NUMERICAL MODELLING OF TIME DEPENDENT PORE PRESSURE RESPONSE INDUCED BY HELICAL PILE INSTALLATION ALEXANDER M. VYAZMENSKY

Transcription

1 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

2 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 k r. 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

3 Table of contents. TABLE OF CONTENTS. ABSTRACT...ii TABLE OF CONTENTS...iii LIST OF TABLES...vii LIST OF FIGURES...viii ACKNOWLEDGEMENTS...xiii 1.0. INTRODUCTION CHALLENGES IN AXIAL PILE CAPACITY PREDICTIONS IN SOFT FINE-GRAINED SOILS HELICAL PILES PURPOSES AND OBJECTIVES OF RESEARCH SCOPE AND LIMITATIONS OF STUDY THESIS ORGANIZATION OVERVIEW OF FIELD STUDY OF HELICAL PILE PERFORMANCE IN SOFT SENSITIVE SOIL INTRODUCTION SCOPE OF WEECH'S STUDY SITE SUBSURFACE CONDITIONS SITE STRATIGRAPHY SOIL PROPERTIES FIELD INVESTIGATION BY MINISTRY OF TRANSPORTATION AND HIGHWAYS RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (1) RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (2) HELICAL PILES AND PORE PRESSURE MEASURING EQUIPMENT TEST PILES GEOMETRY AND INSTALLATION DETAILS MEASURING EQUIPMENT SUMMARY OF WEECH S STUDY RESULTS PORE WATER PRESSURE RESPONSE DURING HELICAL PILE INSTALLATION PORE WATER PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION SUMMARY LITERATURE REVIEW INTRODUCTION iii

4 Table of contents PORE PRESSURE RESPONSE INDUCED BY PILE INSTALLATION INTO FINE GRAINED SOIL AND ITS INFLUENCE ON PILE CAPACITY FIELD GENERATION OF EXCESS PORE PRESSURE FIELD DISSIPATION OF EXCESS PORE PRESSURE OBSERVED AXIAL PILE CAPACITY AS FUNCTION OF DISSIPATION OF EXCESS PORE PRESSURE PREDICTION OF TIME-DEPENDENT PORE PRESSURE RESPONSE PREDICTION METHODS BASIC CONCEPTS BEHIND EXISTING PREDICTION SOLUTIONS MODELLING ANALOGUE FOR SIMULATION OF PILE OR CONE PENETRATION MODELLING FRAMEWORK OVERVIEW OF EXISTING PREDICTION SOLUTIONS CAVITY EXPANSION SOLUTIONS SOLUTIONS BASED ON STRAIN PATH METHOD SUMMARY FORMULATION OF MODELLING APPROACH INTRODUCTION MODELLING APPROACH TO SIMULATION OF HELICAL PILE INSTALLATION INTO FINE GRAINED SOIL MODELLING FRAMEWORK MODELLING PROCEDURE FOR SIMULATION OF HELICAL PILE INSTALLATION NORSANDBIOT FORMULATION NORSAND CRITICAL STATE MODEL MODEL DESCRIPTION MODEL PARAMETERS BEYOND SAND BIOT COUPLED CONSOLIDATION THEORY FINITE ELEMENT IMPLEMENTATION OF NORSANDBIOT FORMULATION FINITE ELEMENT CODE VERIFICATION SUMMARY SELECTION OF SITE-SPECIFIC SOIL PARAMETERS FOR MODELLING INTRODUCTION SOIL PARAMETERS FOR MODELLING ELASTIC PROPERTIES G, ν iv

5 Table of contents OVERCONSOLIDATION RATIO OCR COEFFICIENT OF LATERAL EARTH PRESSURE K HYDRAULIC CONDUCTIVITY DERIVATION COEFFICIENT OF CONSOLIDATION COEFFICIENT OF VOLUME CHANGE, m v RADIAL HYDRAULIC CONDUCTIVITY, k r VERTICAL EFFECTIVE STRESS σ vo AND EQUILIBRIUM PORE PRESSURE u o NORSAND MODEL PARAMETERS DERIVATION CRITICAL STATE COEFFICIENT, M crit STATE DILATANCY PARAMETER, χ HARDENING MODULUS, H mod SLOPE OF CRITICAL STATE LINE, λ INTERCEPT OF CRITICAL STATE LINE AT 1 KPA STRESS, Γ STATE PARAMETER, ψ NORSAND PARAMETERS ANALYSIS SUMMARY NORSAND-BIOT CODE PARAMETRIC STUDY INTRODUCTION MODELLING PARTICULARS REFERENCE RESPONSE PARAMETRIC STUDY SCENARIOS PARAMETRIC STUDY RESULTS INFLUENCE OF COEFFICIENT OF LATERAL EARTH PRESSURE INFLUENCE OF MEASURES OF SOIL OCR INFLUENCE OF ELASTIC PROPERTIES INFLUENCE OF CRITICAL STATE LINE PARAMETERS INFLUENCE OF HARDENING MODULUS INFLUENCE OF STATE DILATANCY PARAMETER INFLUENCE OF HYDRAULIC CONDUCTIVITY CONCLUDING REMARKS ON PARAMETRIC STUDY RESULTS SUMMARY MODELLING OF PORE PRESSURE CHANGES INDUCED BY PILE INSTALLATION IN 1-D v

6 Table of contents INTRODUCTION D SIMULATIONS STAGE I. MODELLING OF HELICAL PILE INSTALLATION AS SINGLE CAVITY EXPANSION COMPARISON OF MODELED AND FIELD PORE PRESSURE RESPONSES NORSANDBIOT BEST FIT WITH FIELD DATA STAGE II. MODELLING OF HELICAL PILE AS SERIES OF CAVITY EXPANSIONS DETAILS OF HELIX MODELLING EFFECT OF CAVITY EXPANSION/CONTRACTION CYCLING ON PORE PRESSURE RESPONSE IMPLICATIONS FROM 1-D MODELLING PREDICTED VERSUS MEASURED/INTERPRETED PORE PRESSURE RESPONSE FROM PORE PRESSURE RESPONSE PREDICTIONS TO PILE BEARING CAPACITY SUMMARY CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY SUMMARY AND CONCLUSIONS RECOMMENDATIONS FOR FURTHER RESEARCH LABORATORY STUDY D NUMERICAL MODELLING REFERENCES NOTATION APPENDIX A. SOURCES OF SUBSURFACE INFORMATION FOR COLEBROOK SITE APPENDIX B. PIEZOMETERS RESPONSE APPENDIX C. VALIDATION OF NORSAND MODEL AGAINST BONNIE SILT APPENDIX D. NORSAND-BIOT COUPLING APPENDIX E. NORSAND-BIOT CODE VERIFICATION APPENDIX F. COUPLED MODELLING OF OBSERVED PORE PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION (PAPER) vi

7 List of tables. LIST OF TABLES TABLE PAGE 2.1. Average index properties of clayey silt/silty clay layer Solutions for prediction of pore response induced by penetration of piles and piezocones NorSand model formulation NorSand code input parameters List of correlations used to estimate K 0 from CPT test data Calculation of radial hydraulic conductivity, k r Estimation of slope of critical state line, λ, based on laboratory derived values of C c reported by Crawford & Campanella (1991) Summary of NorSand parameters for Colebrook silty clay Undrained shear strength and sensitivity estimated from field measurements and NorSand simulation of triaxial test NorSand-Biot input parameters for Colebrook silty clay List of scenarios for NorSandBiot code sensitivity analysis Parametric study results Ranking of NorSandBiot formulation input parameters Modelling parameters for base case and best fit simulations Undrained shear strength and sensitivity estimated from simulation of triaxial test with base case and best fit set of parameters Pore pressure response for base case, best fit and field data (Weech, 2002) Variation of effective stresses with time for base case and best fit simulations Piezometers considered for the analysis Final stress state for base case, best fit and Case A simulation with 5 helices vii

