect of Soil Remoulding on Pore Pressure Response.
Pile installation creates a zone of severe deformations in the adjacent soil due to remoulding.
Soil in the remolded zone, exhibits quite different properties from the intact state. Moreover,
within the remoulded zone there will be subzones with different degrees of remoulding.
It is possible to account for soil remoulding during modelling by introducing several zones with
properties varying with the degree of remoulding. Works by Leifer et al. (1980) and Bolton &
Whittle (1999) provide some guidance relevant to this issue and should be used as a starting
point for the analysis.
179
References.
REFERENCES
Allman, M.A. & Atkinson J.H. (1992). “Mechanical Properties of Reconstituted Bothkennar Soil.” Geotechnique, Vol. 42, No. 3, pp. 289-301.
Armstrong, J.E. (1984). “Environmental and Engineering Applications of the Surficial Geology of the Fraser Lowland, British Columbia.” Geological Survey of Canada, Paper 83-23.
Baligh, M.M. & Levadoux, JN. (1980). “Pore Pressure Dissipation After Cone Penetration.” Research Report R80-11, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
Baligh, M.M. (1985). “Strain Path Method.” Journal of Geotechnical Engineering, ASCE Vol. 111, No. 9, pp. 1108-1136.
Baligh, M.M. & Levadoux, J.N. (1986). “Consolidation after Undrained Piezocone Penetration. II: Interpretation.” Journal of Geotechnical Engineering, Vol. 112, No. 7, pp. 727-745.
Battaglio, M., Jamiolkowski, M., Lancellotta, R. & Maniscalco, R. (1981). “Piezometer probe Test in Cohesive Deposits.” Proceedings, Cone Penetration Testing and Experience, G.M. Norris & R.D. Holtz, Ed., American Society of Civil Engineers, New York, pp. 264- 302.
Been, K. & Jefferies, M. G. (1986). “Discussion on a state parameter for sands.” Geotechnique, 36, No. 1, pp. 123-132.
Biot, M.A. (1941). “General Theory of Three-Dimensional Consolidation.” Journal of Applied Physics, Vol. 12, pp 64-155.
Bjerrum, L. & Johannessen, I. (1960). “Pore Pressures Resulting from Driving Piles in Soft Clay.” Proceedings, Conference on Pore Pressure and Suction in Soils, London, pp. 108-111.
Bolton, M.D. (1986). “The Strength and Dilatancy of Sands.” Geotechnique, 36, No 1, pp. 65-78.
Bolton, M.D. & Whittle, A.W. (1999). “A Non-Linear Elastic/Perfectly Plastic Analysis for Plane Strain Undrained Expansion Tests.” Geotechnique, 49, No 1, pp. 133-141.
Bond, A.J. & Jardine, R.J. (1991). “Effects of Installing Displacement Piles in a High OCR Clay.” Geotechnique, Vol. 41, No. 3, pp. 341-363.
Bozozuk, M., Fellenius, B.H. & Samson, L. (1978). “Soil Disturbance from Pile Driving in Sensitive Clay.” Canadian Geotechnical Journal, Vol. 15, No. 3, pp. 346-361.
Burland, J. B. (1965). “Deformation of soft clay.” PhD thesis, Cambridge University.
Burns, S.E. & Mayne, P.W. (1995). “Coefficient of Consolidation from Type 2 Piezocone Dissipation in Overconsolidated Clays.” Proceedings of International Symposium on Cone Penetration Testing, Linköping, Sweden, Vol. 2, pp. 137-142.
180
References.
Burns, S.E. & Mayne, P.W. (1998). “Monotonic and dilatory pore pressure decay during piezocone tests in clay.” Canadian Geotechnical Journal, No. 35, pp. 1063-1073.
Byrne, P.M. & Srithar, T. (1989). “CONOIL – II: A computer program for non-linear consolidation analysis of stress, deformation and flow in oil sand masses.” A report to Alberta Oil technology and research Authority, Edmonton, Alberta, Agreement No. 272B, Department of Civil Engineering, University of British Columbia, Vancouver.
Campanella, R.G, Robertson, P.K. & Gillespie, D.G. (1983). “Cone Penetration Testing in Deltaic Soils.” Canadian Geotechnical Journal, 20, pp. 23-35.
