THE CONE PENETRATION TEST IN UNSATURATED SILTY SANDS

Transcription

1 THE CONE PENETRATION TEST IN UNSATURATED SILTY SANDS Hongwei Yang BEng A thesis submitted in fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY School of Civil and Environmental Engineering The University of New South Wales Sydney, Australia July 214

2 PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet Surname or Family name: YANG First name: HONGWEI Other name/s: Abbreviation for degree as given in the University calendar: Ph.D School: Civil and Environmental Engineering Faculty: Engineering Title: The Cone Penetration Test in Unsaturated Silty Sands Abstract 35 words maximum: (PLEASE TYPE) The cone enetration test (CPT) is widely used for in-situ characterization of saturated or dry soils for which interretation methods are well established. The CPT is also erformed in unsaturated soils yet very little is known about how to interret the recovered results. The few ublished studies on the CPT in unsaturated soils have focused on either clean sands or a silt. Never before have the effects of hydraulic hysteresis and suction hardening, features known to influence the mechanical behavior of many unsaturated soils, on cone enetration resistance been investigated. This research aims to fill these knowledge gas. The soil considered in the study is a silty sand, a soil for which hydraulic hysteresis and suction hardening are resent. A theoretical comonent includes a new cavity exansion analysis. This is useful since the ressure required to exand a cavity has a relationshi with the cone enetration resistance. The effects of where the initial hydraulic state is located on the soil-water characteristic curve is investigated and found to have a significant influence on cavity ressure. Also, the effects of three different drainage conditions on cavity ressure are studied. It is found that the condition in which the contribution of suction to the effective stress is constant offers a good aroximation to the others. One exerimental comonent includes soil element tests to obtain the constitutive roerties of the silty sand. Test results were used to calibrate a bounding surface lasticity model and generate cavity exansion results. Another exerimental comonent includes laboratory-controlled CPTs in silty sand samles. Suction is observed to have a ronounced affect on cone enetration resistance. A new fractal-based hydraulic conductivity model is develoed to study the time needed to achieve suction equilibrium in the samles during set u. Based on the cavity exansion and exerimental test results, a semi-theoretical exression is resented that links cone enetration resistances to initial relative density and mean effective stress along with a arameter to account for suction hardening. It is shown that failing to account for suction may result in significant overestimation and unsafe redictions of soil roerties from measured cone enetration resistances. Declaration relating to disosition of roject thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in art in the University libraries in all forms of media, now or here after known, subject to the rovisions of the Coyright Act I retain all roerty rights, such as atent rights. I also retain the right to use in future works (such as articles or books) all or art of this thesis or dissertation. I also authorise University Microfilms to use the 35 word abstract of my thesis in Dissertation Abstracts International (this is alicable to doctoral theses only). Signature.. Witness..... Date The University recognises that there may be excetional circumstances requiring restrictions on coying or conditions on use. Requests for restriction for a eriod of u to 2 years must be made in writing. Requests for a longer eriod of restriction may be considered in excetional circumstances and require the aroval of the Dean of Graduate Research. FOR OFFICE USE ONLY Date of comletion of requirements for Award: THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS

3 COPYRIGHT STATEMENT I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or art in the University libraries in all forms of media, now or here after known, subject to the rovisions of the Coyright Act I retain all rorietary rights, such as atent rights. I also retain the right to use in future works (such as articles or books) all or art of this thesis or dissertation. I also authorise University Microfilms to use the 35 word abstract of my thesis in Dissertation Abstract International (this is alicable to doctoral theses only). I have either used no substantial ortions of coyright material in my thesis or I have obtained ermission to use coyright material; where ermission has not been granted I have alied/will aly for a artial restriction of the digital coy of my thesis or dissertation.' Signed... Date... AUTHENTICITY STATEMENT I certify that the Library deosit digital coy is a direct equivalent of the final officially aroved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format. Signed... Date...

4 ORIGINALITY STATEMENT I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials reviously ublished or written by another erson, or substantial roortions of material which have been acceted for the award of any other degree or diloma at UNSW or any other educational institution, excet where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is exlicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the roduct of my own work, excet to the extent that assistance from others in the roject's design and concetion or in style, resentation and linguistic exression is acknowledged. Signed... Date...

5 Abstract ABSTRACT The cone enetration test (CPT) is widely used for in-situ characterization of saturated or dry soils for which interretation methods are well established. The CPT is also erformed in unsaturated soils yet very little is known about how to interret the recovered results. The few ublished studies on the CPT in unsaturated soils have focused on either clean sands or a silt. Never before have the effects of hydraulic hysteresis and suction hardening, features known to influence the mechanical behavior of many unsaturated soils, on cone enetration resistance been investigated. This research aims to fill these knowledge gas. The soil considered in the study is a silty sand, a soil for which hydraulic hysteresis and suction hardening are resent. A theoretical comonent includes a new cavity exansion analysis. This is useful since the ressure required to exand a cavity has a relationshi with the cone enetration resistance. The effects of where the initial hydraulic state is located on the soil-water characteristic curve is investigated and found to have a significant influence on cavity ressure. Also, the effects of three different drainage conditions on cavity ressure are studied. It is found that the condition in which the contribution of suction to the effective stress is constant offers a good aroximation to the others. One exerimental comonent includes soil element tests to obtain the constitutive roerties of the silty sand. Test results were used to calibrate a bounding surface lasticity model and generate cavity exansion results. Another exerimental comonent includes laboratory-controlled CPTs in silty sand samles. Suction is observed to have a ronounced affect on cone enetration resistance. A new fractalbased hydraulic conductivity model is develoed to study the time needed to achieve suction equilibrium in the samles during set u. Based on the cavity exansion and exerimental test results, a semi-theoretical exression is resented that links cone enetration resistances to initial relative density I

6 Abstract and mean effective stress along with a arameter to account for suction hardening. It is shown that failing to account for suction may result in significant overestimation and unsafe redictions of soil roerties from measured cone enetration resistances. II

7 Acknowledgements ACKNOWLEDGEMENTS The financial suort from China Scholarshi Council and the University of New South Wales is gratefully acknowledged. I would like to exress my deeest gratitude and areciation to my suervisor, Associate Professor Adrian Russell, for insiring my interest in unsaturated soil mechanics and for his invaluable guidance, technical suervision and continuous encouragement during the course of this research. I extend my gratitude to my cosuervisor, Professor Nasser Khalili, for his helful discussions and invaluable suggestions. I thank Dr Arman Khoshghalb for roviding the code and software for flow analysis. I wish to thank rofessional and technical staff in the School of Civil and Environmental Engineering. Particularly, I am grateful to Mr Richard Berndt and Mr Paul Gwynne for their safety guidance and great hel in rearing and conducting laboratory tests. I would also like to thank my fellow research colleagues in the geotechnical engineering grou who have been of great hel to me and made my stay at UNSW memorable. I am extremely grateful to my arents and brother for their love, encouragement and suort throughout my life. Hongwei Yang July 214 III

8 Table of contents TABLE OF CONTENTS ABSTRACT... I ACKNOWLEDGEMENTS... III LIST OF FIGURES... IX LIST OF TABLES... XVIII CHAPTER 1. INTRODUCTION OVERVIEW, PROBLEM STATEMENT AND METHODOLOGY SCOPE AND OBJECTIVES OF THE STUDY THESIS OUTLINE... 5 CHAPTER 2. LITERATURE REVIEW INTRODUCTION BASIC FEATURES OF UNSATURATED SOILS Stress state in unsaturated soils Hysteretic SWCC due to hydraulic hysteresis Effects of hydraulic hysteresis on hydraulic conductivity and shear strength Collasible behavior Hydro-mechanical constitutive modeling of unsaturated soils CONE PENETRATION TESTS General descrition of cone enetration tests General descrition of calibration chambers Methods of rearing large soil samles INTERPRETATION OF CPT RESULTS General overview Cavity exansion theory as a tool to interret cone enetration tests in saturated soils Cavity exansion theory as a tool to interret cone enetration tests in unsaturated soils CONCLUDING REMARKS IV

9 Table of contents CHAPTER 3. AN EXPERIMENTAL STUDY INTO STRESS-STRAIN BEHAVIOR OF UNSATURATED LYELL SILTY SAND INTRODUCTION TEST SOIL: LYELL SILTY SAND Index roerties Static comaction tests at bench scale SOIL-WATER CHARACTERISTIC CURVE DETERMINATION TESTS General Pressure late tests Mercury Intrusion/Extrusion tests Discussion OEDOMETRIC COMPRESSION TESTS FOR SATURATED SOILS General Conventional tests Discussion TRIAXIAL TESTS General Triaxial aaratus Calibration of triaxial aaratuses Samle rearation Testing rogram Test results and discussions CONCLUDING REMARKS CHAPTER 4. AN EXPERIMENTAL STUDY OF THE CPT IN UNSATURATED LYELL SILTY SAND INTRODUCTION THE UNSW CALIBRATION CHAMBER AND TESTING SETUP PREPARING UNSATURATED SAMPLES FOR LABORATORY CONTROLLED CPTS Samle formation with axis translation technique Samle formation with suction as-comacted CONE PENETRATION TESTS RESULTS V

10 Table of contents Presentations of cone enetration resistance (q c ) and moisture content distribution General observations DISCUSSIONS Assessing uniformity of soil samles Suction verification Effects of suction on cone enetration resistance CONCLUDING REMARKS CHAPTER 5. A CONSTITUTIVE MODEL FOR LYELL SILTY SAND INTRODUCTION NOTATION THE CONSTITUTIVE MODEL Effective stress and the effective stress arameter Mechanical model Hydraulic model Couling of the mechanical and hydraulic models Comlete stress-strain relationshi MODEL CALIBRATIONS Mechanical model calibration Hydraulic model calibration MODEL SIMULATIONS Simulation results for saturated triaxial tests Simulation results for unsaturated triaxial tests Simulation results for oedometric comression and isotroic comression tests CONCLUDING REMARKDS CHAPTER 6. A NEW MODEL FOR HYDRAULIC CONDUCTIVITY INTRODUCTION A DESCRIPTION OF A SOIL WITH IDEALISED PORE GEOMETRIES FROM FRACTALS AND SWCCS TO HYDRAULIC CONDUCTIVITY FUNCTIONS VI

11 Table of contents Caillary tubes and volume flux Hydraulic conductivity on the main wetting curve Hydraulic conductivity on the main drying curve Hydraulic conductivity on scanning curves COMPARISONS AGAINST EXPERIMENTALLY MEASURED HYDRAULIC CONDUCTIVITY DATA APPLY THE MODEL TO LARGE UNSATURATED SAMPLES CONCLUDING REMARKS CHAPTER 7. CAVITY EXPANSION ANALYSIS CONSIDERING HYDRAULIC HYSTERESIS INTRODUCTION NOTATIONS GOVERNING EQUATIONS FOR ELASTIC REGION GOVERNING EQUATIONS FOR ELASTIC-PLASTIC REGION Equilibrium equation Constitutive equations Hardening rule Consistency equation Continuity equation Three drainage conditions A CONCEPTUAL UNDERSTANDING OF THE EFFECTS OF HYDRAULIC HYSTERESIS SOLUTION PROCEDURE CAVITY EXPANSION IN UNSATURATED SITLY SAND Inut arameters Cavity exansion results CONCLUDING REMARKS CHAPTER 8. INTERPRETATION OF CPT RESULTS AND PRACTICAL GUIDELINES INTRODUCTION BACKGROUND VII

12 Table of contents An existing method for interretation of CPT results in saturated cohensionless soils Existing methods for interretation of CPT in unsaturated soils CAVITY EXPANSION ANALYSIS IN LYELL SILTY SAND Purose of cavity exansion analysis Fitting results of sherical cavity exansions for saturated conditions Fitting results of sherical cavity exansions for unsaturated conditions Transition between saturated and unsaturated states COMPARISON WITH CALIBRATION CHAMBER DATA Comarison of cavity exansion results with calibration chamber data and two ossible semi-theoretical correlations Examles of alication CONCLUDING REMARKS CHAPTER 9. SUMMARY AND CONCLUSIONS GENERAL LABORATORY INVESTIGATIONS OF UNSATURATED LYELL SILTY SAND AND CALIBRATION CHAMBER STUDY OF CPT A NEW FRACTAL-BASED HYDRAULIC CONDUCTIVITY MODEL A NEW CAVITY EXPANSION SOLUTION FOR UNSATURATED LYELL SILTY SAND METHOD FOR INTERPRETING CPT RESULTS IN UNSATURATED LYELL SILTY SAND SUGGESTIONS FOR FURTHER RESEARCH REFERENCES 266 VIII

13 List of Figures LIST OF FIGURES Figure 2.1. Unsaturated soils consist of three hases: solid soil articles, air and water in the ore saces Figure 2.2. Illustration of a hysteretic soil-water characteristic curve Figure 2.3. Illustration of ink-bottle effect using caillary tube model (after Lu and Likos, 24) Figure 2.4. Illustration of fractal geometry by Menger songe with first and second generation of cubes (after Russell, 21) Figure 2.5. Detailed features of a modern (iezocone) enetrometer (after Lunne et al., 1997) Figure 2.6. Overview of the Cone Penetration system. (after Mayne, 27) Figure 2.7. Schematic diagram of University of Oklahoma calibration chamber (after Tan, 25) Figure 2.8. Schematic diagram of the calibration chamber at the University of New South Wales (after Pournaghiazar et al., 211a) Figure 2.9. Definition of state arameter (after Been and Jefferies, 1995) Figure 2.1. Correlation between state arameter and eak friction angle of sand (after Been and Jefferies, 1995) Figure 3.1. Particle size distribution (PSD) curve for Lyell silty sand Figure 3.2. PSD data with the fractal estimation of ercent assing Figure 3.3. Photograh of the comaction mould Figure 3.4. Static comaction curves Figure 3.5. Samle arrangements in ressure late tests Figure 3.6. Photograh of the ressure late aaratus Figure 3.7. Cross-section views of (a) volume decrease and (b) samles lost contact from the rings Figure 3.8. Soil-water characteristic curves from ressure late tests, in the moisture content versus logs lane. Loose indicates an initial void ratio of.68, medium an initial void ratio of.59 and dense an initial void ratio of Figure 3.9. Cumulative intrusion er ore volume versus ore diameter for samles SCL-6, SCD-8, insitu-1 and insitu-2 with void ratios of.48,.62,.41 and.345, resectively Figure 3.1. Soil-water characteristic curves from Mercury Intrusion/Extrusion tests.. 67 Figure Relationshi between air entry values and void ratios together with the best fitting line of s ae = 1.5e kpa IX

14 List of Figures Figure Pressure late test results and Mercury Intrusion/Extrusion test results lotted in the lns r ~ lns/s ae lane together with estimations of sloe of main curves and scanning curves, resectively Figure Oedometric comression tests results for three starting void ratios of.391,.413 and.435 in the v ~ σ' 1 lane Figure A hotograh of the dismantled high ressure triaxial aaratus. (after Russell, 24) Figure Schematic layout of samle setu for triaxial tests Figure Photograh of the Stress-Path aaratus Figure Photograh of a Modified Bisho-Wesley triaxial aaratus Figure Results of saturated isotroic comression tests for initial void ratio of.323 (Iso-S-L) together with calibration curve of digital image-rocessing technique and for initial void ratio of.335 (Iso-S-M) at relatively high ressure Figure Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε q ~ q lane Figure 3.2. Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε q ~ q lane Figure Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε ~ε q lane Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ε q ~ q lane Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ε q ~ u w lane Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ' ~ q and lane Figure Results of unsaturated isotroic comression tests (Iso-s1 and Iso-s3) in the v ~ ln lane together with the result for Iso-S-M Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa in the ε ~ε q lane Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa in the ε q ~ q lane Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa in the ε ~ε q lane Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa in the ε q ~ q lane Figure 3.3. Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa in the ε ~ε q lane Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa in the ε q ~ q lane Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 3 kpa and 6 kpa in the ε ~ε q lane X

15 List of Figures Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 3 kpa and 6 kpa in the ε q ~ q lane Figure Results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa in the ε ~ε q lane Figure Results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa in the ε q ~ q lane Figure Critical state line in the q ~ net lane (The suction for constant moisture content conditions at critical state was unknown in the tests and was estimated) Figure 4.1. Cross-section of the UNSW calibration chamber (after Pournaghiazar et al., 211a) Figure 4.2. The general calibration control system (after Pournaghiazar et al., 211a). 95 Figure 4.3. Cross-section of a samle after drilling Figure 4.4. To late being lowered into osition once the iezometers were installed.96 Figure 4.5. Boundary condition Figure 4.6. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL6SAC) Figure 4.7. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL6S1) Figure 4.8. Moisture content results for UL6S1 for equilibrium time of 79.5 hours Figure 4.9. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of 3 kpa and with initial as-comacted void ratio of.68 (UL6S3) Figure 4.1. Moisture content distribution results for UL6S3 for equilibrium time of 1625 hours Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL12SAC) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL12S1) Figure Moisture content distribution results for UL12S1 for equilibrium time of 56.5 hours Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, the as-comacted suction and with initial as-comacted void ratio of.56 (UD12SAC) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.56 (UD12S1) XI

16 List of Figures Figure Moisture content distribution results for UD12S1 for equilibrium time of 1126 hours Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL24SAC) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL24S1) Figure Moisture content distribution results for UL24S1 for equilibrium time of hours Figure 4.2. Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with σ h of 1 kpa, target suction of 1 kpa and with initial ascomacted void ratio of.68 (K6S1-1) Figure Moisture content distribution results for K6S1-1 for equilibrium time of hours Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with σ h of 1 kpa, target suction of 1 kpa and with initial ascomacted void ratio of.68 (K6S1-N) Figure Moisture content distribution results for K6S1-N for equilibrium time of 35.5 hours Figure Volume of water exelled from samle vs. time elased for samle of K6S Figure Comaction curves (Vo and Russell, 213) together with initial states of CPT samles before testing (Numbers next to markers denoting suctions). Note the time allowed for suction change is different for each test denoted by hollow circle Figure SWCC (Vo and Russell, 213) together with initial back-calculated suction values of CPT samles before testing Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of as-comacted value, 1 kpa and 3 kpa and with test void ratio of.655 ± Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of as-comacted value and 1 kpa and with test void ratio of.635 ± Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, target suction of as-comacted value and 1 kpa and with test void ratio of.585 ± Figure 4.3. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of as-comacted value and 1 kpa and with test void ratio of.52 ± Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with horizontal stress of 1 kpa, target suction of 1 kpa and with test void ratio of.625± XII

17 List of Figures Figure Comarison of moisture content distribution results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with horizontal stress of 1 kpa, target suction of 1 kpa and with test void ratio of.625± Figure 5.1. Evolution of effective stress arameter with suction Figure 5.2. Illustration of loading surface, bounding surface and maing rule in the q~ lane Figure 5.3. Saturated and unsaturated CSLs and LICLs in the lne ~ ln' lane Figure 5.4. The exerimental data (from Tarantino and De Col, 28) of soil-water characteristic curves with D estimation for 5 void ratios in the lns r ~lns lane Figure 5.5. Critical state line in the q ~ 'lane Figure 5.6. Results of saturated drained triaxial tests in the M cs -q/ ~ ε /ε q lane with determination of arameter A Figure 5.7. Saturated triaxial shear tests results in the lne ~ ln' lane Figure 5.8. Unsaturated triaxial tests results under constant suction conditions in the lne ~ ln' lane Figure 5.9. Results of undrained triaxial tests conducted on the loosest samles and loading surface with Q = 2 and R = 1 in the q/' /M cs ~ q/' lane Figure 5.1. Results of Mercury Intrusion/Extrusion tests (MIP) and Pressure late tests (P.P.) in the lns r ~ lns/s ae lane Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the q ~ ε q lane Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the u w ~ε q lane Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the q ~ 'lane Figure Results of saturated drained tests and model simulations for CD5, CD1, CD25, CD3, CD36 and CD5 in the ε ~ ε q lane Figure Results of saturated drained tests and model simulations for CD25, CD3, CD36 and CD5 in the q ~ ε q lane Figure Results of saturated drained tests and model simulations for CD5, and CD1 in the q ~ ε q lane Figure Illustration of initial states determination for loose and dense soils Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa for suction of 1 kpa (u6s1l-cs and u6s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa for suction of 3 kpa (u6s3l-cs and u6s3d-cs) in the ((a) ε ~ ε q and (b) q ~ ε q lane, resectively XIII

18 List of Figures Figure 5.2. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa (u12s1l-cs, u12s3l-cs and u12s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa (u24s1l-cs and u24s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of more than 24 kpa (u6s3l-cs and u3s3d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa (u6s1l-cw and u6s1d-cw) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Figure Comarison of model simulations and isotroic comression test results of saturated condition at low ressure and relative high ressure (iso-s-l and iso-s-m), s=1 kpa (iso-s1) and s=3 kpa (iso-s3) in the lne ~ ln lane Figure Comarison of model simulations and oedometric comression test results of 1-D-L-1, 1-D-L-2 and 1-D-H in the lne ~ ln lane Figure Comarison of model simulations and saturated oedometric comression test results of 1-D-L-1, 1-D-L-2 and 1-D-H in the σ' 3 / σ' 1 ~ lnσ' 1 lane Figure 6.1. Grahically illustration of SWCC and hydraulic conductivity functions in lns r ~ lns and lnk R ~ lns lane Figure 6.2. Measured SWCC data of Caribou silt loam (To, 1971) together with fractal simulations for (a) drying along scanning curves and (b) wetting along scanning curves Figure 6.3. Measured hydraulic conductivity of Caribou silt loam (To, 1971) against model simulations for (a) main drying, drying along scanning curves and (b) wetting along scanning curves Figure 6.4. Model simulations against exerimental data of Quartz sand (Dury et al., 1998) for (a) SWCC and (b) relative hydraulic conductivity Figure 6.5. Model simulations against exerimental data for samle A35 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity Figure 6.6. Model simulations against exerimental data for samle A55 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity Figure 6.7. Model simulations against exerimental data for samle B62 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity Figure 6.8. Moisture content distribution data against model simulations for K6S1-N together with sensitivity check for β = -.16, -.2 and -.24 at time = 35 hours XIV

19 List of Figures Figure 6.9. Moisture content distribution data against model simulations for K6S1-1 together with sensitivity check for T = 1.5, 2 and 2.5 at time = hrs Figure 6.1. Moisture content distribution data against model simulations for K6S1-2 for T = 1.5, 2 and 2.5 at time = 126 hours and 2795 hours, resectively Figure Back-calculated suction rofiles with cone enetration resistance along the samles of K6S1-N and K6S Figure 7.1. Simlified illustrations of the analogy between cone enetration resistance (q c ) from CPTs and the limiting cavity ressure (σ L ) and the analogy between wall ressure (P L ) from a Pressuremeter test and the cylindrical cavity ressure Figure 7.2. Cavity exansion in elastic-lastic material Figure 7.3. Illustration of how suction changes during cavity exansion for different initial states without a void ratio-deendent SWCC for (a) initially loose soil and (b) initially dense soil Figure 7.4. Sherical cavity exansion results for net = 6 kpa, s = 2 kpa and e =.64,.51 and.38 under constant suction conditions in the (a) lne ~ ln lane and (b) q ~ lane Figure 7.5. Cylindrical cavity exansion results for net = 6 kpa, s = 2 kpa and e =.64,.51 and.38 under constant suction conditions in the (a) lne ~ ln lane and (b) q ~ lane Figure 7.6. Sherical cavity exansion results in the lne ~ ln lane for initial state on SWCC at MD and net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of drainage conditions Figure 7.7. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main wetting curves (MW) Figure 7.8. Sherical cavity exansion results in the net ~ σ L lane s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main wetting curves (MW) Figure 7.9. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states at the midoint along scanning curves (SC) Figure 7.1. Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states at the midoint along scanning curves (SC) Figure Cylindrical cavity exansion results in the net ~ σ L lane for; s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main drying curves (MD) XV

20 List of Figures Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main drying curves (MD) Figure (a) Sherical and (b) cylindrical cavity exansion results in the lne ~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant moisture content conditions Figure (a) Sherical and (b) cylindrical cavity exansion results in the ln e~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant suction conditions Figure (a) Sherical and (b) cylindrical cavity exansion results in the lne ~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant χs conditions Figure Sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.64 under (a) constant moisture content conditions and (b) constant χs conditions Figure Sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.38 under (a) constant moisture content conditions and (b) constant χs conditions Figure Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant suction conditions Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant suction conditions Figure 7.2. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant moisture content conditions Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant moisture content conditions Figure Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions Figure Cylindrical cavity exansion results in the ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions Figure Sherical cavity exansion results in the ~ σ L lane s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions XVI

21 List of Figures Figure 8.1. The limiting cavity ressure (σ L ) from saturated drained sherical cavity exansion analysis fitted with Equation (8.3) Figure 8.2. Estimated σ L using Equation (8.3) comared with simulated σ L from saturated drained sherical cavity exansion solutions Figure 8.3. The limiting cavity ressure σ L fitted with Equation (8.4) Figure 8.4. Estimated σ L using Equation (8.4) comared with simulated σ L from unsaturated sherical cavity exansion solutions Figure 8.5. Limiting cavity ressure σ L normalized by '.65 versus D r with concetual illustration of suction hardening effects. All results are for drained conditions Figure 8.6. Illustration of arameter ξ LICL Figure 8.7. Initial states for the cavity exansion analysis and associated LICLs Figure 8.8. A ossible relationshi between C 3 D r 6.18D r and ξ Figure 8.9. Associated errors using Equation (8.8) Figure 8.1. Normalized lateral limit ressure from sherical cavity exansion simulation (Q sh = (σ L - net )/ ) together with normalized cone enetration resistance (Q cc = (q c - net )/ ) against initial state arameter Figure A relationshi between Q cc and Q sh Figure A ossible correlation between q c measured from chamber and σ L from sherical cavity exansion Figure Comarison of cavity exansion data and estimations using Equation (8.12) Figure Associated errors using Equation (8.12) Figure Estimation of ξ LICL using Equation (8.12) XVII

22 List of Tables LIST OF TABLES Table 3.1 Index roerties of Lyell silty sand Table 3.2. List of tests conducted in the triaxial aaratuses Table 4.1. Test conducted and relevant test conditions for unsaturated Lyell silty sand Table 4.2. Suction values along with moisture contents at deth of.3 m and.5 m Table 5.1. Parameters N(s) and λ(s) defining the limiting isotroic comression lines Table 5.2. List of initial conditions for oedometric comression tests and isotroic comression tests Table 5.3. List of initial conditions for saturated triaxial tests Table 5.4. List of initial conditions for unsaturated triaxial tests Table 6.1. Proerties of ores and cells of different orders Table 6.2. Soil hydraulic roerties and arameters for hydraulic conductivity model Table 6.3. Initial conditions and hydraulic arameters for each samle Table 8.1. Values of C 3 for unsaturated sherical cavity exansion results XVIII

23 CHAPTER 1. INTRODUCTION 1.1 OVERVIEW, PROBLEM STATEMENT AND METHODOLOGY The cone enetration test (CPT) is one of the most oular in-situ test methods and is used to determine the engineering roerties of soils. It has major advantages over traditional methods of field site investigations, such as drilling and samling, as it rovides a combination of a continuous data record with excellent reeatability and accuracy at relatively low cost (Lunne et al., 1997). This has driven a steady increase in the develoment and alication of the CPT around the world (Robertson, 29). However, the CPT, as for other in-situ methods, does not rovide a direct measurement of any articular soil roerty. Rather, it measures the load resonses as the cone enetrates into a deformable soil mass. The interretation of the CPT therefore becomes a ivotal area of ractical interest. Many correlations have been made to relate results of the CPT, e.g. cone enetration resistance, sleeve friction, ore water ressure and shear wave velocity, to shear strength arameters, stiffness and in-situ states (e.g. Robertson and Camanella, 1983a,1983b; Lunne et al., 1997; Mayne, 27; Robertson, 29; Salgado, 213). However, the focus of the interretations in the ast was on saturated or comletely dry soils. 1

24 Chater 1 Introduction Unsaturated soils, also known as artially saturated soils, consist of three hases: soil skeleton, water and air hases. The air-water interface gives rise to suction and it acts as a force to ull adjacent soil articles together and makes the roerties of unsaturated soils greatly different from those of saturated or comletely dry soils. Unsaturated soils occuy the majority of shallow ground rofiles and need to be dealt with in almost every asect of geotechnical engineering. In recent decades, our knowledge about unsaturated soils has been greatly advanced through both exerimental investigations (e.g. Barden et al., 1969; Laroussi and Debacker, 1979; Ramino et al., 2; Sun et al., 27a; Alonso et al., 211) and theoretical develoments (e.g. Alonso et al., 199; Wheeler and Sivakumar, 1995; Loret and Khalili, 22; Russell and Khalili, 26a; Khalili and Zargarbashi, 21; Alonso et al., 213). It is found that the resence of suction can affect the engineering behaviour of unsaturated soils to a great extent. There are increasing evidences that the cone enetration resistance can be influenced by the resence of suction significantly, as was observed in exeriments by Hryciw and Dowding (1997), Tan (25) and Pournaghiazar et al. (213b) and in field tests by Lehane et al. (24), Collins and Miller (214) and Woodburn and Herraman (214). However, engineers are left to interret the CPT conducted in unsaturated soils using correlations develoed for saturated and comletely dry soils. This will inevitably lead to unknown errors in estimations of soil roerties (Russell and Khalili, 26; Pournaghiazar et al., 213). Limited research has been done on the CPT conducted in unsaturated soils and considerable further research is needed to identify the effect of unsaturation on the interretation of CPT results, both theoretically and exerimentally. This is the motivation for this research. In ractice, moisture content in a soil is much easier to be measured than suction. Moisture content is strongly related to suction. However, the moisture content-suction relationshi is not unique due to hydraulic hysteresis and differences during drying and wetting. Hydraulic hysteresis is one of the basic features of unsaturated soils. Former studies showed that the hydraulic hysteresis can affect shear strength arameters that are associated with suction (e.g. Han et al.,1995; Nishimura and Fredlund, 22; Shemsu et al., 25; Thu et al., 26; Gallage and Uchimura, 26; Khalili and Zargarbashi, 21; 2

25 Chater 1 Introduction Khoury and Miller, 211). The suction change exerienced by a soil element may not be monotonic, esecially for dense soil. Also, the hydraulic hysteresis affects hydraulic conductivity (e.g. To, 1971; Vachaud and Thony, 1971; Dury et al., 1998; Basile et al., 23; Gallage et al., 213; Lu et al., 213). It is necessary to take hysteresis into account when calculating the hydraulic conductivity. Furthermore, it is known that suction can increase the shear strength and comressibility of unsaturated soils. Also subsequent wetting may induce large irreversible volumetric collase. This wetting-induced collase can be exerienced by any unsaturated soils under articular conditions of stress, density and saturation (Barden et al., 1969; Lawton et al., 1991) and it only occurs in soils which exhibit suction hardening. This is extremely imortant for infrastructures that are founded on soils at shallow deth where they are likely to be encountered. The CPT can be studied by laboratory controlled exeriments using calibration chambers where stresses and strain histories, boundary conditions, densities and moisture contents of samles can be fully controlled. Calibration chamber testing has been ivotal in the ast when establishing emirical correlations for CPT interretation in saturated soils (e.g. Schertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1982; Houlsby and Hitchman, 1988). Only recently, calibration chamber tests were conducted in unsaturated soils attemting to establish new emirical correlations (Tan, 25) or to extend existing correlations at saturated states to those at unsaturated states (Pournaghiazar et al., 213). The CPT can also be studied theoretically by cavity exansion analysis (Lunne et al., 1997; Yu and Mitchell 1998). The cone enetration roblem is analogous to cavity exansion as first noticed by Bisho et al. (1945). The results of sherical cavity exansion analysis were usually related to cone enetration tests results (e.g. Vesic, 1972; Yu, 1993; Salgado and Prezzi, 27; Pournaghiazar et al, 212, 213a). Numerous cavity exansion solutions have been develoed for saturated soils (e.g. Vesic, 1972; Carter, 1986; Yu, 1993; Salgado and Prezzi, 27; Pournaghiazar et al., 212, 213). But only a few can be found for unsaturated soils (Ortigao et al., 1996; 3

26 Chater 1 Introduction Muraleetharan et al., 1998; Russell and Khalili, 26b). However, never before has the effect of hydraulic hysteresis and the location of the hydraulic state in the moisture content suction relationshi on the ressure required to exand a cavity been investigated. 1.2 SCOPE AND OBJECTIVES OF THE STUDY This research aims at enlarge our understanding of the CPT conducted in unsaturated soils where hydraulic hysteresis and suction hardening are resent. A series of soil element tests and laboratory-controlled CPTs are conducted. Cavity exansion theory is emloyed where a bounding surface lasticity model is used to describe the stress-strain behavior of unsaturated soils. Four major contributions are made: 1. Conduct and reort results of an extensive rogram of laboratory-controlled exeriments to study the stress-strain behavior of Lyell silty sand, a soil for which hydraulic hysteresis and suction hardening are resent. Conduct and reort results of CPT tests in unsaturated Lyell silty sand. The effects of suction on cone enetration resistance for various net stresses and densities are highlighted. 2. Investigate the effect of hydraulic hysteresis on the hydraulic conductivity. A new fractal-based model is used to describe hydraulic conductivity and enables estimation of the soil hydraulic state located on scanning curves. This model is combined with a numerical method for flow analysis to estimate the time needed for large unsaturated samles, where suction is alied by axis translation, to aroach moisture equilibrium. This contribution has already been ublished in a journal aer (Yang et al., 214). 3. Develo a new cavity exansion solution for unsaturated soils where hydraulic hysteresis and suction hardening are included in the constitutive model. Secifically, the effects of where the initial hydraulic states are located on the 4

