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Numerical modelling of time dependent pore pressure response induced by helical pile installation Vyazmensky, Alexander M. 2004

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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. T A B L E O F C O N T E N T S . A B S T R A C T ii T A B L E O F C O N T E N T S i« L I S T O F T A B L E S vii L I S T O F F I G U R E S viii A C K N O W L E D G E M E N T S xiii 1.0. I N T R O D U C T I O N 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. O V E R V I E W O F F I E L D S T U D Y O F H E L I C A L P I L E P E R F O R M A N C E I N S O F T S E N S I T I V E S O I L 8 2.1. INTRODUCTION V 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 L I T E R A T U R E R E V I E W 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. F O R M U L A T I O N O F M O D E L L I N G A P P R O A C H 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. S E L E C T I O N O F S I T E - S P E C I F I C S O I L P A R A M E T E R S F O R M O D E L L I N G 67 5.1. INTRODUCTION 67 5.2. SOIL PARAMETERS FOR MODELLING 67 5.2.1. ELASTIC PROPERTIES G, V 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 a'vo AND EQUILIBRIUM PORE PRESSURE UQ 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, x 75 5.2.6.3. HARDENING MODULUS, Hmod 75 5.2.6.4. SLOPE OF CRITICAL STATE LINE, X 75 5.2.6.5. INTERCEPT OF CRITICAL STATE LINE AT 1 KPA STRESS, r 77 5.2.6.6. STATE PARAMETER, y/ 77 5.2.7. NORSAND PARAMETERS ANALYSIS 79 5.3. SUMMARY 80 6.0. N O R S A N D - B I O T C O D E P A R A M E T R I C S T U D Y 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 O C R 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 I l l 6.7. SUMMARY 113 7.0. M O D E L L I N G O F P O R E P R E S S U R E C H A N G E S I N D U C E D B Y P I L E I N S T A L L A T I O N I N 1-D 138 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 A P P E N D I X A . SOURCES OF SUBSURFACE INFORMATION FOR COLEBROOK SITE 189 A P P E N D I X B. PIEZOMETERS RESPONSE 191 A P P E N D I X C . VALIDATION OF NORSAND MODEL AGAINST BONNIE SILT 193 A P P E N D I X D . NORSAND-BIOT COUPLING 197 A P P E N D I X E . NORSAND-BIOT CODE VERIFICATION 200 A P P E N D I X F. COUPLED MODELLING OF OBSERVED PORE PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION (PAPER) 209 vi List of tables. L I S T O F T A B L E S T A B L E P A G E 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 Ko from CPT test data 70 5.2. Calculation of radial hydraulic conductivity, kr 74 5.3. Estimation of slope of critical state line, X, 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 I l l 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=\.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 r, A, y/t and R 62 4.6. Definitions of internal cap, pt,pc, M,c, Mj and r\L on yield surface for a very loose sand .. 63 4.7. Conventional and NorSand representation of overconsolidation ratio for soil initially at/?' = 500 kPa subject to decreasing mean stress 63 4.8. NorSand fit to Bothkennar Soft clay in CKOU 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 Ko 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, X 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 withp' for "base case", 20 & 21 scenarios 117 6.8. Effect of Ko on radial distribution of generated excess pore pressure at the end of cavity expansion 117 6.9. Effect of Ko 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 & y/on radial distribution of excess pore pressure response at the end of cavity expansion 119 6.12. Effect of coupled R & if/on time dependent pore water pressure response at cavity wall 119 6.13. Effect of uncoupling R & if/ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with positive if/ 120 6.14. Effect of uncoupling R & ^on time dependent pore water pressure response at the cavity wall, for simulations with positive if/ 120 6.15. Effect of uncoupling R & if/on time dependent pore pressure response at the cavity wall, for simulations with negative if/. 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 & if/on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with negative if/. 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/?'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 v on radial distribution of excess pore pressure at the end of cavity expansion .. 126 6.27. Effect of v 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 r on radial distribution of excess pore water pressure at the end of cavity expansion 128 6.30. Effect of f on time dependent pore water pressure response at cavity wall 128 List of figures. 6.31. Stress paths for scenarios "base case", 10 & 11 '. 129 6.32. Effect of J 1 & A on radial distribution of excess pore pressure at the end of cavity expansion 129 6.33. Effect of r& A on time dependent pore water pressure response at cavity wall 130 6.34. Stress paths for scenarios "base case", 12 & 13 130 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 6.37. Stress paths for scenarios "base case", 14 & 15 132 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 6.40. Stress paths for scenarios "base case", 14 & 15 133 6.41. Effect of x on radial distribution of excess pore pressure at the end of cavity expansion... 134 6.42. Effect of % 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 AU/O'VQ and oVcr'vo 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/Rsnaft = 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/Rst,aft = 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/Rshafl=].08) 172 7.26. Comparison of stress paths for central gaussian point of the mesh element adjacent to the cavity wall (r/RSha/i - 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 X l l Acknowledgements. A C K N O W L E D G E M E N T S . 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 fiance 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 A D A S T R A xiii Chapter!. Introduction. 1. I N T R O D U C T I O N . 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 l Chapter 1. Introduction. was balanced by a too high end bearing. Randolph in his Rankine lecture (2003) also recognized the lack of accuracy in pile design. Due to shortcomings in pile capacity predictions geotechnical engineers have to rely on pile load tests to refine final piling foundation design. The ability to accurately predict the variation of stresses and pore pressures in fine-grained soil due to pile installation is a key to improving pile capacity prediction capabilities. The problem of predicting the variation of pile capacity in fine-grained soils is one of predicting the excess pore pressure and associated stresses at the pile shaft as a function of time. It appears that development of a robust technique for evaluation of pore pressure changes due to pile installation will provide a basis from which a method accounting for capacity gain with time in design and testing can be developed. This study is concerned with modelling the time-dependent pore pressure response due to helical pile installation in soft fine-grained soil. 1.2. H E L I C A L 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 0 3.8 - 25 cm and helical plates 0 15 - 36 cm. The diameter of manufactured piles is quite small and their application is currently restricted to relatively small jobs. It appears that the potential of helical piles is not fully exploited to date. A new boost in helical pile's application is expected from recent development of high capacity torque units, which will make possible installation of helical piles with larger diameters, installed to greater depths. 2 Chapter 1. Introduction. Generally, helical piles can be employed in any application where driven and jacketed piles are used, except for the cases where penetration of competent rock is required. Currently helical piles found application in the following areas: • foundation repairs, upgrades & retrofits; • pump-jacks and compressor stations for oil and gas industry (large diameter piles); • pipelines support; • foundations for temporary and mobile structures. Experience with conventional (small diameter) helical piles in soft soils in British Columbia revealed a tendency for buckling of the slender steel shaft during loading. Aiming to reduce the buckling effect, placement of grout around the shaft was proposed and patented by Vickars Developments Co. Ltd, as grouted, or PULLDOWN™, pile, shown in Fig. 1.1.b. Normally, helical piles are installed by sections. The leading section, also called a screw anchor, is placed into the soil by rotation of the pile shaft using a hydraulic torque unit. The pile is screwed into the ground in the same method a wood screw is driven. Helical plates of the leading section create a significant pulling force that makes the shaft advance downwards. Following the screw anchor installation, extension sections are bolted to the top of the screw anchor shaft. Installation continues by resumed rotation, and further extension sections are added until the project depth of the pile is reached. For the grouted helical piles, at each section's connection, displacement plates are attached to the shaft. During pile installation they create a cylindrical void, which is filled by the flowable grout. Helical piles have several distinctive advantages over traditional driven and jacketed piles: • mobilize soil resistance both in compression and uplift; • quick and easy to install: vibration free, no heavy equipment required, possible to install inside buildings (for small diameter piles); • reusable. Helical piles are typically installed in soils that permit the compressive capacity of the pile to be developed through end-bearing below each of the helices at the bottom of the pile. Where the thickness of soft cohesive strata is too extensive to make it practical to advance helical piles to a competent bearing stratum, it may be necessary to develop the capacity of the piles in friction within the soft cohesive soil. However, experience using helical piles in such soils is limited at this time, as is the understanding of the complex sensitive fine-grained soil-helical pile interaction. 3 Chapter 1. Introduction. 1.3. PURPOSES AND O B J E C T I V E S O F R E S E A R C H . 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 O F STUDY. The conducted study is mainly focused on soil pore water pressure response due to pile penetration, as it is believed to be an important factor affecting the variation Of pile bearing 4 Chapter 1. Introduction. capacity with time. Adequate simulation of the pore water pressure response in the soft fine-grained soil requires a realistic soil model and a fully coupled modelling approach. NorSandBiot formulation adopted in the current study incorporates the NorSand soil model (Jefferies, 1993; Jefferies & Shuttle, 2002) to represent the fine-grained soil stress-strain behaviour and the Biot (Biot, 1941) consolidation theory to account for the effect of coupling the pore pressure response to behaviour to the soil stress-strain behaviour. All numerical simulations conducted in the current study were based on the finite element implementation of the NorSandBiot formulation developed by Shuttle (2003). Pore pressure and stress predictions of the NorSandBiot code were successfully verified against a number of available analytical solutions. Given the complexity of helical pile installation process, numerical simulation of excess pore pressure generated due to helical pile installation poses many challenges. It appears that the most realistic simulation of helical pile installation will require a 3-D approach, which is hard to implement and widely apply. The focus of the current research was on developing simple, yet realistic representation of pore pressure response. It was necessary to neglect some features of helical pile-soil interaction while simplifying the analysis. In the present study helical pile installation was analyzed in 1-D employing the cylindrical cavity expansion analogue. A better insight in pore pressure response induced due to helical pile installation may be achieved when the effect of soil remoulding and 2-D effects of soil response are considered. Due to the large volume of the conducted study these issues were left for future research. Laboratory study was also beyond the scope of this work. Modelling input parameters were derived from three previous investigations of Colebrook silty clay properties. They explicitly provided many, but not all, of the input parameters required for the NorSandBiot formulation. Some of the input parameters were taken as a best estimate, believed and shown to be reasonable based on all information available. Another challenge in establishing input parameters resulted from differences between laboratory and in-situ derived values of soil properties. This is not unusual in a silty site where soil disturbance during sampling is a major issue. Local spatial property variation, as seen in the in situ measurements, added to parameter uncertainty. It appears that detailed laboratory study is required to refine the modelling input parameters taken in the current study. 5 Chapter 1. Introduction. 1.5. THESIS ORGANIZATION. In Chapter 1 of this thesis helical piles are introduced, research purposes and objectives are stated, along with the scope and limitations of the conducted study. An overview of the study of helical pile performance in soft fine-grained soils, carried out by Weech (2002), is given in Chapter 2. This comprises a description of the scope of the work, information on site stratigraphy and basic soil properties, geometry of the tested piles and measuring equipment. A brief outline of the results of the Weech's study relevant to the current research is also presented. Chapter 3 reviews the literature to provide information leading to the formulation of the modelling approach. Modelling approach adopted in this study is formulated in Chapter 4. NorSand critical state soil model and Biot consolidation theory are presented along with their finite-element implementation. Formulation input parameters are explained. Chapter 5 describes the selection of site-specific soil parameters for modelling. Overview of all available subsurface information is given. Selection process for all model input parameters is individually analyzed. Best estimates of the soil properties for modelling are presented. In Chapter 6, the description and results of the NorSand-Biot formulation parametric study are presented. An accent is put on highlighting the input parameters that have the most profound influence on the modelling results. Chapter 7 presents modelling results and their analysis. A comparison of modelling with the available field data, including Weech (2002) measurements, is provided and discussed. Effects of the pile shaft and the helices on pore pressure response are separately analysed. Implications from the modelling are presented. Chapter 8 provides conclusions from the current study and recommendations for further research. 6 Chapter 1. Introduction. Fig. 1.1. Helical piles: a - conventional pile; b - grouted (PULLDOWN™) pile. 7 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.0 O V E R V I E W O F F I E L D S T U D Y O F H E L I C A L P I L E P E R F O R M A N C E I N S O F T S E N S I T I V E S O I L . 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. S C O P E O F W E E C H ' S STUDY. Six instrumented full-scale helical piles were installed in soft sensitive marine deposits. Prior to pile installation, an in-situ testing program was carried out, that consisted of: • two profiles of vane shear tests; • five piezocone penetration soundings, with pore pressure dissipation tests carried out at two soundings and shear wave measurements at three soundings. The excess pore pressures within the soil surrounding the piles were monitored during and after pile installation by means of piezometers located at various depths and radial distances from the pile shaft, and using piezo-ports, which were mounted on the pile shaft. After allowing a recovery period following installation, which varied between 19 hours, 7 days and 6 weeks, piles with two different helix plate spacing were loaded to failure under axial 8 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. compressive loads. Strain gauges mounted on the pile shaft were monitored during load testing to determine the distribution of loading throughout the pile at the various load levels up to and including failure. Load-settlement curves were generated for different pile sections at different times after installation. The piezometers and piezo-ports were also monitored during load testing and the distribution of excess pore pressures 2.3. SITE S U B S U R F A C E 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 S T R A T I G R A P H Y . The subsoils found in this area belong to so called Salish Sediments. According to Armstrong (1984): "Salish sediments include all postglacial terrestrial sediments and postglacial marine sediments that were deposited when the sea was within 15 m of present sea level". These deposits were likely laid down during the Quaternary period between 10,000 and 5,000 years ago. Cross-section of site stratigraphy is shown on Fig. 2.2. From the surface there is a layer of fill, about 0.6 m thick, which was placed during 99A Highway construction. The fill is underlain by a layer of firm to stiff peat, possibly bog and swamp deposit, that formed the original ground surface; the thickness of this peat layer is about 0.3 m. Below the peat there is a layer of firm clayey silt of deltaic origin, with some sand inclusions. The thickness of this layer is about 1 m. The layer of clayey silt is underlain by layer of soft silty clay with organic inclusions (peat, plant stalks). Given the proximity of the Serpentine river, this deposit likely has a tidal origin: it was deposited within the inter-tidal zone between the Serpentine river delta and Semiahmoo Bay. Below the silty clay layer there is a thick (around 27 m) layer of soft clayey silt to silty clay of marine origin. The marine deposits are underlain by a stiff layer of sand and gravels of glacial origin. Crawford & Campanella (1991) reported slight artesian pressure at the interface of the silty clay layer and glacial deposits. Weech (2002) indicated that the groundwater table can be found at -2 m elevation (0.7m from the surface), with an upward hydraulic gradient of 5 to 10 %, which is possibly explained by the groundwater recharge from the upland area north of the site. 9 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.3.2. SOIL PROPERTIES. Three subsurface investigations were performed at, or close to, the helical piles performance research site. Site plan and locations of all subsurface investigations are presented in Fig. 2.3. A brief description of each investigation and their reviews reported in the literature are presented below in chronological order. 2.3.2.1. F I E L D INVESTIGATION BY MINISTRY O F T R A N S P O R T A T I O N A N D H I G H W A Y S . 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 3 2 testing, an average coefficient of consolidation in the horizontal direction, cn = 1.5TO" cm /s, an average coefficient of secondary consolidation, Ca = 0.014 and an initial void ratio, for all three tests, eo = 1.25. A summary of typical soil properties from MoTH investigation given by Crawford & deBoer (1987) are presented in Table A. l (Appendix A). 2.3.2.2. R E S E A R C H BY UNIVERSITY O F BRITISH C O L U M B I A (1). Crawford & Campanella (1991) reported the results of a study of the deformation characteristics of the subsoil, using a range of in-situ methods and laboratory tests to predict soil settlements underneath the embankment, and compare them with the actual settlements. In-situ tests included field vane shear tests, piezocone penetration test (CPTU) and a flat dilatometer test (DMT). Laboratory tests were limited to constant rate of strain odometer consolidation tests on 10 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. specimens obtained with a piston sampler. Results of a series of the CRS consolidation tests are presented in Table A.2 (Appendix A). As a continuation of previous works by Crawford & deBoer (1987) and Crawford & Campanella (1991), Crawford et al. (1994) studied the possible reasons for the difference between predicted and measured consolidation settlements underneath the embankment using the finite-element consolidation analysis with CONOIL computer program (by Byrne & Srithar, 1989). The soil properties employed in the numerical analysis are shown in Table A.3 (Appendix A). 2.3.2.3. R E S E A R C H BY UNIVERSITY O F BRITISH C O L U M B I A (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 (w„) 42%+/-3% -liquid limit (wr) 40%+/-4% -plasticity index (PT) 13.5%+/-4.5%, below -8m in elevation PI is up to 21% unit weight (y) 17.8+/-0.3 kN/m3 -in-situ void ratio (e0) 1.16+/-0.09 derived from moisture content data, assuming specific gravity of 2.75 Weech (2002) carried out a detailed in-situ site characterization program, which included field vane shear tests; cone penetration tests with pore pressure (CPTU) and shear wave travel time measurements (SCPT). Locations of sampling and in-situ soundings are presented in Fig. 2.4. A summary of engineering parameters for the silty clay layer, estimated from in-situ tests by Weech, are presented in Table A.4 (Appendix A). 11 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. Field vane shear strength profiles for the Colebrook site measured by Weech (2002) and Crawford & Campanella (1991) are shown in Fig. 2.5. In Fig. 2.5a the peak undrained shear strength is plotted with depth. For the clayey silt/silty clay layer it varies from 15 to 30 kPa. The profile of the remoulded shear strengths, (Su)rem, is also plotted on Fig. 2.5a, showing a variation from 2 to 0.7 kPa within the clayey silt/silty clay layer. Due to such low remoulded strengths, the sensitivity, St = (su)peai/(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, <r'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 SJ<J'VO ratio is quite high -around 0.7, which indicates moderately overconsolidated soil. At lower depths the deposit is lightly overconsolidated, with the sjcr\0 ratio around 0.4. A typical CPT cone test result for Colebrook site, including profiles of corrected tip resistance, qr, sleeve friction,/^, and excess penetration pore pressure, Au, 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. H E L I C A L PILES AND P O R E PRESSURE M E A S U R I N G E Q U I P M E N T . 2.4.1. T E S T PILES G E O M E T R Y A N D I N S T A L L A T I O N D E T A I L S . 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 (5) is 3 times the diameter (£>) of the lower plate. In this case, current thinking based on small scale model tests (Narasimho Rao et al., 1991) is that during loading to failure, failure occurs at individual helices. For the closer spacing of the helical plates, the failure mechanism is believed to be different - all helices fail simultaneously, so that a cylindrical failure surface is generated 12 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. coinciding with the outside edge of the helical plates. To investigate such a possibility the testing was carried out on piles which had either 3 plates at S/D = 3, or 5 plates at S/D = 1.5, so that the total length from the top to bottom helix was equal for the two pile types (2.1 m). The pitch of the helix plates was 7.5 to 8 cm, which is the standard pitch on helical piles manufactured by Chance Anchors. The geometry of both types of lead sections is shown in the Fig. 2.7. In total six helical piles - three for each leading section type were installed, their locations are shown in Fig. 2.8. Two piles, TP-1 - with three helices (S/D = 3) and TP-2 with five helices (S/D = 1.5), were chosen for the detailed monitoring. The other piles served as a source of additional information. All piles were installed to a tip depth of 8.5 m (-9.8 in elevation). Installation of a single pile, including breaks for section mounting and adjustments to maintain pile verticality, usually took about 2 hours. Deducting interruptions, the average rate of soil penetration by helical pile was about 1.5 cm/s. 2.4.2. M E A S U R I N G E Q U I P M E N T . 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.l (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. l . 13 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.5. SUMMARY OF WEECH'S STUDY RESULTS. This summary is based on Weech's interpretations of pore pressure response measured during and after helical pile installation. Only key points are presented here, more details can be found in Weech (2002). 2.5.1. PORE W A T E R 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 Au/cr'vo are plotted against the depth of the pile tip below the elevation of the piezometer filter (zpne - zpiez0). 