MASc thesis: NUMERICAL MODELLING OF TIME DEPENDENT PORE PRESSURE RESPONSE INDUCED BY HELICAL PILE...

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

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE STUDIES

(Civil Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

February 2005

© Alexander M. Vyazmensky, 2005

Abstract.

ABSTRACT.

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.

ii

Table of contents.

TABLE OF CONTENTS.

ABSTRACT ...................................................................................................................................ii

TABLE OF CONTENTS ............................................................................................................iii

LIST OF TABLES ......................................................................................................................vii

LIST OF FIGURES ...................................................................................................................viii

ACKNOWLEDGEMENTS ......................................................................................................xiii

1.0. INTRODUCTION ..............................................................................................................1 1.1. CHALLENGES IN AXIAL PILE CAPACITY PREDICTIONS IN SOFT FINE-GRAINED SOILS .........1

1.2. HELICAL PILES ..................................................................................................................2

1.3. PURPOSES AND OBJECTIVES OF RESEARCH........................................................................4

1.4. SCOPE AND LIMITATIONS OF STUDY..................................................................................4

1.5. THESIS ORGANIZATION .....................................................................................................6

2.0. OVERVIEW OF FIELD STUDY OF HELICAL PILE PERFORMANCE IN SOFT SENSITIVE SOIL ..............................................................................................................8

2.1. INTRODUCTION ...................................................................................................................8

2.2. SCOPE OF WEECH'S STUDY.................................................................................................8

2.3. SITE SUBSURFACE CONDITIONS..........................................................................................9

2.3.1. SITE STRATIGRAPHY. ..................................................................................................9

2.3.2. SOIL PROPERTIES ......................................................................................................10

2.3.2.1. FIELD INVESTIGATION BY MINISTRY OF TRANSPORTATION AND HIGHWAYS.10

2.3.2.2. RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (1). ................................10

2.3.2.3. RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (2). ................................11

2.4. HELICAL PILES AND PORE PRESSURE MEASURING EQUIPMENT .......................................12

2.4.1. TEST PILES GEOMETRY AND INSTALLATION DETAILS.. .............................................12

2.4.2. MEASURING EQUIPMENT ..........................................................................................13

2.5. SUMMARY OF WEECH’S STUDY RESULTS........................................................................14

2.5.1. PORE WATER PRESSURE RESPONSE DURING HELICAL PILE INSTALLATION..............14

2.5.2. PORE WATER PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION. ...........15

2.6. SUMMARY ........................................................................................................................17

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

3.3.1. PREDICTION METHODS..............................................................................................34

3.3.2. BASIC CONCEPTS BEHIND EXISTING PREDICTION SOLUTIONS. .................................37

3.3.2.1. MODELLING ANALOGUE FOR SIMULATION OF PILE OR CONE PENETRATION ....37

3.3.2.2. MODELLING FRAMEWORK .............................................................................38

3.3.3. OVERVIEW OF EXISTING PREDICTION SOLUTIONS.....................................................39

3.3.3.1. CAVITY EXPANSION SOLUTIONS ....................................................................39

3.3.3.2. SOLUTIONS BASED ON STRAIN PATH METHOD ..............................................42

3.4. SUMMARY ........................................................................................................................42

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

4.2.1. MODELLING FRAMEWORK ........................................................................................49

4.2.2. MODELLING PROCEDURE FOR SIMULATION OF HELICAL PILE INSTALLATION. .........50

4.3. NORSANDBIOT FORMULATION. ......................................................................................52

4.3.1. NORSAND CRITICAL STATE MODEL .........................................................................52

4.3.1.1. MODEL DESCRIPTION ......................................................................................52

4.3.1.2. MODEL PARAMETERS......................................................................................55

4.3.1.3. BEYOND SAND ................................................................................................56

4.3.2. BIOT COUPLED CONSOLIDATION THEORY.................................................................57

4.3.3. FINITE ELEMENT IMPLEMENTATION OF NORSANDBIOT FORMULATION....................58

4.3.4. FINITE ELEMENT CODE VERIFICATION......................................................................58

4.4. SUMMARY .......................................................................................................................59

5.0. SELECTION OF SITE-SPECIFIC SOIL PARAMETERS FOR MODELLING .....67 5.1. INTRODUCTION. ..............................................................................................................67

5.2. SOIL PARAMETERS FOR MODELLING. .............................................................................67

5.2.1. ELASTIC PROPERTIES G, ν. .......................................................................................67

iv

Table of contents.

5.2.2. OVERCONSOLIDATION RATIO OCR. .........................................................................69

5.2.3. COEFFICIENT OF LATERAL EARTH PRESSURE K0. .......................................................70

5.2.4. HYDRAULIC CONDUCTIVITY DERIVATION. ...............................................................71

5.2.4.1. COEFFICIENT OF CONSOLIDATION....................................................................71

5.2.4.2. COEFFICIENT OF VOLUME CHANGE, mv...........................................................73

5.2.4.3. RADIAL HYDRAULIC CONDUCTIVITY, kr..........................................................74

5.2.5. VERTICAL EFFECTIVE STRESS σ΄vo AND EQUILIBRIUM PORE PRESSURE uo. ..............74

5.2.6. NORSAND MODEL PARAMETERS DERIVATION..........................................................74

5.2.6.1. CRITICAL STATE COEFFICIENT, Mcrit ...............................................................75

5.2.6.2. STATE DILATANCY PARAMETER, χ .................................................................75

5.2.6.3. HARDENING MODULUS, Hmod ..........................................................................75

5.2.6.4. SLOPE OF CRITICAL STATE LINE, λ .................................................................75

5.2.6.5. INTERCEPT OF CRITICAL STATE LINE AT 1 KPA STRESS, Γ .............................77

5.2.6.6. STATE PARAMETER, ψ.....................................................................................77

5.2.7. NORSAND PARAMETERS ANALYSIS ..........................................................................79

5.3. SUMMARY. .....................................................................................................................80

6.0. NORSAND-BIOT CODE PARAMETRIC STUDY .....................................................95 6.1. INTRODUCTION. ..............................................................................................................95

6.2. MODELLING PARTICULARS. ............................................................................................95

6.3. REFERENCE RESPONSE. ...................................................................................................96

6.4. PARAMETRIC STUDY SCENARIOS. ...................................................................................98

6.5. PARAMETRIC STUDY RESULTS. . ...................................................................................100

6.5.1. INFLUENCE OF COEFFICIENT OF LATERAL EARTH PRESSURE ..................................102

6.5.2. INFLUENCE OF MEASURES OF SOIL OCR ................................................................103

6.5.3. INFLUENCE OF ELASTIC PROPERTIES ......................................................................106

6.5.4. INFLUENCE OF CRITICAL STATE LINE PARAMETERS................................................108

6.5.5. INFLUENCE OF HARDENING MODULUS....................................................................109

6.5.6. INFLUENCE OF STATE DILATANCY PARAMETER......................................................110

6.5.7. INFLUENCE OF HYDRAULIC CONDUCTIVITY ............................................................110

6.6. CONCLUDING REMARKS ON PARAMETRIC STUDY RESULTS ..........................................111

6.7. SUMMARY .....................................................................................................................113

7.0. MODELLING OF PORE PRESSURE CHANGES INDUCED BY PILE INSTALLATION IN 1-D ..............................................................................................138

v

Table of contents.

7.1. INTRODUCTION. ............................................................................................................138

7.2. 1-D SIMULATIONS. .......................................................................................................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

7.4. SUMMARY .....................................................................................................................156

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

8.2.2. 2-D NUMERICAL MODELLING ...........................................................................178

REFERENCES .........................................................................................................................180

NOTATION ..............................................................................................................................187

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

4.2. NorSand code input parameters.......................................................................................... 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

vii

List of figures.

LIST OF FIGURES

Figure Page

1.1. Helical piles .......................................................................................................................... 7

2.1. Helical pile performance research site location.................................................................. 18

2.2. Site subsurface conditions at the research site .................................................................. 18

2.3. Approximate locations of subsurface investigations at the Colebrook site........................ 19

2.4. Location of CPT tests and solid-stem auger holes ............................................................. 19

2.5. Variation of field vane shear strength test results with elevation....................................... 20

2.6. Example of cone penetration test results (CPT-7).............................................................. 21

2.7. Helical piles geometry ....................................................................................................... 22

2.8. Helical piles locations......................................................................................................... 23

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

3.3. Typical pore pressure dissipation measured during CPTU tests ....................................... 45

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

6.10. Stress paths for “base case”, 1 & 2 scenarios .................................................................. 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

6.25. Stress paths for scenarios “base case”, 7, 8 & 9 ............................................................... 126

6.26. Effect of ν on radial distribution of excess pore pressure at the end of cavity expansion .. 126

6.27. Effect of ν on time dependent pore water pressure response at cavity wall .................... 127

6.28. Stress paths for scenarios “base case”, 22 & 23. .............................................................. 127

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

x

List of figures.

6.31. Stress paths for scenarios “base case”, 10 & 11 ................................................................ 129

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


6.35. Effect of Mcrit on radial distribution of excess pore pressure at the end of cavity expansion .131

6.36. Effect of Mcrit on time dependent pore water pressure response at cavity wall. .............. 131


6.38. Effect of Hmod on radial distribution of excess pore pressure at the end of cavity expansion 132

6.39. Effect of Hmod on time dependent pore water pressure response at cavity wall ............... 133


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

6.46. Stress paths for scenarios “base case”, 20 & 21. .............................................................. 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

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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.

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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.

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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

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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.

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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.

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a b

Fig. 1.1. Helical piles: a – conventional pile; b – grouted (PULLDOWNTM) pile.

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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

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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.

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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


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).

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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

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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.

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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


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


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


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


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).


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


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


Fig. 2.7. Helical piles geometry (modified after Weech, 2002).

22


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


-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


-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


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


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


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


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

∆u/

σ'vo

Between Helices, r/R = 1 (TP1-PP1)Below Helices, r/R = 1 (TP4-PP3)Opposite Helices, r/R = 6.3 (PZ-TP4-2)Below Helices, r/R = 5.5 (PZ-TP1-9)Opposite Helices, r/R = 8.1 (PZ-TP3-2)Opposite Helices, r/R = 12 (PZ-TP1-7)Below Helices, r/R = 16 (PZ-TP2-9)

Fig. 2.16. Dissipation curves from piezometers/piezo-ports located at different radial distances from pile (after Weech, 2002).

29

Chapter 3. Literature review.

3.0. LITERATURE REVIEW.

3.1. INTRODUCTION.

Pore water pressure response, including pore pressure generation and subsequent dissipation, due

to helical pile installation into fine-grained soil has not been addressed until very recently. A field

study by Weech (2002) provided the necessary factual information. However it is rather difficult

to explain complex soil response based solely on interpretation of the field measurement.

Prediction of pore water pressure response during and after pile installation into fine-grained

soils has been the subject of a number of theoretical studies. Moreover, an extensive body of

work exists in the field of cone penetration testing, where dissipation solutions were employed

for the prediction of soil consolidation characteristics. Essentially, the CPT cone is a scaled

instrumented pile and the pore pressure prediction solutions developed for cones may be

applicable for prediction of the pore water response due to installation of driven and jacked piles.

The main objective of this chapter is to establish a theoretical background upon which a

numerical formulation for the analysis of pore pressure response due to helical pile penetration

can be developed. To meet this objective, the existing state of knowledge on field observation of

time dependent pore pressure response due to penetration of piles and piezocones is summarized,

and a brief review of well known methodologies for pore pressure predictions is provided.

3.2. PORE PRESSURE RESPONSE INDUCED BY PILE INSTALLATION INTO FINE GRAINED SOIL

AND ITS INFLUENCE ON PILE CAPACITY.

3.2.1. FIELD GENERATION OF EXCESS PORE PRESSURE.

Pile installation causes disturbance in the soil adjacent to the pile. Flaate (1972) studied impact

of timber pile installation on fine-grained soils. It was observed that installation of a circular

timber pile 0.33m in diameter formed a zone of up to 0.10 – 0.15 m from the pile shaft where the

soil was completely remoulded. Stiffness and undrained strength in this zone were found

severely diminished. It was also observed that outside the remoulded zone exists a zone of

reduced stiffness and undrained strength, or transition zone. According to Flaate (1972) the

extent of the transition zone largely depends on natural soil properties, pile dimensions and the

mechanism of penetration. The concept described by Flaate (1972) is shown in Fig. 3.1.

30


Soil deformations cause high pore pressures in excess of equilibrium hydrostatic values. The

magnitude of generated excess pore pressures will depend on the type of soil and its properties. A

number of accounts (Bjerrum & Johannessen, 1961; Lo & Stermac, 1965; Orrje & Broms, 1967;

Koizumi & Ito, 1967; Bozozuk et al., 1978; Roy et al., 1981 and Pestana et al., 2002) report

generation of significant positive excess pore pressures due to pile driving in fine-grained soils.

Baligh & Levadoux (1980) compiled data from a number of sites where pore pressures were

measured during pile installation (Fig. 3.2). It was found that, for most of the cases, the excess

pore pressures at the pile shaft were about twice the vertical effective stress and that the extent of

the generated pore pressures, having any significance (∆u/ σ΄v > 0.1), was about 20-30 pile radii.

For penetration under undrained conditions, generated excess pore pressure can be represented as

a sum of pore pressure generated due to change in the mean stress, and deviator shear stress, as

show in Eq. 3.1.

∆u = ∆umean + ∆ushear (3.1)

The components of excess pore pressure from Eq. 3.1 cannot be measured individually in the

field and can only be separated in the laboratory.

The pore pressure generated due to a change in mean stress, ∆σmean, is equal to the magnitude of

∆σmean change (assuming that water is incompressible relative to the soil). The magnitude of the

pore pressure in fine grained soils induced by shear is highly dependent on soil stress history

(OCR). Normally consolidated to lightly overconsolidated clays are contractive when sheared,

hence positive ∆ushear pore pressures are generated. Moderately to heavily overconsolidated

clays demonstrate dilatant behaviour when sheared, hence negative ∆ushear pore pressures are

generated. The magnitude of shear induced pore pressure is usually small for soft normally to

lightly overconsolidated clays, whereas more structured highly overconsolidated clays exhibit

larger magnitude of shear induced pore pressure.

3.2.2. FIELD DISSIPATION OF EXCESS PORE PRESSURE.

When pile installation into fine-grained soil is complete, the induced excess pore pressure will

gradually dissipate to the equilibrium value in time.

Water flow naturally takes the path of lowest resistance and due to the complex soil stratigraphy

and layering, accurate estimation of in-situ drainage characteristics is quite difficult. Field

studies by Bjerrum & Johannessen (1961), Koizumi & Ito (1967) and Roy et al. (1981), where

31


pore pressures were monitored during and after pile penetration into soft-fine grained soils,

indicate that over most of the pile length horizontal flow of water is predominant.

Gillespie & Campanella (1981) compared pore pressures measured at the different locations on

the CPT cone shaft. They conducted dissipation tests at the same depth in holes 1-2 meters apart,

with four different measurements locations: on the cone shoulder (standard u2 position, shown in

Fig. 3.3), 12.5, 25 and 38 cm from the cone shoulder. They found that the dissipation rate for u2

is only slightly higher than for the other tested locations. This implies that horizontal drainage

dominates the consolidation process.

Similar conclusions were reached from the theoretical studies of the effect of linear anisotropy in

soil consolidation characteristics on pore pressure dissipation behaviour by Levadoux & Baligh

(1980), Tumay et al (1982) and Houlsby & Teh (1988).

The rate of pore pressure dissipation largely depends on the soil hydraulic conductivity and its

consolidation characteristics. Immediately after pile installation the rate of pore pressure

dissipation may not be constant due to highly disturbed state of soil. However, after some initial

consolidation, it becomes constant (Komurka et al., 2003).

Dissipation behaviour varies depending on soil stress history. Dissipation response in normally

consolidated or lightly-overconsolidated clays is usually monotonic, with the pore pressure

magnitude gradually decreasing with time, as shown in Fig. 3.3a. Whereas dissipation behaviour

of overconsolidated clays is quite different. Coop & Wroth (1989) document pore pressures which

increase and then decrease after the driving of cylindrical steel piles in the heavily

overconsolidated Gault clay. Similar observations were made by Lehane & Jardine (1994), while

studying pore pressure response due to penetration of closed-ended pipe piles in the stiff glacial

clay deposit at Cowden, England. Coop & Wroth (1989) have suggested that the maximum

penetration pore pressure in overconsolidated soils is located at some distance away from the shaft.