8 List of figures. LIST OF FIGURES Figure Page 1.1. Helical piles Helical pile performance research site location Site subsurface conditions at the research site Approximate locations of subsurface investigations at the Colebrook site Location of CPT tests and solid-stem auger holes Variation of field vane shear strength test results with elevation Example of cone penetration test results (CPT-7) Helical piles geometry Helical piles locations Variation of excess pore pressure with pile tip depth, S/D= Variation of excess pore pressure with pile tip depth, S/D= Radial distribution of excess pore pressure generated by penetration of pile shaft Radial distribution of maximum excess pore pressure after penetration of helices Radial distribution of excess pore pressure around helical piles (above level of bottom helix) during dissipation process Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process Average dissipation trends for different radial distances from pile Dissipation curves from piezometers/piezo-ports located at different radial distances from pile Effect of pile installation on soil conditions Measured excess pore pressures due to installation of piles Typical pore pressure dissipation measured during CPTU tests Increase in pile bearing capacity with time Increase in pile bearing capacity and pore pressure dissipation Comparison of variation of pile bearing capacity with time and theoretical decay of excess pore pressure Idealized schematics of soil set-up phases Cavity expansion zones along pile Comparison of measured and theoretical soil displacements due to pile penetration Schematic representation of 2-D modelling approach viii

9 List of figures Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 2-D Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 1-D Normal compression lines from isotropic compression tests on Erksak sand Definition of NorSand parameters Γ, λ, ψ, and R Definitions of internal cap, p i, p c, M tc, M i and η L on yield surface for a very loose sand Conventional and NorSand representation of overconsolidation ratio for soil initially at p = 500 kpa subject to decreasing mean stress NorSand fit to Bothkennar Soft clay in CK0U triaxial shear NorSand simulation fit to constant p=80kpa drained triaxial test on Bonnie silt Flow chart for large strain numerical code Typical shear modulus reduction with strain level for plasticity index between 10% and 20% Level of shear strain for various geotechnical measurements Variation of small strain shear modulus G max with elevation Inferred variation of rigidity index with depth Variation of shear modulus G with elevation Range of overconsolidation ratio OCR with elevation Variation of coefficient of earth pressure K 0 with elevation Variation in estimated coefficient of horizontal consolidation with depth Variation in estimated coefficient of horizontal consolidation with elevation with corrected CPTU derived values Variation of vertical effective stress with elevation Variation of equilibrium pore water pressure with elevation Probable range of slope of critical state line, λ Variation of void ratio with mean effective stress based on data reported by Crawford & Campanella (1988) Variation of state parameter and overconsolidation ratio with mean effective stress Simulation of drained triaxial test with NorSand model, using base case set of input parameters Simulation of undrained triaxial test with NorSand model, using base case set of parameters FE Mesh for Parametric Study Cylindrical cavity expansion from non-zero radius Radial distribution of generated excess pore water pressure at the end of cavity expansion for base case scenario ix

10 List of figures Time dependent pore pressure response at cavity wall for base case scenario Stress path for base case scenario Variation of void ratio, e, with mean effective stress, p for base case simulation Variation of e with p for base case, 20 & 21 scenarios Effect of K 0 on radial distribution of generated excess pore pressure at the end of cavity expansion Effect of K 0 on time dependent pore water pressure response at cavity wall Stress paths for base case, 1 & 2 scenarios Effect of coupled R & ψ on radial distribution of excess pore pressure response at the end of cavity expansion Effect of coupled R & ψ on time dependent pore water pressure response at cavity wall Effect of uncoupling R & ψ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with positive ψ Effect of uncoupling R & ψ on time dependent pore water pressure response at the cavity wall, for simulations with positive ψ Effect of uncoupling R & ψ on time dependent pore pressure response at the cavity wall, for simulations with negative ψ Generation of excess pore pressure during cavity expansion for the first mesh element adjacent to the cavity, presented in terms of pore pressure components Effect of uncoupling R & ψ on radial distribution of excess pore water pressure response at the end of cavity expansion, for simulations with negative ψ Radial distribution of different excess pore pressure components for scenario 5a Radial distribution of generated pore pressure, for scenario 5a, at different levels cavity expansion Initial conditions in e-ln (p ) space for scenarios 3..6 and base case Stress paths for scenarios 3 6 and base case Variation of e with p for scenarios 3 6 and base case Effect of G on radial distribution of excess pore pressure at the end of cavity expansion Effect of G on time dependent pore pressure response at cavity wall Stress paths for scenarios base case, 7, 8 & Effect of ν on radial distribution of excess pore pressure at the end of cavity expansion Effect of ν on time dependent pore water pressure response at cavity wall Stress paths for scenarios base case, 22 & Effect of Γ on radial distribution of excess pore water pressure at the end of cavity expansion Effect of Γ on time dependent pore water pressure response at cavity wall x

11 List of figures Stress paths for scenarios base case, 10 & Effect of Γ & λ on radial distribution of excess pore pressure at the end of cavity expansion Effect of Γ & λ on time dependent pore water pressure response at cavity wall Stress paths for scenarios base case, 12 & Effect of M crit on radial distribution of excess pore pressure at the end of cavity expansion Effect of M crit on time dependent pore water pressure response at cavity wall Stress paths for scenarios base case, 14 & Effect of H mod on radial distribution of excess pore pressure at the end of cavity expansion Effect of H mod on time dependent pore water pressure response at cavity wall Stress paths for scenarios base case, 14 & Effect of χ on radial distribution of excess pore pressure at the end of cavity expansion Effect of χ on time dependent pore water pressure response at cavity wall Stress paths for simulations with base case, scenario 18 & 19 set of input parameters Effect of permeability, k, on radial distribution of excess pore pressure at the end of cavity expansion Effect of permeability, k, on time dependent pore pressure response at cavity wall Stress paths for scenarios base case, 20 & Location of final stress state in q-p space, at the end of pore pressure dissipation, in relation to critical state line 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 Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with base case parameters Comparison of modelled undrained triaxial response for best fit and base case sets of NorSandBiot input parameters 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 Time-dependent pore pressure response at the pile shaft/soil interface measured by Weech (2002) and simulated with best fit parameters Comparison of u/σ v0 and σ v /σ v0 vs. time for best fit and base case simulation and the field measurements Stress path plot for central gaussian point of the mesh element adjacent to the cavity wall (r/r shaft = 1.08) for simulation of helical pile shaft installation with best fit parameters Void ratio versus mean stress (e-ln(p )) plot for central gaussian point of the mesh element adjacent to the cavity wall (r/r shaft = 1.08) for simulation with best fit parameters xi

12 List of figures Modelling cases considered in the analysis of the effect of the helices Modelling algorithm of helical piles installation in 1-D Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case A) Comparison of time dependent pore pressure response during helical pile installation measured in the field and simulated using NorSandBiot formulation (Case B) Comparison of radial pore distribution for simulations with and without helices and the field measurements Radial pore pressure distribution during first helix expansion (Case A) Radial pore pressure distribution during first helix contraction (Case B) Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A) Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case A) Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case B) Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 3 helices (Case B) Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case A) Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case A) Time dependent pore pressure response at the cavity wall for simulation of helical pile with 5 helices (Case B) Time dependent pore pressure response at the cavity wall for simulation of helical pile with 3 helices (Case B) Stress path plot for mesh element adjacent to the cavity wall (r/r shaft = 1.08) for simulation of helical pile shaft installation Void ratio versus mean stress (e ln(p )) plot for mesh element adjacent to the cavity wall (r/r shaft = 1.08) Comparison of stress paths for central gaussian point of the mesh element adjacent to the cavity wall (r/r shaft = 1.08) for simulations with different set of input parameters and modelling schemes Radial pore pressure distribution during expansion/contraction cycles for simulation of helical pile with 5 helices (Case A. Assumption 2) xii