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 Aut 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/Rshafi = 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 - t^) appears to respond directly to the penetration of 1 In this overview, radial distance is represented by the r/Rshaf, ratio, where Rshaf, is the radius of the pile shaft (in the current study, identical for all piles), r - radial distance from the pile centre. 14 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. the helix plates. Within this zone, distinctly different responses are observed for the S/D -1.5 and S/D = 3 piles. • At radial distances larger than about 10-12 t„x 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/Rsha/t = 5 to 17, Aushaf/cfVo decreases steeply and almost linearly. After r/Rshaft = 17, Aushaft becomes quite small (< 0A(fVo) 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/Rsha/, = 6, the pore pressures generated by the helices make up to 20% of the total pore pressures and at distances greater than r/Rsnaf, = 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/Rsnaft 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. P O R E W A T E R PRESSURE DISSIPATION A F T E R H E L I C A L P I L E I N S T A L L A T I O N . Weech (2002) compiled a combined dataset of all (for piles with both S/D =1.5 and 3) normalized piezometric measurements, taken at different times, at the locations above the bottom helical plate as presented in Fig. 2.13. Despite some scatter in the data there is a trend in the observed pore pressure dissipation behaviour, represented by the fitted curves. According to Fig. 15 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.13, excess pore pressure, Au, 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 Au(r)/a'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 Auhx is observed in the soil (from r/Rshaf, = 5 to at least 17) below the level of the bottom helix within 10 minutes after stopping penetration • Dissipation of Au 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/Rsnaft > 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 Au(t)/a rvo data from individual piezometers/piezo-ports located at different radial distances from the test piles (above the bottom helix). Based on this figure Weech (2002) made the following observations: • The dissipation occurs much more quickly below the bottom helix than above, at radial distances close to the pile. • Even though greater proportions of dissipation occur sooner at larger radial distances, all of the curves tend to converge at the end of the dissipation process. For all monitored piles 100% dissipation occurred at about 7 days for most locations around the piles. • The dissipation process appears to be essentially independent of the number or spacing of the helix plates. 16 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.6. SUMMARY. A comprehensive study of helical pile performance carried out by Weech (2002) was an important step towards better understanding of a complex helical pile - fine-grained soil interaction. Weech reported details of the pore pressure response observed during and after installation of helical piles at the Colebrook site and attempted to interpret them. However, the presented problem analysis cannot be considered complete. The applicability of the observations made during Weech's study on sites with different soil conditions and different helical piles geometries is questionable. According to Terzaghi2: "Theory is the language by means of which lessons of experience can be clearly expressed". It appears that the lessons of experience gained during Weech's study may be effectively utilized using numerical modelling. In the current study the field measurement of the pore water pressure response measured by Weech (2002) is employed as a reference point for analysing the results of numerical modelling. 2 Quote from Karl Terzaghi biography by Goodman (1999). 17 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. < - Si 53 Ave - 53 Ave 53 Ava 5 J A A v s i 200ft 3 3 56 Ave 0 Halifax PI -.7 h„-a 56 A Ave ' ^Panorama Ridge N t Surrey, BC 2 SSXlvs ' Serpentine Fen Nature Reserve 44 Ava : I O 2 0 0 3 Mapquest.com, Inc.; 0 2 0 0 3 Navigation Technobqias Fig. 2.1. Helical pile performance research site location. Ground Surface at approx. -1.3 m ekv. FILL PEAT CLAYEY SILT with Sandy Silt Seams Organic SILTY CLAY Marine CLAYEY SILT to SILTY CLAY -ss-0.0 m i 0.5 g-0.8 2.0 2.9 3.37 Fig. 2.2. Site subsurface conditions at the research site (modified after Weech, 2002). 8.62 18 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. SO _! L i _ J u u i l . •o C CM scale - metres S O U T H E M B A N K M E N T Si SHOULDER' TOE OF SLOPE Old King George Highway Fig. 2.3. Approximate locations of subsurface investigations at the Colebrook site (modified after Crawford & Campanella, 1991). 3M bridge pier from South abutment O § 0} o © o 1-j % ol o <j> o AH/CPT-2 -fy VH-2 PP1 © 2*° bridge piet from South abutment AH-3 b ® AH-3c ^CPT-5 ® ^.CPT<. pile cap 300 mm wide hexagonal RC piles gemerlineof J L Hwy 99A above j LeaiM _^.AH AH-1 CPT-7 SdW-Stem Auger Hole Cone Penetration Test PP2 » CPT-1 ® O ^ O VH-1 Hetica* Test Pile - ^ V H Vane Soring Fig. 2.4. Location of CPT tests and solid-stem auger holes (after Weech, 2002) 19 5 m a) Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils c) Field Vane Shear Strength (su)FV (kPa) 10 20 30 b) Sensitivity St = (Su)peak^(Su)rem 40 0 10 20 30 40 50 0.0 -3 E - 7 # -c o A | -8 LU -10 , — i o i — 0 « L_J l _©i 1 ,---\ • K_i @ \ -• a ruSoiuiy ffected by sandy silt -i -<> - XJ : <3> • + *• - o * > _ y — o < > - U -9 © o • « • • / • • \ • •to O © • VH-1&2 .©... Crawford & Campanella (1991) Strength Ratio S u /rj vo 0.2 0.4 0.6 0.8 • • • • • • • Peak Strength (VH-1&2) - -o - - Remoulded Strength (VH-1&2) © Peak (from Craw ford & Campanella, 1991) o Rem (from Crawford & Campanella, 1991) Fig. 2.5. Variation of field vane shear strength test results with elevation (after Weech, 2002). 20 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. a) Tip Resistance b) Sleeve Friction c) Excess Pore Pressure QT(bar) fs(kPa) atU2-Au(kPa) 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 -50 0 50 100 150 200 250 Fig. 2.6. Example of cone penetration test results (CPT-7) (after Weech, 2002). 21 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Lead Section Type 1 Type 2 (Lower Ext.) 0:78 m Grout0isc; • "• ' S9 mrnOlP.'. 74 mm:L0. 0 - 0.356: m .:S©><3-8.5 m tip depth ('9,8 m elevation) •Helix-Piste; S t u n ih'tck. \Piezo-P6rt ^LoweT'JExt:)-0.76m fc 2 12 m 8.5'tn:tip depth Gtmrt D'm •(0;l5m;diiarrie r^) -CylEii^ tlegl^ ShaW:: 89 m'mOiQ:. ?4!mm ID: Belix Plate: 76 mm flitch .9 mm tHick, iPiezo-Port Fig. 2.7. Helical piles geometry (modified after Weech, 2002). 22 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. 3rd bridge pier from South abutment pile cap PP1 2nd bridge pier from South abutment i G week 6 week TP2 ® ® TP1 (Type 1) (Type 2) 19 hours 7 days TPS # . • ;TP4 : (Type 2) (Type 1) 19 hours 7 days IPS # (Type 1) (Type 2) w Q 300 mm wide hexagonal RC piles O -4- o Hwy 89A. 3 m PP2 8 rn "o f Q 19 m 5 m Helical piles  JW>e % 5 helices Type 2: 3 helices 19 hours - recovery period Fig. 2.8. Helical piles locations (modified after Weech, 2002). 23 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Excess Pore Pressure during Pile Installation - Au/o'v > m o N Oi K o a> CD Q. a . a -0.2 _ 3 E .= 1 0 -1 -2 0.0 — i — 0.2 —i— 0.4 — i — Note: Dissipation during breaks in installation removed. Line of Max + Pore Pressure Grout Column 1.6 1.8 2.0 1 Grout Disc Helix Plates •PZ-TP4-1 (r/R = 4.8) - r— PZ-TP2-5 (r/R = 7.3) - o - PZ-TP2-1 (r/R = 8.0) na— PZ-TP2-7 (r/R = 11) r = radial distance from pile center X PZ-TP2-3 (r/R - 17) R = radius of pile shaft PZ-TP2-4 (r/R = 30) Fig. 2.9. Variation of excess pore pressure with pile tip depth, S/D=1.5. (after Weech, 2002) 24 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Excess Pore Pressure during Pile Installation - AuJa'vo .2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 > H I CO. O N CD E 5 o CD m Q. o JO Q. CO Q Fig. 2.10. Variation of excess pore pressure with pile tip depth, S/D=3. (after Weech, 2002). 25 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. 3 < i C o to (A C O) c 3 •a a> k. 3 10 (A a> k_ OL a> i-o a. (A (A CD O X UJ 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -A Pile Piezos (due to pile tip penetration) • Pile Piezo-Ports (End of Installation) u Linear Tn 2nd Lin \ e \ \ \ -\ \ i \ V 1 n n a r i t h m i r T r A n r l 1 i n o | U I 111 II 1 1 1 w - TP' \ -14 \ « TP 3-1 -IPI-UP1-C i j r r II 34 A »EM 2 TF'f i-2 - } 1 '6-- T =2-; A J ^ " P3-2 3!-1 -_ — ^ P2 l\ -i \ inearT rend Lin< slices I -eof Hi il V Jk - Edg .^ Jb"P1-7 \ -\ \ . PI-3 A i r i-9 -r i v TP2-3»A TP 1-4 -A — -1— \ . \ \ i » TF :2-4 10 Radial Distance from Pile Center (shaft radii) - r/Rshaft 100 Fig. 2.11. Radial distribution of excess pore pressure generated by penetration of pile shaft (modified after Weech, 2002). 26 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 o _> IS 0.9 3 < 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 A Peak u at Piezos after Passing of Pile Tip ms< M o v I I rx\ D i o 7 r » _ D n r + c / P n H r\i l n c t a l l a t i . n n i ™ L Shaft Penetration (best fit of data from Fig. 2.11) Shaft Penetration (best estimate for r < 5R) • - A A u h x & V > (best ej timate) [ \ A \ \ —^_ \ J A \ ) L \ ices \ \ j i of Hel | ^ \ \ Edge \ \ kr \A _ \ V \ \ ) \ i i\ \ . . . . \ . N s V \ V A L \ \ N 1 s N .^ 4 > * < A r. 10 Radial Distance from Pile Center (shaft radii) - r/RShaft 100 Fig. 2.12. Radial distribution of maximum excess pore pressure after penetration of helices (after Weech, 2002). 27 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Radial Distance from Pile Center (shaft radii) - r/Rshaf t Fig. 2.13. Radial distribution of excess pore pressure around helical piles (above level of bottom helix) during dissipation process (after Weech, 2002). Radial Distance from Pile Center (shaft radii) - r/Rshaft Fig. 2.14. Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process (after Weech, 2002). 28 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. o 3 3 < 10 100 1000 Time after Stopping Installation (min) 10000 Fig. 2.15. Average dissipation trends for different radial distances from pile (after Weech, 2002) •»•• 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) - -A - 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) 10 100 1000 Time (min) from End of Installation 1 0 0 0 0 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. L I T E R A T U R E R E V I E W . 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. P O R E PRESSURE RESPONSE INDUCED BY P I L E I N S T A L L A T I O N INTO F I N E G R A I N E D SOIL A N D ITS I N F L U E N C E ON P I L E C A P A C I T Y . 3.2.1. F I E L D G E N E R A T I O N O F E X C E S S P O R E 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 Chapter 3. Literature review. 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 (Au/ o'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. Au = Aumean + Aushear (3-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, Aamea„, is equal to the magnitude of A<7m e a„ 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 AuShear pore pressures are generated. Moderately to heavily overconsolidated clays demonstrate dilatant behaviour when sheared, hence negative Aushear 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. F I E L D DISSIPATION O F E X C E S S P O R E 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 Chapter 3. Literature review. 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 Chapter 3. Literature review. 3.2.3. O B S E R V E D A X I A L PILE CAPACITY AS FUNCTION OF DISSIPATION O F 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 Chapter 3. Literature review. 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 O F T I M E - D E P E N D E N T P O R E PRESSURE RESPONSE. 3.3.1. PREDICTION M E T H O D S . 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 Chapter 3. Literature review. 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 Chapter 3. Literature review. 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 Au/Aui=R/r 1-D Consolidation around driven piles; Finite Differences Torstensson (1977) Cylindrical Spherical Elasto-plastic Aui=2suln(rp/r) Au i = 4s u ln(r„/r) 1-D No shear stresses; Finite Difference. Randolph & Wroth (1979) Cylindrical Elasto-plastic Aui=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 Au i =2suln(rp/r) 1-D Shear by empirical method; Finite Difference Sennesetetai. (1982) Cylindrical Elasto-plastic Aui=2Suln(rp/r) 1-D Tumay etai. (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 O C dissipation Burns & Mayne (1995) Spherical Elasto-plastic Au o c t =4s uln(r p/r) Au s h e a r =o' v o Tl-(OCR/2)0 81 1-D Incorporates shear stresses; models O C dissipation; Finite Difference Collins & Y u ( 1996) Cylindrical Non-linear Closed form solutions. -No consolidation analysis Burns & Mayne (1998) Spherical Elasto-plastic Au o c t =4s uln(r p/r) Au, h r a r =a' v Jl - (OCR/2) 0 8 l 1-D Incorporates shear stresses; models O C dissipation; Analytical Caoet al. (2001) Cylindrical Non-linear Closed form solution. -No consolidation analysis Whittle etai. (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-! 36 Chapter 3. Literature review. 3.3.2. BASIC C O N C E P T S BEHIND EXISTING PREDICTION SOLUTIONS. 3.3.2.1. M O D E L L I N G A N A L O G U E FOR SIMULATION O F P I L E O R C O N E P E N E T R A T I O N . 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 Chapter 3. Literature review. 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. M O D E L L I N G F R A M E W O R K . 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-Tl), or the effective stress soil models (such as Cam Clay, Modified Cam Clay, MIT-E2, MIT-ES). 38 Chapter 3. Literature review. 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. O V E R V I E W O F 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. C A V I T Y 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 Chapter 3. Literature review. • 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 Aushear 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 Aushear = 0 at any point around the cavity and therefore Au = Aumean, 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 a 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 Aushear 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 Aumean and Ausnear can be accounted for. 40 Chapter 3. Literature review. 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 Chapter 3. Literature review. 3.3.3.2. SOLUTIONS B A S E D ON STRAIN P A T H M E T H O D . 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. S U M M A R Y . 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 Chapter 3. Literature review. 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 Chapter 3. Literature review. PILE i i i i Natural Soil Fig. 3.1. Effect of pile installation on soil conditions. 2.6 2.4 ac «•> V) U l cc a. u rr O a. LU O X LLl N < s cr o 2! + {6,?).t 1 1 i i i i | i i I I I ! P o + -• i -A -^ 0 s --A I t -- + • -i i : (-0.13)1 1 1 i IT 5 10 30 NORMALIZED RADIUS, r / R 50 • o o Is 7.5 10 7.6 10.7 11.5 14 OCR 2.5? 2.3 2.3 O H 24 to 30 12.2 1.2 5.8 6 to 9 7? fTSMli (I) 2 to 2.5 i l ! 2 to 2.5 3 to 3.5«>| 1.3 2.0 (l! 5.5 (0 3.510 4.5<0 ,(3) 37 2.5. to 4.5 PI 25 20 60 20 20 40 10 s 1 " 1 to 8 4 to S very hiqh 16 37 cloy 7silt |) Field Van« (2! Dutch Cone (3! Unconfined 100 Fig. 3.2. Measured excess pore pressures due to installation of piles (after Baligh & Levadoux, 1980). 44 Chapter 3. Literature review. a). 600 400 8> 3 (A (0 0) k. CL _ 200 o CL 0 Bothkennar, Scotland -10 cm 2 Fugro Cone Depth = 12 m (Jacobs and Coutts, 1992) l I r I I I I 11 I • l l l l l 11 i i i i i i i i 1 > • I 10 b). 100 Time (sec) 1000 2500 ro CL £ 1500 + 3 (A </> O 0> o CL 500 + 10 100 Time (sec) 1000 V 10000 Baton Rouge, LA 1 15 cm 2 Fugro Cone Depth = 37.4 m (Chen and Mayne, 1994) -" 2 . . - • ' • " ' * ' " x 1 1 1 1 1 1 1 II 1 1 1 1 1 1 1 U J 1_ • 1 L 1 1 1 1 1 11 V 10000 Fig. 3.3. Typical pore pressure dissipation measured during CPTU tests (modified after Burns & Mayne, 1998). a), lightly overconsolidated Clay; b). heavily overconsolidated Clay. 45 Chapter 3. Literature review. 8000 in sr CL 6000 E o CO Q. ca u c» E CD CD . Q QJ CO E 4000 2000 *"••• • f 1 1 1 1 • 1 0 100 200 300- 400:. . 500 600 Hours after driving Fig. 3.4. Increase in pile bearing capacity with time (after Seed & Reese, 1957). 700 800 1.25'r-Depth •305 m •4 60 m ,610 m Shaft bearing capacity Excess pore pressure 005 01 1 10 100 1000 time after driving: days Fig. 3.5. Increase in pile bearing capacity and pore pressure dissipation (modified after Konrad &Roy, 1987). 46 Chapter 3. Literature review. O u 0 8 • 20 °fo of ittaximum bearing capacity 4 Q 60 80 l O O ' x :. S««d & Raese 11955) o"- •. E id re i at {19615 . r theoretical decoy of esesiss pore pressure ot pile feet l G / c t f * f 0 O } •'.In (t/t^o) . Fig. 3.6. Comparison of variation of pile bearing capacity with time and theoretical decay of excess pore pressure (after Randolph & Wroth, 1979). 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 f ; 1 : — 1—— 1 ~ 1 ~~" Time (log) Fig. 3.7. Idealized schematics of soil set up phases (modified after Komurka et al., 2003). 47 Chapter 3. Literature review. c 1 o I N X o M l<-| i t I I —1> I 1MM 9) C o N y 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). l.O c *» E «* u o "5. in 6» > 0.8 0.6 a 04 0.2 Theoretical Plane strain at Constant Volume Measured Randolph. Steenfelt and Wroth (1976) Cooke and Price (1973) I 2 3 4 Radial Position before Pile Driving Pile Radius 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. F O R M U L A T I O N O F M O D E L L I N G A P P R O A C H . 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. M O D E L L I N G A P P R O A C H T O SIMULATION O F H E L I C A L P I L E I N S T A L L A T I O N INTO FINE-G R A I N E D SOIL. 4.2.1. M O D E L L I N G F R A M E W O R K . There is a consensus of opinions in the reviewed literature: accurate prediction of pore pressure response due to pile installation requires coupled analysis where a realistic soil model is employed. The volume changes in the silty-clay during and following pile installation influence the magnitude and distribution of time-dependent pore pressure and effective stress. Therefore, it is important that the chosen soil model generate realistic volume changes during shearing. A generalized critical state based soil model, NorSand (Jefferies, 1993; Jefferies & Shuttle, 2002), was adopted here to represent fine-grained soil stress-strain behaviour. In order to predict the changes in stresses and pore pressure under partially drained conditions, an analysis that accounts for the coupling between the rate of loading and the generation of fluid pressures is required. The Biot consolidation theory (Biot, 1941) was used to incorporate the effect of the coupling the pore pressure behaviour to the soil response. 49 Chapter 4. Formulation of modelling approach. 4.2.2. M O D E L L I N G P R O C E D U R E FOR SIMULATION O F H E L I C A L P I L E I N S T A L L A T I O N . The following major aspects of pore water pressure response due to helical pile installation are of interest in this study: • excess pore pressure induced by helical pile installation; • dissipation process of the induced excess pore pressure. In the coupled numerical analysis dissipation of the excess pore water pressure is typically automatically handled within the formulation. At the same time generation of the realistic excess pore water pressure requires a special modelling procedure for simulation of the helical pile installation. Conventional procedures for helical pile installation are outlined in Section 1.2. Helical piles consist of the pile shaft and the helices attached to the leading section of the pile. The mechanism of pore pressure generation induced by the helical pile shaft penetration is similar to the one for conventional piles, discussed in Section 3.2. The mechanism of pore pressure generation induced by the helical pile shaft penetration is much more complex. The helices cut through the soil by a spiral trajectory generating a significant pulling force that advances the helical pile shaft. As the helical plates move downward by one flight they displace and release the volume of the soil equal to the volume of the plate. It should be noted that the volume of the soil displaced by the helical plate is quite small in comparison to the volume displaced by the pile shaft. Generally the pore pressures induced by the helices will be a complex combination of the pore pressures generated by soil displacement, soil shearing and the impact of the pulling force. Due to such complexities a detailed simulation of helical pile penetration would require a 3-D modelling approach, where the interaction between the rigid helical pile and deformable soil, and the effect of the pulling force can be comprehensively addressed. This is theoretically possible by employing a 3-D large strain Lagrangian finite difference analysis (e.g. FLAC 3-D). This method may realistically represent the process of pile installation accounting for changes in soil properties with depth and influence of the free soil surface. However, there are numerous numerical difficulties involved in this process, including problems of formulation of the non-linear contact interfaces between the pile tip and the soil (Klar & Einav, 2003). Additionally, the problem of formulating the interface between soil and advancing helical plates, would make the modelling process especially challenging. 50 Chapter 4. Formulation of modelling approach. In this study we are primarily interested in the magnitude and trends of the generated excess pore water pressure, rather than reproducing the exact mechanism of pore pressure generation. This allows us to simplify the modelling of helical pile installation and ignore the 3-D effect. Similarly to conventional piles, simulation of the helical pile shaft installation can be modelled using the cylindrical cavity expansion analogy, described in Section 3.3.2.1. Penetration of the individual helical plates can be modelled as an expansion of a cylindrical cavity over one flight, where the expanded cavity volume is equivalent to the volume of the displaced soil, as shown in Fig. 4.1. If such an approach is employed, considering the circular cross-section of the helical pile shaft, cylindrical modelling of helical pile installation can be simplified to a 2-D axisymmetric problem. For 2-D analysis the mesh could be set up so that the size of the elements in a vertical direction is equal to one flight of the helical plate. In this case helical pile installation can be modelled as shown in Fig. 4.2. This figure presents the helical pile shaft, modelled as expansion of a cylindrical cavity, advancing each step downwards by the distance equal to one flight, at the same time at the locations of the helices local cylindrical cavities are expanded. Each consequent step as pile and helical plates move downwards by one flight, previously expanded cavities, that correspond to the helices, are contracted up to pile shaft surface and the next set of local cavities, corresponding to a new location of the helical plates and the shaft is expanded. This procedure is executed until pile tip reaches its final position. A 2-D simulation procedure can be further simplified if it is assumed that only radial deformations and water flow have any significance. As discussed in Section 3.3.2.1 the assumption of predominantly radial deformation is reasonable for modelling of conventional piles penetration, hence the same assumption is valid for simulation of helical pile shaft. At the same time penetration of helical plates may cause some vertical soil movement due to the pulling force. The effect of the pulling force on the pore pressure magnitude is largely unknown and could only be addressed within a full 3-D analysis. In 1 -D axisymmetric analysis the helical pile installation can be simulated with one row of finite elements. Assuming that the left boundary of this row is adjacent to the central axis of helical pile shaft and that the row is located within the pile penetration path (so that the pile tip and all pile helices are passing through this location) helical pile installation can be modelled according to the scheme shown in Fig. 4.3. In this figure the modelling location remains constant through 51 Chapter 4. Formulation of modelling approach. out the simulation. Helical pile installation is simulated as helical pile shaft and helices passing through the modelling location. First, penetration of a helical pile shaft is modelled. After a pause equal to the time required for the first helix to reach the modelling location, a cavity corresponding to the first helix is expanded and contracted. Following a pause necessary for the second helix to reach the modelling location, a cavity corresponding to the second helix is expanded and contracted. This cycle is repeated for each subsequent helix. Knowing the geometry of the pile and the rate of pile penetration, the time spans for each modelling stage, shown in Fig. 4.3, can be readily computed. Overall, it appears that the main features of the pore pressure response induced by the helical pile installation may be captured with the 1-D axisymmetric analysis, which offers a simple modelling set up and fast computation times. Adding additional levels of complexity will likely refine the modelling predictions, although significantly increasing the time necessary for the computation and modelling set up. Considering these facts and following the logical progression rule "from simple to complex", a 1-D modelling approach was adopted for the current study. 