This causes a rise of pore pressure at the shaft at early dissipation times due to redistribution effect.

Pore pressure measured at a standard monitoring location (u2) during CPTU dissipation tests in

overconsolidated clays also shows an initial increase followed by a subsequent decrease in

excess pore pressure with time, as shown in Fig. 3.3b (Davidson, 1985; Campanella et al., 1986;

Lutenegger & Kabir, 1988 and Sully & Campanella, 1994). Sully & Campanella (1994)

suggested that this phenomenon is related to the inflow of pore pressure from the zone of higher

gradients at the tip to the zone of lower gradients behind the tip.

32


3.2.3. OBSERVED AXIAL PILE CAPACITY AS FUNCTION OF DISSIPATION OF EXCESS PORE

PRESSURE.

Typically, when a pile is installed into fine-grained soil, high excess pore water pressures are

generated in the vicinity of pile. Over time the pore pressures induced by pile installation begin

to dissipate, primarily in a radial direction. Consequently the soil in the vicinity of the pile

consolidates. As the water content of the soil gradually decreases during the dissipation process,

the soil strength and stiffness recover and may increase. A number of studies linked pore

pressure dissipation, induced by pile installation, with the increase in pile bearing capacity.

One of the first documented accounts of such behaviour belongs to Seed & Reese (1957). They

studied the effect of pile driving on soil properties and pile bearing capacity on an instrumented

pipe pile, 0.15 m in diameter installed into sensitive soft clay at the San-Francisco – Oakland

bridge site, in California. Pore pressure measurements were taken in the vicinity of the pile after

installation. The pile was loaded seven times in a time span from 3 hours after installation to 33

days (800 hours). A dramatic increase in pile capacity (5.4 times) was reported, as shown in Fig.

3.4. The pore pressure measurements indicated full dissipation of the excess pore pressures due

to pile installation about 20 days after installation, the same period over which the pile acquired

most of its bearing capacity.

Konrad & Roy (1987) performed a comprehensive analysis of bearing capacity of friction piles

in the marine clays at St.Alban, Quebec. Soil-pile interaction was studied on two closed ended

instrumented pipe piles. Combined results of pile loading tests and pore pressure measurements,

shown in Fig. 3.5, indicate an increase in pile bearing capacity with dissipation of the excess pore

pressures, so that after full dissipation of the excess pore pressures in about 25 days, pile bearing

capacity had increased by about 97% of the total capacity observed in two years.

Other field studies of pile capacity in fine-grained soils, including Eide et al. (1961), Flaate

(1972) and Chen et al. (1999), confirm the increase in pile bearing capacity with dissipation of

excess pore pressures generated during pile installation.

Randolph & Wroth (1979) compared the theoretical decay of pore pressure with time with the

measured bearing capacity of driven piles, reported by Seed & Reese (1957) and Eide et al

(1961), as a percentage of their long term bearing capacity, as shown in Fig. 3.6. The main

implication of this figure is that the pile bearing capacity is strongly dependent on the degree of

excess pore pressure dissipation.

33


Komurka et al. (2003) studied the effect of soil/pile set up (increase of pile capacity with time).

They idealized the mechanism of set up as follows:

• Phase 1 - Logarithmically Nonlinear Rate of Excess Porewater Pressure Dissipation.

• Phase 2 - Logarithmically Linear Rate of Excess Porewater Pressure Dissipation.

• Phase 3 – Aging/Thixotropy.

The first two phases are associated with the dissipation of excess pore pressure induced by pile

installation. During the third stage, increase in pile capacity occurs with no change in pore

pressure (constant effective stress). The phenomenon of aging is related to the particle frictional

interlocking and the thixotropy related to chemical bonding or cementation between the particles.

The concept of soil/pile set up proposed by Komurka et al. (2003) is schematically represented in

Fig. 3.7. It can be seen that the majority of the pile capacity increase is related to the pore

pressure dissipation and the effect of aging and thixotropy on pile capacity increase may not be

very significant. Here we should recognize that in fine grained soils it is likely that aging and

thixotropy may begin to occur before complete pore pressure dissipation takes place. However,

due to the slow rate of these processes they are expected to take place over a much longer time

span than the excess pore pressure dissipation.

As such, the treatment of thixotropic and aging effects is impractical in most piling analysis.

Based on the works of Soderberg (1962) and Randolph & Wroth (1979), Guo (2000) suggested

that the problem of predicting the variation of capacity is one of predicting the excess pore

pressure at the pile shaft as a function of time.

3.3. PREDICTION OF TIME-DEPENDENT PORE PRESSURE RESPONSE.

3.3.1. PREDICTION METHODS.

Prediction of pore water pressure response is quite complex. A number of factors complicate the

analysis: vertical drainage, soil remoulding in the vicinity of penetrating body, soil non-linearity

and anisotropy, boundary effect of soil layering, soil stress and strain history (Campanella &

Robertson, 1988).

There is no method available, among those published to date, which can account for the full

complexity of the pore water pressure response. However, a reasonable approximation of the

problem is possible. Discussed herein are well known prediction solutions, varying in their

degree of complexity and comprehensiveness, that provide some capabilities for estimation of

34


pore water pressure response generated due to pile (or cone) penetration and subsequent pore

pressure dissipation.

A selection of such solutions is shown in chronological order in Table 3.1. It should be noted that

the majority of these solutions were specifically developed for prediction of the pore pressure

dissipation around piezocones. Due to observed similarities between pile and piezocone

penetration, all of these solutions are generally assumed applicable to pore prediction around

piles.

The following sections will present basic concepts behind the prediction methods and address

their predictive capabilities.

35


Tale 3.1. Solutions for prediction of pore response induced by penetration of piles and piezocones (modified after Burns & Mayne, 1998).

Reference Cavity Type

Soil Model

Initial Pore Pressure

Consoli-dation

Comments

Soderberg (1962) Cylindrical, radius R Elasto-plastic1 ∆u/∆ui=R/r 1-D Consolidation around driven piles;

Finite Differences

Torstensson (1977) Cylindrical Spherical Elasto-plastic ∆ui=2suln(rp/r)

∆ui=4suln(rp/r) 1-D No shear stresses;

Finite Difference.

Randolph & Wroth (1979) Cylindrical Elasto-plastic ∆ui=2suln(rp/r) 1-D Consolidation around driven piles; Analytical.

Baligh & Levadoux (1980) Levadoux & Baligh (1986)

Piezocone Model Non-linear From strain path method;

Total stress soil model 2-D

Battaglio et al. (1981) Cylindrical Spherical Elasto-plastic ∆ui=2suln(rp/r)

∆ui=4suln(rp/r) 1-D Shear by empirical method;

Finite Difference Senneset et al. (1982) Cylindrical Elasto-plastic ∆ui=2suln(rp/r) 1-D

Tumay et al. (1982) Piezocone Model Linear From strain path method; Experimental data 1-D

Gupta & Davidson (1986) Piezocone Model Elasto-plastic Modified cavity expansion; Dissipation as

cone penetrates 1-D Isotropic and anisotropic

Houlsby & Teh (1988); Teh & Houlsby (1991)

Piezocone Model Non-linear Predicted by large strain finite element

analysis and strain path method 1-D Finite Difference

Whittle (1992) Pile Model Non-linear From strain path method; Effective stress-strain model 1-D Coupled consolidation.

Sully & Campanella (1994) Piezocone Model Non-linear Predicted by large strain finite element

analysis and strain path method 1-D Empirical time shift for OC dissipation

Burns & Mayne (1995) Spherical Elasto-plastic ∆uoct=4suln(rp/r) ∆ushear=σ′vo [1-(OCR/2)0.8] 1-D Incorporates shear stresses; models OC

dissipation; Finite Difference Collins & Yu (1996) Cylindrical Non-linear Closed form solutions. - No consolidation analysis

Burns & Mayne (1998) Spherical Elasto-plastic ∆uoct=4suln(rp/r) ∆ushear=σ′vo[1-(OCR/2)0.8] 1-D Incorporates shear stresses; models OC

dissipation; Analytical Cao et al. (2001) Cylindrical Non-linear Closed form solution. - No consolidation analysis

Whittle et al. (2001) Tapered Piezocone Model Non-linear From strain path method;

Effective stress-strain model 1-D Coupled consolidation

1 – simple elastic plastic soil models, such as Tresca, Von Mises,; 2 – advanced soil models, such as Cam Clay, Modified Cam Clay, MIT-E2 and etc

36


3.3.2. BASIC CONCEPTS BEHIND EXISTING PREDICTION SOLUTIONS.

3.3.2.1. MODELLING ANALOGUE FOR SIMULATION OF PILE OR CONE PENETRATION.

The majority of methods for predicting the pore pressure response due to pile, or cone,

penetration uses either a cavity expansion analogy or the strain path method for simulation of

the impact of a penetrating body on the surrounding medium.

During pile installation, a volume of soil equal to the volume of pile is displaced. The soil

displacement occurs in the direction of least resistance, as shown in Fig. 3.8. Initial pile

penetration may cause a surface heave (zone I in Fig. 3.8). With continuing pile installation,

such effect becomes less evident and eventually ceases to occur. Soil in a region around the pile

tip (zone III in Fig. 3.8) undergoes extensive disturbance and remoulding. Model studies of the

displacement pattern in this region by Clark & Meyerhoff (1972) and Roy et al. (1975) have

shown that, if compared, the displacements are somewhat in-between deformation patterns

caused by the expansion of a spherical cavity and a cylindrical cavity. These studies have also

shown that little further vertical movement of soil occurs at any level once the tip of the pile has

passed that level. Randolph et al. (1979a) compared measurements of the radial movement of

soil near the pile mid-depth taken from model tests by Randolph et al. (1979b), field

measurements by Cooke & Price (1973) and their own theoretical predictions using cylindrical

cavity expansion in an elastic-plastic medium under plane strain conditions, as shown in Fig.

3.9. In this figure, the radial displacement of the soil during pile driving has been plotted against

radial position before driving. It can be seen that the measured radial displacements agree very

well with the theoretical predictions. This indicates that it is reasonable to expect that the stress

changes in the soil over much of the length of the pile shaft (zone II in Fig. 3.8) will be similar

to those produced by the expansion of a cylindrical cavity.

The installation of a pile may be modelled as the expansion of a cavity from zero radius to the

radius of the pile. Cavity expansion analogue for prediction of stresses and pore pressures

changes induced by pile (or cone) penetration was applied by a number of researchers, including

Soderberg (1962), Torstensson (1977), Randolph & Wroth (1979c), Battaglio et al. (1981),

Senneset et al. (1982), Gupta & Davidson (1986), Burns & Mayne (1995), Burns & Mayne

(1998), Collins & Yu (1996) and Cao et al. (2001).

37


Baligh (1985) criticized solutions based on the cavity expansion analogy, existing to that date,

for their inability to predict the correct strain path in the vicinity of the cone, or pile tip and

proposed an alternative modelling approach. Studying soil deformation under deep undrained

penetration of rigid objects in saturated clays, Baligh (1985) found that, given kinematic

constraints for deep penetration problems, soil deformations could be treated as independent

from soil shearing resistance and essentially strain-controlled. Hence, deep steady-state

penetration of a rigid body in saturated clay may be reduced to a flow problem, where soil

particles move along streamlines around a fixed rigid body. Using this analogy Baligh (1985)

developed an approximate analytical technique for analysing deep penetration problems, called

the strain path method. Applying this method, stresses and pore pressures induced by

installation of the rigid body into the ground can be predicted.

The strain path method was applied to pore pressure predictions by Levadoux & Baligh (1980),

Tumay et al. (1982), Houlsby & Teh (1988), Teh & Houlsby (1991), Whittle (1992), Sully &

Campanella (1994) and Whittle et al. (2001).

Generally, neither the cavity expansion analogue nor the strain path method are capable of fully

modelling the soil conditions during pile or cone penetration, due to the simplifications of soil

response involved in the analysis. Randolph (2003) indicated that, if compared, the strain path

method produces more realistic and detailed predictions for the changes in stresses and strains in

the vicinity of the pile tip. However, moving a few diameters away from the pile tip, the radial

displacement fields modelled by the strain path method and cavity expansion solutions are very

similar, apart from a very narrow zone (with thickness of about 10% of the pile radius) around

the pile shaft.

Randolph (2003) suggested that the use of the cylindrical analogy for the modelling of the pore

pressure response due to installation of conventional piles provides a reasonable approximation.

3.3.2.2. MODELLING FRAMEWORK.

Changes in soil stresses and pore pressures due to pile or cone penetration are typically

computed using either the total stress soil models (such as Tresca, Von Mises, Hyperbolic, MIT-

T1), or the effective stress soil models (such as Cam Clay, Modified Cam Clay, MIT-E2, MIT-

E3).

38


Total stress soil models can provide realistic predictions of stresses and pore pressures caused by

undrained penetration. However, these soil models are unable to describe changes in the

effective stress that occurs during consolidation. Total stress model are used to estimate

distribution of excess pore pressure at the end of pile, or cone, penetration that can be employed

as an input into uncoupled linear consolidation solution derived from the diffusion theory by

Rendulic (1936) and Terzaghi (1943). This solution accounts for one way “solid to fluid”

coupling that occurs when a change in applied stress produces a change in fluid pressure or fluid

mass.

Effective stress soil models allow the simulation of soil behaviour throughout pore pressure

generation and subsequent consolidation. These models are often used in conjunction with

consolidation solution derived from the theory of elasticity by Biot (1941). The Biot consolidation

solution is fully coupled, i.e. accounts for both “solid to fluid” and “fluid to solid” coupling, where

“fluid to solid” coupling occurs when a change in fluid pressure or fluid mass is responsible for a

change in the volume of the soil.

Fully coupled analysis using the effective stress soil models is more realistic and more accurate

in comparison with uncoupled analysis with total stress soil models.

3.3.3. OVERVIEW OF EXISTING PREDICTION SOLUTIONS.

The accuracy of pore pressure dissipation response predictions largely depends on correct

estimate of the distribution of generated excess pore pressures. Approaches to modelling of the

pore pressure dissipation have not changed significantly over the years, whereas the cavity

expansion and strain path based methodologies for prediction of the excess pore pressure

generated during soil penetration have undergone many revisions. In the sections presented

below major developments in these methodologies are discussed.

3.3.3.1. CAVITY EXPANSION SOLUTIONS.

Vesic (1972) used a framework of the cavity expansion theory for development of closed form

solutions for prediction of stresses and pore pressure distribution around an expanding cavity

under undrained conditions in a linear elastic perfectly plastic medium.

The pore pressure predictions were based on the following assumptions:

• the soil is isotropic;

39


• the cavity wall is impermeable;

• outside of the plastic zone, pore pressures are equal to zero;

Closed form solution for pore pressure predictions, due to expansion of cylindrical or spherical

cavity, developed by Vesic (1972) in its original or modified form were applied to the problem

of prediction of pore pressure distribution due to penetration of piles and piezocones by

Soderberg (1962), Torstensson (1977), Randolph & Wroth (1979c), Battaglio et al. (1981),

Senneset et al. (1982) and Gupta & Davidson (1986).

Prediction of pore pressure generation using simple linear elastic perfectly plastic models holds

an important limitation - no shear-induced pore pressure will be generated if the medium is

linear-elastic. Hence, for the linear elastic-plastic model ∆ushear equal to 0 up to failure and the

effective stress path is vertical. Failure is assumed to occur when the effective stress path

reaches the effective stress strength envelope. Once the strength envelope is reached, no change

in effective stress will take place during perfectly plastic shearing since shear stress is 0. Thus,

the linear elastic perfectly plastic model predicts ∆ushear = 0 at any point around the cavity and

therefore ∆u = ∆umean.

Battaglio et al. (1981) and Gupta & Davidson (1986) attempted to overcome this limitation by

introducing into the solution laboratory derived Skempton’s A and Henkel’s α pore pressure

parameters. Provided that these parameters are normally estimated from the measured pore

pressure at failure, they may not represent correctly the large strain ∆ushear response expected at

the cavity/soil interface and its immediate vicinity. Therefore the effectiveness of their use is

questionable.

Generally cavity expansion solutions based on simple linear elastic perfectly plastic soil models

may provide reasonable prediction of pore pressure response for normally consolidated to lightly

overconsolidated fine-grained soil. However, they may not be accurate for heavily over-

consolidated soils (Randolph et al., 1979a; Coop & Wroth, 1989). Cavity expansion solutions

based on advanced soil models, such as critical state soil models, allows this limitation to be

overcome. The major advantage of the critical state type soil models is their ability to link

compression and shear behaviour in a more realistic way than their linear elastic perfectly plastic

counterparts, so that both ∆umean and ∆ushear can be accounted for.