Campanella, R.G., Robertson, P.K., & Gillespie, D. (1986). “Factors Affecting the Pore Water Pressure and Its Measurement Around a Penetrating Cone.” Proceedings of 39th Canadian Geotechnical Conference, Ottawa, pp. 291-299.
Campanella, R.G. & Robertson, P.K. (1988). “Current Status of the Piezocone.” Proceedings of International Symposium on Penetration Testing, Editor J.D. Ruiter, A.A. Balkema, Rotterdam, Vol. 1, pp. 93-116.
Cao, L.F., Teh, C.I. & Chang, M.F. (2001). “Undrained Cavity Expansion in Modified Cam Clay I: Theoretical Analysis.” Geotechnique, Vol. 51, No. 4, pp. 323-334.
Carter, J.P., Randolph, M.F. & Wroth, C.P. (1979). “Stress and Pore Pressure Changes in Clay During and After the Expansion of a Cylindrical Cavity.“ International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 3, 305-322.
Carter J.P, Booker J.R. & Yeung SK. (1986). “Cavity Expansion in Cohesive Frictional Soils.” Geotechnique, Vol. 36, No. 3, pp. 349-358.
Casagrande, A. (1975). "Liquefaction and Cyclic Deformation of Sands - A Critical Review.” Proceedings of 5th Pan-American Conference on Soil Mechanics and Foundation Engineering, Buenos Aires.
Chen, B.S. & Mayne, P.W. (1995). “Type 1 and 2 Piezocone Evaluations of Overconsolidation Ratio in Clays.” Proceedings of International Symposium on Cone Penetration Testing, Linköping, Sweden, SGF Report 3:95, Vol. 2, pp. 143-148.
Chen, C.S., Liew, S.S. & Tan, Y.C. (1999). "Time Effects on Bearing Capacity of Driven Piles." Proceedings of 11th Asian Regional Conference of ISSMGE, Seoul, South Korea.
Clark, J.I. & Meyerhof, G.G. (1972). “The Behaviour of Piles Driven in Clay. An Investigation of Soil Stress and Pore Water Pressure as Related to Soil Properties.” Canadian Geotechnical Journal, 9, No. 3, 351-373.
Collins, I.F. & Yu, H.S. (1996). “Undrained Cavity Expansions in Critical State Soils.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 20, No. 7, pp. 489-516.
181
References.
Cooke, R.W. & Price, G. (1973). “Strains and Displacements Around Friction Piles.” Proceedings of 8th International Conference in Soil Mechanics, Moscow, Vol. 2.1, pp. 53-60.
Coop, M.R. & Wroth, C.P. (1989). “Field studies of an instrumented model pile in clay.” Geotechnique, Vol. 39, No. 4, pp. 679-696.
Crawford, C.B. & deBoer, L.J. (1987). “Field Observations of Soft Clay Consolidation in the Fraser Lowland.” Canadian Geotechnical Journal, Vol. 24, pp. 308-317.
Crawford, C.B. & Campanella, R.G. (1991). “Comparison of Field Consolidation with Laboratory and In-Situ Tests.” Canadian Geotechnical Journal, Vol. 28, pp. 103-112.
Crawford, C.B., Jitno H. & Byrne, P.M. (1994). “The Influence of Lateral Spreading on Settlements Beneath a Fill.” Canadian Geotechnical Journal, Vol. 31, pp. 145-150.
D’Appolonia, D.J., Poulos, H.G. & Ladd, C.C. (1971). “Initial Settlement of Structures on Clay.” ASCE Journal of the Soil Mechanics and Foundations Division, Vol. 97, No. SM10, pp. 1359-1377.
Davidson, J.L. (1985). “Pore Pressures Generated During Cone Penetration Testing in Heavily Overconsolidated Clays.” Proceedings of 11th International Conference on Soil Mechanics and Foundation Engineering, Vol. 5.
Dolan, K. (2001). “An in-depth Geological and Geotechnical Site Characterization Study, Colebrook Road Overpass, Highway 99A, Surrey, B.C.” B.A.Sc. Thesis, University of British Columbia, Vancouver, B.C.
Eide, O., Hutchinson, J.N. & Landva, A. (1961). “Short and Long-Term Loading of a Friction Pile in Clay.” Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Paris, Vol. 2, pp. 45-53.
Flaate, K. (1972). “Effects of Pile Driving in Clays.” Canadian Geotechnical Journal, Vol. 9, No. 1, pp. 81-88.