4.3. N O R S A N D B I O T F O R M U L A T I O N . 4.3.1. N O R S A N D C R I T I C A L S T A T E SOIL M O D E L . 4.3.1.1. M O D E L 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 Chapter 4. Formulation of modelling approach. inability to reproduce the softening and dilatancy observed in sands. This lead to the development of CSSM models based on the state parameter y 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 y/ is a measure of the current soil state, defined as the difference between the void ratio at the current state and the void ratio at critical state at the same mean stress. Overconsolidation ratio, R, within NorSand 53 Chapter 4. Formulation of modelling approach. represents the proximity of a stress state to its yield surface, when measured along the mean effective stress axis. Conceptually this is demonstrated in Fig. 4.5. NorSand has an internal cap, required for self-consistency of the model, so that the soil cannot unload to very low mean stress without yielding. The internal cap is taken as a flat plane, and its location depends on the soil's current state parameter. Fig. 4.6 shows the NorSand yield surface for a very loose sand. The location of the internal cap is dependent on the limiting effective stress ratio rjL 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 i// becomes more negative. This indicates that the one cannot directly compare NorSand with standard views of the effect of overconsolidation without varying y/. 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 y/. This idea can be demonstrated by simulation soil unloading and computing variation of R and ^/with changing mean effective stress. To simulate this is to compute two things: first, to compute the void ratio change for a reduced mean stress via the swelling line from which the new state parameter can be determined; second, allow the overconsolidation ratio to increase to its limiting value (R ~ 3) and then hold it at that. The example of soil unloading from p -500 kPa shown in Fig. 4.7. Considering the infinity of NCL, in accordance with the second critical state mechanic's axiom, the problem of coupling the yield surface size to void ratio is solved within NorSand by introducing an incremental hardening rule - by defining an image of the critical state on the yield surface and requiring that the image state become critical with shear strain. The idea of an image state is based on the fact that, in general, yield surfaces do not intersect the critical state. The critical state is achieved when dilatancy and rate of change of dilatancy is zero. Soil is at the image state when former condition is satisfied and latter is not satisfied. The concepts of image and critical stress are demonstrated in Fig. 4.6. There is no closed form solution available for the NorSand model. The stress-strain relationship is established by integrating stresses and strains increments. Mathematical representation of the NorSand model is summarized in Table 4.1. 54 Chapter 4. Formulation of modelling approach. Table 4.1. NorSand model formulation (all stresses are effective). Internal Model Parameters =t// + A\n(pj/p ), where y/ = e-ec Critical State ec =r-/Un(/?) nc=M=(MMC+MMN)/2 where MMC = (3 V3 )/(cos 6>(l + 6 / M,c) - V3 sin o) and 27-3A/' _ 27-3M 2 S - M ^ + ^ M ^ s i n ^ - s i n 2 ^ ) ) 3 - M ( c 2 + % M , c 3 Flow Rule Dp =Ml-rj Yield Surface & Internal Cap 7 7 = l - ln M, P f with —- = e x p ( - ^ 6 ^ , / M „ c ) 'max Hardening Rule ( — n mod P, \ ( > P exp Elasticity G, v - constant (input parameters) 4.3.1.2. M O D E L P A R A M E T E R S . 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 V Poisson ratio OCR (R)' overconsolidation ratio K0 coefficient of lateral earth pressure at rest Cfv0 vertical effective stress NorSand critical state coefficient state dilatancy parameter w state parameter X slope of CSL in e-ln(p) space r intercept of the CSL at 1 KPa stress Hmod hardening coefficient 1 - overconsolidation ratio is often referred to as OCR = (7vmax/av which is not the same as R = pmax/p. The relation between them depends on K0, which tends to increase with OCR, however assuming that K0 is constant, both definition produce numerically identical results. 55 Chapter 4. Formulation of modelling approach. The "general" set of parameters in Table 4.2 includes parameters common for geotechnical analysis that require no additional introduction. Only parameters that are related to the variant of NorSand soil model employed in the current analysis, are explained here: • Critical state coefficient, Mcrit, describes the ratio between stresses at critical state and is a function of Lode angle. For triaxial compression conditions, critical state coefficient is directly related to friction angle at constant volume q> Mcritftc) = 6sin <p 'J(3-sin (/>„) (4.3) where tp^ is usually determined from triaxial tests on loose samples. • Parameters describing critical state line: X - slope of CSL in e-ln(p) space; r - 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, (//, 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, Hm0(j, 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 Hmoej. 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, %, is also unique to NorSand, and is a function of soil structure and fabric. Parameter % is a proportionality coefficient between soil state and minimum dilatancy: Dmin = X¥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. B E Y O N D SAND. It is a misconception to associate the NorSand model explicitly with sands. Even though its name suggests sand, NorSand model has no intrinsic limitations for application to fine-grained soils. 56 Chapter 4. Formulation of modelling approach. Studying the effect of pore water pressure dissipation on pressuremeter test results, Shuttle (2003) modelled a pressuremeter test in soft Bothkennar clay, employing the NorSand model coupled with the Biot consolidation formulation. Input parameters for numerical simulation were obtained by calibrating the model to the Bothkennar triaxial test data, as shown in Fig. 4.8. Results of that study show that the NorSand model can be applied to fine-grained soils, showing good agreement with the experimental data. In the current study, validity of application of NorSand model to fine-grained soils was analysed by modelling a series of drained constant p triaxial tests on Bonnie silt, carried out for the VELACS1 project. An example of a NorSand model fit to the Bonnie silt data is shown in Fig. 4.9. More NorSand fits along with the input parameters used in the analysis are provided in Appendix C. All conducted simulations showed a very good agreement with the laboratory triaxial data. It appears that NorSand model can represent fine-grained soil triaxial behaviour very well, which is in agreement with the conclusions of Shuttle (2003). 4.3.2. B I O T C O U P L E D CONSOLIDATION T H E O R Y . 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: K' dr r dr 0? (4.7) dt dt where: K' - bulk modulus of the soil [kN/m2]; Yw - unit weight of water [kN/m ]; 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: ' VELACS - Verification of Liquefaction Analysis with Centrifuge Studies 57 Chapter 4. Formulation of modelling approach. - u0 - initial pore pressure (the code is actually using the change in pore pressure); kr - hydraulic conductivity in radial direction. 4.3.3. FINITE E L E M E N T I M P L E M E N T A T I O N O F N O R S A N D B I O T F O R M U L A T I O N . 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 E L E M E N T C O D E V E R I F I C A T I O N . There are no analytical solutions available for cavity expansion within the NorSand soil model. Therefore prediction of stresses and pore pressure by NorSandBiot code cannot be verified directly. However correctness of particular aspects of the finite element code implementation and predictions can be checked, as described below. 58 Chapter 4. Formulation of modelling approach. Finite element implementation of the NorSand soil model was verified against direct integration of the NorSand equations (see Section E . l , 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. S U M M A R Y . A realistic simulation of fine-grained soil requires partially drained analysis with both a fully coupled modelling approach and a realistic soil model. NorSand critical state soil model was chosen to represent the soil medium, the coupling between changes in stress-strain conditions and the pore water pressure response is provided by Biot equations. A special modelling procedure was developed to simulate helical pile installation using a cylindrical cavity expansion analogue. The conducted verification of the finite element code showed excellent agreement with existing analytical solutions. 59 Chapter 4. Formulation of modelling approach. one flight (9.5 cm) Fig. 4.1. Schematic representation of 2-D modelling approach. a) , helix is represented as helical plate, with the volume equivalent to the volume of the helix. b) . helical plate penetration is modelled as cylindrical cavity expansion, where expanded volume is equivalent to the volume of the helical plate. For axisymmetric conditions - it is one half of the volume (Volume A on the figure). 60 Chapter 4. Formulation of modelling approach. Time initial state 1st penetration step 2 n d step 3 n d step a a 3 a = one flight Q pile shaft | |hel nx m V mesh width • • pile shaft expansion pause first helix expansion first helix contraction pause second helix expansion second helix contraction pause third helix expansion third helix contraction pause forth helix expansion forth helix contraction pause fifth helix expansion fifth helix contraction Fig. 4.2. Conceptual representation of modelling of helical pile F i8- 4 - 3 - Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 2-D. installation as an expansion of cylindrical cavity in 1 -D. 61 Chapter 4. Formulation of modelling approach. i _ , — — —i • 10 100 1000 MEAN STRESS, p: tPa Fig. 4.4. Normal compression lines from isotropic compression Fig. 4.5. Definition of NorSand parameters r, A, y% and tests on Erksak sand (after Been & Jefferies, 1986). (modified after Jefferies, 1993). 62 Chapter 4. Formulation of modelling approach. mean effective stress ratio, p' / p'j Fig. 4.6. Definitions of internal cap, ph pc, Mtc, M, and nL on yield surface for a very loose sand (modified after Jefferies & Shuttle, 2005). mean effective stress: kPa Fig. 4.7. Conventional and NorSand representation of overconsolidation ratio for soil initially at p'= 500 kPa subject to decreasing mean stress. 63 Chapter 4. Formulation of modelling approach. Fig. 4.8. NorSand fit to Bothkennar Soft clay in CKOU triaxial shear (after Shuttle, 2003). 64 Chapter 4. Formulation of modelling approach. 150 125 kPa 100 -tress, 75 -in ator 50 -devi 25 4 Nor! 5an< iBonnie Si tCD BS-25 10 axial strain: % 15 20 fi 1 H NorSand Bonnie Silt GD BS-25 10 axial strain: % 15 20 120 100 80 60 40 20 0 NorSand \ • » i t Bonnie Silt CD BS-25 +\ 20 40 60 p, kPa 80 100 Fig. 4.9. NorSand simulation fit to constant p=80kPa drained triaxial test on Bonnie silt. 65 Chapter 4. Formulation of modelling approach. * Read in material properties * Initialize original state * Define geometry & number of time steps * Define elastic stress-strain matrix, D * Set initial element stresses Loop number of steps * lterations=0 ' * Null loads, excess loads (bodyloads), incremental strain Ae, incremental plastic strain As p, 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 {8}=[K]~' {f} * Check whether yield criterion is reached Loop Elements * ds = B da total strain increment * dee = ds - dep elastic strain increment * Ao = D Ae e elastic stress increment * a = a s ,ep . i + Aa "new" stress * Update new yield surface Does element stress state exceed yield? No * continue to next element Yes * calculate dsvp, increment viscoplastic strain rate * dsvp = d S v P . d t increment of viscoplastic strain this iteration * £vp — Evp iter-1 ~^ d E y p track viscoplastic strain this increment * J B T D S v p calculate bodyloads increment * bodyloads = bodyloadsiter-i + 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. S E L E C T I O N O F S I T E S P E C I F I C S O I L P A R A M E T E R S F O R M O D E L L I N G . 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 P A R A M E T E R S FOR M O D E L L I N G . 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. E L A S T I C PROPERTIES G, V. Elastic properties of the soil in the NorSandBiot formulation are represented by the shear modulus G and Poisson's ratio v. 67 Chapter 5. Selection of site specific soil parameters for modelling. 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(y)/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(y)/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 Chapter 5. Selection of site specific soil parameters for modelling. 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 /so « 0.15%. According to Fig. 5.1 this level of strain corresponds to the range of G(/)/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 EJsu (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 = EJJ). 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 ofGis5.8 ... 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, v, is within a range 0.1 ... 0.3. For the current analysis it was assumed equal to 0.2. 5.2.2. O V E R C O N S O L I D A T I O N R A T I O 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 Chapter 5. Selection of site specific soil parameters for modelling. 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. C O E F F I C I E N T O F L A T E R A L E A R T H PRESSURE K0. The coefficient of lateral earth pressure, Ko, can be estimated based on empirical correlations developed for the interpretation of CPT test data, or by linking Ko to other soil properties. Table 5:1 shows the correlations employed in this study. Table 5.1. List of correlations used to estimate Ko from CPT test data. Author Formulation Mayne & Kulhawy (1982) K0 = (l-sinf)-OCRsin*' </>' =35° was assumed Sully & Campanella (1991) Ko = 0.5 + 0.11PPSV where PPSV = (ui-U2)/cr'vo Weech (2002) interpreted profiles of K0 using Sully & Campanella's (1991) correlation and also estimated Ko from the OCR profile shown in Fig. 5.6. The result is presented in Fig. 5.7. According to this figure, the Ko estimated from both of these methods are generally in good agreement, starting from elevation -5.5 m. Overall, Ko for the silty clay layer varies primarily within a range of 0.56 to 0.76. For the modelling purposes, a midrange Ko equal to 0.66 was assumed. 70 Chapter 5. Selection of site specific soil parameters for modelling. 5.2.4. H Y D R A U L I C C O N D U C T I V I T Y D E R I V A T I O N . 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 = cnmvyw* (5.3) In this study they were determined as described in the following sections. 5.2.4.1. C O E F F I C I E N T O F 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 c//cv between 2 and 5. According to Crawford & Campanella (1991), experience with the Fraser River Delta clayey silts suggest that a value of Cf/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, cn, 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 yw- unit weight of water, constant taken as 9.8 kN/m 71 Chapter 5. Selection of site specific soil parameters for modelling. ch = T50-R%o . (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 cn 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 c/, 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 cm /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 cn = 0.003 cm /s was derived from the MoTH data. Crawford & Campanella (1991) reported a very similar average value of cn = 0.004 cm Is. 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 Chapter 5. Selection of site specific soil parameters for modelling. • 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 cn is found, as shown in Fig. 5.9. According to this figure, the majority of the values of coefficient of horizontal consolidation, cn, are within a range from 0.002 to 0.008 cm Is. This range is similar to the range of cn = 0.002 ... 0.007 cm Is (Table A.3, Appendix A), used by Byrne & Srithar (1989) in their numerical analysis. The average value of coefficient of horizontal consolidation, c„, is 0.005 cm Is. 5.2.4.2. C O E F F I C I E N T O F V O L U M E C H A N G E , m v The coefficient of volume change is a function of the constrained modulus: M 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= 4.2510"4 kPa"1. 73 Chapter 5. Selection of site specific soil parameters for modelling. 5.2.4.3. R A D I A L H Y D R A U L I C C O N D U C T I V I T Y , kT 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 Range 0.002 4.25-10"4 8.5-10"10 0.008 4.25-10"4 3.4-10"y Average 0.005 4.25 TO"4 2.M0"y The average kh = 2.\ TO"9m/s was assumed for further analysis 5.2.5. V E R T I C A L E F F E C T I V E STRESS a ' v o A N D EQUILIBRIUM P O R E PRESSURE U0. 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: a \0 (kPa) = -8.0(Elevation) -3.7 (5.7) For the range of elevations from -4.57 to -9.92 metres, a'vo increases from 32.9 to 75.7 kPa. The average o\oover 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, uo increases from 39.5 to 94.1 kPa. The average uo over this elevation range is 66.8 kPa. 5.2.6. N O R S A N D M O D E L P A R A M E T E R S D E R I V A T I O N . There are six NorSand specific parameters that are required for the current analysis: Mcrit, %, Hmod, X, r, and i//. 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 Chapter 5. Selection of site specific soil parameters for modelling. 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. C R I T I C A L S T A T E C O E F F I C I E N T , M C „ , The critical state coefficient Mcrit under triaxial conditions can be calculated by Eq. 4.3 if the constant volume friction angle, (f)'^ is known. According to Crawford & deBoer (1987), for the silty clay layer tj>' 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 (/>', 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, tf>'cv, using the correlation developed by Bolton (1986). Assuming loose alluvial soil values of </>'cv will be approximately 2 degrees lower than for peak friction angles, the constant volume friction angle would vary in between range 31 ... 33 degrees. This leads to values of critical state coefficient Mcril between 1.113 to 1.374. For average <f>'cv= 32 degrees, Mcrit = 1.243. 5.2.6.2. S T A T E D I L A T A N C Y P A R A M E T E R , % State dilatancy parameter, 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 %= 3.0...4.0 is assumed. 5.2.6.3. H A R D E N I N G M O D U L U S , 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. S L O P E O F C R I T I C A L S T A T E L I N E , X The slope of the critical state line, X, 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, X can be: 1). Assessed empirically using the plasticity index, PI. 75 Chapter 5. Selection of site specific soil parameters for modelling. Schofield & Wroth (1968) found the following relationship between PI, specific gravity, G 5 , and slope of the critical state line, X: Assuming Gs equal to 2.75, using Eq. 5.9 the profile of A 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 X are in a range 0.13 ... 0.362. This range is rather wide, but is in a good agreement with the values of X = 0.09.. .0.363 reported by Allman & Atkinson (1992) for Bothkennar silty clay. 2). Estimated very approximately using compression index Cc. Compression index, C c, is typically determined from odometer tests and is defined as: The slope of the critical state line in e-loge(p') space, X, is defined as: where X 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 X. 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 C c to X, but it is possible to use laboratory values of Cc to provide an estimate of the lower bound value of X. 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, Ko, e0 and Mcril, as shown in Table 5.3, the range of 0.073 ... 0.130 for the lower bound values of X was calculated using Eq. 5.11. This range is X = PIGS/160 (5.9) (5.10) 76 Chapter 5. Selection of site specific soil parameters for modelling. generally in a good agreement with the lower bound X estimated from PI - X correlation by Schofield & Wroth (1968), see Fig. 5.12. Table 5.3. Estimation of slope of critical state line, X, based on laboratory derived values of C c reported by Crawford & Campanella (1991). Elevation, m eo kPa Ko X -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 X = 0.073 ... 0.362, estimated from PI and Cc, was taken. As stated above, this range of X is large and encompasses values of X that are at the upper end of those reported in the literature. However, a wide range of X encompassing some high plastic compressibility is in a good agreement with the values of X = 0.09...0.363 reported by Allman & Atkinson (1992) for Bothkennar silty clay. As a best estimate X for the silty clay layer was taken as an average of all values of X shown in Fig. 5.12: X = 0.165, which is close to the best estimate of the slope of the critical state line for the Bothkennar silty clay, X = 0.181, used by Shuttle (2003). 5.2.6.5. I N T E R C E P T O F C R I T I C A L S T A T E L I N E A T 1 K P A STRESS, r. 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 o f c a n be established, as shown in Fig. 5.13. Assuming loose and dense bounds for the in-situ void ratios we can estimate values of 77 so that for the loose bound r= 2.25 and for the dense bound r= 1.55. For the average line in Fig. 5.13, r= 1.86. 5.2.6.6. S T A T E P A R A M E T E R , y/. The state parameter, y/, of the silty clay layer is unknown, and the absence of triaxial test data complicates its assessment. In this study y/ has been estimated based on the stress history of the soil. 77 Chapter 5. Selection of site specific soil parameters for modelling. 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 y/ = 0.2. An encompassing feasible range of state parameter for the site would be yi = -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 X = 0.181 and r= 1.86 the critical void ratio can be determined from the following equation: ecril=Y-X\n(p) (5.12) The current void ratio can be determined as following: e = ej-Kln(p'/p'max) (5.13) where K~ MAX A wide range of conditions is possible at the start of unloading. Normally consolidated clays/silts correspond to the initial condition of about y/ ~ 0.75/1 (Jefferies & Been, 2005), giving an initial state parameter y/ = 0.124. The initial void ratio can be estimated as following: et=r-Mn(p') + i// (5.14) Knowing that OCR = 2.2 and the mean effective stress 42 kPa (based on a \0= 54.5 kPa and Ko = 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 Chapter 5. Selection of site specific soil parameters for modelling. 5.2.7. N O R S A N D P A R A M E T E R S A N A L Y S I S . 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 1.113 ... 1.374 1.243 y. 3.0 ... 4.0 3.5 w -0.05 ... 0.2 0.026 l 0.073 ... 0.362 0.165 r 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 S,. 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 1 Simulation with best estimate NorSand parameters su, kPa 15...29 22.6 s, 1 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 Chapter 5. Selection of site specific soil parameters for modelling. 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 V 0.1 ... 0.3 0.2 -kr 3.4-10"y... 8.5-10"10 2.1-10"y m/s OCR 1.2 ... 2.8 2.2 -Ko 0.56 ... 0.76 0.66 -cr\o 32.9 ... 75.7 54.28 kPa u0 39.5 ... 94.1 66.8 kPa NorSand specific Mcril 1.113 ... 1.374 1.243 -X 3.0 ... 4.0 3.5 -V -0.05 ... 0.2 0.026 -X 0.073 ... 0.362 0.165 base loge r 1.55 ... 2.25 1.86 at 1 kPa Hmod 50 ... 450 100 1 - within elevations -4.57 ... -9.92 m 80 Chapter 5. Selection of site specific soil parameters for modelling. 10- 10 10 2 10 1 Shear Strain -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). Small strain Medium strain Large strain Level of strain 10s 10"* 10* 10"3 Itf1 I I 1 1 1 In-situ tests • Down hole • Cross hole .SASW • Pressuremet. • Plate loading • Dilatometer »SPT • CPT « Vane Lab. tests « Resonant column « Wave propagation • Bender element . LDT • Tests on undisturbed samples Fig. 5.2. Level of shear strain for various geotechnical measurements (after Ishihara, 1996). 81 Chapter 5. Selection of site specific soil parameters for modelling. -3 T E -7 c o > o -8 LU -10 -11 -12 . • r*~ « C T 8 s MARIr SILT T E CLAY: J SILTY : L A Y j . 1 ~~n Y— 1 \ i \ 1 i L - — t \ ! 