40


Burns & Mayne (1995) developed a hybrid formulation, where the pore pressure generated by

the change in the mean normal stress was estimated from the spherical cavity expansion

derivations by Torstensson (1977) and shear induced pore pressure was derived using the

concept of Modified CamClay.

Collins & Yu (1996) studied undrained cylindrical and spherical large strain cavity expansion in

soil modelled by different critical state soil models (CamClay, CamClay Model with Hvorslev

yield surface, Modified CamClay). The analysis was performed for both normally and

overconsolidated clays. The main objective of their work was developing analytical and semi-

analytical solutions for cavity expansion in critical state soil. Analysis by Collins & Yu (1996)

showed that for cavity expansion in critical state soil with high OCR the excess pore water

pressure close to the pile shaft is negative. That is in good agreement with the field observations

by Coop & Wroth (1989) and Bond & Jardine (1991).

Cao et al. (2001) studied undrained cavity expansion in modified CamClay. They derived

closed form solution for effective and total stress around the cavity and, also, for generated

excess pore pressures. Their derivations are akin to the solution by Burns & Mayne (1995).

Comparison of the pore pressures computed by Collins & Yu (1996) and Cao et al. (2001)

solutions for Modified CamClay showed no differences.

Overall, there is a solid body of cavity expansion solutions for predicting pore pressure

response, starting from solutions based on simple elasto-plastic total stress soil models to

solutions based on relatively complex effective stress critical state soil models. The problem

with solutions based on simple elasto-plastic soil models is their inability to realistically account

for shear induced pore pressures, which is limiting their applications to normally consolidated to

lightly overconsolidated soils. A more realistic representation of soil behaviour and pore

pressure response can be achieved by employing critical state soil models. A limited number of

solutions exist in this area and available solutions are focused on predicting generation of the

excess pore pressures. Only the uncoupled hybrid cavity expansion theory - critical state

solution by Burns & Mayne (1998) is able to predict both pore pressure generation and

subsequent dissipation. Yu (2000) published a comprehensive review of the existing cavity

expansion methods in geomechanics. In the chapter related to the modelling of axial capacity of

driven piles it was acknowledged that: “Further work is needed to develop consolidation

solutions using critical state soil models such as those used by Collins & Yu (1996).

41


3.3.3.2. SOLUTIONS BASED ON STRAIN PATH METHOD.

Levadoux & Baligh (1980) utilized the strain path method for predicting pore pressures induced

by penetration of CPT cones. The cone was treated as a static penetrometer with soil flowing

around it like a viscous fluid. Excess pore pressures generated by cone penetration were

calculated by predicting soil velocities and strain rates using potential theory (neglecting soil

shearing resistance and assuming incompressible fluid flow); integrating the strain rates along

the continuous stream lines, located axisymmetrically at different radial distances from the cone,

to determine the strain history of the soil elements, and computing the deviatoric and shear-

induced pore pressures using a total stress model MIT-T1.

A comprehensive analytical study of cone penetration in clay was conducted by Houlsby & Teh

(1988). In their study, initial pore pressures due to cone penetration were estimated based on

strain path method combined with a simple elasto-plastic total stress von Mises soil model.

As discussed in the previous section total stress models are unable to link the strength of the soil

and its change with the current effective stresses and soil stress history, so their prediction

capabilities are limited.

More realistic analysis was proposed by Whittle (1992) who applied the strain path method in

conjunction with effective stress soil model MIT-E3 and coupled consolidation to the piling

analysis. This solution was later extended to tapered piezocones (Whittle et al., 2001).

It appears that the most advanced of the reviewed solutions employing the strain path method is

the solution by Whittle (1992). According to Whittle (1992), this solution is able to provide

reliable prediction of stresses and pore pressures during and after pile installation. It should be

noted however that numerical implementation of this approach is not available in the public

domain. Moreover, this solution did not find wide application in the geotechnical analysis due

to its high complexity.

3.4. SUMMARY.

Available pore pressure prediction methods are evolved from simple solutions based on total

stress soil models and uncoupled consolidation to more rigorous solutions employing effective

stress soil models and coupled consolidation. Solutions based on the effective stress soil models

and coupled consolidation are the most realistic.

42


It appears that the choice of the modelling framework has a decisive influence on the pore

pressure predictions, whereas the choice of either cavity expansion or strain path analogues for

modelling pile, or cone, penetration within a particular framework does not have a significant

impact on the pore pressure predictions.

The complexities involved in implementation of existing coupled effective stress solutions

employing the strain path method have limited their practical application

In the field of cavity expansion solutions, fully coupled effective stress solutions are only

beginning to emerge. It appears that any advances in the current state of knowledge of the

subject should follow recommendations by Yu (2000) who stated: “… work is however needed

to develop further consolidation solutions with critical state models that are accurate for both

normally consolidated and heavily overconsolidated clays”.

43


Fig. 3.1. Effect of pile installation on soil conditions.

Fig. 3.2. Measured excess pore pressures due to installation of piles (after Baligh & Levadoux, 1980).

44


45

Fig. 3.3. Typical pore pressure dissipation measured during CPTU tests (modified after Burns


45

Fig. 3.3. Typical pore pressure dissipation measured during CPTU tests (modified after Burns & Mayne, 1998). a). lightly overconsolidated Clay; b). heavily overconsolidated Clay.

a).

b).


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


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


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


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


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


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

models were developed: CamClay (Roscoe, Schofield & Thurairajah, 1963), Modified CamClay

(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


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


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


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


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


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).

4.3.2. BIOT COUPLED CONSOLIDATION THEORY.

Natural fine-grained soils exhibit low hydraulic conductivity, so excess generated pore pressures

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


- 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


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


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


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


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


Fig. 4.8. NorSand fit to Bothkennar Soft clay in CK0U triaxial shear (after Shuttle, 2003).

64


-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


0

20

40

60

80

100

120

0 20 40 60 80 1p, kPa

q, k

Pa

NorSand


00

Fig. 4.9. NorSand simulation fit to constant p=80kPa drained triaxial test on Bonnie silt.

65


* 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=.

. * εvp = εvp iter-1 + dεvp track viscoplastic strain this increment

* ∫ BTDεvp calculate bodyloads increment

* bodyloads = bodyloadsiter-1 + bodyloads increment

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

Crawford & deBoer, 1987), Crawford & Campanella (1991), Dolan (2001) & Weech (2002)

carried at or in a close vicinity of the Colebrook site. Information on the soil properties obtained

during these investigations was used to derive the input parameters for modelling and are

presented in this chapter. It should be noted that the in-situ component of the dataset was the

most significant; the information on laboratory tests was limited to consolidation tests only.

As in any modelling study the choice of input parameters for numerical simulation is very

important and will govern the modelling results. Thus a comprehensive critical analysis of all

available information is required to derive a parameter set reasonable for modelling.

5.2. SOIL PARAMETERS FOR MODELLING.

The NorSand-Biot code requires 13 input parameters. Due to the fact that not all of the

parameters may be determined with the necessary degree of confidence for every modelling

parameter an acceptable range and the best estimate values are alternatively derived. In the

following sections the choice of all NorSand modelling parameters is discussed, the related

parameters are grouped where possible.

5.2.1. ELASTIC PROPERTIES G, υ.

Elastic properties of the soil in the NorSandBiot formulation are represented by the shear

modulus G and Poisson’s ratio ν.

67


There are many references in the technical literature to a shear modulus dependence on shear

strain. In the geotechnical analysis shear modulus G is quite often derived through empirical

shear modulus degradation schemes, such as G(γ)/Gmax,, to the level of strain the analysis is

performed for. Sun et al. (1988) proposed such a correlation for fine-grained soils with

plasticity index PI within a range of 10 to 20% (predominant range for the Colebrook silty clay,

for the elevations of interest), as shown in shown Fig. 5.1. It should be noted that in this figure

the shear modulus G is not the real elastic shear modulus but an implied shear modulus which

would be obtained if we assume that all of the strains are elastic, i.e. we are treating an elasto-

plastic response as purely elastic. For many laboratory and field measurement techniques, the

test itself applies shear strains above those required for a plastic response. Fig. 5.2 shows the

levels of shear strain applied for a range of in situ and laboratory tests. For the higher strain

tests it is only possible to calculate G, and the true value of Gmax is unknown.

The true elastic shear modulus, Gmax, is observed at shear strains less than about 0.001 – 0.002%

(a G(γ)/Gmax of 1.0 in Fig. 5.1). Above this strain level, particle reorientation, among other

effects, means that the soil behaviour is not truly recoverable. However, most numerical models

do not account for these very small strain effects and assume true elastic behaviour within the

yield surface. For the modelling presented in this thesis, we have also incorporated some of the

very small strain plastic response into the elastic portion of the constitutive model.

The two methods of achieving accurate measurements of the true elastic shear modulus, Gmax,

are to incorporate bender elements into laboratory testing or to measure the shear wave velocity

in-situ using the seismic cone. At the Colebrook site, in-situ shear wave velocities were

measured using the seismic cone (Weech, 2002).

A profile of Gmax determined from shear wave velocities by Weech (2002) is presented in Fig.

5.3. A best fit linear trend line of variation of Gmax with elevation shown in Fig. 5.3, can be

expressed as following:

Gmax= - 2.36(Elevation) + 1.9 (5.1)

Based on Eq. 5.1, for the range of elevation –4.57 to –9.92 metres, Gmax increases from 12.7 to

25.3 MPa.

To estimate the value of G for the Colebrook site Weech (2002) employed a linear-elastic

perfectly plastic analytical solution, together with Sun et al. (1988) shown in Fig. 5.1. From the

68


measured pore pressure distribution caused by installation of the pile shaft, a linear elastic G was

inferred from cylindrical cavity expansion theory with a Tresca yield criterion. Assuming that

this linear G corresponds to the tangent value at 50% of failure Weech obtained γ50 ≈ 0.15%.

According to Fig. 5.1 this level of strain corresponds to the range of G(γ)/Gmax from 0.25 to 0.4.

Correcting previously cited values of Gmax by a factor of 0.4 we have the following range of G

values: 5.1 MPa for the elevation of -4.57 m and 10.1 MPa for the elevation –9.92 m.

D’Appolonia et al. (1971) compare the rigidity index Ir = G/su with soil plasticity. According to

them Eu/su (where Eu is the undrained Young’s modulus) typically ranges between 1000 and

1500 for low-plasticity inorganic clays of moderate to high sensitivity, and therefore G/su should

range from 330 to 500 (G = Eu/3). Estimated average Ir for the Colebrook soft sensitive silty

clay will be around 350 (based on the derived earlier range of G values and su values taken from

Fig. 2.5), which is in agreement with D’Appolonia et al. (1971).

Weech established a profile of rigidity index Ir for the silty clay layer, as shown in Fig. 5.4.

Based on this profile and profile of undrained shear strength (Fig. 2.5) a variation of shear

modulus with elevation was inferred, as shown in Fig. 5.5. The average best fit linear trend line

of variation of G with elevation is also shown in Fig. 5.5, based on this linear trend:

G = - 0.75(Elevation) + 2.4 (5.2)

The shear modulus profile developed from the Weech (2002) analysis is assumed to be

reasonable for the current analysis. Therefore, for the studied elevations, using Eq. 5.2, the

range of G is 5.8 … 9.8 MPa, with the average of 7.8 MPa.

There are no data available for the value of Poisson’s ratio for the silty clay layer. For most

soils the effective Poisson’s ratio, ν, is within a range 0.1 … 0.3. For the current analysis it was

assumed equal to 0.2.

5.2.2. OVERCONSOLIDATION RATIO OCR.

A dataset of stress history information for the Colebrook site can be comprised by the OCR

profiles interpreted from CPT soundings by Weech (2002) (using empirical correlations by

Schmertman, 1978; Sully et al., 1990; Mayne, 1991 and Chen & Mayne, 1995) and OCRs

estimated from the consolidation tests performed during MoTH and Crawford & Campanella

(1991) investigations. All available OCR data is presented in Fig. 5.6.

69


According to the OCR data interpreted from the CPT, shown in Fig. 5.6, all CPT soundings

display a similar trend for the silty clay layer that can be divided in three distinctive zones:

• Zone 1: elevation -4.1 m … -5.0 m, moderate overconsolidated, OCR 3 … 7, with a

midrange value of 5;

• Zone 2: elevation -5.0 m … -9.0 m, lightly overconsolidated, OCR 1.7 … 3, with a

midrange value of 2.35;

• Zone 3: elevation -9.0 m … -12.0 m, lightly overconsolidated, OCR 1.2 … 2.2, with a

midrange value of 1.7.

Fig. 5.6 indicates consistent trends with depth from all CPT data and laboratory specimens, with

the values of OCR estimated from the laboratory data being at the lower bound of the CPT

derived values. The CPT data indicate variability in the derived OCR values for a given depth

possibly due to spatial variability of the site. The degree of sample disturbance for the

laboratory estimated values is unknown, and is likely to reduce the inferred OCR. Therefore, for

the current analysis the full range of laboratory and in-situ estimated values of OCR are

employed. For the silty clay layer, within elevation –4.57 to –9.92 metres the acceptable range

of overconsolidation ratio is 1.2 … 2.8, with an average OCR of 2.2.

5.2.3. COEFFICIENT OF LATERAL EARTH PRESSURE K0.

The coefficient of lateral earth pressure, K0, can be estimated based on empirical correlations

developed for the interpretation of CPT test data, or by linking K0 to other soil properties. Table

5.1 shows the correlations employed in this study.

Table 5.1. List of correlations used to estimate K0 from CPT test data.

Author Formulation

Mayne & Kulhawy (1982)

Ko = (1-sinφ΄)·OCRsinφ′

φ′ =35° was assumed Sully & Campanella (1991)

Ko = 0.5 + 0.11·PPSV where PPSV = (u1-u2)/σ΄ vo

Weech (2002) interpreted profiles of K0 using Sully & Campanella’s (1991) correlation and also

estimated K0 from the OCR profile shown in Fig. 5.6. The result is presented in Fig. 5.7. According

to this figure, the K0 estimated from both of these methods are generally in good agreement,

starting from elevation –5.5 m. Overall, K0 for the silty clay layer varies primarily within a

range of 0.56 to 0.76. For the modelling purposes, a midrange K0 equal to 0.66 was assumed.

70


5.2.4. HYDRAULIC CONDUCTIVITY DERIVATION.

Published accounts of geotechnical investigation performed at the Colebrook site provide no

information on direct measurements of hydraulic conductivity. Therefore hydraulic

conductivity should be estimated based on the coefficient of consolidation and the coefficient of

volume change, mv, as expressed by the following equation:

kr = ch mv γw 1 (5.3)

In this study they were determined as described in the following sections.

5.2.4.1. COEFFICIENT OF CONSOLIDATION.

All subsurface investigations carried out at the Colebrook site (MoTH; Crawford & Campanella,

1991 and Weech, 2002) included estimation of the coefficient of consolidation, either from

consolidation or from CPTU tests.

In the conventional one-dimensional consolidation test, deformation of the soil skeleton and the

movement of pore fluid are restricted to the vertical direction, while studies of in-situ soil

behaviour indicates that the movement of pore fluid tends to flow radially (as discussed in

Section 3.2.2). Thus, from conventional consolidation test the coefficient of consolidation in a

vertical direction can be estimated, whereas the piezocone dissipation test provides an estimate

of the coefficient of consolidation in a horizontal direction.

If the soil fabric is isotropic, the horizontal and vertical values of the coefficient of consolidation

would be identical. However, natural fine-grained soils are anisotropic and exhibit different

consolidation characteristics in the horizontal and vertical directions. For natural sedimentary

clays with some evidence of layering, Baligh & Levadoux (1980) suggested the use of

coefficient of horizontal to vertical consolidation ratio ch/cv between 2 and 5. According to

Crawford & Campanella (1991), experience with the Fraser River Delta clayey silts suggest that

a value of ch/cv = 2.5 is appropriate. This value was adopted for the current analysis.

To obtain in-situ estimates of the coefficient of consolidation in the horizontal direction, ch, it is

common to use the time required to achieve 50% dissipation during the CPTU dissipation test,

according to the following equation (by Baligh & Levadoux, 1980):

1 γw – unit weight of water, constant taken as 9.8 kN/m3

71


ch = T50⋅R2/t50 (5.4)

where T50 is the normalized time factor corresponding to 50% dissipation, which is derived from

theoretical dissipation curves.

For the Colebrook site Crawford & Campanella (1991) reported ch of 0.020 cm2/s based on the

data from a CPTU dissipation test at 10 m depth (elevation –11.3 m).

