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The effect of gradation and fines content on the undrained loading response of sand 1989

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THE EFFECT OF GRADATION AND FINES CONTENT ON THE UNDRAINED LOADING RESPONSE OF SAND by Ralph H. Kuerbis B.A.Sc, The Un i v e r s i t y of B r i t i s h Columbia, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of C i v i l Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 1989 © Ralph H. Kuerbis In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C i v i l E n g i n e e r i n g The University of British Columbia Vancouver, Canada Date July 5. 1989 DE-6 (2/88) ABSTRACT A systematic study of the e f f e c t of grain si z e , gradation and s i l t content on the monotonic and c y c l i c undrained loading response of sand i s presented. The objective of the study i s to gain an improved understanding of the behaviour of f l u v i a l and hydraulic f i l l sands. A s l u r r y method of deposition i s developed to prepare homogeneous specimens of well-graded and s i l t y sands, and to simulate hydraulic f i l l or f l u v i a l deposition processes. Various s o i l gradations consolidated from loosest state of s l u r r y deposition are shown to have s i m i l a r t r i a x i a l compression loading behaviour, but quite d i f f e r e n t t r i a x i a l extension loading behaviour. Well-graded sands are shown to be generally more r e s i s t a n t to s o i l l i q u e f a c t i o n . Loose s i l t y sands are shown to possess s i m i l a r c y c l i c strengths regardless of s i l t content, even though they have widely d i f f e r e n t void r a t i o s . The concept of sand skeleton void r a t i o i s introduced i n order to explain the observed behaviour of s i l t y sands with varying fines content. The e f f e c t of s o i l sample preparation technique on laboratory t e s t r e s u l t s i s discussed. Water pluviated sand i s shown to have a c h a r a c t e r i s t i c f a b r i c and strength anisotropy. An int e r p r e t a t i o n of the factors which contribute to sand f a b r i c and strength anisotropy i s provided. The p r a c t i c a l performance of water pluviated sand i s discussed. TABLE OF CONTENTS P a g e ABSTRACT i i LIST OF FIGURES v i i LIST OF TABLES . . XV NOTATIONS xvi ACKNOWLEDGEMENT x v i i I. INTRODUCTION . 1 I I . THE UNDRAINED BEHAVIOUR OF SAND - BACKGROUND CONCEPTS 5 2.1 Monotonic Loading Behaviour 6 2.1.1 C r i t i c a l Stress Ratio Line 9 2.1.2 Phase Transformation State 9 2.1.3 Steady-State Concepts 10 2.2 S o i l Fabric 16 2.2.1 Rowe's S o i l P a r t i c l e Interaction Model 18 2.3 C y c l i c Loading Behaviour 32 2.4 E f f e c t of Gradation and Fines Content on the Undrained Loading Response of Sand 36 I I I . EXPERIMENTAL WORK 41 3.1 Testing Apparatus 41 3.1.1 Load Controlled Testing System 41 3.1.2 S t r a i n Controlled Testing System ..... 44 3.1.3 Resolution of Measurement 45 3.2 Materials Tested 45 3.2.1 General Description of Materials Tested 45 - i i i - 3.2.2 Physical Properties of Materials Tested 50 3.2.3 C r i t e r i a for Choosing Test S o i l s 61 3.3 Sample Preparation - The Slurry Deposition Method 62 3.3.1 Summary of Sand Sample Preparation Techniques 63 3.3.2 The Slurry Deposition Method 70 3.3.3 Evaluation of Slurry Deposition Method 79 3.3.4 Summary of Slurry Deposition Method .. 90 3.4 Assembly of T r i a x i a l Test Apparatus 91 3.5 Uniformity of Sample Str a i n During Monotonic and C y c l i c Loading 92 3.6 Test Program 93 IV. TRIAXIAL TEST CONSOLIDATION RESULTS 97 4.0 Introduction '. 97 4.1 Accuracy of Consolidation Data 97 4.2 Void Ratio and Relative Density During Consolidation 98 4.3 Volumetric S t r a i n During Consolidation 103 4.4 A x i a l and Radial S t r a i n During Consolidation 111 V. TRIAXIAL TEST UNDRAINED MONOTONIC LOADING RESULTS 116 5.0 Introduction 116 5.1 Uniqueness of Undrained Response 117 5.2 Behaviour of Clean Sands 119 5.2.1 Stress-Strain Response 119 5.2.2 E f f e c t i v e Stress Path Response 125 5.2.3 Pore Pressure Response 126 - i v - 5.2.4 E f f e c t of Consolidation Stress 128 5.2.5 E f f e c t of Grain Size and Gradation ... 129 5.3 Material Parameters 130 5.3.1 Ultimate F a i l u r e Envelope 13 0 5.3.2 Angle of Phase Transformation 13 3 5.3.3 C r i t i c a l Stress Ratio 134 5.3.4 Steady-State Concepts 136 5.4 E f f e c t of S i l t Content Upon Undrained Monotonic Loading Response 138 VI. CYCLIC TRIAXIAL TEST RESULTS 144 6.0 Introduction 144 6.1 General Response 149 6.2 Stress-Strain Response Within Loading Cycles 157 6.3 Pore Pressure Generation During C y c l i c Loading 163 6.3.1 E f f e c t of C y c l i c Stress Ratio 164 6.3.2 E f f e c t of S i l t Content 168 6.3.3 E f f e c t of Relative Density 173 6.3.4 Relationship Between Induced S t r a i n and Residual Pore Pressure 176 6.3.5 Relationship Between Residual Pore Pressure and Hysteretic Work 176 6.4 C y c l i c Resistance Data 182 6.4.1 C y c l i c Resistance Curves at Constant S i l t Content 182 6.4.2 E f f e c t of S i l t Content on C y c l i c Resistance 195 - v - VIII. DISCUSSION AND INTERPRETATION OF TEST RESULTS 212 7.1 Sand Fabric 215 7.2 Interpretation of Factors Which Produce and Control Water Pluviated Sand Fabric 218 7.2.1 Sample Preparation 219 7.2.2 Sample Consolidation 223 7.2.3 Compression Loading Response 231 7.2.4 Extension Loading Response 233 7.2.5 Stress Reversal 237 7.2.6 The E f f e c t of Stress History Upon CSR 241 7.3 Interpretation of Factors Which Produce and Control Moist Tamped Sand Fabric 242 VII. PRACTICAL IMPLICATIONS 247 IX. SUMMARY AND CONCLUSIONS 262 REFERENCES 270 APPENDIX A: Membrane Penetration Correction 278 APPENDIX B: Calculation of Membrane Stress Correction 283 - v i - LIST OF FIGURES Figure Page 2.1(a) C h a r a c t e r i s t i c monotonic undrained loading s t r e s s - s t r a i n response of sandy s o i l s 7 2.1(b) C h a r a c t e r i s t i c monotonic undrained loading e f f e c t i v e stress path response of sandy s o i l s (modified Mohr diagram) 8 2.2 Comparison of undrained monotonic loading e f f e c t i v e stress path response of two d i f f e r e n t loose sands 12 2.3 E f f e c t of sample pre - s t r a i n upon t r i a x i a l t e s t undrained monotonic loading response ... 15 2.4 S t r e s s - s t r a i n mechanisms i n an i d e a l i z e d two dimensional s o i l structure 19 2.5 Mohr's c i r c l e for stresses required to cause s l i p on a p a r t i c l e contact plane 22 2.6 S t a b i l i t y contours f o r Rowe's p a r t i c u l a t e model as a function of p a r t i c l e dimension fac t o r and i n t e r p a r t i c l e contact angle 26 2.7 Constant incremental s t r a i n r a t i o contours for Rowe's p a r t i c u l a t e model as a function of p a r t i c l e dimension factor and i n t e r p a r t i c l e contact angle 27 2.8 Undrained c y c l i c loading response of an a n i s o t r o p i c a l l y consolidated sandy s o i l subject to l i m i t e d l i q u e f a c t i o n 34 2.9 Typical undrained c y c l i c loading response of an i s o t r o p i c a l l y consolidated sandy s o i l t r i a x i a l t e s t sample 35 3.1 Schematic layout of load controlled c y c l i c t r i a x i a l t e s t i n g apparatus 42 3.2 Gradation of Ottawa C-109 sand 47 3.3 Gradations of Kamloops s i l t and various clean Brenda t a i l i n g s sands tested 49 3.4 Gradations of s i l t y 20/200 Brenda t a i l i n g s sands tested 51 - v i i - 3.5 Va r i a t i o n of maximum and minimum ASTM void r a t i o s of s i l t y 20/200 Brenda sand with s i l t content 56 3.6 Comparison of maximum void r a t i o s obtained by a i r p l u v i a t i o n and s l u r r y deposition of s i l t y 20/200 Brenda sand 59 3.7 Schematic drawing of s l u r r y deposition method for preparation of t r i a x i a l t e s t sand specimens 72 3.8 Grain si z e d i s t r i b u t i o n curves f o r horizont- a l l y quartered sections of a water pluviated sand sample 82 3.9 Grain si z e d i s t r i b u t i o n curves f o r horizont- a l l y quartered sections of s l u r r y deposited sands 83 3.10 Repeatability of s l u r r y deposited Brenda sand t e s t r e s u l t s 86 3.11 Comparison of t e s t r e s u l t s for s l u r r y deposited and water pluviated 20/40 Brenda sand 88 3.12 Comparison of t e s t r e s u l t s for s l u r r y deposited and water pluviated Ottawa C-109 sand 89 3.13 Uniformity of sample s t r a i n during loading .. 94 4.1 T r i a x i a l t e s t i s o t r o p i c consolidation r e s u l t s for loose coarse grained 20/40 Brenda t a i l i n g s sand 99 4.2 T r i a x i a l t e s t i s o t r o p i c consolidation r e s u l t s for loose medium grained 60/100 Brenda t a i l i n g s sand 100 4.3 T r i a x i a l t e s t i s o t r o p i c consolidation r e s u l t s for loose f i n e grained 100/140 Brenda t a i l i n g s sand 101 4.4 T r i a x i a l t e s t i s o t r o p i c consolidation r e s u l t s f o r s i l t y well-graded 20/200 Brenda t a i l i n g s sand 102 4.5 Volumetric s t r a i n s of various clean sands during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 104 - v i i i - 4.6 Volumetric s t r a i n s of s i l t y 20/200 Brenda sand during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 105 4.7 Bulk modulus of various clean Brenda sands during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 107 4.8 Bulk modulus of s i l t y 20/200 Brenda sands during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 108 4.9 Summary of compressibility c h a r a c t e r i s t i c s of s i l t y well-graded 20/200 Brenda t a i l i n g s sand 109 4.10 Summary of i n i t i a l compressibility c h a r a c t e r i s t i c s of s i l t y well-graded 20/200 Brenda t a i l i n g s sand 110 4.11 S t r a i n paths of various clean sands during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 112 4.12 Incremental s t r a i n r a t i o s of various clean sands during i s o t r o p i c consolidation from loosest state of s l u r r y deposition 113 5.1 V e r i f i c a t i o n of independence of e f f e c t i v e stress path from t o t a l stress path i n undrained monotonic compression loading of Brenda 20/40 sand 118 5.2 Undrained monotonic t r i a x i a l t e s t r e s u l t s f o r 20/40 Brenda sand 120 5.3 Undrained monotonic t r i a x i a l t e s t r e s u l t s f o r 60/100 Brenda sand 121 5.4 Undrained monotonic t r i a x i a l t e s t r e s u l t s for 20/200 Brenda sand 122 5.5 Undrained monotonic t r i a x i a l t e s t r e s u l t s f o r various sand gradations 123 5.6 Plot of Henkel's Pore Pressure Parameter 'a' Versus Str a i n for Various Gradations of Undrained Brenda Sand 127 5.7 Undrained monotonic t r i a x i a l t e s t r e s u l t s for s i l t y 20/200 Brenda sand 140 - i x - 5.8 V a r i a t i o n of near loosest state s i l t y 20/2 00 sand undrained f r i c t i o n angles with s i l t content 142 6.1 Typical undrained c y c l i c loading response of i s o t r o p i c a l l y consolidated s i l t y well-graded 20/200 Brenda sand 147 6.2 Development of shear s t r a i n i n well-graded 20/200 sand during c y c l i c loading 151 6.3 V a r i a t i o n of boundary envelope f r i c t i o n angle during c y c l i c mobility loading 155 6.4 V a r i a t i o n of maximum boundary envelope f r i c t i o n angle of s i l t y well-graded 20/200 Brenda sand with s i l t content and sand skeleton r e l a t i v e density 156 6.5 C y c l i c loading s t r e s s - s t r a i n response of well-graded sand at low s t r a i n l e v e l 158 6.6 C y c l i c loading s t r e s s - s t r a i n response of well-graded sand subject to l i m i t e d l i q u e - f a c t i o n i n extension loading 159 6.7 Development of c y c l i c mobility s t r a i n i n loose s i l t y well-graded 20/200 Brenda sand .. 