Gibson, R.E. & Anderson, W.F. (1961). “In-situ Measurements of Soil Properties with the Pressuremeter.” Civ. Eng. Public Works Rev. 56, 615-618.
Gillespie, D. & Campanella, R.G. (1981). “Consolidation Characteristics from Pore Pressure Dissipation After Piezometer Cone Penetration.” Soil Mechanics Series 47, Department of Civil Engineering, The University of British Columbia, Vancouver, 17 pp.
Goodman, R.E. (1999). “Karl Terzaghi: The Engineer as Artist.” ASCE Press, Reston, VA.
Ground Engineering. (1999). “Uncertainty Principle.” Ground Engineering, November, pp. 32-34.
Guo, W. D., (2000). “Visco-elastic consolidation subsequent to pile installation.” Computers and Geotechnics, Vol. 26, No.2, pp. 113-144.
Gupta, R.C. & Davidson, J.L. (1986). “Piezoprobe Determined Coefficient of Consolidation.” Soils and Foundations, Vol. 26, No. 3, pp. 12-22.
182
References.
Houlsby, G.T. & Teh, C.I. (1988). “Analysis of the Piezocone in Clay.” Proceedings of 1st International Symposium on Penetration Testing (ISOPT-1), Orlando, pp. 777-783.
Houlsby, G.T. & Withers, N.J (1988). “Analysis of the Cone Pressuremeter Test in Clay.” Geotechnique, Vol. 38, No. 4, pp. 575-587.
Ishihara, K. (1996). “Soil Behaviour in Earthquake Geotechnics.” Oxford University Press, New York.
Jefferies, M.G. (1993). “NorSand: A Simple Critical State Model for Sand.” Geotechnique, Vol. 43, No. 1, pp. 91 -103.
Jefferies, M.G. & Shuttle, D.A. (2002). “Dilatancy In General Cambridge-Type Models.” Geotechnique, Vol. 52, No. 9, pp. 625-638.
Jefferies, M.G. & Been, K. (2005). “Soil liquefaction: a critical state approach.” In print. Spon Press.
Jefferies, M.G. & Shuttle, D.A. (2005) “NorSand: Features, Calibration and Use.” Invited paper for the ASCE Geo-Institute Geo-Frontiers Conference, January 2005, session on Calibration of Constitutive Models (in press).
Klar, A. & Einav, I. (2003). “Numerical Simulation of Pile Installation using FLAC.” Third International FLAC Symposium, pp. 273-278.
Koizumi, Y. & Ito, K. (1967). “Field Tests with Regard to Pile Driving and Bearing Capacity of Piled Foundations.” Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, Vol. 7, No. 3, pp. 30-53.
Komurka, V.E, Wagner, A.B. & Edil, T.B. (2003) “Estimating Soil/Pile Set-Up.” Report for Wisconsin Department of Transportation.
Konrad, J.M. & Roy, M. (1987). “Bearing Capacity of Friction Piles in Marine Clay.” Geotechnique, Vol. 37, No. 2, pp. 163-175.
Leifer, S.A., Kirby R.C. & Esrig, M.I. (1980). “Effect of radial variation in modulus on stresses after consolidation around a driven pile.” Numerical methods in offshore piling, ICE, London, pp. 157-163.
Lehane, B.M. & Jardine, R.J. (1994). "Displacement-Pile Behavior in a Soft Marine Clay." Canadian Geotechnical Journal, Vol. 31, pp. 181-191.
Levadoux, JN, & Baligh, M.M. (1980). “Pore Pressures During Cone Penetration in Clays.” Research Report R80-15, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
Levadoux, JN, & Baligh, M.M. (1986). “Consolidation after Undrained Piezocone Penetration. I: Prediction.” Journal of Geotechnical Engineering, Vol. 112, No. 7, pp. 707-726.
183
References.
Lo, K.Y. & Stermac, A.G. (1965). “Induced Pore Pressures During Pile Driving Operations.” Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering, Montreal, Vol. 2, pp. 285-289.