Weech (2002) compared CPTU dissipation curves from the Colebrook site, plotted in a root

time and log time scales, with a number of theoretical solutions. Weech found that the shape of

the post-peak portion of the corrected CPTU dissipation curves is in good agreement with the

dissipation solutions based on the strain path method used by Teh & Houlsby (1991) and

Levadoux & Baligh (1980, 1986). The closest agreement with measured response was produced

by the Teh & Houlsby (1991) solution, when the CPTU data were plotted in a “log time” scale.

Based on this solution, for the silty clay layer, an average ch of 0.019 cm2/s (standard deviation

of 0.005) was estimated. This value is in an excellent agreement with the ch of 0.020 cm2/s

reported by Crawford & Campanella (1991).

In-situ estimated coefficient of consolidation can be complemented by the laboratory derived

values reported by Crawford & deBoer (1987) and Crawford & Campanella (1991), see Table

A.1 and A.2 (Appendix A). An average ch = 0.003 cm2/s was derived from the MoTH data.

Crawford & Campanella (1991) reported a very similar average value of ch = 0.004 cm2/s.

Both in-situ and laboratory estimated coefficients of consolidation are presented in Fig. 5.8.

According to this figure there is a difference, of up to an order of magnitude, between laboratory

and in-situ estimated coefficients of horizontal consolidation.

There are important differences between in-situ and laboratory estimated coefficients of

consolidation that should be considered while comparing the data. They can be summarized as

follows:

• During penetration, the cone remoulds the soil in its vicinity (this has an impact on soil

properties around the cone). Consequently, during a piezocone dissipation test,

consolidation takes place in a partially remoulded soil, which differs from the laboratory

situation where consolidation takes place in a sampled, but not remoulded, soil specimen

(Gillespie & Campanella, 1981).

72


• One-dimensional consolidation tests use a very small sample of soil, while the cone test

is performed in-situ in the deposit affecting a large volume of soil surrounding the cone.

• One-dimensional consolidation tests begin with a homogeneous initial distribution of

excess pore pressure throughout the soil specimen, while the pore pressures resulting

from a piezocone test has a radial gradient.

Additionally, it is important to consider that after stopping cone penetration, less than 50% of

the consolidation around the cone for the pore pressure dissipation occurs in the recompression

mode (Baligh & Levadoux, 1980). To obtain the equivalent values in the normally

consolidated (NC) mode, CPTU data has to be corrected. Based on experience, Campanella et

al. (1983) showed that for Fraser River Delta normally to slightly overconsolidated (OCR ≈ 2)

clayey silts:

ch(NC) = 0.25 ch(CPTU) (5.5)

If the coefficients of horizontal consolidation presented in Fig. 5.8, estimated from in-situ data,

are corrected according to Eq. 5.5, a quite good agreement between in-situ and laboratory

derived values of ch is found, as shown in Fig. 5.9. According to this figure, the majority of the

values of coefficient of horizontal consolidation, ch, are within a range from 0.002 to 0.008

cm2/s. This range is similar to the range of ch = 0.002 … 0.007 cm2/s (Table A.3, Appendix A),

used by Byrne & Srithar (1989) in their numerical analysis. The average value of coefficient of

horizontal consolidation, ch, is 0.005 cm2/s.

5.2.4.2. COEFFICIENT OF VOLUME CHANGE, mv

The coefficient of volume change is a function of the constrained modulus:

M

mv1

= (5.6)

Crawford & Campanella (1991) reported values of constrained modulus derived from DMT and

CPTU in-situ tests and from the laboratory consolidation tests. Based on the in-situ data, for

the silty clay layer, they report an average M = 2400 kPa, which is in agreement with the

average derived from consolidation tests, M = 2300 kPa (see Table A2, Appendix A). For the

current analysis overall average M = 2350 kPa was assumed. According to Eq. 5.6

corresponding value of mv = 4.25·10-4 kPa-1.

73


5.2.4.3. RADIAL HYDRAULIC CONDUCTIVITY, kr

Knowing the coefficient of horizontal consolidation and the coefficient of volume change, radial

hydraulic conductivity can now be estimated according to Eq. 5.3, as shown in Table 5.2.

Table 5.2. Calculation of radial hydraulic conductivity, kr.

ch cm2/s

mv 1/kPa

kh m/s

0.002 4.25·10-4 8.5·10-10Range 0.008 4.25·10-4 3.4·10-9

Average 0.005 4.25·10-4 2.1·10-9

The average kh = 2.1 ·10-9 m/s was assumed for further analysis

5.2.5. VERTICAL EFFECTIVE STRESS σ΄vo AND EQUILIBRIUM PORE PRESSURE uo.

A profile of vertical effective stress, shown in Fig. 5.10 was established based on an average unit

weight of silty clay layer of 17.8 kN/m3, estimated from index tests performed by Dolan (2001).

The linear trend can be expressed by the following equation:

σ΄v0 (kPa)= -8.0(Elevation) – 3.7 (5.7)

For the range of elevations from –4.57 to –9.92 metres, σ΄v0 increases from 32.9 to 75.7 kPa.

The average σ΄v0 over this elevation range is 54.3 kPa.

The profile of equilibrium pore water pressure, shown in Fig. 5.11 was established based on

piezometers measurements taken prior to helical piles installation by Weech (2002). The plotted

equilibrium pore pressure measurements are artesian, tend to increase with depth almost

linearly, and can be approximately described as following:

u0 (kPa)= -10.2(Elevation) - 7.1 (5.8)

For the range of elevation from -4.57 to -9.92 metres, u0 increases from 39.5 to 94.1 kPa. The

average u0 over this elevation range is 66.8 kPa.

5.2.6. NORSAND MODEL PARAMETERS DERIVATION.

There are six NorSand specific parameters that are required for the current analysis: Mcrit, χ,

Hmod, λ, Γ, and ψ. Normally these parameters are selected based on comparisons between

modelling and triaxial test data. No such data exist for the Colebrook site. Hence, this

74


discussion is focused on establishing reasonable estimates for the NorSand parameters for the

silty clay layer based on all available information.

5.2.6.1. CRITICAL STATE COEFFICIENT, Mcrit

The critical state coefficient Mcrit under triaxial conditions can be calculated by Eq. 4.3 if the

constant volume friction angle, φ΄cv, is known.

According to Crawford & deBoer (1987), for the silty clay layer φ΄ varied between 33…35

degrees. Using the correlation by Mitchell (1993) between effective friction angle and

plasticity, for the range of plasticity index PI observed at the Colebrook site 10 … 20 %, a range

of acceptable friction angles is between 30 and 36 degrees. This range was assumed for the

analysis. None of the mentioned earlier sources provide the exact definition of φ΄, so for the

current study it is assumed that reported values are for peak effective friction angle.

Knowing the peak effective friction angle, we can estimate a constant volume friction angle,

φ΄cv, using the correlation developed by Bolton (1986). Assuming loose alluvial soil values of

φ΄cv will be approximately 2 degrees lower than for peak friction angles, the constant volume

friction angle φ΄cv would vary in between range 31 … 33 degrees. This leads to values of critical

state coefficient Mcrit between 1.113 to 1.374. For average φ΄cv = 32 degrees, Mcrit = 1.243.

5.2.6.2. STATE DILATANCY PARAMETER, χ

State dilatancy parameter, χ, is a function of soil fabric, and typically does not vary significantly

for different soils (Jefferies & Been, 2005). In the absence of more detailed information it is

often taken as 3.5. In the current modelling, a range of χ = 3.0…4.0 is assumed.

5.2.6.3. HARDENING MODULUS, Hmod

Hardening Hmod is a dimensionless plastic modulus. A typical range of Hmod = 50 ... 450 has

been assumed, where 50 indicates softer material and 450 indicates stiffer material. Hmod = 100

was selected as the base case value for the analysis.

5.2.6.4. SLOPE OF CRITICAL STATE LINE, λ

The slope of the critical state line, λ, in e-ln(p΄) space is normally estimated from triaxial test data at

different pressures. There are no triaxial data available for the Colebrook site. However, λ can be:

1). Assessed empirically using the plasticity index, PI.

75


Schofield & Wroth (1968) found the following relationship between PI, specific gravity, Gs, and

slope of the critical state line, λ:

λ = PI Gs / 160 (5.9)

Assuming Gs equal to 2.75, using Eq. 5.9 the profile of λ corresponding to the variation of

plasticity index can be derived as shown in Fig. 5.12. Given the plasticity index for the silty

clay layer varies from 7.6% to 21.1% (Weech, 2002) corresponding λ are in a range 0.13 …

0.362. This range is rather wide, but is in a good agreement with the values of

λ = 0.09…0.363 reported by Allman & Atkinson (1992) for Bothkennar silty clay.

2). Estimated very approximately using compression index Cc.

Compression index, Cc, is typically determined from odometer tests and is defined as:

( )'10log v

ceC

σ∆∆

= (5.10)

The slope of the critical state line in e-loge(p′) space, λ, is defined as:

( )'log pee∆

∆=λ (5.11)

where λ can be measured directly from an isotropic compression test.

For some critical state models, such as CamClay, the slope of the isotropic compression line is

parallel to the slope of the critical state line. However, within NorSand the slopes are not

identical, the isotropic compression line being a lower bound to the value of λ. The slopes of

the isotropic compression line and critical slope line tend to converge at very loose states.

Therefore it is not possible to use a constant factor to convert from Cc to λ, but it is possible to

use laboratory values of Cc to provide an estimate of the lower bound value of λ.

The following assumptions are necessary for conversion:

• it is assumed that the elastic compressibility is much lower than the plastic

compressibility and can be ignored;

• 1-D and isotropic compression are approximated as interchangeable.

Using the NorSand flow rule, for a range of Cc 0.16 … 0.29 (an approximate range for studied

elevations, established based on values reported by Crawford & Campanella, 1991, - see Table

A.2; Appendix A) and assuming stress level, K0, eo and Mcrit, as shown in Table 5.3, the range

of 0.073 … 0.130 for the lower bound values of λ was calculated using Eq. 5.11. This range is

76


generally in a good agreement with the lower bound λ estimated from PI - λ correlation by

Schofield & Wroth (1968), see Fig. 5.12.

Table 5.3. Estimation of slope of critical state line, λ, based on laboratory derived values of Cc reported by Crawford & Campanella (1991).

Elevation, m

Cc e0σ΄vkPa Ko Mcrit λ

-5.2 0.29 1.292 37.9 0.66 1.33 0.130 -5.4 0.16 1.026 39.5 0.66 1.33 0.073 -6.3 0.22 1.114 46.7 0.66 1.33 0.102 -6.9 0.28 1.398 51.5 0.66 1.33 0.130 -8.4 0.24 1.119 63.5 0.66 1.33 0.112

For the current analysis a combined range of λ = 0.073 … 0.362, estimated from PI and Cc, was

taken. As stated above, this range of λ is large and encompasses values of λ that are at the upper

end of those reported in the literature. However, a wide range of λ encompassing some high

plastic compressibility is in a good agreement with the values of λ = 0.09…0.363 reported by

Allman & Atkinson (1992) for Bothkennar silty clay. As a best estimate λ for the silty clay

layer was taken as an average of all values of λ shown in Fig. 5.12: λ = 0.165, which is close to

the best estimate of the slope of the critical state line for the Bothkennar silty clay, λ = 0.181,

used by Shuttle (2003).

5.2.6.5. INTERCEPT OF CRITICAL STATE LINE AT 1 KPA STRESS, Γ.

Knowing the void ratio from consolidation tests by Crawford & Campanella (1991), the mean

stress corresponding to the depth of specimen sampling, and the slope of the critical state line, a

range of Γs can be established, as shown in Fig. 5.13. Assuming loose and dense bounds for the

in-situ void ratios we can estimate values of Γ, so that for the loose bound Γ = 2.25 and for the

dense bound Γ = 1.55. For the average line in Fig. 5.13, Γ = 1.86.

5.2.6.6. STATE PARAMETER, ψ.

The state parameter, ψ, of the silty clay layer is unknown, and the absence of triaxial test data

complicates its assessment. In this study ψ has been estimated based on the stress history of the

soil.

77


The Colebrook site is lightly overconsolidated down through most of the elevations of interest,

which is consistent with a relatively loose soil state. Loose soil state corresponds to a positive

state parameter, the loose limit of the soil state range is about ψ = 0.2. An encompassing

feasible range of state parameter for the site would be ψ = -0.05 to 0.2.

The overconsolidation ratio and state parameter within NorSand model are interdependent as

discussed in Section 5.3.2. For OCR < 3, the state parameter and OCR must be correlated, as

demonstrated on the example provided in Fig. 4.6. A similar correlation can be developed by

simulating soil unloading from a normally consolidated state to the current site conditions.

The state parameter can be computed at each unloading step as the difference between the

current void ratio and critical void ratio and the overconsolidation ratio can be estimated as a

ratio of maximum and current mean normal effective stresses.

Given λ = 0.181 and Γ = 1.86 the critical void ratio can be determined from the following

equation:

)ln( 'pecrit λ−Γ= (5.12)

The current void ratio can be determined as following:

e = ei – κ ln(p΄/p΄max) (5.13)

where κ ~ 1/4λ

A wide range of conditions is possible at the start of unloading. Normally consolidated

clays/silts correspond to the initial condition of about ψ ~ 0.75λ (Jefferies & Been, 2005),

giving an initial state parameter ψ = 0.124. The initial void ratio can be estimated as following:

ei = Γ - λ ln(p΄) + ψ (5.14)

Knowing that OCR = 2.2 and the mean effective stress 42 kPa (based on σ΄vo= 54.5 kPa and K0 =

0.66), the starting mean normal effective stress at normally consolidated state p΄max = 92.4 kPa.

The simulated soil unloading is shown in Fig. 5.15. According to this figure, the state parameter

corresponding to an average mean effective stress 42 kPa and overconsolidation ratio 2.2, is

equal to +0.026. The void ratio for these conditions equals 1.269, which is within the range

reported for the site by Crawford & Campanella (1991).

A state parameter of +0.026 was adopted as a reasonable best estimate for the Colebrook silty

clay.

78


5.2.7. NORSAND PARAMETERS ANALYSIS.

A summary of chosen NorSand parameters in given in Table 5.4.

Table 5.4. Summary of NorSand parameters for Colebrook silty clay.

NorSand Parameters Acceptable Range Best Estimate Mcrit 1.113 … 1.374 1.243 χ 3.0 … 4.0 3.5 ψ -0.05 … 0.2 0.026 λ 0.073 … 0.362 0.165 Γ 1.55 … 2.25 1.86 Hmod 50 … 450 100

The parameter set shown in Table 5.4 is based on both derivations from actual Colebrook silty

clay testing and assumptions made based on a typical clay behaviour. To confirm reasonableness

of the “best estimate” parameter set, a simulation of drained and undrained triaxial tests was

performed using NorSand incremental formulation, coded into an MS Excel spreadsheet.

The results of triaxial simulations are presented in Fig. 5.15 and Fig. 5.16. Both drained and

undrained simulations showed triaxial behaviour reasonable for soft clayey soils. It should be

however noted that the response was rather “stiff” and non-sensitive.

As an indicator of how reasonable the selected NorSand input parameters are, the peak

undrained shear strength su and sensitivity St. can be assessed. NorSand is an effective stress

model and does not require su as an input parameter, however values of peak and residual

undrained shear strength can be interpreted from the modelled undrained triaxial response.

A comparison of su and St values estimated from the field data and the values backcalculated

from the modelled undrained triaxial tests are given in Table 5.5.

Table 5.5. Undrained shear strength and sensitivity estimated from field measurements and NorSand simulation of triaxial test.

Property Field Estimated Range for

Colebrook silty clay 1Simulation with best estimate

NorSand parameters su, kPa 15…29 22.6

St 6 …24 1 1 - within elevations -4.57 … -9.92 m

It can be seen that even if the backcalculated undrained shear strength fits nicely in the middle

of the range observed in the field, the backcalculated sensitivity is largely underestimated. This

issue is further addressed in Section 7.2.1.2.

79


5.3. SUMMARY.

Establishing NorSandBiot code parameters demanded comprehensive knowledge of soil

properties of the modelled site. Despite the extensive dataset of available information on

Colebrook silty clay soil properties the input parameter selection process was rather challenging.

Selection of the appropriate input parameters was complicated by the differences between

laboratory and in situ estimated 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 had also added to parameter uncertainty. Moreover, lack of

triaxial data complicated the selection of appropriate NorSand model parameters.