160 6.8 V a r i a t i o n of pore pressure generation i n loose clean 20/200 sand with change i n c y c l i c stress r a t i o 165 6.9 V a r i a t i o n of pore pressure generation with s i l t content i n 20/200 sand subject to l i m i t e d l i q u e f a c t i o n 169 6.10 V a r i a t i o n of pore pressure generation with s i l t content i n 20/200 sand subject to l i m i t e d l i q u e f a c t i o n 170 6.11 V a r i a t i o n of pore pressure generation with s i l t content i n 20/200 sand not subject to l i m i t e d l i q u e f a c t i o n 171 6.12 V a r i a t i o n of pore pressure generation with s i l t content i n 20/200 sand not subject to l i m i t e d l i q u e f a c t i o n 172 6.13 V a r i a t i o n of pore pressure generation i n clean well-graded 20/200 sand with change i n r e l a t i v e density 174 - x - 6.14 Va r i a t i o n of pore pressure generation i n clean well-graded 20/200 sand with change i n r e l a t i v e density 175 6.15 V a r i a t i o n of pore pressure generation i n clean 20/200 sand with c y c l i c loading shear s t r a i n l e v e l 177 6.16 Calculation of irrecoverable work absorbed by a s o i l specimen from s t r e s s - s t r a i n response observed during c y c l i c loading 179 6.17 V a r i a t i o n of pore pressure generation i n loose clean 20/200 sand with h y s t e r e t i c work absorbed during c y c l i c loading 180 6.18 Va r i a t i o n of pore pressure generation i n loose to dense clean 20/200 sand with hyster- e t i c work absorbed during c y c l i c loading .... 183 6.19 C y c l i c loading l i q u e f a c t i o n resistance curves of clean 20/200 Brenda sand 185 6.20 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (4.3% s i l t ) 20/200 Brenda sand 186 6.21 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (7.5% s i l t ) 20/200 Brenda sand 187 6.22 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (13.5% s i l t ) 20/200 Brenda sand 188 6.23 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y 20/200 sand at near loosest state of s l u r r y deposition 189 6.24 C y c l i c loading l i q u e f a c t i o n resistance curves of clean 20/200 Brenda sand 191 6.25 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (4.3% s i l t ) 20/200 Brenda sand 192 6.26 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (7.5% s i l t ) 20/200 Brenda sand 193 6.27 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (13.5% s i l t ) 20/200 Brenda sand 194 - x i - 6.28 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (4.3% s i l t ) 20/200 Brenda sand 196 6.29 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (7.5% s i l t ) 20/200 Brenda sand 197 6.30 C y c l i c loading l i q u e f a c t i o n resistance curves of s i l t y (13.5% s i l t ) 20/200 Brenda sand 198 6.31 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 10 load cycles with c o n s o l i - dation void r a t i o 199 6.32 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 20 load cycles with c o n s o l i - dation void r a t i o 200 6.33 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 50 load cycles with c o n s o l i - dation void r a t i o 201 6.34 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 100 load cycles with consolidation void r a t i o 202 6.35 Va r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 10 load cycles with r e l a t i v e density 204 6.36 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 20 load cycles with r e l a t i v e density 205 6.37 Va r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 50 load cycles with r e l a t i v e density 206 6.38 V a r i a t i o n of s i l t y 20/200 sand resistance to l i q u e f a c t i o n i n 100 load cycles with r e l a t i v e density 207 6.39 Summary of the v a r i a t i o n of s i l t y 20/200 sand c y c l i c strength with v a r i a t i o n of s i l t content at constant sand skeleton r e l a t i v e density 209 6.40 Va r i a t i o n of s i l t y 20/200 sand c y c l i c strength with s i l t content at constant c y c l i c stress r a t i o 211 - x i i - 7.1 S t a b i l i t y contours for Rowe's p a r t i c u l a t e model as a function of p a r t i c l e dimension factor and i n t e r p a r t i c l e contact angle 220 7.2 Constant incremental s t r a i n r a t i o contours for Rowe's p a r t i c u l a t e model as a function of p a r t i c l e dimension factor and i n t e r - p a r t i c l e contact angle 222 7.3 Range of stable p a r t i c l e contacts a f t e r K Q consolidation 224 7.4 Range of stable p a r t i c l e contacts a f t e r i s o t r o p i c consolidation 225 7.5 Range of p a r t i c l e contacts which undergo Mode B s l i p i n the transformation from K Q to i s o t r o p i c consolidation 226 7.6 Range of p a r t i c l e contacts which are sub- jected to s l i p i n extension loading, a f t e r a K 0 and i s o t r o p i c consolidation stress h i s t o r y 234 7.7 Zone of stable p a r t i c l e contacts at high stress r a t i o during compression loading 238 7.8 Explanation of the large contractive s t r a i n s associated with p r i n c i p a l stress reversal following loading to a high stress r a t i o .... 240 8.1 Undrained loading response of Ottawa sand C109 at various densities 249 8.2 Change i n l a t e r a l t o t a l stress with change i n e f f e c t i v e stress state 260 A . l Unit membrane penetration of various Brenda sand gradations determined by the single specimen method 280 A.2 S t r a i n i n various gradations of Brenda sand under v i r g i n i s o t r o p i c consolidation and unloading 281 A. 3 S t r a i n i n Ottawa sand C109 during i s o t r o p i c v i r g i n consolidation and unloading 282 B. l Rubber membrane s h e l l 285 B.2 Measurement of membrane modulus a f t e r Bishop and Henkel (1962) 290 - x i i i - C y l i n d r i c a l rubber membrane stress correction v e r i f i c a t i o n by t r i a x i a l t e s t constant rate of s t r a i n loading of a Geotest membrane f i l l e d with water - x i v - LIST OF TABLES Table P a g e 3.1 Brenda mine t a i l i n g s sand mineralogy 48 3.2 Physical properties of materials tested 52 5.1 Sand sample undrained f r i c t i o n angles 131 - xv - NOTATIONS CSR C r i t i c a l e f f e c t i v e stress r a t i o Dr Relative density Dr c Relative density a f t e r consolidation D r c ( s k e l ) S a n c * skeleton r e l a t i v e density a f t e r consolidation e Void r a t i o e c Void r a t i o a f t e r consolidation e c ( s k e l ) S a n c * skeleton void r a t i o a f t e r consolidation e.:,Dr^ I n i t i a l density a f t e r set-up and consolidation to J J 20 kPa N Number of loading cycles N-L Number of loading cycles to i n i t i a l l i q u e f a c t i o n (2.5% strain) U Porewater pressure AU Excess porewater pressure £ a,€ r,e v A x i a l , r a d i a l and volumetric s t r a i n €^£3 Strains i n maximum and minimum stress d i r e c t i o n s ^ u l t Undrained loading boundary envelope e f f e c t i v e f r i c t i o n angle ^p t E f f e c t i v e f r i c t i o n angle at phase transformation o ' a , o ' r A x i a l and r a d i a l e f f e c t i v e stress a ' 1 , a / 3 Maximum and minimum e f f e c t i v e stress CT^ Deviator stress a'c E f f e c t i v e i s o t r o p i c consolidation stress a'2c E f f e c t i v e confining stress m Membrane penetration factor (see Appendix A) B Bulk modulus during consolidation x v i - ACKNOWLEDGEMENTS The author expresses h i s thanks to h i s supervisor, Dr. Y.P. Vaid, for h i s guidance during t h i s research. The author also wishes to thank Dr. D. Negussey f o r h i s advice during the course of the laboratory work, and Dr. W.D.L. Finn f o r reviewing the manuscript and making h e l p f u l suggestions. The he l p f u l discussions with my colleagues i n the Graduate S o i l Mechanics Laboratory at U.B.C. are also appreciated. The help of the C i v i l Engineering Department Workshop with the development and construction of t e s t equipment i s g r a t e f u l l y acknowledged. Mrs. Kel l y Lamb i s thanked for preparation of the manuscript. Fi n a n c i a l support provided by the University of B r i t i s h Columbia and the Natural Science and Engineering Research Council of Canada i s acknowledged with deep appreciation. - x v i i - 1 CHAPTER 1 INTRODUCTION The occurrence of sand l i q u e f a c t i o n or loss of strength during rapid loading has been the focus of considerable s o i l s engineering research i n the past f i f t y years. Extensive damage due to s o i l foundation f a i l u r e s during the 1964 earthquakes i n Niigata (Japan) and Alaska (U.S.A.) sparked considerable i n t e r e s t i n understanding the undrained and dynamic loading behaviour of saturated sand. Much e f f o r t has gone into the development of sand l i q u e f a c t i o n evaluation techniques, including laboratory t e s t i n g , i n s i t u t e s t i n g , and the development of p r e d i c t i v e models. The dynamic loading behaviour of sand has been shown to be the c r i t i c a l design factor i n many geotechnical projects. In the past, an understanding of the fundamentals of sand l i q u e f a c t i o n behaviour has been derived from laboratory t e s t s and observations. To ensure that fundamental material strength properties determined i n the laboratory are applicable to p r a c t i c a l f i e l d problems, two fundamental questions must be considered: (1) i s the s o i l sample tested i n the laboratory representative of the i n s i t u s o i l being modelled; and (2) does the laboratory t e s t i n g technique employed simulate the loading conditions that occur i n s i t u . Differences i n opinion about s o i l behaviour and methods of s t a b i l i t y evaluation can often be d i r e c t l y a t t r i b u t e d to these questions. To address these questions one must be 2 able to define representative i n s i t u s o i l and loading conditions. This i s a very d i f f i c u l t process, as s o i l properties are dependent upon many d i f f e r e n t factors. In addition, the loading conditions on any s p e c i f i c s o i l element are d i f f i c u l t to quantify because they are cont r o l l e d to a large extent by the mechanical properties of adjacent s o i l elements. Material properties may also be changed dramatically by the process of loading. Most fundamental laboratory studies of sand l i q u e f a c t i o n behaviour conducted i n the past have been performed using poorly-graded clean sands, to ensure homogeneity and r e p e a t a b i l i t y of s o i l samples fo r systematic comparison of r e s u l t s . Many natural sands which are encountered i n geotechnical design problems are s i l t y or well-graded. In order to successfully evaluate the l i q u e f a c t i o n s u s c e p t i b i l i t y of such i n s i t u sands, i t would be useful to i d e n t i f y the e f f e c t s of s i l t content and gradation upon the behaviour of laboratory sand samples. This has been i d e n t i f i e d as a major research objective by the U.S. N.R.C. (1985) report on earthquake engineering. Some s i l t y and well-graded sands have been tested i n the past, but due to the d i f f e r e n t methods employed i n sample preparation and laboratory t e s t evaluation, contradictory conclusions as to the e f f e c t s of s i l t content and sand gradation have been reported by various researchers. Samples have generally been prepared i n a dry or moist state. Such sample preparation methods do not 3 simulate the depositional f a b r i c of hydraulic f i l l or natural f l u v i a l deposits, where sediment s e t t l e s through water. A majority of loose sandy materials which are prone to l i q u e f a c