27 Chater 1 Introduction moisture content- suction relationshi are investigated, as are different drainage conditions. 4. Proose a method for interreting CPT results in unsaturated Lyell silty sand. The method is based on others develoed for saturated soils, but with a new arameter introduced to account for the effect of suction hardening. 1.3 THESIS OUTLINE Chater 2 reviews literature on relevant features of unsaturated soil mechanics, basic features of the cone enetration test and methods for interretation of the cone enetration test results. Chater 3 resents an exerimental study on the stress-strain behavior of Lyell silty sand in both saturated and unsaturated states. The test soil characteristics are also resented. Chater 4 resents an exerimental study of the CPT in unsaturated Lyell silty sand. The effects of different densities, net stresses, comression conditions (anisotroic condition and isotroic condition) and suctions on CPT results are investigated. Chater 5 resents a constitutive model to describe the stress-strain behavior of Lyell silty sand in saturated and unsaturated states. The model is fitted to the results of an extensive rogram of laboratory tests conducted on Lyell silty sand. Chater 6 resents a new hydraulic conductivity model. The effect of hydraulic hysteresis on the hydraulic conductivity is investigated with the aid of fractals. The model ermits estimation of hydraulic conductivity using fractals when the soil state is located on scanning curves. Chater 7 resents a new cavity exansion solution in unsaturated soils where hydraulic hysteresis and suction hardening are resent. The effects of where the initial hydraulic states are located on the moisture content suction relationshi are investigated, as are different drainage conditions. 5

28 Chater 1 Introduction Chater 8 rooses a new method to interret CPT results conducted in soils where hydraulic hysteresis and suction hardening are resent. Chater 9 summarizes the major conclusions drawn from this study and also outlines recommendations for further research. 6

29 CHAPTER 2. LITERATURE REVIEW 2.1 INTRODUCTION The literature review comrises four main sections. In Section 2.2 basic features of unsaturated soil mechanics are reviewed. The henomena of hydraulic hysteresis and volumetric collase in articular are focused on. General features of cone enetration tests (CPT) are then reviewed in Section 2.3 which also includes general descritions of calibration chambers and methods to roduce large samles for laboratory controlled CPT testing. Interretations of the CPT are reviewed in Section 2.4. Secifically, uses of cavity exansion theory in both saturated and unsaturated soils to interret CPTs are reviewed. Section 2.5 resents concluding remarks and limitations identified through the above reviews. 2.2 BASIC FEATURES OF UNSATURATED SOILS Unsaturated soils, also known as artially saturated soils, are widesread in nature, esecially in the shallow arts of a soil rofile. A lot of infrastructures involve unsaturated soils including shallow foundations, retaining walls, embankments, sloes and road avements. Unsaturated soils consist of three hases: solid soil articles with air and water in the surrounding ore saces (see Figure 2.1). The existence of the air and water hases 7

30 Chater 2 Literature Review gives rise to an air-water interface. The interface surface tension induces a force that ulls adjacent soil articles together, a henomenon referred to as suction. The suction adds comlexity to the understanding of the stress-strain behavior of unsaturated soils. Their stress-strain behavior is influenced by numerous factors including the externally alied stress, suction, soil tye, structure and density. In the following some asects of unsaturated soil mechanics are reviewed including the influence of stress state, hydraulic hysteresis, suction hardening and collasible behavior Stress state in unsaturated soils The stress state and the associated shear strength of unsaturated soils are usually exressed using either the effective stress aroach (Bisho, 1959) or the indeendent state variables aroach (Fredlund and Morgenstern, 1977). Over the last decade, several state-of-the-art reviews can be found (e.g. Kohgo, 23; Sheng and Fredlund, 28; Sheng, 211). The two aroaches are briefly reviewed here. In the indeendent state variables aroach the total stress in excess of air ressure and the suction are considered searately. The shear strength (τ) is exressed as (Fredlund and coworkers): b b u tan ' u u tan c' u tan ' stan c' (2.1) a a w a where σ is the total stress, u a is the ore air ressure, u w is the ore water ressure, s= u a u w is the matric suction, c' is the effective cohesion, is the effective internal fiction angle and is the internal friction angle with resect to matric suction. On the other hand, the effective stress aroach utilizes a single stress variable (Bisho, 1959): ' u u u u s a a w a (2.2) 8

31 Chater 2 Literature Review where σ' is the effective stress and χ is the effective stress arameter. Different definitions of χ were reorted (e.g. Kohgo et al., 1993; Khalili and Khabbaz, 1998; Jommi, 2 and Pereira et al., 25). They all attain a value of 1 for saturated soils and for dry soils. A detailed review of those χ is given by Nuth and Laloui (28a). The definition of χ is given by, for examle, (Khalili and Khabbaz, 1998):. 55 se (2.3) s where s e is the suction value searating saturated and unsaturated states. The shear strength is then exressed as: c ' 'tan' (2.4) The indeendent state variables aroach can be used to exlain some asects of unsaturated soils behavior. However, it requires sohisticated and time-consuming laboratory testing to determine the material arameters. Conversely the effective stress aroach can be emloyed with quicker and simler laboratory testing (e.g. Loret and Khalili, 22; Khalili et al., 24; Russell and Khalili, 26a). Another merit of the effective stress aroach is that it is simler to use in the constitutive modeling of unsaturated soils (e.g. Vaunat et al.,2; Wheeler et al., 23; Morvan et al., 21, 211) and in the interretation of laboratory test results Hysteretic SWCC due to hydraulic hysteresis For unsaturated soils there exists a relationshi between suction and the volumetric or gravimetric moisture content or degree of saturation, which is generally referred to as a soil-water characteristic curve (SWCC). The SWCC is ivotal in understanding the behavior of unsaturated soils and estimating the shear strength, volume change and hydraulic conductivity. General reviews of the models alied in the field of geotechnical engineering are in Fredulund and Xing (1994), Leong and Rahardjo (1997), Sillers et al. (21) and Lu and Likos (24). However, Haines (193) showed that there was a strong hysteresis between the moisture content and suction, which means the moisture content and the suction are not uniquely 9

32 Chater 2 Literature Review related. This is usually referred to as hydraulic hysteresis. As shown in Figure 2.2, there are two main branches to a SWCC, namely the main drying curve for drainage and the main wetting curve for infiltration. The curves connecting them are scanning curves. According to Lu and Likos (24), hysteretic behavior is attributed to several mechanisms that act on both microscoic and macroscoic scales. They include: 1. Ink-bottle effect which is associated with nonhomogeneity in ore size and shae distribution; 2. Swelling and shrinkage which may alter the ore fabric of fine-grained soils in different ways during wetting and drying rocesses; 3. Contact angle hysteresis which is related to the intrinsic difference between drying and wetting contact angles at the soil article-ore water interface. 4. Caillary condensation, which becomes a unique wetting rocess at relatively low water content. 5. Entraed air or occluded air. The ink-bottle effect and contact angle effect are considered to be robably the most imortant factors for relatively coarse-grained soils (Lu and Likos, 24). This effect arises due to nonhomogeity in ore size and shae distribution. The ink-bottle effect is illustrated in Figure 2.3 using a caillary tube model. This model is characterized by two different radii: R being the radii of ore, r being the radii of tube. Here r < R. During wetting the height of the uward flow is controlled by the tube radii (r) which corresonds to certain suction (s). The suction is inversely roortional to r. The uward flow during wetting will cease before reaching the emty ore as continuing uward flow requires current s to be smaller than the s corresonding to R. During drying initially both the tube and the ore are filled with water. The drainage of the tube is controlled by R which corresonds to a suction value smaller than that of r, so that under the same suction the water retained is always larger during drying than wetting rocess. Aart from this, it was observed that the contact angle for wetting can be as high as 6 º ~8 º (e.g. Kumar and Malik, 199) whereas the contact angle for drying ranging from º to around 2º ~3 º (e.g. Laroussi and Debacker, 1979). This may contribute to the hysteresis as well. 1

33 Chater 2 Literature Review Numerous models have been roosed to describe the hysteretic SWCC, esecially by the researchers in the field of soil science, water resources and agriculture science (e.g. To, 1969; Mualem, 1973, 1974; Nimmo, 1992 and Kool and Parker, 1998). Those models aimed to cature not only the two main branches but also the hysteretic loos inside the main curves. Of articular interest here is the alication of hysteretic SWCC models in geotechnical engineering, where the accuracy of estimations of the models may be comromised slightly in order to increase ease of utilization. In this case, among the most adoted SWCC models is the Brooks and Corey (1964) tye model which is reresented by constant sloes for main curves and scanning curves in the double logarithmic degree of saturation and suction lane. Variations of this tye of model have been adoted in geotechnical engineering (e.g. Vaunat et al., 2; Wheeler et al., 23; Khalili et al., 28). Furthermore, it is widely recognized that the SWCC varies with void ratio (e.g. Gallioli et al., 23a; Miller et al., 28; Zargarbashi, 211) and several tyes of void ratio-deendent hysteretic SWCC have been roosed (e.g. Sun et al., 28; Nuth and Laloui, 28b; Tarantino, 29; Muraleetharan et al., 29; Khoshghalb and Khalili, 212). Sun et al. (28) considered a linear relation of the SWCC and the sloes of main curves changed with the void ratio. Nuth and Laloui (28b) roosed an elastolastic relation for the SWCC in which the variations of the scanning curves are reversible whereas the variations of main wetting and drying curves are searated into elastic and lastic variations. Masin (21) made the deendence of a SWCC on void ratio through varying sloes, although did not consider hydraulic hysteresis. Khoshghalb and Khalili (212) built uon this model by considering hydraulic hysteresis and the sloes of main drying and main wetting to be different. Sheng and Zhou (211) roosed a SWCC function for constant ressure conditions. All the aforementioned SWCCs are, however, mostly henomenological in origin. On the other hand, fractals are often used for the characterization of the article size distribution or ore size distribution in soils (e.g. Perfect and Kay, 1995; Gimenez et al., 1997). Several methods can be found in the literature to describe a fractal s self-similar geometry, which includes Cantor bar, Sierinski caret, Menger songe and Koch curve 11

34 Chater 2 Literature Review (Perfect and Kay, 1995). Shown in Figure 2.4 is the fractal Menger songe from Russell (21). Initially it is a solid cube with a side length of, for examle, one unit. Smaller cubes of side length of 1/3 are generated. The smaller cubes at both the center of each face and the cube center are then removed so that 2 solid cubes remain. In a similar way, each remaining solid cube is again divided into 27 smaller cubes. In a limit, a fractal ore size distribution is achieved, and the fractal dimension would be 2.73 (Perfect and Kay, 1995). A soil s self-similar fractal geometry was observed exerimentally and has motivated a number of exressions for the SWCC (Tyler and Wheatcraft, 1989; Bird et al., 2; Hunt and Gee, 22; Cihan et al., 27; Yu et al., 29; Russell, 21) but without considering hydraulic hysteresis. Only recently, Russell and Buzzi (212) made the derivations of SWCC for a state on scanning curves by treating a ore to consist of either a throat or a body whose drainage or infiltration was controlled by throat size, through which the defining arameters of the SWCC model were linked with the microstructure of the soils. Later, Russell (214) accounted the deendency of this hysteretic SWCC on void ratio by couling the ore shae and article shae roerties and imlied that a SWCC for a single voids ratio can be made alicable to any other voids ratio using just the article size distribution. As will be shown later, this tye of orosity-deendent hysteretic model can be successfully incororated with the mechanical model to describe the stress-strain behavior of unsaturated soils with good accuracies Effects of hydraulic hysteresis on hydraulic conductivity and shear strength Effects of hydraulic hysteresis on hydraulic conductivity Hydraulic conductivity is a key arameter used to redict flow and transortation rocesses within orous media including soils. Numerous exerimental studies have reorted the effect of hydraulic hysteresis on hydraulic conductivity (e.g. To, 1971; Vachaud and Thony, 1971; Dury et al., 1998; Basile et al., 23; Gallage et al., 213; Lu et al., 213). To (1971) measured the hydraulic conductivity for a silt loam and a clay loam soil using a vertical column of soil subjected to several circles of infiltration and evaoration. The hysteresis was observed more obviously in a silt loam than in a clay loam. Using a similar method, Vachaud and Thony (1971) investigated the 12

35 Chater 2 Literature Review hysteretic behavior on a sandy soil. Dury et al. (1998) conducted steady-state column exeriments on a quartz sand mixture using a wetting fluid containing butanol solutions of 2% and 6% by weight. Air conductivity was also measured. The hysteresis was not obvious in the lnk r ~ lns r lane due to the high sand content. Basile et al. (23) investigated the hydraulic hysteresis in both field and laboratory conditions using the instantaneous rofile method (Watson, 1966) and the modified evaoration method (Tamari et al., 1993), resectively, on samles of sandy loam. Differences of the hydraulic conductivity measured between field and laboratory conditions were observed and were found to be related to the hysteresis. Lu et al. (213) used the transient release and imbibitions method (Wayllace and Lu, 212) to measure the hydraulic conductivity on samles ranging in tye from silty sand to clayey soils. All the above studies reorted that the hydraulic conductivity is different for different initial hydraulic states on the SWCC. The hydraulic conductivity for the initial hydraulic state on the main drying curve is larger than that for the initial hydraulic state on the main wetting curve. The difference can be as large as a few orders of magnitude. It is therefore necessary to be able to calculate the hydraulic conductivity when the initial state is on a scanning curve Effects of hydraulic hysteresis on shear strength Only a few researchers have studied the effect of hydraulic hysteresis on the shear strength of unsaturated soils (Han et al., 1995; Nishimura and Fredlund, 22; Shemsu et al., 25; Thu et al., 26; Gallage and Uchimura, 26; Khoury and Miller, 211). Han et al. (1995) studied the hysteresis effect on the shear strength of residual soils. Nishimura and Fredlund (22) studied hysteresis effects, resulting from drying and wetting under relatively high total suction conditions, on the shear strength (mainly comressive strength) of a comacted silty soil and comacted kaolin. Thu et al. (26) investigated the effects of hysteresis on shear strength enveloes from constant water content and consolidated drained triaxial tests. Results from these studies indicate that a soil undergoing drying tends to have slightly higher shear strength comared to the same soil at the same suction along a wetting ath. It is suggested that the difference in strength for drying and wetting aths is related to the interfacial contact area of water and solids in the soil, which affects the interarticle forces and results in lower shear 13

36 Chater 2 Literature Review strength for wetting. However, Gallage and Uchimura (26) studied the effects of wetting and drying on the unsaturated shear strength of silty sand under low suctions and reorted that the shear strength in the wetting rocess is higher as comared to the shear strength in the drying rocess under the same suction. This may be due to the void ratio of the samle not being constant and is smaller during drying-wetting than in a samle subjected only to drying. Shemsu et al. (25) conducted triaxial tests under constant moisture content and constant suction conditions to study the cyclic suction influence on the shear strength of unsaturated cohesionless soil (e.g. sandy-silt). They found that the soil under cyclic suction loading tended to have higher eak shear strength, more volumetric comression and more dilatancy. Khoury and Miller (211) conducted a series of suction-controlled direct shear tests on soil and soil on rough steel interfaces. For the test conditions and test soil which has a grain size distribution similar to that of fine sandy soil, they revealed that the shear strength after drying-wetting was greater than the shear strength after only drying at the same net normal stress and matric suction. It was concluded that secimens that underwent cyclic suction showed higher eak shear strength. Based on the exerimental results of 5 soils, Khalili and Zarbargashi (21) found that the effective stress arameter was different for main drying and wetting curves. According to Equation (2.2) the difference of shear strength may arise from different effective stress arameters along main drying and wetting curves. Results from the studies discussed above show that shearing behaviors of unsaturated soils are affected by the hydraulic hysteresis as well as the loading history associated with suction Collasible behavior Unsaturated soils may exerience significant volumetric decrease when wetted (Barden et al., 1969, Barden et al., 1973). This wetting-induced collase is defined by Lawton et al. (1991) as densification of a soil caused by the addition of water at constant total vertical stress. Many unsaturated soils can exerience collase under articular conditions of stress, density and saturation. (Barden et al., 1969; Lawton et al., 1991) 14

37 Chater 2 Literature Review According to Dudley (197), Barden et al. (1973), Mitchell (1976) and Lawton et al. (1991), four factors are needed for collase to occur: 1. An oen, artially unstable, unsaturated fabric. 2. A high enough net total stress that will cause the structure to be metastable. 3. A bonding or cementing agent that stabilizes the soil in the unsaturated condition 4. The addition of water to the soil, which causes the bonding or cementing agent to be reduced and the interaggregate or intergranular contacts to fail in shear, resulting in a reduction in total volume of the soil mass. Quantification of wetting induced collase is of engineering interest. Jennings and Knight (1957) quantified the collasible behavior by means of double oedometer tests. They roosed that the collase otential (c ) can be estimated as: c e e e i s (2.5) 1 e 1 e where Δe is the change in void ratio uon wetting, e i is the void ratio at natural state, e s is the corresonding void ratio at saturation and e is the initial void ratio. Variations of this definition can also be found in Foss (1973) and Reznik (1993). The collase otential is a basic arameter to exerimentally investigate the collase behavior and is widely used (e.g. Thevanayagam et al., 22; Trivedi and Sud, 24; Lim and Miller, 24; Sun et al., 27a; Medero et al., 29; Alonso et al., 213). Recently, Gallioli et al. (23b) found that there may be a unique function of the void ratio (e) of unsaturated soil and the void ratio (e s ) corresonding to the saturated state at the same average skeleton stress (Jommi, 2). This function is defined by introducing a variable that is related to the bonding effect (ξ bond ), which is given as: e e 1 1 ex a b bond (2.6) s where a and b are fitting arameters. Jotisankasa et al. (27) found these two arameters to be deendent on the initial fabrics of the soil created by comaction under different conditions and that the exression is less successful for ξ bond more than.8 and 15

38 Chater 2 Literature Review for soils at extremely dry states. This correlation has gained some oularity (e.g. Tarantino and Tombolato, 25; Jotisankasa et al., 27 and Jotisankasa et al., 29). On the other hand, with the recent advances in unsaturated soil mechanics (notably Alonso et al., 199; Gallioli et al., 23a, b; Wheeler et al., 23; Loret and Khalili, 24; Russell and Khalili, 26a; Khalili et al., 28; Alonso et al., 213), it is ossible to model the collasible behavior through constitutive models. The model roosed by Alonso et al. (199), the so-called Barcelona Basic Model (BBM), and its variations (e.g. Gallioli et al., 23a, b; Wheeler et al., 23) defined a loading-collase surface from which the amount of collase can be calculated. The model of Loret and Khalili (24), and its variations (e.g. Russell and Khalili, 26a; Khalili et al., 28; Morvan et al., 21 and 211), link the amount of collase with the reconsolidation ressure which is a function of suction and comressibility. Recently Alonso et al. (213) defined a arameter to account for the microstructure through which the intrinsic collasible behavior of comacted soils can be exlained. However, though that model may roduce a reasonable rediction of the collase, it requires many inut arameters determined through sohisticated exerimental testing. Also it should be noted that the actual collase mechanism may be influenced by more factors (Dudley, 197) than the factors considered in the models. Suction hardening needs to be resent for collase to occur as evidenced by exerimental results in Wheeler and Sivakumar (1995) and Cui and Delage (1996). Loret and Khalili (22) used suction hardening to account for volumetric collase. Lawton et al. (1991) showed through a literature review that almost all tyes of comacted soils are subject to collase under certain conditions as the comacted soils tend to exhibit an unstable structure under wetting. But not all unsaturated soils resent suction hardening. Russell and Khalili (26a) reared unsaturated sand samles for triaxial testing by luviating dry sand into a triaxial mould and before inducing suction the samle was saturated, freezed and transferred to the triaxial aaratus. Triaxial results indicated that suction hardening was not resent. Also, collase was never observed. 16

39 Chater 2 Literature Review Hydro-mechanical constitutive modeling of unsaturated soils It is well acknowledged that the agreement between model simulations and the observed exerimental behavior is only ossible by couling the hydraulic and mechanical behaviors. Couling hydraulic and mechanical behaviors in unsaturated soils has been an intense research area in the recent two decades (Vaunat et al., 2, Wheeler et al., 23 and Nuth and Laloui, 28 among others). Some notable contributions to this area are reviewed in the following. The first comlete hydro-mechanical model which also takes into account the hydraulic hysteresis is robably due to Vaunat et al. (2). Their roosed model is based on the work of Alonso et al. (199). Two yield surfaces are defined in addition to the loading collase yield surface in order to simulate the irreversible changes of degree of saturation during wetting-drying cycles. However, the model does not include the effects of mechanical comonents on the hydraulic comonent. The same roblem also aears in Sheng et al. (24) and Nuth and Laloui (28b). Wheeler et al. (23) then roosed a model that can fully coule the hydraulic and mechanical comonents of unsaturated soil behavior. They adot an average skeleton stress aroach and a modified suction which is a combination of suction and orosity. Therefore, the influence of hydraulic behavior on the stress-strain relationshi is considered via the definition of the effective stress. However, one of the difficulties in using this model is to quantify the synchronized movement between the loadingcollase surface and the suction-decrease and suction-increase surfaces. Sheng et al. (24) extended Wheeler s model to deviatoric loading and decouled the movement between these three surfaces. Building on this model, Sun and his colleagues (Sun et al, 27a, Sun et al, 27b, Sun et al, 28) took into account the effect of void ratio change on the SWCC and also the initial density deendency of the comacted soil behavior which was catured by defining the relationshi between the initial density and the normal comression line. Tarantino and De Col. (28) studied the comaction behavior of clay and observed that ost-comaction suction may increase as the degree of saturation increases. This effect was demonstrated to be associated with the hydro-mechanical couling using the 17

40 Chater 2 Literature Review model of Tarantino and Tombolato (25) which also used an average skeleton stress and modified suction as in Wheeler et al. (23). The same air of stresses was also used in Fuentes and Triantafyllidis (213). Using effective stress aroach Khalili et al. (28) roosed a fully couled constitutive model for orous media. The effective stress arameter (χ) (Khalili and Khabbaz, 1998) was found to be not equal to the degree of saturation, which was confirmed by exerimental results of Khalili and Zargarbashi (21). The deendency of the SWCC on void ratio was not exlicitly defined in this model but was considered later in Khoshghalb and Khalili (212) where a orosity deendent SWCC was utilized. Microstructure was later incororated. Masin (213) roosed a hydromechanical couling framework for soils with a double orosity structure. Macromechanical and micromechanical effective stresses were used in the model and the behavior was modelled indeendently. Similarly Alonso et al. (213) introduced a new arameter to account for the microstructure. It was shown that the intrinsic collase otential and yielding of unsaturated comacted soils could be exlained by incororation of this single arameter which was the ratio of the microstructural void ratio and the total void ratio. It has long been agreed that a mechanical model alone can no longer rovide an accurate descrition of the comlex behaviors of unsaturated soils which consist of three hases. Couling of mechanical and hydraulic models is necessary to describe roerly the stress-strain and volumetric behavior of unsaturated soils. 2.3 CONE PENETRATION TESTS General descrition of cone enetration tests The cone enetration test (CPT) is an in-situ test used to determine the engineering roerties of soils and delineate the soil stratigrahy. It was initially develoed in the Netherlands in The earliest test setus involved a cone ushed by hand and the systems were of a mechanical tye (Broms and Flodin, 1988). A modern cone enetration system consists 18

41 Chater 2 Literature Review of a cone that can measure the cone enetration resistance (q c ), sleeve friction (f s ) and ore water ressure (u w ), a hydraulic ushing system to ush the cone into the ground at a controlled rate, deth recorder and data acquisition unit (Mayne, 27). Detailed features of a modern (iezocone) enetrometer are shown in Figure 2.5. The standard test equiment (ASTM D 5778) consists of a cone with an aex angle of 6º, ti area of 1 cm 2 and a friction sleeve area of 15 cm 2 located above the cone. The ushing rate of the cone is maintained at 2 mm/s. An overview of the Cone Penetration system as er ASTM D 5778 is shown in Figure 2.6. Additional arameters such as shear wave velocity and electrical conductivity can also be obtained through Seismic Piezocone tests and Resistivity Piezocone tests, resectively. Comared to the traditional boring-and-test-at-laboratory method, the CPT has a articular advantage including rovision of a continuous data record with excellent reeatability and accuracy at relatively low cost (Lunne et al., 1997). The test has broad alications and is suited to soft to medium stiff clays and loose to medium dense sand and to situations where the difficulties of recovering undisturbed samles are encountered. The CPT interretation has been studied both theoretically and exerimentally. However as real soil behavior is often comlex semi-emirical correlations for interretation still tend to dominate in the CPT ractice (Robertson, 29). Laboratory-controlled exeriments are done in calibration chambers. Deending on the size of a chamber cones of a standard or smaller size are ushed at a controlled rate into a samle of known roerties. The cone resonses are recorded during enetration. Issues relevant to calibration chamber testing are reviewed in the next two sub-sections General descrition of calibration chambers Desite the accuracy and reeatability of the CPT, uncertainty surrounds the quantitative use of CPT data due to the comlex nature of soils. Calibration chambers, used for calibrating field instruments in a laboratory controlled environment, have layed a ivotal role in develoing emirical correlations for CPTs conducted in 19

42 Chater 2 Literature Review saturated soils in the ast. One main advantage of calibration chamber testing over field testing is that it allows researchers to fully control the stress and strain history, boundary conditions, density and water content of the test samles (Tan, 25). The first flexible wall calibration chamber was designed by Holden (1971) at the Country Road Boards, Australia, which consisted of a double wall cylinder and a membrane enclosing a sand secimen. After that, calibration chambers with similar designs but of different sizes were manufactured for the rearation and testing of sand samles (Bellotti et al. 1982; Sweeney, 199 and de Lima, 199). The first calibration chamber for testing cohesive soils was develoed by Huang (1988). It included instrumentation and orous disks at the to and down the sides of the secimens enabling double drainage and ore ressure monitoring during testing. As for calibrating in-situ devices in small-size laboratory deosits, significant errors may occur due to boundary effects (Parkin and Lunne, 1988 and Schnaid and Houlsby, 1991), thus there was a trend towards increasing the deosit size to imrove calibration accuracy. A larger calibration chamber for cohesive soils caable of simulating constant stress boundary conditions was designed by Anderson et al. (1991). The above designs of calibration chambers are all for rearation and testing of saturated or dry soils. More recently at the University of Oklahoma (Miller et al. 22) a calibration chamber for erforming CPTs and PMTs in unsaturated soils was develoed. The schematic diagram of this calibration chamber is shown in Figure 2.7. It allows indeendently measurement and control of ore water ressure, ore air ressure, and the radial and axial stress alied to the soil samles. Furthermore, at the University of New South Wales, based on the features of revious chambers (Bellotti et al. 1982; Sweeney, 199; Miller et al., 22; Anderson et al., 1991), a new calibration chamber was designed and built as detailed by Pournaghiazar et al. (211a) to study the CPT in unsaturated soils. The schematic diagram of this calibration chamber is shown in Figure 2.8. Key imrovements have been incororated, including a novel secimen formation system, a modified axial load alication system and measurement and control of suction within the system. 2

43 Chater 2 Literature Review Methods of rearing large soil samles There are several methods to reare soil samles used for calibration chamber testing. Mostly adoted is the luviation method for sandy soils, slurry consolidation for saturated cohesive soils, and comaction including dynamic and static comaction for unsaturated silts. Some work (Tan, 2) has comared the different methods used to reare large soil samles Slurry consolidation For the rearation of cohesive soils the slurry consolidation method is well-known to roduce homogeneous, reroducible high quality cohesive samles. Sheeran and Krizek (1971) indicated that an initial slurry water content of 1.5 to 2 times the liquid limit was aroriate for ease of deairing and roviding uniform and reroducible secimens. Voyiadjis (1993) stated that when the initial moisture content was lower than this, the air entrament in the slurry during mixing and lacement in the consolidometer would not be aroriately minimized. A higher slurry moisture content would lead to segregation of soil grains and, most imortantly, higher consolidation times. However, such high initial moisture contents might result in an initial slurry height of aroximately two times of the desired samle height. This required the equiment to be large enough to accommodate the initial samle which was not always ractical. Thus a two stage consolidation rocess was required. During the first stage the slurry was consolidated inside a slurry consolidometer under K conditions, and then laced into the calibration chamber under triaxial consolidation for the second stage (Anderson et al., 1991; Huang et al., 1988). A two-staged method was found to be essential to reduce the rigid boundary effects of the first ste (Voyiadjis, 1993). Another way to minimize the boundary effects was to increase the deosit size to imrove laboratory accuracy (Parkin and Lunne, 1982). Thus, after the first attemt (Huang, 1988) to construct a triaxial calibration chamber for clay using the slurry consolidation method, Anderson et al. (1991) built a larger calibration chamber for clay with the similar design to Huang (1988) to better simulate the field conditions using field test devices. 21

44 Chater 2 Literature Review Calibration chamber tests involving soils with a large amount of fines content (Huang, 1988; Anderson, 1991; McManus, 1991; Voyiadjis, 1993; Kuru, 1994; Sheeran, 1971) encounter difficulties in maintaining saturation and monitoring the ore water ressure. They are also time-consuming and laborious in rearing samles. Many researchers (e.g. Anderson, 1991 and McBride, 1992) reorted that the time required for the consolidation was very large, which was due to the fact that the comressibility, hydraulic conductivity and rate of consolidation of the samle decreased with time as the samle consolidated. Also, as the degree of saturation decreases, the hydraulic conductivity droed significantly Pluviation The luviation method is commonly used to reare sand samles. It involves raining or droing dry sand articles into a mould. The dry density achieved is a function of deosition intensity and falling height of articles from sieve to the samle surface. Tan (2) examined two ossibilities to reare unsaturated silt samle. One was by dry luviating the entire samle and then introducing water from both ends and the other was by dry luviating the samle in layers followed by adding a redetermined volume of water on to of each lift. Tan (2) concluded from the test results that the dry unit weight of the samle reared was too low which may cause great volume changes during consolidation. The moisture contents were uniformly distributed but the time required for the moisture content to reach equilibrium was very long. For sands Pournaghiazar et al. (211a) showed that this method can roduce a uniform samle in terms of dry density Comaction Comaction is the densification of soils by the alication of mechanical energy. It may also involve a modification of the moisture content as well as the gradation of the soil. After several samles of the same soil with different moisture contents are comacted, comaction curves which are unique to the soil tye, the tye of comaction method and comactive effort can be obtained. Several tyes of comaction methods are usually emloyed in laboratory testing including imact or dynamic, kneading and static comactions (Holtz et al., 1981). 22

45 Chater 2 Literature Review The dynamic comaction method is a common tye to reare remoulded triaxial soil samles in the laboratory. The density of the samle is controlled by the moulding moisture content, number of layers, number of blows er layer, taming forces and thickness of each layer. The standard Proctor comaction technique is used to determine the comaction curve which is unique to the soil tye, the tye of comaction method and comactive effort. It seems like the reason why it is not adoted in rearing large calibration chamber samles is that the time and labour involved would be very extensive. Tan (2) stated in his thesis that moist taming was quite similar to dynamic comaction with the excetion that it involved using a light-taming rod to comact thin layers of soil instead of using high comaction efforts. Static comaction is often used to reare laboratory samles to examine the roerties of unsaturated soils (e.g. Tarantino, 25; Sivakumar, 2; Oh, 28). The arameters that control the dry density of the samle are the number of layers, the thickness of the layer and the static ressure. Leonards (1953) conducted some unublished investigations at Purdue (through Gau and Olson, 1971) and had demonstrated that uniform secimens could only be reared by statically comacting secimens using diameters several times of the thickness of layer. It was found that substantial density variations existed in statically comacted samles when the height was aroximately equal to the diameter. In order to avoid the over-densification of the bottom most layers, an under-comaction rocedure develoed by Ladd (1978) is often used. This method urosely makes the dry density of layer at the bottom less than required. The influence of succeeding layers makes the bottom layers reach the desired dry density. When it comes to unsaturated soils, esecially soils with a large amount of fines content, comaction is mostly used to reare samles for triaxial tests, oedometer tests and other laboratory tests (e.g. Blight, 1967; Fredlund, 1977; Escario, 1989). The comaction method to reare unsaturated soils is very effective and valid, since current well-adoted unsaturated soil mechanics theory is develoed based uon the data mostly obtained from this method. However, only a few attemts have been made to aly the comaction method to reare large samles for calibration chambers. The 23

46 Chater 2 Literature Review first one that used this method to reare large calibration chamber samles for the study of field devices in unsaturated soils was Tan (25). Prior to adoting comaction methods to reare large samles, Tan (25) made comarisons between the methods of luviation and comaction (dynamic, taming, static) at bench-scale. Conclusions were drawn by him that luviation was not a viable method for rearing samles of silt due to the considerable time required and the non-uniformity of the samle comared to that reared by comaction. Among the three tyes of the comaction methods, static comaction was most reeatable and reliable through both grahical and scientific analyses, which has been further illustrated by additional comarisons of dry unit weight and water content distribution within each comacted layer at full bench scale. In order to verify the uniformity of the bench-scale soil samles, a thin-wall soil samle was used, though Gau and Olson (1971) recommended using CPT equiment to study the samle uniformity as they found that error may occur for tests on small samles caused by trimming disturbance and evaoration during samling. Also Tan (2) found that no matter what tye of comaction method was used, the moisture content distribution was quite uniform. He suggested that great effort should be taken to ensure that the soil was evenly distributed in the mould Conclusions on the comarison of various methods based on literature review From the above reviews on the methods to reare soil samles, it can be seen that the samles reared by comaction methods are more likely to have the homogeneous moisture content distribution, while the other two methods (luviation and slurry consolidation), esecially when used to reare large unsaturated samles with a large amount of fines content, require an imractical amount of time for consolidation and water equilibrium. Also, Tan (25) found that regulating the ore air and ore water ressure to obtain certain matric suction was not ractical. It required a tremendous amount of time to induce a small change in matric suction due to the low ermeability of the unsaturated soil and the large samle dimensions. Thus Tan suggested comacting soils at rescribed moisture content with reference to a target matric suction based on the soil-water characteristic curve, and this in return required homogeneous moisture content distribution in order to reach a homogeneous matric suction distribution. Among the comaction methods, from the bench-scale study of Tan (2), static comaction can roduce samles that are not only homogeneous in their 24