13 Acknowledgements. ACKNOWLEDGEMENTS. I wish to thank my scientific supervisors, Dr. Dawn Shuttle and Dr. John Howie for their invaluable guidance throughout this project. Dr. Shuttle was always willing to assist with solving the most challenging problems and had always been a source of brilliant ideas. Her ability to explain complex concepts with clarity and ease and her truly endless patience are greatly appreciated. Dr. Shuttle s enthusiasm for this project had never run out and her pressure, in a good sense, kept me going. My study at the University of British Columbia was a great learning experience. I would like to thank Dr. Howie for taking me into the UBC Geotechnical Group. It was always a great pleasure to work with him. Thoughtful contributions of Dr. Howie to many discussions related to this project are sincerely appreciated. I would like to express my gratitude to Dr. Michael Jefferies for shearing the code and for his valuable suggestions. Special thanks for the ideas and helpful information belongs to my fellow graduate students: Sung Sik Park, Mavi Sanin, Ali Amini and Somasundaram Sriskandakumar. My deep appreciation goes to my fiancé Valeria and my stepson Vadim, who inspired me all the way through. Their patience and moral support are greatly acknowledged. Most of all, I would like to thank my parents Sofia & Mikhail, and my elder brother Alexei. Their unconditional love has always been there for me. I am indebt for their steadfast backing of my intellectual and spiritual growth. This thesis is one of the fruits of their dedication and love. There will be many more to come. I dedicate this work to my beloved family. PER ASPERA AD ASTRA xiii

14 Chapter 1. Introduction. 1. INTRODUCTION CHALLENGES IN AXIAL PILE CAPACITY PREDICTIONS IN SOFT FINE-GRAINED SOILS. Piles are relatively long and normally slender structural foundation units that transfer superstructure loads to underlying soil strata. Presently there are more than 100 different types of piles. The major share in piling foundations belongs to driven or jacked piles of various shapes, which are often referred to as traditional piles. In geotechnical practice, piles are usually employed when soil conditions are not suitable for use of shallow foundations, i.e. when the upper soil layers are too weak to support heavy vertical loads from the superstructure. Piles transfer vertical loads by friction along their surface and/or by direct bearing on the compressed soil at, or near, the pile tip. Given that the pile material is not over-stressed, the ultimate axial load capacity of a pile is equal to the sum of end bearing and side friction. The amount of resistance contributed by each component varies according to the nature of load support, soil properties and pile dimensions. Prediction of pile capacity is complicated by the fact that during installation the soil surrounding the pile is severely altered. This is particularly relevant for piles installed in thick deposits of soft fine-grained soils, where the friction along the shaft is usually a prime factor governing the pile capacity. Soft-fine grained soils are known for their tendency to lose strength when disturbed, and their slow rate of strength recovery following disturbance. Gradual gain of pile capacity with time after pile installation is a well-known occurrence. Although factors such as thixotropy and aging contribute to this phenomenon, the most significant cause for gain of capacity with time is associated with the dissipation of the excess pore water pressure generated during pile installation. The processes occurring during and after pile installation has a very limited analytical treatment and pile design is still largely relies on empirical correlations. At a recent symposium on pile design (Ground Engineering, 1999) the participants were asked to provide a prediction of the capacity of a single driven steel pile. The general success rate was very poor with only 2 of 16 teams getting within 25% of the correct capacity. The best prediction of the pile s capacity was obtained from compensating errors; a too low side friction capacity 1

15 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 HELICAL PILES. A helical pile is an assembly of mechanically connected steel shafts with a series of steel helical plates welded at particular locations on the lead section, as shown in Fig. 1.1.a. Historically helical piles have evolved from early foundations known as screw piles. The screw piles have been in use since the early 19 th century. Early applications of these piles were based on hand installation. The first power installed screw piles were employed during construction of a series of lighthouses in England in 1833 (Wilson & Guthlac, 1950). Generally, the screw piles had a very limited use until the 1960 s; when reliable truck mounted hydraulic torque motors became readily available. Nowadays the major helical piles manufacturer is a USA based company - AB Chance Ltd. They manufacture piles with the shaft Ø cm and helical plates Ø 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

16 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 TM, 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

17 Chapter 1. Introduction PURPOSES AND OBJECTIVES OF RESEARCH. Helical piles are gaining popularity in North America as an alternative foundation solution to traditional driven and jacked piles. To date the major research efforts in the field of helical piles have concentrated on their lateral and uplift capacity. However, limited knowledge of the timedependent 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 SCOPE AND LIMITATION OF STUDY. The conducted study is mainly focused on soil pore water pressure response due to pile penetration, as it is believed to be an important factor affecting the variation of pile bearing 4

18 Chapter 1. Introduction. capacity with time. Adequate simulation of the pore water pressure response in the soft finegrained 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

19 Chapter 1. Introduction 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

20 Chapter 1. Introduction. a b Fig Helical piles: a conventional pile; b grouted (PULLDOWN TM ) pile. 7

21 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.0 OVERVIEW OF FIELD STUDY OF HELICAL PILE PERFORMANCE IN SOFT SENSITIVE SOIL 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 SCOPE OF WEECH S STUDY. Six instrumented full-scale helical piles were installed in soft sensitive marine deposits. Prior to pile installation, an in-situ testing program was carried out, that consisted of: two profiles of vane shear tests; five piezocone penetration soundings, with pore pressure dissipation tests carried out at two soundings and shear wave measurements at three soundings. The excess pore pressures within the soil surrounding the piles were monitored during and after pile installation by means of piezometers located at various depths and radial distances from the pile shaft, and using piezo-ports, which were mounted on the pile shaft. After allowing a recovery period following installation, which varied between 19 hours, 7 days and 6 weeks, piles with two different helix plate spacing were loaded to failure under axial 8

22 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. compressive loads. Strain gauges mounted on the pile shaft were monitored during load testing to determine the distribution of loading throughout the pile at the various load levels up to and including failure. Load-settlement curves were generated for different pile sections at different times after installation. The piezometers and piezo-ports were also monitored during load testing and the distribution of excess pore pressures 2.3. SITE SUBSURFACE CONDITIONS. The test site, also referred to as the Colebrook site, is located under the King George Highway (99A) overpass over Colebrook Road and the adjacent BC Railway line, South Surrey, BC; approximately 25 km southwest of downtown Vancouver, as shown in Fig SITE STRATIGRAPHY. The subsoils found in this area belong to so called Salish Sediments. According to Armstrong (1984): Salish sediments include all postglacial terrestrial sediments and postglacial marine sediments that were deposited when the sea was within 15 m of present sea level. These deposits were likely laid down during the Quaternary period between 10,000 and 5,000 years ago. Cross-section of site stratigraphy is shown on Fig 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