t i o n and of p r a c t i c a l concern i n geotechnical designs are deposited by natural f l u v i a l deposition or a r t i f i c i a l hydraulic f i l l placement. Previous laboratory t e s t i n g programs performed on s i l t y and well-graded sand have also generally concentrated on one p a r t i c u l a r type of laboratory strength t e s t , such as t r i a x i a l compression loading, even though numerous laboratory t e s t r e s u l t s have shown sand strength properties to be highly dependent upon d i r e c t i o n and type of loading. This t h e s i s presents a systematic study of undrained sand response, with the objective of gaining an improved understanding of the behaviour and performance of natural f l u v i a l and hydraulic f i l l sands. The e f f e c t s of gradation and f i n e s content on undrained behaviour are investigated. Se l e c t i v e s i e v i n g of a t a i l i n g s sand was employed to obtain uniform and well-graded sands. S i l t y sands were simulated by adding various percentages of a cohesionless s i l t to the processed sand. Identical s o i l mineralogy i n various s o i l gradations i s ensured by use of the same parent material. Fundamental studies of material behaviour require t e s t s on homogeneous specimens. Homogeneity of laboratory t e s t specimens i s mandatory i n order to determine elemental s o i l properties. Consequently, a s l u r r y method of deposition was developed that y i e l d s homogeneous specimens of well-graded 4 as well as s i l t y sands. This method of sample preparation simulates well the placement of sand through water i n a hydraulic f i l l or f l u v i a l sand deposit. The behaviour of each material a f t e r consolidation from loosest state of s l u r r y deposition i s studied under undrained monotonic loading conditions. Both t r i a x i a l extension and compression t e s t s are conducted to explore the e f f e c t of loading d i r e c t i o n upon material properties. The behaviour of s i l t y sand at various d e n s i t i e s i s also studied under c y c l i c loading. Test r e s u l t s are evaluated to determine i f there i s a systematic v a r i a t i o n i n sand behaviour with change i n gradation and s i l t content. 5 CHAPTER 2 THE UNDRAINED BEHAVIOUR OF SAND - BACKGROUND CONCEPTS Several approaches have been developed f o r modeling and evaluating s o i l behaviour under undrained loading conditions, based upon the observed behaviour of various laboratory and f i e l d s o i l s . The d i f f e r e n t approaches to mechanical behaviour modeling can be divided into two groups: 1) l i m i t state models where a s o i l i s deemed eithe r stable when applied shear stress i s below shear strength or unstable when shear stress i s above shear strength, and 2) s t r a i n development models where s t r a i n s induced within a s o i l are d i r e c t l y related to stresses applied. Limit state models have been developed s p e c i f i c a l l y f o r flow s l i d e forms of f a i l u r e , where s o i l i s observed to flow i n a manner s i m i l a r to that of a viscous f l u i d . S t r a i n development models have been developed f o r use i n numerical analysis, s p e c i f i c a l l y f o r denser s o i l s which may not be susceptable to flow f a i l u r e , but nevertheless may be subject to large undesirable s t r a i n s under c y c l i c loading conditions. The a p p l i c a b i l i t y of any given s o i l model or s o i l evaluation method to a s p e c i f i c s t a b i l i t y problem i s determined by the s o i l being modeled, the conditions under which the s o i l e x i s t s i n the f i e l d , and the mechanism of expected f i e l d loading which w i l l be applied to the s o i l . 6 2 . 1 MONOTONIC LOADING BEHAVIOUR The range of undrained monotonic loading s t r e s s - s t r a i n response of sand i s shown i n Figure 2.1. (e.g., Castro, 1969, Castro et. a l . , 1982, Chern, 1985). Types 1 and 2 are c h a r a c t e r i s t i c of contractive response exhibited by loose sand and sand at higher e f f e c t i v e confining s t r e s s . Type l response i s generally associated with flow f a i l u r e . Type 3 i s a c h a r a c t e r i s t i c d i l a t i v e response exhibited by dense sand and sand at lower e f f e c t i v e confining stresses. Type 1 and 2 response represent s t r a i n softening behaviour. In s o i l s responding i n t h i s manner, Type 1 behaviour has been c a l l e d l i q u e f a c t i o n (Castro, 1969). To avoid confusion with other uses of the term " l i q u e f a c t i o n " Type 1 resonse w i l l henceforth be c a l l e d steady-state l i q u e f a c t i o n . In Type 1 response, sand ultimately reaches a minimum constant shear strength at which unlimited shear s t r a i n may occur at constant shear and e f f e c t i v e confining stresses. This shear strength c a l l e d the steady-state undrained strength i s considered to be uniquely r e l a t e d to the void r a t i o of the sand, and i s believed to be independent of factors such as s o i l structure (which may be affected by the method of sample preparation), or p r i o r s t r a i n h i s t o r y (Castro, 1982). Type 2 response has been c a l l e d l i m i t e d l i q u e f a c t i o n (Castro, 1969). The term " l i m i t e d " implies that s t r a i n hardening follows s t r a i n softening a f t e r a minimum i n undrained strength. This Figure 2.1(a) Characteristic monotonic undrained loading stress- strain response of sandy soils Figure 2.1(b) Characteristic monotonic undrained loading effective stress path response of sandy soils (modified Mohr diagram) CD 9 s t r a i n hardening that i s accompanied by increasing e f f e c t i v e confining stress and decreasing pore pressure l i m i t s the amount of shear s t r a i n possible under constant shear stress. 2 . 1 . 1 C r i t i c a l Stress Ratio Line C r i t i c a l stress r a t i o (CSR) refer s to the e f f e c t i v e p r i n c i p a l stress r a t i o at which contractive deformation of ei t h e r steady-state l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n types i s triggered. CSR has been shown to be unique for a given s t r a i n softening sand i n t r i a x i a l compression loading (Vaid and Chem, 1985; Chung, 1985) but dependent upon deposition void r a t i o i n t r i a x i a l extension loading (Chung, 1985). Other researchers such as Sladen et. a l . (1985) and Castro (1982) however, show t e s t data which implies that CSR varies as a function of confining stress l e v e l i n t r i a x i a l compression loading. These differences may be at t r i b u t e d to t h e i r specimen preparation by moist tamping as opposed to pl u v i a t i o n by Vaid and Chem and Chung. Specimen uniformity and f a b r i c i s d i f f i c u l t to control by the moist tamping method. Chung (1985) shows that t r i a x i a l extension CSR values are considerably lower than compression CSR values. 2 . 1 . 2 Phase Transformation State The point at which the induced pore pressure stops increasing and s t a r t s decreasing i n responses of li m i t e d l i q u e f a c t i o n or d i l a t i v e type sand behaviour has been termed "phase transformation state" (Ishihara et. a l . , 1975). In 10 the former case, t h i s state apears as an elbow on an e f f e c t i v e stress path diagram (see Figure 2.1(b)). The f r i c t i o n angle at phase transformation state has been shown to be unique f o r a given sand (Vaid and Chem, 1985) . Among d i f f e r e n t sands i t i s dependent upon s o i l mineralogy (Negussey et. a l . , 1988). Under undrained loading, the phase transformation angle equals the f r i c t i o n angle mobilized at steady state and under drained loading i t equals constant volume f r i c t i o n angle <f>cv (Vaid and Chem, 1985; Negussey et a l . , 1988). A f t e r passing the phase transformation state, the e f f e c t i v e stress path moves up to and follows the undrained f a i l u r e envelope that represents the l i n e of maximum o b l i q u i t y (Ishihara et. a l . 1975). 2.1.3 Steady-State Concepts I f the sand shows response type 1, void r a t i o and undrained strength (or e f f e c t i v e confining pressure) at steady-state are assumed uniquely related (Castro et a l . , 1982). This r e l a t i o n s h i p between void r a t i o and confining pressure (or undrained strength) i s c a l l e d the steady-state l i n e . The steady-state l i n e has been used as a boundary that separates i n i t i a l states of sand into regions of contractive and d i l a t i v e behaviour. Steady-state concepts were o r i g i n a l l y developed from drained t r i a x i a l t e s t s and the concept of c r i t i c a l void r a t i o (Casagrande, 1975) . The a p p l i c a b i l i t y of steady-state concepts to undrained loading conditions was postulated for 11 several years, u n t i l Castro (1969) provided the f i r s t experimental evidence i n i t s support from extensive undrained compression t e s t s on several moist tamped sands. 2.1.3.1 C r i t i q u e of Steady-State Concepts Steady-state concepts imply that a s o i l i s either d i l a t i v e or contractive to f a i l u r e , depending on the state of the s o i l r e l a t i v e to the steady-state l i n e . The l i m i t e d l i q u e f a c t i o n type of s o i l response shows that a s o i l may be both contractive and d i l a t i v e , depending upon s t r a i n l e v e l . Such behaviour cannot be explained using steady-state concepts. For the l i m i t e d l i q u e f a c t i o n type of s o i l response, one must decide which stage of the stress s t r a i n curve i s indeed defined as steady-state. Most researchers who have used steady-state concepts have treated phase transformation state as steady-state. This treatment adds conservatism to slope s t a b i l i t y analyses based on steady- state concepts, because the e f f e c t s of strength gain due to d i l a t i o n a f t e r phase transformation state are ignored. In contrast, Castro (1982) suggests that steady-state i s only achieved a f t e r a l l s o i l d i l a t i o n i s complete, which may be at very large undrained strength i f a s o i l i s s u b s t a n t i a l l y d i l a t i v e past phase transformation state (see Figure 2.2). Figure 2.2 also shows that the degree of d i l a t i o n of d i f f e r e n t s o i l s which have been strained past phase transformation state i s dependent upon s o i l type as well as s o i l density. A s o i l such as Ottawa C-109 sand may Figure 2.2 Comparison of undrained monotonic loading effective stress path response of two different loose sands 13 have a l i m i t e d l i q u e f a c t i o n type of response yet s t i l l have a s u b s t a n t i a l l y higher ultimate undrained strength than a sand such as Brenda sand, which does not show a li m i t e d l i q u e f a c t i o n type of response. Vaid and Chem (1985) treated both l i m i t e d l i q u e f a c t i o n and steady-state types of response within a u n i f i e d framework. They considered stress conditions at phase transformation state f o r l i m i t e d l i q u e f a c t i o n and found a unique r e l a t i o n s h i p between void r a t i o and e f f e c t i v e confining stress (or undrained strength) i n t r i a x i a l compression loading t e s t s . This l i n e also encompassed the steady-state data i f the true steady-state type of response was observed i n undrained loading. Several researchers have shown that at a given void r a t i o and stress-state, undrained response of sand may be a function of sample f a b r i c . Sand f a b r i c i s governed by the technique of sample formation and any s t r a i n h i s t o r y that may be a r e