1 \ ! -V — B m „ \ - 1 e \ Fl 1'max -2-- 6(Elevath m) + 1.9 1 . l-g s i t \* r\| • ! I 0 5 10 15 20 25 30 35 Small Strain Shear Modulus - Gmax (MPa) 40 • SCPT-5 (Weech, 2002) SCPT-7 (Weech, 2002) -SCPT-6 (Weech, 2002) - Linear (A\erage Gmax) Fig. 5.3. Variation of small strain shear modulus Gmax with elevation (modified after Weech, 2002). 82 Chapter 5. Selection of site specific soil parameters for modelling. -4 - 5 H MARINE CLAYEY SILT TO SILTY CLAY I "7 c o '& CO > - ft UJ - O -9 -10 -11 •12 0 — - G(CPT-5)/Su(CPT-2) — -G(CPT-6)/Su(CPT-1) •G/Su (CPT-7) r ? I L LJ • I -i 1 r~ 100 200 300 400 Rigidity Index - lr = G/su 500 600 Fig. 5.4. Inferred variation of rigidity index with depth (after Weech, 2002). 83 Chapter 5. Selection of site specific soil parameters for modelling. -3 -12 A 1 1 1 1 0 5 10 15 20 Shear Modulus - G (MPa) — - - SCPT-5 (Weech, 2002) - - - -SCPT-6 (Weech, 2002) — _ SCPT-7 (Weech, 2002) Linear (Average G) Fig. 5.5. Variation of shear modulus G with elevation. 84 Chapter 5. Selection of site specific soil parameters for modelling. Fig. 5.6. Range of overconsolidation ratio OCR with elevation (modified after Weech, 2002). 85 Chapter 5. Selection of site specific soil parameters for modelling. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Coefficient of Lateral Earth Pressure Ko Fig. 5.7. Variation of coefficient of earth pressure Ko with elevation (modified after Weech, 2002). 86 Chapter 5. Selection of site specific soil parameters for modelling. c o -2 -3 -4 -5 -6 -7 -8 to > UJ -9 •10 -11 -12 -13 -14 root jT=r'root [Time!" log | = '| log Time", T&H - Teh & Hdulsby (1991) L&B! = LevMo|uki&| Baligh MARINE C L A Y E Y qrEL SIL TTTT1 AM correction of Colebrook dissip. curves correctioniof!Colebrook dissipation cuijv.es, fordist'n IromSPlVf solut (1986) s ion lution for dist'n 4> H t t •o 1 o WfrS o fromSPM! A L U 0.0001 0.001 0.01 0.1 Coefficient of Horizontal Consolidation - ch (cm2/s) • C P T U - U2 (log T - T&H) - (Weech, 2002) O C P T U - U2 (root T - T&H) - (Weech, 2002) o C P T U - U3 (log T - T&H) - (Weech, 2002) A C P T U - U3 (root T - T&H) - (Weech, 2002) A C P T U U2 (root T - L&B) - (Crawford & Campanella, 1991) • Lab Data - (MoTH, 1969) • Lab Data -(Crawford & Campanella, 1991) Fig. 5.8. Variation in estimated coefficient of horizontal consolidation with depth (modified after Weech, 2002). 87 Chapter 5. Selection of site specific soil parameters for modelling. > o UJ -2 -3 -A -6 E " 7 2 -8 -9 •10 -11 -12 -13 imer root |T = "root log T- " log Ti T&If-Teh& L&B |= l.evadoux& rrji j — r ~ f Time" correction of Co correction ofColebrook rHp^byt lk l ) ) e|Bijookdfcsip. qurves^  BaligH(19«6)sb solution lition curves dissipation fordist'n frontSPM for dist'ri frbrn ft -14 0.0001 0.001 0.01 0.1 Coefficient of Horizontal Consolidation - Ch (cm2/s) • cor. C P T U - U2 (log T - T&H) - (Weech, 2002) S co r . C P T U - U2 (log T - L&B) - (Weech, 2002) Ocor . C P T U - U2 (root T - T&H) - (Weech, 2002) A cor. C P T U U2 (root T - L&B) - (Crawford & Campanella, 1991) • Lab Data - (MoTH, 1969) • Lab Data -(Crawford & Campanella, 1991) Fig. 5.9. Variation in estimated coefficient of horizontal consolidation with elevation with corrected CPTU derived values. 88 Chapter 5. Selection of site specific soil parameters for modelling. -3 Vertical effective stress o-'vo (kPa) Fig. 5.10. Variation of vertical effective stress with elevation. 89 Chapter 5. Selection of site specific soil parameters for modelling. 0 50 100 150 200 Equilibrium pore pressure uo (kPa) Fig. 5.11. Variation of equilibrium pore water pressure with elevation. 90 Chapter 5. Selection of site specific soil parameters for modelling. c o (0 > -2 -7 UJ -8 -10 -^ • MARINE CL TO SILTY C; A.YEY SILT .AY i 1 • 1 • • • i 1^ • • HI -Hi «= 1 • - — ~  •3^r-— -i i i i 0 0 i i i i .2 0 Slope of critic I I I I .4 0 ;a! state line, X 1 [ 1 1 .6 0 • based on Schofield & Wroth (1968) correlation • approximated from Cc reported by Crawford & Campanella (1991) Fig. 5.12. Probable range of slope of critical state line, A. 91 Chapter 5. Selection of site specific soil parameters for modelling. 3.000 2.500 100 Lab data after Crawford and Campane l l a (1988) Fig. 5.13. Variation of void ratio with mean effective stress based on data reported by Crawford & Campanella (1991). 3 2.8 2.6 2.4 2.2 2 o « c o « O w | 18 O 1.6 1.4 1.2 1 p' = 42 kPa - average for elevations -4.57 ... -9.92 m NorSand state parameter y s 2.2 r4 s uvei p' = 4 ^ U M b U M U c 2 kPa UIUII I d IK 1 IUI — — / J y r V / NorSand overconsolidation ratio J / / / / State parameter for p' = 42 kPa ? 0.026 0.14 0.12 0.1 0.08 | 2 ra Q. 0.06 S S co 0.04 0.02 10 20 30 40 50 60 70 Mean effective stress, p, kPa 80 90 100 Fig. 5.14. Variation of state parameter and overconsolidation ratio with mean effective stress. 92 Chapter 5. Selection of site specific soil parameters for modelling. 80 70 4 T3 10 - I t 0 -I 1 1 1 1 1 1 1 0 5 10 15 20 25 30 35 40 axial strain: % 3.5 axial strain: % Fig. 5.15. Simulation of drained triaxial test with NorSand model, using "base case" set of input parameters. 93 Chapter 5. Selection of site specific soil parameters for modelling. n Q_ 80 70 -60 -50 -co 2 40 l _ *-» co 5 30 ro '§ 20 TJ 10 -t 0 --— — — — - - •- - I— — — j- — 0 4 6 8 axial strain: % 10 121 80 70 60 50 (0 & 40 cr 30 20 10 0 Stress Path CSL 0 10 20 30 p, kPa 40 50 60 Fig. 5.16. Simulation of undrained triaxial test with NorSand model, using "base case" set parameters. 94 Chapter 6. NorSandBiot code parametric study. 6. N O R S A N D B I O T C O D E P A R A M E T R I C 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. M O D E L L I N G P A R T I C U L A R S . The 1-D parametric study was carried out by running NorSand-Biot on a one-row mesh of 50 elements, shown in Fig. 6.1. The boundary conditions of the analysis were as follows: • displacements were allowed only in a radial direction; • inner, top and bottom boundaries were set impermeable, so that there is no vertical flow or gradient. The outer boundary was set permeable to allow radial flow. • outer boundary was placed far enough from the inner boundary so that it had negligible effect on the pore water pressure response. 95 Chapter 6. NorSandBiot code parametric study. To examine the effect of variation of NorSandBiot input parameters on pore pressure response, the pile penetration was modelled as a single cylindrical cavity expansion up to the helical pile shaft radius. Simulation of the helices was omitted to simplify the analysis. For realistic simulation, a cavity corresponding to the helical pile shaft, must be created from zero initial radius. However, numerical modelling of a cavity with zero radius creates a problem of infinite circumferential strain that would occur for an initial cavity radius of zero. Carter et al. (1979) found that expanding a cavity from initial radius ao to 2ao can give the adequate approximation to what happens in a soil when cavity is expanded from zero radius to ro, as shown on Fig. 6.2. If both types of deformation occur at constant volume then relation between ro and ao'. r0 =V3a0 (6.1) At the helical pile research site all helical piles had identical pile shaft radius Rshaft (ro) = 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 uo = 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. R E F E R E N C E RESPONSE. Generally, the reference response is a response simulated with a set of parameters representing average, or typical, behaviour. Such response is required in a parametric study to provide a reference line of typical behaviour. The magnitude of deviation from this response may serve as a measure of the influence of changing modelling conditions. For the current analysis the reference response was obtained using the best estimate of Colebrook silty clay properties established in Chapter 5, Table 5.4, also shown in Table 6.1 as a "base case" scenario. 96 Chapter 6. NorSandBiot code parametric study. The pore pressure response due to pile, or cone, installation is normally represented by pore pressure distribution with distance and time. The same approach was adopted in the current study. Pore pressure response, due to helical pile shaft penetration, simulated for the base case input parameters, is presented in Fig. 6.3 and 6.4. Fig. 6.3 shows excess pore pressure distribution with radial distance away from the expanded cavity wall. On this plot, as on all following plots showing simulated pore pressure response, the generated excess pore pressure was normalized by the vertical effective stress (vertical axis Au/a'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/Rsnaft)-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 Au/<y'vo = 2.36. The shape of radial pore pressure distribution exhibits almost a linear trend in a log scale. Fig. 6.4 shows time dependent pore pressure response, where time is counted from the start of cavity expansion. It should be noted that cavity expansion stage (first 3.85 seconds) are omitted in this figure and only the pore pressure dissipation stage is shown. As follows in Fig. 6.4, the generated excess pore pressure induced by cavity expansion fully dissipates after 11000 minutes (-183 hours). Fig. 6.5 and Fig. 6.6 show the stress path and variation of void ratio with mean normal effective stress of the element adjacent to the cavity wall (identical abbreviations were used for both figures). These figures provide a valuable insight into the complex stress-strain behaviour of the medium during and after cavity expansion. For the period of the initial stage of cavity expansion, deformations are elastic and the deviator stress, q, increases with no change in mean normal stress (region AB, Fig. 6.5). As the cavity expansion progresses the soil yields and deformations become irreversible. Because the soil is soft and of low OCR, shear causes the soil to contract. This generates an increase in pore 97 Chapter 6. NorSandBiot code parametric study. pressure, and as such, the mean normal effective stress decreases as the deviator stress increases. This pattern continues until the stress path reaches the critical state line, where deformation occurs under constant ratio of deviator to normal stress (region BC, Fig. 6.5). The soil yields to failure at constant void ratio, indicating an absence of any volumetric strains, or fully undrained behaviour (regions AB and BC, Fig. 6.6). Interestingly, after failure is reached, an initial dilative response is observed (region CD, Fig. 6.5) and then, at some point, the rate of dilation slows and eventually the response becomes contractive (region DE, Fig. 6.5). This effect can be explained by the effect of partial drainage. For simulations with higher hydraulic conductivity, where partial drainage is larger, such effect is more significant, and is almost negligible when a lower hydraulic conductivity is assumed, as demonstrated in Fig. 6.7. It should be noted that the overall effect of partial drainage on the reference, or, base case pore pressure response is very insignificant. At the end of cavity expansion, the pore pressure dissipates; it triggers a consolidation process in the medium, when the void ratio is decreasing with dissipating pore pressure (region EF, Fig. 6.6). During the dissipation period, shear stress is diminishing, and then gradually rises with decreasing pore pressure (region EF, Fig. 6.4). The position of the critical state line shown in figures Fig. 6.5 and Fig. 6.6 (as in all other figures in this chapter) is inferred. The actual slope of critical state line, Mcrih depends on the Lode angle and varies from triaxial expansion to triaxial compression. 6.4. P A R A M E T R I C 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, Ko; • overconsolidation ratio, OCR; • shear modulus, G; • state parameter, (//; • intercept of the critical state line (CSL) at 1 kPa stress, /] • slope of CSL in e-ln(p') space, X; • hardening modulus, Hmoci; 98 Chapter 6. NorSandBiot code parametric study. • critical state coefficient in triaxial compression, Mcrit; • model parameter, %, • hydraulic conductivity in the radial direction, kr; • Poisson ratio, v. Table 6.1. List of scenarios for NorSand-Biot formulation sensitivity analysis. Scenarios Input Parameters Varie( Constant Ko OCR G MPa V ¥ r X Hmod Mcrit X K m/s MO* 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 ft 56 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.5 2.H0"y 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.H0"y 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 2.110"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.H0"y 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.H0"y 54.3 0.0 7 0.66 2.2 5. a 0.2 0.026 1.86 0.165 100 1.243 3.5 2.H0 _ y 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.H0"y 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.H0"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"y 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.H0~y 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.H0~y 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.H0"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.H0"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.H0"y 54.3 0.0 20 0.66 2.2 7.8 0.2 0.026 1.86 0.165 100 1.243 3.5 ii-nr'" 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.hi<r* 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.H0- y 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.H0~y 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 99 Chapter 6. NorSandBiot code parametric study. 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. P A R A M E T R I C STUDY R E S U L T S . 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 Ko, were quite narrowly defined, and the range of their variation was not large: 0.56 ... 0.76. For other parameters, such as X, 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 Au/cTvo 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 7pj 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. 100 Chapter 6. NorSandBiot code parametric study. Table 6.2. Parametric study results. Sc. Varied Values Magnitude of generated excess pore pressure at the end of cavity expansion, as Au/a'vo ratio Magnitude of generated excess pore pressure at the end of cavity expansion, as % of the base case value T95 hours T9S 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 24.4 122 2 K0=0.76 2.58 109.3 32.9 97.0 18.6 93 3 OCR=1.6 iy=0.085 1.97 83.5 50.7 149.6 35.2 176 4 OCR=3.4 iy=-0.036 2.88 122.0 19.2 56.6 15.7 78.5 5 OCR=5.6 v=-0.115 3.57 151.3 8.4 24.8 17.5 87.5 5a OCR=5.6 iy=-0.2 2.17 91.9 10.9 32.1 18.0 90.0 6 OCR=2.2 ty=0.1 2.18 92.4 42.4 123.9 20.0 100 7 G=5.8Mpa 2.25 95.3 34.8 102.7 16.5 82.5 8 G=9.8MPa 2.43 103.0 33.2 97.9 22.5 112.5 9 G=25.3MPa 2.72 115.3 31.1 91.7 38.1 190.5 10 r=i.75 2.36 100.0 33.9 100.0 20.0 100 11 r=2.45 2.36 100.0 33.9 100.0 20.0 100 12 r=1.44 A=0.073 2.32 98.3 35.9 105.9 20.0 100 13 r=2.77 X=0.362 2.43 103.0 30.5 90.0 20.0 100 14 Hmod=50 2.32 98.3 35.3 104.1 20.0 100 15 Hmod=450 2.41 102.1 30.6 90.3 19.5 97.5 16 Mcnt=1.113 2.15 91.1 35.9 105.9 21.0 105 17 Mcril=1.374 2.55 108.1 31.9 94.1 18.2 91 18 Z=3.0 2.35 99.6 33.8 99.7 20.0 100 19 X=4.0 2.37 100.4 34.0 100.1 20.0 100 20 kr=2.1-10-JUm/s 2.36 100.0 203.9 601.5 20.0 100 21 kr=3.1-10'ym/s 2.36 100.0 22.5 66.4 20.0 100 22 v=0.1 2.37 100.4 38.1 112.4 19.5 97.5 23 v=0.3 2.35 99.6 28.2 83.2 21.0 105 101 Chapter 6. NorSandBiot code parametric study. 6.5.1. I N F L U E N C E O F C O E F F I C I E N T O F L A T E R A L E A R T H PRESSURE. The coefficient of lateral earth pressure at rest, Ko, defines the level of horizontal stress in relation to the vertical stress. Typically, lower Ko indicates lower horizontal stress. For the current analysis three scenarios with different Ko were considered, all using the same vertical effective stress of 54.3 kPa: - base case: Ko = 0.66; scenario 1: Ko = 0.56; scenario 2: Ko = 0.76. It should be noted that the considered Ko 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 Ko values. As follows from Fig. 6.9 and Table 6.2, despite the divergence in magnitudes of initial pore pressures, all Ko 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 Ko 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 Ko (scenario 1) initial p' is the lowest and q is the highest, the opposite is true for simulations with higher ^ (scenario 2). For simulation with lower Ko 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 KQ. During pore pressure dissipation all simulations exhibit a similar pattern of initial slight softening, followed by gradual hardening. The simulation with the highest Ko (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. 102 Chapter 6. NorSandBiot code parametric study. 6.5.2. I N F L U E N C E O F M E A S U R E S O F SOIL O C R . There are two input parameters that represent soil OCR in the NorSandBiot formulation -overconsolidation ratio, R, and state parameter, y/. State parameter yi 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: y/ 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, y/ = 0.026; scenario 3: R = 1.6, y/ = 0.085; - scenario 4: R = 3.4, y/ = -0.036; scenario 5: R = 5.6, y/ = -0.115; scenario 5a: R = 5.6, y/ = -0.2; scenario 6: R = 2.2, y/ = 0.1. Simulations studied in this section are divided into two groups: • Scenarios with coupled R and y/ variation covering lightly to moderately overconsolidated soils: base case, scenarios 3, 4 and 5; • Scenarios where ^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 y/ at constant R on pore pressure response was of interest. 103 Chapter 6. NorSandBiot code parametric study. For convenience of the analysis pore pressure response for simulations with coupled and uncoupled R and y/ are discussed separately and then contrasted. Radial distribution of pore water pressure at the end of cavity expansion for simulations with coupled R and y/ 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 y/ (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/Rsnaft = 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 y/. 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 y/ (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/Rsnajt = 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 ^(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 104 Chapter 6. NorSandBiot code parametric study. 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 if/ (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 y 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/Rsnaft = 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 oiR and if/ 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 if/ is primarily in the magnitude of shear induced pore pressures. 105 Chapter 6. NorSandBiot code parametric study. 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. I N F L U E N C E O F E L A S T I C 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, v, - a ratio of axial compression to lateral expansion in triaxial compression. Higher G and v 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. 106 Chapter 6. NorSandBiot code parametric study. 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, v, on pore water pressure response was investigated in three scenarios with different v values: base case: v=0.2; scenario 22: v=0.1; scenario 23: v=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. 107 Chapter 6. NorSandBiot code parametric study. 6.5.4. I N F L U E N C E O F C R I T I C A L S T A T E P A R A M E T E R S . The following three input parameters in NorSand-Biot formulation define soil behaviour at the critical state: r, X and Mcrit. The position of the critical state line in e-ln(p') space is governed by the slope of the critical state line, X, and intercept of the critical state line at 1 kPa stress, r. Five different simulations were run to analyse the effect of variation of critical state line parameters on the pore pressure response: - base case: r= 1.86, X = 0.165; - scenario 10: r = 1.75, X = 0.165; - scenario 11: r= 2.45, X = 0.165; - scenario 12: r= 1.44, X = 0.073; - scenario 13: r= 2.77, X = 0.362. In scenarios 10 and 11 the effect of varying r for a constant X was of interest, whereas in scenarios 12 and 13 the influence of a coupled variation of r and X was analysed. A very broad range of values chosen for analysis is based on interpretations presented in Section 5.3.6.1. Generally, varying r while keeping X 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 JT 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 rand X has a small effect on pore pressure magnitude and dissipation time. A steeper slope of the critical state line (higher X) and higher r, 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 r and X (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 X and higher 7" (base case & scenario 13). For all simulations at the end of dissipation, the stress path shows different levels of stress. Generally, with increase in r and X, the final mean stress (p") increases. 108 Chapter 6. NorSandBiot code parametric study. 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 (<p'cv = 31° ); scenario 16: Mcril= 1.113 = 32°); scenario 17: Mcrit = 1.374 (g>'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 Mcri, shows a larger1 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 Mcri, 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 Mcril. 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. I N F L U E N C E O F H A R D E N I N G M O D U L U S . Hardening modulus, Hm0(j, is a unique NorSand parameter that governs the extent of the yield surface. Normally, a stiffer soil response is related to a higher Hm0d. 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. 109 Chapter 6. NorSandBiot code parametric study. 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. I N F L U E N C E O F S T A T E D I L A T A N C Y P A R A M E T E R . The state dilatancy parameter, #, 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 x variation on pore water pressure response: base case: #=3.5; scenario 18: #=3.0; scenario 19: #=4.0. The range of variation of x 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. I N F L U E N C E O F H Y D R A U L I C C O N D U C T I V I T Y . 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 = 2.1-10~10m/s; scenario 21: k = 3.0-10"9m/s. 110 Chapter 6. NorSandBiot code parametric study. 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. C O N C L U D I N G R E M A R K S O N P A R A M E T R I C S T U D Y R E S U L T S . 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. Input Influence on parameter magnitude of excess excess pore water radial distribution of ranking pore water pressure pressure dissipation excess pore pressures generated during cavity time expansion 1 V/&OCR L y/& OCR 2 K„ y& OCR ": K0 ' - 'I 3 MCrit V Z G .* 4 G Hmod Merit 5 r&x r&x V 6 Hmod Merit Hmod 7 V G kr, r&Xx,r 8 X Ko 9 K, r X 10 r 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. Chapter 6. NorSandBiot code parametric study. If we assume as significant, a change in pore pressure response in excess of +10 percent of a base case value, the variation of the following input parameters (shaded cells in Table 6.3) have significant effect on pore pressure response: • Measures of soil state (y/& 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 (Ko) 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 (v) 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 (%) and slope of the critical state line (I~), in a studied range, have an insignificant affect on soil stress state at the end of pore pressure dissipation; 112 Chapter 6. NorSandBiot code parametric study. • Lowering elastic parameters (v and G), horizontal stress (Ko) and position of the critical state line in e-log (p) space (T'& A) 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 (y/& OCR); • Standalone variation of hardening modulus (Hmoa) 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. S U M M A R Y . 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, y/, 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, Ko) and soil elasticity (represented by shear modulus, G, and Poisson ratio, v) have a major influence on pore pressure response. Results of the parametric study will be used in Chapter 7 as a guide to match modelled pore pressure response, with the field measurements by Weech (2002). 113 Chapter 6. NorSandBiot code parametric study. 1 i • Cic_ i I m 50 m -/- — • : t-Fig. 6.1. FE Mesh for Parametric Study. I of pile .JrtitioS cavity interface Fina I cavity interface •Equivalent pile interface i i t i i i . i r i i i 1 I 1 ! I * i r i . i i Fig. 6.2. Cylindrical cavity expansion from non-zero radius (after Carter et al., 1979). 114 Chapter 6. NorSandBiot code parametric study. 10 r/Rshaft 100 Fig. 6.3. Radial distribution of generated excess pore water pressure at the end of cavity expansion for "base case" scenario. 3.0 dissipation stage starts at -0.064 min 0.1 10 100 1000 10000 100000 Time (min) Fig. 6.4. Time dependent pore pressure response at cavity wall for "base case" scenario. 115 Chapter 6. NorSandBiot code parametric study. 20 40 60 p", kPa 80 100 120 Fig. 6.5. Stress path for "base case" scenario. 