Despite these difficulties every effort was made to produce a set of parameters which is

reasonable for the Colebrook silty clay. The results of selection of site specific parameters for

numerical simulation are compiled in Table 5.6.

Table 5.6. NorSand-Biot input parameters for Colebrook silty clay.

Input Parameters

Acceptable Range 1

Best Estimate Units

General G 5.8 … 9.8 7.8 MPa ν 0.1 … 0.3 0.2 - kr 3.4·10-9… 8.5·10-10 2.1·10-9 m/s OCR 1.2 … 2.8 2.2 - K0 0.56 … 0.76 0.66 - σ΄v0 32.9 … 75.7 54.28 kPa u0 39.5 … 94.1 66.8 kPa NorSand specific Mcrit 1.113 … 1.374 1.243 - χ 3.0 … 4.0 3.5 - ψ -0.05 … 0.2 0.026 - λ 0.073 … 0.362 0.165 base loge

Γ 1.55 … 2.25 1.86 at 1 kPa Hmod 50 … 450 100 -

1 - within elevations -4.57 … -9.92 m

80


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


-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)


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)


Linear (Average Gmax)

max with elevation (modified after Weech,


-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)


Fig. 5.4. Inferred variation of rigidity index with depth (after Weech, 2002).

83


-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


10Modulus -

)

)

elevation.

84

G = - 0.75(Elevation) + 2.375

15 20 G (MPa)


Linear (Average G)


-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


Fig. 5.6. Range of overconsolidation ratio OCR with elevation (modified after Weech, 2002).

85


-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

0 0.2 0.4 0.6

Coefficient of Later

Ele

vatio

n (m

)


Fig. 5.7. Variation of coefficient of earth pressure

86

Estimated based on:

0.8 1 1.2 1.4 1.6

al Earth Pressure Ko

PPSV - CPT1&7 (Weech, 2002) PPSV - CPT1&2, (Weech, 2002)OCR - CPT-1, (Weech, 2002)OCR - CPT2 (Weech, 2002)

OCR - CPT7, (Weech, 2002)OCR - lab data (Crawford & Campanella, 1991)OCR - lab data (MoTH, 1969)

K0 with elevation (modified after Weech, 2002).


-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


Fig. 5.8. Variation in estimated coefficient of horizontal consolidation with depth (modified after Weech, 2002).

87


-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


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

)


σ′vo (kPa)= -8.0(Elevation) – 3.7

s with elevation.

89

100 150 200

ive stress σ 'v0 (kPa)σ΄vo (kPa)


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

)


uo (kPa) = -10.2(Elevation) - 7.1


-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)


Fig. 5.12. Probable range of slope of critical state line, λ.

91


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


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


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


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


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


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


• 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

1 0.56 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 2 0.76 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 3 0.66 1.6 7.8 0.2 0.085 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 4 0.66 3.4 7.8 0.2 -0.036 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 5 0.66 5.6 7.8 0.2 -0.115 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 5a 0.66 5.6 7.8 0.2 -0.2 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 6 0.66 2.2 7.8 0.2 0.1 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 7 0.66 2.2 5.8 0.2 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 8 0.66 2.2 9.8 0.2 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 9 0.66 2.2 25.3 0.2 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0

10 0.66 2.2 7.8 0.2 0.026 1.75 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 11 0.66 2.2 7.8 0.2 0.026 2.45 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 12 0.66 2.2 7.8 0.2 0.026 1.44 0.073 100 1.243 3.5 2.1·10-9 54.3 0.0 13 0.66 2.2 7.8 0.2 0.026 2.77 0.362 100 1.243 3.5 2.1·10-9 54.3 0.0 14 0.66 2.2 7.8 0.2 0.026 1.86 0.165 50 1.243 3.5 2.1·10-9 54.3 0.0 15 0.66 2.2 7.8 0.2 0.026 1.86 0.165 450 1.243 3.5 2.1·10-9 54.3 0.0 16 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.113 3.5 2.1·10-9 54.3 0.0 17 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.374 3.5 2.1·10-9 54.3 0.0 18 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.0 2.1·10-9 54.3 0.0 19 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 4.0 2.1·10-9 54.3 0.0 20 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.5 2.1·10-10 54.3 0.0 21 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.5 3.1·10-9 54.3 0.0 22 0.66 2.2 7.8 0.1 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0 23 0.66 2.2 7.8 0.3 0.026 1.86 0.165 100 1.243 3.5 2.1·10-9 54.3 0.0

1 – initial pore pressure was taken as zero to simplify the analysis, so that all computed pore pressures are excess.

Input parameters were varied independently, or in pairs where the effect of parameter’s coupling

was of interest (scenarios 3 … 6, 12 & 13).

At least two simulations were run for each parameter variation. Generally, the variation of

parameter values for this parametric study was based on the upper and lower bounds of the

acceptable range for Colebrook silty clay parameters established in Table 5.4, with the

exceptions of scenarios 4, 5, 5a and 9. In scenarios 4, 5, 5a assumed overconsolidation ratio

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and state parameter were beyond the range estimated for Colebrook silty clay. In scenario 9

assumed shear modulus exceeded the upper bound of G estimated for Colebrook silty clay. The

reasoning behind these exceptions is provided in Sections 6.5.2 and 6.5.3.

6.5. PARAMETRIC STUDY RESULTS.

The main purpose of the parametric study is to determine the sensitivity of the simulated pore

pressure response to variation of model input parameters. As was mentioned in the previous

section, with a few exceptions, the range of parameters variations was based on available data

for the Colebrook site. Some parameters, such as K0, were quite narrowly defined, and the range

of their variation was not large: 0.56 … 0.76. For other parameters, such as λ, the parameter

value was poorly constrained and a very broad range of values was analysed: 0.073 … 0.362

(the difference between lower and upper values is about 500%). This obviously has a significant

importance when comparing the effect of different input parameters on pore pressure response.

The results presented here should therefore be viewed as being site specific.

For each studied parameter the following criteria were chosen as a measure of influence on pore

pressure response:

• Magnitude of generated excess pore pressure at the end of cavity expansion, in terms of

∆u/σ′vo ratio;

• Time to achieve dissipation of excess pore pressure at the pile wall down to 5% of value

at the end of cavity expansion. This criterion is akin to T95 in Terzaghi’s terminology.

• Radial extent of generated excess pore pressures at the end of cavity expansion;

• Shape of radial distribution of pore pressure at the end of cavity expansion (this criterion

was considered only for special cases).

The results of the parametric study are compiled in Table 6.2 and will be presented in the

following sections.

Prior to presenting modelling results it should be noted that log scale representation of time

dependent pore pressure response complicates visual comparison of dissipation times for

different scenarios, particularly when the difference in dissipation times is less than 100%. This

effect is demonstrated in Fig. 6.8, where dissipation times appear identical until the last stage of

pore pressure dissipation is magnified. The reader is encouraged to use Table 6.2, where

numerical comparison of different scenarios, in relation to the base case, are presented.

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Table 6.2. Parametric study results.

Sc. Varied Values

Magnitude of generated excess pore pressure at the end of cavity expansion, as ∆u/σ′vo ratio

Magnitude of generated excess pore pressure at the end of cavity expansion, as % of the base case value

T95

hours

T95

as % of the base

case value

Radial extent of generated excess pore pressures at the end of cavity expansion, r/Rshaft ratio

Radial extent of generated excess pore pressures at the end of cavity expansion, as % of the base case value

base case - 2.36 100 33.9 100 20.0 100 1 K0=0.56 2.11 89.4 34.2 100.9 24.4 1222 K0=0.76 2.58 109.3 32.9 97.0 18.6 933 OCR=1.6 ψ=0.085 1.97 83.5 50.7 149.6 35.2 1764 OCR=3.4 ψ=-0.036 2.88 122.0 19.2 56.6 15.7 78.55 OCR=5.6 ψ=-0.115 3.57 151.3 8.4 24.8 17.5 87.55a OCR=5.6 ψ=-0.2 2.17 91.9 10.9 32.1 18.0 90.06 OCR=2.2 ψ=0.1 2.18 92.4 42.4 123.9 20.0 1007 G=5.8Mpa 2.25 95.3 34.8 102.7 16.5 82.58 G=9.8MPa 2.43 103.0 33.2 97.9 22.5 112.59 G=25.3MPa 2.72 115.3 31.1 91.7 38.1 190.5

10 Γ=1.75 2.36 100.0 33.9 100.0 20.0 10011 Γ=2.45 2.36 100.0 33.9 100.0 20.0 10012 Γ=1.44 λ=0.073 2.32 98.3 35.9 105.9 20.0 10013 Γ=2.77 λ=0.362 2.43 103.0 30.5 90.0 20.0 10014 Hmod=50 2.32 98.3 35.3 104.1 20.0 10015 Hmod=450 2.41 102.1 30.6 90.3 19.5 97.516 Mcrit=1.113 2.15 91.1 35.9 105.9 21.0 10517 Mcrit=1.374 2.55 108.1 31.9 94.1 18.2 9118 χ=3.0 2.35 99.6 33.8 99.7 20.0 10019 χ=4.0 2.37 100.4 34.0 100.1 20.0 10020 kr=2.1·10-10m/s 2.36 100.0 203.9 601.5 20.0 10021 kr=3.1·10-9 m/s 2.36 100.0 22.5 66.4 20.0 10022 ν=0.1 2.37 100.4 38.1 112.4 19.5 97.523 ν=0.3 2.35 99.6 28.2 83.2 21.0 105

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6.5.1. INFLUENCE OF COEFFICIENT OF LATERAL EARTH PRESSURE.

The coefficient of lateral earth pressure at rest, K0, defines the level of horizontal stress in

relation to the vertical stress. Typically, lower K0 indicates lower horizontal stress.

For the current analysis three scenarios with different K0 were considered, all using the same

vertical effective stress of 54.3 kPa:

- base case: K0 = 0.66;

- scenario 1: K0 = 0.56;

- scenario 2: K0 = 0.76.

It should be noted that the considered K0 values reflect the coefficient of lateral earth pressure

estimated for normally to lightly overconsolidated Colebrook silty clay, and, is relatively narrow

in comparison to the range of values observed in fine-grained soils.

According to Fig. 6.8 and Table 6.2, a higher horizontal stress (scenario 2) leads to an increase

in the pore pressure magnitude at the pile-soil interface and shrinks the zone of generated pore

pressures, whereas lower horizontal stress (scenario 1) decreases the magnitude of generated

pore pressures and extends the zone of generated pore pressures. The shape of the generated

pore pressure profile is approximately linear with the log of distance for all K0 values.

As follows from Fig. 6.9 and Table 6.2, despite the divergence in magnitudes of initial pore

pressures, all K0 simulations show similar dissipation times. This is possibly due to

compensating effect of the radial extent of the field of generated excess pore pressures, when

lower pore water pressure magnitude and larger radial extent result in lower pore water

migration gradients and vice versa.

The stress paths for all K0 simulations exhibit similar trends, as shown in Fig. 6.10, considering the

fact that their initial level of stress is different. For simulations with lower K0 (scenario 1) initial

p΄ is the lowest and q is the highest, the opposite is true for simulations with higher K0 (scenario 2).

For simulation with lower K0 initial state of stress is the closest to the critical state line,

consequently, during cavity expansion, after a short period of elastic deformations (constant p΄),

the stress path approaches the critical state line the fastest and at the lowest values of p΄ and q, in

comparison to simulations with higher K0.

During pore pressure dissipation all simulations exhibit a similar pattern of initial slight softening,

followed by gradual hardening. The simulation with the highest K0 (scenario 2) that started with the

highest p΄ and lowest q, shows the largest p΄ and q values at the end of pore pressure dissipation.

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6.5.2. INFLUENCE OF MEASURES OF SOIL OCR.

There are two input parameters that represent soil OCR in the NorSandBiot formulation –

overconsolidation ratio, R, and state parameter, ψ.

State parameter ψ measures the current soil state, defined as a difference between the void

ratio in the current state and the critical state at the same mean stress. Overconsolidation ratio,

R, represents a proximity of a state point to its yield surface, when measured along the mean

effective stress axis. Their variation is interrelated as described in Section 4.1.1.

Based on the observed behaviour of natural clays:

• normally to lightly overconsolidated clays are contractive and imply positive state parameter;

• moderately to highly overconsolidated clays are dilative and imply negative state parameter.

As was discussed in the literature review, soil OCR is one of the most important factors that may

influence pore pressure response. To study the influence of measures of OCR:ψ and R on the

generated excess pore pressure in details, including denser soils than found at the Colebrook site, a

wide range of values was considered for the sensitivity analysis. A total of six scenarios were run:

- base case: R = 2.2, ψ = 0.026;

- scenario 3: R = 1.6, ψ = 0.085;

- scenario 4: R = 3.4, ψ = -0.036;

- scenario 5: R = 5.6, ψ = -0.115;

- scenario 5a: R = 5.6, ψ = -0.2;

- scenario 6: R = 2.2, ψ = 0.1.

Simulations studied in this section are divided into two groups:

• Scenarios with coupled R and ψ variation covering lightly to moderately

overconsolidated soils: base case, scenarios 3, 4 and 5;

• Scenarios where ψ was uncoupled from R: scenario 5a - an uncoupled version of scenario

5, where the state parameter was increased while keeping R constant, to achieve a strongly

contractive behaviour and scenario 6 - an uncoupled version of the base case, where the

state parameter was increased while keeping R constant to achieve strongly contractive

behaviour. In these scenarios the effect of variation of ψ at constant R on pore pressure

response was of interest.

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For convenience of the analysis pore pressure response for simulations with coupled and

uncoupled R and ψ are discussed separately and then contrasted.

Radial distribution of pore water pressure at the end of cavity expansion for simulations with

coupled R and ψ is shown in Fig. 6.11. As follows from this figure, scenarios with

overconsolidation ratio less than 3 and positive state parameter (base case and scenario 3) show

lower magnitudes of generated excess pore pressure in comparison with the response for

scenarios with R > 3 and negative ψ (scenarios 4 & 5). According to Fig. 6.11 and Table 6.2,

similar to the Ko scenarios, for simulations with larger pore pressure magnitudes, radial extent

of generated excess pore pressures was smaller and vice versa. For scenarios 3, 4 and the base

case, the shape of pore pressure distribution is almost linear, whereas for simulation 5 a rapid

drop in pore pressure is observed at radial distances of up to r/Rshaft = 3. This issue will be

discussed separately later in this section.

Fig. 6.12 shows time dependent pore pressure distribution for simulations with coupled R and ψ.

According to Fig. 6.12 and Table 6.2 larger dissipation times are observed for simulations with

lower R and more positive state parameter. Even though they exhibit lower initial pore

pressures due to a larger zone of pore pressure distribution, the gradient of migrating pore water

is lower, hence dissipation will take longer.

In Fig. 6.13, a comparison is shown of the radial pore pressure distribution for coupled and

uncoupled simulations with low R and positive ψ (base case and scenario 6). According to

Table 6.2 an increase in state parameter of more than 300%, at constant overconsolidation ratio,

resulted only in a slight decrease in the pore pressure magnitude - less than 8 % and had no

effect on pore pressure distribution. The shape of the radial pore pressure distribution appears to

be flatter, at least up to r/Rshaft = 3, for the simulation with uncoupled parameters.

In the time domain, shown in Fig. 6.14, increasing the state parameter resulted in a longer

dissipation time (> 20%, see Table 6.2).

Comparison of time dependent pore pressure response for coupled and uncoupled simulations

with high R and negative ψ (scenarios 5 & 5a) is shown in Fig. 6.15. According to Table 6.2,

decrease in state parameter approximately by 70% caused a drop in the pore pressure magnitude

at the end of cavity expansion by about 40%. Meanwhile only an insignificant (< 5%) increase

in pore pressure dissipation time was observed. Both simulations exhibit some decrease in

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generated pore pressure between 0.001 and 0.01 minutes (~ 2…8% of cavity expansion). Such

behaviour is particularly apparent for scenario with increased dilatancy (scenario 5a), where

generation of excess pore pressure during cavity expansion has wave like shape.

In Fig. 6.16, the pore pressure generation during cavity expansion is shown in terms of pore

pressure components. It can be seen that a significant drop in generated pore pressure during the

early stage of cavity expansion (2 … 8 %) is related to the highly negative shear induced pore

pressure component. This negative pore pressure is a result of dilation occurring at the initial

stage of cavity expansion. As cavity expansion progresses, pore pressures due to change in

mean normal stress increases and reverses the drop in generated pore pressures at about 8% of

cavity expansion. When the critical state is reached no dilation is possible and all generated

pore pressure is due to the change in mean normal stress.