47 Chater 2 Literature Review moisture content distribution but also are more accetable in their dry density distribution. Thus, so far, the static comaction seems to be the most lausible method to reare large unsaturated soil samles with a large amount of fines content. 2.4 INTERPRETATION OF CPT RESULTS General overview Generally, interretation methods for CPT results fall into two main categories (Lunne et al., 1997): one is based on emirical correlations and the other one involves using semi-theoretical correlations. All rely on calibration chamber testing for their validation. The interretation methods differ significantly for coarse-grained soils and for finegrained soils. Emirical correlations were usually develoed using calibration chamber test results where stress and strain history, boundary condition, density and water content of the samles could be fully controlled. For dry/saturated coarse-grained soils, fully drained conditions were normally considered. One of the emirical correlations links cone enetration resistance (q c ) with relative density (D r ) (e.g. Schertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1982; Salgado et al., 2; Cudmani and Osinov, 21; Huang and Hsu, 25) and it takes the form: q c C2 C 1 ' ex( C 3 Dr ) (2.7) where C 1, C 2, C 3 are constants and σ' is the initial effective stress. Houlsby and Hitchman (1988) found that the q c is more influenced by horizontal effective stress (σ' h ) than vertical effective stress (σ' v ). Also, as ointed out by Jamiolkowski and Robertson (1988), enetration resistance is strongly influenced by σ' h, and any normalization to account for increasing stress should include the imortant influence of σ' h (Robertson, 29). When overconsolidated or aged sands were encountered σ' h should be used (Robertson and Camanella, 1983). For normally consolidated sands, vertical effective stress (σ' v ) was usually adoted (Schertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1982; Kumar and Raju, 27). Considering the above it has been suggested that the initial mean effective stress (' ) has a wider alication for both normally consolidated 25

48 Chater 2 Literature Review sands and overconsolidated sands (e.g. Baldi et al., 1982; Jamiolkowski et al., 21; Cudmani and Osinov, 21 and Huang and Hsu, 25). Setting σ'= ', Jamiolkowski et al. (21) obtained some tyical values of C 1, C 2 and C 3 which are 23.19,.56 and 2.97 for Ticino sand and are 24.94,.46 and 2.96 for other siliceous sands. CPTs conducted in dry/saturated coarse-grained soils have also been interreted in terms of the state arameter (ξ) (Been and Jefferies, 1995). The state arameter is defined as the difference in the void ratio of a soil at a given mean effective stress and the void ratio on the critical state line, as shown in Figure 2.9. Been and Jefferies (1985) found that the state arameter correlates well with eak friction angle determined in a triaxial test, as shown in Figure 2.1. Been et al. (1986, 1987) suggested an equation to relate ξ to q c : q c ' net kex( m ) (2.8) where m is the sloe of the normalized q c ~ ξ relationshi and k is the normalized q c at ξ =. m and k differ from one sand to another. The interretation rocedure involves carrying out triaxial tests to determine the critical state line. For saturated fine-grained soils, undrained conditions were normally considered in the interretation. Interretations for the undrained shear strength arameter were made through: s u q k v T (2.9) N where q T is a corrected cone enetration resistance and N k is a dimensionless cone factor. Kjekstad et al. (1978) suggested N k may be assumed to be 17 for non-fissured overconsolidated clays. Lunne and Kleven (1981) obtained s u from field vane tests and showed that N k varies between 11 and 19 for normally consolidated marine clays. 26

49 Chater 2 Literature Review Robertson and camanella (1983) suggested using N k values of 15 for reliminary assessment of undrained shear strength and for sensitive clays. Aas et al. (1986) resented correlations between cone factor and lasticity index. It was observed that cone factor increased with increasing lasticity and the cone factor varied between 11 and 18 for the range of lasticity considered. The emirical correlations are very useful in interretations of CPTs conducted in dry or saturated soils. However, it usually requires a large quantity of data to establish them. For unsaturated soils very a few eole have investigated this roblem and the existing database is very limited. On the other hand, theoretical solutions can rovide a useful framework to investigate the influence of certain soil arameters on CPT results. Exerimental data can later be fitted into the theoretical framework to form semi-theoretical correlations. For the theoretical solutions, Lunne et al. (1997) stated that cavity exansion theory is the most acceted and adoted theory, more so than the classical bearing caacity theory, strain ath theory and conservation of energy combined with cavity exansion theory. Yu and Mitchell (1998) reviewed the bearing caacity theory, cavity exansion theory and steady state aroach and concluded that the cavity exansion theory gave the closest overall agreement between the redicted and measured enetration resistances. The cavity exansion theory rovides a simle and yet reasonably accurate method for the analysis of the CPT and thus remains one of the most common aroaches to theoretically investigate the CPT. A more recent review of theoretical methods can also be found in Pournaghiazar (211b) where cavity exansion theory was also recommended. Therefore the following review concentrates on cavity exansion theory. Here the interretations using cavity exansion theory are laced into two categories: interretation in saturated or dry soils and interretation in unsaturated soils Cavity exansion theory as a tool to interret cone enetration tests in saturated soils The alication of cavity exansion theory in solving enetration roblems was ioneered by the work of Bisho et al. (1945). They indicated that there existed an analogy between cavity exansion and cone enetration after observing that the ressure required to roduce a dee hole in an elastic-lastic medium was roortional to that 27

50 Chater 2 Literature Review necessary to exand a cavity of the same volume under the same conditions. Similar investigations were also reorted by Chadwick (1959 and 1962). The ressure at the wall of an exanding cavity aroaches a limiting value at large strains and this is analogous to cone resistance of the cone enetration tests. Since then the theory has received a lot of attention (e.g. Vesic, 1972; Carter, 1986; Yu, 1993; Norman, 25; Salgado and Prezzi, 27; Russell and Khalili, 26b; Pournaghiazar et al., 212). Vesic (1972) roosed an aroximate cavity exansion solution for comressible soil. A Mohr-Coulomb tye soil was assumed in the lastic zone surrounding the cavity. Volumetric strain was initially introduced to the analysis as a known value and then determined for a certain amount of stress change through an iterative rocedure. Baligh (1976) used the same framework but with a curved Mohr-Coulomb failure enveloe and concluded that ignoring the curvature of the enveloe may result in significant error in the cavity limit ressure. However, the results deended greatly on volumetric strain which can hardly be estimated. Carter et al. (1986) develoed a closed form solution for the limit ressure at the cavity wall using a Mohr-Coulomb model. A non-associative flow rule and constant mobilized friction and dilation angles were assumed. However, the solution was restricted by the assumtions of small strain made throughout the urely lastic region, thus these solutions are more alicable to the interretation of ressuremeter tests where strains are tyically less than 1%. Afterwards, a similarity technique was develoed by Collins et al. (1992) and Collins and Stimson (1994) to analyze the exansion of created cavities from zero initial radius. The similarity technique stated that the cavity exands in a geometrically selfsimilar manner, and thus the ratio of the radius of the cavity to that of the elastic-lastic interface remain constant during the exansion. This solution enables the incororation of more realistic and also more comlex models into the cavity exansion roblem than the Mohr-Coulomb model. Thus a more comlex model, the Cam-Clay model, was first incororated in the cavity exansion analysis (Collins et al., 1992) to account for the evolution of the dilatancy with accumulated strain and stress. 28

51 Chater 2 Literature Review Shuttle and Jefferies (1998) used a critical state model that is able to cature the strainsoftening behavior to erform the sherical cavity exansion analysis at large strain. They found that the normalized limiting radial stress from a sherical cavity exansion analysis is strongly related to the normalized cone enetration resistance when lotted against the state arameter (Been and Jefferies, 1985). Thus, a correlation was roosed to relate the normalized limiting radial stress to the normalized cone enetration resistance. Effects of various arameters on cavity exansion analysis were also investigated. Cudmani and Osinov (21) develoed solutions to the cavity exansion roblem based on hyolasticity. A shae factor, that is a function of the ressure-deendent relative density, was introduced to account for the mismatch between the limiting radial stress and the cone enetration resistance obtained in calibration chamber, so that the state of cohesionless soil could be estimated. Salgado and Prezzi (27) used asects of the Salgado et al. (1997) s analysis where the stress rotation around the cone was considered. The cavity exansion analysis used was from Salgado and Randolh (21) where mobilized friction and dilation angles using the state arameter were defined. A series of grahs relating limiting radial ressure to horizontal stress were resented for different critical state friction angles. Neglected in the above analyses is the article crushing which can occur in sands due to the high stresses resent around the cavity. Russell and Khalili (22) incororated the effect of article crushing by considering a steeening of the critical state line with increasing mean stress. The effect of the article crushing is a reduction in the limiting radial ressure of the cavity exansion analysis Cavity exansion theory as a tool to interret cone enetration tests in unsaturated soils The above contributions were focused on saturated soils. For unsaturated soils very few works are documented (Muraleetharan et al., 1998; Russell and Khalili, 26b). Similarly only two calibration chamber studies of CPTs in unsaturated soils have been conducted. One was erformed by Tan (25) on unsaturated Minco silt at the University of Oklahoma. The cavity exansion solutions develoed by Muraleetharan et 29

52 Chater 2 Literature Review al. (1998) were used to interret the results. The other one was by Pournaghiazar (211b) on unsaturated Sydney sands at the University of New South Wales. The interretation of the tests was made through the theoretical solutions develoed by Russell and Khalili (26b). The interretations of unsaturated soils are as follows. Muraleetharan et al. (1998) develoed solutions for cavity exansion of sherical and cylindrical cavities in unsaturated soils by extending Vesic s (1972) original cavity exansion equations. Thus the elastic deformation was still ignored in the lastic zone which was defined by the Mohr-Coulomb model. The interretation of CPT and PMT results from the calibration chamber tests using this solution was detailed in Tan (25). When analyzing the results of CPT tests in unsaturated Minco Silt, Tan first conducted a statistical analysis to investigate the general effect of several arameters on the cone enetration resistance of the CPT. An assumtion was made that the limiting radial ressure at the cavity wall (σ L ) was equal to the cone enetration resistance of the CPT tests. The results of CPTs conducted in the calibration chamber and the volumetric strain were couled. Several curves were then established between the volumetric strain (ε v ) and the cone enetration resistance (q c ) through: q c F' F' c (2.1) L q c where F' q and F' c are related to the shear strength arameters (c' and φ'), the elastic modulus (E) and the volumetric strain (ε v ) of the soil. Using the curves between ε v and q c it is ossible to redict the q c for field conditions. The difference of q c measured at field conditions and in calibration chamber conditions was corrected imlicitly and emirically by adjusting the estimation of ε v. The established curves were only alicable for Minco Silt at certain conditions. Russell and Khalili (26b) adoted the bounding surface lasticity model resented in Russell and Khalili (26a) to investigate the cavity exansion roblem in unsaturated Sydney sands. This model is able to cature the strain softening behavior and the smooth change between elastic deformations and lastic deformations was accurately 3

53 Chater 2 Literature Review modelled. Using this model, eight governing equations were defined and solved using the similarity technique. Constant suction and constant moisture content conditions were considered in the analysis of cylindrical and sherical cavities corresonding to the PMT tests and CPT tests, resectively. The results show that q c for constant suction and constant moisture content conditions were almost undistinguishable, which imlied that drained conditions can be assumed to revail for both saturated and unsaturated Sydney sand to simlify the interretation. Hydraulic hysteresis was not considered. Drawing suort from this theoretical solution Pournaghiazar et al. (213b) converted the q c values measured in calibration chambers to those of field conditions (Pournaghiazar et al. 212), during which a solution for cavity exansion in soils of finite radial extent (Pournaghiazar et al., 213a) was develoed. Equation (2.11) was roosed:. 85 q c 45' ex(2. 78Dr ) (2.11) For the unsaturated Sydney sand the effect of suction was incororated by using the effective stress concet. A relationshi between q c for saturated conditions and that for unsaturated conditions is then: q q c,sat c,unsat. 85 net s. u 85 net w (2.12) where q c,sat and q c,unsat are the values at saturation and at unsaturation, resectively. Once the contribution of χs to the effective stress (' ) is known, the corresonding cone enetration resistance (q c,sat ) can also be calculated, and vice versa. 2.5 CONCLUDING REMARKS General features of unsaturated soils and their mechanics have been reviewed. It is found that hydraulic hysteresis can have a significant effect on the shear strength and hydraulic conductivity of unsaturated soils. Many unsaturated soils have the otential to collase under certain conditions, esecially comacted soils (Lawton et al., 1991). 31

54 Chater 2 Literature Review Also, couling hydraulic and mechanical behaviors is imerative to roerly model the stress-strain behavior of unsaturated soils. Asects of cone enetration tests are also reviewed. There have been many studies of the CPT in a calibration chamber under laboratory controlled conditions. Methods to reare large samles for CPT tests were reviewed and comared. It was found that static comaction may roduce satisfactory large unsaturated samles for soils with significant fines content. Alications of cavity exansion theory to interretation of CPTs are romising but are almost limited to saturated soils. And only few alications can be found for unsaturated soils (Tan, 25; Pournaghiazar et al., 213b). Through the above reviews a number of limitations have been identified. Firstly, although hydraulic hysteresis has been observed exerimentally to be influential on the shear strength and hydraulic conductivity, the effects of hydraulic hysteresis on cavity exansion analysis results has not been investigated. Furthermore, the method of Pournaghiazar et al. (213b) for the interretation of CPTs in unsaturated sand, a soil in which suction hardening is absent, may not be alicable to other soils where suction hardening is resent. The knowledge gas are then as follows. (1) the effect of hydraulic hysteresis on cavity exansion analysis and (2) the effect of suction hardening are not accounted in the current interretations of CPTs conducted in unsaturated soils. 32

55 Chater 2 Literature Review Soil article Water Air Figure 2.1. Unsaturated soils consist of three hases: solid soil articles, air and water in the ore saces. Figure 2.2. Illustration of a hysteretic soil-water characteristic curve. 33

56 Chater 2 Literature Review 2r 2R wetting drying Figure 2.3. Illustration of ink-bottle effect using caillary tube model (after Lu and Likos, 24). Figure 2.4. Illustration of fractal geometry by Menger songe with first and second generation of cubes (after Russell, 21). 34

57 Chater 2 Literature Review Figure 2.5. Detailed features of a modern (iezocone) enetrometer (after Lunne et al., 1997). 35

58 Chater 2 Literature Review Figure 2.6. Overview of the Cone Penetration system. (after Mayne, 27). 36

59 Chater 2 Literature Review Figure 2.7. Schematic diagram of University of Oklahoma calibration chamber (after Tan, 25). 37

60 Chater 2 Literature Review Figure 2.8. Schematic diagram of the calibration chamber at the University of New South Wales (after Pournaghiazar et al., 211a). 38

61 Chater 2 Literature Review Figure 2.9. Definition of state arameter (after Been and Jefferies, 1995). Figure 2.1. Correlation between state arameter and eak friction angle of sand (after Been and Jefferies, 1995). 39

62 CHAPTER 3. AN EXPERIMENTAL STUDY INTO STRESS-STRAIN BEHAVIOR OF UNSATURATED LYELL SILTY SAND 3.1 INTRODUCTION This chater resents exerimental results on the stress-strain behavior of Lyell silty sand in both saturated and unsaturated states. The test soil characteristics are also resented. The laboratory tests conducted include: I. Soil-water characteristic curve determination tests; II. Oedometric comression tests; III. Isotroic comression tests; IV. Triaxial shear tests. 4

63 Chater 3 Exerimental Investigation 3.2 TEST SOIL: LYELL SILTY SAND Index roerties The soil used in this study is a decomosed granite from the catchment area of Lyell dam, NSW, Australia. It is classified as silty sand (SM) according to the Unified Soil Classification System. Therefore it is referred to as Lyell silty sand. Index roerties are listed in the Table 3.1. It is a non-lastic silty sand. Noticeable is the 27% fines content. The resence of such an amount of fines, for a given value of void ratio, can increase the contractiveness and collasibility or decrease the dilativeness of the host clean sand (Pitman et al., 1994; Lade and Yamamuro, 1997; Salgado et al., 2; Thevanayagam et al., 2, 22; Ni et al., 24). The article size distribution curve (PSD) is shown in Figure 3.1. Lyell silty sand is redominantly a coarse-grained but well-graded soil that is tyical of decomosed granite (Lee and Coo, 1995). The coefficient of uniformity C u and the coefficient of curvature C c are found to be 63.6 and 2., resectively, with the grain sizes D 1, D 3, D 6, corresonding to 1%, 3% and 6% of the samle assing by weight, being.88 mm,.1 mm and.56 mm, resectively. The soil articles exhibit a fractal size distribution. Shown in Figure 3.2 is the PSD data with its fractal estimation. The ercent assing for a fractal soil is defined as (Russell, 21): 3Ds 3Ds d s dsmin 1% Percent assing 3Ds d d 3 smax Ds smin (3.1) where the maximum article size d smax used is 1.8 mm, the minimum article size d smin is.333 mm and the article fractal dimension D s is Static comaction tests at bench scale Static comaction tests were first conducted at bench scale to obtain comaction curves. The soil was firstly oven dried and then subsamles were mixed with rescribed amounts of distilled water. The moistened subsamles were then comacted into a 5 mm diameter mould in five layers so the final comacted thickness of each layer was 2 41

64 Chater 3 Exerimental Investigation mm. A hotograh of the mould is shown in Figure 3.3. Samles were weighed after comaction to calculate the dry density. Different static comaction ressures were used to comact the soil. Four comaction curves corresonding to static ressures of 6 kpa, 21kPa, 6kPa and 8 kpa are shown in Figure 3.4. Those comaction curves highlight the difference in the dry densities achieved. The dry densities generally increase with increasing static comaction ressure. They also increase with increasing moisture content. The maximum dry density was not achieved in the range of moisture contents considered. Similar observations were made by Reddy and Jagadish (1993), Sun et al., (27a) and Tarantino (29) for other silty sands. 3.3 SOIL-WATER CHARACTERISTIC CURVE DETERMINATION TESTS General The soil-water characteristic curve (SWCC) is a term used to refer to a lot of volumetric moisture content, gravimetric moisture content or degree of saturation against suction. Due to hydraulic hysteresis, the SWCC has two main branches, generally referred to as a main wetting curve and a main drying curve. Curves connecting those two main branches are referred to as scanning curves. Those are illustrated in Figure 2.2. In this investigation, two tyes of tests were used to exlore the SWCC - Pressure Plate (P.P.) tests and Mercury Intrusion/Extrusion (MIP) tests. The results are used to characterize the SWCC and its hysteretic behavior Pressure late tests Test rogram Nine samles for use on the ressure late were reared (each being of 5 mm diameter and 25 mm thickness) at three different void ratios (.5,.59 and.68) by comacting them at the same moisture content (7.%) but under different static comaction ressures. Their arrangement on the ressure late rior to testing is shown in the Figure 3.5. Samles were not saturated before ressure late testing. This revented volumetric collase. The testing involved increasing suction in increments until 45 kpa was reached (drying), then reducing suction in increments (wetting). Seven days were found to be sufficient for each increment to reach water equilibrium. 42

65 Chater 3 Exerimental Investigation The hotograh of the ressure late aaratus is shown in the Figure 3.6. The test setu is similar to that of others (e.g. Tinjum et al., 1997). The volume of each samle was checked at the end of each suction increment. During the increase of suction no volume change was observed. During the decrease of suction negligible volume change occurred between suctions of kpa and 27.6 kpa. However, abrut significant volume decrease were observed as suction was reduced further from 13.8 kpa to 6.9 kpa (as shown in the Figure 3.7 (a) and (b)). The void ratio change during this stage was estimated to be around.8. The results are resented in Figure 3.8 showing the moisture contents versus alied suctions. A unique relationshi between moisture content and suction can be obtained regardless of the void ratio or the density. This may enable the modelling of the influence of the void ratio or the density on the degree of saturation Mercury Intrusion/Extrusion tests Basic features Mercury Intrusion/Extrusion tests are used to infer various asects of a material s orous nature, such as ore diameter, total ore volume, surface area, and bulk and absolute densities. They involve the intrusion or extrusion of mercury at a certain ressure which can be used to infer the ore size where the mercury assed into or out of. The Mercury Intrusion/Extrusion tests used here were conducted by Particle & Surface Sciences Pty. Limited, Gosford, Australia Samle rearation Samles were reared using two methods. One involves comacting soil into a comaction mould at a known moisture content. The comaction curve in Figure 3.2 was used to determine the suitable static ressure needed to achieve the desired void ratio. Samles were reared at two void ratios by comacting them at moisture contents of 6.% and 8. % and at static comaction ressures of 6 kpa and 6 kpa, resectively. The two samles were denoted by SCL-6 and SCD-8, resectively. The void ratios of the test samles immediately rior to MIP testing were measured to be.62 and.48, resectively. 43

66 Chater 3 Exerimental Investigation The other involves taking subsamles out from a much larger unsaturated samle used for CPT testing which was statically comacted at moisutre content of 4.5% and static ressure of 6 kpa. Subsamles were taken from two ositions after CPT testing. The testing void ratios of the subsamles were.345 and.41, corresonding to dry densities of 1.9 g/cm 3 and 1.82 g/cm 3, resectively. The two subsamles are denoted by insitu-1 and insitu-2, resectively Results and interretation The results of cumulative ore volume versus ore entrance diameter for all four samles are resented in Figure 3.9. A ore diameter as small as.16 μm was intruded. During the tests void ratios were assumed constant. As indicated by Kelvin s equation, the alied ressre (P) and the ore entrance radius (r) through which a nonwetting fluid can ass can be related to surface tension (T m ) according to: 2Tm cos m P (3.2) r where θ m is the contact angle of mercury ranging from 13 to 147 as reorted in the literature (Diamond, 197). A contact angle of 13 was adoted here (Aung et al., 21) and interfacial tension of.485 N/m for nonwetting mercury was assumed. The MIP tests can be used to infer the soil-water characterisitc curve. The mercury intrusion rocedure is analogous to the ore emtying rocedure of an initially saturated soil during drying. For the equivalent drying of water, a contact angle (θ w ) of and surface tension (T w ) of.7275 N/m at 2 C were used to calculate the corresonding suction (s): Twcos w s P (3.3) T cos m m The degree of saturation S r is calculated using the volume of ores not intruded by the mercury, which is given by (Romero et al., 1999): 44

67 Chater 3 Exerimental Investigation S n n r r 1 (3.4) n sat n where n is the intruded orosity, n is the total orosity, ω r and ω sat are the residual and saturated moisture contents, resectively. ω r was taken as for all four samles. The soil-water characterisitc curve obtained are resented in Figure Discussion Different void ratios were tested and air entry and air exulsion values for each void ratio were determined from the lots in the lns r ~ lns lane. Presented in Figure 3.11 is the relationshi between air entry values and void ratios together with a best fitting line of s ae = 1.5e -Ds kpa, with D s =2.61 being the fractal dimension of the articles size distribution, according to Russell (214). Hydraulic hysteresis was observed in both the ressure late test results and Mercury Intrusion/Extrusion test results. The results of the Mercury Intrusion/Extrusion tests san a wider range of degree of saturation comared to ressure late test results. They also exhibit a larger hysteretic loo. Presented in Figure 3.12 are results of the P.P. tests and MIP tests lotted in the lns r ~ lns/s ae lane. The results are fitted with the SWCC model of Russell and Buzzi (212). The model features constant sloes for main curves and scanning curves and the constant sloes arise from the fractal-based derivations. The SWCC is defined as (Russell and Buzzi, 212): S r 1 s s e for for s s s s ex ex (3.5) for the main wetting and drying curves and 45

68 Chater 3 Exerimental Investigation s rw s for wetting ath reversal sex srw S r (3.6) s rd s for drying ath reversal sae srd for the scanning curves. Note that s e = s ex when the state is on a main wetting curve and s e = s ex when the state is on a main drying curve. α and β are the sloes of main curves and scanning curves, resectively. s rw and s rd are the suction values for wetting ath and drying ath reversals. It is found that this model fitted the exerimental data quite well. The sloes of the main curves are given by α =-.52. α is related to the fractal dimension of the ore size (D ) with α = D -3.The sloe of the scanning curves are estimated by the first wetting to drying scanning curve to be β = -.2. The ratio between the air entry value s ae and the air exulsion value s ex is found to be constant and equal to 3 (ie. s ae = 3s ex ). These relationshis will be used later in simulations of the stress-strain behavior and the cavity exansion analysis. Wetting collase was observed in the ressure late tests between 13.8 kpa and 6.9 kpa. Using s ex =.5e kpa, the air exulsion values were.46 kpa,.3 kpa and.2 kpa for void ratio of.5,.59 and.68, resectively. According to Loret and Khalili (22), there may exist a suction value where volume collase commenced. This suciton value must be higher than the suction value searating saturated from unsaturated states, which is in line with the observations. The suction value at which volumetric collase commenced was estimated to be 1 kpa and will be used later in Chater 5 and Chater OEDOMETRIC COMPRESSION TESTS FOR SATURATED SOILS General Oedometric comression tests involve soil samles being subjected to one-dimensional comression under vertical load while horizontal dislacement is revented. Different maximum loads were used for the oedometric comression tests on saturated samles in 46

69 Chater 3 Exerimental Investigation a conventional aaratus. One was loaded to 8 kpa and the other was loaded to 18 kpa Conventional tests Three conventional oedometric comression tests were conducted. The aaratus and rocedures are as er AS (1998). Samles were reared by static comaction while different comaction ressures were used to achieve different initial void ratios (either.485 or.574). Volume collases occurred during saturation under static loads of 5 kpa. The ost-collase void ratios were.413 and.435, resectively, which also reresent the starting void ratios of the tests. Those two samles were loaded to 8 kpa and are referred to as1-d-l-1 and 1-D-L-2, resectively. Another samle was reared at void ratio of.574 with the ost-collase void ratio being.369 under a static load of 15.8 kpa. It was loaded to 18 kpa and is referred to as 1-D-H. Unloading data was also recorded. The results are shown in Figure 3.13 as a lot of secific volume versus the logarithm of vertical effective stress Discussion Tests were erformed at three starting void ratios (.391,.413 and.435). Three distinct curves were obtained. A gradual increase in comressibility was observed which is tyical for soils with high sand contents. 3.5 TRIAXIAL TESTS General The triaxial tests conducted included isotroic comression tests and triaxial comression tests on both saturated and unsaturated samles. The triaxial aaratus and its calibration techniques are described in sections and 3.5.3, samle rearation and testing rogram in sections and 3.5.5, test results and discussions in sections and

70 Chater 3 Exerimental Investigation Triaxial aaratus Five sets of triaxial testing aaratuses were used to erform the triaxial tests. All of the triaxial shear tests for saturated drained conditions and the isotroic comression tests at low confining ressures on saturated samles were conducted using a Stress-Path triaxial aaratus. Additional isotroic comression tests on saturated samles were conducted at confining ressures u to 2MPa using a high ressure triaxial aaratus. Triaxial comression tests on saturated samles for undrained conditions were conducted using conventional Bisho-Wesley triaxial aaratus. Triaxial shear tests and isotroic comression tests on unsaturated samles were conducted using two modified Bisho-Wesley triaxial aaratuses Conventional Bisho-Wesley aaratus A conventional Bisho-Wesley aaratus was used which can accommodate a samle of 5 mm diameter and 1 mm height. Cell ressure and back ressure were sulied by two air-water interface bladders and were measured by two transducers, resectively, which were connected to a comuter. While the samle was being sheared, the axial load and dislacement were measured by two transducers, resectively. No volume measurements were required as this aaratus was only used for undrained saturated triaxial shear tests High ressure triaxial aaratus With the high ressure triaxial aaratus an 8 kpa caacity GDS digital controller was used to control cell ressure and a 2 kpa caacity GDS digital controller to control back ressure and measure its volume change. A hotograh of the dismantled aaratus is shown in Figure Saturated isotroic comression tests were conducted using this aaratus Stress-Path Triaxial aaratus A classic Bisho-Wesley stress ath triaxial aaratus, ermitting a maximum cell ressure of 1 kpa, was also used. Three standard 2 MPa/25 cm 3 digital Automatic Pressure Controllers (APCs) were used to control axial load and axial dislacement, cell ressure, and back ressure and volume change measurement, resectively. 48

71 Chater 3 Exerimental Investigation The three APCs were linked with a comuter through a MPX3 data logger which was built into the system via WinCLISP software from VJ Technology. In order to conduct unsaturated tests, an air ressure line was connected to the to of samles in the triaxial cell. To revent local drying of samles, the air suly was assed through a moist air cell before being alied to the samle. The air ressure was controlled by a ressure regulator and measured by a hydraulic ressure gauge. The schematic of the samle setu is shown in Figure A hotograh of the aaratus is shown in Figure For unsaturated soil testing a digital image-rocessing technique was used to infer samle volume changes, which will be exlained in the next section. This aaratus was used for the saturated triaxial shear tests under drained conditions and for unsaturated isotroic comression tests. In the unsaturated isotroic comression tests suction was controlled by the axis-translation technique (Hilf, 1956) which involves elevating the ore air ressure above atmosheric level and keeing ore water ressure below ore air ressure to induce suction Thermal triaxial aaratus and modified Bisho-Wesley triaxial aaratus The thermal triaxial aaratus shares common features with the modified Bisho- Wesley triaxial aaratus. The only difference is its caability of temerature measurement which was not used in this investigation. Thus those two aaratuses are described under a same heading. Classic Bisho-Wesley hydraulic triaxial cells with caacities of 1 kpa were used for the two aaratuses. Cell ressures and back ressures were sulied by two airwater interface bladders. Volume changes of cell and ore water were measured by two searate digital volume measurement units with caacities of 8 cm 3 and accuracy of.1 cm 3. The same setu to suly air ressure in the Stress-Path triaxial aaratus (section ) was used. Several transducers were connected to the systems to measure axial loads, axial dislacements, back ressures, cell ressures and air ressures which were recorded together with volume changes of cell and ore water. A hotograh of a modified Bisho-Wesley aaratus is shown in Figure

72 Chater 3 Exerimental Investigation Calibration of triaxial aaratuses Pore water ressure, cell ressure and ore air ressure transducers were calibrated using a digital ressure indicator with a high-accuracy ressure transducer embedded in it. The calibration rocess involved ressurizing and de-ressurizing the system using the digital ressure indicator with three full cycles (Zargarbashi, 211). The differences of transducer and ressure indicator readings were less than 1 kpa and no significant hysteresis was observed. The load cells were calibrated against a loading roof ring in a loading frame. Three cycles of loading and unloading were conducted over full range of the load cells. Linear calibration equations were obtained giving standard errors of less than 1 N. Dislacement transducers were calibrated against a micrometer to give linear calibration curves. The digital volume measurement units in the thermal triaxial aaratus and modified triaxial aaratus were calibrated according to the rocedure of Sharma (1998). The calibration involved: firstly, filling and emtying the units several times and then dissolving any remaining air in the unit by ressurizing water at 2 kpa for over 24 hours; then injecting or releasing a known amount of water from the units through a 1 cm 3 burette with a recision of.2 cm 3. During the rocess the dislacements of the transducer attached to the units were monitored. A linear relationshi between the volume change and the dislacement was obtained. For unsaturated soil testing a digital image-rocessing technique was used to infer samle volume changes. The digital image-rocessing technique refers to maniulation of the information stored in a digital image using a comuter algorithm in order to obtain information on certain asects of the image. Details of the digital imagerocessing technique can be found in Zargarbashi (211) and Uchaiichat (25). The technique was used to calculate the void ratio after consolidation and to calculate the volume change during shearing of unsaturated triaxial tests. The results of a single saturated isotroic comression test using burette readings were used to confirm the accuracy of the technique. The curve given by the image rocessing technique is shown 5

73 Chater 3 Exerimental Investigation in Figure 3.18 against the results of the saturated isotroic comression test. The initial oint is assumed to be the same. A linear calibration curve is obtained and the maximum difference of secific volume between the two is aroximately.7 which is less than.5% Samle rearation Static comaction was used to reare samles. By referring to the comaction curves, samles of two void ratios (.466 and.555 corresonding to dry densities of 1.74 g/cm 3 and 1.64 g/cm 3, resectively) were comacted at a moisture content of 6.2 %. For isotroic comression tests samles were reared at a void ratio of.677 corresonding to a dry density of 1.52 g/cm 3 at 6.2 % moisture content. Samles were comacted within a greased slit mould (as in Figure 3.3) of 5 mm diameter in five equal layers, with each being 2 mm in height. The interface between each layer was scarified to minimize weak zones within samles. After comaction and removal from mould, the samle was weighed and the dimensions were measured using a vernier calier Testing rogram Before tests, all the drainage lines were flushed with de-aired water to exel air bubbles from the system. In addition, high-air-entry discs for unsaturated tests were carefully saturated by the rocedures described by Uchaiichat (25) which involves submerging the disc in de-aired water and using a vacuum um to suck the air out of the disc. Two tyes of test setu were used. One involves saturating the samles first before testing and the other involves testing samles without saturation. A wide range of initial void ratios before shearing were obtained Saturated tests For saturated tests, samles were initially air-dried for more than 24 hours with an aim to fasten the samle flushing rocess. A saturated ceramic disk was then ut on the edestal with a filter aer on to. A samle was laced on the edestal and another filter aer and ceramic disk were laced on to. A rubber membrane was ut around 51

74 Chater 3 Exerimental Investigation the samle and O-rings were laced at the base edestal and the to ca. The cell was then ut in osition and was filled with de-aired water. A samle was then flushed from bottom to to under a cell ressure of 3 kpa and back ressure of 15 kpa for around 24 hours. Then both cell ressure and back ressure were elevated at the same time to more than 3 kpa while keeing the ressure difference at 15 kpa. The samle was subjected to these ressures for more than two days to dissolve air bubbles traed inside the samle into the ore water. Isotroic comression was erformed once the B-value exceeded 95 %. For the isotroic comression tests, the back ressure was ket constant while the cell ressure was increased to desired values. The volume change of the samle during this stage was indicated by the volume change of the back-ressure GDS. After the samle comleted rimary consolidation, the next stress level was alied and the test continued. While measuring the volume change of the samle in the triaxial aaratus, the digital image-rocessing technique was erformed at the same time to ascertain a second record of volume change. For the isotroic comression tests conducted in the high ressure triaxial aaratus, the initial void ratio after saturation was assumed to be an average of all the other known initial void ratios of saturated tests, a necessary assumtion as the cell is not transarent and digital image-rocessing technique could not be used. The triaxial shearing tests involved shearing at a constant rate of.6 mm/min for drained tests and at.5 mm/min for undrained tests. Most of the tests were continued to a shear strain of 18 % or more Triaxial shear tests on unsaturated samles in which test setu involved saturating the samles first For unsaturated tests, samles were reared according to section A saturated high-air-entry disc was ut on the edestal with a filter aer on to. A samle was then 52