1.275 1.27 1.265 a> 1.26 1.255 1.25 1.245 C B T A -m I D C i 10 p', kPa 100 Fig. 6.6. Variation of void ratio, e, with mean effective stress, p' for "base case" simulation. 116 Chapter 6. NorSandBiot code parametric study. 1.275 1.27 1.265 a> 1.26 1.255 1.25 1.245 10 A - Base case k = 2.1 e-9 m/s B - Sc. 20: k = 2.1e-10 m/s C - Sc. 21: k = 3.1 e-9 m/s p, kPa 100 Fig. 6.7. Variation of e with/?'for "base case", 20 & 21 scenarios. 100 Fig. 6.8. Effect of Ko on radial distribution of generated excess pore pressure at the end of cavity expansion. 117 Chapter 6. NorSandBiot code parametric study. A-Base Case. Ko = 0.66 B-Sc.1 Ko = 0.56 C-Sc.2 Ko = 0.76 10 100 1000 Time (min) 10000 100000 Fig. 6.9. Effect of Ko on time dependent pore water pressure response at cavity wall. Fig. 6.10. Stress paths for "base case", 1 & 2 scenarios. 118 Chapter 6. NorSandBiot code parametric study. 10 r/Rshaft 100 Fig. 6.11. Effect of coupled R & if/on radial distribution of excess pore pressure response at the end of cavity expansion. 3.0 cavity expansion pore pressure! dissipation 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 Time (min) Fig. 6.12. Effect of coupled R& i//on time dependent pore water pressure response at cavity wall. 119 Chapter 6. NorSandBiot code parametric study. 100 Fig. 6.13. Effect of uncoupling R & y/ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with positive y/. 3.0 2.5 2.0 o > "& 1.5 3 < 1.0 0.5 0.0 cavity expansion pore pressure dissipation Base Case. R = 2.2; v|/ = 0.026 Sc. 6. R = 2.2; v =0.1 .0001 0.001 0.01 0.1 1 10 Time (min) 100 1000 10000 100000 Fig. 6.14. Effect of uncoupling R & y/on time dependent pore water pressure response at the cavity wall, for simulations with positive y/. 120 Chapter 6. NorSandBiot code parametric study. 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 Time (min) Fig. 6.15. Effect of uncoupling R & y/on time dependent pore pressure response at the cavity wall, for simulations with negative y/. 4-\ 3 o 5 1 -i 3 < 0 -1 -2 -3 normal s t ress induced pore p ressure full r e s p o n s e 10 M i l l ! I .' ! ' I I I I I I ! -!—h 20 30 40 50 60 70 80 90 100 shear induced pore p ressure cavity expansion, % Fig. 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 Chapter 6. NorSandBiot code parametric study. Sc. 5a. R = 5.6; y = -0.2 Sc. 5. R = 5.6; y = -0.115 100 Fig. 6.17. Effect of uncoupling R & y/ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with negative y/. normal stress induced pore pressure full response 100 shear induced pore pressure r/Rshaft Fig. 6.18. Radial distribution of different excess pore pressure components for scenario 5a. 122 Chapter 6. NorSandBiot code parametric study. Cavity Expansion: 100 percent 50 percent 30 percent 10 percent 5 percent 1 percent 10 r/Rshaft 100 Fig. 6.19. Radial distribution of generated pore pressure, for scenario 5a, at different levels cavity expansion. Sc . 6. R = 2.2; yp = 0.1 Sc . 3. R = 1.6; v|; = 0.085 Base Case . R = 2.2; v> = 0.026 contractive behaviour 10 100 p' KPa 1000 Fig. 6.20. Initial conditions in e-ln (p) space for scenarios 3..6 and base case. 123 Chapter 6. NorSandBiot code parametric study. 200 180 -160 -140 -120 -n D_ 100 -cf 80 -60 -40 -20 -0 -50 CSL Sc. 5a. R = 5.6; w = -0.2 Sc. 5. R = 5.6; v|/=-0.115 Sc. 4. R = 3.4; v = -0.036 Base Case. R = 2.2; y = 0.026 Sc. 3. R = 1.6; v = 0.085 Sc. 6. R = 2.2;\|/ = 0.1 100 150 p1, kPa 200 250 Fig. 6.21. Stress paths for scenarios 3.. .6 and base case. 10 Sc. 6. R = 2.2; i)/=0.1 Sc. 3. R = 1.6; v|/ = 0.085 Base Case. R = 2.2; y = 0.026 Sc. 4. R = 3.4; vy = -0.036 Sc. 5. R = 5.6; =-0.115 » \ Sc. 5a. R = 5.6; vi; =-0.2 100 p' KPa 1000 Fig. 6.22. Variation of e withp' for scenarios 3.. .6 and base case. 124 Chapter 6. NorSandBiot code parametric study. 2.5 24 ^ 1.5 4 0.5 H Sc. 9. G = 25.3 MPa Sc. 8. G = 9.8 MPa Base Case. G = 7.8 MPa Sc. 7. G = 5.8 MPa Edge of Pile 10 r/Rshaft 100 Fig. 6.23. Effect of G on radial distribution of excess pore pressure at the end of cavity expansion. 3.0 2.5 2.0 .51.5 3 < 1.0 0.5 0.0 0.1 1 10 100 1000 Time (min) 10000 100000 Fig. 6.24. Effect of G on time dependent pore pressure response at cavity wall. 125 Chapter 6. NorSandBiot code parametric study. C S L / b C . /. (J = D.O MHa •••••^  » Base Case. ^ G = 7.8 MPa / > v S c - 8 - ( 3 = 9.8 MPa 1 Sc. 9. G = 25.3 MPa i 0 20 40 60 80 100 120 p", kPa Fig. 6.25. Stress paths for scenarios "base case", 7, 8 & 9. 100 r/Rshaft Fig. 6.26. Effect of v on radial distribution of excess pore pressure at the end of cavity expansion. 126 Chapter 6. NorSandBiot code parametric study. 2.5 0.1 1 10 100 1000 10000 100000 Time (min) Fig. 6.27. Effect of v on time dependent pore water pressure response at cavity wall. 60 0 20 40 60 80 100 120 140 p', kPa Fig. 6.28. Stress paths for scenarios "base case", 22 & 23. 127 Chapter 6. NorSandBiot code parametric study. 10 r/Rshaft 100 Fig. 6.29. Effect of r on radial distribution of excess pore water pressure at the end of cavity expansion. 0.1 10 100 Time (min) 1000 10000 100000 Fig. 6.30. Effect of Ton time dependent pore water pressure response at cavity wall. 128 Chapter 6. NorSandBiot code parametric study. 60 50 40 ra S: 30 20 10 CSL / •••/•• \-t Base Case, r = 1.86 Sc. 10. r = 1.75 Sc. 11. r = 2.45 : i > i i 20 40 60 p\ kPa 80 100 120 Fig. 6.31. Stress paths for scenarios "base case", 10 & 11 2.5 -i 10 r/Rshaft 100 Fig. 6.32. Effect of r & X on radial distribution of excess pore pressure at the end of cavity expansion. 129 Chapter 6. NorSandBiot code parametric study. Fig. 6.33. Effect of r& X on time dependent pore water pressure response at cavity wall. Fig. 6.34. Stress paths for scenarios "base case", 12 & 13. 130 Chapter 6. NorSandBiot code parametric study. A - Base case . Merit = 1.243 B-Sc . 16. Mcrit= 1.113 C - S c . 17. Mcrit =1.374 10 r/Rshaft 100 Fig. 6.35. Effect of Mcrit on radial distribution of excess pore pressure at the end of cavity expansion. 3.0 n Sc. 17. Merit = 1.374 Base case. Merit = 1.243 SC. 16. Merit = 1.113 0.1 1 10 100 Time (min) 1000 10000 100000 Fig. 6.36. Effect of Mcrit on time dependent pore water pressure response at cavity wall. 131 Chapter 6. NorSandBiot code parametric study. 60 p', kPa Fig. 6.37. Stress paths for scenarios "base case", 14 & 15. 100 r/Rshaft Fig. 6.38. Effect of Hmod on radial distribution of excess pore pressure at the end of cavity expansion. 132 Chapter 6. NorSandBiot code parametric study. 2.5 0.1 1 10 100 1000 10000 100000 Time (min) Fig. 6.39. Effect of Hmoa- on time dependent pore water pressure response at cavity wall. 120 p\ kPa Fig. 6.40. Stress paths for scenarios "base case", 14 & 15. 133 Chapter 6. NorSandBiot code parametric study. 2.5 T 1.5 o > "3 < Base case, i Sc. 18. x = 3 Sc. 19. x = 4 = 3.5 0.5 H 100 Fig. 6.41. Effect of % on radial distribution of excess pore pressure at the end of cavity expansion. 100 Time (min) 10000 100000 Fig. 6.42. Effect of % on time dependent pore water pressure response at cavity wall. 134 Chapter 6. NorSandBiot code parametric study. 120 p\ kPa Fig. 6.43. Stress paths for simulations with "base case", scenario 18 & 19 set of input parameters. 2.5 -r 100 r/Rshaft Fig. 6.44. Effect of permeability, k, on radial distribution of excess pore pressure at the end of cavity expansion. 435 Chapter 6. NorSandBiot code parametric study. 2.5 2.0 1.5 j o < 1.0 0.5 0.0 Sc. 20: k = 2.1e-10 m/s Base case, k = 2.1 e-9 m/s Sc. 21: k = 3.1 e-9 m/s 0.1 10 100 1000 10000 100000 1000000 Time (min) Fig. 6.45. Effect of permeability, k, on time dependent pore pressure response at cavity wall. ra CL 50 45 40 35 30 25 20 15 10 5 0 / a i / H \ c SL / • Base case: k = 2.1 e-9 m/s Sc. 20: k = 2.1e-10 m/s Sc. 21: k = 3.1 e-9 m/s • 20 40 60 p", kPa 80 100 120 Fig. 6.46. Stress paths for scenarios "base case", 20 & 21. 136 Chapter 6. NorSandBiot code parametric study. 120 100 80 re ! * 60 40 20 CSL / © • base case • scenario 1 A scenario 2 X scenario 3 ^ A scenario 7 A scenario 8 scenario 10 - scenario 11 A scenario 12 * scenario 13 • scenario 14 il scenario 15 scenario 18 # scenario 19 a scenario 20 A scenario 21 o scenario 22 X scenario 23 200 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 for base case scenario). 137 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 7.0. M O D E L L I N G O F P O R E P R E S S U R E C H A N G E S I N D U C E D B Y H E L I C A L P I L E I N S T A L L A T I O N I N 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 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 7.2.1. S T A G E I. M O D E L L I N G OF H E L I C A L PILE INSTALLATION AS SINGLE C A V I T Y EXPANSION. 7.2.1.1. C O M P A R I S O N O F M O D E L E D AND F I E L D P O R E 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 (Au/cr'vo = 1.45) at the pile shaft in comparison with data for traditional piles (Au/a'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 S, = 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 Au/a'vo >0.1 to be significant, significant pore pressure are observed up to about r/Rsnaf, - 50 for the helical piles and, for the traditional piles, r/Rs/,aft 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 (Au/cr'vo = 2.36) and the extent of significant pore pressures near the lower bound {r/Rshafi = 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/Rshafi = 5, a very slow decrease, followed by a sudden drop in pore pressure at distances from r/Rs„aji, = 5 to 20 is observed. 139 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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/Rsnafi - 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. 140 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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 D A T A . 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 & y/) 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, r & X and Hmod. The time dependent pore pressure distribution was adjusted by increasing Poisson's ratio, v. 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. 141 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Table 7.1. Modelling parameters for "base case" and "best fit" simulations. Input Parameters Acceptable Range1 Base Case Best Fit Units General G 5.8-9.8 7.8 7.8 MPa V 0.1-0.3 0.2 0.3 -3.4-10"y... 8.5-10"10 2.H0"y 2.1-10"9 m/s OCR 1.2 ... 2.8 2:2 1.45 -Ko 0.56 ... 0.76 0.66 0.66 -(TvO 32.9 ... 75.7 54.28 54.28 kPa u0 39.5 ... 94.1 66.8 66.8 kPa NorSand MCri, 1.24 ... 1.33 1.285 1.33 -X 3.0 ... 4.0 3.5 3.5 -w -0.05 ... 0.2 0.026 0.12 -X 0.073 ... 0.362 0.165 0.08 base loge r 1.55 ... 2.25 1.86 1.55 at 1 kPa Hmod 50 ... 450 100 200 -1 - within elevations -4.57 . . . -9.92 m 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 (r& X and Mcru) 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 6 ...24 1 2.4 1 - within elevations -4.57 . . . -9.92 m 142 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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/Rsnafi = 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 Au/a'Vo at the cavity wall T95 Hours Maximum radial extent of generated excess pore pressures at the end of cavity expansion Measured in the field (S, = 6... 24) 1.42 92 65 Simulated with "best fit" parameters (S, - 2.4) 1.74 73 38 Simulated with "base case" parameters (S, = 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 143 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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. Simulated Response Time after end of cavity expansion 1 minute 1000C 1 minutes a'h/a'v0 (kPa) <y\„ (kPa) Au/a'v0 a'h/a'vo <y'ho (kPa) <T'V (kPa) "best fit" parameters (5, = 2.4) 0.30 16.3 54.3 1.68 1.11 108.1 48.9 0.9 "base case" parameters (S,= l) 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 144 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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 oVtr 'vo, SO that for a sensitive low OCR soil, cr't/cr'vo 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 o'h/o'vo 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 mp'. 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. 145 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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 146 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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, 147 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 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/Rshafi) 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 148 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. there is a significant mismatch between predicted and measured pore pressures near the cavity wall at the end of helical pile installation. This limitation should be considered when analyzing the modelling results. The fact that the purpose of the modelling presented here is not the exact fitting of the pore pressure at the pile wall, but rather capturing general trends observed in the field and producing reasonable response predictions also should be considered. Fig. 7.13 shows a comparison between the radial pore pressure distribution at the end of helical pile installation, for simulations with and without helices, and the field measurements. Based on this figure the following observations related to the effect of the simulated helices on radial pore pressure distribution can be made: 1) . The presence of the helices (cavity expansion/contraction cycles) extends the zone of excess pore pressure generated during shaft penetration (expansion of a single cavity). The amount of this increase is dependent on the length of the helix at its maximum extent (the magnitude of the cavity expansion). It can be seen that cavity expansion/contraction cycles with smaller magnitudes (Case B) have practically no influence on the maximum extent or radial pore pressure distribution r/Rsf,af, = 38, whereas cavity expansion/contraction cycles with greater magnitudes (Case A) extend the zone of generated excess pore pressure up to r/Rsnaft = 70, which is very close to the observed in the field r/Rshajt = 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/Rsha/t = 21; for Case B - r/Rshaft = 6.6). Beyond these peaks the trend of pore pressure distribution appears to be in good agreement with the pore pressure response simulated by expansion of a single cavity and the field measurements. 149 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Further understanding of the pore pressure changes induced by the helices may be gained by examining the process of pore pressure response during cavity expansion/contraction cycling. Fig. 7.14 shows the mechanism of pore pressure generation during expansion of the cavity corresponding to the first helix, for Case A. It can be seen that gradual pore pressure increase is observed during the whole period of expansion of the cavity corresponding to the first (bottom helix). At the end of helix cavity expansion, the pore pressure is increased both in magnitude and radial extent. The new shape of the pore pressure distribution is nearly parallel to the response simulated with a single cavity expansion and provides a reasonably good agreement with the field measurements. After the expanded cavity has reached its full extent, it is contracted back to the pile shaft boundary. The mechanism of pore pressure response during this process is shown in Fig. 7.15. As cavity contraction progresses, pore pressures are significantly diminished, reaching at 100% contraction a distribution similar to the one shown in Fig. 7.13. It should be noted that more than 80% of the pore pressure drop was observed before 50% of the cavity contraction was reached. The effect of continuing expansion/contraction cycling for simulation of installation of helical pile with 5 helices is shown in Fig. 7.16. As follows from this figure, at the end of each subsequent expansion or contraction, the pore pressure magnitude is gradually increasing. There appears to be a threshold at r/Rshaft = 21 beyond which subsequent cavity expansion/contractions cycles have no substantial impact on the pore pressure generated during the expansion of the cavity, corresponding to the first helix. The zone of influence of cavity contraction is three times smaller than the area affected by cavity expansion (maximum extent of generated excess pore pressure is observed at r/Rshaft - 70). Fig. 7.17 shows that a reduction in the number of cycles given the same cavity expansion/contraction magnitude does not change the trends observed in Fig. 7.16. The pore pressure response for smaller expansion/contraction magnitudes (Case B), shown in Figs. 7.18 and 7.19, confirms the overall trends observed for Case A. Time dependent pore pressure responses at the cavity wall for Case A and Case B simulations with 3 and 5 helices are shown in Fig. 7.20 - 7.23. From these figures we can infer the following: 1). Cavity expansion/contraction cycling significantly alters the pore pressure magnitude in the close vicinity of the cavity wall. Pore pressure magnitude at the end of the cycling is a function of the number of cycles and the length of the expanded cavity, so that maximum pore pressure 150 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. alteration is observed for simulation with the lengthiest cavity expansion and the fewer number of expansion/contraction cycles (Case A with 3 helices, shown in Fig. 7.21). 2) . After the end of the expansion/contraction cycling some recovery of altered pore pressure is observed, so that an additional peak in pore pressure response is clearly visible. The magnitude of "recovered" pore pressure is the largest for the simulation with the fewer expansion contraction cycles and smaller length of cavity expansion (Case B with 3 helices, Fig. 7.23). It appears that that the observed pore pressure recovery is related to the pore pressure redistribution after the end of cycling. 3) . Interestingly, despite significant pore pressure alteration after expansion/contraction cycling all simulations showed reasonable dissipation time predictions. However, none of them improve prediction of the pore pressure dissipation time obtained from simulation of the helical pile shaft installation (marked as "shaft only on the figures). Dissipation trends for both Case B simulations (see Fig. 7.22, 7.23) join with the "shaft only" trend at about 1000 minutes. For Case A simulations (see Fig. 7.20, 7.21) dissipation time for 95 % dissipation is slightly longer than for the "shaft only" case. The effect of cycling on stress level and void ratio variation, for the Case A with 5 cavity expansion/contraction cycles, is shown in Figs. 7.24 and Fig. 7.25. It can be seen that during cycling (region C in both figures) the stress path is moving along the critical state line, as schematically shown for the first expansion/contraction cycle in Fig. 7.24. Cavity expansion corresponding to the first helix causes yielding of the medium and contractive response (corresponding to decrease in void ratio in Fig. 7.25) is observed. As the cavity is contracted it causes dilation (corresponding to increase in void ratio in Fig. 7.25) and the stress path moving back towards and even slightly beyond the point where the cavity expansion had started, which eventually leads to some stress level increase (see point B and D on the figure). During a pause between cycling pore pressure begins to dissipate and the stress path is moving away from the critical state line exhibiting some decrease in shear stress. As the next cavity expansion begins, yielding of the medium quickly brings the stress path to the critical state line and the pattern described for the first expansion/contraction cycle is repeated. After the end of cycling, as pore pressures dissipate (region DE), shear stress decreases and eventually begins to increase close to the end of the dissipation process. Comparison of the stress paths for simulations of single cavity expansion with "base case" and "best fit" input parameters, and Case A simulation with 5 cavity expansion/contraction cycles is 151 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. shown in Fig. 7.26. The quantitive comparison of the final level of stress for this simulation is provided in Table 7.6. Table 7.6. Final stress state for "base case", "best fit" and Case A simulation with 5 helices. Stress, kPa Simulation with "base case" parameters Simulation with "best fit" parameters Case A simulation with 5 helices q 45.2 17.3 7.5 P' 102 57.2 30.9 The following observation can be made from Fig. 7.26 and Table 7.6: • Given the same initial conditions the final level of stress appears to be very different depending on a choice of input parameters and simulation particulars. Generally for simulations with the sensitive set of parameters ("best fit" and Case A), the final stress level is much lower than for the simulation with non-sensitive parameters ("base case"). The maximum reduction is observed for the shear stress q. • Expansion/contraction cycling significantly reduces the mean normal effective stress, so that after five such cycles q is reduced by 57% andp' 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 1 between the pile wall and soil was discussed. Due to the anomalously low pore pressure generated at the pile wall, Assumption 2 is investigated further. Fig. 7.27 shows a comparison of the pore pressure generated due to the first helix penetration (expansion/contraction cycle) for Case A with 5 helices simulation based on different assumptions of soil/cavity interface boundary conditions during unloading and the corresponding field measurements. As follows from this figure, fixed soil/cavity interface (Assumption 1) significantly diminishes the pore pressure generated during the helix expansion. This is likely related to the stress relief in the zone adjacent to the cavity wall, which is triggering suction, resulting in the pore pressure drop. Simulation based on this 152 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. assumption correspond to the general trend of pore pressure drop during unloading observed in the field, although exaggerates this effect severely. At the same time no substantial changes in the pore pressure during cavity contraction is shown by the simulation where the soil was left to rebound freely (Assumption 2). This indicates absence of any plastic deformations. In reality when the penetrating helical plate releases the displaced volume of the soil some plastic yielding, stress relief and some pore pressure suction are likely to occur. Assumption 2 is unable to replicate these effects, whereas Assumption 1 exaggerates them. It appears that the field pore pressure response can potentially be fitted by assuming smaller degree of unloading for Assumption 1. As the purpose of the analysis was not to achieve an exact fit to the field data, this approach was not pursued since it will not yield any additional insights into the complex pore pressure response induced by the helices. Summarizing the section's findings we should emphasize the following: • introduction of the helices extends the zone of generated excess pore pressure; • assumption of a fixed soil/cavity interface exaggerates the effect of helices unloading leading to underprediction of the pore pressure magnitude at the cavity wall; • NorSandBiot code is able to capture observed field trends of the pore pressure response induced by the helices • conducted simulations provided an interesting insight into the complex pore pressure and stress response of the fine-grained soil; 7.3. IMPLICATIONS FROM 1-D MODELLING. 7.3.1. PREDICTED VERSUS MEASURED/INTERPRETED PORE PRESSURE RESPONSE. A comprehensive field study of helical pile performance in sensitive fine-grained soils, conducted at Surrey, British Columbia, by Weech (2002) provided an initial framework of expected soil response and served as a reference point for the current numerical study. Having completed the modelling, we may now specifically address some of the observations and propositions made during the field study: Weech (2002) observed that excess pore pressures generated by the penetration of the helical pile shaft appear to be significant (Au > 0.1 cr'vo) out to a radial distance of at least 17 shaft radii 153 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. from the centre of the pile, which is in a close agreement with the modelling carried out at Stage I of the current analysis. The simulation of expansion of a single cavity predicted the generation of significant (Au > 0.1cr'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/Rsnaft = 8 ... 20) where a pore . pressure build up and gradual radial propagation with each subsequent expansion/contraction cycle is observed. At the same time the maximum extent of the radial pore pressure distribution appears to be unaffected by the cycling. Pore pressures reach their maximum extent during the first cycle and penetration of the subsequent helices does not advance or alter the extent of the pore pressure distribution zone. It appears that the vertical component neglected in 1-D modelling may be a significant factor affecting the mechanism of pore pressure distribution due to penetration of the helical plates. 