s u l t of past seismic events. Miura and Toki (1982) show that there i s a large difference i n s t r e s s - s t r a i n response between sands prepared by 1) p l u v i a t i o n through a i r , 2) moist tamping, and 3) moist rodding. Ishihara and Okada (1978, 1982) and Chung (1985) show that undrained response i s softened i f the sand i s pre-strained (even though reconsolidated to a lower void ra t i o ) i n a d i r e c t i o n opposite to subsequent undrained loading. Conversely, undrained response i s strengthened by i n i t i a l l y p r e - s t r a i n i n g i n the same d i r e c t i o n of subsequent undrained 14 reloading (see Figure 2.3). A large p r e - s t r a i n i n a d i r e c t i o n opposite to subsequent shearing may transform an i n i t i a l l y d i l a t i v e sand into a contractive sand (Chung, 1985). The undrained response of s o i l s i s p a r t i c u l a r l y s e n s i t i v e to the d i r e c t i o n of loading. This i s a consequence of s o i l s being inherently anisotropic. The degree of t h i s anisotropy i s intimately r e l a t e d to s o i l f a b r i c . Chung (1985) shows that undrained water pluviated sand i s considerably weaker i n t r i a x i a l extension than i n compression loading. At a given i n i t i a l void r a t i o and stress state, compression behaviour could be d i l a t i v e and extension contractive (see Figure 2.3). Miura et. a l . (1982) show the e f f e c t of sample preparation technique upon the difference between t r i a x i a l extension and compression undrained loading response. The greatest difference i s shown to occur i n pluviated sand specimens. Undrained extension response i n a l l cases i s shown to be considerably s o f t e r and weaker than compression response. Recent research on the undrained behaviour of water pluviated sand using the hollow cylinder device shows s i m i l a r dependence of undrained behaviour on the d i r e c t i o n of loading (Symes et. a l . , 1985, Shibuya and Hight, 1987). Water pluviated sand i s shown to be l e a s t contractive and l e a s t susceptable to l i q u e f a c t i o n i n the t r i a x i a l compression mode of loading, and most contractive or most susceptable to l i q u e f a c t i o n i n the t r i a x i a l extension mode of loading. D i r e c t i o n a l TRIAXIAL TEST ^ DIRECTION OF PRESTRAIN COMPRESSION LOADING LOADING v O ^ V ^ © EXTENSION iti^ss' ® CD A S DEPOSITED / L?J V \ (3) COMPRESSION ^ ^ \ : / EFFECTIVE STRESS PATHS \ ; > - ® / X V © \ AFTER ISHIHARA ET. AL. (1 982) TRIAXIAL TEST % ^ ^ A N D CHUNG (1985) EXTENSION LOADING ^ \ \ \ Figure 2.3 Effect of sample pre—strain upon triaxial test undrained monotonic loading response 16 dependence of response may be q u a l i t a t i v e l y explained i n r e l a t i o n to the f a b r i c of sand. 2 . 2 SOIL FABRIC Although several researchers have observed and i d e n t i f i e d the e f f e c t s of s o i l f a b r i c and r e s u l t i n g anisotropy i n laboratory t e s t r e s u l t s , the physical structures and mechanisms which produce and control f a b r i c and anisotropy have been r e l a t i v e l y inadequately described and generally only q u a l i t a t i v e l y assessed. The reasons f a b r i c and anisotropy have been r e l a t i v e l y neglected i s that, i n practice, most models tr e a t s o i l as an i s o t r o p i c macroscopic continuum, while f a b r i c and anisotropy are derived from the microscopic i n t e r a c t i o n of di s c r e t e p a r t i c l e s . Various workers i n the f i e l d of p a r t i c u l a t e s o i l mechanics have attempted to analyze the e f f e c t s of stress upon an assembly of p a r t i c l e s (for example Rowe, 1962,1971; and Home, 1965). Others (Oda et a l . , 1972,1974,1978,1985) have recognized the s i g n i f i c a n t dependence of o v e r a l l s o i l properties upon the spaci a l arrangement of p a r t i c l e s . Workers such as Nemat-Nasser (1980), Matsuoka et a l . (1980) and Mehrabadi et a l . (1982) have attempted to formulate s t a t i s t i c a l a n a l y t i c a l methods based on simple p a r t i c u l a t e models to r e l a t e macroscopic behaviour to the mechanics of p a r t i c l e s . 17 Of a l l the p a r t i c u l a t e s o i l models described i n the past, the s i m p l i f i e d physical model described by Rowe (1962,1971) and Home (1965) provides perhaps the best physical d e s c r i p t i o n of the factors which contribute to sand f a b r i c . The p a r t i c u l a t e model described by Rowe forms the basis f o r h i s stress-dilatancy theory. A mathematical representation of the physical p a r t i c u l a t e model i s used i n a work function to derive the stress-dilatancy equation R = KD, where R i s the p r i n c i p a l e f f e c t i v e stress r a t i o , K i s a constant which i s dependent upon the i n t r i n s i c angle of f r i c t i o n of the surface of i n d i v i d u a l s o i l p a r t i c l e s , and D i s the dilatancy produced by app l i c a t i o n of the stress r a t i o R (D = - 2 d e 3 / d € 1 f o r t r i a x i a l compression loading). The stress- d i l a t a n c y equation has been shown to adequately represent the mono-directional drained loading behaviour of a large number of d i f f e r e n t p a r t i c u l a t e materials. The equation has also been shown to be independent of s o i l f a b r i c , anisotropy, or p r i n c i p a l stress d i r e c t i o n (Oda, 1972b). Although the stress dilatancy equation i s independent of s o i l f a b r i c f o r drained t e s t r e s u l t s , t h i s does not imply that s t r e s s - s t r a i n behaviour i s independent of d i r e c t i o n of loading. Drained s t r e s s - s t r a i n response has been shown to be a function of p r i n c i p a l stress d i r e c t i o n which implies s o i l anisotropy (Oda, 1972b,1981; Arthur and Menzies, 1972; Negussey, 1984). This apparent c o n f l i c t of the non-dependence of the stress dilatancy equation yet the dependence of s t r e s s - s t r a i n response upon s o i l anisotropy i s 18 due to the fac t that the stress dilatancy equation i s based upon stress and s t r a i n r a t i o s , not the magnitude of p r i n c i p a l stresses and s t r a i n s . Although incremental s t r a i n magnitudes at a given stress r a t i o may be considerably d i f f e r e n t under d i f f e r e n t d i r e c t i o n s of loading, the incremental s t r a i n r a t i o i s shown to be independent of d i r e c t i o n of loading. The physical model which Rowe used to derive the stress dilatancy equation may be used to explain why s t r e s s - s t r a i n behaviour i s dependent upon s o i l anisotropy and p r i n c i p a l stre s s d i r e c t i o n , although the model was not o r i g i n a l l y derived nor employed to explain s o i l anisotropy. The basic ideas behind the model are summarized i n the following section. The model i s used to explain factors and mechanisms which control s o i l anisotropy, and i s subsequently used to explain and interpret observed t e s t r e s u l t s . 2.2.1 Rowe's S o i l P a r t i c l e Interaction Model A s o i l sample i s i d e a l i z e d as an assemblage of uniformly shaped p a r t i c l e s i n contact with one another, as shown i n Figure 2.4. The externally applied stress r a t i o (R) required to cause movement on contact planes and thus s t r a i n i n the two dimensional model i s derived from: (1) the dimensions of the i d e a l i z e d s o i l structure (Figure 2.4); (2) the i n t e r n a l stress l e v e l on p a r t i c l e contacts; and (3) Mohr's diagram for stress conditions on a contact plane 19 CJ v G a (b) S i n g l e r e p e t i t i v e element (a) I d e a l i z e d s o i l s t r u c t u r e ( c ) Elemental f r e e body diagram CO. |3 = I n t e r p a r t i c l e contact angle c-hB CT " P r i n c i p a l s t r e s s 5 ° Deformation £ = S t r a i n 0M = I n t r i n s i c angle of f r i c t i o n 0 = M o b i l i z e d f r i c t i o n angle f a c t o r a (1 V h F i g u r e 2.4 S t r e s s - s t r a i n mechanisms i n an i d e a l i z e d two dimensional s o i l s t r u c t u r e Figure 2. 4 (d) Var ia t ion of <=* and p5 parameters with s t r a i n level 21 (Figure 2.5). The structure may be defined by two parameters; the i n c l i n a t i o n of the p a r t i c l e contact plane, p, and the shape of a s i n g l e r e p e t i t i v e element, defined by the structure dimension factor a. The model may undergo s l i p i n only two modes. The f i r s t mode (Mode A) was analyzed by Rowe and other workers, and involves movement i n the d i r e c t i o n of maximum p r i n c i p a l stre s s (Figure 2.4c). The second mode of movement (Mode B) has not been previously i d e n t i f i e d ; t h i s i s probably because i t involves movement against the d i r e c t i o n of maximum external p r i n c i p a l stress. Mode B movement i s only possible fo r those combinations of p a r t i c l e dimension fa c t o r a and p a r t i c l e contact angle 0 where the maximum in t e r n a l p r i n c i p a l stress d i r e c t i o n at a contact plane i s opposite to the external maximum p r i n c i p a l stress d i r e c t i o n . The mathematical representation of the stress r a t i o required to cause s t r a i n i n the two dimensional model i s derived i n Section 2.2.1.1. 22 2.2.1.1 Mathematical Representation of Stress—Strain Behaviour in Rowe's Two Dimensional Particulate Structure From particle dimensions shown in Figure 2.4: — = t a n « — = c v = — t n = — r5h t a n 9 v j a L cr v v *h V Oh CTh Q vtan (JS) CTh t an (« ) tan( fi) MODE A DEFORMATION: 5vt, and r5hA directions, r5vA strain in same direction as CJ (see Figure 2.4) Figure 2.5a Mohr's circle for stresses required to cause slip on a particle contact plane and produce MODE A deformation ° i = tan (P+0M) = Minimum stress ratio Q- (j tan (/3 ) required to cause slip 3 h 23 CRITERION FOR MODE A DEFORMATION: CT > CT Crv tan(0+&) ' f " f l ^ < tan"(flf n 0 S " P CT tan + CT CT V V CTh CTh tan(«) tan(jS) CT If — < tan + tan ( « ) n o s | j p E q n 2 . 1 a h CT l f — > tan (0 + 1) tan ( « ) slip Eqn. 2.1b h . tan ( fi + fa) tan Sm L = Z 77~7\ Eqn. 2.2 m tan ( p + fl.) tancx + 1 g v . -1 £ h tanfJ tanoc E c ! n - 2 - 3 MODE B DEFORMATION: (5VB and directions, C5«B strain against direction of CT (see Figure 2.4) Figure 2.5b Mohr's circle for stresses required to cause slip on a particle contact plane and produce MODE B deformation on contact plane to produce slip ° i ° h t a n (/0 Minimum stress ratio CJ CT tan (B - 0 J required to cause slip 3 v CRITERION FOR MODE B DEFORMATION: CTV < cr & h tan (p) If - < —— no slip a t a n ( p - & ) CT tan (p) If -z- £ ; — - slip (J t a n ( p - i ) cr cr V V crh a h tan(«) tan(|3) 25 cr If — > tan ( p - n p tan ( « ) no slip £ q n . 2.4a 0" If < tan tan (tx) slip Eqn. 2.4b h _ tan ( tan« - 1 ^ Sin 0 = Eqn. 2.5 m tan ( P - 0 J t an« + 1 -1 tanp tan« E c 1 n - Z 6 Equations 2.1 and 2.4 are plotted as constant stress ratio contours in Figure 2.6. The contours segregate an inner zone of stable particle contact population f rom outer zones of unstable particle contact populat ions. Equation 2.6 which defines the strain ratio derived f rom slip under either MODE A or MODE B deformation is plotted in Figure 2.7. Although strain ratio is not a funct ion of mode of deformat ion (MODE A and MODE B), the degree of volume change or dilatancy is a funct ion of mode of deformat ion. When MODE A deformation is contract ive, MODE B deformation is dilative, and when MODE A deformation is dilative, MODE B deformation is contract ive at a given strain ratio, unless strain ratio equals —1.0, in which case no volume change occurs under any mode of deformat ion. F i g u r e 2.6 S t a b i l i t y contours f o r Rowe's p a r t i c u l a t e model as a f u n c t i o n of p a r t i c l e dimension f a c t o r « and i n t e r p a r t i c l e c o n t a c t angle jS INTERPARTICLE CONTACT ANGLE JS (DEGREES) 7 Constant incremental s t r a i n r a t i o contours f o r Rowe's p a r t i c u l a t e model INTERPARTICLE CONTACT ANGLE j S (DEGREES) 28 2 . 