75 Chater 3 Exerimental Investigation laced on the edestal while having another filter aer and ceramic disk on to. Next a rubber membrane was wraed around the samle and O-rings were laced around the base edestal and the to ca. The cell was then ut in osition and was filled with deaired water. Before saturating the samle, air traed in the siral circuit was removed by flushing water through it. Then a cell ressure of 75 kpa and back ressure of 5 kpa were alied for around one week to flush the samle. Both cell ressure and back ressure were elevated at the same time, u to more than 3 kpa, keeing the ressure difference at 25 kpa. The samle was ket at this level of ressures for more than two days to dissolve any air bubbles that remained traed inside the samle. Isotroic comression was then erformed after confirming the B-value exceeded 95 %. The samle was subjected to isotroic comression by increasing cell ressure. Once the target isotroic confining stress was reached and consolidation was finished. An air ressure of the same magnitude as ore water ressure was alied. Next ore water ressure was reduced to induce the desired suction value. A eriod of seven days was found to be sufficient to achieve suction equilibrium Triaxial shear tests on unsaturated samles in which test setu did not involve saturating the samles A samle reared according to section was ut directly onto a saturated high-airentry disc (with filter aer between discs and samle) laced on to of the edestal. Another filter aer and ceramic disk was laced on to. Next a rubber membrane was wraed around the samle and O-rings were laced at base edestal and the to ca. The cell was then ut in osition and was filled with de-aired water. Water was flushed through the siral circuit to remove any entraed air. Without saturating the samle, the samle was subjected to isotroic comression directly by increasing cell ressure from 2 kpa to the desired ressure. Suction was then induced by setting ore water ressure equal to atmosheric ressure and elevating ore air ressure, during which cell ressure was increased at the same rate, in order to kee the 53

76 Chater 3 Exerimental Investigation difference between cell ressure and ore air ressure constant. A eriod of seven days was found to be sufficient for suction equilibrium. Triaxial shear tests were then conducted for one of two conditions: (i) a constant suction condition at a shear rate of.5 mm/min, or (ii) a constant moisture content condition at a shear rate of.25 mm/min. For both conditions tests were continued u to a shear strain of 2 % Isotroic comression tests on unsaturated samles in which test setu did not involve saturating the samles The test setu for isotroic comression tests was the same as in section Once a samle was ready for testing, instead of shearing, cell ressure was increased in stes while keeing ore air ressure constant and ore water ressure at atmosheric ressure. For each ste, ressures were ket constant for a eriod of seven days to reach suction equilibrium. The volume change of the samle was determined using the digital image-rocessing technique once suction equilibrium had been reached Test results and discussions Tests conducted in the various triaxial aaratuses are listed in Table 3.2. Test identification numbers indicate the consolidation ressure, shear tye (consolidated drained-cd or consolidated undrained-cu, constant moisture content-cw or constant suction-cs), densities (Loose-L and Dense-D) and suction values. For examle, CD3 means the samle was consolidated to a ressure of 3 kpa and was sheared under a consolidated drained condition. U12S1L-CS indicates the samle was subjected to an isotroic confining ressure of 12 kpa and suction of 1 kpa. The samle was loose and was sheared under a constant suction condition Saturated isotroic comression tests The results of a saturated isotroic comression test at low ressure (Iso-S-L) are shown in Figure 3.18 with volume change measured by two methods: digital image-rocessing technique and recorded ore water volume change. The two sets of results are in good agreement, with differences in secific volume always less than.7. Also shown in this figure is the result of a saturated isotroic comression test at relatively high 54

77 Chater 3 Exerimental Investigation ressure (Iso-S-M). The curves for those two tests are almost arallel with gradual increase in comressibility with increasing ressure Saturated triaxial shear tests The results of saturated triaxial shear tests under drained conditions are resented in Figure 3.19, Figure 3.2 in the ε q ~ q lane and in Figure 3.21 in the ε ~ε q lane. The tests conducted at isotroic confining ressures of 5 kpa, 1 kpa and 25 kpa on samles that had, after isotroic comression, initial void ratios of e =.352,.32 and.37 are referred to using symbols of CD5, CD1 and CD25, resectively. The tests conducted at isotroic confining ressures of 3 kpa, 36 kpa and 5 kpa on samles that had, after isotroic comression, initial void ratios of e =.33,.312 and.295 are referred to using symbols of CD3, CD36 and CD5, resectively. Those test samles were at loose states before shearing. As at a given confining ressure no other comarable void ratio was tested, the L does not aear in the test ID. A urely hardening behavior accomanied by volumetric contraction is observed for all drained tests. The volumetric strain curves gradually become horizontal with increasing shear strain as the samles aroach critical states. Results of saturated triaxial shear tests under undrained conditions are resented in Figure 3.22 to Figure 3.24 in the ε q ~ q, ' ~ q and ε q ~ u w lanes, resectively. The tests conducted at isotroic confining ressures of 5 kpa and 1 kpa on samles that had, after isotroic comression, initial void ratios of e =.37 and.365 are referred to using symbols of CU5 and CU1, resectively. The shear stresses exhibit a eak at about 1.8 % deviator strain, followed by a gradual decrease. The loss of shear stresses is accomanied by a gradual increase in the excess ore water ressure. The deviator stress and ore water ressure changes very little at 1 % deviator strain as the critical states are aroached. The results are tyical of those for other soils as were observed by, for examle, Ng et al. (24) for loose decomosed granite similar to Lyell silty sand Unsaturated isotroic comression tests Results of the unsaturated isotroic comression tests in the v ~ ln lane are resented in Figure The number of oints obtained for each tests were, in general, limited by 55

78 Chater 3 Exerimental Investigation the cell ressure caacity of 1 kpa. The tests were conducted at constant suctions of 1 kpa and 3 kpa and are referred to as Iso-s1 and Iso-s3, resectively. The membrane rutured for the suction of 1 kpa when the cell ressure was 36 kpa meaning it had to be terminated early at that instant. Another samle was used to investigate the isotroic comression behavior under suction of 3 kpa. Also shown in this figure is the result for Iso-S-M. It can be seen that the sloe of the Iso-s1 is larger than that of Iso-S-M. There are significant differences between results of the unsaturated and saturated tests, which are similar to the results of e.g. Wheeler and Sivakumar (1995) and Jotisankasa et al. (27). These significant differences may mean there is collase otential in the unsaturated samles because if they are wetted to saturated states under constant net mean stress volumetric decrease may occur Unsaturated triaxial shear tests Tested samles can be groued according to initial void ratios: one grou having samles with initial void ratios around.32 and the other with initial void ratios more than.45. Samles in each grou are referred to as D (Dense) and L (Loose), resectively, in the test identification number. The dense samles were formed by initially saturating them then inducing the desired suction. The loose samles were not saturated rior to inducing the desired suction. For triaxial tests where samles were saturated the samles were first reared at unsaturated states by the static comaction method. Before a samle was ut onto the triaxial aaratus it was air-dried. Then it was flushed with water while under a low confining ressure ranging from 1 kpa to 2 kpa. During flushing significant volume decrease was observed as was also observed by Lee and Coo (1995) in a decomosed granite similar to Lyell silty sand. Samles with initial void ratios of both.466 and.555 mostly collaased to void ratios of around.3 to.33. The triaxial tests were erformed on samles subjected to various suctions, being 1 kpa and 3 kpa, and net stresses of 6 kpa, 12 kpa, 24 kpa, 3 kpa and 6 kpa. Tests were conducted under two drainage conditions: namely a constant suction condition or a constant moisture content condition. 56

79 Chater 3 Exerimental Investigation Presented in Figure 3.26 to Figure 3.33 are the results for the constant suction conditions at confining stresses of 6 kpa, 12 kpa, 24 kpa, 3 kpa and 6 kpa both in the ε ~ε q lane and ε q ~ q lane, resectively. Presented in Figure 3.34 and Figure 3.35 are the results for the constant moisture content conditions at a confining stress of 6 kpa, in the ε ~ε q lane and ε q ~ q lane, resectively. The volumetric curves, as in the ε ~ε q lanes, are not as smooth as those in saturated triaxial tests due to the small error (less than.5%) between digital image-rocessing technique and the recorded ore water volume change (Gachet et al., 27). But the overall trends are as er exectations. Results for all dense samles exhibit a hardening behavior followed by a softening behavior, accomanied by an initial volumetric contraction followed by a volumetric exansion. A gentle volumetric exansion is also observed for loose samles excet for u12s1l-cs and u6s3l-cs where a urely volumetric comression is observed. Samles with higher suction or density show a greater dilatancy and also a greater eak shear stress. Shown in Figure 3.36 are the estimated critical states using end oints of each test in the q ~ net lane, where netcs = cs u w for saturated tests and netcs = cs u a (u a being air ressure) for unsaturated tests. The sloe of saturated tests is estimated to be The sloe of unsaturated tests can be the same as that of saturated tests as assumed by Alonso et al. (199). The intercet on the q axis varies slightly and is suction deendent. A more obvious suction deendent effect was observed by Wheeler and Sivakumar (1995) and Geiser et al. (26) on clayey soils. 3.6 CONCLUDING REMARKS An extensive rogram of laboaratory testing was comleted. A hysteretic SWCC was obtained from Mercury Intrusion/Extrusion tests and ressure late tests. The stressstrain behavior was obtained for both loose and dense samles. It was observed that: 1. Lyell silty sand exhibits fractal article and ore size distributions, as shown in Figure 3.2 and Figure 3.12, resectively. The the fractal dimension of ore size (D ) is found to be A hysteretic loo in the SWCC was observed. The air 57

80 Chater 3 Exerimental Investigation entry value (s ae ) was found to follow s ae = 1.5 e -D s dimension of artical size (D s ) equals to kpa, where the fractal 2. Lyell silty sand exhibits collasible behaviour, evidenced by abrut and large volume decreases during ressure late tests as suction was reduced from 13.8 kpa to 6.9 kpa. Large volume decreases were also observed in triaxial samles when saturating the samles. There is collase otential in unsaturated samles as a large sace exists between the results of saturated and unsaturated isotroic comression tests, as shown in Figure Samles with a larger suction or density show a greater amount of dilatancy and also a greater eak shear stress. 4. There is a clear suction deendence of the CSL in q~ net lane. 58

81 Chater 3 Exerimental Investigation Table 3.1 Index roerties of Lyell silty sand. Proerty Value Liquid Limit, % Plastic Limit, % 15.2 N/A Plasticity Index, % N/A Secific Gravity 2.55 Gravel, % Sand, % Fines, % Clay Size Fraction, % 4.35 Unified Soil Classification System SM Table 3.2. List of tests conducted in the triaxial aaratuses. Isotroic comression Void ratio Test ID (-u a ) max Shear tye before suction, s (kpa) (kpa) shearing CU5 5 - undrained.37 CU1 1 - undrained.365 CD5 5 - drained.352 CD1 1 - drained.32 CD drained.37 CD3 3 - drained.33 CD drained.312 CD5 5 - drained.295 Iso-S-L Iso-S-M u6s1l-cs 6 1 constant suction.49 u12s1l-cs 12 1 constant suction.536 u24s1l-cs 24 1 constant suction.43 u6s1d-cs 6 1 constant suction.327 u12s1d-cs 12 1 constant suction.312 u24s1d-cs 24 1 constant suction.327 u6s1l-cw 6 1 constant moisture content.557 u6s1d-cw 6 1 constant moisture content.324 Iso-s u6s3l-cs 6 3 constant suction.52 u12s3l-cs 12 3 constant suction.494 u6s3l-cs 6 3 constant suction.451 u6s3d-cs 6 3 constant suction.33 u3s3d-cs 3 3 constant suction.31 Iso-s

82 Chater 3 Exerimental Investigation Percent Passing (%) Particle Size (mm) Figure 3.1. Particle size distribution (PSD) curve for Lyell silty sand. 1 Percent Passing (%) 1 Fractal estimation PSD data Particle Size, d s (mm) Figure 3.2. PSD data with the fractal estimation of ercent assing. 6

83 Chater 3 Exerimental Investigation Figure 3.3. Photograh of the comaction mould. 61

84 Chater 3 Exerimental Investigation Dry density (g/cm 3 ) kPa 21kPa 6kPa saturation line 8 kpa S r =1% S r =8% S r =6% 1.45 S r =1% S r =2% S r =4% % 4.% 6.% 8.% Moisture content 1.% 12.% Figure 3.4. Static comaction curves. 62

85 Chater 3 Exerimental Investigation Figure 3.5. Samle arrangements in ressure late tests. 63

86 Chater 3 Exerimental Investigation Pressure gauge Pressure late Connected to the laboratory air suly. Burette indicating the water equilibrium. Figure 3.6. Photograh of the ressure late aaratus. a b Large volume decrease Samle lost contact from the rings. Figure 3.7. Cross-section views of (a) volume decrease and (b) samles lost contact from the rings. 64

87 Chater 3 Exerimental Investigation Moisture content 18.% 16.% 14.% 12.% 1.% 8.% 6.% Significant volumetric collase occurred. loose medium dense Initial states drying 4.% 2.% wetting.% Suction, s (kpa) Figure 3.8. Soil-water characteristic curves from ressure late tests, in the moisture content versus logs lane. Loose indicates an initial void ratio of.68, medium an initial void ratio of.59 and dense an initial void ratio of.5. 65

88 Chater 3 Exerimental Investigation.25 Cumulative intrusion ore volume, ml/g SCL-6 SCD-8 insitu-1 insitu Pore diameter, μm Figure 3.9. Cumulative intrusion er ore volume versus ore diameter for samles SCL-6, SCD-8, insitu-1 and insitu-2 with void ratios of.48,.62,.41 and.345, resectively. 66

89 Chater 3 Exerimental Investigation 1% 9% 8% Degree of saturation, S r 7% 6% 5% 4% 3% 2% 1% SCL6 SCD-8 insitu-1 insitu-2 % Suction, s (kpa) Figure 3.1. Soil-water characteristic curves from Mercury Intrusion/Extrusion tests. Air entry value, s ae (kpa) Air entry values from Mercury Intrusion/Extrusion tests Fitting line Void ratio, e Figure Relationshi between air entry values and void ratios together with the best fitting line of s ae = 1.5e kpa. 67

90 Chater 3 Exerimental Investigation 1% MIP-SCL6 e=.62 β=-.2 1 MIP-SCD-8 e=.48 MIP-insitu-1 e=.345 MIP-insitu-2 e=.41 Degree of saturation 1% α= P.P e=.68 P.P e=.59 P.P e=.5 1% s/s ae Figure Pressure late test results and Mercury Intrusion/Extrusion test results lotted in the lns r ~ lns/s ae lane together with estimations of sloe of main curves and scanning curves, resectively D-L-2 1-D-L-1 1-D-H Effective vertical stress, σ 1 (kpa) Figure Oedometric comression tests results for three starting void ratios of.391,.413 and.435 in the v ~ σ' 1 lane. 68 Secific volume, v=1+e

91 Chater 3 Exerimental Investigation Figure A hotograh of the dismantled high ressure triaxial aaratus. (after Russell, 24) 69

92 Chater 3 Exerimental Investigation Figure Schematic layout of samle setu for triaxial tests. 7

93 Chater 3 Exerimental Investigation Control anel APCs MPX3 data logger Moist air cell Figure Photograh of the Stress-Path aaratus. Burettes for coarse volume measurement of cell and ore water. Pressure regulator for ore water and cell ressure. Two cameras for digitalimage rocessing technique. Digital volume measurement units for ore water and cell. Figure Photograh of a Modified Bisho-Wesley triaxial aaratus. 71

94 Chater 3 Exerimental Investigation Digital image-rocessing technique (Iso-S-L) Volume change of cell (Iso-S-L) Iso-S-M Secific volume, v=1+e Mean effectives stress, '(kpa) Figure Results of saturated isotroic comression tests for initial void ratio of.323 (Iso-S-L) together with calibration curve of digital image-rocessing technique and for initial void ratio of.335 (Iso-S-M) at relatively high ressure Deviatoric stress, q (kpa) CD25 e=.37 4 CD3 e=.33 2 CD36 e=.312 CD5 e=.295.% 5.% 1.% 15.% 2.% Deviatoric strain, ε q Figure Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε q ~ q lane. 72

95 Chater 3 Exerimental Investigation Deviatoric stress, q (kpa) CD5 e=.352 CD1 e=.32.% 5.% 1.% 15.% 2.% Deviatoric strain, ε q Figure 3.2. Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε q ~ q lane. Volumetric strain, ε.%.5% 1.% 1.5% 2.% 2.5% 3.% CD5 e=.352 CD1 e=.32 CD25 e=.37 CD3 e=.33 CD36 e=.312 CD5 e= % 4.% % 5% 1% 15% 2% Deviatoric strain, ε q Figure Results of saturated triaxial shear tests under drained conditions (tests as listed in the figure) in the ε ~ε q lane. 73

96 Chater 3 Exerimental Investigation 6 5 Deviatoric stress, q (kpa) CU5 e=.37 CU1 e= % 2% 4% 6% 8% 1% Deviator strain, ε q Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ε q ~ q lane. 1 9 Excess ore water ressure, u w (kpa) CU5 e=.37 CU1 e=.365 % 2% 4% 6% 8% 1% Deviator strain, ε q Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ε q ~ u w lane. 74

97 Chater 3 Exerimental Investigation 6 5 CU5 e=.37 CU1 e=.365 Deviatoric stress, q (kpa) Mean effective stress, ' (kpa) Figure Results of saturated triaxial shear tests under undrained conditions (CU5 and CU1) in the ' ~ q and lane Iso-s1 Iso-s3 Iso-S-M Secific volume, v=1+e Mean net stress, (kpa) Figure Results of unsaturated isotroic comression tests (Iso-s1 and Isos3) in the v ~ ln lane together with the result for Iso-S-M. 75

98 Chater 3 Exerimental Investigation Volumetric strain, ε -1.% -8.% -6.% -4.% -2.% u6s1d-cs u6s3d-cs u6s1l-cs u6s3l-cs.% 2.% % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa in the ε ~ε q lane. Deviator stress, q (kpa) u6s1d-cs u6s3d-cs u6s1l-cs u6s3l-cs 1 % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa in the ε q ~ q lane. 76

99 Chater 3 Exerimental Investigation -8.% -6.% Volumetric strain, ε -4.% -2.%.% 2.% u12s1d-cs u12s1l-cs u12s3l-cs 4.% 6.% % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa in the ε ~ε q lane. Deviator stress, q (kpa) u12s1d-cs u12s1l-cs u12s3l-cs 2 1 % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa in the ε q ~ q lane. 77

100 Chater 3 Exerimental Investigation -6.% -5.% Volumetric strain, ε -4.% -3.% -2.% -1.%.% 1.% u24s1l-cs u24s1d-cs 2.% 3.% % 5% 1% 15% 2% 25% Deviator strain, ε q Figure 3.3. Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa in the ε ~ε q lane Deviator stress, q (kpa) u24s1l-cs 2 u24s1d-cs % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa in the ε q ~ q lane. 78

101 Chater 3 Exerimental Investigation -6.% -4.% Volumetric strain, ε -2.%.% 2.% 4.% 6.% u3s3d-cs u6s3l-cs 8.% 1.% % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 3 kpa and 6 kpa in the ε ~ε q lane Deviator stress, q (kpa) u3s3d-cs u6s3l-cs % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 3 kpa and 6 kpa in the ε q ~ q lane. 79

102 Chater 3 Exerimental Investigation -1.% -8.% Volumetric strain, ε -6.% -4.% -2.% u6s1l-cw u6s1d-cw.% 2.% % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa in the ε ~ε q lane. 7 6 u6s1l-cw u6s1d-cw Deviator stress, q (kpa) % 5% 1% 15% 2% 25% Deviator strain, ε q Figure Results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa in the ε q ~ q lane. 8

103 Chater 3 Exerimental Investigation Deviator stress at critical state, q cs (kpa) M cs =1.45 Estimated critical state data for saturated drained tests Estimated critical state data for s=1 kpa (constant suction) Estimated critical state data for s=3 kpa (constant suction) Estimated critical state data for saturated undrained condition Saturated critical state line Mean net stress at critical state, netcs (kpa) Figure Critical state line in the q ~ net lane (The suction for constant moisture content conditions at critical state was unknown in the tests and was estimated). 81

104 CHAPTER 4. AN EXPERIMENTAL STUDY OF THE CPT IN UNSATURATED LYELL SILTY SAND 4.1 INTRODUCTION The cone enetration tests (CPTs) were conducted using the University of New South Wales calibration chamber (Pournaghiazar et al., 211a). Tests were erformed on unsaturated Lyell silty sand for which suction hardening and hydraulic hysteresis were resent. The effects of different densities, net stresses, confining ressure conditions (anisotroic condition and isotroic condition) and suctions on CPT results were investigated. In this chater, the calibration chamber and testing setu is briefly described in section 4.2. The method used to reare unsaturated samles for laboratory controlled CPTs is exlained in section 4.3. Test results are resented in section 4.4. The synthesis of the CPT results will be resented in Chater 8. 82

105 Chater 4 Exerimental Investigation of CPT 4.2 THE UNSW CALIBRATION CHAMBER AND TESTING SETUP The calibration chamber design used here was detailed by Pournaghiazar et al. (211a). Key imrovements over other designs include a novel samle formation system, a modified axial load alication system, and measurement and control of suction within the system. A schematic cross section of the calibration chamber is shown in Figure 4.1. Noticeable is the movable former which makes the chamber more versatile for samle formations. Lateral confining ressure is alied by water ressure acting on the rubber membrane. Vertical ressure is alied by a hydraulic loading ram jacking u the chamber iston connected to the base of the secimen. The chamber can accommodate cylindrical samles of 84 mm in height and 46 mm in diameter. The samle is enclosed by a rubber membrane between a bottom late and a to late. The chamber shell is bolted to the chamber base. It is sealed using a to ca on to. Water fills the sace in between the chamber shell and the rubber membrane. The chamber is equied with several control and measurement devices to record ressures and volume changes. The general control system is shown in Figure 4.2. The cell ressure is alied through an air-water interface cylinder which is connected to a laboratory air suly. Pore water ressure is also alied by air-water interface cylinders. The ore water ressure can be alied to the samle through erforated coer tubes at the bottom late, which quickens the saturation of a samle, and through high air-entry-value disks embedded in the bottom late in order to control suction using the axis translation technique. Pore air ressure is sulied to the to of a samle using the laboratory air suly. All ressures are monitored by analogue ressure gauges on a control anel. Volume changes of cell and ore water are indicated by glass burettes and water-oil interfaces (accurate to about ±.5 ml). The cell volume change can also be measured coarsely by a transarent lastic tube ositioned outside the cylinder (accurate to about ± 1 ml). 83

106 Chater 4 Exerimental Investigation of CPT To aly and maintain vertical stress, a hydraulic ram (Model 12) manufactured by Simlex Cylinders is used and it is oerated by an electric micro um (Model GMP- 8-12) manufactured by Riken Kiki. Along with the um is a DPS7A ressure switch, a manual hand um, secondary reservoir and an analogue ressure gauge. The contribution of the cell ressure acting on the bottom late to vertical stress is also included. The cone used in the testing is a miniature electrical cone, manufactured by A.P van den Berg (model ELC2), with a diameter of 16 mm and a cone ti area of 2 cm 2. The machine used to ush the cone is a HYSON 1 kn single cylinder static cone enetrometer owered by a etrol-driven ower ack. A constant ushing rate of.2 to 2 cm/s can be used. During the test cone enetration resistance (q c ) was recorded. 4.3 PREPARING UNSATURATED SAMPLES FOR LABORATORY CONTROLLED CPTS In this investigation, the unsaturated samles tested were reared by two methods. One involves the axis translation technique. The other is simly by static comaction with no change to suction from the as-comacted value. A static comaction ressure of 6 kpa was used for both samle formation methods. Axis translation technique gives direct control of the suction alied. But the test soil had a low hydraulic conductivity. It took 2 months to observe an aroach to equilibrium (being 1125 hours for UD12S1). Even after this time the suction equilibrium was not fully reached as the moisture content distribution of the samle was still not uniform as shown in Figure Analysis using a new fractal hydraulic conductivity model shows that a full uniform distribution of moisture content would require more than three months. Detailed analyses are in Chater 6. Static comaction on its own does not ermit accurate suction control. Therefore the suction values were measured by three vibrating wire iezometers (model PWS5 from Roctest). 84

107 Chater 4 Exerimental Investigation of CPT Samle formation with axis translation technique Before assembling the chamber, the high air-entry (HAE) ceramic discs embedded in the base late were carefully saturated under a ressure of 2 kpa for more than 24 hours. To ensure better contact between the soil and the HAE discs, a thin layer (about 3 mm) of kaolin wetted at its liquid limit was smeared across the to of the discs. Then a rubber membrane of 8 mm thickness was fastened to the bottom late using a 25 mm wide hose clam. Once the membrane was in lace, an o-ring coated with silica grease was carefully ushed into the groove at the base, and the chamber shell was then bolted into osition. A feature of the calibration chamber design is the four movable formers which can be fastened together to make a rigid cylindrical mould in which a samle can be comacted, reventing side bulging during comaction. Soils were statically comacted to the target dry densities in thin layers. The surface of a comacted layer was scarified rior to comaction of the next layer. Seven layers in total were comacted. The first (bottom) layer had a thickness of 14 mm after comaction, while the six other layers had a ost-comaction thickness of 11 mm. After comacting the seventh layer, a 5 mm thick gravel layer was ut in lace on to of the samle to ensure that the air ressure alied to the samle as art of the axis translation technique could evenly distribute across the to surface. Another hose clam was used to fasten the membrane to the to ca after which the to ca was bolted to the shell with o-rings in between. Vertical ressure and cell ressure were then alied. To revent localized drying near the to of the samle air was assed through a water bath cylinder as also done by Pournaghiazar et al. (211a). The vertical ressure, cell ressure and the air ressure were then increased in stes to target values and the axis translation technique was alied to achieve the target suction. The volume of water exiting through the base of the samle was recorded to indicate the rate of water exulsion. 85

108 Chater 4 Exerimental Investigation of CPT Samle formation with suction as-comacted The samle formation was the same as that detailed in section To measure suction three vibrating wire iezometers (model PWS5 from Roctest) were used. Before inserting the iezometers their tis comrising high air-entry-value disks were carefully saturated according to the method of Vo and Russell (213). They used a similar laboratory system to that of Take and Bolton (23). The system consisted of a saturation cell connected to a ressurized gas bottle and a rotary vacuum um. The ositions of the gas and the vacuum valves on the saturation cell were designed such that rotating the saturation cell by 9 while connected to the iezometer caused deaired water to be introduced to the iezometer cavity under comlete vacuum. After comaction, before utting on the to late, three vertical holes at a horizontal distance of 1 cm from the center of samle were drilled using an electric drill. They were drilled to deths of.2 m,.3 m and.4 m, resectively. The cross-section of the samle after drilling is shown in Figure 4.3. The iezometers were embedded inside the vertical holes. A hoto of the to late being lowered on to the samle with the iezometers in lace is shown in Figure 4.4. With the to late in osition and the chamber assembled, vertical ressure and cell ressure were then alied. The readings of three iezometers changed as the samle consolidated. Once the readings were stable, the cone enetration tests were erformed. 4.4 CONE PENETRATION TESTS RESULTS. Once samle consolidation was nearly comleted, which was indicated by small or no further volume change of cell, or a very slowly changing suction, cone enetration tests were conducted. All the tests were conducted with the enetration rate of 1 mm/s. The boundary condition used is for constant vertical and horizontal stresses, which is illustrated in Figure 4.5. For samles reared using the axis translation technique, immediately after a test, the moisture contents at different deths were determined by taking subsamles from hand augered boreholes located at the centre and 1 cm from the center of samles. 86

109 Chater 4 Exerimental Investigation of CPT Presentations of cone enetration resistance (q c ) and moisture content distribution Tests conducted and their relevant test conditions are listed in Table 4.1. The tested samles had initial densities of g/cm 3 and g/cm 3 corresonding to initial as-comacted void ratios of.68 and.56, resectively. They were subjected to a range of isotroic net confining stresses of 6 kpa, 12 kpa and 24 kpa. Suction values of 1 kpa and 3 kpa were targeted using axis translation. Other samles were tested at their as-comacted suctions. Figure 4.6, Figure 4.7 and Figure 4.9 show the lots of cone enetration resistance (q c ) versus deth for CPTs erformed in unsaturated samles at an isotroic net confining stress of 6 kpa and initial as-comacted void ratios of.68 (which corresonds to a dry density of g/cm 3 ). The tests conducted at the as-comacted suction, and target suctions of 1 kpa and 3 kpa, are referred to as UL6SAC, UL6S1 and UL6S3, resectively. The time allowed for suction change by axis translation is 79.5 and 1625 hours for UL6S1 and UL6S3, resectively. Figure 4.8 and Figure 4.1 show the moisture content distributions with deth for UL6S1 and UL6S3, resectively. Figure 4.11 and Figure 4.12 resent the lots of cone enetration resistance (q c ) versus deth for CPTs erformed in unsaturated samles at an isotroic net confining stress of 12 kpa and initial as-comacted void ratios of.68. The tests conducted at the ascomacted suction, and a target suction of 1 kpa, are referred to as UL12SAC and UL12S1, resectively. The test results for CPTs conducted in unsaturated samles with initial as-comacted void ratio of.68 are resented in Figure 4.14 and Figure Tests were also conducted at an isotroic net confining stress of 12 kpa but initial ascomacted void ratios of.56, and are referred to as UD12SAC and UD12S1, resectively. The time allowed for suction change by axis translation is 56.6 and 1125 hours for UL12S1 and UD12S1, resectively. Figure 4.13 and Figure 4.16 show the moisture content distributions for UL12S1 and UD12S1, resectively. Figure 4.17 and Figure 4.18 resent the lots of cone enetration resistance (q c ) versus deth for CPTs erformed in unsaturated samles at an isotroic net confining stress of 87

110 Chater 4 Exerimental Investigation of CPT 24 kpa and initial as-comacted void ratios of.68. The tests conducted at the ascomacted suction, and a target suction of 1 kpa, are referred to as UL24SAC and UL24S1, resectively. The time allowed for suction change by axis translation is hours for UL24S1. Figure 4.19 shows the moisture content distributions for UL24S1. Figure 4.2 and Figure 4.22 resent the lots of cone enetration resistance (q c ) versus deth for CPTs erformed in unsaturated samles at initial as-comacted void ratios of.68 and subjected to a net horizontal stress of 1 kpa, net vertical stress of 6 kpa (σ h /σ v =1.67) and target suction of 1 kpa and are referred to as K6S1-1 and K6S1-N, resectively. The time allowed for suction change by axis translation is and hours for K6S1-1 and K6S1-N, resectively, with the corresonding moisture content distributions shown in Figure 4.21 and Figure General observations It is observed that generally the q c value increases in the uer.15 m of samles. For some tests conducted at isotroic net confining stress of 6 kpa (UL6SAC, UL6S1 and K6S1-2) a eak value of q c was recorded at deth of around.1 m which is due to the interaction of the cone induced zones of lasticity with the rigid to late, as also observed by Parkin and Lunne (1982), Sweeney and Clough (199), Puala et al. (1995) and Pournaghizar et al. (213b). This was only observed in tests with low isotroic net confining stress and loose samles, as also shown in Puala et al. (1995). For the remaining tests, the results are similar to Houlsby and Hitchman (1988) and Huang and Hsu (25) where no eak value was observed. The q c value fluctuates a little in the middle art of the samles, between.3 m and.5 m, then increases again after.5 m which is due to the interaction with the rigid base boundary. Below the deth of.5 m for tests conducted at isotroic net confining ressure of 24 kpa where the effect of suction becomes small, the cone enetration resistance starts to dro, which is similar to the behavior of a flexible base in Houlsby and Hitchman (1988). Thus, the average q c values used for calibration are taken from deths of.3 m to.5 m where the values are aroximately constant and unaffected by to and bottom boundary conditions. 88

111 Chater 4 Exerimental Investigation of CPT Listed in the last column of Table 4.2 are the averaged q c values of CPTs conducted in unsaturated samles, along with other test details. Note that a straight line is assumed to reresent the variation of q c rofile for each test, as shown in some of the figures from Figure 4.6 to Figure The average q c values are then calculated from data between the deths of.3 m and.55 m for each test using the straight line. These data are shown in Table 4.2. Also shown in Table 4.2 are the recorded moisture contents at the deths of.3 m and.5 m as well as the average values for samles reared by axis translation technique. For samles reared by axis translation technique, suctions corresonding to these moisture contents are calculated using known suction degree of saturation states according to the SWCC of Lyell silty sand. For samles formatted with suction ascomacted, suctions are measured using iezometers at deths of.3 m and.5 m, resectively. These will be discussed in the following. 4.5 DISCUSSIONS Assessing uniformity of soil samles The uniformity of a reared soil samle is assessed based on the uniformity of the cone enetration resistance rofile and moisture content distribution with deth. No obvious sinusoidal attern in the cone enetration resistances was observed, which indicates that layering effects caused by static comaction are negligible or non-existent. However, for samles in which suction was alied by axis translation, slight gradients in the moisture contents with deth existed, although were less ronounced as the equilibrium times were increased. The slight moisture content gradients corresond to a slight suction gradient, and are consistent with the slight increases of cone enetration resistances with deth. This will be discussed in more detail in Chater Suction verification When using the axis translation technique to aly suction to large unsaturated samles (46 mm diameter and 8 mm height in this investigation) with a low hydraulic conductivity (around 3e-7 m/s for saturated Lyell silty sand), the time required for suction equilibrium is very long. It is observed from Figure 4.24 that, for samle 89