Lutenegger, A.J. & Kabir, M.G. (1987). “Pore Pressures Generated by Two Penetrometers in Clays.” Report #87-2. Department of Civil and Environmental Engineering, Clarkson University, Potsdam, 45 pp. Mayne, P.W. & Kulhawy, F.H. (1982). "Ko-OCR Relationships in Soil." Journal of the Geotechnical Engineering Division, ASCE, Vol. 108, GT6, pp. 851-872. Mayne, P.W. (1991). “Determination of OCR in Clays by PCPT using Cavity Expansion and Critical State Concepts.” Soils and Foundations, Vol. 31, No. 2, pp. 65-76.
Mitchell, J.K. (1993). “Fundamentals of Soil Behaviour.” 2nd ed., John Willey, New York.
Narasimha Rao, S., Prasad, Y.V.S.N. & Veeresh, C. (1993). “Behaviour of Model Screw Anchors in Soft Clays.” Geotechnique, Vol. 43, pp. 605-614.
Orrje, O. & Broms, B. (1967). “Effects of Pile Driving on Soil Properties.” ASCE Journal of the Soil Mechanics and Foundations Division. Vol. 93, No. SM5, pp. 59-73.
Pestana, J. M., Hunt, C. E. & Bray, J. D. (2002). "Soil deformation and excess pore pressure field around a closed-ended pile." ASCE, Journal of Geotechnical and Geoenvironmental Engineering. Vol.128, No. 1, pp. 1-12.
Randolph, M. F., Carter, J. P. & Wroth, C. P. (1979a). “Driven Piles in Clay - the Effects of Installation and Subsequent Consolidation.” Geotechnique, Vol. 29, No. 4, pp. 361-393.
Randolph, M. F., Steenfelt, J. S. & Wroth, C. P. (1979b). “The Effect of Pile Type on Design Parameters for Driven Piles.” Proceedings, Seventh European Conference on Soil Mechanics Foundation Engineering, Vol. 2, pp. 107-114.
Randolph, M.F. & Wroth, C.P. (1979c). “An Analytical Solution for the Consolidation Around a Driven Pile.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 3, pp. 217-229.
Randolph, M. F. (2003). “Science and Empiricism in Pile Foundation Design.” Geotechnique Vol. 53, No. 10, pp. 847–875
Rendulic, L. (1936) “Porenzier und Porenwasser Druck in Tonen.” Der Bauingenieur 17.
Roscoe, K.H., Schofield, A.N. & Wroth, C.P. (1958). “On the Yielding of Soils.” Geotechnique, Vol. 9, pp. 22-53.
Roscoe, K.H. & Schofield A.N. (1963). “Mechanical Behaviour of Idealized ‘Wet Clay.” Proceedings, Second European Conference on Soil Mechanics, Wiesbaden I, pp. 47-54.
Roscoe, K. H., Schofield, A. N., & Thurairajah (1963). “Yielding of Clays in States Wetter Critical.” Geotechnique, Vol. 13, pp. 211-240.
184
References.
Roscoe, K.H. & Burland J.B. (1968). “On the Generalized Behaviour of Wet Clay.” Engineering Plasticity, Eds. Heyman J. & Leckie F.A., Cambridge University Press, pp. 535-609.
Roy, M., Michaud, D., Tavenas, F. A., Leroueil, S. & La Rochelle, P. (1975). “The interpretation of static cone penetration tests in sensitive clays.” Proceedings of European Symposium on Penetration Testing, Stockholm Vol. 2.1, pp. 323-331.
Roy, M., Blanchet, R., Tavenas, F. & La Rochelle, P. (1981). “Behaviour of a Sensitive Clay During Pile Driving.” Canadian Geotechnical Journal, Vol. 18, No. 1, pp. 67-85.
Seed, H.B. & Reese, L.C. (1957). “The Action of Soft Clay Along Friction Piles.” Transactions of the American Society of Civil Engineers, Vol. 122, pp. 731-755.
Senneset, K., Janbu, N. & Svan, G. (1982). “Strength and Deformation Parameters from Cone Penetration Tests.” Proceedings of Second European Symposium on Penetration Testing, Vol. 2, (ESOPT-2, Amsterdam), Balkema, Rotterdam, pp. 863-870.
Schiffman, R.L. (1958). “Consolidation of Soil under Time Dependent Loading and Varying permeability.” HBR Proc., Vol. 37, pp. 584-617.
Schiffman, R.L. (1960). “Field Applications of Soil Consolidation Time-Dependent Loading and Variable Permeability.” Highway Research Board, Bulletin 248, Washington, USA.