2 . 1 . 2 Discussion of Rowe/a P a r t i c u l a t e Model Equation 2.1 and Equation 2.4 show that the stress r a t i o required to cause Mode A and Mode B s t r a i n r e s p e c t i v e l y within the model p a r t i c u l a t e structure of Figure 2.4(a) i s a function of angle of p a r t i c l e contact fi, and structure dimension factor a . Within the i d e a l i z e d model, a i s a function of p a r t i c l e dimensions and s t r a i n l e v e l . I f p a r t i c l e s were rounded i n nature (Rowe's o r i g i n a l analysis assumed spherical p a r t i c l e s as shown i n Figure 2.4d), p a r t i c l e contact angle fi could also vary with s t r a i n l e v e l . Since the developed f r i c t i o n angle of the material i s c a l c u l a t e d from the stress r a t i o required to cause s l i p , the developed f r i c t i o n angle i s also shown to be a function of p a r t i c l e contact angle fi and structure dimension factor a (see Equation 2.2 and Equation 2.5). Thus developed f r i c t i o n angle i s also affected by p a r t i c l e dimensions and s t r a i n l e v e l . Figure 2.6 shows that the external stress r a t i o required to cause s l i p i n the i d e a l i z e d model may range from 1.0 (which implies s l i p along contact surfaces under i s o t r o p i c external stress, or a developed f r i c t i o n angle of zero degrees) to a value of stress r a t i o or developed f r i c t i o n angle much greater than the i n t r i n s i c angle of f r i c t i o n between p a r t i c l e s , depending upon the values of a and fi. The stress r a t i o contours shown i n Figure 2.6 separate stable from unstable p a r t i c l e contact populations at a p a r t i c u l a r stress r a t i o l e v e l . The middle zone between 29 two s i m i l a r stress r a t i o contours, of Mode A and B s t r a i n respectively, represents a stable p a r t i c l e contact population under the s p e c i f i e d external stress r a t i o . The outer zone towards a = 0, p = 0 represents an unstable p a r t i c l e population with s t r a i n type A. The outer zone towards a - 90, p = 90 represents an unstable p a r t i c l e population, with s t r a i n type B. The middle zone of stable p a r t i c l e contacts i s shown to be a function of external stress r a t i o . In the id e a l i z e d model, i f a p a r t i c l e structure with a s p e c i f i c stable combination of a and p under i s o t r o p i c stress i s subjected to increasing stress r a t i o , no s t r a i n i s induced u n t i l the p a r t i c l e contact combination of a and p i s subjected to an unstable stress r a t i o . Figure 2 .4(d) suggests that the s t r a i n induced i n the structure at an unstable stress r a t i o may cause a reduction i n a and p values, which may cause large s t r a i n s or a collapse i n the structure u n t i l a stable combination of a and p i s induced by s t r a i n . The two dimensional model also shows how dilatancy or volume change during shear may be affected by p a r t i c l e contact structure. The p r i n c i p a l s t r a i n r a t i o f o r both Mode A and Mode B s t r a i n may be calculated using Equation 2.3 or 2.6. I f the p r i n c i p a l s t r a i n r a t i o equals -1.0, there i s no change i n volume during shear. I f the s t r a i n r a t i o i s less than -1.0, then the structure contacts i n volume during shear under Mode A s t r a i n , but d i l a t e s i n volume under Mode B s t r a i n . When the s t r a i n r a t i o i s greater than -1.0, the 30 structure expands i n volume under Mode A s t r a i n , but contracts under Mode B s t r a i n . Constant s t r a i n r a t i o contours calculated from Equation 2.3 are shown i n Figure 2.7. This figure shows how both s t r a i n r a t i o and dilatancy are a function of a and fi population. The s t r a i n induced by a change i n stress r a t i o i s dependent upon the population of a and fi which was previously within the stable zone but i s now exposed to an unstable zone as stress r a t i o i s changed. In order to maintain a stable structure under increasing stress r a t i o , the s t r a i n induced by an increase i n stress r a t i o must push unstable a and fi value combinations of p a r t i c l e contacts into the stable zone. This may not occur i n an incremental fashion i n the two s t r u c t u r a l l y homogeneous models shown i n Figure 2.4, but could be expected i n a va r i a b l y sized, v a r i a b l y shaped p a r t i c u l a t e material such as sand. The two p a r t i c u l a t e structures i n Figure 2.4 can be shown to have an anisotropic or va r i a b l e response to d i f f e r e n t d i r e c t i o n s of loading. I f stress d i r e c t i o n s are reversed or p r i n c i p a l maximum and minimum stresses are interchanged, the previous combination of a and fi p a r t i c l e contact values would become a' = (90-a) and fi' = (90-fi) . This change i n a and fi values f o r the same p a r t i c l e contact configuration would tend to make a previously more stable structure considerably l e s s stable, or a previously less stable structure considerably more stable under the new d i r e c t i o n of loading. The s t r e s s - s t r a i n response observed 31 under the reversed d i r e c t i o n of loading could be s u b s t a n t i a l l y d i f f e r e n t from that which may have been observed under the previous loading conditions. Although the structures shown i n Figure 2 . 4 are not a true representation of the structure of sand, they do show that the structure of a p a r t i c u l a t e material controls s t r e s s - s t r a i n and dilatancy behaviour under loading. The models also show that loading response i s a function of stress d i r e c t i o n and s t r a i n l e v e l . The two dimensional structure shown i n Figure 2 . 4 can not model a l l the mechanisms which a f f e c t shear resistance of p a r t i c u l a t e s o i l s , but the model does provide i n s i g h t into some of the factors which control shearing resistance, and how these factors may contribute to d i r e c t i o n a l s o i l behaviour. Some key points to consider are: 1) f r i c t i o n a l resistance of s o i l i s not only governed by the i n t r i n s i c f r i c t i o n angle of the p a r t i c l e s which make up the s o i l , but also by the s p a c i a l r e l a t i o n s h i p between p a r t i c l e s which may be described as s o i l structure or s o i l f a b r i c ; 2) a random assemblage of s o i l p a r t i c l e s may have a complex d i s t r i b u t i o n of i n t e r p a r t i c l e contact angles and s o i l p a r t i c l e o r i entations; 3) the factors which make up cohesionless s o i l f a b r i c , such as i n t e r p a r t i c l e contact angle, spacial o r i e n t a t i o n , and p o s i t i o n of p a r t i c l e s , can be e a s i l y a l t e r e d by a change i n method of placement or by induced s t r a i n s ; 4 ) dilatancy i s governed by s o i l structure; and 5) a s o i l may show d i f f e r e n t dilatancy response when subjected to d i f f e r e n t d i r e c t i o n s of loading. In a natural s o i l structure there i s a complex d i s t r i b u t i o n of contact angles and p a r t i c l e orientations. S l i p i s generally more l i k e l y to occur on p a r t i c u l a r p a r t i c l e contacts which are p r e f e r e n t i a l l y oriented with respect to the d i r e c t i o n of loading. P a r t i c l e contacts which s l i p during loading may be reoriented to develop a more stable f a b r i c that i s able to support greater applied load, or a l t e r n a t i v e l y disturb other parts of the s o i l f a b r i c to reduce strength. 2.3 CYCLIC LOADING BEHAVIOUR There are many s i m u l a r i t i e s between c y c l i c and monotonic loading behaviour (Castro, 1982; Vaid and Chem, 1985; Chung, 1985). Both steady-state and c r i t i c a l stress r a t i o l i n e s are independent of the mode of loading, monotonic or c y c l i c . Many researchers have found that a s o i l which i s d i l a t i v e and develops only l i m i t e d s t r a i n under monotonic loading may develop large s t r a i n s when subjected to c y c l i c loading. This i s a consequence of the development of c y c l i c mobility. C y c l i c loading leads to a gradual softening of response as pore pressure and shear s t r a i n develop. In general, very low shear s t r a i n occurs u n t i l a pore pressure i n excess of about 60% of the i n i t i a l e f f e c t i v e stress has developed (Seed, 1979). S t r a i n development during c y c l i c loading may be due to: 1) steady-state or l i m i t e d l i q u e f a c t i o n (classed together as contractive deformation), or 2) c y c l i c mobility (Castro, 1969; Seed, 1979). The development of c y c l i c mobility s t r a i n i s represented on the e f f e c t i v e stress path diagram by movement up and down the undrained f r i c t i o n envelope i n both compression and extension phases of loading (see Figure 2.9). A transient state of zero e f f e c t i v e stre s s occurs at the point when the shear stres s i s zero. The magnitude of c y c l i c mobility s t r a i n developed during c y c l i c loading i s governed by r e l a t i v e density. I f a sand i s dense i t may develop only l i m i t e d c y c l i c mobility s t r a i n . In contrast, a looser sand may develop very large c y c l i c mobility s t r a i n , even i f i t i s d i l a t i v e under monotonic loading. C y c l i c mobility s t r a i n may develop without the occurrence of li m i t e d l i q u e f a c t i o n , or following the occurrence of l i m i t e d l i q u e f a c t i o n (see Figure 2.8). Due to the various mechanisms which are responsible f o r s t r a i n development during c y c l i c loading ( i . e . steady-state l i q u e f a c t i o n , l i m i t e d l i q u e f a c t i o n , or c y c l i c m o b i l i t y ) , the r e s u l t s of c y c l i c loading are generally assessed i n terms of a s t r a i n c r i t e r i o n . The c y c l i c strength or resistance of a sample i s defined as the c y c l i c stress amplitude required to cause a s p e c i f i e d l e v e l of s t r a i n (2, 5, or 10%) i n a fixed number of load cycles. 0 CYCLIC LOADING FROM A STATE OF ANISOTROPIC CONSOLIDATION CYCLIC MOBILITY LOADING LIMITED LIQUEFACTION 0 ( L X + C T )/2 MONOTONIC LOADING CYCLIC MOBILITY LOADING CYCLIC LOADING AXIAL STRAIN £„ (%) Figure 2.8 Undrained cyclic loading response of an anisotropically consolidated sandy soil subject to limited liquefaction 35 Figure 2.9 Typical undrained cyclic loading response of an isotropically consolidated sandy soil triaxial test sample o a. CM b - 2 0 - w - 6 0 - CYCUC MOBILITY LOADING COMPRESSION 100 200 ( L T ' < ) / 2 ( k P a ) 300 EXTENSION — i 400 150 - i ^—- a 0_ 100 - "—' 5 0 - to I 0 - b ° - 5 0 - - 1 0 0 - - 1 5 0 - - 1 SILTY 20/200 BRENDA SAND 4.55% SILT CONTENT e c = 0.673 Dr.= 46% 0 ' d / 2 0 i - DEVELOPMENT OF CYCLIC MOBILITY STRAIN 15 - 1 0 - 5 5 10 AXIAL STRAIN £.(%) 24 26 NUMBER OF LOAD CYCLES N 36 2 . 