23 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil 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 A brief description of each investigation and their reviews reported in the literature are presented below in chronological order FIELD INVESTIGATION BY MINISTRY OF TRANSPORTATION AND HIGHWAYS. Prior to construction of the Colebrook Road overpass (Highway 99), the Ministry of Transportation and Highways (MoTH) performed an extensive geotechnical study of the soil conditions along the alignment of a planned overpass (in 1969). The MoTH investigation included dynamic cone penetration tests and drilling with diamond drill to establish the depth and profile of the competent stratum underlying the soft sediments. Field vane shear tests were performed at selected depths. Undisturbed samples of the soft soils were recovered with a Shelby tube sampler. A number of laboratory tests were carried out on the MoTH samples, including index tests, consolidated and unconsolidated triaxial tests and laboratory vane shear tests. Crawford & deboer (1987) studied the long-term consolidation settlements underneath the approach embankments, located in the vicinity of the helical piles performance research site. They reported some of the data obtained during the MoTH investigation - typical for the Colebrook site soil properties and results of three unidirectional consolidation tests performed in a triaxial cell, with radial drainage. Crawford & deboer (1987) report, based on laboratory testing, an average coefficient of consolidation in the horizontal direction, c h = cm 2 /s, an average coefficient of secondary consolidation, C α = and an initial void ratio, for all three tests, e 0 = A summary of typical soil properties from MoTH investigation given by Crawford & deboer (1987) are presented in Table A.1 (Appendix A) RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (1). Crawford & Campanella (1991) reported the results of a study of the deformation characteristics of the subsoil, using a range of in-situ methods and laboratory tests to predict soil settlements underneath the embankment, and compare them with the actual settlements. In-situ tests included field vane shear tests, piezocone penetration test (CPTU) and a flat dilatometer test (DMT). Laboratory tests were limited to constant rate of strain odometer consolidation tests on 10

24 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) RESEARCH BY UNIVERSITY OF BRITISH COLUMBIA (2). As a part of his study of helical pile performance in soft soils, a comprehensive investigation of site soil conditions was carried out by Dolan (2001) and Weech (2002). Dolan (2001) obtained continuous piston tube samples from ground level to 8.6 m depth and performed index testing to determine natural moisture content, Atterberg limits, grain-size distribution, organic and salt content. Results of index tests carried out by Dolan (2001) on samples obtained with the piston tube sampler are summarized in Table 2.1 Table 2.1. Average index properties of clayey silt/silty clay layer (elevation -4.1 m and below). Soil Property Average Value Comments natural moisture content (w n ) 42%+/-3% - liquid limit (w L ) 40%+/-4% - plasticity index (PI) 13.5%+/-4.5%, below 8m in elevation PI is up to 21% unit weight (γ) 17.8+/-0.3 kn/m 3 - in-situ void ratio (e o ) 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 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

25 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 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, (s u ) 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, S t = (s u ) peak /(s u ) 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 s u to the effective overburden pressure, σ vo, is presented in Fig. 2.5c. In the upper part of the marine deposits (from 4.1 to 4.4 m in elevation) the s u /σ vo ratio is quite high around 0.7, which indicates moderately overconsolidated soil. At lower depths the deposit is lightly overconsolidated, with the s u /σ vo ratio around 0.4. A typical CPT cone test result for Colebrook site, including profiles of corrected tip resistance, q T, sleeve friction, f s, and excess penetration pore pressure, u, measured behind the shoulder of the cone (u2 filter position), are presented on Fig A detailed overview of the soil properties, relevant to the current study, is given in Chapter HELICAL PILES AND PORE PRESSURE MEASURING EQUIPMENT TEST PILES GEOMETRY AND INSTALLATION DETAILS. For the purpose of studying different failure mechanisms, piles with two different lead sections were used. The largest helical piles manufacturer, Chance Anchors, commonly uses helical plates attached to the lead section such that the distance between successive plates (S) is 3 times the diameter (D) of the lower plate. In this case, current thinking based on small scale model tests (Narasimho Rao et al., 1991) is that during loading to failure, failure occurs at individual helices. For the closer spacing of the helical plates, the failure mechanism is believed to be different - all helices fail simultaneously, so that a cylindrical failure surface is generated 12

26 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 In total six helical piles - three for each leading section type were installed, their locations are shown in Fig 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 MEASURING EQUIPMENT. A total of 26 UBC push-in piezometers were installed at different depths and radial distances from the 6 test piles, and a total of 10 piezo-ports were located at 3 different positions on the shaft of the piles, as indicated in Table B.1 (Appendix B). Piezo-ports, which contained an electric pore pressure transducer with a porous filter, were installed within the wall of the pile shaft on the lead sections. The piezometers were pushed into the soil at least one week prior to pile installation so that full dissipation of the excess pore pressures generated during piezometer installation could occur. These piezometers were then used to monitor the variation in pore pressures caused by pile installation and their subsequent dissipation. During pile installation piezometers were continuously monitored using the multi-channel data acquisition system. After the end of pile installation piezoports located on the pile shaft were also connected to the data acquisition system and were continuously monitored in conjunction with the piezometers. Two types of electronic pore pressure transducers were employed for the piezometers and the piezoports, with measuring capacity 345 and 690 kpa. The resolution of the automatic acquisition system used to monitor the piezometers was to 0.07 kpa (for 345 and 690 kpa transducers, respectively). The rated accuracy of the pressure transducer measurements was ±0.1% of full scale. Even though every attempt was made to carefully assemble and install measuring equipment, the response of many piezometers and piezoports was less than perfect, as shown in Table B.1. 13

27 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil 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) PORE WATER PRESSURE RESPONSE DURING HELICAL PILE INSTALLATION. Pore pressure profiles measured at different radial distances during installation for piles TP-1 and TP-2 are shown in Fig. 2.9 and Fig In these figures profiles of normalized peak pore pressure u i /σ vo are plotted against the depth of the pile tip below the elevation of the piezometer filter (z pile z piezo ). 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 u i 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/r 1 shaft = 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 hx ) appears to respond directly to the penetration of 1 In this overview, radial distance is represented by the r/r shaft ratio, where R shaft is the radius of the pile shaft (in the current study, identical for all piles), r radial distance from the pile centre. 14

28 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 t hx 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 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/r shaft = 5 to 17, u shaft /σ vo decreases steeply and almost linearly. After r/r shaft = 17, u shaft becomes quite small (< 0.1σ vo ) and the slope of the pore pressure decay with distance flattens. For r/r shaft 60 generated pore pressures are practically negligible. In Fig 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/r shaft = 6, the pore pressures generated by the helices make up to 20% of the total pore pressures and at distances greater than r/r shaft = 17 make up to 75%. Penetration of the helices extends the radial distance of generated pore pressures from r/r shaft about 60, estimated for penetration of pile shaft alone, to r/r shaft 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 PORE WATER PRESSURE DISSIPATION AFTER HELICAL PILE INSTALLATION. Weech (2002) compiled a combined dataset of all (for piles with both S/D = 1.5 and 3) normalized piezometric measurements, taken at different times, at the locations above the bottom helical plate as presented in Fig 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

29 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. 2.13, excess pore pressure, u, decreases monotonically throughout the soil around the pile, out to a radial distance of at least 30 shaft radii. The rate of dissipation at different radial distances appears to vary such that the u(r)/σ vo -log(r) curve becomes more and more linear as the dissipation process progresses. Fig 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 u hx is observed in the soil (from r/r shaft = 5 to at least 17) below the level of the bottom helix within 10 minutes after stopping penetration Dissipation of u within the soil close to the helices (r/r shaft < about 10) is much more rapid below the level of the bottom helix than above, at least during the first hours of dissipation. The elevated pore pressures at the tail of the distribution (r/r shaft > 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 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 shows the dissipation curves based on u(t)/σ vo data from individual piezometers/piezo-ports located at different radial distances from the test piles (above the bottom helix). Based on this figure Weech (2002) made the following observations: The dissipation occurs much more quickly below the bottom helix than above, at radial distances close to the pile. Even though greater proportions of dissipation occur sooner at larger radial distances, all of the curves tend to converge at the end of the dissipation process. For all monitored piles 100% dissipation occurred at about 7 days for most locations around the piles. The dissipation process appears to be essentially independent of the number or spacing of the helix plates. 16