112 Chater 4 Exerimental Investigation of CPT K6S1-2 which involved the suction equilibrium time of 126 hours, with a target suction of 1 kpa, the rate of water exelling from samle decreased significantly but still had not ceased. Therefore, as suction equilibrium was not reached, the SWCC is used to infer suction for samles reared using the axis translation technique. Suctions corresonding to the moisture content determined after a test are estimated based on known suction degree of saturation states according to the SWCC of Lyell silty sand. The suction values are averaged values at deths of.3 m and.5 m, which are shown in Table 4.2. Shown in Figure 4.25 are the initial states of CPT samles before testing lotted in the ρ d ~ω lane together with comaction curves for Lyell silty sand obtained from Vo and Russell (213). The numbers next to markers denote suctions. The suctions on the comaction lines were measured by iezometers by Vo and Russell (213). Those suction values, as exected, show that suction decreases with increasing degree of saturation or with decreasing dry density. Suctions that were measured by iezometers in CPT samles are denoted by a combined cross and circle. Note that the suctions at those oints denoted by hollow circles were induced by axis translation. The times allowed for suction change are different for each test, so are the ositions on the SWCC. When calculating the suctions for those tests using the SWCC, the states are assumed to move along scanning curves as suction is induced during which negligible change to void ratio occurred. Also a change of moisture content induces a larger suction variation for a state on a scanning curve than that on a main curve for a given void ratio, which makes those suctions induced by axis translation higher than those for initial comaction states. Figure 4.26 resents the SWCC obtained from Vo and Russell (213) for Lyell silty sand together with initial back-calculated suction values of CPT tests. The initial states are bounded by the 32% Standard Proctor line and Moist Taming and Vibration line. The back-calculated suction values are between 13 kpa and 72 kpa Effects of suction on cone enetration resistance Samles UL6S3 and UL12S1 have more variations in q c between deths of.3 m and.5 m than others, which is consistent with the fact that those samles have more variations in suctions than others (Table 4.2). For UL6S3 a suction increase from 64 kpa at the deth of.3 m to 81 kpa at the deth of.5 m causes an increase in the cone 9

113 Chater 4 Exerimental Investigation of CPT resistance values by about 2 % from 3.5 MPa to 3.66 MPa. For UL12S1 a suction increase from 31 kpa at the deth of.3 m to 43 kpa at the deth of.5 m causes an increase in the cone resistance values by about 24 % from 4.7 MPa to 5.8 MPa. The variations of q c in other samles are all less than 1 %. The effects of suction on the cone enetration resistance for different samles subjected to a range of isotroic confining net stresses are shown in Figure 4.27 to Figure 4.3. For samles with a void ratio of around.655±.5 subjected to an isotroic net confining stress of 6 kpa, it is observed, as shown in Figure 4.27, that larger suctions caused larger cone enetration resistances. A suction of 37 kpa is associated with a q c that is 5 % larger than the value for a suction of 24 kpa. A suction of 74 kpa is associated with a q c that is 55 % larger than the value for a suction of 24 kpa. It should be noted that q c is the averaged value at deth between.3 m and.55 m which is suosed to be free of rigid effects of to and bottom lates, as discussed in section For samles with test void ratio of around.635±.5 subjected to an isotroic net confining stress of 12 kpa, as shown in Figure 4.28, an increase of average cone enetration resistance by 16% (from 4.5 MPa to 5.24 MPa) is also observed. The slight increase may due to the slight increase of suction values from 31 kpa to 37 kpa. Figure 4.29 shows that for samles with test void ratios of around.585±.5, subjected to an isotroic net confining stress of 24 kpa. The average cone resistances for suction values of 38 kpa and 47 kpa are almost undistinguishable due to the slight difference in suction and initial samle states. Figure 4.3 shows that for samles with test void ratio of around.52±.1 subjected to an isotroic net confining stress of 12 kpa a suction increase from 13 kpa to 55 kpa cause an increase in the average cone resistance values by about 35% (from 7.8 MPa to 1.5 MPa). Figure 4.31 resents the effects of suction on the cone enetration resistance for samles subjected to a σ h /σ v = 1.67 condition with horizontal stresses of 1 kpa, target suctions of 1 kpa and with test void ratio of around.625±.15. Figure 4.32 shows the comarison of the moisture content distribution of the two tests. Suction increase from 91

114 Chater 4 Exerimental Investigation of CPT 34 kpa to 42 kpa increased the average cone resistance values slightly by about 1% (from 4.97 MPa to 5.45 MPa). Comaring the results for various isotroic net confining stresses, consistent with the findings of Pournaghiazar et al. (213b), reveals that the contribution of suction to cone enetration resistance becomes more significant as the confining stress decreases. 4.6 CONCLUDING REMARKS Large unsaturated samles were reared by static comaction. No sinusoidal attern of cone enetration resistance was observed which indicates that layering effects caused by static comaction are negligible or non-existent. Axis translation did not enable the target suction to be reached within a reasonable time due to the large dimensions and low hydraulic conductivity of the samle. Instead suctions were back-calculated using the SWCC. The back-calculated suction values were within the range of suction values measured by vibrating wire iezometers on same soil at similar densities and degrees of saturation. Several CPTs were conducted on samles subjected to different densities, confining net stresses, comression conditions and suctions. It is observed that suction can increase the cone enetration resistance by as much as 5% for an isotroic net confining stress of 6 kpa. 92

115 Chater 4 Exerimental Investigation of CPT Table 4.1. Test conducted and relevant test conditions for unsaturated Lyell silty sand. Test number Tye Comression Net stress or vertical stress (kpa) Initial moisture content Test void ratio Target suction * (kpa) Time allowed for suction change by axis translation (hour) UL6SAC Isotroic %.66 as comacted UL6S1 Isotroic 6 6.4% UL6S3 Isotroic % UL12SAC Isotroic %.64 as comacted UL12S1 Isotroic % UD12SAC Isotroic %.53 as comacted UD12S1 Isotroic % UL24SAC Isotroic %.58 as comacted UL24S1 Isotroic % K6S1-1 K= % K6S1-N K= % * denotes the air ressure as ore water ressure was ket atmosheric. 93

116 Chater 4 Exerimental Investigation of CPT Table 4.2. Suction values along with moisture contents at deth of.3 m and.5 m. Test number Post-test moisture content at the deth of.3 m Post-test moisture content at the deth of.5 m Average moisture content Back-calculated or measured suction at the deth of.3 m (kpa) Back-calculated suction at the deth of.5 m or measured at the deth of.4 m (kpa) Average suction (kpa) q c at the deth of.3 m (MPa) q c at the deth of.5 m (MPa) Average q c between the deths of.3 m and.5 m (MPa) UL6SAC / / 4.65% 23.4* 24.8* UL6S1 5.48% 5.19% 5.34% UL6S3 4.2% 3.83% 3.93% UL12SAC / / 4.5% 29.* 32.4* UL12S1 5.83% 5.47% 5.65% UD12SAC / / 6.4% 11.9* 13.7* UD12S1 4.85% 4.8% 4.83% UL24SAC / / 4.4% 35.* 39.7* UL24S1 5.53% 5.29% 5.41% K6S % 5.16% 5.3% K6S1-N 5.83% 5.53% 5.68% Symbol (*) indicates suctions were measured by iezometers. 94

117 Chater 4 Exerimental Investigation of CPT Figure 4.1. Cross-section of the UNSW calibration chamber (after Pournaghiazar et al., 211a). Figure 4.2. The general calibration control system (after Pournaghiazar et al., 211a). 95

118 Chater 4 Exerimental Investigation of CPT Figure 4.3. Cross-section of a samle after drilling. Three vibrating wire iezometers Logging system Figure 4.4. To late being lowered into osition once the iezometers were installed. 96

119 Chater 4 Exerimental Investigation of CPT Figure 4.5. Boundary condition. 97

120 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure 4.6. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL6SAC). 98

121 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure 4.7. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL6S1). 99

122 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle 1cm from center.2 Deth (m) Figure 4.8. Moisture content results for UL6S1 for equilibrium time of 79.5 hours..7 1

123 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure 4.9. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of 3 kpa and with initial as-comacted void ratio of.68 (UL6S3). 11

124 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8% Center of the samle.1 1cm from center.2 Deth(m) Figure 4.1. Moisture content distribution results for UL6S3 for equilibrium time of 1625 hours. 12

125 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL12SAC). 13

126 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL12S1). 14

127 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle 1cm from center.2 Deth(m) Figure Moisture content distribution results for UL12S1 for equilibrium time of 56.5 hours. 15

128 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, the as-comacted suction and with initial as-comacted void ratio of.56 (UD12SAC). 16

129 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.56 (UD12S1). 17

130 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle.2 Deth(m) Figure Moisture content distribution results for UD12S1 for equilibrium time of 1126 hours. 18

131 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, the as-comacted suction and with initial as-comacted void ratio of.68 (UL24SAC). 19

132 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (UL24S1). 11

133 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle 1cm from center.2 Deth(m) Figure Moisture content distribution results for UL24S1 for equilibrium time of hours. 111

134 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure 4.2. Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with σ h of 1 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (K6S1-1). 112

135 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle 1cm from center.2.3 Deth(m) Figure Moisture content distribution results for K6S1-1 for equilibrium time of hours. 113

136 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) Deth (m) Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with σ h of 1 kpa, target suction of 1 kpa and with initial as-comacted void ratio of.68 (K6S1-N). 114

137 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1 Center of the samle 1cm from center.2.3 Deth (m) Figure Moisture content distribution results for K6S1-N for equilibrium time of 35.5 hours. 115

138 Chater 4 Exerimental Investigation of CPT 24 2 Volume of water exelled (ml) Time elased (hour) Figure Volume of water exelled from samle vs. time elased for samle of K6S

139 Chater 4 Exerimental Investigation of CPT Dry density, ρ d (g/cm 3 ) > S r =1% S r =8% S r =6% S r =1% S r =2% S r =4% 2.% 4.% 6.% 8.% 1.% 12.% Water content saturation line Standard Proctor Modified Proctor 32% Standard Proctor Moist Taming& Vibration Initial states of CPT samles before testing Suction measured Figure Comaction curves (Vo and Russell, 213) together with initial states of CPT samles before testing (Numbers next to markers denoting suctions). Note the time allowed for suction change is different for each test denoted by hollow circle. 117

140 Chater 4 Exerimental Investigation of CPT 1% Moist Taming Moist Taming & Vibration Degree of saturation, S r 32% Standard Proctor Standard Proctor Modified Proctor 1% Suction,s (kpa) Figure SWCC (Vo and Russell, 213) together with initial back-calculated suction values of CPT samles before testing. Initial states of CPT samles with suction backcalculated Suction measured 118

141 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) UL6S1.2 UL6S3 UL6SAC.3 Deth (m).4 s=74 kpa.5 s=37 kpa.6.7 s=24 kpa.8 Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 6 kpa, target suction of ascomacted value, 1 kpa and 3 kpa and with test void ratio of.655 ±

142 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) UL12S1 UL12SAC.2.3 Deth (m) s=31 kpa s=37 kpa.8 Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of ascomacted value and 1 kpa and with test void ratio of.635 ±.5. 12

143 Chater 4 Exerimental Investigation of CPT. Cone enetration resistance, q c (MPa) UL24S1 UL24SAC.3 Deth (m).4.5 s=47kpa s=38 kpa Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 24 kpa, target suction of ascomacted value and 1 kpa and with test void ratio of.585 ±

144 Chater 4 Exerimental Investigation of CPT.1 Cone enetration resistance, q c (MPa) UD12S1 UD12SAC.2.3 Deth (m) s=13 kpa s=55 kpa.8 Figure 4.3. Cone enetration test results for unsaturated Lyell silty soil subjected to a constant isotroic net confining stress of 12 kpa, target suction of ascomacted value and 1 kpa and with test void ratio of.52 ±

145 Chater 4 Exerimental Investigation of CPT Cone enetration resistance, q c (MPa) K6S1-N K6S1-1 Deth (m).4.5 s=53kpa.6 s=25 kpa.7.8 Figure Cone enetration test results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with horizontal stress of 1 kpa, target suction of 1 kpa and with test void ratio of.625±

146 Chater 4 Exerimental Investigation of CPT Moisture content % 1% 2% 3% 4% 5% 6% 7% 8%.1.2 K6S1-1 K6S1-N.3 Deth(m) Figure Comarison of moisture content distribution results for unsaturated Lyell silty soil subjected to a σ h /σ v =1.67 condition with horizontal stress of 1 kpa, target suction of 1 kpa and with test void ratio of.625±

147 CHAPTER 5. A CONSTITUTIVE MODEL FOR LYELL SILTY SAND 5.1 INTRODUCTION This chater resents a constitutive model to describe the stress-strain behavior of Lyell silty sand in saturated and unsaturated states. The model is based on that of Russell and Khalili (26a) and Khalili et al. (28). In the model resented here both hydraulic hysteresis and a deendency of the SWCC on volumetric strain are accounted for. The isotroic comression line is defined to be linear in the lne~ln lane as it reduces the curvature of comression lines defined in a semi-log' lane or logv~log' lane beyond the yield oint (McDowell, 25 and 213). This is a oint of difference from the above two models but there are no differences in the main underlying features. The resulting stress-strain relationshis are very similar to each other. The model is fitted to the results of an extensive rogram of laboratory tests conducted on Lyell silty sand detailed in Chater 3. Model simulations of the oedometric comression tests for saturated states, the triaxial comression tests and isotroic comression tests for both saturated and unsaturated states are resented in this chater. The calibrated model is then imlemented into an analysis of cavity exansion in soils exhibiting suction hardening and hydraulic hysteresis in chater

148 Chater 5 Constitutive model 5.2 NOTATION Conventional triaxial ~ q notation is used, where is the mean effective stress and q is the deviator stress. The corresonding strain variables are the soil skeleton volumetric strain ε and shear (deviatoric) strain ε q. They are related to axial and radial stresses and strains in the usual way, where: ' ' 2 ' 3, ' ', 2, a r q a r a r q a r (5.1) 2 3 and subscrits a and r denote the axial and radial comonents, resectively. Comressive stresses and strains are assumed ositive and volumetric strain is linked to secific volume according to: v ln (5.2) v where v =1+e, e is the void ratio and v is the secific volume at the reference configuration. In incremental form Equation (5.2) can be rewritten as: v (5.3) v where a suerimosed dot indicates an increment. Elastic and lastic strain increments sum to give total strain increments in the usual way: q e e q q (5.4) where the suerscrits e and denote the elastic and lastic comonents, resectively. The stresses and strains are written in vector form σ' = [', q] T and ε = [ε, ε q ] T, resectively. 126

149 Chater 5 Constitutive model 5.3 THE CONSTITUTIVE MODEL The constitutive model used is based on the bounding surface lasticity model of Russell and Khalili (26a) and Khalili et al. (28). The differences between the model resented in the following and the above two are that this model adots linear isotroic comression lines defined in the lne ~ ln lane and that this model considers a different hydraulic model which accounts for both hydraulic hysteresis and a deendency of the SWCC on volumetric strain. The linear isotroic comression lines in the lne ~ ln lane are used as it reduces the curvature of comression lines defined in a semi-log' lane or logv ~ log' lane beyond the yield oint (McDowell, 25 and 213). But the main underlying model features are no different, as will be demonstrated later Effective stress and the effective stress arameter The effective stress and the effective stress arameters used are the same as those of Russell and Khalili (26a) and Khalili et al. (28). The mean effective stress (Bisho, 1959; Khalili et al. 28) is exressed as: ' net s (5.5) where net =-u a is the net stress, s= u a u w (u a and u w being the ore air and ore water ressure) is the matric suction and is the effective stress arameter, attaining a value of 1 for saturated soils and for dry soils. The equation for χ roosed by Khalili and Khabbaz (1998) based on shear strength data for various unsaturated soil tyes is adoted here. When the soil is undergoing a major wetting or drying event χ is defined as: s 1 for 1 se Ω (5.6) s for s 1 se se 127

150 Chater 5 Constitutive model where s e is the suction value reresenting the transition between saturated and unsaturated states and Ω is material arameter with a best fit value of.55. Recall that when a soil exhibits hydraulic hysteresis (Section 2.2.2), the SWCC has two main braches, namely the main drying curve and the main wetting curve. The curves connecting the two main curves are scanning curves. For a state on the main drying curve, s e = s ae, where s ae is the air entry value. For a state on the main wetting curve, s e = s ex, where s ex is the air exulsion value. For suction reversals the equation formulated by Khalili and Zargarbashi (21) is adoted: Ω s rd s s Ω ζ ex for dryingath reversal srd s srd sae srd sae Ω (5.7) s rw s s Ω ζ ae for wetting ath reversal s rw s srw sex srw sex where ζ is the sloe of the transition line between the main drying and wetting curves in a lnχ ~ lns lane, and s rd, s rw are the oints of suction reversal on the main drying and main wetting curves, resectively. Figure 5.1 resents the effective stress arameter evolving with suction in the lnχ~lns lane. The incremental form of the mean effective stress is: ' net s (5.8) where ψ=d(χs)/ds is the incremental effective stress arameter Mechanical model Elasticity A simle isotroic elastic rule is adoted. Incremental elastic volumetric strain accomanies a change in ' according to a linear relationshi between lne and ln'. The 128

151 Chater 5 Constitutive model isotroic comression line is defined to be linear in the lne~ln lane as it reduces the curvature of comression lines defined in a semi-log' lane or logv~log' lane beyond the yield oint (McDowell, 25 and 213). As suggested by Pestana and Whittle (1995) when a linear comression line is used in the lne ~ ln' lane, the elastic bulk modulus K should be inversely roortional to the orosity. Therefore, K is defined as: 1 e ' K (5.9) e where κ is a material constant and reresents the sloe of the elastic unload-reload line in the lne ~ ln' lane. For triaxial conditions the elastic shear modulus, G, is then defined as: G K (5.1) where is Poisson s ratio. The incremental elastic deformation is given by: e 1 ' K e 1 q q 3G (5.11) These definitions of the bulk modulus K and the shear modulus G are different to others where the elastic unloading-reloading line is linear in the v ~ ln lane (e.g. Russell and Khalili, 26a; Khalili et al., 28; Morvan et al., 21) Bounding surface and loading surface The constitutive model used is based on the bounding surface lasticity model of Russell and Khalili (26a) and Khalili et al. (28). In their models, urely elastic deformation was regarded negligible based on the observation of Bellotti et al.(21) that truly elastic behavior can be very small and can only be observed for shear strains 129

152 Chater 5 Constitutive model smaller than.1 in sands. The same assumtion was made here. Therefore all deformation is elastic-lastic. According to bounding surface lasticity theory (Dafalias and Herrmann, 198; Dafalias, 1986), lastic deformation occurs when the current stress state, which is always located on a loading surface, lies on or within a bounding surface. This is achieved by defining the hardening modulus as a decreasing function of the distance between σ' and an image oint denoted by σ ' on the bounding surface. The image oint is selected such that the unit normal vector n at σ' on the loading surface and at σ ' on the bounding surface are the same as illustrated in Figure 5.2. The bounding surface is defined as (Russell and Khalili, 26a), 1/ Q ln ' c / ' F tq M cs ' lnr (5.12) where the suerimosed bar denotes stress conditions on the bounding surface, Q is a material constant controlling the curvature, R is another material arameter controlling the ratio between ' c and the value of ' at the intercet of with the critical state line in the ' ~ q lane. M cs is the sloe of the critical state line in the ' ~ q lane: M cs q ' cs (5.13) cs 6sin' 3t sin' cs where ' cs is the critical state triaxial friction angle and is a material constant, t=+1 for comressive loading (q>) and t= 1 for extensive loading (q<). The loading surface is defined in such a way that it is of the same shae as the bounding surface and homologous at the origin in the ' ~ q lane (Russell and Khalili, 26a): 13

153 Chater 5 Constitutive model 1/ Q ln ' c / ' f tq M cs ' ln (5.14) R Critical state lines (CSL) and limiting isotroic comression lines (LICL) In this investigation linear critical state and limiting isotroic comression lines are assumed in lne ~ ln lane. The limiting isotroic comression line (LICL) is defined as: ln e LICL s s ln ' ln N (5.15) where N(s) and λ(s) are its intercet at ln' = and its sloe for a given suction s, resectively. N(s) and λ(s) may vary with suction as evidenced by exerimental results, for examle those of Wheeler and Sivakumar (1995) and Ramino et al. (2). The critical state line (CSL) is deduced imlicitly by an elastic shift of magnitude κlnr along the κ line, as illustrated in Figure 5.3. It is given as: ln e CSL s slnr' ln R ln N (5.16) Plastic otential A non-associated flow rule (Gajo and Muir Wood, 1999 and Khalili et al., 28) is assumed: d q g ' g q A M cs q ' (5.17) where d is dilatancy and A is a ositive material constant. The unit vector of lastic flow (m) at σ' is then: 131

154 Chater 5 Constitutive model 132 T T m m d t d td q 2 2, 1 1 m (5.18) Hardening rule As is common when alying the bounding surface lasticity theory the hardening modulus h is divided into two comonents: h b h f h (5.19) where h b is the lastic modulus at ' σ on the bounding surface and h f is some arbitrary modulus at σ' defined as a function of some distance between σ' and ' σ. The consistency condition at the bounding surface, noting that isotroic hardening stems from change in and s, results in: c c c ' s s ' ' F q q F ' ' F F (5.2) The incremental lastic strains are defined by (Khalili et al., 28): q g g q ' (5.21) where a scalar multilier Λ is recovered from: b Λh ' ' F ' F F T σ σ σ (5.22) It follows that:

155 Chater 5 Constitutive model h b F ' c ' c ' s c s m F σ' (5.23) The arbitrary modulus h f may take one of many different forms. One examle is (Khalili et al., 28): h f k m ' c ' s c s ' ' c ' c ' ' c c b q ' (5.24) where η b =(1-2ξ)M cs controls the sloe of the eak strength line in the q ~ ε q lane, and ξ is the state arameter (Been and Jefferies, 1985) defined as the vertical distance between the current state and critical state line (CSL) in the lne ~ ln lane. Though the comression lane is defined as the lne ~ ln lane, the state arameter is calculated in the same way as Been and Jefferies (1985). It is ositive above the current CSL line and is negative below the current CSL and is zero at the current CSL line. An increase in suction may increase the comressibility of the soil and shift the comression line. This is referred to as suction hardening (Barden, 1973). When a sudden diminishment of suction occurs, for examle by wetting the soil, the secific volume of the soil will be decreased significantly, esecially in soils when the suction hardening effect is obvious. This is commonly known as wetting collase in unsaturated soils. This collasible behavior was observed for Lyell silty sand as described in Section 3.3 and Section 3.5. Note that during ressure late tests, no or negligible volume change was observed to occur by the naked eyes during wetting from a suction of kpa to 27.6 kpa. However, an abrut and significant volume decrease was observed as suction reduced from 13.8 kpa to 6.9 kpa. Loret and Khalili (22) exlained that there may exist a suction value where volume collase commenced. Before reaching this suction value during wetting the volume change is much less ronounced. This suciton value may be higher than the suction value searating saturated from unsaturated states, which 133

156 Chater 5 Constitutive model is consistent with the behavior observed here. (The air exulsion values ranged from.14 kpa to.31 kpa for the samles used in the ressure late tests). A suction hardening rule should describe mathematically the suction effects in unsaturated soils as mentioned above. There are several methods to incororate the suction hardening effect using the effective stress concet. One is referred to as a multilicative rule, in which the equivalent saturated reconsolidation stress is multilied by a term to account for suction (Loret and Khalili, 22; Khalili et al., 28). Another involves a term added to the saturated reconsolidation stress and is referred to as an additive rule (Russell and Khalili, 26a). On the other hand, the suction hardening can be described through the definition of a loading collase surface which denotes the onset of irreversible volumetric deformations (e.g. Wheeler and Sivakumar, 23; Alonso et al., 213). In this study, a multilicative suction hardening rule is adoted in a similar way to Khalili et al. (28). The relationshi between reconsolidation stress, suction and void ratio is given by Equation (5.15). The incremental form of Equation (5.15) is: e e N N s s ' c sln' c s (5.25) ' c In the lne ~ ln lane, where elastic unloading-reloading occurs along a line of sloe κ, elastic volumetric strain is defined as: e e ' (5.26) 1 e ' Combining Equations (5.4), (5.25) and (5.26) leads to: ' c ' c v 1 ' 1 s s v 1 s N c N s s ln ' c s s s (5.27) 134

157 Chater 5 Constitutive model Thus / and / s are easily recovered from Equation (5.27) for inclusion in the hardening modulus. A radial maing rule (Russell and Khalili, 24, Russell and Khalili, 26a and Morvan et al., 21) is used to link σ' and σ '. According to the rule, the actual stress and its image oint are on the same straight line assing through the origin (refer to Figure 5.2). The unit normal vector n defining the direction of loading is then: n F f n,n σ' σ' q (5.28) F f σ' σ' with comonents written in exanded form: n f ' f σ' t q ' q ' 1 Qln 1 Qln 1 ' / c c 1 ' / ' 2 ' 1 (5.29) n q f q f σ' q ' t 1 Qln 1 ' / c 2 ' 1 (5.3) The final incremental lastic stress-strain relationshi is then: 135

158 Chater 5 Constitutive model n m 1 h nm q q n qm ' nqmq q (5.31) where h, m and n are defined above Hydraulic model The hydraulic model relates the volumetric moisture content or degree of saturation to suction and is commonly referred to as a soil-water characteristic curve (SWCC). The relationshi can be non-unique due to the existence of hydraulic hysteresis which is often encountered in unsaturated soils. Hydraulic hysteresis is incororated in the SWCC model used here together with the additional feature of a deendence on void ratio (eg. Gallioli et al., 23a, Miller et al., 28; Russell, 214). The hydraulic model roosed by Khoshghalb and Khalili (212) was considered initially. This model, based on the aroach of Khalili et al. (28) and Masin (21), accounts for a deendency of not only the air entry value and air exulsion value on void ratio, but also the sloes of main drying curve, main wetting curve and scanning curves. In this study a simler hydraulic model is used (Russell and Buzzi, 212; Russell, 214), in which the sloe of main drying and wetting curves and scanning curves are constant. The deendence of air entry and air exulsion values on void ratio is determined exerimentally in a similar way to Russell (214). The effective degree of saturation (S r ) on the main drying and wetting curves is defined as: S r 1 s se for for s s s s e e (5.32) 136

159 Chater 5 Constitutive model where s e = s ae for main drying and s e = s ex for main wetting. α=d -3 (D is the fractal dimension of the ore size distribution) controls the sloe of the curves. On scanning curves S r is defined as (Russell and Buzzi, 212): S r s s s s ae rd ex rw -α -α s s rd s s rw -β -β for dryingath reversal for wetting ath reversal s s s rw ex ae α α β s rd s s s ae ex s s rd (5.33) srw where β is the sloe of the scanning curves. Samles of different densities are tested to determine the SWCC. From Chater 3 it is found theoretically using the geometry of the soil structure that the deendence of s ae on the void ratio is (Russell, 214) which gives s ae with units of kpa: s ae Ds Ce (5.34) where D s is the fractal dimension of soil article size distribution and C is a constant deending on the geometry of the soil. For Lyell silty sand, D s = 2.61 and C = 1.5 (Russell, 214). The value of the air exulsion suction is found to obey (Russell, 214): sae 3s ex (5.35) Couling of the mechanical and hydraulic models The hydraulic and mechanical behaviors of unsaturated soil interact with each other (Wheeler, 1996; Vaunat et al., 2; and Alonso et al., 211). The hydraulic and mechanical behaviors are couled as exlained below. Note v w = S r e. It can be written in an incremental form as: 137

160 Chater 5 Constitutive model S r e Sr e v (5.36) w The degree of saturation is a function of the suction and the void ratio so that: S r Sr Sr s e (5.37) s e in which S r / s is deendent on where the hydraulic state is located on the SWCC. S r / e e reresents the change in the degree of saturation due to a change in void ratio at a constant suction. For Lyell silty sand S r / e can be exressed as: S e D r 3 e D s S r (5.38) Combining the above and making use of v = 1+e leads to: S s vw r S v 1s Sr Ds 1v v w or r r v s S D Ds v s (5.39) while S r / s = αs r /s for main wetting or drying aths and S r / s = βs r /s for scanning curves. α and β have negative values. According to Equation (5.39), for a constant moisture content condition and for soils with (D -3)D s +1>, an increase in e will result in an increase in the suction thus a decrease in degree of saturation (S r =v w /e). This is most commonly observed in exeriments and is intuitive. When (D -3)D s +1=, suction will be constant for constant moisture content conditions. However, when (D -3)D s +1<, a decrease in e will result in an increase in s, which has been observed in some exeriments (Tarantino and De Col, 28). In this case an increase in degree of saturation leads to an increase of suction. Tarantino and De Col (28) tested a Seswhite Kaolin which has 8% clay content and 2 % silt content. No article size distribution was reorted for D s to be determined. However, Ghanbarian-Alavijeh and Millan (29) investigated 172 soil samles and found that D s is well related to clay content. With 8% clay content the 138

161 Chater 5 Constitutive model Seswhite Kaolin would have a D s greater than 2.9 (referring to Table 1 in Ghanbarian- Alavijeh and Millan, 29). D of the Seswhite Kaolin is estimated to be 2.65 from the SWCC at 5 constant void ratios in the lns r ~ lns lane, as shown in Figure 5.4. Therefore, (D -3)D s +1=(2.65-3)2.9+1 = -.15 < which is consistent with the decrease in e causing an increase in s Comlete stress-strain relationshi The comlete stress-strain relationshi is: 1 nm K h nmq q h n q m h 1 nqm 3G h q ' q (5.4) Hydraulic couling considers both hydraulic hysteresis and the deendency of the SWCC on volumetric strain and is done outside of the matrix. This hydro-mechanical model is similar to those of Russell and Khalili (26a) and Khailli et al. (28). The difference is that it adots linear isotroic comression lines in the lne ~ ln lane, which results in different forms of K and G. Aart from this the underlying features of model are the same. s can be removed from h b (Equation (5.23)) by rearranging Equations (5.2) to (5.22) (Morvan et al., 21, 211). Also, Equation (5.4) can be rearranged as: D q D D v w D D D D D D ' q s (5.41) where 139

162 Chater 5 Constitutive model r s s r 33 q s r 32 s r 31 q s 23 q q 22 q 21 s 13 q v s S ĥ m nˆ D S e D ĥ m nˆ D S e D ĥ m nˆ K D S e D ĥ m nˆ D ĥ m nˆ G D ĥ m nˆ D ĥ m nˆ D ĥ m nˆ D ĥ m nˆ K D In this case, m remains unchanged. But the hardening modulus becomes f ĥ b ĥ ĥ and the unit normal vector is ] [ s q nˆ,,nˆ nˆ n (Morvan et al., 21) with comonents written in exanded form: 2 c c 1/ c cs c 2 c c ' ' / ' ln ln ' / ' ln ' ' 1 ' / ' ln 1 1 ' ' / ' ln 1 1 ' ' ' ' ' ˆ s Q R M Q q Q q t s F q F F F n Q c c (5.42) 2 c c 1/ c cs c 2 c q ' ' / ' ln ln ' / ' ln ' ' 1 ' / ' ln 1 1 ' ' ' ' ˆ s Q R M Q q t s F q F F q F n Q c c (5.43)

163 Chater 5 Constitutive model c c 1/ c cs c 2 c c c 1/ c cs c s ' ' / ' ln ln ' / ' ln ' ' 1 ' / ' ln 1 1 ' ' ' / ' ln ln ' / ' ln ' ' ' ' ' ˆ s Q R M Q q s Q R M t s F q F F s F n Q Q c c (5.44) These rearranged equations, although seemingly quite different, corresond to exactly the same model. Note that this rearrangement may aid imlementation into some roblems which involve numerical methods to comute the hardening modulus for constant moisture content conditions. m is unchanged. The only differences surround h f (Equation (5.24)) and h b (Equation (5.23)). f ĥ and b ĥ can be obtained from h f and h b using: f f ' ' ' ' ˆ s F q F F q F F h h c c and ) ' ' (1 1 ' ' ' ' ˆ b b c c c c s s s F q F F q F F h h In this study, the rearranged equations are used and f ĥ and b ĥ are assumed to be: ' q ' ' ' ' ' ' kˆ h b c c c c c m f (5.45)

164 Chater 5 Constitutive model hˆ b F ' c ' c m F (5.46) σ' 5.4 MODEL CALIBRATIONS Mechanical model calibration Elasticity arameters used in this model are and μ. κ is the sloe of the unloadingreloading line in isotroic loading tests. A value of κ =.12 is used throughout this study. is the Poisson s ratio and a value of μ =.4 is assumed throughout. The critical state arameter M cs = 1.45 (corresonding to = 35.7 ) is obtained using the sloe of a lot of deviator stress against the mean effective stress at the critical state, which is shown in Figure 5.5. M cs is unique and indeendent of suction when the χ as defined in Equation (5.6) is used to ut suction into the effective stress. Figure 5.6 resents the result of saturated drained triaxial tests in the M cs q/ ~ ε /ε q lane to aid determination of arameter A. When ε /ε q = and M cs q/ = the critical state is reached. A line of best fit through the data has a sloe equal to the value of A, according to Equation (5.17), which is found to be 1.2. Note that drained test data is used so that ε /ε q can be assumed. Shown in Figure 5.7 are saturated triaxial shear tests result in the lne ~ ln lane. The sloe and intercet of the limiting isotroic comression line (LICL) in the lne ~ ln lane for saturated conditions are λ =.8 and N =.515, resectively. The critical state line (CSL) is then lotted at a constant shift of κlnr from the LICL and R = 1 is obtained. Presented in Figure 5.8 are unsaturated triaxial shear test results in the lne ~ ln lane. It is assumed the states stay on the main drying curve during shearing. For calibration this assumtion is necessary to calculate the effective stress as for some tests the initial hydraulic states are unknown. Again R = 1 is used. The sloes and intercets of the LICLs for s s e, s * = 1 kpa, s = 1 kpa and s = 3 kpa are summarized in Table 5.1, where s * is the suction value indicating the commencement of wetting collase. This 142

165 Chater 5 Constitutive model value is observed to be between 13.8 kpa and 6.9 kpa during ressure late tests and here an averaged value of 1 kpa is chosen. The maximum deviator strain for all unsaturated tests is less than 25% due to the limitations of triaxial aaratus. For some of the tests the deviator strain is not large enough for the end state to be near the critical state. Where this is the case hollow symbols are used in Figure 5.7 and Figure 5.8. The sloes and intercets of the LICLs for suctions between s s e, s = s * = 1 kpa, s = 1 kpa and s = 3 kpa are linearly interolated. Note that the assumtion of the existence of s * is necessary and reasonable as significant volume decrease during wetting only haened for s less than s *. The Q value is obtained by fitting the loading surface to the results of undrained tests conducted on the loosest samles as shown in Figure 5.9. It is noted that for materials where the contribution of elasticity to volumetric change is small, the undrained resonse of the material in the effective stress lane follows closely the loading surface, which remains very close to the bounding surface (Russell and Khalili, 24). It is found that Q = 2 and R = 1 fit the data well. The kˆ m value as in Equation (5.23) is found by trial and error to be: kˆ m e e. 8 (5.47) where is the initial state arameter, that is the distance between initial state and current critical state line in the lane and the symbol means that when x > and when x Hydraulic model calibration Results of Mercury Intrusion/Extrusion tests (MIP) and ressure late tests (P.P.) are used to calibrate the hydraulic model as resented in Section Samles of different densities are tested and Russell (214) found that s ae = 1.5e kpa and s ex = s ae /3. 143