Schofield, A. & Wroth, C. (1968). “Critical State Soil Mechanics.” McGraw-Hill, New York.
Schmertmann, J.H. (1978). “Guidelines for Cone Penetration Test Performance and Design.” Federal Highways Administration, Report FHWA TS-78-209, Washington D.C.
Shuttle, D.A. & Jefferies, M.G. (1998). "Dimensionless and Unbiased CPT Interpretation in Sand." International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 22, No.5, pp 351-391.
Shuttle, D.A. (2003). “Effect Of Pore Pressure Dissipation On SBP Tests In Clay.” 56th Canadian Geotechnical Society Conference.
Shuttle, D.A. (2004). “Implementation of a Viscoplastic Algorithm for Critical State Soil Models.” NUMOG IX conference. In print.
Smith, I.M. & Griffith, D.V. (1998). “Programming the Finite Element Method.” Third Edition, John Wiley and Sons.
Soderberg, L.O. (1962). “Consolidation Theory Applied to Foundation Pile Time Effects.” Geotechnique, Vol. 12, pp. 217-225.
Sully, J.P., Campanella, R.G. & Robertson, P.K. (1990). “Overconsolidation Ratio of Clays from Penetration Pore Pressures.” Journal of Geotechnical Engineering, Vol. 116, No. 2, pp. 340-342.
Sully, J.P. & Campanella, R.G. (1991). “The Effect of Lateral Stress on CPT Penetration Pore Pressures.” Journal of Geotechnical Engineering, Vol. 117, No. 7, pp. 1082-1088.
185
References.
Sully, J.P. & Campanella, R.G. (1994). “Evaluation of Field CPTU Dissipation Data in Overconsolidated Fine-Grained Soils.” Proceedings of 13th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, New Delhi, pp. 201-204.
Sun, J.I., Golesorkhi, R. & Seed, H.B. (1988). “Dynamic Moduli and Damping Ratios for Cohesive Soils.” Report No. UCB/EERC-88/15, University of California, Berkeley, California.
Teh, C.I. & Houlsby, G.T. (1991). “An Analytical Study of the Cone Penetration Test in Clay.” Geotechnique, Vol. 41, No. 1, pp. 17-34.
Terzaghi, K.V. (1943). “Theoretical soil mechanics.” New York: John Wiley and Sons.
Torstensson, B.A. (1977). “The Pore Pressure Probe.” Nordiske Geotekniske Mote, Oslo, Paper No. 34, pp. 34.1 to 34.15.
Tumay, M.T., Acar, Y., & Deseze, E. (1982). “Soil Exploration in Soft Clays with the Quasi-Static Electric Cone Penetrometer.” Proceedings, 2nd European Symposium on Penetration Testing, Amsterdam.
Vesic, A.S. (1972). “Expansion of Cavities in Infinite Soil Mass.” Journal of the Soil Mechanics and Foundation Division, American Society of Civil Engineers, Vol. 98, No. SM3, pp. 265-290.
Vyazmensky, A.M., Shuttle, D.A. & Howie J.A. “Coupled Modelling of Observed Pore Pressure Dissipation After Helical Pile Installation.” Proceedings of 57th Canadian Geotechnical conference, Quebec City.
Yu, H.S. & Houlsby, G.T. (1991). “Finite Cavity Expansion in Dilatant Soils: Loading Analysis.” Geotechnique, Vol. 41, No.2, pp. 173-183.
Weech, C.N. (2002). “Installation and Load Testing of Helical Piles in a Sensitive Fine-Grained Soil.” M.A.Sc. Thesis, University of British Columbia
Wilson & Guthlac, (1950). “The Bearing Capacity of Screw Piles and Screwcrete Cylinders.” Journal of Institute of Civil Engineers, London, Vol. 34, pp 4-93.
Whittle, A.J. (1992). “Assessment of an Effective Stress Analysis for Predicting the Performance of Driven Piles in Clays.” Advances in Underwater Technology, Ocean science and offshore engineering. Vol. 28, Offshore Site Investigation and Foundation Behaviour, pp. 607 – 643. London.
Whittle, A.J., Sutabutr, T., Germaine, J.T. & Varney, A. (2001). “Prediction and Interpretation of Pore Pressure Dissipation for a Tapered Piezoprobe.” Geotechnique. Vol. 51, No. 7, pp 601-617.