2-D modelling is required to confirm this idea. 154 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 7.3.2. F R O M PORE PRESSURE RESPONSE PREDICTIONS TO PILE BEARING CAPACITY. To date, the ability of current geotechnical practice to accurately predict pile capacity for all pile types is limited. According to the recent Rankine Lecture presented by Randolph (2003): "... despite continuous advances in approaches to pile design, estimation of (axial) pile capacity - relies heavily upon empirical correlations. Improvements have been made in identifying the processes that occur within the critical zone of soil immediately surrounding the pile, but quantification of the changes in stress and fabric is not straightforward ". It appears that numerical solutions may offer the necessary means to overcome these problems. As shown in Chapter 6 and in the current chapter, fully coupled NorSandBiot formulation provides a valuable insight in the pore pressure and stress response during and after helical pile installation. One important factor controlling the pile's capacity is the long-term effective stress at the pile-soil interface and around the helices. This stress is controlled by the evolution of pore pressures and effective stress during pile installation and subsequent pore pressure dissipation. For all piles, and particularly helical piles where less case history data exists, an ability to accurately predict and understand the evolution of effective stress and pore pressures at the pile wall would provide a basis for accurate pile design. As shown in Section 7.2.1.2, the variation of effective stresses with pore pressure dissipation can be readily estimated using the NorSandBiot formulation. No measurements of total stress during and after helical pile installation were taken at the Colebrook site, so direct comparison of the modelling results and the fields measurements is not possible. However, comparison of simulations with sensitive and non-sensitive sets of input parameters showed a good agreement with the trend observed at the other sites by Lehane & Jardine (1994). The modelling process is not without challenges: depending on the choice of the modelling input parameters, the predicted response varies significantly. As shown in the parametric study, even a small variation of some of the input parameters may have a large impact on the modelling predictions. Even if the pore pressure at the cavity wall following pile installation was correctly estimated, the time-dependent magnitude of the lateral stresses and pore pressures over time can be very different, as discussed in the paper by Vyazmensky et al (2004) given in Appendix F. This highlights the importance of good engineering judgement while establishing input parameters for modelling and interpreting the numerical simulation results. 155 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 7.4. SUMMARY. Within a framework of the NorSandBiot formulation two conceptual approaches to the modelling of the helical pile in 1 -D were considered in the present study: I. Modelling of the helical pile as a single cylindrical cavity expansion; II. Modelling of the helical pile as a combination of a single cylindrical cavity expansion and series of additional cylindrical cavity expansion/contraction cycles. It has been shown that, provided a careful selection of input parameter values applicable to the Colebrook site, single cavity expansion produced quite accurate prediction of the pore pressure dissipation time and satisfactory estimate of pore pressure distribution at the end of helical pile installation observed by Weech (2004). Introduction of the expansion/contraction cycles (helices) on top of a single cavity expansion helped to improve prediction of the maximum extent or the radial pore pressure distribution and the pore pressure dissipation time. Assumption of a fixed soil/cavity interface during cycling, exaggerated the effect of helices unloading leading to underprediction of the pore pressure magnitude at the cavity wall and its immediate vicinity. Although, at greater distances the modelling was able to capture effectively general trends of pore pressure behaviour measured in the field, including gradual pore pressure build up and outward propagation during penetration of the helices. Largely, given the complexity of the modelled process and taking into account the major simplifications involved in the analysis, overall results of the Stage I and Stage II modelling were more than satisfactory. The conducted modelling proved that as a fully coupled formulation, NorSandBiot is able to provide a realistic framework for studying complex response of fine-grained soils. Applying numerical methods to the analyse of the soil behaviour observed at the Colebrook site allowed for valuable insights to be gained into the nature of changes of pore pressures during and after helical pile installation. The modelling confirmed many of the field observations and propositions made by Weech (2004). At the same time some of them may not be fully confirmed or dismissed until additional levels of complexity to the modelling are added, in particular the effect of soil remoulding and the effect of deformations and drainage in the vertical direction. 156 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. In addition the modelling showed that sensitivity has a large effect on the equalized lateral effective stress ratio oVcTvo, which is in agreement with findings of Lehane & Jardine (1994). This is an important step towards ability to predict lateral stress and pile capacity with reasonable degree of accuracy. 157 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. r V V* o u Symbol 51 la M a *> «» £ 0 OCR S u iTSM! PI Sf 0 0 7.5 d ! 2 to 2.5 25 Ii! 6 to 8 o • (0 «/) UI b 7.6 10.7 si (i! 2 to 2.5 20 4 to 6 _J a 1 c + 5 2.5? 3 to 3.5«> 60 very hio.h i~ z Ui • 3 2.3 ,.3 t i ! 20 16 2 Ui u J d o 6 2.3 il) 2.0. a (/> o 11.5 4 (!) 5.5 ' Q o JZ » e o 14 3 5 ( l ! 20 6 o 0 24 to 30 1.2 5.5to < t f 0 12.2 7? , l i 3 ! 40 u 9 H 5.8 10 a C h 1 6 to 9 3? 2.5 37cloyj rsilt j 5 10 20 NORMALIZED RADIUS, r/R iOFietti Vone {2} Dutch Cone (3) unconfined 100 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. Fig. 7.2. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with "base case" parameters. 158 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 60 40 ns Q_ 20 0 1 1 base case (S t = 1; s u = 22.6 kPa) best fit (S t = 2.4; s „= 15.1 kPa) v / 4 6 8 axial strain: % 10 12 B 80 60 £ 40 20 critical state line Merit = 1.33 critical state line Mem =1.243 best fit parameters (St = 2.4) base case parameters (St=1) 10 20 30 p\ kPa 40 50 60 Fig. 7.3. Comparison of modelled undrained triaxial response for "best fit" and "base case" sets of NorSandBiot input parameters. A - Variation of deviator stress with axial strain. B - Stress paths. 159 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. o O 7.5 10 7.6 10.7 11.5 o 0 H 24 to1 30 12.2 OCR 2.5? 2.3 2.3 1.2 5.8 6 to 9 3? S, ITSMjl (l) 2 to 2.5 3 to 3.5<2)] 1.3 (0 2.0 5.5 3.5to 15»> ,(3) 2.5 to*5 25 20 60 20 20 40 (I) 6 to 8 very high 16 37cloyi 7»ilt UjFieidVone (2) Dutch Cone (3) Unconfined 00 NORMALIZED RADIUS, r/R 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. 2.5 2.0 1.5 3 1.0 0.5 4 0.0 NorSandBiot simulation with base case input parameters NorSandBiot simulation with best fit parameters "TTT Weech (2002) average field data (from piezoelements located below helices) 10 100 1000 Time (min) 10000 100000 Fig. 7.5. Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with "best fit" parameters. 160 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 10 100 Time (min) 1000 10000 Fig. 7.6. Comparison of AU/<J'VO and aV<7'vo vs. time for "best fit" and "base case" simulation and the field measurements. 30 25 20 15 10 10 20 B initial state r •A c end of cavirv exoansion AC - cavity expansion AB - failure towards critical state line BC - failure along critical state line CD - pore pressure dissipation 1 1 1 30 40 p\ kPa 50 60 70 Fig. 7.7. Stress path plot for central gaussian point of the mesh element adjacent to the cavity wall {r/Rshaft = 1.08) for simulation of helical pile shaft installation with "best fit" parameters. 161 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 1.362 1.358 A C - cavity expansion AB - failure towards critical state line BC - failure along critical state line C D - pore pressure dissipation 10 p\ kPa 100 Fig. 7.8. Void ratio versus mean stress (e - ln(p')) plot for central gaussian point of the mesh element adjacent to the cavity wall (r/Rshaft = 1.08) for simulation with "best fit" parameters. 162 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Case A Ipile shaft IheTix Case B Ipile shaft I 1.54 cm 2.57 cm FTelTxl J 1 . J 4.74 cm Fig. 7.9. Modelling cases considered in the analysis of the effect of the helices. Shaft + 3 Helices Shaft + 5 Helices case A B time, sec 3.85 3.85 6.3 6.3 3.16 1.03 3.16 1.03 66.9 62.7 3.16 1.03 3.16 1.03 66.9 62.7 3.16 1.03 3.16 1.03 time case A B time, sec 3.85 3.85 6.3 6.3 3.16 1.03 3.16 1.03 30.3 30.3 3.16 1.03 3.16 1.03 30.3 30.3 3.16 1.03 3.16 1.03 30.3 30.3 3.16 1.03 3.16 1.03 30.3 30.3 3.16 1.03 3.16 1.03 Legend: P'le s n a f t expansion |^—| pile shaft contraction | P | pause in installation helix expansion helix contraction Fig. 7.10. Modelling algorithm of helical pile installation in 1-D. 163 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. o _> < 300 Time (sec) after pile tip passed piezometer location 300 Time (sec) after pile tip passed piezometer location Fig. 7.11. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case A). (a) - for helical pile with five helices; (b) - for helical pile with three helices. 164 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 50 100 150 200 250 T i m e (sec) after pile tip p a s s e d p i e z o m e t e r locat ion 300 50 100 150 200 250 300 Time (sec) after pile tip passed piezometer location Fig. 7.12. Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case B). (a) - for helical pile with five helices; (b) - for helical pile with three helices. 165 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Fig. 7.13. Comparison of radial pore distribution for simulations with and without helices and the field measurements. 1 10 r/Rshaft 100 Fig. 7.14. Radial pore pressure distribution during first helix expansion (Case A). 166 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. r/Rshaft 100 Fig. 7.15. Radial pore pressure distribution during first helix contraction (Case A). Fig. 7.16. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A). 167 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. i .1 j Edge of i Helifces 'for field data - average field data - end of pile inst. - shaft only - end of expansion end of 1 st helix expansion end of 1st contraction - end of 2nd helix expansion end of 2nd helix contraction •end of 3rd (last) helix expansion -end of 3rd (last) helix contraction 100 r/Rshaft Fig. 7.17. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case A). 100 Fig. 7.18. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case B). 168 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. 1 10 100 r/Rshaft Fig. 7.19. Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case B). 169 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Time (min) Fig. 7.20. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case A). Time (min) Fig. 7.21. Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case A). 170 Chapter 7. Modelling of pore pressure changes induced by helical pile installation in 1-D. Time (min) 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 0 1 0 . 0 0 1 0 . 0 1 0.1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 Time (min) 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. Fig. 7.24. Stress path plot for mesh element adjacent to the cavity wall (r/Rshaf, = 1.08) for simulation of helical pile shaft installation. 1.374 1.372 1.364 1.362 1.36 1.358 pause between shaft & 1st helix expansion pause between end of • 1st helix contraction & 2nd helix expansion 2nd helix contraction AB - shaft expansion; C - helices: expansion/contraction cycles; DE - dissipation stage 10 100 p', kPa Fig. 7.25. Void ratio versus mean stress (e - ln(p)) plot for mesh element adjacent to the cavity wall (r/Rshafl=\.08). 172 Chapter 7. Modelling of pore pressure changes induced by pile installation in 1-D. 0 20 40 60 80 100 120 p", kPa Fig. 7.26. Comparison of stress paths for central gaussian point of the mesh element adjacent to the cavity wall (r/Rsnaft - 1-08) for simulations with different set of input parameters and modelling schemes. 173 Chapter 7. Modelling of pore pressure changes induced by pile installation in 1-D. 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. S U M M A R Y , C O N C L U S I O N S & R E C O M M E N D A T I O N S F O R F U R T H E R S T U D Y . 8.1. SUMMARY AND CONCLUSIONS. Predictions of the pore pressure response induced by traditional piles and CPT piezocones has been analysed in a number of studies. However, the pore pressure response due to installation of helical piles has not been addressed until very recently. Weech (2002), during a field study of helical pile performance in soft fine-grained soil, measured pore pressures during and after helical pile installation. According to Terzaghi: "Theory is the language by means of which lessons of experience can be clearly expressed". Following this view the current study is a theoretical attempt to reproduce the pore pressure response observed in the field by applying numerical methods. The field experimental data obtained during Weech's study provided the necessary background information for the numerical analysis. There is a consensus of opinions in the reviewed literature - realistic simulation of the time dependent pore pressure response induced by pile installation requires a framework that utilizes advanced soil models coupled with consolidation analysis. Simulation of the pile installation process within this framework can be achieved using either cavity expansion or a strain path analogue. In the present study, the critical state model NorSand, coupled with Biot's consolidation equations, was chosen as the framework for a cavity expansion analysis. Even though its name suggests sand, the NorSand model has no intrinsic limitations for application to fine-grained soils. Modelling of the triaxial tests on Bonnie silt carried out during the present study, further reaffirmed this idea. The finite element implementation of the coupled NorSandBiot formulation developed by Shuttle (e.g. 2003) was adopted in this study. Thorough verification of the NorSandBiot code has shown that its numerical predictions fully match available theoretical solutions. The NorSandBiot code requires 13 input parameters. The extensive dataset of available information on Colebrook silty clay properties provided information on many, but not all, of the input parameters. Some of the parameters required for NorSandBiot code were not directly measured during previous investigations, thus in a present study their values were derived based on the information available. Despite the difficulties, reasonable acceptable ranges for all 175 Chapter 8. Summary, conclusions and recommendations for further study. NorSandBiot input parameters were established and a best estimate set of input parameters for modelling was proposed. A comprehensive parametric study of the NorSandBiot code has shown that several of the input parameters, varied within the range acceptable for the Colebrook site, do not have a significant effect on the calculated pore water pressure response. The computed pore water pressure response was however very sensitive to the soil OCR (in the NorSandBiot formulation represented by the state parameter, y/, 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, Ko) and soil elasticity (represented by shear modulus, G, and Poisson's ratio, v) have a major influence on the pore pressure response. The study was conducted in 1-D, so a special simplified procedure was developed to simulate helical pile installation using a series of cylindrical cavity expansion/contraction cycles. The modelling of the helical pile installation into Colebrook silty clay was conducted in two stages: I. Modelling of the helical pile as a single cylindrical cavity expansion; II. Modelling of the helical pile as a combination of a single cylindrical cavity expansion and series of additional cylindrical cavity expansion/contraction cycles. It has been shown that, provided a careful selection is made of input parameter values applicable to the Colebrook site, single cavity expansion produced quite accurate prediction of the pore pressure dissipation time and a satisfactory estimate of the pore pressure distribution at the end of helical pile installation observed by Weech (2004). Introduction of the expansion/contraction cycles (helices) on top of a single cavity expansion helped improve prediction of the maximum extent of the radial pore pressure distribution and the pore pressure dissipation time. Assumption of a fixed soil/cavity interface during cycling, exaggerated the effect of unloading after passage of the helices leading to underprediction of the pore pressure magnitude at the cavity wall and its immediate vicinity. Nevertheless, at greater distances the modelling was able to capture effectively the general trends of pore pressure behaviour measured in the field, including gradual pore pressure build up and outward propagation during penetration of the helices. Largely, given the complexity of the modelled process and taking into account the major simplifications involved in the analysis, the overall results of the Stage I and Stage II modelling were encouraging. 176 Chapter 8. Summary, conclusions and recommendations for further study. The following major conclusions can be drawn from the study: • A fully coupled NorSandBiot modelling framework provides a realistic environment for simulation of the fine-grained soil behaviour. • The proposed modelling approach of simulating helical pile installation provides a simplified technique that allows reasonable predictions of stresses and pore pressure variations during and after helical pile installation; • The modelling highlighted the importance of careful input parameter selection and significance of modelling assumptions. • The modelling showed a generally good agreement with the pore water pressure response trends observed at the Colebrook site by Weech (2004). • The modelling demonstrated that soil sensitivity has a large effect on the equalized lateral effective stress ratio oVc'vo, which is in agreement with findings of Lehane & Jardine(1994). It appears that the modelling approach developed in this study has a great potential for application in geotechnical practice: • NorSand-Biot code can be integrated into independent geotechnical software tools that will be capable of estimating variation of bearing capacity with time after pile installation. • Simulation of a single cavity expansion in the NorSandBiot framework can be readily applied for studying pore pressures and stress predictions induced by traditional piles and piezocones. However, before these tasks are undertaken further research is needed. 8.2. RECOMMENDATIONS FOR FURTHER RESEARCH. 8.2.1. LABORATORY TESTING. The Colebrook site investigations performed by MoTH, Crawford & Campanella (1991) and Weech (2002) provided a good basis for establishing many, but not all, of the input parameters required for the NorSand-Biot formulation. 177 Chapter 8. Summary, conclusions and recommendations for further study. Limited knowledge of triaxial behaviour of Colebrook silty clay made it difficult to establish accurately NorSand model parameters, including: • critical stress ratio, Mcrit; • slope of the critical state line, X; • intercept of the CSL at 1 kPa stress, P, • hardening coefficient, Hmoa-; • state parameter, y/; • state dilatancy parameter, %. 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 (Mcri,; Hmod\ X) a n ^ undrained (P; X) triaxial tests to establish NorSand parameters and falling head permeability tests to evaluate hydraulic conductivity, h. 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 kf/ky of 2 to 5 for the layered clays with silt inclusions, Gillespie & Campanella (1981) recommended use of kf/kv = 2.5 for the silty clays 178 Chapter 8. Summary, conclusions and recommendations for further study. found in the Fraser river delta. It would be particularly interesting to model helical pile installation in 2-D with the "best fit" set of parameters established in Chapter 7, assuming different ratios for horizontal and vertical permeability and taking kh/kv = 2.5 as a reference. Modelling results can be contrasted and compared to the 1-D simulation and field measurements by Weech (2002). Effect of Soil Remoulding on Pore Pressure Response. Pile installation creates a zone of severe deformations in the adjacent soil due to remoulding. Soil in the remolded zone, exhibits quite different properties from the intact state. Moreover, within the remoulded zone there will be subzones with different degrees of remoulding. 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Advances in Underwater Technology, Ocean science and offshore engineering. Vol. 28, Offshore Site Investigation and Foundation Behaviour, pp. 607-643. London. Whittle, A.J., Sutabutr, T., Germaine, J.T. & Varney, A. (2001). "Prediction and Interpretation of Pore Pressure Dissipation for a Tapered Piezoprobe." Geotechnique. Vol. 51, No. 7, pp 601-617. Zienkiewicz, O.C. & Cormeau I.C. (1974). "Viscoplasticity, Plasticity and Creep in Elastic Solids. A Unified Numerical Approach." International Journal for Numerical Methods in Engineering, Vol. 8, pp. 821-845. 186 Notation. N O T A T I O N . A = Skempton's pore pressure parameter [-] Cc = compression index [-] Ca = coefficient of secondary consolidation [-] D = helical plate diameter [m] D° - plastic dilatancy = E^\B P [-] 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(y) = strain dependent shear modulus [mN/m2] Hmod = hardening parameter [-] Ir = rigidity index = G/su [-] K' = Bulk modulus [mN/m2] Ko = 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 [-] M = slope of the critical state line in q - p 'space in triaxial compression [-] OCR = overconsolidation ratio = ap'/avo' [-] PI = plasticity index [-] Rshaft = radius of the pile shaft [m] R = ratio of/? '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] Cf, = coefficient of consolidation in the horizontal direction [cm2/s] cv = coefficient of consolidation in the vertical direction [cm2/s] e0 - void ratio et = 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] Pent = mean stress at the critical state [kN/m2] p' - mean normal effective stress ={a\ +o-'2 +a'3)/3 [kN/m2] P 'max ~ maximum mean normal effective stress [kN/m2] Pi = mean stress at the image state [kN/m2] <1 = deviatoric stress invariant=(/2(at -cr2)2 +y2{cr2 -cr3)2 +/2(cr3 -cr,)2)^ [kN/m2] 187 Notation. 2 qr = corrected cone tip resistance [kN/m ] r0 - initial radius [m] r = radial distance from the pile centre [m] su = undrained shear strength [kN/m2] (SiJrem = remoulded undrained shear strength [kN/m2] (Su)peak ~ peak undrained shear strength [kPa] thx = helical plate thickness [mm] uw = pore pressure [kN/m2] u0 = initial pore pressure [kN/m2] ul — pore pressure measured on the face of a cone penetrometer u2 = pore pressure measured behind the tip of a cone penetrometer w„ ~ natural moisture content [%] M>L - liquid limit [%] a = Henkel's pore pressure parameter [-] X = state dilatancy parameter [-] Sq = shear strain invariant = 2/3(£/-£3) in triaxial compression [%] ev = volumetric strain, dot superscript denoting rate [%] £1, 2,3 = principal strains (assumed coaxial with principal stresses) [%] (f> — effective friction angle [degrees] <p cv = effective friction angle at constant volume [degrees] y - shear strain [%] yw = unit weight of water [kN/m3] rj = stress ratio =q/p' [-] K = slope of the unload-reload line [-] X = slope of CSL in e-ln(p) space [-] a'h = lateral effective stress [kN/m2] a',0 = in-situ lateral effective stress [kN/m2] a'p = preconsolidation stress [kN/m2] cr'v0 = vertical (overburden) effective stress [kN/m2] v = Poisson coefficient [-] 0 = Lode angle [rad] y/ = state parameter [-] y/j = state parameter at image stress [-] r = intersection of critical state line with mean stress at 1 kPa [-] n = dot superscript denotes increment of the value n A = delta denotes change relative to initial or in-situ value An(r) = change of value n as a function of distance An(t) ~ change of value n as a function of time 188 Appendix A. Sources of available subsurface information. A P P E N D I X A . SOURCES OF A V A I L A B L E S U B S U R F A C E I N F O R M A T I O N . Table A . l . Typical test hole log (T.H.#2) (after Crawford & deBoer, 1987). Depth m Assumed Elevation m Shear Strength kPa Index Properties Consolidation Triaxial Compression Fv U U wL wp w 3 -4.3 - - - 38 25 39 7 -7.3 22 17 25 27 22 42 c?'