166 Chater 5 Constitutive model Presented in Figure 5.1 are the results in the lns r ~ lns/s ae lane. α =.52 and β =.2 fits the data well, while Ω =.55 and ζ = βω/α= MODEL SIMULATIONS Oedometric comression tests for saturated states and isotroic comression tests and triaxial shear tests for both saturated and unsaturated states are simulated. The initial conditions of oedometric comression tests and isotroic comression tests are listed in Table 5.2. The initial conditions for saturated triaxial tests and unsaturated triaxial tests are listed in Table 5.3 and Table 5.4, resectively. The initial state on the SWCC is either on a main drying curve (MD) or a scanning curve (SC) as will be exlained below Simulation results for saturated triaxial tests Presented in Figure 5.11 to Figure 5.13 are results of saturated triaxial shear tests under undrained conditions and model simulations in the q ~ ε q, u w ~ε q and q ~ ' lanes, resectively. The tests are erformed on loose samles, where a eak in the shear resistance followed by a reduction is observed. Presented in Figure 5.14 Figure 5.15, Figure 5.16 are results of saturated triaxial shear tests under drained conditions and model simulations in the q ~ ε q and ε ~ ε q lanes, resectively. The tests are conducted on samles initially looser than critical state. A tyical urely hardening behaviour is observed for all drained tests where shear resistance ket increasing and is accomanied by volumetric contraction. The simulations for saturated triaxial shear tests match the exerimental data reasonably well Simulation results for unsaturated triaxial tests For unsaturated tests under constant suction conditions, the initial state on the SWCC (whether it be on a main drying, main wetting or scanning curve) influences the initial value of mean effective stress and the stress ath. 144

167 Chater 5 Constitutive model Dense samles (denoted by D in the test identification number) are reared by initially comacting the samles at an unsaturated state, making the samles air-dried, then flooding the samles with water causing volumetric collase, then inducing suction (1 kpa or 3 kpa). The state during the final introduction of suction moves along the first wetting to drying scanning curve (as shown in Figure 5.17) and then, if suction is high enough, along the main drying curve. The initial state for samle subjected to s=1 kpa and e= is on first wetting to drying scanning curve whereas the initial state for samles subjected to s=3 kpa and e=.31 or.33 is on main drying curve, as shown in Figure Loose samles (denoted by L in the test identification number) are reared by direct alication of suction. The moisture content corresonding to the target suction rior to shearing is unknown, so is the initial state on the SWCC other than it will be on a scanning curve or main drying curve. The moisture content after a test is measured and it is around 4.2% and 2.7% for s=1 kpa and s=3 kpa, resectively. While the initial state is unknown, as shown in Figure 5.17, two simulations are made assuming initial states on the main drying curve and on the scanning curve to give a range of ossible simulation lines. The simulations for initial states on a scanning curve are indicated using dotted lines and for initial states on main drying curves using solid lines. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa for s= 1 kpa and for s=3 kpa (u6s1l-cs, u6s3l-cs, u6s1d-cs and u6s3d-cs) are resented in Figure 5.18 and Figure 5.19 in the (a) ε ~ ε q lane and (b) q ~ ε q lane, resectively. It is observed that shear resistance increases to a eak value accomanied by volumetric contraction followed by volumetric exansion, while for loose samle the exansion is small. Model simulations follow the trend quite well, while the volumetric strains for loose samles are overestimated as the critical state oints of these two tests in lne ~ ln' lane are above the corresonding CSL lines. This overestimation may arise from the initial e which is estimated by the digital image-rocessing technique. The difference of secific volume between this technique and burette readings is within.5% which is satisfactory, as discussed in Chater 3. For u6s1l-cs, u6s3l-cs, the maximum error in estimation of initial e using this technique is around.8, which may cause the overestimation of the volumetric strains. 145

168 Chater 5 Constitutive model Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa (u12s1l-cs, u12s3l-cs and u12s1d-cs) are resented in Figure 5.2 in the (a) ε ~ ε q lane and (b) q ~ ε q lane, resectively. Model simulations for both the deviatoric and volumetric resonses follow the trend of exerimental data well. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa (u24s1l-cs and u24s1d-cs) are resented in Figure 5.21 in the (a) ε ~ ε q lane and (b) q ~ ε q lane, resectively. The shear stresses are both underestimated slightly when aroaching critical state, which is consistent with the critical state oints of the two tests lying slightly above the critical state line in the lane in Figure 5.5. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of more than 24 kpa (u6s3l-cs and u3s3d-cs) are resented in Figure 5.22 in the (a) ε ~ ε q lane and (b) q ~ ε q lane, resectively. Model simulations for both the deviatoric and volumetric resonses agree well with the exerimental data. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa (u6s1l-cw and u6s1d-cw) are resented in the Figure 5.23 in the (a) ε ~ ε q lane and (b) q ~ ε q lane, resectively. For dense soil, the initial state on the SWCC is assumed to lie on a scanning curve. The observed trends are similar to those for constant suction conditions as a result of the interactions between the air, water and solid hases (in Equation 5.4). The suction increase for the constant moisture content conditions is very small (around 8 kpa) comared to the initial suction of 1 kpa for constant suction conditions, which may result in the similar trends and magnitudes between the results for constant moisture content and constant suction conditions. The simulation results are influenced by the initial state on the SWCC. The shear strength is increased by as much as 18% from an initial state on a SC (corresonding to moisture content of 4.2 %) to initial state on the MD for net = 6 kpa, s= 1 kpa and 146

169 Chater 5 Constitutive model for both constant suction and constant moisture content conditions. The magnitude of the change in stress and volume is smaller for simulations where initial state is on a SC than on the MD due to a smaller initial mean effective stress on the SC. With increasing confining net stresses the influence of initial hydraulic state on the shear strength is reduced Simulation results for oedometric comression and isotroic comression tests Figure 5.24 shows the isotroic comression tests results for a saturated condition, along with test results for s=1 kpa and s=3 kpa conditions, overlaid by model simulations. The model simulations match the exerimental data for saturated and unsaturated states very well. Figure 5.25 and Figure 5.26 show the saturated oedometric comression test results with model simulations in the lne ~ lnσ' 1 and σ' 3 /σ' 1 ~ lnσ' 1 lanes, resectively. Elastic volumetric strain is assumed from ' = to '. The value of σ' 3 /σ' 1 is found to increase with σ' 1. The three lines in the σ' 3 /σ' 1 ~ lnσ' 1 lane seem to aroach an uer limit. This uer limit leads to a constant value of q/ =.275. Again the model simulations match the exerimental data quite well. 5.6 CONCLUDING REMARKDS The model is based on that of Russell and Khalili (26a) and Khalili et al. (28) with differences surrounding comression lines which are resented in the lane here. It takes into account a hysteretic SWCC and a deendence of the SWCC on void ratio. The model is calibrated against Lyell silty sand both for saturated and unsaturated conditions. Model simulations are in good agreement with exerimental results of oedometric comression tests for saturated conditions, isotroic comression tests and triaxial shear tests for both saturated and unsaturated conditions under drained (or constant suction) and undrained (or constant moisture content) conditions. It is found that the contribution of variation of void ratio to the degree of saturation is related to the ore size distribution through D (and α) and article size distribution through D s. 147

170 Chater 5 Constitutive model Different initial states on the SWCC are exected from different samle rearation methods and initial conditions. The initial hydraulic state may have a great effect on the stress-strain relationshis, esecially at a low confining net stress. The model will be imlemented into the cavity exansion analysis in Chater

171 Chater 5 Constitutive model Table 5.1. Parameters N(s) and λ(s) defining the limiting isotroic comression lines. s (kpa) s s ex s * = N(s) λ(s) Table 5.2. List of initial conditions for oedometric comression tests and isotroic comression tests. Test ID Comression tye net, kpa Suction, kpa Initial void ratio 1-D-L-1 Oedometric, K = D-L-2 Oedometric, K = D-H Oedometric, K = Iso-S-L Isotroic Iso-S-M Isotroic Iso-1 Isotroic Iso-3 Isotroic Table 5.3. List of initial conditions for saturated triaxial tests. Test ID Isotroic comression net, kpa Shear tye Void ratio at start of shearing CU5 5 undrained.37 CU1 1 undrained.356 CD5 5 drained.352 CD1 1 drained.32 CD25 25 drained.37 CD3 3 drained.33 CD36 36 drained.312 CD5 5 drained

172 Chater 5 Constitutive model Table 5.4. List of initial conditions for unsaturated triaxial tests. Test ID Isotroic comression net, kpa Suction, kpa Shear tye Void ratio at start of shearing Initial state location on SWCC u6s1l-cs 6 1 constant suction.49 MD and SC u12s1l-cs 12 1 constant suction.536 MD and SC u24s1l-cs 24 1 constant suction.43 MD and SC u6s1d-cs 6 1 constant suction.327 SC u12s1d-cs 12 1 constant suction.312 SC u24s1d-cs 24 1 constant suction.327 SC u6s1l-cw 6 1 constant moisture content.54 MD and SC u6s1d-cw 6 1 constant moisture content.324 SC u6s3l-cs 6 3 constant suction.52 MD and SC u12s3l-cs 12 3 constant suction.494 MD and SC u6s3l-cs 6 3 constant suction.451 MD and SC u6s3d-cs 6 3 constant suction.33 MD u3s3d-cs 3 3 constant suction.31 MD ln(χ) ln(1.) ln(s ex ) ln(s ae ) When hydraulic state is on main wetting curve When hydraulic state is on main drying curve When hydraulic state is on scanning curves ln(s) Figure 5.1. Evolution of effective stress arameter with suction. 15

173 Chater 5 Constitutive model Figure 5.2. Illustration of loading surface, bounding surface and maing rule in the q~ lane. 151

174 Chater 5 Constitutive model Figure 5.3. Saturated and unsaturated CSLs and LICLs in the lne ~ ln' lane. 1% D -3= Degree of saturation, S r e=1. e=1.2 e=1.4 e=1.6 e=1.8 Main wetting curves 1% Suction, s(kpa) Figure 5.4. The exerimental data (from Tarantino and De Col, 28) of soil-water characteristic curves with D estimation for 5 void ratios in the lns r ~lns lane. 152

175 Chater 5 Constitutive model Deviator stress at critical state, q cs (kpa) M cs =1.45 Estimated critical state data for drained saturated tests Estimated critical state data for constant suction unsaturated tests critical state line Mean effective stress at critical state, ' cs (kpa) Figure 5.5. Critical state line in the q ~ 'lane CD25 CD3 CD36 CD5 A=1.2 M cs -q/' Fitting line for arameter A ε ṗ /ε q Figure 5.6. Results of saturated drained triaxial tests in the M cs -q/ ~ ε /ε q lane with determination of arameter A. 153

176 Chater 5 Constitutive model 1 Start oint for Saturated tests Saturated LICL Saturated CSL Drained tests Undrained tests End oints where critial state had been reached End oint where critical state had been aroached Void ratio, e Mean effectives stress, ' (kpa) Figure 5.7. Saturated triaxial shear tests results in the lne ~ ln' lane. 1 CSL for s=1 kpa CSL for s=3 kpa Void ratio, e LICL for s=1 kpa LICL for s=3 kpa Start oints for unsaturated tests.1 Figure 5.8. Unsaturated triaxial tests results under constant suction conditions in the lne ~ ln' lane. End oints for s=1 kpa where critical state had been reached End oints for s=3 kpa where critical state had been reached End oints for s=1 kpa where critical state had been aroached End oints for s=3 kpa where critical state had been aroached Mean effective stress, ln' (kpa) 154

177 Chater 5 Constitutive model.6 Loading surface with Q=2 and R=1 q/ '/Mcs CU5 CU '/ ' Figure 5.9. Results of undrained triaxial tests conducted on the loosest samles and loading surface with Q = 2 and R = 1 in the q/' /M cs ~ q/' lane. Degree of saturation 1% 1% β α 1 1 MIP-SCL6 e=.62 MIP-SCD-8 e=.48 MIP-insitu-1 e=.345 MIP-insitu-2 e=.41 P.P e=.68 P.P e=.59 P.P e=.5 1% s/s ae Figure 5.1. Results of Mercury Intrusion/Extrusion tests (MIP) and Pressure late tests (P.P.) in the lns r ~ lns/s ae lane. 155

178 Chater 5 Constitutive model 6 CU1 CU5 5 Deviator stress, q (kpa) Deviator strain, q Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the q ~ ε q lane. 1 9 Excess ore water ressre, u w, (kpa) CU1 CU Deviator strain, q Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the u w ~ε q lane. 156

179 Chater 5 Constitutive model 6 CU1 CU5 5 Deviator stress, q (kpa) Mean effective stress, ' (kpa) Figure Results of saturated undrained tests and model simulations for CU5 and CU1 in the q ~ 'lane. Volumetric strain, CD5 CD1 CD25 CD3 CD36 CD5 CD1 CD25 CD3 CD5 CD5 CD Deviator strain, q Figure Results of saturated drained tests and model simulations for CD5, CD1, CD25, CD3, CD36 and CD5 in the ε ~ ε q lane. 157

180 Chater 5 Constitutive model CD25 CD3 CD36 CD5 Deviator stress, q (kpa) CD36 CD Deviator strain, q Figure Results of saturated drained tests and model simulations for CD25, CD3, CD36 and CD5 in the q ~ ε q lane. 3 CD5 CD1 25 Deviator stress, q (kpa) Deviator strain, q Figure Results of saturated drained tests and model simulations for CD5, and CD1 in the q ~ ε q lane. 158

181 Chater 5 Constitutive model S r (log scale) s ex /s ae 1. S r at main drying curve S r =? First wetting to drying scanning curve States for dense samles follow the first wetting to drying scanning curve towards main drying curve and can be calculated at target suction. States for loose samles are unknown at target suction, but are assumed to be between MD and SC that is based on the measured moisture content at the end. S r at main wetting curve s target /s ae s/s ae (log scale) Figure Illustration of initial states determination for loose and dense soils. 159

182 Chater 5 Constitutive model a.4.2 u6s1d-cs u6s1l-cs Volumetric strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q b 6 5 u6s1d-cs u6s1l-cs Deviator stress, q (kpa) Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa for suction of 1 kpa (u6s1l-cs and u6s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively. 16

183 Chater 5 Constitutive model a.4.2 u6s3d-cs u6s3l-cs Volumetric strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q b 8 7 u6s3d-cs u6s3l-cs 6 Deviator stress, q (kpa) near critical state at q =.5 Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 6 kpa for suction of 3 kpa (u6s3l-cs and u6s3d-cs) in the ((a) ε ~ ε q and (b) q ~ ε q lane, resectively. 161

184 Chater 5 Constitutive model a.6.4 Volumetric strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC -.6 u12s1l-cs u12s3l-cs u12s1d-cs Deviator strain, q b u12s1l-cs u12s1d-cs u12s3l-cs Deviator stress, q (kpa) Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q Figure 5.2. Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 12 kpa (u12s1l-cs, u12s3l-cs and u12s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively. 162

185 Chater 5 Constitutive model a.3.2 u24sl-cs u24s1d-cs.1 Volumetric strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q b 15 q/'=1.674 at critical state u24s1d-cs u24s1l-cs Deviator stress, q (kpa) 1 5 Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of 24 kpa (u24s1l-cs and u24s1d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively Deviator strain, q 163

186 Chater 5 Constitutive model a.8.6 Deviator strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC -.4 u6s3l-cs u3s3d-cs Deviator strain, q b Deviator stress, q (kpa) u6s3l-cs u3s3d-cs Deviator strain, q Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant suction conditions at a confining stress of more than 24 kpa (u6s3l-cs and u3s3d-cs) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively. solid line-initial state on main drying curve dotted line- initial state on scanning curve 164

187 Chater 5 Constitutive model a.4.2 Volumetric strain, Solid line indicates initial state on MD Dotted line indicates initial state on SC -.8 u6s1l-cw u6s1d-cw Deviator strain, q b 6 5 u6s1l-cw u6s1d-cw Deviator stress, q (kpa) Solid line indicates initial state on MD Dotted line indicates initial state on SC Deviator strain, q Figure Comarison of model simulation and exerimental results of unsaturated triaxial shear tests under constant moisture content conditions at a confining stress of 6 kpa (u6s1l-cw and u6s1d-cw) in the (a) ε ~ ε q and (b) q ~ ε q lane, resectively. 165

188 Chater 5 Constitutive model.6.5 iso-s3 iso-s1 iso-s-m iso-s-l Void ratio, e Mean net stress, (kpa) Figure Comarison of model simulations and isotroic comression test results of saturated condition at low ressure and relative high ressure (iso-s-l and iso-s-m), s=1 kpa (iso-s1) and s=3 kpa (iso-s3) in the lne ~ ln lane. 166

189 Chater 5 Constitutive model D-L-1 1-D-L-2 1-D-H Void ratio, e (kpa) Figure Comarison of model simulations and oedometric comression test results of 1-D-L-1, 1-D-L-2 and 1-D-H in the lne ~ ln lane D-L-1 1-D-L-2 1-D-H.7.6 ' 3 /' (kpa) Figure Comarison of model simulations and saturated oedometric comression test results of 1-D-L-1, 1-D-L-2 and 1-D-H in the σ' 3 / σ' 1 ~ lnσ' 1 lane. 167

190 CHAPTER 6. A NEW MODEL FOR HYDRAULIC CONDUCTIVITY 6.1 INTRODUCTION In this chater, the effect of hydraulic hysteresis on the hydraulic conductivity is investigated with the aid of fractals. By treating a soil s ore geometry as a fractal it is ossible to derive hydraulic conductivity functions (eg. Rieu and Sosito, 1991; Sheard, 1993; Fuentes et al., 1996; Kravchenko and Zhang, 1999; Xu and Dong, 24; Xu, 24; Gimenez et al., 1997) as well as exressions for soil-water characteristic curves (SWCCs) (eg. Tyler and Wheatcraft, 199; Perrier, et al., 1996; Russell and Buzzi, 212). However, there have been no derivations for hydraulic conductivity using fractals when the soil state is located on scanning curves arising from hydraulic hysteresis, even though it has been shown both exerimentally and numerically that hydraulic hysteresis significantly affects water flow and transort (eg. Vachaud and Thony, 1971; Gillham et. al., 1979; Basile et.al., 23). This chater resents the newly develoed model for hydraulic conductivity considering hydraulic hysteresis using fractals. The model enables estimation of hydraulic conductivity when the soil state is on a scanning curve, main wetting curve or main drying curve. All the defining arameters can be obtained from fitting the fractal-based SWCC to exerimental data, excet the tortuosity ratio which is a fitting arameter. The 168

191 Chater 6 Hydraulic model exressions were fitted to exerimental data for a range of soils and showed good agreement. This work has been ublished in Geotechnical Letters, 214, Volume 4, Issue January to March: 1-1. The model is used for the analysis of the time required to aroach suction equilibrium in the large unsaturated samles in the calibration chamber using axis translation technique. This is imortant as it is necessary to know when the suction equilibrium will be aroached and to determine if the target suction has been reached. 6.2 A DESCRIPTION OF A SOIL WITH IDEALISED PORE GEOMETRIES The soil is assumed to be made u of a series of geometrically similar but different sized cells, where each cell comrises solid and a ore configured in the same way, irresective of cell size. The restriction that only a single ore can occuy a cell is imosed. No similar restriction is imosed on the solid. In other words, the solid in a cell may reresent a single article, multile articles, or arts of articles which extend into multile cells. If the ore in a cell has a characteristic size d, then the volume of the ore in the cell is d 3, where is a dimensionless geometrical arameter. d is inversely roortional to the suction which will cause the ore to drain or fill with water, as defined later. The cross sectional area of a ore is shae arameter. d 2 and is a dimensionless The numbers and sizes of cells exist according to a geometric series, bound within limits of finite maximum and minimum sizes. The largest ores, which occuy the largest cells, are of size d 1, so that the volume of a ore in a single cell is 3 d 1. The number of ores of size d er unit volume is denoted N. The volume of all ores 1 occuying the largest cells is N. 3 d 1 169

192 Chater 6 Hydraulic model The second largest ores, which occuy the second largest cells, are of size 1 3 d2 d1 n, where n is a material constant larger than unity and controls the volumes of ores of successively smaller sizes. The volume of a ore in a cell of the second largest size is d 3 1 n. The number of ores of size d is Nn, where is 2 another material constant less than unity which, together with n, controls the numbers of ores of different sizes. The volumes of all ores occuying the second largest cells is N. 3 d 1 The same geometrical series is assumed to aly to successively smaller ores and cells. Cell order is denoted by an integer x, with x being 1 for the largest cell increasing to i for the smallest cell. d ( x1 ) 3 x d1 n then reresents the size of the ores of order x. The sizes, volumes, numbers and cross sectional areas for a sequence of successively smaller ores and cells are given in Table 6.1. The total volume of ores is: i 2 i N d1 1 3 VT N d1 (6.1) The total number of ores is: N T N i 2 i1 n 1 n n n N 1 (6.2) n 1 When x and n are significantly larger than unity the number of ores of size d larger than or equal in size to d x is given by: d d N n x x1 N (6.3) 3ln d1 d Realising that x 1 lnn x, a rearranged Equation (6.3) is: 17

193 Chater 6 Hydraulic model N d in which D d x dx N (6.4) d 1 D ln 3 1. Equation (6.4) is a roerty of a soil with a fractal ore size lnn distribution, in which D is the fractal dimension of the distribution. As er Russell and Buzzi (212) it is suosed for ores of each order that q reresents the volumetric fraction that act as throats and (1 - q) reresents the volumetric fraction that act as bodies. On the main wetting curve as suction is reduced, water first collects in the smallest ores (both bodies and throats), then fills larger ores in order of increasing size. For a given value of suction s x, all bodies of size d x and larger are dry. s x is related to d x+1 and d x by: s x 4tcos 4tcos n d d x 1 x 1 3 (6.5) where t is the surface tension of the air-water interface ( N/m at 2 degrees Celsius) and θ is the contact angle (which varies from about to 7 degrees for different soil minerals). On the main drying curve for a given value of suction s x n 1/3, all ore bodies of size d x and larger are dry while throats of size d x+1 and larger are dry. The scanning curves are lines connecting s x on the main wetting curve to s x n 1/3 on the main drying curve. The exressions for the SWCCs are given below. For the main wetting curve: ex max,w smax,w s s Sr (6.6a) s 171

194 Chater 6 Hydraulic model in which S r is the degree of saturation, s ex 4tcos d is the air exulsion suction (ie. 1 the suction value where the main wetting curve intercets S r = 1), D 3 is the fractal ore size distribution index (also denoted λ in the literature) and s 4t cos 1 3 max,w n is the maximum suction achievable on the main wetting curve, that d min is the suction value at which the smallest ores of size d min are dry. For large i, d min and Equation (6.6a) simlifies to: r s s ex S (6.6b) For the main drying curve: S r ae max,d max,d s s (6.7a) s s in which s s n is the air entry suction (ie. the suction value where the main ae ex drying curve intercets S r = 1), ln 1 q qn ln n / 3 1/ 3 is the sloe of linear scanning curves in the lns r ~ lns lane (also denoted in the literature), and s max, d s max,w n is the maximum suction achievable on the main drying curve. For large i this simlifies to: r s s ae S (6.7b) The SWCC is resented grahically in the lns r ~ lns lane in Figure 6.1. Notice that for an initially saturated soil, as suction is increased, the instant when S r begins to become less than unity is when s = s ex. As suction is increased further the state moves along a scanning curve until s = s ex n 1/3 is reached on the main drying curve. The small dashed line bounds a hysically inaccessible region which contains the oint S r = 1 and s = s ae (Russell and Buzzi, 212). 172

195 Chater 6 Hydraulic model It is noted that the Russell and Buzzi (212) fractal analogy and SWCC exressions are somewhat idealised, and more comlicated exressions would be required to cature the incomlete saturation observed in some soils during rimary wetting as suction is reduced to zero (e.g. Basile et al., 23; Lu et al., 213). Also, the rimary and secondary drying (or wetting) curves are considered to be the same, contrary to what is observed for some soils where slight differences exist (e.g. Miller et al., 28). However, even with these idealisations, it it demonstrated in the following that the main relationshis between suction, degree of saturation and hydraulic conductivity are catured well. 6.3 FROM FRACTALS AND SWCCS TO HYDRAULIC CONDUCTIVITY FUNCTIONS Caillary tubes and volume flux To derive exressions for hydraulic conductivity it is suosed that ores of size d x form caillary tubes of cross-sectional area A x d 2 x d 2 1 n 2( x1 ) 3. The total length of a single caillary tube er unit length of soil, P x, is assumed equal to (Sheard, 1993): x Px T (6.8) in which T is the tortuosity ratio. The length of the tube increases as x increases. Since the volume of a single ore of order x is V the tube that is equal to: x d 3 1 n x1, then it has a length along V d x 1 L x 1 (6.9) x 3 Ax n The combined length of all ores of size d is then: x x1 2x1 3 x1 L xt Nn Lx N d1n (6.1) The total number of caillary tubes of order x er unit length of soil is then: 173

196 Chater 6 Hydraulic model 174 x x x T n d N P L C x xt x (6.11) The volume flux er unit of hydraulic gradient for C x caillary tubes of order x is (Sheard, 1993): x 4 x x x 128 P gd C F (6.12) in which η is the kinematic viscosity and g is acceleration due to gravity. This can be rearranged as: n T D n T D n T D d T d gn d d T d gn F ln ln 6 5 x 2 ln ln 6 1 ln ln x x (6.13) Hydraulic conductivity on the main wetting curve By direct analogy with Darcy s law (Mualem, 1978; Fuentes et.al., 1996) the hydraulic conductivity for the soil with suction s x is: n T D / x i n T D / n T D n T D x i n T D / n T D / n T D n T D n T D n T D n T D n T D x i x k k x n n d T d gn n n d T d gn d d d T d gn F K ln ln ln ln ln ln x 2 ln ln ln ln ln ln ln ln x 2 ln ln 6 1 ln ln 6 5 i ln ln x ln ln x 2 ln ln (6.14)

197 Chater 6 Hydraulic model 175 Note that for a suction s x on the main wetting curve, ore orders of x + 1 and larger are saturated, hence the summation starts at x + 1. As the soil becomes saturated on the main wetting curve, that is when x = (a necessary assumtion to make ores orders of x = 1 and larger saturated), it follows that the saturated hydraulic conductivity is: n T D / i n T D / n T D n T D n n d T d gn K ln ln ln ln ln ln ln ln (6.15) The relative hydraulic conductivity for a suction s x on the main wetting curve is then: i n T D / x i n T D / n T D x Rx n n d d K K K ln ln ln ln ln ln x (6.16) For large i this simlifies to: n T D Rx d d K ln ln x (6.17) Again for large i the relative hydraulic conductivity can be written as a function of degree of saturation S r : D / n T D S K 3 ln ln 6 5 r R (6.18a) or / S K r R (6.18b)

198 Chater 6 Hydraulic model 176 where n T D ln ln Hydraulic conductivity on the main drying curve When on the main drying curve the contribution of the ore bodies to the hydraulic conductivity is: n T D / x i n T D / n T D n T D n T D n T D n T D n T D x i x k k n n d T d gn q d d d T d gn q F q K ln ln ln ln ln ln x 2 ln ln 6 1 ln ln 6 5 i ln ln x ln ln x 2 ln ln bx (6.19) This summation starts at x + 1 since ore bodies of orders x + 1 and larger are saturated. The contribution of the ore throats to the hydraulic conductivity is: n T D / x i n T D / n T D n T D n T D n T D n T D n T D ) x ( i x k k n n d T d gn q d d d T d gn q F q K ln ln ln ln ln ln x 2 ln ln 6 1 ln ln 6 5 i ln ln x ln ln x 2 ln ln tx (6.2) The combined hydraulic conductivity is then:

199 Chater 6 Hydraulic model 177 n T D / x i n T D / n T D / n T D / x i n T D / n T D n T D n n n q n n q d T d gn K K K ln ln ln ln ln ln ln ln ln ln ln ln x 2 ln ln 6 1 tx bx x (6.21) The relative hydraulic conductivity is then: i n T D / x i n T D / n T D / x i n T D / n T D n n n q n q d d K ln ln ln ln ln ln ln ln ln ln x Rx (6.22) For large i this simlifies to: n T D / n T D n q q d d K ln ln ln ln x Rx 1 (6.23) The relative hydraulic conductivity can be written as a function of S r, and for large i is: r R 1 qn q n S K / / (6.24) Hydraulic conductivity on scanning curves The relative hydraulic conductivity is assumed to vary linearly in the lnk R ~ lns lane as suction changes between s x on the main wetting curve and s x n 1/3 on the main drying curve. The sloe of the line connecting relative hydraulic conductivity on the main wetting curve (K R,wett ) to the value on the main drying curve (K R,dry ) is then:

200 Chater 6 Hydraulic model K lnk ln R,wett R,dry (6.25) 1/ 3 s x sxn ln ln sae sae in which K R,wett and K R,dry are obtained from Equations (6.18) and (6.24). For large i this simlifies to: /3 ln 1 q qn (6.26) 1/3 ln n An exression for K R as the state moves from the main wetting curve to the main drying curve along a scanning curve is: K R s rw S r s (6.27) ex in which s rw is the suction value on the main wetting curve where it is interceted by the scanning curve. An exression for K R as the state moves from the main drying curve to the main wetting curve along a scanning curve is: K / 1 3 / 3 s rd s 3 rd n q qn S n (6.28) R 1 r Sr s ae s ae in which s rd is the suction value on the main drying curve where it is interceted by the scanning curve. 6.4 COMPARISONS AGAINST EXPERIMENTALLY MEASURED HYDRAULIC CONDUCTIVITY DATA Once SWCC data has been fitted using Equations (6.6b) and (6.7b) and scanning curves of constant sloe, all arameters defining the hydraulic conductivity functions, excet 178

201 Chater 6 Hydraulic model T, are known. T is a function of soil texture and can san a wide range (Wosten and van Genucheten, 1988; van Genuchten et al., 1989). In this study T was found for a range of soils by fitting Equations (6.18b), (6.24) and (6.28) to exerimental data by trial and error. Table 6.2 summarizes the hydraulic roerties and arameters for hydraulic conductivity model for soils from literature. Figure 6.2 shows measured SWCC data for Caribou silt loam (To, 1971) together with fitted curves. Figure 6.3 shows measured hydraulic conductivity data along with fitted curves, including aths when states were on scanning curves. The main drying ath data is fitted well, as is the data for drying along scanning curves. The data for wetting along scanning curves is fitted less well, due to assumed constant sloe for scanning curves not roducing an accurate fit to the SWCC data. Figure 6.4 shows measured SWCC data for Quartz sand (Dury et al., 1998) together with fitted curves for main drying and wetting aths. Figure 6.4 also shows measured hydraulic conductivity data along with fitted curves. Model fits against exerimental data for the SWCC and hydraulic conductivity for silty sand (Lu et al., 213) are resented in Figure 6.5 to Figure 6.7. If hysteresis exists in SWCCs then hysteresis also exists in the hydraulic conductivity. In other words, searate relationshis aly for hydraulic conductivity, deending whether the state is on a main wetting curve or a main drying curve. The existance of hysteresis in hydraulic conductivity data may be more obvious in the lnk R ~ lns lane than the lnk R ~ lns r lane (e.g. Gallage et al., 213). Dury et al. (1998) suosed no hysteresis exists in their hydraulic conductivity data, yet a reresentation in the lnk R ~ lns r lane shows this to not be the case (Figure 6.4b). The hysteresis is fitted well by the model roosed here. 6.5 APPLY THE MODEL TO LARGE UNSATURATED SAMPLES The model was then alied to cylindrical samles (46mm diameter and 8mm height) reared by static comaction as described in Chater 4 in the UNSW calibration chamber. Suction was then alied by axis translation, with air ressure alied uniformly across the to of a samle, exelling water through the base of a 179

202 Chater 6 Hydraulic model samle as suction aroached the target value. The numerical method of Khoshghalb and Khalili (213) for flow analysis is used to redict the moisture content distribution along samle heights at different times after commencement of axis translation. SWCC data for Lyell dam soil was obtained using ressure late tests and mercury intrusion/extrusion tests, resented in Figure 5.7 together with fitting the fractal model to exerimental data. Recall that samles of different densities were tested and it was found that s ae = 1.5e kpa (e is the voids ratio) (in Chater 3). Also, the initial suctiondegree of saturation state after comacting a large samle was always on a scanning curve. The initial suction was estimated based on known suction degree of saturation states measured in similar samles. Also, in all cases considered here, the state remained on a scanning curve as suction increased aroaching the target value. Thus Equation (6.28) was used for redicting soil hydraulic conductivity in the numerical analysis. The saturated hydraulic conductivity used is m/s. A summary of initial conditions and hydraulic arameters for each samle is rovided in Table 6.3. Shown in Figure 6.8 are moisture content distribution data against model simulations for K6S1-N for different values of β to examine sensitivity. It can be seen that β has a minor effect on results. Figure 6.9 and Figure 6.1 show moisture content distribution data against model simulations for K6S1-1 and K6S1-2 (not resented in Chater 4 as a CPT was not conducted, but the samle was reared using the same method as K6S1-1) with different values of T. It is shown that T has a significant effect on the results and that the best fit value for all three tests is T = 2. Also notice the moisture contents at the tos of samles were overestimated by the model, robably due to air sulied to the tos of the samles causing localised drying, desite the air being assed through a moisture tra. Even so, the model roduces reasonable matches, esecially in the bottom half of the samles. Figure 6.11 shows the suction rofiles together with cone enetration resistances along the samles for K6S1-N and K6S1-1. The suctions were back-calculated. The slight suction gradient, increasing with deth, corresonding to a slight moisture content gradient, are consistent with the slight increases of cone enetration resistances with deth. The cone enetration resistance q c was averaged from deth of.3 m to.5 m for each samle using axis translation. So were the suction values. 18