30 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil 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 Terzaghi 2 : 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

31 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. Test Site N Surrey, BC Fig Helical pile performance research site location. Fig Site subsurface conditions at the research site (modified after Weech, 2002). 18

32 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soil. scale - metres Fig Approximate locations of subsurface investigations at the Colebrook site (modified after Crawford & Campanella, 1991). Fig Location of CPT tests and solid-stem auger holes (after Weech, 2002) 19

33 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. -3 a) Field Vane Shear Strength (s u ) FV (kpa) b) Sensitivity S t = (s u ) peak /(s u ) rem c) Strength Ratio s u /σ' vo Possibly affected by sandy silt Elevation (m) Peak Strength (VH-1&2) Remoulded Strength (VH-1&2) Peak (from Craw ford & Campanella, 1991) Rem (from Craw ford & Campanella, 1991) VH-1&2 Craw f ord & Campanella (1991) Fig Variation of field vane shear strength test results with elevation (after Weech, 2002). 20

34 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. a) -3 Tip Resistance Q T (bar) b) Sleeve Friction f s (kpa) c) Excess Pore Pressure at U2 - u (kpa) Elevation (m) Fig Example of cone penetration test results (CPT-7) (after Weech, 2002). Note: Breaks in profile correspond to data recorded upon resuming penetration after seismic tests 21

35 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Fig Helical piles geometry (modified after Weech, 2002). 22

36 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. 3 rd bridge pier from South abutment 2 nd bridge pier from South abutment pile cap 300 mm wide hexagonal RC piles Helical piles Fig Helical piles locations (modified after Weech, 2002). 23

37 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Excess Pore Pressure during Pile Installation - u i /σ' vo Note: Dissipation during breaks in installation removed. 4 Grout Column Depth of Pile Tip Below Piezo Filter Elev. (m) Line of Max Pore Pressure Grout Disc Helix Plates PZ-TP4-1 (r/r = 4.8) PZ-TP2-5 (r/r = 7.3) -1 PZ-TP2-1 (r/r = 8.0) PZ-TP2-7 (r/r = 11) r = radial distance from pile center R = radius of pile shaft PZ-TP2-3 (r/r = 17) PZ-TP2-4 (r/r = 30) -2 Fig Variation of excess pore pressure with pile tip depth, S/D=1.5. (after Weech, 2002) 24

38 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. Excess Pore Pressure during Pile Installation - u i /σ' vo Note: Dissipation during breaks in installation removed. 4 Grout Column Depth of Pile Tip Below Piezo Filter Elev. (m) Line of Max Pore Pressure Grout Disc Helix Plates PZ-TP3-1 (r/r = 5.8) -1 PZ-TP3-2 (r/r = 8.1) PZ-TP1-7 (r/r = 12) r = radial distance from pile center R = radius of pile shaft PZ-TP1-3 (r/r = 14) PZ-TP1-4 (r/r = 25) -2 Fig Variation of excess pore pressure with pile tip depth, S/D=3. (after Weech, 2002). 25

39 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils Pile Piezos (due to pile tip penetration) Pile Piezo-Ports (End of Installation) 1.5 Linear Trend Line 1.4 Excess Pore Pressure during Installation - u i /σ' vo Edge of Helices Logarithmic Trend Line TP4-1 TP3-1 TP1-9 TP5-1 TP1-6 TP4-2 TP2-6 TP6-2 TP6-1 TP3-2 TP2-2 TP2-1 TP2-5 TP1-5 Linear Trend Line TP2-7 TP TP1-3 TP TP2-3 TP TP Radial Distance from Pile Center (shaft radii) - r/r shaft Fig Radial distribution of excess pore pressure generated by penetration of pile shaft (modified after Weech, 2002). 26

40 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils Peak u at Piezos after Passing of Pile Tip Max u at Piezo-Ports (End of Installation) Shaft Penetration (best fit of data from Fig. 2.11) Shaft Penetration (best estimate for r < 5R) u hx (best estimate) u/σ 'vo Edge of Helices u hx Radial Distance from Pile Center (shaft radii) - r/r shaft 100 Fig Radial distribution of maximum excess pore pressure after penetration of helices (after Weech, 2002). 27

41 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils. u/σ' vo min (U shaft = 0%) 10 min (U shaft = 4%) 1 hr (U shaft = 16%) 5 hrs (U shaft = 35%) Edge of Helices 0.1 min after stopping 10 min after stopping 1 hr after stopping 5 hrs after installation hrs after installation 2 days after installation Initial Shaft Penetration hrs (U shaft = 57%) days (U shaft = 76%) Radial Distance from Pile Center (shaft radii) - r/r shaft Fig Radial distribution of excess pore pressure around helical piles (above level of bottom helix) during dissipation process (after Weech, 2002). u/σ' vo min 1 hr 5 hrs Edge of Helices 10 min (Below Helices) 1 hr (Below Helices) 5 hrs (Below Helices) hrs (Below Helices) 2 days (Below Helices) 10 min (Above Bottom Helix) 1 hr (Above Bottom Helix) 5 hrs (Above Bottom Helix) hrs (Above Bottom Helix) 2 days (Above Bottom Helix) hrs days Radial Distance from Pile Center (shaft radii) - r/r shaft 100 Fig Radial distribution of excess pore pressure above & below level of bottom helix during dissipation process (after Weech, 2002). 28

42 Chapter 2. Overview of the field study of helical pile performance in soft sensitive soils u o = u at 0.1 min after stopping installation u(t)/ u o r/r = 1(Pile Shaft) 0.4 r/r = 4 (Edge of Helices) 0.3 r/r = 6 r/r = r/r = r/r = 16.5 r/r = Time after Stopping Installation (min) Fig 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) 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) 1.0 u/σ' vo Time (min) from End of Installation Fig Dissipation curves from piezometers/piezo-ports located at different radial distances from pile (after Weech, 2002). 29

43 Chapter 3. Literature review LITERATURE REVIEW 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 PORE PRESSURE RESPONSE INDUCED BY PILE INSTALLATION INTO FINE GRAINED SOIL AND ITS INFLUENCE ON PILE CAPACITY FIELD GENERATION OF EXCESS PORE PRESSURE. Pile installation causes disturbance in the soil adjacent to the pile. Flaate (1972) studied impact of timber pile installation on fine-grained soils. It was observed that installation of a circular timber pile 0.33m in diameter formed a zone of up to 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

44 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 ( u/ σ v > 0.1), was about 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 u = u mean + u shear (3.1) The components of excess pore pressure from Eq. 3.1 cannot be measured individually in the field and can only be separated in the laboratory. The pore pressure generated due to a change in mean stress, σ mean, is equal to the magnitude of σ mean 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 u shear pore pressures are generated. Moderately to heavily overconsolidated clays demonstrate dilatant behaviour when sheared, hence negative u shear 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 FIELD DISSIPATION OF EXCESS PORE PRESSURE. When pile installation into fine-grained soil is complete, the induced excess pore pressure will gradually dissipate to the equilibrium value in time. Water flow naturally takes the path of lowest resistance and due to the complex soil stratigraphy and layering, accurate estimation of in-situ drainage characteristics is quite difficult. Field studies by Bjerrum & Johannessen (1961), Koizumi & Ito (1967) and Roy et al. (1981), where 31