4 THE EFFECT OF GRADATION AND FINES CONTENT ON THE UNDRAINED LOADING RESPONSE OF SAND Few studies have been conducted to determine the e f f e c t of gradation and fines content on the undrained loading response of sand. This i s primarily due to the d i f f i c u l t y of preparing homogeneous t e s t specimens. Homogeneous well mixed laboratory s o i l specimens are required f o r the determination of elemental s o i l properties. Most researchers who have studied the strength properties of s i l t y sand have employed moist tamping or a i r p l u v i a t i o n techniques f o r the preparation of t e s t specimens. Many well-graded and s i l t y sands found i n the f i e l d are deposited by settlement within water. A fundamental question which must be addressed i n the evaluation of well-graded and s i l t y sand properties i s how does the method of sample preparation a f f e c t s o i l response. Castro and Poulos (1976) studied the e f f e c t of gradation upon steady-state behaviour of sand using samples prepared by moist tamping. When compared i n terms of r e l a t i v e density, gradation i s shown to have the same magnitude of e f f e c t upon steady-state l i n e as changes i n mineralogy and angularity. Sands with generally more well rounded grains or higher C u show a general trend towards lower steady-state void r a t i o s . Absolute trends are d i f f i c u l t to i d e n t i f y . Ishihara et a l . (1980) present the r e s u l t s of an undrained c y c l i c t r i a x i a l t e s t program conducted to investigate the c y c l i c resistance of various types of mine t a i l i n g s sands and slimes. Sand samples were a i r pluviated and e i t h e r tamped or vibrated to the required density before saturation with water. Slimes samples were consolidated from s l u r r y . When compared i n terms of void r a t i o , various gradations of mine t a i l i n g s sands are shown to have s i m i l a r or s l i g h t l y lower c y c l i c strength than clean poorly-graded sands. Slurr y reconstituted cohesionless slimes are shown to have c y c l i c resistance s i m i l a r to that of cohesionless t a i l i n g s sands, while cohesive slimes are shown to have generally greater c y c l i c resistance than e i t h e r t a i l i n g s sands or non-cohesive slimes. Lee and F i t t o n (1969) show that well-graded sands have c y c l i c strengths s i m i l a r to those of poorly-graded sands of the same r e l a t i v e density. Samples were prepared by both p l u v i a t i o n i n a i r and i n water. The undrained loading response of well-graded but non-homogeneous segregated water pluviated sand i s compared with that of l e s s segregated a i r pluviated sand. I t i s shown that water pluviated segregated sand has a higher c y c l i c strength than unsegregated sand. The c y c l i c strength of s i l t y sands tested by Lee and F i t t o n (1969) i s s i m i l a r to that of clean sands at the same r e l a t i v e density, although the data set shown i s too l i m i t e d to make broad generalizations. Sladen et. a l . (1985) have also used the moist tamping technique of sample preparation to determine the e f f e c t of s i l t content upon steady-state strength i n t r i a x i a l 38 compression loading. Test r e s u l t s were used to back-analyse the f a i l u r e of h y d r a u l i c a l l y placed s i l t y sand i n the Nerlerk berm i s l a n d i n the Canadian Beaufort sea. S i l t content i s shown to reduce steady-state strength considerably at a given void r a t i o , leading Sladen et. a l . to the conclusion that s i l t y sands are always more susceptible to l i q u e f a c t i o n than clean sands. Troncoso and Verdugo (1985) derive s i m i l a r conclusions f o r s i l t y Chilean t a i l i n g s sands. Their samples were also prepared by moist tamping. From r e s u l t s of s t a t i c and c y c l i c t r i a x i a l t e sts on i s o t r o p i c a l l y consolidated samples at the same void r a t i o , Troncoso and Verdugo show: 1) drained f r i c t i o n angle decreases with increasing s i l t content; 2) higher s i l t content makes the sand less d i l a t i v e during drained loading; 3) undrained dynamic shear modulus as a function of s t r a i n l e v e l decreases with increasing s i l t content; 4) pore pressure generation during c y c l i c undrained loading occurs more e a s i l y i n sands with a higher s i l t content; and 5) c y c l i c strength decreases s u b s t a n t i a l l y with increasing s i l t content. Many of the conclusions described above concerning the e f f e c t of gradation and fines content upon s o i l behaviour under s t a t i c and c y c l i c loading are c o n f l i c t i n g . This may be due to the following factors: 1) differences i n s o i l types tested; 2) differences i n method of sample preparation; and 3) differences i n method of s o i l density comparison, f o r example constant void r a t i o versus constant r e l a t i v e density versus constant compactive e f f o r t applied during sample preparation. The method of sample preparation and the r e s u l t i n g s o i l f a b r i c have been shown to have a great influence upon the undrained behaviour of sand (see Sections 2.1 and 2.2). Ladd (1974) shows the extent of the e f f e c t of sample preparation technique on the behaviour of s i l t y well-graded sand. The undrained c y c l i c strength of well-graded s i l t y sands prepared by both p l u v i a t i o n i n a i r and moist tamping was compared. Sample preparation method i s shown to have a large e f f e c t on c y c l i c strength at a given void r a t i o . A i r pluviated sand i s shown to be up to 50% weaker than comparable moist tamped sand. M u l i l i s et a l . (1977) show s i m i l a r t e s t r e s u l t s . In the i n t e r p r e t a t i o n of the e f f e c t of gradation and fin e s content upon s o i l behaviour one must recognize the e f f e c t of sample preparation technique. I f t e s t r e s u l t s are to be meaningful, simulation of the f a b r i c of the f i e l d s o i l to be modelled must be ensured. Since many well-graded and s i l t y sands of i n t e r e s t i n f i e l d investigations are deposited through water, such as i n hydraulic f i l l or f l u v i a l deposits, i t i s imperative to reproduce s i m i l a r f a b r i c i n laboratory samples. I t i s also important to know the expected range of density and stress path dependent behaviour possible within a hydraulic f i l l or f l u v i a l f i e l d deposit. This can only be achieved by simulating c l o s e l y the expected method of f i e l d deposition i n the preparation of laboratory samples and by subjecting samples to the range of loading paths anticipated i n the f i e l d . Unfortunately, simple water p l u v i a t i o n of sand, which i s thought to best simulate the f a b r i c of sand deposited i n water, r e s u l t s i n segregated well-graded samples (Lee and F i t t o n , 1969). They can not be considered homogeneous or repeatable, a necessary condition f o r a fundamental and systematic assessment of element properties i n cont r o l l e d laboratory t e s t s . 41 CHAPTER 3 EXPERIMENTAL WORK This chapter describes 1) the apparatus used for undrained monotonic and c y c l i c t r i a x i a l loading, 2) the materials used i n the t e s t program, 3) the sample preparation technique developed to produce homogeneous s o i l specimens f o r t e s t i n g purposes, and 4) the objectives of the t e s t program. 3.1 TESTING APPARATUS T r i a x i a l specimens were approximately 12.7 cm high and 6 . 4 cm i n diameter. Tests were conducted using the t r i a x i a l apparatus and loading system described by Chern (1985) . A schematic diagram of the equipment i s shown i n Figure 3.1. A x i a l load, confining c e l l pressure, pore pressure and a x i a l displacement were measured using e l e c t r o n i c transducers coupled to a data a c q u i s i t i o n system interfaced with a microcomputer. Volume changes were measured with a pipette. 3.1.1 Load Controlled system 3.1.1.1 Consolidation Samples were i s o t r o p i c a l l y consolidated by stepwise increasing c e l l pressure i n reservoir A and using a back pressure of 100 kPa (valves 1, 3 and 6 open and 7 closed) . Anisotropic consolidation requires that c e l l pressure and ///////s////// R A T I O R E L A Y E L E C T R O - P K E U M T I C T D A N S D U C E R T O R E C O R D E R L V D T ' A 1 I A L C Y C L I C L O A t l W S Y S T E R F U N C T I O N 6 E N E R A T 0 R I E R O P R E S S U R E D A T U X L E 6 E N D © P R E S S U R E M U S E (g) A I R S U P P L Y P R E S S U R E R E 6 U I A T 0 R ® V R L V E XL ///)?>>/>> M U I L E A C T I N G A I R P I S T O N L O A D C E L L L O A D C O K K E C T I W R I R S R A T I O R E L A Y =«>= MOTORIZED PRESSURE REGULATOR -KB) A N I S O T R O P I C C O N S O L I D A T I O N S Y S T E R A R D S T R E S S C O N T R O L L E D R O N O T O N I C L O A D I N G S Y S T E R 2 P O R E P R E S S U R E T R A N S D U C E R T O R E C O R D E R '/ 1 I I I I ) ) 111 I I I C E L L P R E S S U R E T R A N S D U C E R S N I T C H V A L V E Figure 3.1 Schematic layout of load controlled monotonic and cyclic triaxial testing system a x i a l stress be increased simultaneously i n a predetermined r a t i o . This was accomplished by feeding c e l l pressure as a s i g n a l to a r a t i o relay and the output of the relay to the upper chamber of the double acting a i r piston (valves 7, 8 and 10 open and 6, 9 closed) . The c e l l pressure was increased by the motorized regulator. P r i o r to i n i t i a t i n g anisotropic consolidation, both chambers of the piston were pressurized to an approximate equal base pressure, the difference serving to compensate the u p l i f t on the loading ram during s e t t i n g up of back pressure. 3.1.1.2 Monotonic Loading System Monotonic shear t e s t s were conducted by increasing or decreasing the a i r pressure i n one of the chambers of the double acting a i r piston by the motorized pressure regulator. V e r t i c a l load i s increased to achieve monotonic compression loading, or decreased to achieve monotonic extension loading at constant c e l l pressure. 3.1.1.3 C y c l i c Loading C y c l i c loading i s applied by means of an electropneumatic transducer driven by a function generator. A f t e r consolidation, valve 8 i s closed and valve 9 opened to the c y c l i c loading system i n which a pressure equal to the current piston pressure i s preset by the D.C. o f f s e t on the function generator. The low pressure output from the electro-pneumatic transducer i s amplified by a r a t i o relay before admission to one chamber of the double acting a i r piston. A sinusoidal c y c l i c load pulse was applied at 0.1 Hz and c a l i b r a t e d p r i o r to se t t i n g up of the t e s t specimen by use of a dummy rod i n place of the s o i l sample. A 0.1 hz c y c l i c loading rate i s generally slower than anticipated i n most earthquake loading conditions. However, the slower rate of loading was chosen f o r a better r e s o l u t i o n of measurements with the data a c q u i s i t i o n system. During c y c l i c loading, c e l l pressure was maintained through r e s e r v o i r B rather than reservoir A. This provided a large bore convection to the c e l l water and thus prevented any fluctuations i n c e l l pressure due to the displacement of water by the loading ram moving i n and out of the c e l l when large deformations developed. 3.1.2 S t r a i n Controlled Testing System This was done using a simple Wykeham Farrance Eng. Ltd. (Slough, England) s t r a i n c o n t r o l l e d loading machine. Tests were conducted at an a x i a l s t r a i n rate of 0.5 percent per minute to ensure confident measurement of pore water pressures i n s i l t y sand specimens. S t r a i n c o n t r o l l e d tests provide a better record of s t r e s s - s t r a i n and pore pressure response than load controlled t r i a x i a l t e s t s , e s p e c i a l l y i f the s o i l tested i s subject to l i m i t e d l i q u e f a c t i o n or l i q u e f a c t i o n . The undrained response may d i f f e r with rate of loading due to s o i l creep. However, several workers (Chang et. a l . , 1982; Castro et. a l . , 1982; Chem et. a l . , 1985) report that undrained shear properties of sand are r e l a t i v e l y unaffected by the rate of loading. 