203 Chater 6 Hydraulic model 6.6 CONCLUDING REMARKS The effect of hydraulic hysteresis on the hydraulic conductivity has been investigated. It was demonstrated for a range of soils that the hydraulic conductivity can be reasonably well redicted from known SWCCs. The model was also adoted in a flow analysis of large unsaturated soil samles. The simulations were in good agreement with measured moisture content distribution data. From the flow analysis, as exected, a longer time results in a more uniform moisture content distribution, as shown in Figure 6.1. However, to reach the target suction values for samle K6S1-2 at least 2795 hours is required. And this amount of time for one test is not ractical within the duration of this study. Therefore, the suction resent in samles at the time of cone enetration testing was back calculated using the measured moisture contents and void ratios, knowing that the state was on a scanning curve. The back-calculated suction values were summarized in Table 4.1 (in Chater 4, Section 4.5.2). 181

204 Chater 6 Hydraulic model Table 6.1. Proerties of ores and cells of different orders. Cell order x i Pore size (body or throat) in a single cell Pore volume (body or throat) in a single cell Pore cross sectional area (body or throat) in a single cell Number of ores (bodies lus throats) Pore volume (bodies lus throats) in all cells Pore throat volume in all cells Pore body volume in all cells d d n n d 1 n d 3 1 d d1 n d ( i1 ) 3 d n d 3 1 N Nn N n 2 3 d 1 n i1 d 1 n d1 n 2 2( i1 ) 3 d1 n i1 N N N d 1 3 N i d 3 d 1 d 1 qn qn qn d 1 3 qn i d d qn d 1 qn d 1 qn d i1 3 1 qn d N n

205 Chater 6 Hydraulic model Table 6.2. Soil hydraulic roerties and arameters for hydraulic conductivity model. Samle USCS K d sat, K w sat, K sat, cm/s cm/s cm/s D α β q n s ex, kpa s ae, kpa T Source Caribou To / 3.12E-4 / silt loam (1971) Dury, Quartz / 1.18E-4 / et al. sand (1998) A35 CL-ML 5.E-5 1.E-5 2.5E Lu, et A55 SP 5.E E-6 5.E al. B62 SM 1.E E-6 3.3E (213) Table 6.3. Initial conditions and hydraulic arameters for each samle. Test ID Initial water content Void ratio Initial S r Test time, hour Target suction, kpa D α β q n s ex, kpa s ae, kpa s i, kpa T K6S1-N 6.15% % K6S % % K6S % %

206 Chater 6 Hydraulic model ln(s r ), ln(k R ) Inaccessible triangular region ln(1.) Scanning curves Main drying curve Main wetting curve ln(s ex ) ln(s x ) ln(s ex n 1/3 ) ln(s x n 1/3 ) Soil-water characteristic curve Hydraulic conductivity ln(s) Figure 6.1. Grahically illustration of SWCC and hydraulic conductivity functions in lns r ~ lns and lnk R ~ lns lane. 184

207 Chater 6 Hydraulic model a 1% Degree of saturation, S r Main drying Drying along scanning curve Drying along scanning curve Drying along scanning curve 6% Suction, s (kpa) b 1% Degree of Saturation, S r Main drying Wetting along scanning curve Wetting along scanning curve Wetting along scanning curve 6% Suction, s (kpa) Figure 6.2. Measured SWCC data of Caribou silt loam (To, 1971) together with fractal simulations for (a) drying along scanning curves and (b) wetting along scanning curves. 185

208 Chater 6 Hydraulic model a 3E-2 Hydraulic conductivity, cm/s 3E-3 Main drying Drying along scanning curve Drying along scanning curve 3E-4 6% 1% Degree of saturation, S r b 3E-2 Hydraulic conductivity, cm/s 3E-3 Wetting along scanning curve Wetting along scanning curve 3E-4 6% 1% Figure 6.3. Measured hydraulic conductivity of Caribou silt loam (To, 1971) against model simulations for (a) main drying, drying along scanning curves and (b) wetting along scanning curves. Degree of saturation, S r 186

209 Chater 6 Hydraulic model a 1% Main drying Degree of saturation, S r 1% Main wetting b 1% Suction, s(kpa) 1.E+ Main drying Relative hydraulic conductivity, K R 1.E-1 1.E-2 Main wetting 1.E-3.1 Degree of saturation, S 1 r Figure 6.4. Model simulations against exerimental data of Quartz sand (Dury et al., 1998) for (a) SWCC and (b) relative hydraulic conductivity. 187

210 Chater 6 Hydraulic model a 1% Degree of saturation, S r A35-main drying A35-main wetting b 1% Suction, s (kpa) 1.E-4 A35-main drying 1.E-5 A35-main wetting Hydraulic conductivity (cm/s) 1.E-6 1.E-7 1.E-8 1.E-9 1.E-1 1% Degree of saturation, S 1% r Figure 6.5. Model simulations against exerimental data for samle A35 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity. 188

211 Chater 6 Hydraulic model a 1% Degree of saturation, S r A55-main drying A55-main wetting b 1% Suction, s (kpa) 1.E-4 1.E-5 A55-main drying A55-main wetting Hydraulic conductivity (cm/s) 1.E-6 1.E-7 1.E-8 1.E-9 1.E-1 1.E-11 1% 1% Degree of saturation, S r Figure 6.6. Model simulations against exerimental data for samle A55 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity. 189

212 Chater 6 Hydraulic model a 1% Degree of saturation, S r B62-main drying B62-main wetting b 1% Suction, s (kpa) 1.E-4 1.E-5 Hydraulic conductivity (cm/s) 1.E-6 1.E-7 1.E-8 B62-main drying B62-main wetting 1.E-9 1.E-1 1% Degree of saturation, S 1% r Figure 6.7. Model simulations against exerimental data for samle B62 (Lu et al., 213) for (a) SWCC and (b) hydraulic conductivity. 19

213 Chater 6 Hydraulic model.7 Samle height (m) Data for time=35 hours Initial condition time= Condition of time=infinity for beta=-.16 Condition of time=inifinity for beta=-.2 Condition of time=infinity for beta=-.24 Simulation at time=35 hours for beta=-.16 Simulation at time=35 hours for beta=-.2 Simulation at time=35 hours for beta= % 3.% 4.% 5.% 6.% 7.% 8.% Moisture content Figure 6.8. Moisture content distribution data against model simulations for K6S1-N together with sensitivity check for β = -.16, -.2 and -.24 at time = 35 hours. 191

214 Chater 6 Hydraulic model.7.6 Data for time=591.5 hours Samle height (m) Initial condition at time= Condition of time=inifinity Simulation at time=591.5 hours for T=1.5 Simulation at time=591.5 hours for T=2 Simulation at time=591.5 hours for T= % 3.% 4.% 5.% 6.% 7.% 8.% Moisture content Figure 6.9. Moisture content distribution data against model simulations for K6S1-1 together with sensitivity check for T = 1.5, 2 and 2.5 at time = hrs. 192

215 Chater 6 Hydraulic model.7.6 Data for time=126 hours Initial condition at time= Samle height (m) Condition of time=inifinity Simulation at time=126 hours for T=1.5 Simulation at time=2795 hours for T=1.5 Simulation at time=126 hours for T=2 Simulation at time=2795 hours for T=2 Simulation at time=126 hours for T=2.5 Simulation at time=2795 hours for T= % 3.% 4.% 5.% 6.% 7.% 8.% Moisture content Figure 6.1. Moisture content distribution data against model simulations for K6S1-2 for T = 1.5, 2 and 2.5 at time = 126 hours and 2795 hours, resectively. 193

216 Chater 6 hydraulic model Cone enetration resistance, q c (MPa) Deth (m).4.4 Deth (m) Cone enetration resistance for K6S1-N Cone enetration resistance for K6S1-1 Suction rofile for K6S1-N.6.7 Suction rofile for K6S Suction, s (kpa) Figure Back-calculated suction rofiles with cone enetration resistance along the samles of K6S1-N and K6S

217 CHAPTER 7. CAVITY EXPANSION ANALYSIS CONSIDERING HYDRAULIC HYSTERESIS 7.1 INTRODUCTION This chater resents details of a cavity exansion analysis in unsaturated soils considering hydraulic hysteresis. The analogy between cavity exansion and the enetration roblem was first noticed by Bisho et al. (1945). The results of sherical cavity exansion analysis are usually related to cone enetration tests results (e.g. Vesic, 1972; Yu, 1993; Salgado and Prezzi, 27; Pournaghiazar et al, 212, 213a), while the results of cylindrical cavity exansion analysis are usually related to ressuremeter test results (Palmer, 1972; Yu et al., 1996; Tan, 25). Simlified illustrations of the analogy between cone enetration resistance (q c ) from CPTs and the limiting cavity ressure is shown in Figure 7.1, as is the analogy between wall ressure (P L ) from a Pressuremeter test and the cylindrical cavity ressure. There are reorts (e.g. Nishimura and Fredlund, 22; Shemsu et al., 25; Thu et al., 26; Khoury and Miller, 211) that for the same soil and the same suction the shear strength during a drying rocess is different to that during a wetting rocess. In other words the loading history and hydraulic hysteresis can influence the shear strength 195

218 Chater 7 Cavity exansion analysis arameters that are associated with suction. However, no one has investigated the effect of hydraulic hysteresis on the ressure required to exand a cavity. Therefore, the main objective in this chater is to investigate the effect of hydraulic hysteresis on cavity exansion, secifically how different initial states on the SWCC affect the cavity exansion ressure. Different drainage conditions (constant moisture content, constant suction and constant χs conditions) are also considered to study how sensitive cavity exansion ressures (and thus cone enetration resistance) are to these. A constant moisture content condition usually alies in a field CPT, even in sand, as unsaturated hydraulic conductivity is too low to ermit a constant suction condition. A constant χs condition serves as an intermediate condition and is aealing from an interretation view oint as the contribution of suction to effective stress is constant. Pournaghiazar et al., (213) assumed a constant suction condition when interreting CPT results in unsaturated sand after cavity exansion results of Russell and Khalili (26b) showed constant suction and constant moisture content conditions gave very similar cavity exansion ressures. This assumtion is only ermissible for unsaturated clean sand when suction hardening is absent. However, for a different soil tye, and when suction hardening is resent, the effect of drainage condition needs to be investigated. The results of the cavity exansion analysis resented here will be used to inform assumtions about what suction should be adoted when interreting the CPT results in Chater NOTATIONS An exanding cavity is surrounded by soil in which deformation comrises a combination of elastic and lastic strains. This, in turn, is encomassed by soil in which deformation is urely elastic. The configuration is illustrated in Figure 7.2, where the radius of the exanding cavity is denoted c and the radius of the elastic-lastic boundary is denoted R. The radius of a articular soil element is denoted r. Only cavities exanded from zero initial radius are considered. 196

219 Chater 7 Cavity exansion analysis Cylindrical olar notations (r, z, θ) are used for cylindrical cavities and sherical olar notations (r, ω, θ) are used for sherical cavities. The radial stress (σ r ) reresents the major rincial stress and the tangential stress (σ θ ) reresents the minor rincial stress. For cylindrical cavities σ z reresents an intermediate stress and for sherical cavities there is a symmetry such that the intermediate stress (σ ω ) is equal to σ θ. The variables and q are defined in terms of σ r and σ θ according to: ' r k' ' 1 k θ q ' (7.1) r ' θ where k = 1 for the lane strain conditions of a cylindrical cavity and k = 2 for the sherically symmetric conditions of a sherical cavity (e.g. Carter et al., 1986). The corresonding strains ε and ε q are related to radial strain ε r and tangential strain ε θ by: k r θ k r θ q (7.2) 1 k where ε z = for cylindrical cavities and ε ω = ε θ for sherical cavities. Comression strains are assumed to be ositive. Following Collins and Wang (199), it is further assumed that at the initial condition, when time t =, the cavity radius is c = and the soil element of interest is located at radius r. As time is increased, the cavity radius is assumed to be c (Figure 7.1). The radial and tangential strains at r are defined in terms of radial dislacement u by: r u r u θ (7.3) r Stress or strains exressed in rate form using the symbol ( ) denote the material time derivative. ( ) denotes the local time derivative at r. These are related by: 197

220 Chater 7 Cavity exansion analysis ( ) ( ) w () r (7.4) where w is the radial velocity of the soil element at r. The cavity exansion roblem, when the initial cavity radius is zero, obeys similarity (Colllins et al., 1992) which means that the cavity exands in a geometrically self-similar manner. The radial and tangential strain rates at any instant are then defined in terms of w and r as (Collins and Wang, 199): w r r w θ (7.5) r It follows that: ε w r kw r ε q w w k r r 1 k (7.6) 7.3 GOVERNING EQUATIONS FOR ELASTIC REGION The solution for dislacement in an elastic region for R r is (Carter et al., 1986): k R u ε R R (7.7) r where ε R is the tangential strain at the elastic-lastic boundary (r=r). For cavities exanded in soils of infinite radial extent, the elastic region has zero volumetric strain (r, u ), thus, K and G are constant throughout the entire elastic region and an exression for q then becomes (Russell and Khalili, 26b): k R q 21 kg R R (7.8) r 198

221 Chater 7 Cavity exansion analysis Then at the elastic-lastic boundary it follows (Russell and Khalili, 26b): R q R G R R 21 k r k (7.9) The K defined by Equation (5.9) is assumed to aly to both lane strain conditions and sherically symmetric conditions. However, searate definitions of G aly for lane strain and sherically symmetric conditions. Following Collins and Stimson (1994), Equation (5.1) may be rewritten as: 1 k1 2 v' 21 k 1 e G (7.1) where the void ratio is resent in the denominator as linear elastic comression lines are defined in the lne~ln lane. The elastic stress-strain relationshi in Equation (5.11) needs to be modified for the cavity exansion roblem and is rewritten as: e 1/ K e q k 2 1 ' k G q (7.11) The values of κ should be slightly different for cylindrical and sherical cavity exansions. However, for all ractical uroses, and for the Poisson s ratios tyical of real soils, the two κ values can be taken as equal, and hence a single value is adoted here for simlicity as is commonly done (Pournaghiazar et al., 213; Collins and Stimson, 1994; Russell and Khalili, 26b). In addition, the critical state arameter M cs (in Equation (5.13)) in the ~q lane for comressive loading is rewritten as (Russell and Khalili, 26b): 199

222 Chater 7 Cavity exansion analysis cs 2k 1sin ' cs k 1 k 1sin ' cs M (7.12) where ' cs is the critical state friction angle. It is assumed that ' cs ' tr for sherically symmetric conditions (k = 2) and ' 1.25 ' for lane strain conditions (k = 1), in which ' tr cs tr is triaxial critical state friction angle. This assumtion (aroximately) accounts for the effect of the intermediate rincial stress on soil stress-strain behaviour during lane strain conditions that is otherwise ignored in the Mohr-Coulomb criterion (Wroth, 1984). 7.4 GOVERNING EQUATIONS FOR ELASTIC-PLASTIC REGION The stress-strain behavior of the unsaturated soil is described using the bounding surface lasticity model in Chater 5. Ten differential equations govern the behavior of the soil in the elastic-lastic region around an exanding cavity. The ten equations feature ten variables, which can be resented in differential form and solved as an initial value roblem, as will be discussed in more detail later Equilibrium equation The stress equilibrium equation around the cavity in terms of net and q is exressed as (e.g. Carter et al., 1986): r net k 1 k q r kq r (7.13) Noting that χ is a function of s e and s, it follows: s s s s r s r s e se r (7.14) where 2

223 Chater 7 Cavity exansion analysis s s s s e s e s (7.15) In terms of effective stress, combining the Equations (7.13), (7.14) and (7.15), the equilibrium equation becomes: ' r k 1 k q kq s s s e (7.16) r r r se r in which ψ = (1 Ω)χ when the soil state is on main drying or wetting curves, ψ=(1 ζ)χ when on scanning curves and Ω is a material constant and equals to.55. ζ is also a material constant and equals to βω/α (Khoshghalb and Khalili, 212). Note that the calculation of χ deends on whether the hydraulic state is on a main wetting or drying curve or a scanning curve Constitutive equations The incremental forms of lastic strains of the solid hase come directly from the bounding surface lasticity model and are: e ε ε 1 nˆ hˆ ' nˆ q q nˆ s sm (7.17) and q e q ε ε 1 nˆ hˆ ' nˆ q q nˆ s sm q (7.18) The interactions between the solid hase and air and water hases are accounted for through: S r v 1s Sr αds 1v v w (7.19) s or 21

224 Chater 7 Cavity exansion analysis v s S D 3 S r 1 r Ds 1 v v w (7.2) s where D s and D are fractal dimensions of soil articles and ores, resectively, v is the secific volume and v w is the secific water volume. Recall that the SWCC evolves with void ratio. Secifically s ae and s ex deend on the secific volume or void ratio. It follows that: s ae 15. D s s 1 v 1 v D (7.21) and s s (7.22) ae 3 ex Hardening rule For isotroic loading suction has a multilicative effect on hardening so that: c c v λ(s) κ v K c λ(s) κ c 1 ' s N s N s s ln c s s s (7.23) Consistency equation The consistency equation causes the stress state to remain on the loading surface so that: f ' f f ' q q ' c ' c (7.24) Continuity equation The continuity equation links the rate of volumetric change to the total strain rates ensuring the conservation of solid mass: 22

225 Chater 7 Cavity exansion analysis v w v r kw r (7.25) Three drainage conditions Two conditions were considered for unsaturated soils by Russell and Khalili (26b), namely constant a suction condition and a constant moisture content condition, which were controlled by: s (7.26) and v w (7.27) In this study, a third condition is also considered, that is a constant χs condition. It is exressed as: s s Ω s Ω se for main drying or wetting curves se s s s (7.28) s s Ω se for scanning curves se Making use of Equation (7.15), Equation (7.28) collases to: s s s s Ω se (7.29) s e This drainage condition accounts for a change in void ratio causing a variation in both χ and suction. This drainage condition is aealing as the contribution of suction to the effective stress is constant. When the deendence of the SWCC on void ratio is not considered the constant suction condition would be the same as constant χs condition. 23

226 Chater 7 Cavity exansion analysis 7.5 A CONCEPTUAL UNDERSTANDING OF THE EFFECTS OF HYDRAULIC HYSTERESIS The effects of hydraulic hysteresis are studied by considering different locations of initial states in the lns r ~lns lane. The states considered are on a main drying curve (MD), main wetting curve (MW) or a oint on a scanning curve midway between the main drying and wetting curves (SC). To illustrate how the state in the lns r ~ lns lane changes during cavity exansion, first consider only the effect of suction on the degree of saturation, that is for when there is no void ratio deendency in the SWCC. A soil element at the cavity wall is considered. For a soil in an initially loose state, during cavity exansion the soil is comressed (e.g. Collins et al., 1992), and the degree of saturation increases. For a soil in an initially dense state, during cavity exansion the soil may initially comress, then exand followed by another comression (e.g. Russell and Khalili, 26b). Corresondingly, the degree of saturation will initially increase then decrease and be followed by another increase. For a given initial suction value the suction variation follows different aths deending on the initial location on the SWCC and has very different ending oints, as shown in Figure 7.3(a) for initially loose soil and Figure 7.3(b) for initially dense soil. When considering the effect of volume change on the degree of saturation, or more secifically the deendence of s ae and s ex on void ratio (Equations (7.21) and (7.22)), the suction ath can be quite different to that just described, as exerimentally shown in e.g. Tarantino and Tombolato (25). For comressive resonses during cavity exansion the degree of saturation increases which may make the state on the SWCC move leftward either along a main wetting curve or along a drying to wetting scanning curve. At the same time, the SWCC tends to shift rightward as a result of larger s ae and s ex. The oosite occurs for exansive resonses. The state on the SWCC moves rightward either along a main drying curve or along a wetting to drying scanning curve while the SWCC tends to shift leftward as a result of smaller s ae and s ex. The suction may increase or decrease deending on how significant the effect of volume change on the degree of saturation is. If the effect of volume change is dominant, the suction can increase when degree of saturation increases, as observed by Tarantino and Tombolato (25). As discussed in Chater 5, Equation (7.19) or (7.2) (reroduced from Equation (5.4)) 24

227 Chater 7 Cavity exansion analysis may be used to determine which affect dominates under constant moisture content conditions. Different suction aths due to the effect of hydraulic hysteresis cause different changes to the effective stress arameter, χ, and the stress state through χs during cavity exansion. The suction change exerienced by a soil element may not be monotonic, esecially for dense soil. A soil undergoing a wetting-drying cycle may have a higher shear strength than the shear strength after only drying at the same net normal stress and suction (Gallage and Uchimura, 26; Shemsu et al., 25). The effects on cavity exansion ressures are yet unknown. 7.6 SOLUTION PROCEDURE In the elastic region, the solution rocedure is straightforward and involves using the closed form exressions (Equations (7.7), (7.8) and (7.9)) for stresses, strains, and dislacement (or velocity) in terms of r and R. In the elastic-lastic region, the solution rocedure is far more comlex and involves solving a set of differential equations as an initial-value roblem to evaluate the stress and strain around the exanded cavity using the similarity technique (Collins et al., 1992). Following Russell and Khalili (26b), some of the initial values of ten variables ( ', q, ', ', v, w, s, v, s c c w ae and s ex ) at the elastic-lastic boundary are taken as being equal to the far-field values (, v, s, v w, s ae and s ex, where the subscrit denotes initial values at the elastic-lastic boundary) as the dislacements, strains and incremental stresses are very small in the elastic region (Chen, 212). c at the elastic-lastic boundary, which controls the size of the urely elastic region, is assumed to satisfy the condition: ' N M y c ex ln R ' M (7.3) cs 25

228 Chater 7 Cavity exansion analysis and M y is a constant for the cavity exansion load ath (Russell and Khalili, 26b). q is associated with M y through: q (7.31) M y ' ' c controls the size of the bounding surface and is also the maximum re-consolidation ressure. At the elastic-lastic boundary it can be exressed as: ln N(s) ln e ln ' ' c ex (7.32) (s) The non-dimensional radial velocity ~w at the elastic-lastic boundary is determined as er (Collins et al., 1992): w ~ u q R 2G (7.33) The comlete set of initial values of the ten variables at the elastic-lastic boundary ( ', q, ', ', v, w, s, vw, s and s ) are now known. Equations (7.16), (7.17), (7.18), c c ae ex (7.19) or (7.2), (7.21), (7.22), (7.23), (7.24), (7.25) and one of (7.26), (7.27) and (7.29) are then used to solve the cavity exansion in the elastic-lastic region and the equations are exressed as functions of a dimensionless radial coordinate, η, defined as: r r (7.34) R Wt where W is the velocity of the exansion at elastic-lastic boundary. The variables can then be converted from a rate form to differential form by substituting: r d 1 d R and d (7.35) t t d into Equation (7.4) so that: 26

229 Chater 7 Cavity exansion analysis W ( w η) d R dη (7.36) where w is the radial velocity at r and w ~ =w/w is the non-dimensional radial velocity at r. The stress variables are ut into a non-dimensional form using a reference stress, r, which is assumed to be 1kPa. The non-dimensional stress variables are denoted by a suerimosed ~. The variables v w, v and w ~ are already dimensionless. Then the governing equations may be resented in matrix form as: C C C C C C C C C C 63 C 44 C C C C C C C C C C C C C C C C C 19 C C C C C d ~ '/dη kq ~ /η dq ~ /dη kw ~ /η d ~ c'/dη kw ~ / 1 k ~ d c'/dη dv/dη kw ~ v/η dw ~ /dη ds ~ /dη dvw /dη ds ~ ae /dη ds ~ ex /dη η (7.37) where C k 1, C12, C 1 k C C s 19 and C11 sae 19 s ae for main drying curves or drying to wetting scanning curves s and C for main wetting curves or wetting to drying scanning curves 11 27

230 Chater 7 Cavity exansion analysis C ~ 1 nˆ m K hˆ w η r 21 ' C ~ nˆ qm w η ' r, 26 1 h 22 ˆ ~ nˆ m ' h s C, C w η r 27 ˆ C nˆ m q w~ η ' r, C w η 31 ˆ h ~ k nˆ m 2 1 h q q 32 ' r kg ˆ C k 1 C nˆ m ~ s q w η ' 36, 37 r k ˆ h C ' v λ(s) κ K 1 c 41 ', 1 44 r v 1 C, C ' λ(s) κ 1 c 45 ' r v 1 C 47 ' c (s) N 1 (s) N(s) ln' s c s s ' r C w ~ 55, C 1 56 C f ' 61, C f q 62, C 63 f ' c C 75 Sr Ds 1, v 1 Sr C 77, s C 78 1 v 1 C C 1, C, C for constant moisture content condition 87, C C, C, C for constant suction condition 87 1, C C for constant χs condition 87, 88 28

231 Chater 7 Cavity exansion analysis Ωs, s C89 C81 ae C 89, C 81 ex Ωs s for main drying curves or drying to wetting scanning curves for main wetting curves or wetting to drying scanning curves C 95 s D 1 s v 1 1.5D, C 1 95 C, C The first of the ten rows of the matrix in Equation (7.37) corresonds to the equation of stress equilibrium, the second, third, seventh, ninth and tenth rows to the constitutive laws, the fourth, fifth and sixth rows to the hardening rule, the consistency condition and the continuity equation of the solid mass, and the eighth row to one of the drainage conditions. A differential equation solver is then used to solve, q, c, ' c, v, w, s, v w, s ex and s ae at any articular value of η throughout the elastic-lastic region. Of articular interest is when η = as it reresents the state at the cavity wall. The stresses at this location reresent the cavity limit ressure and can be related to the cone enetration resistance of CPTs. Also, it should be noted that η = corresonds to the condition of zero total volumetric strain rate as controlled by the fifth row of the matrix in Equation (7.37). Constant stresses at the cavity wall ensure that the elastic volumetric strains are constant at the cavity wall, and, the lastic volumetric strains are constant at the cavity wall. More concisely, the soil at the cavity wall is at the critical state (Collins et al., 1992; Collins and Stimson, 1994). 7.7 CAVITY EXPANSION IN UNSATURATED SITLY SAND Inut arameters The stress-strain behaviour is described by the bounding surface lasticity model which is calibrated for Lyell silty sand as resented in Chater 5. The arameters are summarised here for comleteness. 29

232 Chater 7 Cavity exansion analysis The elastic arameters include κ =.12 (the sloe of the elastic unloading-reloading line in isotroic loading tests) and μ =.4 (the Poisson s ratio). As discussed earlier, it is reasonable to assume the same κ alies to both lane strain and triaxial conditions. The critical state frictional angle ' cs is The shae arameters defining a bounding surface are R = 1 and Q = 2. The sloes and intercets of the LICLs for s s e, s * = 1 kpa, s = 1 kpa and s = 3 kpa are summarized in Table 5.1. In the simulations, following Loret and Khalili (22), linear interolation of N(s) and Λ(s) are used between the known values listed in Table 5.1 For suctions larger than 3 kpa a linear extraolation based on the last interval is used. A = 1.2 is assumed for the lastic flow rule (refer to Equation (5.17)). k m in the hardening modulus is defined (as in Equation 5.41) as: k m e e. 8 (7.38) where is the initial state arameter, that is the distance between initial state and current critical state line in the lane. The symbol means that when x > and when x. The arameters assumed for the hydraulic model are as followings: s ae = 1.5e -Ds kpa (with D s =2.61), s ex = s ae /3, α =D 3=.52 and β =.2, while Ω =.55 and ζ = βω/α= Cavity exansion results The cavity exansion roblem is analysed for a range of initial states involving mean net stresses ( net ) of 6 kpa, 9 kpa, 12 kpa or 24 kpa, suctions of 2 kpa, 4 kpa and 8 kpa and void ratios (e ) of.38,.51 or.64 under constant suction, constant moisture content and constant χs conditions. Initial states on a main drying curve (MD), main wetting curve (MW) or at the midoint of a scanning curve (SC) are also considered. 21

233 Chater 7 Cavity exansion analysis General stress-strain resonses Full stress-strain resonses are resented for net = 6 kpa, s = 2 kpa and e =.64,.51 and.38 with constant suction and both sherical and cylindrical cavities in Figure 7.4 and Figure 7.5. The results reresent the variation of e and through the elasticlastic region starting at the elastic-lastic boundary and aroaching the cavity wall at the critical state. Results for e =.64 and.51 exhibit entirely comressive resonses towards the CSL. The curves for different starting ositions on the SWCC end at aroximately the same oint. Results for e =.38 exhibit an initial small comression, and a large volumetric exansion followed by another comression. The curve for initial state MW exhibits the largest exansion while that at MD exhibits the smallest exansion but ends with the lowest void ratio. The stress resonses in the q~ lane show the variation of the effective stress state during the exansion. The curves for different initial states are, however, virtually undistinguishable in this lane for different starting ositions on the SWCC. A wider range of results are considered with articular reference to the limiting cavity ressure, which is the net radial stress at the cavity wall and is denoted σ L, resented in Figure 7.7 to Figure 7.12 and Figure 7.18 to Figure It is in these figures that the effects of hydraulic hysteresis, locations of initial states on the SWCC, and drainage conditions can be observed Effect of different drainage conditions To illustrate the effect of drainage conditions on volumetric resonses, shown in Figure 7.6 are sherical cavity exansion results in the lane for net = 12 kpa, s = 8 kpa, e =.64,.51and.38. The initial state is MD. All the trajectories converge to their corresonding suction-deendent CSL in the lne ~ ln lane. For e =.64 and.51, the soil is being comressed at all times, and the suction value at critical state for the constant moisture content condition is higher (being 13kPa and 96 kpa, resectively) than that for constant suction condition (8kPa). This makes the CSLs lie above the CSL for the constant suction condition in the lne~ln lane. The suction 211

234 Chater 7 Cavity exansion analysis value at the critical state for constant χs condition is 39 kpa and 34 kpa, resectively, much smaller than the initial value. As void ratio decreases there is an increase in s e and χ which forces the suction to decrease to enable χs to remain constant. This makes the CSL lie below those for the other two drainage conditions. By contrast, for e =.38, the soil exeriences exansion followed by a contraction. Therefore the suction value for the constant moisture content condition decreases then increases, and vice versa for the constant χs condition. The variation in suction for different initial states on the SWCC has more effect on volumetric resonses for loose soil than for dense soil. Figure 7.7, Figure 7.9 and Figure 7.11 resent the cylindrical cavity exansion results in the ~ σ L lane for net = 6 kpa, 9 kpa, 12 and 24 kpa; s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main wetting curves (MD), midoint along scanning curves (SC) and main drying curves (MD), resectively. The sherical cavity exansion results are shown in Figure 7.8, Figure 7.1 and Figure As shown in those figures, simulations are made using initial net stresses of 6 kpa, 12 kpa and 24 kpa for e =.51 and.38, and initial net stresses of 6 kpa, 9 kpa and 12 kpa for e =.64. This is because for this soil a high void ratio is ractically unattainable at high net stress. In Figure 7.7 to Figure 7.12 it can be seen that the lines for different drainage conditions are distinguishable for a given initial suction value. For e =.64 the lines are most distinguishable. The limit ressure under the constant χs condition has the smallest value. A large void ratio during comression leads to a large increase in s e or χ thus a large decrease in suction occurs to kee χs constant. The suction may decrease below the threshold value of s = 1 kpa for which much larger volume decreases occur (see Chater 5). For e =.51 the line for the constant χs condition is between that of the constant suction condition and constant moisture content condition. The result for the constant moisture content condition has the largest limit ressure as during cavity exansion the suction increases as a result of the effect of volume change on the degree of saturation being significant. For e =.38 the limit ressure value for the constant χs condition for e =.38 is close to or slightly higher than the largest value among the other drainage conditions. 212

235 Chater 7 Cavity exansion analysis The effect of the drainage conditions on the limit ressure reduces as e decreases as all the three lines tend to merge together. Even for e =.64, where this effect is most ronounced, the maximum difference of limit ressures between different drainage conditions is less than 1 %. The line for constant χs for e around.51 is in between those for the other two drainage conditions. As discussed above, there is a cometing effect between volume change and suction change on degree of saturation, and this would affect the suction ath during cavity exansion. For a soil where the actual suction ath is unknown (e.g. for comressive resonses, suction may increase or decrease), the constant χs condition can be assumed to aly at all times, with errors less than 1 % Effect of various initial hydraulic states on SWCC This section investigates the effects of locations of initial hydraulic states on sherical and cylindrical cavity exansion results. Results for the constant moisture content condition, net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 are resented in Figure The results for different initial hydraulic states yield different suction values at the cavity walls. For e =.64 and.51 the soil resonse for the initial state at MD is most comressible. For e =.38 and the initial state at MW the soil resonse is most exansive. Figure 7.14 and Figure 7.15 show volumetric resonses under constant suction conditions and constant χs conditions for sherical and cylindrical cavities and for = 12 kpa, s = 8 kpa, e =.64,.51 and.38. The results follow the same trend as for the constant moisture content condition. To illustrate how the hydraulic states move around for loose soil during cavity exansion, sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.64 under (a) constant moisture content conditions and (b) constant χs conditions are resented in Figure During cavity exansion the soil is comressed, which causes the SWCC to shift rightward (refer to Equation (7.21)). Under constant moisture content conditions suction increases for initial hydraulic states on both MD and MW, as discussed in section 7.5, as the effect of volume change dominates. The suction increases are almost the same for both initial hydraulic states. By contrast, under constant χs conditions, suction decreases as χ increases (due to a large s ex and s ae ). The decrease of suction is larger for MW than MD. For both drainage 213