45 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

46 Chapter 3. Literature review OBSERVED AXIAL PILE CAPACITY AS FUNCTION OF DISSIPATION OF EXCESS PORE PRESSURE. Typically, when a pile is installed into fine-grained soil, high excess pore water pressures are generated in the vicinity of pile. Over time the pore pressures induced by pile installation begin to dissipate, primarily in a radial direction. Consequently the soil in the vicinity of the pile consolidates. As the water content of the soil gradually decreases during the dissipation process, the soil strength and stiffness recover and may increase. A number of studies linked pore pressure dissipation, induced by pile installation, with the increase in pile bearing capacity. One of the first documented accounts of such behaviour belongs to Seed & Reese (1957). They studied the effect of pile driving on soil properties and pile bearing capacity on an instrumented pipe pile, 0.15 m in diameter installed into sensitive soft clay at the San-Francisco Oakland bridge site, in California. Pore pressure measurements were taken in the vicinity of the pile after installation. The pile was loaded seven times in a time span from 3 hours after installation to 33 days (800 hours). A dramatic increase in pile capacity (5.4 times) was reported, as shown in Fig 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 The main implication of this figure is that the pile bearing capacity is strongly dependent on the degree of excess pore pressure dissipation. 33

47 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 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 PREDICTION OF TIME-DEPENDENT PORE PRESSURE RESPONSE PREDICTION METHODS. Prediction of pore water pressure response is quite complex. A number of factors complicate the analysis: vertical drainage, soil remoulding in the vicinity of penetrating body, soil non-linearity and anisotropy, boundary effect of soil layering, soil stress and strain history (Campanella & Robertson, 1988). There is no method available, among those published to date, which can account for the full complexity of the pore water pressure response. However, a reasonable approximation of the problem is possible. Discussed herein are well known prediction solutions, varying in their degree of complexity and comprehensiveness, that provide some capabilities for estimation of 34

48 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

49 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 Soderberg (1962) Torstensson (1977) Cavity Type Cylindrical, radius R Cylindrical Spherical Soil Model Initial Pore Pressure Consolidation Elasto-plastic 1 u/ u i =R/r 1-D Elasto-plastic u i= 2s u ln(r p /r) u i= 4s u ln(r p /r) Randolph & Wroth (1979) Cylindrical Elasto-plastic u i= 2s u ln(r p /r) 1-D Baligh & Levadoux (1980) Levadoux & Baligh (1986) Battaglio et al. (1981) Piezocone Model Cylindrical Spherical Non-linear Elasto-plastic From strain path method; Total stress soil model u i= 2s u ln(r p /r) u i= 4s u ln(r p /r) Senneset et al. (1982) Cylindrical Elasto-plastic u i= 2s u ln(r p /r) 1-D Tumay et al. (1982) Gupta & Davidson (1986) Houlsby & Teh (1988); Teh & Houlsby (1991) Piezocone Model Piezocone Model Piezocone Model 1-D 2-D 1-D Linear From strain path method; Experimental data 1-D Elasto-plastic Non-linear Whittle (1992) Pile Model Non-linear Sully & Campanella (1994) Piezocone Model Non-linear Burns & Mayne (1995) Spherical Elasto-plastic Modified cavity expansion; Dissipation as cone penetrates Predicted by large strain finite element analysis and strain path method From strain path method; Effective stress-strain model Predicted by large strain finite element analysis and strain path method u oct= 4s u ln(r p /r) u shear =σ vo [1-(OCR/2) 0.8 ] Comments Consolidation around driven piles; Finite Differences No shear stresses; Finite Difference. Consolidation around driven piles; Analytical. Shear by empirical method; Finite Difference 1-D Isotropic and anisotropic 1-D Finite Difference 1-D Coupled consolidation. 1-D Empirical time shift for OC dissipation 1-D Incorporates shear stresses; models OC dissipation; Finite Difference Collins & Yu (1996) Cylindrical Non-linear Closed form solutions. - No consolidation analysis Burns & Mayne (1998) Spherical Elasto-plastic u oct= 4s u ln(r p /r) u shear =σ vo [1-(OCR/2) 0.8 ] 1-D Incorporates shear stresses; models OC dissipation; Analytical Cao et al. (2001) Cylindrical Non-linear Closed form solution. - No consolidation analysis Whittle et al. (2001) Tapered Piezocone Model Non-linear From strain path method; Effective stress-strain model 1 simple elastic plastic soil models, such as Tresca, Von Mises,; 2 advanced soil models, such as Cam Clay, Modified Cam Clay, MIT-E2 and etc 1-D Coupled consolidation 36

50 Chapter 3. Literature review BASIC CONCEPTS BEHIND EXISTING PREDICTION SOLUTIONS MODELLING ANALOGUE FOR SIMULATION OF PILE OR CONE PENETRATION. The majority of methods for predicting the pore pressure response due to pile, or cone, penetration uses either a cavity expansion analogy or the strain path method for simulation of the impact of a penetrating body on the surrounding medium. During pile installation, a volume of soil equal to the volume of pile is displaced. The soil displacement occurs in the direction of least resistance, as shown in Fig 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 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

51 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 MODELLING FRAMEWORK. Changes in soil stresses and pore pressures due to pile or cone penetration are typically computed using either the total stress soil models (such as Tresca, Von Mises, Hyperbolic, MIT- T1), or the effective stress soil models (such as Cam Clay, Modified Cam Clay, MIT-E2, MIT- E3). 38

52 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 OVERVIEW OF EXISTING PREDICTION SOLUTIONS. The accuracy of pore pressure dissipation response predictions largely depends on correct estimate of the distribution of generated excess pore pressures. Approaches to modelling of the pore pressure dissipation have not changed significantly over the years, whereas the cavity expansion and strain path based methodologies for prediction of the excess pore pressure generated during soil penetration have undergone many revisions. In the sections presented below major developments in these methodologies are discussed CAVITY EXPANSION SOLUTIONS. Vesic (1972) used a framework of the cavity expansion theory for development of closed form solutions for prediction of stresses and pore pressure distribution around an expanding cavity under undrained conditions in a linear elastic perfectly plastic medium. The pore pressure predictions were based on the following assumptions: the soil is isotropic; 39

53 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 u shear 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 u shear = 0 at any point around the cavity and therefore u = u mean. Battaglio et al. (1981) and Gupta & Davidson (1986) attempted to overcome this limitation by introducing into the solution laboratory derived Skempton s A and Henkel s α pore pressure parameters. Provided that these parameters are normally estimated from the measured pore pressure at failure, they may not represent correctly the large strain u shear 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 overconsolidated 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 u mean and u shear can be accounted for. 40

54 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 semianalytical 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

55 Chapter 3. Literature review SOLUTIONS BASED ON STRAIN PATH METHOD. Levadoux & Baligh (1980) utilized the strain path method for predicting pore pressures induced by penetration of CPT cones. The cone was treated as a static penetrometer with soil flowing around it like a viscous fluid. Excess pore pressures generated by cone penetration were calculated by predicting soil velocities and strain rates using potential theory (neglecting soil shearing resistance and assuming incompressible fluid flow); integrating the strain rates along the continuous stream lines, located axisymmetrically at different radial distances from the cone, to determine the strain history of the soil elements, and computing the deviatoric and shearinduced 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 SUMMARY. Available pore pressure prediction methods are evolved from simple solutions based on total stress soil models and uncoupled consolidation to more rigorous solutions employing effective stress soil models and coupled consolidation. Solutions based on the effective stress soil models and coupled consolidation are the most realistic. 42

56 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

57 Chapter 3. Literature review. Fig Effect of pile installation on soil conditions. Fig Measured excess pore pressures due to installation of piles (after Baligh & Levadoux, 1980). 44