3.1.3 Resolution of Measurement The measured stresses were generally accurate to 0.4 kPa. A x i a l stress was corrected f o r : 1) membrane loads, as described i n Appendix B, 2) u p l i f t force on the upper loading platen due to c e l l pressure which does not act on sample cap rod area, 3) f r i c t i o n on the rod, depending on s t r a i n d i r e c t i o n (see Appendix B) , 4) buoyant weight of loading rod and top cap, 5) LVDT spring force on sample, and 6) 1/2 t o t a l weight of the sample. C e l l pressure, pore pressure and a x i a l stress measurements were referenced to mid sample height, as shown i n Figure 3.1. The re s o l u t i o n of v e r t i c a l and volumetric s t r a i n s was 0.01%. 3.2 MATERIALS TE8TED Ottawa sand (ASTM-C-109) and Brenda mine t a i l i n g s sand were used i n the t e s t i n g program. The t r i a x i a l behaviour of water pluviated Ottawa sand has previously been studied by Chem (1984), Chung (1985) and others. The t r i a x i a l loading behaviour of a poorly-graded water pluviated Brenda sand has been studied by Chem (1984) . In t h i s study, various mean grain s i z e s and gradations of clean Brenda t a i l i n g s sand were tested i n order to investigate the e f f e c t of grain s i z e and gradation upon undrained behaviour. Kamloops s i l t was mixed with Brenda sand to generate s i l t y sands and thus examine the e f f e c t of s i l t content on the undrained monotonic and c y c l i c loading response of sand. The materials tested are f u l l y described i n the following sections. 3.2.1 General Description of Materials Tested 3.2.1.1 Ottawa Band ASTM-C-109 Ottawa sand (ASTM designation C-109-69) i s a subrounded medium quartz sand from Ottawa, I l l i n o i s . The standard t e s t sand i s used to c a l i b r a t e both the t e s t i n g equipment and the sample preparation technique used i n the t e s t program. The p a r t i c l e s i z e d i s t r i b u t i o n of Ottawa sand i s shown i n Figure 3.2. 3.2.1.2 Brenda T a i l i n g s Sand Brenda t a i l i n g s sand was obtained from the Brenda copper and molybdenum mine situated i n the Okanogan area, B r i t i s h Columbia (Soregaroli, 1974). The t a i l i n g s sand i s coarse to very f i n e grained, s a l t and pepper colored angular sand derived from mechanically crushed unweathered granodiorite rock. The mineralogy of the t a i l i n g s sand i s shown i n Table 3.1. Figure 3.2 Gradation of Ottawa C-109 sand M.l.T GRAIN SIZE CLASSIFICATION SAND S I LT COARSE MEDIUM F INE COARSE MEDIUM F INE 20 40 60 100 140 200 U . S . B . S . S IEVE S I ZE 1 1 l i l l 111 i i I i—r 1.0 0.5 111 i • i r 0.1 0.05 111 i i | i—r 0.01 0.005 GRAIN SIZE (mm) 48 Table 3.1 Mineralogy of Brenda Mine T a i l i n g s Sand (determined by examining grains passing #20 and retained on #40 sieves) Plagioclase Feldspar 41% Potassium Feldspar 20% Quartz 27% B i o t i t e Mica 6% Hornblende 4% Heavy Minerals 2% magnetite,pyrite In order to formulate a s p e c i f i c gradation of t a i l i n g s sand, oven dried t a i l i n g s which had been sieved through a set of U.S. standard #20, #40, #60, #100, #140 and #200 sieves f o r twenty minutes were taken from storage j a r s , weighed to 0.01 g accuracy, and independently remixed for each sample. Three types of poorly-graded sand samples were prepared; the f i r s t obtained from sand passing the number 20 and retained on the number 40 sieve (called 20/40 sand), the second obtained from sand passing the number 60 and retained on the number 100 sieve (called 60/100 sand) and the t h i r d obtained from sand passing the number 100 and retained on the number 140 sieve (called 100/140 sand). A well-graded sand with a grain s i z e d i s t r i b u t i o n from coarse to f i n e grained sand was also prepared (called 20/200 sand). Grain s i z e d i s t r i b u t i o n s of various Brenda sands tested are shown i n Figure 3.3. 3.2.1.3 Kamloops s i l t Kamloops s i l t was obtained from an approximately 10,000 year o l d g l a c i a l lake deposit which occupies the v a l l e y F i g u r e 3.3 G r a d a t i o n s o f Kamloops s i l t and v a r i o u s c l e a n Brenda t a i l i n g s sands t e s t e d M.I.T. GRAIN SIZE CLASSIFICATION SAND SILT COARSE MEDIUM FINE COARSE MEDIUM FINE 20 40 60 100 140 200 U.S. STANDARD SIEVE SIZE 1.0 0.1 0.01 GRAIN SIZE (mm) surrounding the c i t y of Kamloops, B r i t i s h Columbia. Kamloops s i l t i s brownish grey colored medium grained non- cohesive inorganic s i l t . A grain s i z e d i s t r i b u t i o n curve for Kamloops s i l t obtained using the hydrometer t e s t (Lambe, 1951) i s shown i n Figure 3.3. During the t e s t i n g program, previously used s i l t was washed to remove f i n e sand derived from minor p a r t i c l e crushing during t e s t i n g , and oven dried before reuse i n a new s o i l sample. Various amounts of s i l t were mixed with Brenda 20/200 sand samples (as described i n Section 3.3.2) to obtain target s i l t contents of approximately 4.3%, 7.5%, 14%, and 21% by weight of s o l i d s . The grain s i z e d i s t r i b u t i o n s of r e s u l t i n g s i l t y sands are shown i n Figure 3.4. The range of s i l t content i n s i l t y sands tested i s probably representative of that found i n homogeneous natural and hydraulic f i l l sands, where sand has been deposited r a p i d l y through a s i l t y s l u r r y . Higher average s i l t contents which may be found i n sandy f i e l d s o i l s are probably due to non- homogeneous s i l t lenses within sand, produced by intermittent deposition of coarser and f i n e r grained p a r t i c l e s . Material properties of such a non-homogeneous s o i l are d i f f i c u l t to measure or quantify, as such s o i l i s a s t r a t i f i e d assemblage of less well-graded s o i l layers. 3.2.2 Physical Properties of the Materials Tested Table 3.2 presents a summary of the physical properties of the materials tested. The physical properties of the F i g u r e 3.4 G r a d a t i o n s o f s i l t y 20/200 Brenda t a i l i n g s sands t e s t e d M.l.T. GRAIN SIZE CLASSIFICATION SAND SILT COARSE MEDIUM FINE COARSE MEDIUM FINE 20 40 60 100 140 200 U.S. STANDARD S IEVE S I ZE 1.0 0.1 0.01 GRAIN SIZE (mm) TABLE 3.2 Physical properties of materials tested MATERIAL Gs OTTAWA C-109 SAND ASTM VOID RATIO (DRY) MAXIMUM MINIMUM 2.67 0.760 0.50 MAXIMUM SLURRY VOID RATIO DRY SATURATED 0.770 0.770 GRAIN SIZE (mm) D50 D10 0.4 0.25 Cu MEMBRANE PENETRATION FACTOR m (.cm) (see Appendix A) 1.64 0.0048 BRENDA TAILINGS SAND 20/40 2.68 1, ,1370 0. .7734 1. .1618 1. .1576 0, .595 0. .447 1, .41 0.00566 40/60 2.68 0, .323 0. .264 1, .29 60/100 2.689 1. .1850 0. .7899 1. ,1977 1. .1323 0. .192 0. .157 1, .29 0 100/140 2.705 1. .1947 0. .7765 1. .2017 1. ,1504 0. .125 0. .109 1, .19 0 140/200 2.705 0, .088 0. .076 1 .20 0 20/200 2.689 0. .8643 0. .5180 0, ,890 0, .25 0. .093 3. .44 0.00078 KAMLOOPS SILT 2.67 2. ,67 1, ,447 0, .012 0. .0043 3, .09 0 materials shown i n Table 3.2 are discussed and compared i n the following sections. 3.2.2.1 S p e c i f i c Gravity The s p e c i f i c gravity of Brenda sand i s higher than that of Ottawa sand due to mafic and minor heavy minerals i n Brenda sand. The s p e c i f i c gravity of Brenda sand i s f a i r l y constant, although i t increases s l i g h t l y with decreasing grain s i z e due to a higher percentage of heavy minerals such as magnetite i n f i n e r grained Brenda sand. 3.2.2.2 ASTM Standard Void Ratios ASTM standard maximum and minimum dry void r a t i o s were determined f o r a l l sands tested. Maximum void r a t i o s obtained by s l u r r y deposition method (see Section 3.3) are also shown i n Table 3.2 fo r comparison. They are i n general s l i g h t l y larger than the maximum ASTM void r a t i o s . This i s due to the lower energy of deposition obtained using the s l u r r y deposition method. Grains are deposited from e s s e n t i a l l y zero drop height, when deposited i n a s l u r r y , while ASTM maximum void r a t i o samples are deposited from a one inch drop height. Maximum void r a t i o s achieved by simple water p l u v i a t i o n of sand are approximately equal to those obtained by the ASTM maximum void r a t i o method. The various poorly-graded Brenda sand gradations tested have s i m i l a r maximum and minimum void r a t i o s . ASTM maximum and minimum void r a t i o s of well-graded 20/200 sand are much lower than those of poorly-graded sands, due to smaller p a r t i c l e s f i l l i n g void space between larger p a r t i c l e s . The differe n c e between maximum and minimum ASTM void r a t i o s obtained f o r each sand gradation tested i s s i m i l a r . Rounded Ottawa C-109 sand on the other hand has much lower maximum and minimum void r a t i o s than angular t a i l i n g s sand. 3.2.2.3 Maximum B i l t Void Ratio Kamloops s i l t was pluviated through both a i r and water to determine maximum dry and saturated void r a t i o s . Maximum dry void r a t i o was found to be 2.67, almost twice the maximum water pluviated void r a t i o of 1.447. One might expect dry maximum void r a t i o to be smaller than water pluviated maximum void r a t i o f o r the following reasons: 1) dry s i l t i s deposited i n a i r with a higher energy of deposition; 2) oven dried s i l t must be s i f t e d to segregate s i l t p a r t i c l e s , thus s i l t p a r t i c l e s which remain unsegregated by s i f t i n g would tend to produce a lower dry state maximum void r a t i o ; and 3) s i l t pluviated through water tends to segregate according to grain s i z e , which would tend to increase maximum void r a t i o . Thus there must be a fundamental difference i n s i l t p a r t i c l e i n t e r a c t i o n i n a i r and water deposition environments which produces the large d i f f e r e n c e between dry and saturated state maximum void r a t i o . During the determination of maximum ASTM dry void r a t i o s f o r f i n e sands i t was observed that p a r t i c l e s carry a 55 s t a t i c charge which i n some cases was large enough to expel some highly charged p a r t i c l e s from the container into which they were being poured. S i m i l a r l y , the excessively large dry maximum void r a t i o of 2.67 of s i l t i s probably due to the repulsion of e l e c t r i c a l l y charged dry s i l t p a r t i c l e s . In the saturated state, e l e c t r i c a l charges may be somewhat neutralized by water, enabling p a r t i c l e s to s e t t l e into a much denser structure i n a manner s i m i l a r to that of coarser grained sand. 3.2.2.4 Maximum and Minimum Void Ratios of S i l t y Sand Figure 3.5 shows how maximum and minimum dry ASTM void r a t i o s and maximum s l u r r y deposition void r a t i o s of s i l t y well-graded 20/200 Brenda sand vary with s i l t content. The standard ASTM maximum and minimum density t e s t s are not generally considered applicable to s o i l s with greater than 12% f i n e s (passing the number 200 sieve). Nevertheless, ASTM maximum and minimum void r a t i o s have been included to show the difference i n void r a t i o s attained by a i r p l u v i a t i o n i n the dry state and by p l u v i a t i o n through water. From Figure 3.5 i t i s cl e a r that p l u v i a t i o n of s