236 Chater 7 Cavity exansion analysis conditions the hydraulic states are forced to be on main wetting curves for MW while for MD states are bounded by main drying and wetting curves at all times. For dense soil Figure 7.17 shows the sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.38 under (a) constant moisture content conditions and (b) constant χs conditions. Under constant moisture content conditions, suction initially increases and then decreases followed by another increase. The initial suction increase is very small corresonding to a small amount of comression, as discussed in section 7.5. In this case, a soil element at the cavity wall undergoes a cyclic change of suction. For different initial states on the SWCC the suction aths in the lns r ~ lns lane are quite different. For an initial state on the MW suction decreases a little but later increases a lot, which makes the suction at the cavity wall larger than the initial suction. This is associated with a large volumetric exansion leading to a void ratio that is larger than initial void ratio as the final SWCC moves to the left of the initial SWCC. Whereas for an initial state on the MD, suction decreases a lot but then increases a little. This makes the suction at the cavity wall smaller than the initial suction. Under constant χs conditions, the suction change attern is oosite to that under constant moisture content conditions. Though the suction ath is overlaed onto a single line it is not monotonic. There is an initial decrease in suction and then an increase followed by another decrease in suction. The end oints are denoted in the figure. Suction at the end oint for MW is around 8.8 kpa, smaller than that for MD (82.7 kpa). Figure 7.18, Figure 7.2 and Figure 7.22 resent the cylindrical cavity exansion results in the ~ σ L lane for net = 6 kpa, 9 kpa, 12 kpa and 24 kpa; s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial states at MW and MD under constant suction conditions, constant moisture content conditions and constant χs conditions, resectively. Figure 7.19, Figure 7.21 and Figure 7.23 resent the results for sherical cavity exansion. Under constant χs conditions, simulations are also made for s = 4 kpa. The results for initial hydraulic states on the midoint along scanning curves (SC) are always between those for initial hydraulic states on main drying curves (MD) and main wetting curves (MW). Therefore, for clarity uroses, the results for initial hydraulic states on SC are not shown in the figures. 214

237 Chater 7 Cavity exansion analysis As shown in Figure 7.18 to Figure 7.23, the limit ressures σ L for different initial hydraulic states are different. For a given suction, σ L for initial hydraulic states at MD is always larger than that for initial hydraulic states at MW. The differences between σ L at MD and at MW are enlarged as the initial suction s increases. As the suction has a reduced affect as net increases (Russell and Khalili, 26b), the hydraulic hysteresis also has a reduced affect on the σ L. However, the differences are largest for net = 6 kpa and s =8 kpa for all void ratios and conditions, and can be as large as 32% (for constant suctions and sherical cavity exansions in Figure 7.19) for e =.38. For e =.64 and.51, the σ L for a higher initial suction is larger than that for a lower initial suction. However, for e =.38, σ L for a lower suction and initial hydraulic state at MD can be larger than σ L for a higher suction and initial hydraulic state at MW. The results for different drainage conditions are almost the same. Like in the revious section and Figure 7.7 to Figure 7.12 it is also shown that when initial states are on the MD results are most sensitive to initial suctions. There is a more ronounced difference between results for s = 2 kpa and s = 8 kpa for MD than for MW. The limiting cavity ressure σ L is also lotted against initial mean effective stress, as shown in Figure 7.24 and Figure 7.25 for cylindrical and sherical cavity exansions, resectively. For a given suction, the results for initial hydraulic states at MW and at MD almost overla. This may imly that the effects of hydraulic hysteresis can be accounted by using effective stress instead of net stress in the lots. When using effective stress a roer selection of χs is needed, esecially for dense soil near the surface where the confining ressure is low. Therefore, if ' is correctly comuted, the hydraulic hysteresis influence on the subsequent cavity exansion results can be assumed negligible. 7.7 CONCLUDING REMARKS The effect of hydraulic hysteresis on cavity exansion analysis results were investigated in this study. Secifically the effects of three drainage conditions (constant suction, constant moisture content or constant χs condition) and three initial hydraulic state locations on the SWCC (MW, MD or midoint along SC) were investigated. 215

238 Chater 7 Cavity exansion analysis For Lyell silty sand D 1 D is less than. According to equation 7.19 or 7.2, 3 s for a constant moisture content condition, a decrease in void ratio results in an increase in suction. In other words, the effect of volume change outweighs the effect of suction change on the evolution of the degree of saturation. The constant moisture content is associated with the largest limiting cavity ressure whilst the constant suction condition is associated with the lowest. However, with other values of D and D s, the drainage condition which leads to the largest limiting cavity ressures may be different. It is shown in this study that, for Lyell silty sand, the constant χs condition has limiting cavity ressures in between those for the other two drainage conditions. Assuming a constant χs condition throughout would be associated with errors in estimated limiting cavity ressures that are always less than 1%. This roves to be helful when interreting the CPT results as demonstrated in Chater 8. The differences between results for different initial starting ositions on the SWCC are largest for net = 6 kpa and s =8 kpa for all void ratios and drainages. They can be as large as 32% for e =.38 under constant suction conditions. This situation may be relevant when moisture content and density are known but the initial state on SWCC is unknown. The initial state is thought to be associated with seasonal change. The initial state is likely to be on MD or a wetting to drying scanning curve in a drying season and on MW or a drying to wetting scanning curve in a wetting season. As the limit ressure lines for different initial hydraulic states were indistinguishable when lotted using effective stress, the difference in limit ressure may be due to the different initial effective stress. Therefore the initial state on the SWCC should also be taken into consideration when estimating the value of χs, esecially for dense soil near the surface where the confining ressure is low. Therefore, if ' is correctly comuted, the hydraulic hysteresis influence on the subsequent cavity exansion results can be assumed negligible. 216

239 Chater 7 Cavity exansion analysis Borehole Cone ti σ L Sherical cavity exansion Pressuremeter Cylindrical cavity exansion Figure 7.1. Simlified illustrations of the analogy between cone enetration resistance (q c ) from CPTs and the limiting cavity ressure (σ L ) and the analogy between wall ressure (P L ) from a Pressuremeter test and the cylindrical cavity ressure. σ r r c σ θ Exanding R cavity Elastic-lastic region Elastic region Figure 7.2. Cavity exansion in elastic-lastic material. 217

240 Chater 7 Cavity exansion analysis a. ln(s r ) ln(s ex ) ln(s ae ) ln(1.) MD Starting oint Suction ath Soil-water characteristic curve SC MW Initial suction ln(s) 218

241 Chater 7 Cavity exansion analysis b. ln(s r ) ln(s ex ) ln(s ae ) ln(1.) MD Starting oint Suction ath Soil-water characteristic curve SC MW Initial suction ln(s) Figure 7.3. Illustration of how suction changes during cavity exansion for different initial states without a void ratio-deendent SWCC for (a) initially loose soil and (b) initially dense soil. 219

242 Chater 7 Cavity exansion analysis a.6 MD MW SC Void ratio ln e.5.4 CSL for s =2 kpa Mean effective stress,ln' (kpa) b 15 Deviator stress, q (kpa) Mean effective stress, ' (kpa) Figure 7.4. Sherical cavity exansion results for net = 6 kpa, s = 2 kpa and e =.64,.51 and.38 under constant suction conditions in the (a) lne ~ ln lane and (b) q ~ lane. 22

243 Chater 7 Cavity exansion analysis a.7.6 MD MW SC Void ratio ln e.5.4 CSL for s = 2 kpa Mean effective stress,ln' (kpa) b Deviator stress, q (kpa) Mean effective stress, ' (kpa) Figure 7.5. Cylindrical cavity exansion results for net = 6 kpa, s = 2 kpa and e =.64,.51 and.38 under constant suction conditions in the (a) lne ~ ln lane and (b) q ~ lane. 221

244 Chater 7 Cavity exansion analysis.7.6 Constant s condition Constant v w condition Constant s condition Void ratio, lne.5.4 Corresonding critical state lines Mean effective stress,ln' (kpa) Figure 7.6. Sherical cavity exansion results in the lne ~ ln lane for initial state on SWCC at MD and net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of drainage conditions. 222

245 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at MW e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure 7.7. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main wetting curves (MW). 223

246 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at MW e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure 7.8. Sherical cavity exansion results in the net ~ σ L lane s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main wetting curves (MW). 224

247 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at SC e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure 7.9. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states at the midoint along scanning curves (SC). 225

248 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at SC e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure 7.1. Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states at the midoint along scanning curves (SC). 226

249 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at MD e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure Cylindrical cavity exansion results in the net ~ σ L lane for; s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main drying curves (MD). 227

250 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Initial state at MD e =.64 Constant suction condition for s₀=2 kpa Constant moisture content condition for s₀=2 kpa Constant χs condition for s₀=2 kpa Constant suction condition for s₀=8 kpa Constant moisture content condition for s₀=8 kpa Constant χs condition for s₀=8 kpa 25 e =.51 e =.38 3 Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 under a constant suction condition, constant moisture content condition and constant χs condition for initial states on the main drying curves (MD). 228

251 Chater 7 Cavity exansion analysis a.7.6 MD MW SC Void ratio, lne.5.4 Corresonding critical state lines Mean effective stress,ln' (kpa) b.7.6 MD MW SC Void ratio, lne.5.4 Corresonding critical state lines Mean effective stress,ln' (kpa) Figure (a) Sherical and (b) cylindrical cavity exansion results in the lne ~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant moisture content conditions. 229

252 Chater 7 Cavity exansion analysis a.7.6 MD MW SC Void ratio, lne Mean effective stress,ln' (kpa) b.7.6 MD MW SC Void ratio, lne Mean effective stress,ln' (kpa) Figure (a) Sherical and (b) cylindrical cavity exansion results in the ln e~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant suction conditions. 23

253 Chater 7 Cavity exansion analysis a.7.6 MD MW SC Void ratio, lne.5.4 Corresonding critical state lines Mean effective stress,ln' (kpa) b.7.6 MD MW SC Void ratio, lne.5.4 Corresonding critical state lines Mean effective stress,ln' (kpa) Figure (a) Sherical and (b) cylindrical cavity exansion results in the lne ~ ln lane for net = 12 kpa, s = 8 kpa, e =.64,.51 and.38 to illustrate the effects of hydraulic hysteresis on volumetric resonses under constant χs conditions. 231

254 Chater 7 Cavity exansion analysis a 1 Initial suction lns r 1-1 Main drying curves Starting oint at MD 1-2 Main wetting curves Starting oint at MW Final SWCC for MD Final SWCC for MW Initial SWCC lns b 1 Initial sucton Starting oint at MD lns r 1-1 Main drying curves 1-2 Figure Sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.64 under (a) constant moisture content conditions and (b) constant χs conditions. Initial SWCC Final SWCC for MD Final SWCC for MW Starting oint at MW lns Main wetting curves 232

255 Chater 7 Cavity exansion analysis a 1 Initial suction Main drying curves Starting oint at MD lns r Main wetting curves.1 Starting oint at MW Final SWCC for MD Initial SWCC Final SWCC for MW lns b 1 Initial suction Ending oint Starting oint on MD Main drying curves lns r.1.5 Starting oint on MW Ending oint Main wetting curves Initial SWCC Final SWCC for MD Final SWCC for MW lns Figure Sherical cavity exansion results in the lns r ~ lns lane for net = 6 kpa, s = 8 kpa and e =.38 under (a) constant moisture content conditions and (b) constant χs conditions. 233

256 Chater 7 Cavity exansion analysis 5 Limiting cavity ressure, σ L (kpa) Constant suction condition For initial suction= 2 kpa and initial state at MW For initial suction= 2 kpa and initial state at MD Initial mean net stress, net (kpa) e =.64 For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 e =.51 e =.38 3 Figure Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant suction conditions. 234

257 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Constant suction condition e =.64 For initial suction= 2 kpa and initial state at MW For initial suction= 2 kpa and initial state at MD For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 e =.51 e =.38 3 Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant suction conditions. 235

258 Chater 7 Cavity exansion analysis Limiting cavity ressure, σ L (kpa) Constant moisture content condition 5 For initial suction= 2 kpa and initial state at MW Initial mean net stress, net (kpa) e =.64 For initial suction= 2 kpa and initial state at MD For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 e =.51 e =.38 3 Figure 7.2. Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant moisture content conditions. 236

259 Chater 7 Cavity exansion analysis 5 Limiting cavity ressure, σ L (kpa) Constant moisture content condition For initial suction= 2 kpa and initial state at MW Initial mean net stress, net (kpa) e =.64 For initial suction= 2 kpa and initial state at MD For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 e =.51 e =.38 3 Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant moisture content conditions. 237

260 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Constant χs condition e =.64 For initial suction= 2 kpa and initial state at MW For initial suction= 2 kpa and initial state at MD For initial suction= 4 kpa and initial state at MW For initial suction= 4 kpa and initial state at MD For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 3 e =.51 e =.38 Figure Cylindrical cavity exansion results in the net ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions. 238

261 Chater 7 Cavity exansion analysis Initial mean net stress, net (kpa) Limiting cavity ressure, σ L (kpa) Constant χs condition e =.64 For initial suction= 2 kpa and initial state at MW For initial suction= 2 kpa and initial state at MD For initial suction= 4 kpa and initial state at MW For initial suction= 4 kpa and initial state at MD For initial suction= 8 kpa and initial state at MW For initial suction= 8 kpa and initial state at MD 25 3 e =.51 e =.38 Figure Sherical cavity exansion results in the net ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions. 239

262 Chater 7 Cavity exansion analysis Initial mean effective stress, ' (kpa) Limiting cavity ressure, σ L (kpa) Constant χs condition e =.64 For initial state at MW and initial suction =2 kpa For initial state at MD and initial suction= 2 kpa For initial state at MW and initial suction= 4 kpa For initial state at MD and initial suction= 4 kpa For initial state at MW and initial suction= 8 kpa For initial state at MD and initial suction= 8 kpa 25 e =.51 e =.38 3 Figure Cylindrical cavity exansion results in the ~ σ L lane for s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions. 24

263 Chater 7 Cavity exansion analysis Initial mean effective stress, ' (kpa) Limiting cavity ressure, σ L (kpa) Constant χs condition e =.64 For initial state at MW and initial suction =2 kpa For initial state at MD and initial suction= 2 kpa For initial state at MW and initial suction= 4 kpa For initial state at MD and initial suction= 4 kpa For initial state at MW and initial suction= 8 kpa For initial state at MD and initial suction= 8 kpa 25 e =.51 e =.38 3 Figure Sherical cavity exansion results in the ~ σ L lane s = 2 kpa, 4 kpa and 8 kpa; e =.64,.51 and.38 for initial state at MW and MD under constant χs conditions. 241

264 CHAPTER 8. INTERPRETATION OF CPT RESULTS AND PRACTICAL GUIDELINES 8.1 INTRODUCTION This chater resents the interretation of the cone enetration test results in unsaturated Lyell silty sand, a soil for which hydraulic hysteresis and suction hardening are resent. The effects of hydraulic hysteresis and suction hardening on cone enetration test results are investigated. A semi-theoretical correlation is roosed that enables estimation of relative density and account of the effect of suction hardening. The layout of this chater is as follows. The background of the interretation method is resented in Section 8.2. A synthesis of cavity exansion analysis results for Lyell silty sand is resented in Section 8.3. A comarison of cavity exansion results with cone enetration test results and a semi-theoretical correlation for cone enetration test results are resented in Section 8.4. Concluding remarks are in Section

265 Chater 8 Interretation of CPT 8.2 BACKGROUND An existing method for interretation of CPT results in saturated cohensionless soils For saturated cohensionless soils an emirical exression which correlates cone enetration resistance (q c ) with relative density (D r ) and initial effective stress (σ') widely used in ractice (e.g. Schertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1982; Salgado et al., 2; Huang and Hsu, 25) is of the form: q c C2 C ' ex( C D ) (8.1) 1 3 r where C 1, C 2 and C 3 are constants. Houlsby and Hitchman (1988) found that the q c is influenced more by horizontal effective stress (σ' h ) than vertical effective stress (σ' v ) so set σ' = σ' h in Equation (8.1). Also, as ointed out by Jamiolkowski and Robertson (1988), enetration resistance is strongly influenced by σ' h, and any normalization to account for increasing stress should include the imortant influence of σ' h (Robertson, 29). When overconsolidated or aged sands are encountered σ' = σ' h should be used (Robertson and Camanella, 1983). For normally consolidated sands, vertical effective stress (σ' v ) has been adoted for σ' with some success (Schertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1982; Kumar and Raju, 27). However, as suggested by Baldi et al. (1982) and Jamiolkowski et al. (21), setting σ' equal to the initial mean effective stress (' ) has a wider alication for both normally consolidated sands and overconsolidated sands. A ossible drawback of this exression is the use of D r. For sands with non-negligible fines content, it may be difficult to obtain the maximum and minimum void ratios exerimentally (Burmister 1948; Tavenas and La Rochelle, 1972; Selig and Ladd, 1973). However, Salgado et al. (2) suggested that careful testing can lead to reasonable results for a silty sand. They used an electromagnetic vibrating table to densify dry silty sand in order to obtain the minimum void ratio while maximum void ratio is obtained by ouring silty sand into a mould with known volume. A merit of D r is that it is indeendent of moisture content so it rovides a unification of densities for both saturated and unsaturated conditions. 243

266 Chater 8 Interretation of CPT Existing methods for interretation of CPT in unsaturated soils The cone enetration resistance can be influenced by the resence of suction to a great extent, as was observed in exeriments by Hryciw and Dowding (1997), Tan (25) and Pournaghiazar et al. (213b) and in field tests by Lehane et al. (24), Collins and Miller (214) and Woodburn and Herraman (214). Failure to account for the effect of suction would lead to misinterretation of the soil tye (Collins and Miller, 214) and shear strength arameters (Pournaghiazar et al., 213). However, only a few contributions to the interretation of the CPT conducted in unsaturated soils are documented in the literature. Tan (25) used cavity exansion solutions, based on those of Vesic (1972), so that the volumetric strain has to be estimated first in order to redict cone enetration resistances. Correlations between volumetric strain and suction were then established. Pournaghiazar et al. (213b) roosed a method which is based on an equation like Equation (8.1) for interreting CPT results in unsaturated Sydney sand, a soil for which suction hardening is absent. The cavity exansion analysis of Russell and Khalili (26b) showed that, for Sydney sand, constant suction and constant moisture content conditions leaded to almost identical limiting cavity ressures. This meant that a constant suction (drained) condition could be assumed in the CPT result interretation by Pournaghiazar et al. (213b). Cone enetration resistance was linked to ' and D r using: q c ' ex(2.78 Dr ) (8.2) where ' is the initial mean effective stress with unit of kpa taking the form of ' = net + χs for the unsaturated sand and ' = net u w (u w being the ore water ressure) for saturated sand. Once D r and the contribution of χs to ' are known the corresonding cone enetration resistance (q c ) also with unit of kpa can be calculated. Pournaghiazar et al. (213b) showed that, for Sydney sand, existing correlations for saturated states can be easily extended to unsaturated states. However, suction hardening may exist in other tyes of unsaturated soils (Barden et al., 1969). Though unsaturated soils may have relatively low comressibilities due to suction hardening they may exerience large volumetric collase when wetted (Barden 244

267 Chater 8 Interretation of CPT et al., 1973). Lawton et al. (1991) showed through a literature review that almost all tyes of comacted soils are subjected to collase under certain conditions. The suction hardening and its association with volumetric collase can be well exlained by constitutive models, e.g. Alonso et al. (199), Russell and Khalili (26a), Khalili et al. (28) and Alonso et al. (213). However, never before has the effect of suction hardening on the CPT results been investigated. This chater will attemt to address this knowledge ga. From the review of existing methods, that of Pournaghiazar et al. (213b) aears to be a romising one as it relates q c to a suction related arameter (χs) that may be easily estimated. Also it enables utilization of existing correlations develoed for saturated soils. Thus, following Pournaghiazar et al. (213b), the interretation of CPT results for unsaturated Lyell silty sands resented here is based on Equation (8.1), as detailed below. 8.3 CAVITY EXPANSION ANALYSIS IN LYELL SILTY SAND Purose of cavity exansion analysis Cavity exansion analysis is a useful tool to investigate the governing mechanisms imortant to cone enetration roblems (e.g. Carter et al., 1986; Collins et al., 1992; Russell and Khalili, 26; Salgado and Prezzi, 27). When large numbers of exerimental test results are unavailable, cavity exansion analysis can aid the develoment of correlations between q c and insitu soil roerties. The highly time consuming nature of conducting exerimental CPTs was outlined in Chaters 4 and 6. For examle, samle K6S1-2 required more than three months to aroach suction equilibrium. As shown in Chater 4 (Table 4.1), samle rearations which involve axis translation, and allowing from 355 hours to 1625 hours for suction change, still did not enable suction equilibrium to be reached fully. Samle rearations which involve using as-comacted suction takes less time, but still aroximately one month is needed for a single test. The number of tests conducted is therefore constrained by the duration of a study. Though it may not be ractical to construct extensive families of lines based on exerimental data, the influence of net stresses, densities and 245

268 Chater 8 Interretation of CPT suctions can still be observed (Figures 4.27 to 4.32) and be used to establish links between cone enetration tests and cavity exansion analysis results. Furthermore, for some soils, like Lyell silty sand, it may not be ossible to obtain exerimentally the cone enetration resistances at saturated states, esecially when soils have low hydraulic conductivity (being around m/s at saturated states). Also collasible behavior is observed for unsaturated Lyell silty sand (Chater 3). A large volumetric decrease would occur during wetting. This would render the alication of vertical stress inaccurate due to contact loss between the chamber to late and the samle Fitting results of sherical cavity exansions for saturated conditions The sherical cavity exansion solutions for drained conditions in Chater 7 are considered here. The largest void ratio used is limited by the saturated LICL and the stress level. The results are fitted using an Equation similar to (8.1) with q c relaced by σ L and with C 1 =.26, C 2 =.65 and C 3 =6.18, as shown in the Figure 8.1 and Figure 8.2, where the error is less than 5%. The emirical correlation for saturated Lyell silty sand is then:. 65 u ex(6.18 D ) L. 26 w r (8.3) As σ L >> u w, total σ L is used instead of effective σ' L, as σ L σ' L. Using methods of ASTM D4254 the maximum void ratio (e max ) was measured to be.69 and corresonds to a minimum dry density of 1.51 g/cm 3. Lee and Fitton (1968) and Polito and Martin (21) found that the ASTM D4253 methods yielded a minimum void ratio (e min ) similar to that roduced by the modified Proctor test. Thus the minimum void ratio is set equal to.26 corresonding to the maximum dry density (being 2.2 g/cm 3 ) achieved in the Modified Proctor comaction curve, as shown in Figure Fitting results of sherical cavity exansions for unsaturated conditions 246

269 Chater 8 Interretation of CPT As shown in Chater 7, the results for constant χs conditions are between those of constant moisture content conditions and constant suction conditions, and the results for all three drainage conditions are almost indistinguishable. Assuming a constant χs condition throughout would be associated with errors in estimated limiting cavity ressures that are always less than 1%. Therefore, in the following simulations, only constant χs conditions are considered. As shown in Chater 7 the initial hydraulic states can have a great effect on the simulated lateral ressures at the cavity wall. But when effective stress is used, the results in the ' ~ σ L lane for initial states on main wetting curves and that for initial states on main drying curves can be reresented by a single line (see figures 7.24 and 7.25). The sherical cavity exansion results resented are for confining net stresses of 6 kpa, 9 kpa, 12 kpa and 24 kpa, suctions of 2 kpa, 4 kpa and 8 kpa and void ratios of.38,.51 and.64. Results are also generated for initial suction values equal to 8 kpa which is below the threshold value of 1 kpa where large volumetric decrease may commence. It is found that the results can be fitted with errors less than 15%, as shown in Figure 8.3 and Figure 8.4, when using an Equation like (8.1) of the form: r. 26 ' ex( C D ) (8.4) L The values of C 3 roviding best fits are different for different densities and suctions and are given in Table 8.1. As can be seen they increase with increasing suction and void ratio. One oint that should be mentioned about Equation (8.1) is that it does not account for the effect of comressibility on q c in a direct way (Robertson and Camanella, 1983a). In other studies different exonents (C 2 ) were used for different comressibilities (Schmertmann, 1978; Villet et al., 1981; Baldi et al., 1982). Here it can be seen that one value of C 2 =.65 fits cavity exansion results for both saturated and unsaturated states well, so making C 2 deendant on comressibility for this soil is not warranted. 247

270 Chater 8 Interretation of CPT Transition between saturated and unsaturated states.65 Shown in Figure 8.5 is the sherical cavity exansion results σ L normalized by ' versus D r with concetual illustration of the effect of suction hardening. As can be seen, for unsaturated soils the results for different suction values are very similar. The results for suction equal to 8 kpa deviate a little from the other unsaturated results. However, there is a large sace between unsaturated results and saturated results. This is due to suction hardening and suction deendent shifts of the comression lines, features incororated in the constitutive model resented in Chater 5. The challenge to describe the transition between saturated and unsaturated states using an Equation like (8.1) therefore lies in the account of suction hardening. Similar to Wheeler and Sivakumar (1995), Russell and Khalili (26a), Khalili et al. (28) and Alonso et al. (213), the suction hardening is described by its association with the change of reconsolidation ressure and osition of limiting isotroic comression lines. During wetting there is a sudden decrease in suction, which changes the reconsolidation ressure as well as comressibility and triggers the volumetric collase. To account for the change in reconsolidation ressure, a arameter (ξ LICL ) is introduced here. ξ LICL is defined in the lne ~ ln' lane as shown in Figure 8.6. It is exressed mathematically as: LICL s s' s N' s N (8.5) LICL LICL where s ' LICL is the reconsolidation ressure for a given ' and e (denoted ' c in Chater 5) and is given by: s lnn lne ln' ' LICL s ex (8.6) s Collase may occur when ξ LICL >. ξ LICL < is not attainable as there is no collase otential for saturated conditions. The maximum ossible value of ξ LICL is related to the maximum vertical distance between saturated and unsaturated LICLs at a certain mean net stress. This maximum value may be associated with the maximum ossible amount of volumetric collase. Maximum volumetric collase occurs when the mean net stress 248

271 Chater 8 Interretation of CPT at wetting reaches the initial effective reconsolidation stress (e.g. Khalili et al., 28) or reaches the initial yielding net stress (e.g. Alonso et al., 213), as observed in exeriments by e.g. Sun et al. (27c). The initial ' and e used in the cavity exansion analysis and the associated LICLs are shown in Figure 8.7. As shown in Figure 8.8, a relationshi between C 3 D r 6.18D r and ξ LICL is of the form: C 3Dr. 18Dr (8.7) LICL Using this, Equation (8.4) becomes:. 65 r LICL. 26' ex(6. 18D ) (8.8) L Therefore Equations (8.3) and (8.4) can be relaced by Equation (8.8). For saturated conditions and when suction hardening is absent, ξ LICL = and Equation (8.3) is recovered. For unsaturated conditions, ξ LICL >, and using Equation (8.8) results in errors of estimated σ L which are generally less than 2%, as shown in Figure 8.9. It is noted that although Equation (8.3) for saturated drained cavity exansion is used as a basis in the subsequent correlations, CPTs conducted in saturated Lyell silty sand are likely to need an undrained constant volume analysis. When unsaturated conditions are resent, as for all the CPTs conducted here, Equation (8.3) roves to be a useful basis as significant volume changes occurs, even though the CPTs are erformed quickly. 8.4 COMPARISON WITH CALIBRATION CHAMBER DATA Comarison of cavity exansion results with calibration chamber data and two ossible semi-theoretical correlations Cavity exansion analysis results were generated for conditions also used in the calibration chamber tests. It is acknowledged that the cone enetration resistance measured in the calibration chamber is different from that measured in field. Several methods have been roosed to account for the chamber size effect. Some are emirical (e.g. Mayne and Kulhawy, 1991 and Cudmani and Osinov, 21) and some are 249

272 Chater 8 Interretation of CPT numerical or analytical (e.g. Salgado et al., 1998 and Pournaghiazar et al., 213). The vertical stress which goes into the initial mean net stress used to comute limiting cavity ressures is corrected through (Wesley, 22): q c vc v 2 (8.9) (RD ) where σ v is the alied vertical ressure at the chamber base shown in Table 4.1 and R D is the ratio of diameters for the chamber and cone being 46/16= Case 1: Using normalized q c and σ L values. Shown in the Figure 8.1 is the normalized limiting cavity ressure (Q sh = (σ L - net )/' ) for sherical cavities together with normalized cone enetration resistances (Q cc = (q c - net )/ ) against initial state arameter ξ. Equation (8.9) was used to comute the σ v comonent in net and. This value of was used to generate the cavity exansion solutions. The mismatch between Q sh and Q cc has long been recognized. A shae factor is usually introduced to account for the difference (Shuttle and Jefferies, 1998; Cudmani and Osinov, 21; Ghafghazi and Shuttle, 28). A strong relationshi between Q sh and Q cc is observed. Following Shuttle and Jefferies (1998) and Ghafghazi and Shuttle (28), as shown in Figure 8.11 with errors less than 2% and r 2 (coefficient of determination) =.8952, Q cc may be related to Q sh according to: Q cc 1Q (8.1) sh Combining Equation (8.1) with Equation (8.8) leads to: q. 65 s ex(6. 18Dr LICL ) - 2 (8.11) c. 6 9 So, using a semi-theoretical fit to the sherical cavity exansion solution, the corresonding q c value in the calibration chamber can be estimated Case 2: Using absolute q c and σ L values. 25

273 Chater 8 Interretation of CPT Following Cudmani and Osinov (21), a linear relationshi between q c and σ L can also be observed, as shown in Figure This correction factor may be taken as 8.3 for void ratios ranging from.51 to.65, so that: q c. 65 s ex(6. 18D ) r LICL (8.12) For this case, as shown in Figure 8.13 and Figure 8.14, the associated error using Equation (8.12) is less than 2%, which is at the same magnitude as for case 1 using Equation (8.1) but with r 2 =.9123, which is a little better than for Equation (8.1). For unsaturated Lyell silty sand a rearranged Equation (8.12) gives: 1 q c 2. 2 LICL (8.13) D r ln s Case 2 is referred over Case 1 for the following two reasons. Though the associated errors in both Case 1 and Case 2 are less than 2%, Case 2 has a larger r 2, which rovides a better data match. Also, Case 2 enables a simler equation for estimation of D r, as in Equation (8.13) Examles of alication A change in suction will alter the osition of the LICL and the value of ξ LICL. It can be seen that ignoring the effect of suction and ξ LICL may lead to an overestimation of D r. A descritive examle is now used to highlight this. Suose that = 5 kpa, q c = 2 kpa, χs=5 kpa and ξ LICL =.2. A relative density of around 22% is obtained. If suction influence is ignored and ' = 5 kpa and ξ LICL = is assumed incorrectly, a D r = 69% is obtained leading to an overestimation of 2%. The D r estimation is not significantly influenced by hydraulic hysteresis while suction hardening is accounted for. Suose that =5 kpa, q c =2 kpa and χs =1 kpa (where χ=.25 and s=4 kpa) instead of χs =5 kpa (where χ=.5 and s=1 kpa). A D r = 63% is obtained with ξ LICL =.216 instead of D r = 65% with ξ LICL =.199. In this case, different values of χs with different χ and s are assumed to illustrate the effect of 251

274 Chater 8 Interretation of CPT hydraulic hysteresis. The relative density obtained is quite similar as ξ LICL changes accordingly to account for the effect of suction hardening. Suction affects q c imlicitly through χs and exlicitly through ξ LICL, where ξ LICL accounts for effect of suction hardening. q c is more sensitive to the effect of suction hardening than to χs itself so that ξ LICL can be back-calculated accurately with errors of no more than 5% when using Equation (8.12), as shown in Figure As some unsaturated soils may undergo collase under articular conditions of stress, density and saturation (Barden et al., 1969; Lawton et al., 1991), the suction hardening affect which ermits this needs to be incororated in the q c estimation. Therefore, the new arameter (ξ LICL ) has been introduced. Following the idea of Pournaghiazar et al. (213b) the extension of existing correlations can be modified. This modification centres around the estimation of a suction hardening contribution (12.5ξ LICL ). 8.5 CONCLUDING REMARKS The interretation of the CPT in unsaturated Lyell silty sand, where suction hardening and hydraulic hysteresis are resent, is exlained in this chater. There is a strong relation between σ L from the sherical cavity exansion analysis and q c measured in the calibration chamber. A semi-theoretical correlation is obtained and the error is less than 2%. Using an adjustment to the sherical cavity exansion solution the corresonding q c value that would be measured in the calibration chamber can be comuted. It is found that, for a soil where suction hardening is resent but is ignored, the relative density would be overestimated. 252

275 Chater 8 Interretation of CPT Table 8.1. Values of C 3 for unsaturated sherical cavity exansion results. e s =8 kpa s =2 kpa s =4 kpa s =8 kpa Initial mean effective stress, ' (kpa) Limiting cavity ressure, σ L (kpa) e=.29 e=.33 e=.35 e=.36 D r =77% Fitting lines D r =79% D D r =93% r =84% 4 Figure 8.1. The limiting cavity ressure (σ L ) from saturated drained sherical cavity exansion analysis fitted with Equation (8.3). 253

276 Chater 8 Interretation of CPT Identity line +5% Estimated σ L (kpa) 1-5% Simulated σ L (kpa) Figure 8.2. Estimated σ L using Equation (8.3) comared with simulated σ L from saturated drained sherical cavity exansion solutions. Limiting cavity ressure, σ L (kpa) Initial mean effective stress, ' (kpa) e =.64 e =.51 e =.38 s=8 kpa s=2 kpa s=4 kpa s=8 kpa Fitting line for s=8 kpa Fitting line for s=2 kpa Fitting line for s=4 kpa Fitting line for s=8 kpa Figure 8.3. The limiting cavity ressure σ L fitted with Equation (8.4). 254

277 Chater 8 Interretation of CPT 1 s=8 kpa s=2 kpa +15% Estimated σ L (kpa) 1 s=4 kpa s=8 kpa Identity line -15% Simulated σ L (kpa) Figure 8.4. Estimated σ L using Equation (8.4) comared with simulated σ L from unsaturated sherical cavity exansion solutions. 1 1 σ L /('.65 ) Due to suction hardening 1 s= 8 kpa s=2 kpa s= 4 kpa s= 8 kpa Saturated Fitting lines 1 1% 1% Figure 8.5. Limiting cavity ressure σ L normalized by '.65 versus D r with concetual illustration of suction hardening effects. All results are for drained conditions. 255 D r

278 Chater 8 Interretation of CPT Figure 8.6. Illustration of arameter ξ LICL. 1 Void ratio, lne Initial states Saturated LICL Initial states for saturated conditions LICL s=8 LICL s=2 kpa LICL s=4 kpa LICL s=8 kpa Mean effective stress, ln' (kpa) Figure 8.7. Initial states for the cavity exansion analysis and associated LICLs. 256