58 Chapter 3. Literature review. a). b). Fig Typical pore pressure dissipation measured during CPTU tests (modified after Burns & Mayne, 1998). a). lightly overconsolidated Clay; b). heavily overconsolidated Clay. 45

59 Chapter 3. Literature review. Fig Increase in pile bearing capacity with time (after Seed & Reese, 1957). Fig Increase in pile bearing capacity and pore pressure dissipation (modified after Konrad & Roy, 1987). 46

60 Chapter 3. Literature review. Fig 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 Fig Idealized schematics of soil set up phases (modified after Komurka et al., 2003). 47

61 Chapter 3. Literature review. Fig Cavity expansion zones along pile (modified after Klar & Einav, 2003). Zone I displaced soil moves at sides and slightly upwards; Zone II displaced soil moves primarily radially (cylindrical cavity analogue). Zone III displaced soil moves at sides and downwards (spherical cavity analogue). Fig Comparison of measured and theoretical soil displacements due to pile penetration (after Randolph et al, 1979). 48

62 Chapter 4. Formulation of modelling approach. 4. FORMULATION OF MODELLING APPROACH 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 finegrained soil MODELLING APPROACH TO SIMULATION OF HELICAL PILE INSTALLATION INTO FINE- GRAINED SOIL MODELLING FRAMEWORK. There is a consensus of opinions in the reviewed literature: accurate prediction of pore pressure response due to pile installation requires coupled analysis where a realistic soil model is employed. The volume changes in the silty-clay during and following pile installation influence the magnitude and distribution of time-dependent pore pressure and effective stress. Therefore, it is important that the chosen soil model generate realistic volume changes during shearing. A generalized critical state based soil model, NorSand (Jefferies, 1993; Jefferies & Shuttle, 2002), was adopted here to represent fine-grained soil stress-strain behaviour. In order to predict the changes in stresses and pore pressure under partially drained conditions, an analysis that accounts for the coupling between the rate of loading and the generation of fluid pressures is required. The Biot consolidation theory (Biot, 1941) was used to incorporate the effect of the coupling the pore pressure behaviour to the soil response. 49

63 Chapter 4. Formulation of modelling approach MODELLING PROCEDURE FOR SIMULATION OF HELICAL PILE INSTALLATION. The following major aspects of pore water pressure response due to helical pile installation are of interest in this study: excess pore pressure induced by helical pile installation; dissipation process of the induced excess pore pressure. In the coupled numerical analysis dissipation of the excess pore water pressure is typically automatically handled within the formulation. At the same time generation of the realistic excess pore water pressure requires a special modelling procedure for simulation of the helical pile installation. Conventional procedures for helical pile installation are outlined in Section 1.2. Helical piles consist of the pile shaft and the helices attached to the leading section of the pile. The mechanism of pore pressure generation induced by the helical pile shaft penetration is similar to the one for conventional piles, discussed in Section 3.2. The mechanism of pore pressure generation induced by the helical pile shaft penetration is much more complex. The helices cut through the soil by a spiral trajectory generating a significant pulling force that advances the helical pile shaft. As the helical plates move downward by one flight they displace and release the volume of the soil equal to the volume of the plate. It should be noted that the volume of the soil displaced by the helical plate is quite small in comparison to the volume displaced by the pile shaft. Generally the pore pressures induced by the helices will be a complex combination of the pore pressures generated by soil displacement, soil shearing and the impact of the pulling force. Due to such complexities a detailed simulation of helical pile penetration would require a 3-D modelling approach, where the interaction between the rigid helical pile and deformable soil, and the effect of the pulling force can be comprehensively addressed. This is theoretically possible by employing a 3-D large strain Lagrangian finite difference analysis (e.g. FLAC 3-D). This method may realistically represent the process of pile installation accounting for changes in soil properties with depth and influence of the free soil surface. However, there are numerous numerical difficulties involved in this process, including problems of formulation of the nonlinear 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

64 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 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 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 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 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 In this figure the modelling location remains constant through 51

65 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 NORSANDBIOT FORMULATION NORSAND CRITICAL STATE SOIL MODEL MODEL DESCRIPTION. NorSand is a generalized Cambridge-type constitutive model developed from the fundamental axioms of critical state theory and experimental data on sands. A description of the NorSand soil model was published by Jefferies (1993), Shuttle & Jefferies (1998) and Jefferies & Shuttle (2005). The brief outline of the NorSand model given here is largely based on these published accounts. The work of Roscoe, Schofield & Wroth (1958) at Cambridge defined what was understood by the term critical state, which led to the development of the framework of soil behaviour known as critical state soil mechanics (Schofield & Wroth, 1968). In critical state soil mechanics (CSSM), the coupling of yield surface size to void ratio explains why and how soil behaviour changes with density. Based on the CSSM framework several critical state soil constitutive models were developed: CamClay (Roscoe, Schofield & Thurairajah, 1963), Modified CamClay (Burland, 1965) and GrantaGravel (Schofield & Wroth, 1968). The term constitutive model here implies an idealized mathematical relationship that represents the real soil behaviour. These CSSM models were rarely applied for modelling sand behaviour, because of their 52

66 Chapter 4. Formulation of modelling approach. inability to reproduce the softening and dilatancy observed in sands. This lead to the development of CSSM models based on the state parameter ψ that accurately capture the effect of dilatancy. NorSand was the first of these models. Jefferies (1993) described the two fundamental critical state soil mechanics axioms and soil idealizations taken as a basis for the NorSand model development. Axiom 1: A unique locus exists in q, p, e space such that soil can be deformed without limit at constant stress and constant void ratio; this locus is called the critical state locus (CSL). Axiom 2: The CSL forms the ultimate condition of all distortional processes in soil, so that all monotonic distortional stress state paths tend to this locus. Basis assumptions of soil behaviour: a single yield surface exists in stress space at any instant; intrinsic cohesion between soil particles is absent; stress is coaxial with strain increment; associated flow, i.e. strain increment is normal to the yield surface. The critical state axioms have been used to develop a general soil model that complies with the axioms under all choices of initial conditions and with specific application to sand. Many critical state soil models, such as CamClay, Modified CamClay and GrantaGravel, are based on the assumption that any yield surface intersects the CSL. This provides the ability to link the yield surface size with void ratio. However, this assumption is not necessarily valid for real soils, which may exhibit infinity of normal consolidation lines (NCL), not parallel to the CSL, as shown on the example of Erksak sand (Been & Jefferies, 1986) in Fig An infinity of normal consolidation lines prevents the direct coupling between yield surface size and void ratio, so that a separation between the state of the soil and overconsolidation ratio is required. Generally, it is accepted that soil may exist in a number of states. Casagrande (1975) found that during shear, soils experience volume change they may exhibit either contractive or dilative behaviour, until a critical state is reached at which point the soil continues to deform with no volume change under constant stress and void ratio. State parameter ψ is a measure of the current soil state, defined as the difference between the void ratio at the current state and the void ratio at critical state at the same mean stress. Overconsolidation ratio, R, within NorSand 53

67 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 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 η L that the soil can withhold. It should be noted that the presence of the internal cap means that once unloading has reached about R 3, then the yield surface shrinks in size. However, the soil can remain dense and ψ becomes more negative. This indicates that the one cannot directly compare NorSand with standard views of the effect of overconsolidation without varying ψ. Broadly, for unloading a normally consolidated soil to R 3, overconsolidation ratio R in NorSand is the same as R as conventionally viewed. Thereafter, NorSand holds to R 3 and just becomes more negative in ψ. This idea can be demonstrated by simulation soil unloading and computing variation of R and ψ with changing mean effective stress. To simulate this is to compute two things: first, to compute the void ratio change for a reduced mean stress via the swelling line from which the new state parameter can be determined; second, allow the overconsolidation ratio to increase to its limiting value (R 3) and then hold it at that. The example of soil unloading from p =500 kpa shown in Fig 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 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