Zienkiewicz, O.C. & Cormeau I.C. (1974). “Viscoplasticity, Plasticity and Creep in Elastic Solids. A Unified Numerical Approach.” International Journal for Numerical Methods in Engineering, Vol. 8, pp. 821-845.
186
Notation.
NOTATION. A = Skempton’s pore pressure parameter [-] Cc = compression index [-] Cα = coefficient of secondary consolidation [-] D = helical plate diameter [m] Dp = plastic dilatancy p
qp
v εε &&= [-] Dmin = minimum dilatancy [-] E = Young’s modulus [mN/m2] Eu = undrained Young’s modulus [mN/m2] G = elastic shear modulus [mN/m2] Gmax = maximum shear modulus = small strain elastic shear modulus [mN/m2] Gs = specific gravity [-] G(γ) = strain dependent shear modulus [mN/m2] Hmod = hardening parameter [-] Ir = rigidity index = G/su [-] K´ = Bulk modulus [mN/m2] K0 = coefficient of lateral earth pressure at rest [-] M = constrained modulus [mN/m2] Mtc = slope of the critical state line in q - p′ space in triaxial compression [-] Mi = slope of the critical state line in q - p′ space in triaxial compression [-] OCR = overconsolidation ratio = σp'/σvo' [-] PI = plasticity index [-] Rshaft = radius of the pile shaft [m] R = ratio of p′max/p′ on yield surface [-] St = soil sensitivity [-] T50 = time to achieve 50 % of excess pore pressure dissipation [min] T95 = time to achieve 95 % of excess pore pressure dissipation [min] Vs = shear wave velocity [m/s] ch = coefficient of consolidation in the horizontal direction [cm2/s] cv = coefficient of consolidation in the vertical direction [cm2/s] eo = void ratio ei = initial void ratio ecrit = critical void ratio fs = sleeve friction k = hydraulic conductivity [m/s] kh = horizontal hydraulic conductivity [m/s] kv = vertical hydraulic conductivity [m/s] mv = coefficient of volume change [1/kPa] p mean normal total stress [kN/m2] pcrit = mean stress at the critical state [kN/m2] p׳ = mean normal effective stress = ( ) 3/321 σσσ ′+′+′ [kN/m2] p′max = maximum mean normal effective stress [kN/m2] pi = mean stress at the image state [kN/m2] q = deviatoric stress invariant 2
1))()()(( 2132
12322
12212
1 σσσσσσ −+−+−= [kN/m2]
187
Notation.
qT = corrected cone tip resistance [kN/m2] ro = initial radius [m] r = radial distance from the pile centre [m] su = undrained shear strength [kN/m2] (su)rem = remoulded undrained shear strength [kN/m2] (su)peak = peak undrained shear strength [kPa] thx = helical plate thickness [mm] uw = pore pressure [kN/m2] uo = initial pore pressure [kN/m2] u1 = pore pressure measured on the face of a cone penetrometer u2 = pore pressure measured behind the tip of a cone penetrometer wn = natural moisture content [%] wL = liquid limit [%] α = Henkel’s pore pressure parameter [-] χ = state dilatancy parameter [-] εq = shear strain invariant = 2/3(ε1−ε3) in triaxial compression [%] εv = volumetric strain, dot superscript denoting rate [%] ε1, 2, 3 = principal strains (assumed coaxial with principal stresses) [%] φ = effective friction angle [degrees] φ΄cv = effective friction angle at constant volume [degrees] γ = shear strain [%] γw = unit weight of water [kN/m3] η = stress ratio =q/p′ [-] κ = slope of the unload-reload line [-] λ = slope of CSL in e-ln(p) space [-] σ′h = lateral effective stress [kN/m2] σ′h0 = in-situ lateral effective stress [kN/m2] σ׳p = preconsolidation stress [kN/m2] σ΄vo = vertical (overburden) effective stress [kN/m2] ν = Poisson coefficient [-] θ = Lode angle [rad] ψ = state parameter [-] ψi = state parameter at image stress [-] Г = intersection of critical state line with mean stress at 1 kPa [-] n& = dot superscript denotes increment of the value n ∆ = delta denotes change relative to initial or in-situ value ∆n(r) = change of value n as a function of distance ∆n(t) = change of value n as a function of time