Comparison of radial pore pressure distribution at the end of cavity expansion for coupled and

uncoupled simulations, with high R and negative ψ (scenarios 5 & 5a), is shown in Fig. 6.17.

According to Table 6.2, the decrease in state has practically negligible effect on the radial extent

of generated excess pore pressures. In terms of shape of radial pore pressure distribution, both

simulations show a steep drop in pore pressure with distance in the vicinity of the expanded cavity

(up to r/Rshaft = 3). This is particularly evident for scenario 5a, where R and ψ are uncoupled. The

radial pore pressure distribution represented in terms of pore pressure components is shown in Fig.

6.18. Interestingly, the peak in negative shear induced pore pressures is observed not at the cavity

wall, but at some distance (around r/Rshaft = 2…3). In Fig. 6.19, the radial distribution of excess

pore pressures at different stages of cavity expansion is shown. It can be inferred that as cavity

expansion progresses, soil yields and a peak of shear induced pore pressures is gradually moving

away from the cavity causing a drop in total pore pressure in the vicinity of the pile shaft.

Overall, uncoupling of R and ψ has the following effect:

1). For a contractive response (base case and scenario 6): the magnitude of generated excess

pore pressure decreases and makes the curve of radial pore pressure distribution flatter.

2). For a dilative response (scenarios 5 & 5a): the magnitude of generated excess pore pressure

decreases and causes a dramatic drop in pore pressure in the vicinity of the cavity wall.

It appears that the difference between simulations with the coupled and uncoupled R and ψ is

primarily in the magnitude of shear induced pore pressures.

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Visual representation of the initial state conditions, in e-ln(p΄) space, for each of the considered

scenarios is shown in Fig. 6.20. As follows from this figure, all scenarios start at the same mean

effective stress. However, their initial void ratios are different. Starting points for scenarios 4,

5 & 5a are located well below the critical state line CSL, which typically indicates dilative

behaviour, whereas for scenarios 3 & 6 they are far above the CSL, indicating contractive

behaviour; the starting point for the base case is located slightly above CSL in a zone of

contractive behaviour.

Fig. 6.21 shows the stress path for scenarios 3 … 6 and the base case. As expected, scenarios

with initial conditions below the CSL exhibit dilative behaviour and scenarios above the critical

state line show contractive response, with the exception of the base case (detailed description of

the base case stress path is given in Section 6.3).

As follows from Fig. 6.21, the soil state has a significant influence on the level of p΄ and q

stresses. Overall, for the same initial stress level, simulations with dilative behaviour show

higher p΄ and q values at the end of pore pressure dissipation.

Fig. 6.22 shows the variation of void ratio with mean effective stress for scenarios 3 … 6 and the

base case. It can be seen that during cavity expansion mean normal effective stress decreases

for scenarios with initial conditions above CSL and increases for scenarios with initial

conditions below CSL, until the critical state line is reached. Through the dissipation stage all

simulation show, typical for consolidation, gradual decrease in the void ratio.

6.5.3. INFLUENCE OF ELASTIC PROPERTIES.

Elastic properties in the NorSand formulation are represented by the shear modulus, G, which is

defined as a ratio of shear stress to shear strain, and Poisson’s ratio, ν, - a ratio of axial

compression to lateral expansion in triaxial compression. Higher G and ν indicate a stiffer

material.

Four simulations were run to study the effect of shear modulus on pore pressure response:

- base case: G = 7.8 MPa;

- scenario 7: G = 5.8 MPa;

- scenario 8: G = 9.8 MPa;

- scenario 9: G = Gmax = 25.3 MPa.

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For scenarios 7 and 8, the chosen values of shear modulus correspond to the lower and upper

bounds of the G values estimated for the Colebrook silty clay using the methodology described

in Section 5.3.1. For scenario 9 an average of the small strain elastic shear modulus, Gmax,

derived from the seismic cone measurements at the Colebrook site was considered.

According to Fig. 6.23, Fig. 6.24 and Table 6.2 the following is true for all scenarios considered in

this section: the magnitude and extent of the generated excess pore pressures is larger for simulations

with stiffer G values. At the same time, simulations with stiffer G exhibit faster dissipation times.

Using the small strain shear modulus, Gmax, which is more than 300% larger than the base case

value, resulted in a 15 % increase in the pore pressure magnitude, 90 % increase in radial extent

of generated pore pressures and 8 % decrease in pore pressure dissipation time in comparison

with the base case scenario. Therefore, it can be concluded that, using Gmax in numerical

simulations will primarily result in larger zone of generated excess pore pressure.

This stress paths for shear modulus variation, shown in Fig. 6.25, indicate an increase in

softening (decrease in shear stress q) during the pore pressure dissipation phase.

The influence of Poisson ratio, ν, on pore water pressure response was investigated in three

scenarios with different ν values:

- base case: ν = 0.2;

- scenario 22: ν = 0.1;

- scenario 23: ν = 0.3.

The range of studied Poisson ratios corresponds to the values assumed for the Colebrook silty

clay, which are typical Poisson ratio values reported in the literature.

Figs. 6.26 and 6.27 show the time dependent pore pressure distribution for all Poisson ratios

scenarios. Table 6.2 shows that the radial extent of the pore pressure is greater for higher

Poisson ratio and the pore pressure dissipation time is longer for smaller Poisson ratio.

Poisson ratio has a significant influence on the reconsolidation process, as shown in Fig. 6.28.

During cavity expansion stress paths for all simulations are very similar, thus the level of stress

at the beginning of dissipation process is almost identical. As pore pressures dissipate, the

simulation with the higher Poisson ratio (scenario 23) exhibits softening, whereas simulations

with the lower Poisson ratios (base case & scenario 22) exhibits hardening. As a result a very

different stress level is observed at the end of the pore pressure dissipation.

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6.5.4. INFLUENCE OF CRITICAL STATE PARAMETERS.

The following three input parameters in NorSand-Biot formulation define soil behaviour at the

critical state: Γ, λ and Mcrit. The position of the critical state line in e-ln(p΄) space is governed by

the slope of the critical state line, λ, and intercept of the critical state line at 1 kPa stress, Γ.

Five different simulations were run to analyse the effect of variation of critical state line

parameters on the pore pressure response:

- base case: Γ = 1.86, λ = 0.165;

- scenario 10: Γ = 1.75, λ = 0.165;

- scenario 11: Γ = 2.45, λ = 0.165;

- scenario 12: Γ = 1.44, λ = 0.073;

- scenario 13: Γ = 2.77, λ = 0.362.

In scenarios 10 and 11 the effect of varying Γ for a constant λ was of interest, whereas in

scenarios 12 and 13 the influence of a coupled variation of Γ and λ was analysed. A very broad

range of values chosen for analysis is based on interpretations presented in Section 5.3.6.1.

Generally, varying Γ while keeping λ constant influences only the initial void ratio conditions

and has only a small effect on soil behaviour, and hence on pore pressure response. This is

confirmed by Fig. 6.29, 6.30, 6.31 and Table 6.2 - variation of Γ alone has virtually no effect on

pore water pressure response.

According to Fig. 6.32, 6.33 and Table 6.2, the coupled variation of Γ and λ has a small effect on

pore pressure magnitude and dissipation time. A steeper slope of the critical state line (higher λ)

and higher Γ, work to decrease the magnitude of generated excess pore pressure and at the same

time extend the dissipation time (see Table 6.2). It should be noted that the coupled variation of

the critical state line parameters had no effect on the extent of the radial zone of generated

excess pore pressures.

As seen in Fig. 6.34, the simulation with the lower Γ and λ (scenario 12) shows a contractive

response during cavity expansion and hardening is observed during the reconsolidation stage.

The opposite is true for simulations with steeper λ and higher Γ (base case & scenario 13). For

all simulations at the end of dissipation, the stress path shows different levels of stress.

Generally, with increase in Γ and λ, the final mean stress (p΄) increases.

108


The ratio of stresses at critical state and the position of the critical state line in q-p΄ space is

defined by the critical state coefficient, Mcrit. As shown in Section 4.2, Mcrit is directly related to

the large strain friction angle, with higher friction angles corresponding to a higher critical state

coefficient.

In the current analysis, three simulations were run to study the influence of Mcrit variation on

pore water pressure response:

- base case: Mcrit = 1.243 (ϕ΄cv = 31° );

- scenario 16: Mcrit = 1.113 (ϕ΄cv = 32°);

- scenario 17: Mcrit = 1.374 (ϕ΄cv = 33°).

The range of Mcrit considered here correspond with the best estimate values for the Colebrook

silty clay (see Section 5.3.6.1). This range is relatively narrow considering the variety of values

observed in other clays.

Figs. 6.35, 6.36 and Table 6.2 indicate that the simulation with the higher Mcrit shows a larger

magnitude of generated excess pore pressure and at the same time smaller zone of radial pore

pressure distribution, hence faster dissipation time.

Stress paths for all Mcrit related simulations, shown in Fig. 6.37, indicate that a higher level of q

is required to reach failure during cavity expansion for a simulation with higher Mcrit. During

the dissipation stage, a similar pattern of slight softening followed by gradual hardening is

observed for all simulations. Higher final values of q and p′ are observed for simulations with

higher Mcrit.

6.5.5. INFLUENCE OF HARDENING MODULUS.

Hardening modulus, Hmod, is a unique NorSand parameter that governs the extent of the yield

surface. Normally, a stiffer soil response is related to a higher Hmod.

Three simulations were run to study the influence of Hmod on the pore water pressure response:

- base case: Hmod = 100;

- scenario 14: Hmod = 50;

- scenario 15: Hmod = 450.

The considered range of Hmod values covers typical variety used for simulations with NorSand

model.

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As follows from Fig. 6.38 and Table 6.2, simulations with a “stiffer” hardening modulus

(scenario 15) leads to slightly higher pore pressure magnitudes at the shaft. More compliant

Hmod values (base case & scenario 14) produce a flatter curve of radial pore pressure

distribution, and at a distance of r/Rshaft > 6, the magnitude of generated pore pressures with

compliant Hmod becomes more significant. The maximum extent of radial pore pressure

distribution is larger for simulation with more compliant Hmod. According to Fig. 6.39 and

Table 6.2 it took longer to dissipate the pore pressures for simulations with compliant Hmod.

Fig. 6.40 shows the stress path for simulations with “stiffer” Hmod (scenario 15) indicating

contractive behaviour during cavity expansion and hardening during the reconsolidation stage.

As a result, a higher stress level is achieved at the end of pore pressure dissipation. The opposite

is true for simulations with compliant Hmod (base case & scenario 14).

6.5.6. INFLUENCE OF STATE DILATANCY PARAMETER.

The state dilatancy parameter, χ, in the NorSand model links the state parameter and peak

dilatancy. A higher stress dilatancy parameter implies a larger (negative) peak dilatancy.

Two simulations were considered to study the influence of χ variation on pore water pressure

response:

- base case: χ = 3.5;

- scenario 18: χ = 3.0;

- scenario 19: χ = 4.0.

The range of variation of χ considered here is typical for most soils.

According to Fig. 6.41, 6.42, 6.43 and Table 6.2, for the varied ranges, the stress dilatancy

parameter has negligible effect on pore water pressure response.

6.5.7. INFLUENCE OF HYDRAULIC CONDUCTIVITY.

Hydraulic conductivity, k, in the NorSandBiot formulation governs pore water flow. Lower

hydraulic conductivity indicates less permeable material.

Three simulations were considered to study the effect of k on pore pressure response:

- base case: k = 2.0·10-9 m/s;

- scenario 20: k = 2.1·10-10 m/s;

- scenario 21: k = 3.0·10-9 m/s.

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Assumed values of k are within the range estimated for the Colebrook silty clay in Section 5.3.4.

Given that cavity expansion occurs at nearly undrained conditions, hydraulic conductivity has

practically no effect on the magnitude and radial extent of generated excess pore pressure at the

end of cavity expansion, as shown in Fig. 6.44 and Table 6.2. However, the pore pressure

dissipation period is heavily dependent on the hydraulic conductivity. As shown in Fig. 6.45

and Table 6.2, lowering k increases the length of dissipation period. An order of magnitude

decrease in k increases the dissipation time by 600% (see Table 6.2).

The level of stress during cavity expansion and after pore pressure dissipation is generally

unaffected by the varying hydraulic conductivity (see Fig. 6.46).

6.6. CONCLUDING REMARKS ON PARAMETRIC STUDY RESULTS.

Results of the NorSanBiot formulation parametric study, presented in Table 6.2, can be

summarized using ranking of the input parameters in terms of their influence on the pore water

pressure response, as presented in Table 6.3.

Table 6.3. Ranking of NorSand-Biot formulation input parameters.

Influence on Input parameter ranking

magnitude of excess pore water pressure generated during cavity expansion

excess pore water pressure dissipation time

radial distribution of excess pore pressures

1 ψ & OCR kr ψ & OCR 2 K0 ψ & OCR K0 3 Mcrit ν G 4 G Hmod Mcrit5 Γ & λ Γ & λ ν 6 Hmod Mcrit Hmod7 ν G kr , Γ & λ, χ, Γ 8 χ K0 9 kr , Γ χ 10 Γ

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


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


• 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


Fig. 6.1. FE Mesh for Parametric Study.

Fig. 6.2. Cylindrical cavity expansion from non-zero radius (after Carter et al., 1979).

114


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


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


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


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.

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140p', kPa

q, k

Pa

CSL Sc. 2. Ko = 0.76

Base Case. Ko = 0.66

Sc.1 Ko = 0.56

Fig. 6.10. Stress paths for “base case”, 1 & 2 scenarios.

118


0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' v

oEdge of HelicesEdge of Pile

Sc. 4. R = 3.4; ψ = -0.036

Base Case. R = 2.2; ψ = 0.026

Sc. 5. R = 5.6; ψ = -0.115

Sc. 3. R = 1.6; ψ = 0.085

Fig. 6.11. Effect of coupled R & ψ on radial distribution of excess pore pressure response at the end of cavity expansion.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000Time (min)

∆u /

σ' v

o

Sc. 4. R = 3.4; ψ = -0.036

Base Case. R = 2.2; ψ = 0.026

Sc. 5. R = 5.6; ψ = -0.115

Sc. 3. R = 1.6; ψ = 0.085

cavity expansion pore pressure dissipation

Fig. 6.12. Effect of coupled R & ψ on time dependent pore water pressure response at cavity wall.

119


120

sponse at the end of cavity expansion, for simulations with positive ψ.

Fig. 6.14. Effect of uncoupling R & ψ on time dependent pore water pressure response at the cavity wall, for simulations with positive ψ.

Fig. 6.13. Effect of uncoupling re

R & ψ on radial distribution of excess pore water pressure

0.0

0.5

1.0

1.5

2.0

2.5

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000Time (min)

∆u /

σ' vo

3.0cavity expansion pore pressure dissipatio

Base Case. R = 2.2; ψ = 0.026

Sc. 6. R = 2.2; ψ = 0.1

n

0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' v

oEdge of HelicesEdge of Pile

Base Case. R = 2.2; ψ = 0.026

Sc. 6. R = 2.2; ψ = 0.1


Fig. 6.15. Effect of uncoupling R & on time dependent pore pressure response at the cavity wall, for simulations with negative ψ.

Fig. 6.16. Generation of excess pore pre

ψ

ssure during cavity expansion for the first mesh element adjacent to the cavity, presented in terms of pore pressure components.

-3

-2

-1

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100

cavity expansion, %

∆u/

σ'vo

normal stress induced pore pressure

full response

shear induced pore pressure

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000Time (min)

∆u /

σ' v

o

Sc. 5. R = 5.6; ψ = -0.115

Sc. 5a. R = 5.6; ψ = -0.2

cavity expansion pore pressure dissipation

121


122

sponse at the end of cavity expansion, for simulations with negative ψ.

Fig. 6.18. Radial distribution of different excess pore pressure components for scenario 5a.

Fig. 6.17. Effect of uncoupling R & ψ on radial distribution of excess pore water pressure re

3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1 10 100

r/Rshaft

∆u/

σ'vo

0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' vo

Edge f HelicesEdge of Pile o

Sc. 5. R = 5.6; ψ = -0.115

Sc. 5a. R = 5.6; ψ = -0.2

Edge of Helices

Edge of Pile

normal stress induced pore pressure

shear induced pore pressure

full response


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100r/Rshaft

∆u/

σ' v

oCavity Expansion:100 percent50 percent30 percent10 percent5 percent1 percent

Edge of HelicesEdge of Pile

Fig. 6.19. Radial distribution of generated pore pressure, for scenario 5a, at different levels cavity expansion.