68 Chapter 4. Formulation of modelling approach. Table 4.1. NorSand model formulation (all stresses are effective). Internal Model Parameters Critical State Flow Rule Yield Surface & Internal Cap Hardening Rule Elasticity ψ = ψ + λ ln( p ), where ψ = e ec i M e c c i = M ψ = Γ λ ln i p i ( p) η = M = M + M ( MC MN ) / 2 where M ( 3 3) /( cosθ ( 1+ 6/ M ) 3sinθ ) and D 3 M p = M i MC 2 MN = tc + η η p = 1 ln M i p i M M 3 MN sin 2 MN tc = 2 3 ( ) 3 M 2 tc + M tc 2 ( θ ) 3 sin ( θ ) M pi with = exp( χ ψ M ) p max p& p χψ p H p G, ν - constant (input parameters) i i = mod i p exp i M 1 i pi & ε q tc i i, tc MODEL PARAMETERS. The NorSand soil model requires 11 input parameters, shown in Table 4.2. Table 4.2. NorSand code input parameters. Material Properties Description General G shear modulus ν Poisson ratio OCR ( R ) 1 overconsolidation ratio K 0 coefficient of lateral earth pressure at rest σ v0 vertical effective stress NorSand M crit critical state coefficient χ state dilatancy parameter ψ state parameter λ slope of CSL in e-ln(p) space Γ intercept of the CSL at 1 KPa stress hardening coefficient H mod 1 overconsolidation ratio is often referred to as OCR = σ v max /σ v which is not the same as R = p max /p. The relation between them depends on K 0, which tends to increase with OCR, however assuming that K 0 is constant, both definition produce numerically identical results. 55

69 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, M crit, describes the ratio between stresses at critical state and is a function of Lode angle. For triaxial compression conditions, critical state coefficient is directly related to friction angle at constant volume φ cv : M crit(tc) = 6sin φ cv /(3-sin φ cv ) (4.3) where φ cv is usually determined from triaxial tests on loose samples. Parameters describing critical state line: λ - slope of CSL in e-ln(p) space; Γ - intercept of the CSL at 1 KPa stress. Their definition is graphically shown in Fig Critical state line is normally determined by a series of undrained triaxial compression tests. State Parameter, ψ, defines the state of the soil. It relates normal compression line with the critical state line, as shown in Fig 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, H mod, is a NorSand specific parameter that has similar meaning to the rigidity index I r, but for plastic strains. Generally, all hardening/softening models have an equivalent to H mod. 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. H mod is a function of the state parameter, usually derived by calibration of the NorSand model to experimental data. State dilatancy parameter, χ, is also unique to NorSand, and is a function of soil structure and fabric. Parameter χ is a proportionality coefficient between soil state and minimum dilatancy: D min = χ ψ i (4.6) Usually, it is taken within a range , where the exact value can be found by fitting the experimental data BEYOND SAND. It is a misconception to associate the NorSand model explicitly with sands. Even though its name suggests sand, NorSand model has no intrinsic limitations for application to fine-grained soils. 56

70 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 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 VELACS 1 project. An example of a NorSand model fit to the Bonnie silt data is shown in Fig 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) BIOT COUPLED CONSOLIDATION THEORY. Natural fine-grained soils exhibit low hydraulic conductivity, so excess generated pore pressures gradually dissipate in time. During the dissipation process there is a link between changes in pore pressure and soil stresses and vice versa. Realistic pore pressure dissipation prediction methods should account for this relationship; such a theory was developed by Biot (1941). Biot s theory accounts for solid to fluid and fluid to solid coupling. For the radial symmetry assumed in the current analysis, the Biot governing equation is given by: K' k γ w r 2 u r where: K - bulk modulus of the soil [kn/m 2 ]; γ w - unit weight of water [kn/m 3 ]; u w - pore pressure [kn/m 2 ]; k r - radial hydraulic conductivity [m/s] ; p - mean total stress [kn/m 2 ]. r - radial distance [m] w 2 + k r 1 u w uw = r r t p t (4.7) Implementation of the NorSand model in conjunction with Biot consolidation requires two additional parameters: 1 VELACS Verification of Liquefaction Analysis with Centrifuge Studies 57

71 Chapter 4. Formulation of modelling approach. - u o initial pore pressure (the code is actually using the change in pore pressure); - k r hydraulic conductivity in radial direction FINITE ELEMENT IMPLEMENTATION OF NORSANDBIOT FORMULATION. The current study employs a one-dimensional version of the large strain NorSandBiot code developed by Shuttle (Shuttle & Jefferies, 1998; Shuttle, 2003). The NorSand model was implemented within a 1-D finite element code using an incremental viscoplastic formulation. Viscoplasticity (Zienkiewicz & Cormeau, 1974) is an approach for representing plastic behaviour and its irrecoverable strains within the finite element method. Accurate representation of plasticity is essential because irrecoverable strains are a fundamental aspect of soil behaviour. This is particularly relevant to the problem of helical pile installation, where existence of large irrecoverable volumetric strains is apparent. Although not typically used with more complex soil models, the viscoplastic approach has the advantages of being both simple and fast to converge (Shuttle, 2004). The incremental viscoplastic formulation by Zienkiewicz & Cormeau (1974) was implemented according to the general approach described by Smith & Griffith (1998). Description of the code is given by Shuttle & Jefferies (1998). Flow chart illustrating the solution methodology is presented in Fig 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 FINITE ELEMENT CODE VERIFICATION. There are no analytical solutions available for cavity expansion within the NorSand soil model. Therefore prediction of stresses and pore pressure by NorSandBiot code cannot be verified directly. However correctness of particular aspects of the finite element code implementation and predictions can be checked, as described below. 58

72 Chapter 4. Formulation of modelling approach. Finite element implementation of the NorSand soil model was verified against direct integration of the NorSand equations (see Section E.1, Appendix E). Simulation of cavity expansion was verified using Mohr-Coulomb analysis in contrast with analytical solutions by Gibson & Anderson (1961), Carter et al. (1986) and Houlsby & Withers (1988) (see Section E.2, Appendix E). Pore pressure dissipation prediction of the NorSandBiot code were verified against Schiffman s (1960) solution for 1-D consolidation with construction loading, (see Section E.3, Appendix E); Overall, the verifications performed showed that NorSandBiot code produces correct stresses and strains during cylindrical cavity expansion and is able to simulate pore water pressure generation and dissipation process very well SUMMARY. A realistic simulation of fine-grained soil requires partially drained analysis with both a fully coupled modelling approach and a realistic soil model. NorSand critical state soil model was chosen to represent the soil medium, the coupling between changes in stress-strain conditions and the pore water pressure response is provided by Biot equations. A special modelling procedure was developed to simulate helical pile installation using a cylindrical cavity expansion analogue. The conducted verification of the finite element code showed excellent agreement with existing analytical solutions. 59

73 Chapter 4. Formulation of modelling approach. a). helical pile shaft 8.9 cm helical plate Volume A 0.9 cm cm b). Volume A one flight (9.5 cm) 1.54 cm Fig 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

74 Chapter 4. Formulation of modelling approach. Time initial state 1 st penetration step 2 nd step 3 nd step Fig Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 2-D. Fig Conceptual representation of modelling of helical pile installation as an expansion of cylindrical cavity in 1-D. 61