=35;cvJ"=3.1xlO"3 cm'/s cc= 0.27; cv90 = 4.4x10"3 cm2/s 11 -12.3 16 - - 34 23 44 Cc=0.43 cv90 = 2.0x10"3 cm2/s 14 -15.3 18 - - - - - <p'= 33; cc= 0.33; c / 0 = 2.1xl0"3cm2/s 23 -24.3 27 34 31 - - - Cc= 0.61; c9U = 3.0xl0"3 cm2/s c v 5 0 = 3.0xl0"3 cm2/s 26 -27.3 17 35 36 38 25 49 <p'=29; cc=0.67 cv90= 2.0x10"3 cm2/s 34 -35.3 - 9 10 31 20 36 -(Fv, L v - field, lab vane; U - unconfined compression; W L , W p - liquid, plastic limit; w -moisture content) Table A.2. Results of the CRS consolidation tests (after Crawford & Campanella, 1991). Test Depth Assumed Precons. Stress, KPa eo Cc k cv cha W No. m Elevation Casa- Cumulative cm/s cm2/s cm2/s KPa m grande Work x 10'7 x 10"3 x 10"3 12 3.0 -4.0 22 50 1.877 0.55 1.2 0.6 1.5 600 2 4.3 -5.3 50 1.292 0.29 11 4.5 -5.5 75 1.026 0.16 4000 10 5.4 -6.4 67 1.114 0.22 1.0 0.9 2.2 2200 7 6.0 -7.0 30 67 1.398 0.28 1.2 0.3 0.7 1800 6 7.5 -8.5 81 1.119 0.24 0.8 2.0 5.0 2800 4 12.1 -13.1 88 90 1.218 0.34 1.2 2.8 7.0 2400 5 12.2 -13.2 86 91 1.173 0.34 0.7 1.4 3.5 2000 14c 12.3 -13.3 96 93 1.115 0.30 0.9 2.8 7.0 2600 15c 12.3 -13.3 117 120 1.190 0.37 0.9 2.0 6.2 2600 8 15.1 - 16.1 128 131 1.389 0.52 0.9 1.5 3.7 2100 9 18.1 - 19.1 105 110 1.485 0.45 0.7 1.9 4.7 2100 Average: 1.285 0.34 1.0 1.6 4.0 2300 a - ch is assumed to be 2.5 x c v ; b - M=l/mv at average stress (a0+cjf)/2 ; c - test performed at different rate of strain 189 Appendix A. Sources of available subsurface information. Table A.3. Input parameters for the CONOIL program (after Crawford et al., 1994). Depth m Assumed Elevation m e0 kB kE Rf cv cm2/s x 10'3 Ch cm2/s x 10"3 7s kN/m3 9 deg. 0-3.6 -1.0 ... -4.6 2.0 9.3 28.0 0.6 0.9 2.2 17.8 35 3.6-8.6 -4.6 ... -9.6 1.45 14.5 43.5 0.6 2 5 17.8 35 8.6-12.6 -9.6 ... -13.6 1.2 12.7 38.0 0.6 2.8 7 17.8 35 12.6-21.6 -13.6 ... -22.6 1.52 9.4 28.0 0.6 1.7 4.2 17.8 35 Table A.4. Properties of silty clay layer estimated from in-situ tests (after Weech, 2002). Sub-Layer of Marine Silt & Clay Elevation Range(m) Plasticity Index Peak ( S u)F V (kPa) Peak SU/G VO G/su Ch (cmVs) Upper Crust -4.1 to-4.7 8 25-30 0.9 300-500 0.012 Middle Clayey Silt -4.7 to -7 10 19 0.52-0.45 300-400 0.019 Lower Silt & Clay -7 to-10 15 20-32 0.5-0.35 300-400 0.019 (surface is at elevation -1.3m) 190 Appendix B. Response of measuring equipment. APPENDIX B. RESPONSE OF MEASURING EQUIPMENT. Table B.l . Characterization of piezometers & piezo-ports response (after Weech, 2002) Piezometer (PZ) Filter Radial Distance Response During Test Pile or Elevation (r/RShaft) from Installation and (TP) Piezo-Port (PP) (m) Pile Center Dissipation TP1 PZ-TP1-1 -4.57 5.5 Poor PZ-TP1-2 -6.02 8 Poor PZ-TP1-3 -5.99 14 Good PZ-TP1-4 -5.96 25 Good PZ-TP1-5 -7.71 7.8-8.2 Fair PZ-TP1-6 -8.86 5-6 Fair PZ-TP1-7 -8.85 12-13 Good PZ-TP1-8 -8.82 11-12 Fair PZ-TP1-9 -9.80 5-6 Good TP1-PP1 -7.91 1 Good TP1-PP2 -9.01 1 Fair (poor amp setup) TP1-PP3 -9.92 1 None (poor amp setup) TP2 PZ-TP2-1 -4.61 8.0 Good PZ-TP2-2 -5.93 6.6 Good PZ-TP2-3 -5.92 16.5 Good PZ-TP2-4 -5.95 30 Good PZ-TP2-5 -7.67 7.3 Good PZ-TP2-6 -8.82 6.5 Good PZ-TP2-7 -8.77 11.2 Good PZ-TP2-8 -8.80 20 None PZ-TP2-9 -9.74 15.8 Good TP2-PP1 -7.68 1 Good TP2-PP2 -8.83 1 Delayed (1 day) TP2-PP3 -9.75 1 Delayed (7 days) TP3 PZ-TP3-1 -6.03 5.8 Excellent PZ-TP3-2 -8.84 8.1 Excellent TP3-PP -9.68 1 Fair TP4 PZ-TP4-1 -6.07 4.8 Excellent PZ-TP4-2 -8.88 6.3 , Excellent TP4-PP -9.70 1 Excellent TP5 PZ-TP5-1 -6.00 6.7 Poor PZ-TP5-2 -8.81 4.7 Poor TP5-PP -9.7 1 None TP6 PZ-TP6-1 -5.99 7.1 Poor PZ-TP6-2 -8.80 7.5 Poor TP6-PP -9.7 1 None 191 Appendix B. Response of measuring equipment. In Table B.l shown a list of all piezometers with their response ranking. An "excellent" ranking indicates the absence of any delay in the expected pore pressure response. A "good" ranking indicates that some minor time lags were observed; this might be correspond to less than perfect saturation. A "Fair" ranking indicates significant time lags in pore pressure response, due to either poor saturation of piezometers or, in case of piezo-ports, some problems on the contact of the soil and the filter. Despite that, some of the "fair" data was used to extend a database of more reliable results. A "poor" ranking indicates major time lags in the observed pore pressure response; data from the piezometers marked as "poor" were generally not used for results interpretation. Possible reasons for the poor performance were discussed in Weech (2002). 192 Appendix C. NorSand fits to drained triaxial tests on Bonnie silt. APPENDIX C. NORSAND FITS TO DRAINED TRIAXIAL TESTS ON BONNIE SILTS. Table C.l . NorSand input parameters for simulation of drained triaxial tests on Bonnie silt. VELACS Test# Ko OCR W X r H Mcrit X P kPa E kPa V CD-BS-25 1 1.5 -0.02 0.05 l 30 1.32 3.8 80 7700 0.2 CD-BS-26 1 1.5 -0.04 0.05 I 15 1.32 3.8 160 19200 0.2 CD-BS-27 1 1.5 -0.06 0.05 I 45 1.32 3.8 40 5800 0.2 CD-BS-28 1 1.5 -0.06 0.05 I 45 1.32 3.8 40 5800 0.2 CD-BS-39 1 1.5 -0.04 0.05 I 15 1.32 3.8 160 19200 0.2 193 Appendix C. NorSand fits to drained triaxial tests on Bonnie silt. 100 80 H NorSand Bonnie Silt CD BS-27 Bonnie Silt CD BS-28 10 axial strain: % 15 20 MorQanH | ^ ^ B p n n i e Silt C D E IS-27 ^ I ^ ' ' Bonnie Silt CD BS-28 10 axial strain: % 15 20 80 -r 70 -60 -50 -CO CL J £ 40 -C T 30 20 -10 -0 -Bonnie Silt C D BS-27 7 Bonnie Silt C D BS-28 0 10 20 30 40 p, kPa 50 60 Fig. C.l . NorSand simulation fit to constant p=40 kPa drained triaxial tests on Bonnie silt. 194 Appendix C. NorSand fits to drained triaxial tests on Bonnie silt. 2 H £ 1 -1 H -2 120 100 80 60 40 20 0 10 axial strain: % NorS and r ' i Bonnie Silt C D BS-25 10 axial strain: % 15 20 NorSand Bonnie Silt CD BS-25 20 40 60 p, kPa 80 100 Fig. C.2. NorSand simulation fit to constant p=80kPa drained triaxial test on Bonnie silt. 195 Appendix C. NorSand fits to drained triaxial tests on Bonnie silt. 300 Bonnie Silt CD BS-26 Bonnie Silt C D BS-39 10 axial strain: % 15 20 Bonnie Silt CD BS-39 NorSand -1 4 Bonnie Silt CD BS-26 -2 10 axial strain: % 15 20 250 200 Q-150 100 50 NorSand Bonnie Silt CD BS-39 Bonnie Silt C D BS-26 120 140 180 200 Fig. C.3. NorSand simulation fit to constantp=160 kPa drained triaxial tests on Bonnie silt. 196 Appendix D. Description of NorSandBiot coupling. APPENDIX D. DESCRIPTION OF NORSANDBIOT COUPLING. D . l . GENERAL FORMULATION. The equations of Biot (1941) incorporate the effect of coupling the pore pressure behaviour to the soil response. Biot consolidation equation for radial symmetry conditions is given in Section 4.3.2, Eq. 4.7. Separating this equation into its constitutive components, the radial equilibrium of an element (assuming no shear terms) can be written as: F, = ' dar + ar~ + dr r dr r (D.l) where Fr is the body force per unit volume. The net flow rate into an element is computed using Darcy's flow, d2u„, 1 du,. + - r.dr.dO.dz (D.2) dr1 r dr Assuming saturated soil and incompressible fluid and soil matrix, the flow into or out of the element corresponds to the change in void volume of that element. The change in void volume per unit time is given by: dV Aqr =• dt = -—(er + eXr.dO.dr.dz dt dr  r 61 _ d (du u qr~~~dt\dr+~r) .r.dO.dr.dz (D.3) Combining Eq. D.2 and D.3 gives k Y d2uw 1 du„ + -dr' r dr + • dt du u^ — + — dr r j 0 (D.4) Equation D.4 can be represented in terms of the coupled variables radial displacement ur and pore water pressure uw. Using the shape functions to describe both the displacements and fluid pressure, the equations of equilibrium and continuity equations D.l and D.4 may be rewritten after the Gallerkin process is completed in the form (Smith & Griffiths, 1998) KMu-Cuw = F (D.5) -C— -KPu =0 (D.6) dt 197 Appendix D. Description of NorSandBiot coupling. where KM is the standard element elastic stiffness matrix, KP is the fluid element "stiffness" matrix, and C are coupling matrices. Equations D.5 and D.6 can be rewritten in the following matrix form: BK = KM C -Cr KPdt (D.7) D.2. INCREMENTAL FORMULATION. Viscoplastic approach requires the coupled equations D.5 and Eq. D.6 to be solved in incremental form (Smith & Griffiths, 1998). The time domain has been approximated by a low order finite difference scheme, where it is assumed that the displacements at the nodes and the nodal pore pressures are known at two times t' and t'+l. The time interval from t' to t'+! is given by At = t'+l -1'. The displacements and excess pore pressures at these times are also denoted by the superscripts' or , + / . If equation D.5 is considered at the two times t' and t'+l KMu'-Cu'w =F' KMuM-Cu^ =FM by subtraction, KMAu - CAuw = AF where Aw = - u'; Auw = u'? -u'w; AF - F'+x - F' For small At, uM -u' = ( l _ ^ + ^ ' + l At ' dt where #is a number in the range 0 to 1. Writing equation D.6 at the two time intervals gives; dt -C -C T du' dt r duM -KPuL = 0 dt -KPu'f =0 Multiplying (D.l la) by At(l-G) and (D.l lb) by At.0 Af . 0 -0 ) C'-^-L-KPu' dt = 0 (D.S) (D.9) (D.10) (D.l la) (D.l lb) (D.l 2a) 198 Appendix D. Description of NorSandBiot coupling. At.0. .C'^—KPU1:: dt = 0 and adding the two terms in D.l2 gives At.(\-9) -C r—KPu[ dt + At.0 _cr—-KPu:x dt = 0 On rearranging the equations simplify to At.C dt dt + At.KP[(l-0)ul+0ui;l]=O The equation may be further simplified by substituting (D.10) into (D.14) gives C'[ui+] -«''] + At. KP[(\- 0)u'w + ft**1 ] = 0 and on simplifying C'Au + At.KP[u'w + 0Auw ] = 0 or -CTAu-At.KP0Au, = At.KPu' (D.12b) (D.l 3) (D.14) (D.l 5) (D.l 6) (D.17) 199 Appendix E. Verification of NorSandBiot code. A P P E N D I X E. V E R I F I C A T I O N OF NORSANDBIOT C O D E . E . l . VERIFICATION OF NORSAND FINITE E L E M E N T IMPLEMENTATION. Finite element implementation of the NorSand code was verified against direct numerical integration of the NorSand equations by simulation of a drained triaxial test. Computations of triaxial response by direct integration of the NorSand equations were performed using VBA code. Finite element analysis was run on a single finite element representing the triaxial test specimen, in which the stress-strain behaviour is defined by the NorSand model. Both analyses used the identical input parameters given in Table E. l . Table E. 1. Input parameters for triaxial test simulation. OCR X r Mcrit G MPA V m/s 1 1 -0.3 0.04 0.8 100 1.2 52.2 0.15 1 Comparison of the modelling results is shown in Fig E.l . The results show an excellent agreement between the finite element and direct integration solutions, indicating correct implementation of NorSand equations into NorSandBiot finite element code. E.2. VERIFICATION OF PREDICTIONS OF STRESS-STRAIN BEHAVIOUR DURING CAVITY EXPANSION. During cavity expansion in the soil, zone of plastic deformation is developing around the cavity, as schematically shown in Fig. E.2. A number of analytical solutions exist to predict stresses and strains inside and outside of the plastic zone for elastic-plastic models. Given the fact that no such solution is available for the NorSand model, verification of the large strain finite element implementation of viscoplasticity was conducted using simulation of cylindrical cavity expansion in Mohr-Coulomb soil. There are several criteria that can be used to verify the validity of predictions of stresses and strains induced by cavity expansion in elastic - perfectly plastic soil, among them: 1). TRESCA YIELD CONDITION. According to Tresca yield conditions - within the plastic zone: (or- <JQ) = 2su (E.l) 200 Appendix E . Verification of NorSandBiot code. 2). E L A S T I C - P L A S T I C Z O N E B O U N D A R Y . Houlsby & Withers (1988) give the large strain solution for elastic-plastic interface for the cylindrical cavity expanded from zero initial radius, in the following form: R r,.„ = (E.2) where Re - radius of expanded cavity; ree — elastic-plastic radius (see Fig. E.3); Ir=G/su - rigidity index. In our analysis cylindrical cavity is expanded from non-zero radius (the reasons are explained in Section 6.2), hence the Houlsby & Withers solution should to be updated as following: r_=r?{Rl-%V (E.3) 3). S T R E S S E S A N D STRAINS IN E L A S T I C R E G I O N . According to standard solution (Gibson & Anderson, 1961) for cavity expansion in elastic-perfectly plastic soil, elastic stress-strain relationships for cylindrical cavity is given by the following equation: " 1-v2 -v-v2' E — _ - v - v 2 1-v2 _ Hence, Radial strain: Circumferential strain: er=(ar(\-v2) + cje(-v-v2))IE ee=(ar(-v-v2) + <jg(\-v2))IE (E.4) (E.5) (E.6) According to the same solution the stresses in the elastic region for the cylindrical cavity expansion can be computed from the following equations: Radial stress: Circumferential stress: <rr = -2Gsg aa = 2Gsa (E.l) (E.8) 4). LIMIT L O A D . According to Carter et al. (1986) for cylindrical cavity expansion in simple elastic-plastic soil, for a current radius a at the cavity the limit pressure pL being applied is Pi. = 0 " M > 2\ 1 f - i ^ l-e '• V J (E.9) where ao - initial radius of the cavity. 201 Appendix E. Verification of NorSandBiot code. Theoretical solutions obtained from equations E.l , E.3, E.5, E.6, E.7, E.8 and E.9 were compared with the results of numerical simulation of cylindrical cavity expansion. To achieve consistency, the initial conditions for analytical solutions and the modelling input parameters for each individual verification case were identical. Modelling input parameters and cavity expansion particulars are presented in Table E.2. Table E.2. Input parameters and cavity expansion details for verification cases modelling. Verification cases Input parameters Cavity radius, m Ko OCR 9' ¥ c G MPA uo MPa v kh m/s initial final (1),(2),(3) 1.0 1.0 0 0 1 33.5 0 0.495 1 1 1.045 (4) 1.0 1.0 0 0 0.1 20 0 0.495 1 1 2 . The modelling results showed: • Distribution of stresses with distance away from the cavity is presented in Fig. E.4. Tresca condition is fully satisfied within the plastic (yielding) region, as shown in Fig. E.5. • The elastic-plastic interface computed using Eq. E.3 is identical with the one modelled, ree = 5.5 m (as shown in Fig. E.4). • Comparison of the theoretical solutions for strains and stresses in the elastic region with modelling results is presented in Fig. E.6 and Fig. E.7. The results are in excellent agreement. • Modelled radial stress at the cavity wall is in a very good agreement with the theoretical predictions, as shown in Fig. E.8. E.2. VERIFICATION OF PORE PRESSURE PREDICTIONS. Schiffman (1958) proposed an extension to the Terzaghi theory of consolidation to include the Biot coupling terms. One of the proposed improvements was the ability to account for variable loading during the consolidation process. For the case when soil mass is loaded with a construction loading that is linear in time until the end of construction and is constant thereafter (as shown in Fig. E.9), Schiffman (1960) developed an analytical solution for excess pore pressure dissipation: For consolidation during linear loading, when 0 < T < T0: f z ^ — J u 1 ( - \ 202 H (E.10) Appendix E. Verification of NorSandBiot code. For consolidation at constant loading, when T0 < T < oo : u0 {H 1 u0^H — ,T-Tn (E.ll) where — (z) = if H 2 u0 n „ = i ) 3 , 5 " 2 ti Theoretical solutions obtained by Schiffman (1958) were compared with the pore pressure dissipation after cavity expansion. The problem was modelled as a plain strain "odometer" specimen subjected to vertical loading. At initial stage of the modelling the loading was applied and then held constant so that generated excess pore pressures could dissipate. The modelling input parameters are presented in Table E.3. Table E.3. Input parameters for modelling. Ko OCR c G MPA V k„ m/s 1.0 1.0 0 0 0 1 0 1 Comparison of theoretical and modelled pore pressures, presented in Fig. E.10, showed a very good agreement. 203 Appendix E. Verification of NorSandBiot code. Fig. E. l . Comparison of simulations of drained triaxial test with NorSand finite element code (model) and direct integration of NorSand equations. 204 Appendix E. Verification of NorSandBiot code. Fig. E.2. Soil element during cavity expansion (modified after Vesic, 1972). before expansion elastic zone Fig. E.3. Development of elastic/plastic boundary during cavity expansion (modified after Houlsby & Withers, 1988). Distance from cavity center, m — Model Radial Stress — Model Circumferential Stress Fig. E.4. Distribution of stresses resulted from cylindrical cavity expansion. 205 Appendix E. Verification of NorSandBiot code. 2.5 2H 6 1.5 0.5 H plas i I tic z< me -> <-e asti : zoi te I i i cavity w all i i . i i ! 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Distance from cavity center, m Fig. E.5. Validation of Tresca condition. 0.002 0.0015 0.001 0.0005 0 •0.0005 -0.001 •0.0015 -0.002 lastic zone \ s g £ ( ( S k 1 ft 0 5 1 >* 5 2 k < 0 2 J 5 3 i— —f i 0 3 i- ——& 5 40 9 i i 11 Distance from cavity center, m -o— Model Radial strain x Theoretical Radial Strain —•— Model Circumferential Strain - - - E J - - Theoretical Circumferencial Strain Fig. E.6. Comparison of theoretical and computed radial and circumferential strains in the elastic zone. 206 Appendix E. Verification of NorSandBiot code. ra CL Vt w 4-1 CO 1.5 1 0.5 -0.5 -1.5 elastic zone ®"l .ra.— {3 B~ |5 20 25 Distance from cavity center, m 30 40 Model Radial Stress Theory Radial Stress -•- Model Circumpherential Stress <§> Theory Circumpherencial Stress Fig. E.7. Comparison of theoretical and computed radial and circumferential stresses in the elastic zone. 20 40 60 Strain, % 80 100 Fig. E.8. Comparison of theoretical and computed radial stresses at the cavity wall. 207 Appendix E. Verification of NorSandBiot code. u« 0 T'Ct/H* T**CVH* R s Uo/!» SAND u * Imposed Excess Pore Pressure uo = initio! Eicsss Port' Pretsure C 6 Coefficient Of Conwlidction T * Time Factor Fig. E.9. One-dimensional consolidation under construction loading (modified after Schiffman, 1958). 5 0.5 0.01 0.1 10 Time factor, T Fig. E.10. Comparison of NorSandBiot simulated pore pressure response with Schiffman solution (1958). 208 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation APPENDIX F. COUPLED MODELLING OF OBSERVED PORE PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION 1 A. M. Vyazmensky, University of British Columbia, Vancouver D. A. Shuttle, University of British Columbia, Vancouver J . A. Howie, University of British Columbia, Vancouver A B S T R A C T The ability of conventional design approaches to predict pile capacity is unreliable at best. Understanding the generation and evolution of pore pressures and associated effective stress during, and following, pile installation is a first step to improved design approaches. In this study, a fully coupled large strain cylindrical cavity expansion numerical model is used with the NorSand critical state soil model to show that conventional site investigations typically do not provide enough information to constrain the predicted pore pressures. It is also shown that the different parameter assumptions result in a very different evolution of lateral effective stress, even for initially quite similar pore pressures at the pile wall. Given the importance of lateral effective stress on the predicted pile capacity, this may explain why pile capacity is so difficult to predict accurately. R E S U M E L'habilite des approches conventionnelles de calcul pour prevoir la capacite de pile est incertaine au mieux. La comprehension de la generation et de 1'evolution des pressions de pore et des contraintes effectives associes pendant, et apres I'installation de pile, est une premiere etape aux approches de calculs ameliores. Dans cette etude, un modele numerique d'expansion de cavite cylindrique completement couple a grande deformations est employe avec le modele de sol d'etat critique NorSand pour prouver que les investigations conventionnelles de sites, typiquement ne fournissent pas assez d'informations pour contraindre les pressions de pore prevues. On montre egalement que les differentes suppositions de parametre ont comme consequence une evolution tres differente des contraintes effectives laterales, meme pour les pressions de pore au debut tout a fait semblables, au mur de pile. Etant donne l'importance des contraintes effectives laterales sur la capacite prevue de pile, ceci peut expliquer pourquoi la capacite de pile est si difficile de prevoir exactement. 1. INTRODUCTION Helical piles are gaining popularity in North America as an alternative foundation solution to traditional driven and jacked piles. According to the pile manufacturers' these piles have several distinctive advantages over traditional driven and jacketed piles: they mobilize soil resistance both in compression and uplift; they are quick and easy to install without vibration, and no heavy equipment is required for installation of small diameter piles. It is also possible to install them inside buildings and helical piles are reusable. To date, research efforts in the field of helical piles have concentrated on their lateral and uplift capacity. This is understandable as current design methods used to predict pile capacity are unreliable and require the use of large factors of safety. This lack of design accuracy is explicitly recognized by Eurocode 7 (1997). Eurocode 7 requires that all pile installations be checked by a representative pile test. At a recent symposium on pile design (Ground Engineering, 1999) had the participants provide a prediction of the capacity of a single driven steel pile. The general success rate was very poor with only 2 or 16 teams getting within 2 5 % of the correct capacity. And the best prediction of the pile's capacity was obtained from compensating errors; a too low lateral capacity was balanced by a too high end bearing. This lack of predictive capacity in pile design was also recognized by Randolph in his Rankine lecture (2003). One important factor controlling a pile's capacity is the long term effective stress at the pile-soil interface. 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 understand and predict the evolution of effective stress and pore pressure at the pile wall would provide a basis for accurate pile design. A recent field study of helical pile performance carried out by Weech (2002) at the Colebrook site in Surrey, British Columbia, provides quality data on the pore pressure regime during and after helical pile installation. Weech installed six instrumented, full-scale helical piles in soft, sensitive, marine silt and clay soil. He monitored the excess pore pressures within the soil surrounding the piles 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. The measured pore pressure distribution with normalized distance r/R (=radius/ pile shaft radius) is shown in Figure 1, overlain on data from other sites compiled by Levadoux and Baligh (1980). It should be noted that data from the Colebrook site is atypical, showing lower normalized excess pore pressure. This may be attributed to the effect of the helices or unusual site properties. 1 Submitted to 57th Canadian Geotechnical conference in Quebec City. 209 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation N O R M A L I Z E D R A D i U S , r/R Figure 1: Distribution of Au/c/vo with distance measured by Weech (2002) and reported by Levadoux & Baligh (1980) 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 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 distribution of excess pore pressures was also monitored on the piezometers and piezo-ports during load testing. It is difficult to explain the complex soil response observed at the Colebrook site based solely on interpretation of the field measurement. This paper uses a numerical approach to investigate the pore pressures and stresses induced during, and following, helical pile installation. Of particular interest is whether the predicted pore pressure is well constrained based on the properties typically measured during a well performed site investigation. Additionally, we examine whether the time evolution of the lateral effective stress at the pile wall is well constrained for reasonable soil parameters, with reasonable dissipation response. 2. MODELLING APPROACH 2.1 Overview 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 and Shuttle, 2002), is adopted here. Although its name suggests sand, NorSand is a generalization of the well-known Cam Clay model with a specific capability of realistically representing soil dilatancy. NorSand achieves realistic dilatancy by separating the yield surface from the critical state by a distance in void ratio space defined by the state parameter, ¥. Overconsolidation exists within NorSand in the usual sense, expressed as a ratio R = p'max/p', where p' is the mean normal effective stress. In effect, a zone of elastic behaviour can be defined using R with ¥ controlling subsequent plastic yielding. Most of the NorSand parameters are familiar and will be discussed below. In order to predict the changes in stresses and pore pressure under partially drained conditions, an analysis which accounts for the coupling between the rate of loading and the generation of fluid pressures is required. Undrained conditions are not assumed and the pore fluid is free to migrate. The equations of Biot (Biot, 1941) incorporate the effect of coupling the pore pressure behaviour to the soil response. 