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

10 100 1000p' KPa

e

CSL

Sc. 3. R = 1.6; ψ = 0.085

Sc. 4. R = 3.4; ψ = -0.036

Base Case. R = 2.2; ψ = 0.026

Sc. 5a. R = 5.6; ψ = -0.2

Sc. 6. R = 2.2; ψ = 0.1

Sc. 5. R = 5.6; ψ = -0.115

dilative behaviour

contractive behaviour

Fig. 6.20. Initial conditions in e-ln (p′) space for scenarios 3..6 and base case.

123


124

aths for scenarios 3…6 and base case.

Fig. 6.21. Stress p

p', kPa

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200 250

q, k

PaCSL

Sc. 3. R = 1.6; ψ = 0.085

Sc. 4. R = 3.4; ψ = -0.036

Base Case. R = 2.2; ψ = 0.026

Sc. 5a. R = 5.6; ψ = -0.2

Sc. 6. R = 2.2; ψ = 0.1

Sc. 5. R = 5.6; ψ = -0.115

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

10 100 1000

p' KPa

e

CSL

Sc. 3. R = 1.6; ψ = 0.085

Sc. 4. R = 3.4; ψ = -0.036

Base Case. R = 2.2; ψ = 0.026

Sc. 5a. R = 5.6; ψ = -0.2

Sc. 6. R = 2.2; ψ = 0.1

Sc. 5. R = 5.6; ψ = -0.115

initial conditions

Fig. 6.22. Variation of e with p′ for scenarios 3…6 and base case.


Fig. 6.23. Effect of G on radial distribution of excess pore pressure at the end of cavity xpansion.

t cavity wall.

e

0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' v

o


Sc. 8. G = 9.8 MPa

Sc. 7. G = 5.8 MPa

Base Case. G = 7.8 MPa

Sc. 9. G = 25.3 MPa

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

Sc. 8. G = 9.8 MPa

Sc. 7. G = 5.8 MPa

Base Case. G = 7.8 MPa

Sc. 9. G = 25.3 MPa

Fig. 6.24. Effect of G on time dependent pore pressure response a

125


Fig. 6.25. Stress paths for scenarios “base case”, 7, 8 & 9.

0

0.5

1

1.5

2

2.5

1 10 100r/Rshaft

∆u/

σ' v

o


Base case: ν = 0.2Sc. 22. ν = 0.1Sc. 23. ν = 0.3

0

10

20

30

40

50

60

0 20 40 60 80 100 120p', kPa

q, k

PaCSL

Sc. 8. G = 9.8 MPa

Sc. 7. G = 5.8 MPa Base Case. G = 7.8 MPa

Sc. 9. G = 25.3 MPa

Fig. 6.26. Effect of ν on radial distribution of excess pore pressure at the end of cavity expansion.

126


0.0

0.5

1.0

1.5

2.0

2.5

0.1 1 10 100 1000 10000 100000Time (min)

∆u/

σ' vo

Sc. 23. ν = 0.3

Base case: ν = 0.2

Sc. 22. ν = 0.1

Fig. 6.27. Effect of ν on time dependent pore water pressure response at cavity wall.

Fig. 6.28. S

p', kPa

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140

q, k

Pa

CSL

Base case: ν = 0.2

Sc. 22. ν = 0.1

Sc. 23. ν = 0.3

tress paths for scenarios “base case”, 22 & 23.

127


0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' v

o


Base Case. Γ = 1.86Sc. 10. Γ = 1.75Sc. 11. Γ = 2.45

Fig. 6.29. Effect of Γ on radial distribution of excess pore water pressure at the end oexpansion.

f cavity

re response at cavity wall.

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


Fig. 6.30. Effect of Γ on time dependent pore water pressu

128


Fig. 6.31. Stress paths for scenarios “base case”, 10 & 11

0

10

20

30

40

50

60

0 20 40 60 80 100 120p', kPa

q, k

Pa

CSL


0

0.5

1

1.5

2

2.5

1 10 100r/Rshaft

∆u/

σ' v

o


A - Base Case. Γ = 1.86; λ = 0.165B - Sc. 12. Γ = 1.44; λ = 0.073C - Sc. 13. Γ = 2.77; λ = 0.362

B

CA

BC

A

Fig. 6.32. Effect of Γ & λ on radial distribution of excess pore pressure at the endexpansion.

& λ on radial distribution of excess pore pressure at the endexpansion.

of cavity of cavity

129


Fig. 6.33. Effect of Γ & λ on time dependent pore water p

0.0

0.5

1.0

1.5

2.0

2.5

0.1 1 10 100 1000 10000 100000Time (min)

∆u/

σ' vo


B

CA

BC

A

ressure response at cavity wall. Fig. 6.34. Stress paths for scenarios “base case”, 12 & 13.

10

15

20

25

30

35

40

45

50

55

60

10 20 30 40 50 60 70 80 90 100 110 120

p', kPa

q, k

Pa

CSL


C

B

A

C

B

A

130


0

0.5

1

1.5

2

2.5

3

1 10 100r/Rshaft

∆u/

σ' v

oEdge of HelicesEdge of Pile A - Base case. Mcrit = 1.243

B - Sc. 16. Mcrit = 1.113C - Sc. 17. Mcrit = 1.374

B

C

A

B

C

A

Fig. 6.35. Effect of Mcrit on radial distribution of excess pore pressure at the end of cavity

ssure response at cavity wall.

expansion.

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' v

o

Base case. Mcrit = 1.243

Sc. 17. Mcrit = 1.374

Sc. 16. Mcrit = 1.113

Fig. 6.36. Effect of Mcrit on time dependent pore water pre

131


Fig. 6.37. Stress paths for scenarios “base case”, 14 & 15.

mm

0

0.5

1

1.5

2

2.5

1 10 100r/Rshaft

∆u/

σ' v

o


A - Base case. Hmod = 100B - Sc. 14. Hmod = 50C - Sc. 15. Hmod = 450

B

C A

CA, B

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140p', kPa

q, k

Pa

Base case. Mcrit = 1.243

Sc. 17. Mcrit = 1.374

Sc. 16. Mcrit = 1.113

CSL

FFig. 6.38. Effect of H od on radial distribution of excess pore pressure at the end of cavity expansion.

ig. 6.38. Effect of H od on radial distribution of excess pore pressure at the end of cavity expansion.

132


0.0

0.5

1.0

1.5

2.0

2.5

0.1 1 10 100 1000 10000 100000Time (min)

∆u/

σ' vo

B

C A A - Base case. Hmod = 100

B - Sc. 14. Hmod = 50C - Sc. 15. Hmod = 450

Fig. 6.39. Effect of Hmod on time dependent pore water pressure response at cavity wall.

0

10

20

30

40

50

60

70

0 20 40 60 80 100 12p', kPa

q, k

Pa

CSL

A - Base case. Hmod = 100B - Sc. 14. Hmod = 50C - Sc. 15. Hmod = 450

B

C A

B

C

A

0


133


0

0.5

1

1.5

2

2.5

1 10r/Rshaft

∆u/

σ' v

o


Base case. χ = 3.5Sc. 18. χ = 3Sc. 19. χ = 4

100

Fig. 6.41. Effect of χ on radial distribution of excess pore pressure at the end of pressure at the end of cavity

Fig. 6.42. Effect of χ on time dependent pore water pressure response at cavity wall.

cavity

Fig. 6.42. Effect of χ on time dependent pore water pressure response at cavity wall.

expansion. expansion.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.1 1 10 100 1000 10000 100000

∆u/

σ' vo

Time (min)


134


Fig. 6.43. Stress paths for simulations with “base case”, scenario 18 & 19 set of input parameters.

0

10

20

30

40

50

60

0 20 40 60 80 100 120p', kPa

q, k

PaCSL


0

0.5

1

1.5

2

2.5

1 10 100

r/Rshaft

∆u/

σ' v

o


Base case: k = 2.1e-9 m/sSc. 20: k = 2.1e-10 m/sSc. 21: k = 3.1e-9 m/s

Fig. 6.44. Effect of permeability, k, on radial distribution of excess pore pressure at the end of cavity expansion.

135


0.0

0.5

1.0

1.5

2.0

2.5

0.1 1 10 100 1000 10000 100000 1000000Time (min)

∆u/

σ' vo

Base case. k = 2.1e-9 m/s

Sc. 21: k = 3.1e-9 m/s

Sc. 20: k = 2.1e-10 m/s

Fig. 6.45. Effect of permeability, k, on time dependent pore pressure response at cavity wall.

0

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100 12p', kPa

q, k

Pa

Base case: k = 2.1e-9 m/sSc. 20: k = 2.1e-10 m/sSc. 21: k = 3.1e-9 m/s

CSL

0

136



for base case scena

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

0

20

40

60

80

100

0 50 100 150 200p', kPa

q, k

Pabase casescenario 1scenario 2scenario 3scenario 7scenario 8scenario 10scenario 11scenario 12scenario 13scenario 14scenario 15scenario 18scenario 19scenario 20scenario 21scenario 22scenario 23

CSL

B

A

Region C

rio).

137

Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D.

7.0. MODELLING OF PORE PRESSURE CHANGES INDUCED BY HELICAL PILE

INSTALLATION IN 1-D.

7.1. INTRODUCTION.

In this chapter the modelling approach developed in Chapter 4 is applied to a field problem.

Modelling is centred on understanding the pore pressure response observed during and after helical

piles installation at the Colebrook site, Surrey (Weech, 2002). Chapter 7 modelling has two

separate, but related, objectives. The first is to determine whether the NorSand-Biot formulation is

able to produce realistic estimates of the pore pressure generation and dissipation both generally, and

most importantly for the Colebrook site. The second is to provide greater understanding of the

processes occurring during and after helical pile installation at the Colebrook site.

7.2. 1-D SIMULATIONS.

Analysis of complex problems, such as the modelling of pore pressure response due to helical

pile installation, requires a comprehensive approach, where at earlier stages of analysis the

problem is simplified, and at each subsequent stage an additional level of complexity is added.

The numerical modelling presented in this chapter is divided into two stages.

In the first stage, described in Section 7.2.1, helical pile installation is modelled as a single cavity

expanded up to the helical pile shaft radius, similar to the parametric study simulations described

in Section 6.2. An attempt is made to match the pore pressure response observed at the Colebrook

site by adjusting modelling input parameters within the acceptable range shown in Table 5.5. The

purpose of this stage is to evaluate if modelling of only the shaft of the helical pile is sufficient

to provide a reasonable prediction of the pore pressure response induced by the helical pile.

In the second stage, described in Section 7.2.2, the helices are introduced. Numerical analysis is

performed according to the approach adopted in Section 4.2. Particulars of the approach

implemented will be given in Section 7.2.2.1. The input parameters for the modelling will be

based on the best fit simulation produced at stage 1. Introduction of helices will allow singling

out of their effect on pore pressure response and will validate the adopted modelling approach.

Similar to the parametric study, all simulations of helical pile installation were carried out by running a

large strain FE code, developed by Shuttle (e.g. 2003), on a one-row mesh of 50 elements, shown in

Fig. 6.1. The boundary conditions of the analysis were identical to the ones described in Section 6.2.

138


7.2.1. STAGE I. MODELLING OF HELICAL PILE INSTALLATION AS SINGLE CAVITY EXPANSION.

7.2.1.1. COMPARISON OF MODELED AND FIELD PORE PRESSURE RESPONSES.

One of the purposes of the modelling conducted in the current study is to reproduce the pore

pressure response induced by helical pile installation observed in the field by Weech (2002). A

literature review indicates that the study by Weech (2002) was the first attempt to understand pore

pressure response due to helical pile installation; other works in the area of pile-soil interaction are

primarily dedicated to traditional driven and jacked piles. Generally the mechanism of generation

of excess pore pressure due to traditional and helical pile installation are similar. However, due to

the presence of the helices the pore pressure response due to helical pile installation may be

different from the response observed for traditional piles. This is demonstrated in Fig. 7.1, where

the radial distributions of normalized excess pore pressure due to installation of traditional piles

(dataset by Levadoux & Baligh, 1980) and helical pile (Weech, 2002) are compared.

Interestingly, the pore pressure response due to helical pile installation has lower magnitudes

(∆u/σ′vo = 1.45) at the pile shaft in comparison with data for traditional piles (∆u/σ′vo = 1.8 - 2.35).

This could be attributed to the properties of the Colebrook silty clay, which is highly sensitive (for

elevations –4.57 … – 9.92 meters, average St = 16) or to an effect of the helices.

Helical pile data shows a larger extent of the radial pore pressure distribution in comparison

with the trends observed for traditional piles. If we assume normalized pore pressures

∆u/σ′vo >0.1 to be significant, significant pore pressure are observed up to about r/Rshaft = 50 for

the helical piles and, for the traditional piles, r/Rshaft is in a range from 16 to 50. Weech (2002)

explained the larger extent of radial pore pressure distribution on the effect of the helices. The

effect of the helices will be further addressed in Section. 7.2.2.2.

Fig. 7.1 also shows the modelled pore pressure response due to single cavity expansion up to the

helical pile shaft radius, simulated with best estimate (“base case”) input parameters established in

Chapter 5, Table 5.5. The NorSandBiot simulation showed pore pressure magnitudes near the upper

bound (∆u/σ′vo = 2.36) and the extent of significant pore pressures near the lower bound (r/Rshaft =

15) of the values observed for the traditional piles. The shape of the modelled pore pressure

distribution is almost linear, which is in sharp contrast with the trend observed for most of the cases

given by Levadoux & Baligh (1980), where in the vicinity of the shaft, up to r/Rshaft = 5, a very slow

decrease, followed by a sudden drop in pore pressure at distances from r/Rshaft, = 5 to 20 is observed.

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It should be noted that the mismatch between pore pressures measured at the Colebrook site by

Weech (2002) and the “base case” numerical prediction is quite large. As follows from Fig. 7.1, the

simulation with the best estimate parameters overestimates the excess pore pressure magnitude by

about 40% and underestimates the radial extent of significant excess pore pressure by more than

three times (r/Rshaft = 21 vs. r/Rshaft = 65). This mismatch also affects pore pressure dissipation, as

shown in Fig. 7.2. For a NorSandBiot simulation with the base case parameters, 95% of pore

pressure dissipation is reached within about 39 hours (2150 min.), whereas field data indicated 95%

dissipation at about 92 hours (5500 min.). Faster dissipation rates for the simulated response are

likely associated with higher pore pressure gradients due to larger excess pore pressure magnitude

and smaller zones of radial distribution, compared to the field measurements.

There are several possible reasons that could contribute to the observed differences between

predicted and measured pore pressure response, among them:

(1) Modelling assumptions.

• The assumed 1-D deformations and water flow close to the pile are far from being near

the 3-D conditions observed in real soils. In particular the shearing induced by the

helices is not replicated in the 1-D model.

• Simulation of the helical pile installation ignoring the helices may lead to

underprediction of the extent of radial pore pressure distribution.

• Constant properties were assumed during the simulation period. In real soils, pile

installation typically causes severe soil remoulding in the vicinity of the pile which may

result in the strength characteristics in the zone of plastic deformations being diminished.

(2) Input parameters for modelling.

• Input parameters employed for the modelling were based on the best estimate of the

Colebrook silty clay properties, either taken as an average over particular depths, or

assumed from indirect suppositions. As shown in Chapter 6, variation of input

parameters may radically alter the modelling results.

(3) Limitations of NorSandBiot formulation.

• NorSandBiot formulation is an approximate numerical representation of a complex

behaviour of natural soils and may not accurately predict the behaviour of Colebrook

sensitive silty clay.

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However, recognizing the approximate nature of the modelling, it should be noted that the

NorSandBiot simulations showed a good agreement with triaxial behaviour of fine-grained soils

(see Section 4.4.3) and a perfect match with available dissipation solutions (see Appendix E).

No indication of unusual or atypical response was observed throughout the modelling.

Therefore, the NorSandBiot representation of soil behaviour appears to be reasonable.

Simplification involved in the analysis and choice of input parameters are major factors

affecting the modelling results. The analysis other than 1-D and simulation of soil remoulding

are beyond the scope of the current research. In the current study, an attempt is made to

produce a better fit to the field data by adjusting the input parameters within the range

acceptable for Colebrook silty clay and by introducing the effect of the helices.

7.2.1.2. NORSANDBIOT “BEST FIT” WITH FIELD DATA.

During Stage I, the pore pressure response due to helical pile installation by expanding a single

cavity up to the pile shaft radius was simulated, neglecting the effect of the helices. Therefore, a

perfect agreement between modelled and field responses was not expected. However, given a

wide range of acceptable values for NorSandBiot input parameters, the general trend of pore

pressure distribution can be improved to align more closely with the field data.