2.2 Geometric Idealization During pile installation soil in a region around the pile tip undergoes extensive disturbance and remoulding. Model studies of the displacement pattern in this region have shown that the displacements are between the deformation patterns caused by the expansion of a spherical cavity and a cylindrical cavity (Clark and Meyerhof, 1972; Roy et. al., 1975). 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). Randolph et al. (1979b) report measurements of the radial movement of soil near the mid-depth of the pile, taken from model tests and field data, showing measured radial displacements that agree very well with theoretical predictions, based on the assumption of plane strain and cylindrical deformation at constant volume. This indicates that the stress changes in the soil over much of the length of the pile shaft (ignoring the regions close to the ground surface and to the pile tip) can be adequately approximated by cylindrical cavity expansion. If for soil penetration by the helical pile shaft, cylindrical cavity expansion is an obvious analogy, modelling of the helical plates installation is a much more complex process and requires 3-D simulation. However, in this paper we are interested in variability of the pore pressures and lateral stresses, and therefore this effect has been ignored. 2.3 NorSand Input Parameters As described in Section 2.1, NorSand is a generalized Cambridge-type constitutive model developed from the fundamental axioms of critical state theory and experimental data on sands. NorSand has seven material properties (see Table 1): r, X. describe the familiar semi-log approximation to the critical state locus in void ratio, e - p' space; elasticity is described by an elastic shear modulus, G and constant Poisson's ratio, u; M tc (the value of ratio q/p' at the critical state in triaxial compression, qtc= oi'-a3'). Hm 0d and x are the plasticity properties. Of these properties, only Hmod and % are unfamiliar. Hm 0d is a dimensionless 210 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation plastic modulus, akin to lr (= G/p') but for the plastic strains. It arises because NorSand decouples the yield surface from the CSL and consequently X-K can no longer serve as the plastic compliance as it does in Cam Clay. Dilation in NorSand is proportional to vy, and X is the proportionality coefficient. The initial density of the soil is represented by the state parameter, defined as the difference between the current void ratio and the critical void ratio (e - ec) at the same mean effective stress. Additionally, for a partially drained analysis, the radial hydraulic conductivity of the soil, kr, is also required. Table 1. NorSand parameters. Par. Description Merit critical stress ratio r intercept of the CSL at 1 KPa mean stress k slope of CSL in e-ln(p) space X volumetric coupling parameter, function of fabric Hmod hardening parameter G elastic shear modulus u Poisson coefficient 2.4. Finite Element Formulation In a saturated soil, when free drainage conditions prevail, the steady state pore-fluid pressures depend only on the hydraulic conditions and are independent of the soil skeleton response to the external loads. In these circumstances a single phase continuum description of soil behaviour is adequate. Similarly, a single phase description is also adequate when no drainage occurs. However, under intermediate boundary conditions in which some flow can take place, there is an interaction between the skeletal strains and the pore fluid flow through the voids. To analyse this situation accurately requires that soil behaviour be analyzed by incorporating the effect of transient flow of the pore-fluid through the voids. Such a theory was developed by Biot (1941). Biot's theory accounts for solid-to-fluid and fluid-to-solid coupling, where: solid-to-fluid coupling occurs when a change in applied stress produces a change in fluid pressure or fluid mass; 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. For the radial symmetry used in these analyses, the Biot governing equation is given by; K' dr r dr a a where; K' Yw Uw kr P In these analyses both water and the soil particles are assumed to be incompressible, thus all volume change = bulk modulus of the soil [kN/m ] = unit weight of water rkN/m3] = pore pressure [kN/m ] = radial hydraulic conductivity [m/s] = mean total stress [kN/m2] is the result of a change in the void ratio. Early objections to the assumption of a constant coefficient of consolidation, cv, in the Biot formulation are irrelevant with modern numerical approaches in which soil properties can vary every increment (Smith and Hobbs, 1976). The pile installation was modelled as purely radial, using a large strain elasto-plastic finite element code. By representing the helical pile in only the radial dimension the code could be streamlined to minimize simulation time. An incremental viscoplastic formulation was used to represent plasticity (Zienkiewicz and Cormeau, 1974). 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). Biot coupling was implemented using the structured approach described in Smith and Griffiths (1997). 3. ESTIMATION OF NORSAND INPUT PARAMETERS 3.1 Overview of Investigations Three subsurface investigations were performed at, or close to, the helical piles performance research site. The first investigation was undertaken by the British Columbia Ministry of Transportation and Highways (MoTH) in 1969 prior to construction of the Colebrook Road overpass. 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. Additionally, 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. The second study by Crawford and Campanella (1991) reports 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 tests (CPTU) and a flat dilatometer test (DMT). Laboratory tests were limited to constant rate of strain odometer consolidation tests on specimens obtained with a piston sampler. The most recent investigations were undertaken by Dolan (2001) and Weech (2002) as a part of study of helical pile performance in soft soils at the Colebrook site. 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. 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 velocity measurements (SCPT). These site investigations provided many, but not all, of the input parameters required for the NorSand critical 211 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation state soil model. However, the major difficulty in deriving 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. Due to space limitations it is not possible to provide a full explanation of the parameter derivation. A summary is given in the following sections, and full details are provided in Vyazmensky (2004). 3.2 Estimates of Initial State A profile of vertical effective stress was established based on an average unit weight of the silty clay layer of 17.8 kN/m3, estimated from index tests performed by Dolan (2001). For the range of elevations where the pore pressure changes due to pile installation were measured, from -4.57 to -9.92 meters, o'vo increases from 32.9 to 75.7 kPa. The average o'vo of 54.3 kPa is used in these analyses. The profile of equilibrium pore water pressure was established based on piezometer measurements taken prior to helical pile installation. The pore pressure measurements indicate artesian conditions, and can be described by the following equation: u0(kPa)=-10.2(Elevation)-7.1. For the range of elevation from -4.57 to -9.92 meters, uo increases from 39.5 to 94.1 kPa. The coefficient of lateral earth pressure, Ko, was estimated based on empirical correlations developed for interpretation of CPT test data. K0 for the silty clay layer varies primarily within a range of 0^ 56 to 0.76. The midrange K0 of 0.66 was assumed for these analyses. OCR profiles were interpreted from CPT soundings by Weech (2002), and estimated from the consolidation tests performed during MoTH (1969) and Crawford and Campanella (1991) investigations. A mid-range value of OCR derived from CPT and laboratory data is 1.7. The initial state, vy, of the silty clay layer is unknown, and the absence of triaxial test data complicates its assessment. Hence, the state has been estimated based on the stress history of the soil. The Colebrook site is lightly overconsolidated over most of the elevations of interest, consistent with a relatively loose soil state. Additionally, the shear vane testing indicates a low undrained shear strength and highly sensitive response. Using the NorSand constitutive model, a sensitive response is only possible with positive (i.e. loose of critical state) values of state. Therefore a very loose range of \\i = -0.02 to +0.16 is assumed, with +0.08 as a best estimate. 3.3 NorSand Parameters In the absence of triaxial testing, the NorSand specific soil properties were the most difficult to estimate. Two elastic properties, G and u, are needed. Values of Gmax are available from seismic cone measurements, with the input value of G inferred by Weech (2002) being used for the best guess. No data are available on a Poisson's ratio for the silty clay layer For most soils Poisson's ratio, u, is within a range 0.1 to 0.3. The current analysis uses u=0.2 as the best estimate. Crawford and deBoer (1987) quote a friction angle, <)>', for the silty clay layer in the range 33° to 35°. Although not stated, it is assumed that these values are peak values. Assuming a very loose soil gives <t>'Cv of the order of 31 ° to 33°, and Merit in the range 1.24 to 1.33. A value of Mem = 1-24, corresponding to <|>'cv = 31°, was used for the Reference case. The model property, x. is a function of fabric, and typically does not vary significantly for different soils (Jefferies and Been, 2005). In the absence of more detailed information it is often taken as 3.5. In the current modelling, a range of x = 3.0 to 4.0 is assumed. In the absence of triaxial data, the slope of the critical state line, A, in e-ln(p') space may be estimate from an empirical relationship involving the plasticity index, PI. Schofield and Wroth (1968) found the relationship between PI, specific gravity, Gs, and slope of the critical state line, X to be X = PI Gs /160. Assuming Gs equal to 2.75 and given that plasticity index for the silty clay layer varies from 7.6% to 21.1%, X is in the range 0.13 < X < 0.362. This range is large, but is in a good agreement with the range, 0.08 < X < 0.363, reported by Allman and Atkinson (1992) for Bothkennar silty clay. For modelling purposes the lower bound of X was extended to enable representation of the sensitive behaviour observed from shear vane testing, r is back-calculated from the measured void ratio and credible state range. The final NorSand parameter, hardening modulus, Hmod, is typically the most difficult property to estimate in the absence of element test data. A fairly soft response, Hmod = 100 was used as the best estimate. The modelled pore pressures generated during pile installation are insensitive to the value of kr assumed as the installation is quick. For the dissipation analyses, however, a value of kr is also required. This paper assumes a value of 10" m/s, uncorrected for direction, in the middle of the range suggested by Crawford and Campanella (1991). Table 2. Reference and Best Fit NorSand Parameters Par.. Ref. Case Range Best Fit Units G 7.8 5.8 - 9.8 7.8 MPa V 0.2 0.1 -0.3 0.3 -OCR 1.7 1.45-2.2 1.45 -Ko 0.66 not varied 0.66 -Merit 1.24 1.24-1.33 1.33/1. c -X 3.5 3.0-4.0 O 3.5 -0.08 -0.02-0.16 0.16 -X 0.212 0.07 - 0.362 0.08 e-ln(p) r 2.04 related to e 1.55 @1kPa Hmod 100 50 - 450 200 -A reference case (see Table 2), based on mid-range values of the parameters, is used as the startina point 212 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation for this modelling. A second parameter set, derived by fitting the model to the pore pressure distribution at the end of installation, is also given in Table 2. 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. The fit can also be improved by allowing wider flexibility in the parameter ranges. The predicted consolidated undrained triaxial response for the Reference and Best parameter sets are shown in Figures 2 and 3 respectively. The base case properties do not produce a sensitive soil response. The Best Fit is sensitive (St ~ 4.6), although of much lower sensitivity than indicated from shear vane testing. Two values of Merit are shown in Table 2. The lower gives a closer fit to the measured pore pressure. The higher value used for Figure 3 is outside of the reasonable range, but gives an undrained shear strength and pore pressure at the pile wall following installation closer to the Reference case. Figure 4 compares the pore pressure distribution measured at the end of pile installation with those predicted by the Reference and Best simulations. For both of the numerical fits, the field measured pore pressures are lower at the pile and extend further into the surrounding soil. 45 40 S. 35 br 30 3 25 2 % 20 .1 15 4 3 10 T J 5 0 -NorSand 4 6 8 axial strain: % 10 12 60 -i 50 -40 -IB 0_ 30 -je t f 20 10 -0 -- NorSand CSL 10 20 30 p, kPa 40 50 Figure 2: CU Triaxial Response for Reference Parameters 2 3 axial strain: % Figure 3: CU Triaxial Response for Best Parameters Figure 4: Comparison of Weech (2002) measured Au/rj'vo vs. distance with Reference and Best Fit Results The Reference case predicts too high pore pressures between the pile wall and the edge of the helices. Beyond the helices the measured and predicted trends are approximately parallel until r/RShatt exceeds 20, when the modelled pore pressures reduce more quickly. If a Merit value in the middle of the parameter range had been assumed, rather than the minimum, the pore pressures between r/RShaft of 4 and 20 would match for the Reference case. The Best Fit was biased towards achieving a flatter pore pressure distribution between the pile wall and the 213 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation helices' edge. This was achieved primarily by reducing X to obtain a sensitive soil response and increasing \y to make the soil more contractive. Although the two numerical simulations have very similar peak undrained shear strengths the lateral effective stresses at the end of installation are quite different; 54.5 kPa and 13.5 kPa for the Reference case and Best case respectively. 4. COMPARISON OF MODEL WITH MEASURED PORE PRESSURE DISSIPATION 4.1 Pore pressures The pore pressure dissipation measured at the pile wall is compared with those predicted using the Reference and Best case parameter sets in Figures 5 and 6. Figure 5 plots the excess pore pressure normalized by the vertical effective stress. Figure 6 normalizes by the excess pore pressure at the end of expansion (i.e. elapsed time = 0), giving a measure of the inferred percentage dissipation at the pile. Figure 5 shows both simulations provide reasonable estimates of the pore pressure (e.g. Au/o'vo <0.2) at the wall for times greater than 10 minutes. The Best case is closer to the measured values at early time, and gives a better estimate of the percentage dissipation. This is to be expected as the lower gradient at the pile wall under field and Best case conditions affects dissipation rates. -Field Data between Helices - Reference Case - Best Case 100 1.000 Elapsed Time (mins) Figure 5 : Comparison of Weech (2002) measured Au/a'vo vs. time with Reference and Best Fit Results 4.2 Lateral Effective Stresses The magnitude of the pore pressure measured at the pile wall during installation could be expected to affect the long term stresses at the pile. Figure 4 shows a large difference between the end of installation pore pressures for the Reference and Best cases. Therefore, in order to make the comparison between the simulations clearer, the Best Case parameters were adjusted, to make the pore pressure at the pile wall closer to that predicted by the Reference case. This was achieved by increasing Merit to 1.5. This change does not change the shape of the pore pressure response with distance, and increases the peak undrained shear strength of the soil closer to that of the Reference case. Figure 7 compares the evolution of pore pressure and lateral effective stress with time for both of the Best simulations. The figure shows the difference in effective stress against the pile is insensitive at small elapsed times. If the pore pressures from revised Best case are plotted on Figure 6, the response is indistinguishable from the original Best case. &u/uQ 0.6 — Field Data between Helices - - Reference Case -Best Case 100 1,000 Elapsed Time (mins) Figure 6 : Comparison of Weech (2002) measured Au/uo vs. time with Reference and Best Fit Results Field Data between Helices Best Case Best Case with higher M 100 1,000 Elapsed Time (mins) Figure 7 : Comparison of Au/ a'vo and a'v / o'vo vs. time for Best Fit (Merit = 1.33) and Revised Best Fit (Mem = 1.50) Simulations Reference Case - Best Case with high M Elapsed Time (mins) Figure 8 : Comparison of Au/ a'vo and a\ I a'vo vs. time for Reference and Revised Best Fit (Merit = 1.50) Simulations 214 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation Pile design methods in fine grained soils are typically based on undrained shear strengths. The peak undrained shear strength of the two soils shown in Figure 8 is quite similar. However, it is clear that although the pore pressures generated are similar, the evolution of lateral effective stress is very different. At the end of pile installation, the Reference case has a normalized lateral effective stress at the pile wall of 0.978. The corresponding normalized lateral effective stress at the pile wall for the Best case is only 0.265; a factor of 3.7 difference. Over the next week (10,000 mins) the pore pressures dissipated and the effective stresses increased. During this time the Reference case normalized pore pressures fell by 2.04 and the normalized lateral stresses increased by 1.01 to 1.99, corresponding to 50% of the pore pressure reduction being translated into effective stresses. At the end of the simulation the vertical effective stress had increased from 54.3 to 75.1 kPa. Over the same time period the Best case normalized pore pressures fell from 1.79 to 0.08, a fall of 1.71, and the lateral stresses increased from 0.27 to 1.12, an increase of 0.85. Like the Reference case, this corresponds to 50% of the pore pressure reduction being translated into lateral effective stress. The Best case simulation predicts a vertical effective stress at the end of the simulation of 44.5 kPa. For very similar peak undraiiied shear strengths prior to installation, the final lateral effective stresses on the pile were very different. The Base case stress was 108 kPa and the Best case stress was 60 kPa, a factor of 1.8 difference, a much lower reduction than would be attributed to sensitivity. It is worth noting that these simulations cause stress changes and yield in the vertical direction, even though no vertical strain is allowed. Most analytical solutions do not account for out of plane yielding, and hence may give slightly different results even for simple soil models such as Tresca and Mohr-Coulomb. 5. DISCUSSION AND CONCLUSIONS The results presented in this paper form a small part of a numerical study (Vyazmensky, 2004) to improve our understanding of the time dependent behaviour of helical piles in silty soils; specifically focused on changes in pore pressure and how this influences pile capacity. The results presented in this paper highlight the difficulties in designing piles based on standard site investigations. All three site investigations close to the site were of good to excellent quality. Despite the quality of the investigations, wide variations exist between the laboratory and in situ derived values. This is not unusual at silty soil sites where undisturbed sampling is difficult. Additionally, some critical model parameters were not explicitly measured. These include two parameters commonly used by numerical models, iy and Hmod. State parameter (similar to relative density in purpose) was inferred from the geology. Hm 0d is a NorSand specific parameter, but all plasticity models assume some relationship between the expansion/ contraction of the yield surface with plastic strain. Unfortunately, this parameter is sensitive to sampling disturbance and difficult to obtain in situ. The effect of this parameter uncertainty had a large effect on the predicted pore pressures (e.g. Figure 5). 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 (Figures 6 and 8). This is the case, even for smaller differences in the input parameters. It is therefore not surprising that the ability of the geotechnical community to predict pile capacity based on standard site investigations is poor, and that so much of pile design is empirically, or local experience, based. Despite the difficulties, numerical modelling remains an important tool for testing hypotheses of pile behaviour and has the potential to move pile design from the empirical to a true application of engineering mechanics. The next stage is to see whether pile capacities inferred from numerically calculated lateral stresses provide an improved estimate of the pile capacity measured at the Colebrook site. 215 Appendix F. Coupled modelling of observed pore pressure dissipation after helical pile installation 6. REFERENCES Allman, M. A. and Atkinson J. H. 1992. Mechanical properties of reconstituted Bothkennar soil, Geotechnique 42 (2): pp. 289-301. Biot M.A. 1941. General theory of three-dimensional consolidation. Journal of Applied Physics, Volume 12, February, pp155-164. British Standards Institution. 1997. Eurocode 7: Geotechnical design. Clark, J.I. and Meyerhof, G.G. 1972. The Behaviour of Piles Driven in Clay. An Investigation of Soil Stress and Pore Water Pressure as Related to Soil Properties. Canadian Geotechnical Journal, 9, No. 3, 351-373. Crawford, CB. and Campanella, R.G. 1991. Comparison of Field Consolidation with Laboratory and In Situ Tests. Canadian Geotechnical Journal, Vol. 28, pp. 103-112. Crawford, CB. and deBoer, L.J. 1987. Field Observations of Soft Clay Consolidation in the Fraser Lowland. Canadian Geotechnical Journal, Vol. 24, pp. 308-317. Dolan, K. 2001. An in-depth Geological and Geotechnical Site Characterization Study, Colebrook Road Overpass, Highway 99A, Surrey, B.C. B.A.Sc. Thesis, University of British Columbia, Vancouver, B.C. Ground Engineering. 1999. Uncertainty Principle. Ground Engineering, November, pp. 32-34. Jefferies, M.G. 1993. NorSand: A simple critical state model for sand. Geotechnique 43 (1), pp. 91 -103. Jefferies, M. G. and Shuttle, D. A. 2002. Dilatancy In General Cambridge-Type Models, Geotechnique 52 (9), pp. 625-638. Jefferies, M.G. and Been, K. 2005. Soil liquefaction: a critical state approach. In press, publisher Spon Press. Levadoux, JN, and Baligh, M.M. 1980. Pore Pressures During Cone Penetration in Clays, Research Report R80-15, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts. Randolph, M. F. 2003. Science and Empiricism in Pile Foundation Design. Geotechnique 53 (10), pp. 847-875. Randolph, M. F., Steenfelt, J. S. and Wroth, C, P. 1979a. The Effect of Pile Type on Design Parameters for Driven Piles. Proceedings, Seventh European Conference on Soil Mechanics Foundation Engineering, Vol. 2, pp. 107-114. Randolph, M. F., Carter, J. P. and Wroth, C. P. 1979b. Driven Piles in Clay - the Effects of Installation and Subsequent Consolidation. Geotechnique, 29 (4), pp. 361-393. Roy, M., Blanchet, R., Tavenas, F.A., Leroueil, S. and La Rochelle, P. 1975. The interpretation of static cone penetration tests in sensitive clays. Proceedings of European Symposium on Penetration Testing, Stockholm, 2.1, 323-331. Schofield, A. and Wroth, P. 1968. Critical State Soil Mechanics. McGraw-Hill, London. Shuttle, D.A. 2004. Implementation of a Viscoplastic Algorithm for Critical State Soil Models. Accepted for publication in the Ninth International Symposium on Numerical Models in Geomechanics (NUMOG IX), Ottawa, 25-57 August 2004. Smith, I. M. and Hobbs, R. 1976. Biot analysis of consolidation beneath embankments. Geotechnique 26 (1); pp 149-171. Smith, I.M. and Griffiths, D.V. 1997. Programming the Finite Element Method, 3rd Edition. John Wiley and Sons; ISBN: 047196543X. Vyazmensky, A.M. 2005. Numerical modelling of time dependent pore pressure response induced by helical pile installation, M.A.Sc. thesis, University of British Columbia. Weech, CN. 2002. Installation and Load Testing of Helical Piles in a Sensitive Fine-Grained Soil, M.A.Sc. Thesis, University of British Columbia. Zienkiewicz, 0. C. and Cormeau, I. C. 1974. Viscoplasticity, plasticity and creep in elastic solids. A unified numerical approach. International Journal of Numerical Methods in Engineering, Vol. 8, pp. 821-845. 216 

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