Fitting of the modelled response was based on the results of the NorSandBiot parametric study

(see Chapter 5). The pore pressure magnitude was lowered and its radial extent was increased,

primarily by assuming a degree of overconsolidation (OCR & ψ) corresponding to a more

contractive behaviour than the one taken for the “base case”. The shape of radial pore pressure

distribution was corrected by adjusting NorSand parameters, such as Mcrit, Г & λ and Hmod. The

time dependent pore pressure distribution was adjusted by increasing Poisson’s ratio, ν.

Table 7.1 shows the acceptable range of the Colebrook silty clay properties, the “base case”

input parameters and the parameter set derived by fitting the model to the pore pressure

distribution at the end of installation (adjusted parameters are highlighted). Although referred

to as the “best fit”, this parameter combination was still constrained to be reasonably

consistent with the site properties. The fit is non-unique; there is slight flexibility on

parameters, which can produce a similar pore pressure response, and the choice of the “best

fit” is subjective.

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Table 7.1. Modelling parameters for “base case” and “best fit” simulations.

Input Parameters

Acceptable Range 1

Base Case

Best Fit Units

General G 5.8 - 9.8 7.8 7.8 MPa ν 0.1 - 0.3 0.2 0.3 - kr 3.4·10-9… 8.5·10-10 2.1·10-9 2.1·10-9 m/s OCR 1.2 … 2.8 2.2 1.45 - K0 0.56 … 0.76 0.66 0.66 - σ′v0 32.9 … 75.7 54.28 54.28 kPa u0 39.5 … 94.1 66.8 66.8 kPa NorSand Mcrit 1.24 … 1.33 1.285 1.33 - χ 3.0 … 4.0 3.5 3.5 - ψ -0.05 … 0.2 0.026 0.12 - λ 0.073 … 0.362 0.165 0.08 base loge

Γ 1.55 … 2.25 1.86 1.55 at 1 kPa Hmod 50 … 450 100 200 -


As discussed in Section 6.2, the “base case” set of parameters is non-sensitive, which is in

contradiction with the conditions found at the Colebrook site. One of the governing criteria for

selecting the “best fit” combination of parameters was matching the sensitivity observed in the

field. The consolidated undrained triaxial response for the “base case” and “best fit” parameter

sets are shown in Fig. 7.3 and summarized in Table 7.2. It can be seen that the medium with the

“best fit” set of properties is less than half those observed in the field. A better match could not be

achieved unless the values of the critical state line parameters (Γ & λ and Mcrit) are taken out of the

acceptable range. It should be recognized that the current version of NorSand was not developed

to model extremely sensitive soils and cannot reproduce very high sensitivity. Having a more

“sensitive” version would likely help to rectify the mismatch between predicted and measured

responses.

Table 7.2. Undrained shear strength and sensitivity estimated from simulation of triaxial test with “base case” and “best fit” set of parameters.

Property Acceptable range for Colebrook silty clay 1

Simulation with “base case” parameters

Simulation with “best fit” parameters

su, kPa 15…29 22.6 15.1 St 6 …24 1 2.4


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Fig. 7.4 shows the pore pressure distribution predicted by the “base case” and

”best fit” simulations, measured at the Colebrook site (Weech, 2002) and, also a dataset by

Levadoux & Baligh (1980). The quantitive comparison of the excess pore pressure

characteristics is provided in Table 7.3. Based on this table, the magnitude of normalized

excess pore pressure at the cavity wall for the “best fit” simulation is 17% lower and the zone of

radial pore pressure distribution is 45% larger than for the “base case” response. The “best fit”

simulation also shows reasonable agreement with the dataset of Levadoux & Baligh. In

comparison with the average field data, the “best fit” simulation overestimated the pore pressure

magnitude at the shaft by less than 20% and underpredicted the maximum radial extent of pore

pressure generation zone by 42%.

While comparing NorSandBiot simulations and the response observed at the Colebrook site, a

clear distinction can be drawn between pore pressure distribution for low and high sensitivity

cases. For the non-sensitive “base case” simulation, the pore pressure distribution is almost

linear, whereas the sensitive “best fit” and field data produce a more flattened response, where

the pore pressure magnitude up to r/Rshaft = 4…5 is nearly constant. As follows from Table 7.3,

higher sensitivity leads to a lower pore pressure magnitude at the shaft and larger radial extent of

generated excess pore pressures. There is some support of this pattern in the Levadoux &

Baligh dataset.

Table 7.3. Pore pressure response for “base case”, “best fit” and field data (Weech, 2002).

Response ∆u/σ′voat the cavity wall

T95 Hours

Maximum radial extent of generated excess pore pressures at the end of cavity expansion

Measured in the field (St = 6…24) 1.42 92 65

Simulated with “best fit” parameters (St = 2.4) 1.74 73 38

Simulated with “base case” parameters (St = 1) 2.36 39 21

The pore pressure dissipation measured at the pile wall is compared with those predicted using

the “base case” and “best fit” parameter sets in Fig. 7.5. Due to the differences in the starting

initial excess pore pressure distribution magnitudes, both simulations at earlier times (< 40

minutes) show some mismatch with the field data. At larger times (> 40 minutes) the shapes of

measured and predicted pore pressure responses are in good agreement. The quantitive

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comparison of the excess pore pressure dissipation times is provided in Table 7.3. It can be seen

that the “best fit” simulation underestimates the dissipation time period by 21%, which is an

improvement in comparison with the “base case” simulation that underestimates the field value

by 33%.

Based on Table 7.3, the following is true for all presented response cases: as the magnitude of

generated excess pore pressure due to pile installation decreases and the extent of radial pore

pressure distribution increases, the pore pressure dissipation time increases.

The introduction of a new set of parameters has an impact not only on the pore pressure

response, but also on the stress response. The evolution of lateral effective stresses with pore

pressure dissipation at the cavity wall for the “base case” and “best fit” simulations is shown in

Fig. 7.6. A quantitive comparison of the simulations is compiled in Table 7.4.

Table 7.4. Variation of effective stresses with time for “base case” and “best fit” simulations.

Time after end of cavity expansion 1 minute 10000 minutesSimulated

Response σ′h /σ′v0σ′ho

(kPa) σ′vo

(kPa) ∆u /σ′v0 σ′h /σ′v0σ′ho

(kPa) σ′v

(kPa) σ′v/σ′vo

“best fit” parameters (St = 2.4)

0.30 16.3 54.3 1.68 1.11 108.1 48.9 0.9

“base case” parameters (St = 1)

1.17 63.5 54.3 2.09 1.99 60.3 75.1 1.38

Table 7.4 shows that the pore pressures generated at the cavity wall are quite similar (only 20%

difference). However, the variations of lateral effective stress with time for “base case” and

“best fit” simulations are very different. At one minute after the end of pile installation, the

“base case” has a normalized lateral effective stress at the pile wall of 1.17. The corresponding

normalized lateral effective stress at the pile wall for the “best fit” case is only 0.30; a difference

of 3.9 times. Over the next week (10,000 minutes) more than 95% of the excess pore pressures

had dissipated and the effective stresses had increased. During this time the “base case”

normalized pore pressures fell by 2.04 and the normalized lateral stresses increased by 0.82 to

1.99, corresponding to 41% of the pore pressure reduction being translated into effective

stresses. Over the same time period the “best fit” case normalized pore pressures fell from 1.68

to 0.08, a fall of 1.6, and the lateral stresses increased from 0.30 to 1.11, an increase of 0.81.

This corresponds to 48% of the pore pressure reduction being translated into lateral effective

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stress. The final lateral effective stresses at the cavity wall for the “base case” was 108.1 kPa

and for the “best fit” stress was 60.3 kPa, a factor of 1.8 difference.

According to Lehane & Jardine (1994) clay sensitivity has a large effect on the equalized lateral

effective stress ratio σ′h/σ′v0, so that for a sensitive low OCR soil, σ′h/σ′v0 is less than 50% of

the value for a similar, but insensitive, soil. Conducted modelling showed a similar trend. At

about 95% pore pressure dissipation, the lateral effective stress ratio σ′h/σ′v0 for the sensitive

“best fit” simulation is 55% of the one for the non-sensitive “base case” simulation.

Insight into the variation of stresses at the cavity wall, during and after cavity expansion, for the

“best fit” simulation is shown in Fig. 7.7. Comparing the stress path shown in Fig. 7.7 with the

one for the “base case” simulation (see Fig. 6.5), it can be seen that during initial cavity

expansion yielding for the “base case” is slightly delayed by a short period of elastic

deformations due to the higher OCR of 2.2 associated with a rise in q with no change in p′. For

the “best fit” simulation, due to the low OCR the elastic “preface” does not exist, and the

medium yields almost immediately after the load is applied. As cavity expansion continues the

stress paths for both simulations moves towards the critical state line. For the “base case”,

failure occurs on the edge of contraction/dilation behaviour and both dilation and contraction is

observed. The stress path for the “best fit” simulation during cavity expansion is strongly

contractive, which is expected from the medium having an OCR within the lightly

overconsolidated range. During the dissipation stage both cases show gradual hardening. The

final level of stress at the end of the dissipation process is significantly larger for the non-

sensitive “base case” simulation. Variation of void ratio with mean normal effective stress for

the “base case” simulation, shown in Fig. 7.8, does not indicate any atypical behaviour – during

(nearly) undrained cavity expansion, the void ratio is constant and gradually decreases

throughout the pore pressure dissipation period.

Overall, the “best fit” set of parameters provided a reasonable prediction of the pore pressure

response measured in the field. It appears that increased sensitivity of the new parameter set

was one of the major contributing factors. However, some differences between predicted and

measured responses remain – particularly concerning is the radial extent of generated excess

pore pressure, which is still underestimated by 33%. Considering that the best efforts were

made to consider sensitivity of the Colebrook site, the remaining factor that may contribute to

the observed differences is the effect of the helices, neglected during Stage I modelling.

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7.2.2. STAGE II. MODELLING OF HELICAL PILE AS SERIES OF CAVITY EXPANSIONS.

Simulation of helical pile installation as a single cavity expansion showed reasonable prediction

of the pore pressure dissipation time. However, expansion of a single cavity does not take into

account the effect of the helices. The analysis of helical pile installation is not complete unless

the effect of the helices is evaluated. In this section an attempt is made to estimate the impact of

the helices on soil response using very simple 1-D approximations.

7.2.2.1. DETAILS OF HELIX MODELLING.

As described in Section 4.2, simulation of the helical pile installation in 3-D would probably be

the most comprehensive. In 3-D we could consider the full complexity of the helical pile

geometry and attempt to reproduce the effect of helical plates shearing the soil and the effect of

the pulling force. However, implementation of the 3-D approach is complex. Performing the

modelling in 2-D simplifies the simulation set up and reduces the computation time, meanwhile

raising a question of how to represent the helices. The axisymmetric cylindrical cavity

expansion analogue may be used to simulate the process of helical pile installation. If such a

methodology is employed, representation of the helices is based on expansion of the cylindrical

cavity over one flight, equivalent to half of the volume of a spirally shaped helix. The 2-D

approach allows incorporation of the importance of both vertical and horizontal dimensions,

although still requires a sophisticated modelling set up. The objective is to model the general

characteristics of the helical pile installation process reasonably well, yet simply. Simplification

to the 2-D axisymmetric case requires neglecting the importance of the vertical dimension, so

instead of 2-D, a 1-D approach was employed in the current study. The 1-D approach is based

on expansion and contraction of a series of cavities in a single row of finite elements, as

conceptually shown in Fig. 4.3. The magnitudes and timing of the cavities

expansions/contractions are dependent on the helical pile’s geometry and soil penetration rate.

Simulation of the helical pile installation process begins from expansion of a cavity corresponding

to the helical pile shaft, similar to Stage I. Modelling continues based on the field rate of helical

pile installation at 1.5 cm/s as reported by Weech (2004), where the time of the particular cavity

expansion/contraction cycle corresponding to the helix is determined based on its location relative

to the pile tip. Each cavity expansion/contraction cycle should occur during the time a helix

advances through the soil by one flight. Given the flight size of 9.5 cm and the rate of penetration

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of 1.5 cm/s, the helical pile should advance by one flight in 6.33 seconds. Therefore, 3.16 seconds

is required to expand the cavity, the same time is necessary to contract the cavity. Assuming that

the rates of vertical and horizontal penetration are the same, the magnitude of cavity expansion

(and contraction) is 4.74 cm (rate 1.5 cm/s multiplied by expansion time 3.16 sec.. This value is

smaller than the length of the actual helix at its maximum extent - 13.35 cm. Considering that

cavity expansion/contraction cycles are a very approximate analogue for simulation of the helices

penetration, the proposed scheme (Case A in Fig. 7.9 & 7.10) of helical pile installation was

adopted for further the analysis.

In order to have a reference point for the analysis of expansion of a smaller cavity (Case B in

Fig. 7.9 & 7.10), a radius of 1.54 cm was also analysed. This radius comes from the 2-D

approach described earlier where the concept of expanding cavity over the length of one flight,

equivalent to the volume of a helical plate (see Fig. 4.3), is employed. Case B may also serve as

a reference while studying 2-D effects in the future.

For both Case A and Case B, installation of the helical pile was modelled with 3 and 5 helices.

Modelling of the expansion/contraction cycles may be based on two following assumptions:

Assumption 1. During cavity contraction no discontinuity between the cavity wall and the soil is

possible, i.e. as cavity contracts soil is forced to move with the cavity wall.

Assumption 2. During cavity contraction a discontinuity between the cavity wall and the soil is

possible, i.e. as the cavity contracts the soil interface is left free and allowed to naturally rebound.

The Assumption 1 is based on the idea that natural soft fine-grained soil will collapse

immediately as the helical plate releases the displaced volume, whereas the Assumption 2

assumes that on contraction drilling fluids or groundwater may fill a small portion of the void

created during helical expansion. The author believes that void space between the soil and pile

wall is unlikely, therefore the modelling was performed based upon Assumption 1. A single

simulation (Case A with 5 helices) was run using Assumption 2 to contrast different

idealizations.

7.2.2.2. EFFECT OF CAVITY EXPANSION/CONTRACTION CYCLING ON PORE PRESSURE

RESPONSE.

To measure the applicability and limitations of the employed approach, responses of two

piezometers located in the vicinity of the helical piles, for the cases of three and five helices,

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were simulated. For the helices modelling interest is in comparing the pore pressure variation

during installation both at the pile wall and with radial distance: particularly the radial extent of

pore pressure generation. Information on the piezometers taken for the analysis is provided in

Table 7.5.

Table 7.5. Piezometers considered for the analysis (based on Weech, 2002).

Test Pile (TP) Piezometer

(PZ) Filter Elevation

(m)

Radial Distance (r/Rshaft) from Pile

Centre

Response During Installation and

Dissipation TP3 (3 helices) PZ-TP3-1 -6.03 5.8 Excellent TP4 (5 helices) PZ-TP4-1 -6.07 4.8 Excellent

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

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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.

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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

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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

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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

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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


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


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


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


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


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


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


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


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


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


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


-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-TP4-1(r/Rshaft = 4.8)

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


∆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


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


∆u/σ

'vo

Measured response:piezometer PZ-TP4-1(r/Rshaft = 4.8)

Simulated response:Case B. Shaft + 5 helices (r/Rshaft = 4.8)

a

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


∆u/σ

' vo

Measured response:piezometer PZ-TP3-1(r/Rshaft = 5.8)

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


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




direction of pore pressure riseduring expansion of first helix


Edge of Helicesfor Case Asimulations

Edge of Pile

100

Fig. 7.14. Radial pore pressure distribution during first helix expansion (Case A).

166


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 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


5% of 1st helix contraction20% of 1st helix contraction

50% of 1st helix contraction

100% of 1st helix contraction


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


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 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


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


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


-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


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



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).

0.0

0.5

1.0

1.5

2.0

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000Time (min)

∆u/σ

' vo



shaft only

shaft + 5 helices

shaft only

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).


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.


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

∆u/σ

' vo Measured

response: piezometer PZ-TP4-1(r/Rshaft = 4.8)

Simulated response:Case A (Assumption 2). Shaft + 5 helices (r/Rshaft = 4.8)

Simulated response:Case A (Assumption 1). Shaft + 5 helices (r/Rshaft = 4.8)

1st helix contraction

1st helix expansion pause between cycling

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


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


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


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


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.

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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

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