i l t y sand through water y i e l d s a considerably d i f f e r e n t material than p l u v i a t i o n through a i r . A i r p l u v i a t i o n of s i l t y sand y i e l d s much higher void r a t i o s than p l u v i a t i o n through water, although i n both cases p a r t i c l e s i z e segregation i s a minimum. The observed behaviour of s i l t y sand i s s i m i l a r to that of pure s i l t , where the maximum void r a t i o obtained by Fig. 3.5 C o m p a r i s o n of ASTM dry m a x i m u m and m i n i m u m void ra t ios and slurry depos i t ion m a x i m u m void ra t ios of silty 2 0 / 2 0 0 B renda sand 1.0 i 1 0 4 8 12 16 20 2 4 28 PERCENTAGE SILT CONTENT BY WEIGHT p l u v i a t i o n of s i l t through a i r (e = 2.67) i s much larger than that obtained by p l u v i a t i o n through water (e = 1.447). The mechanisms which control the large difference i n maximum void r a t i o s obtained by p l u v i a t i o n i n dry versus saturated state are probably s i m i l a r i n s i l t and s i l t y sands. A major reason f o r the difference i n maximum void r a t i o s obtained by a i r versus water p l u v i a t i o n of s i l t y sands i s that sand has a much higher terminal v e l o c i t y of settlement through water than s i l t . When sand i s deposited through a s i l t y s l u r r y , the sand f r a c t i o n s e t t l e s through the s i u r r y water much fas t e r than the s i l t f r a c t i o n . One could expect the sand to pluviate through a s i l t y s l u r r y i n much the same manner as through clean water, unless the s l u r r y i s very t h i c k and viscous with a large fi n e s content. Consequently, one would expect the maximum void r a t i o of the sand f r a c t i o n of a water pluviated s i l t y sand to vary l i t t l e with increasing s i l t content, on the postulate that the fines f r a c t i o n e f f e c t i v e l y f i l l s void space between sand p a r t i c l e s . Mechanical properties of water pluviated s i l t y sand might also be e s s e n t i a l l y c o n t r o l l e d by the density of the sand f r a c t i o n , or sand skeleton void r a t i o , which may be calculated using Eqn. 3.1: •skeleton = tV TG s /) w/(M-M s i l t) ] - 1 (3.1) where: V.p = t o t a l volume of the specimen 58 G s = s p e c i f i c gravity of sand = density of water M = t o t a l mass of s o i l s o l i d s i n the specimen Mŝ ^^. = mass of s i l t i n the specimen e s k e l e t o n = s a n d skeleton void r a t i o Figure 3.5 i s replotted with respect to sand skeleton v o i d r a t i o as Figure 3.6. I t may be seen that the maximum sand skeleton void r a t i o of unsegregated s l u r r y deposited s i l t y 20/200 sand i s i n fac t e s s e n t i a l l y constant with increasing s i l t content u n t i l the s i l t content exceeds about 20% by weight. At large s i l t contents, the s i l t y s l u r r y through which the sand i s p l u v i a t i n g i s very t h i c k and viscous, and apparently increases maximum sand skeleton void r a t i o . Figure 3.6 also shows the v a r i a t i o n of sand skeleton void r a t i o s calculated from ASTM maximum s i l t y sand void r a t i o s . The ASTM maximum sand skeleton void r a t i o curve shows that an increase i n s i l t content bulks the sand structure during a i r p l u v i a t i o n . This bulking e f f e c t contrasts r a d i c a l l y with only minor influence of s i l t content upon sand structure produced by p l u v i a t i o n of s i l t y sand through water. The change i n ASTM minimum void r a t i o with s i l t content shown i n Figure 3.5 indicates that i t becomes more d i f f i c u l t to compact a dry sand skeleton by v i b r a t i o n as s i l t content i s increased. In contrast, a s l u r r y deposited sand with 20% Fig. 3.6 C o m p a r i s o n of m a x i m u m void ra t ios obta ined by air p luv iat ion and slurry depos i t ion of silty 2 0 / 2 0 0 B renda sand MAXIMUM VOID RATIO ^ ^cB-n°a. i i i i i i i i i i i i i 0 4 8 12 16 20 2 4 28 PERCENTAGE SILT CONTENT BY WEIGHT cn s i l t content i s found to have a 100% ASTM r e l a t i v e density when consolidated to 350 kPa i s o t r o p i c e f f e c t i v e stress from an i n i t i a l l y loosest state of s l u r r y deposition. S i l t y sand i s thus much more compressible when deposited i n a saturated state than i n a dry state. The conclusion that may be drawn from Figures 3.5 and 3.6 i s that ASTM maximum and minimum void r a t i o s p e c i f i c a t i o n s provide a rather poor basis f o r the c l a s s i f i c a t i o n of hydraulic f i l l s i l t y sand behaviour. One may also conclude that the method of preparing s i l t y sand samples may severely a f f e c t s o i l f a b r i c and measured s o i l properties. 3.2.2.5 C o e f f i c i e n t of Uniformity Table 3.2 provides a summary of the c o e f f i c i e n t s of uniformity of the sands tested. C o e f f i c i e n t of uniformity of s i l t y sand shows an abrupt jump from 3.7 to 19 as s i l t content increases from 7.5% to 14.8%. This indicates that c o e f f i c i e n t of uniformity provides a rather poor basis for the c l a s s i f i c a t i o n of s i l t y sand gradation or i t s behaviour. 3.2.2.6 Membrane Penetration Factors Membrane penetration corrections for the sands tested were calculated from load-unload i s o t r o p i c consolidation t e s t r e s u l t s , according to the method described by Vaid and Negussey (1984). Membrane penetration factor c a l c u l a t i o n s are summarized i n Appendix A and the correction factors 'm' 61 at loosest density state for the various sands tested are shown i n Table 3.2. Membrane penetration e f f e c t s are small f o r the we l l - graded 20/200 sand, zero f o r f i n e sands with D50 less than 0.2 mm (grain s i z e l e s s than approximately h a l f the membrane thickness), and f a i r l y large for coarse grained Brenda 20/40 and Ottawa C-109 sands. 3.2.3 C r i t e r i a f o r Choosing Test S o i l s Ottawa sand was chosen as a control sand to show that the t e s t i n g equipment and the s l u r r y deposited sample produce t e s t r e s u l t s s i m i l a r to those obtained f o r water pluviated Ottawa sand by previous workers. Tests on rounded Ottawa sand also enabled comparison with the behaviour of angular Brenda sand. Brenda sand was selected for the study of the e f f e c t of s i l t content upon sand behaviour because well-graded s o i l s generally have more angular p a r t i c l e s , e s p e c i a l l y i n se i s m i c a l l y active areas which are generally mountainous and close to the source of well-graded sediments. The composition of Brenda sand i s f a i r l y uniform across a l l grain s i z e s . The sand i s made up of only a few common minerals such as quartz, feldspar, and mica. Since various gradations selected have the same mineralogy, the e f f e c t of gradation upon material behaviour may be systematically assessed. Brenda sand i s from a t a i l i n g s dam, so there i s a d i r e c t a p p l i c a b i l i t y of t e s t r e s u l t s to the p r a c t i c a l problem of designing and assessing the s t a b i l i t y of a hydraulic f i l l dam composed of well-graded sand. Kamloops s i l t was selected for the study of the e f f e c t of s i l t content upon s o i l behaviour because i t i s inorganic, and was obtained from near the source of Brenda sand. I t has a s i m i l a r composition as Brenda sand or Brenda t a i l i n g s slimes. The s i l t i s probably representative of fines commonly found within well-graded f l u v i a l deposits i n s e i s m i c a l l y active areas. 3.3 SAMPLE PREPARATION - THE SLURRY DEPOSITION METHOD Testing of homogeneous (uniform) samples under uniform states of stress and s t r a i n i s required f o r fundamental studies of s o i l property characterization. I t i s also necessary to be able to p r e c i s e l y r e p l i c a t e several homogeneous specimens for such studies. These requirements have promoted the use of reconstituted s o i l s i n preference to natural materials for fundamental investigations of s o i l behaviour. Each reconstituted cohesionless s o i l specimen must be i n d i v i d u a l l y prepared. This makes the control of uniformity and the a b i l i t y to r e p l i c a t e several specimens considerably more d i f f i c u l t . The technique f o r r e c o n s t i t u t i n g sand samples must f u l f i l l the following c r i t e r i a : 1) the method must produce loose to dense samples i n the density range expected within an i n s i t u s o i l deposit; 2) the samples must have a uniform 63 void r a t i o throughout; 3) the samples must be f u l l y saturated, p a r t i c u l a r l y f o r undrained t e s t i n g ; 4 ) the samples should be well mixed without p a r t i c l e s i z e segregation regardless of p a r t i c l e s i z e gradation or fines content; and 5) the sample preparation method should simulate the mode of s o i l deposition commonly found i n the s o i l deposit being modelled. Several d i f f e r e n t methods of sample preparation which have been used i n the past are f i r s t discussed. The s l u r r y deposition method of sample preparation which models hydraulic f i l l or f l u v i a l deposition and which meets the above c r i t e r i a i s then described. The success of the proposed method i s evaluated by a s e r i e s of t e s t s to determine the homogeneity and monotonic undrained strength of poorly-graded and well-graded sand with and without f i n e s . 3.3.1 Summary of Techniques Used for Sand sample Preparation Since the f i r s t laboratory studies of sand l i q u e f a c t i o n behaviour conducted by Casagrande (1936), a major problem has been to produce sand samples with a low enough density so as to be susceptible to l i q u e f a c t i o n . Numerous sand bulking techniques designed to increase s u s c e p t i b i l i t y to l i q u e f a c t i o n have been described i n s o i l mechanics l i t e r a t u r e . The most e f f e c t i v e sand bulking technique i s sample preparation i n a moist state where water tension forces between p a r t i c l e s tend to expand the s o i l matrix. Many preparation techniques specify a minimum of depositional energy to achieve a loose state. This may be done by reducing p a r t i c l e drop height, or p l u v i a t i n g sand through water. Sand may also be bulked a f t e r deposition by drawing a sieve mesh through i t or by applying an upward seepage gradient s u f f i c i e n t to induce and maintain a uniform quick sand condition. An important factor to consider i n laboratory studies i s whether the f a b r i c of sand sample produced by the method of preparation i s s i m i l a r to that found within the s o i l deposit being modeled. Numerous studies have shown that s o i l behaviour i s highly dependent upon laboratory sample preparation technique (for example M u l i l i s et. a l . , 1977, and Miura et. a l . , 1982). 3.3.1.1 Moist T»i"p-»Tiq The oldest technique for preparing reconstituted sand samples i n the laboratory i s moist or dry tamping of s o i l i n layers (Lambe, 1951). The technique consists of pouring consecutive s o i l layers of s p e c i f i e d thickness into a sample former tube, and tamping each layer f l a t with a s p e c i f i e d force and frequency of tamping before the next layer i s placed. The moist tamping method best models the s o i l f a b r i c of r o l l e d construction f i l l s , f or which the method was o r i g i n a l l y designed. The moist tamping method produces very loose to dense p a r t i a l l y saturated samples which may be somewhat non- uniform with respect to density or p a r t i c l e s i z e gradation. Several studies have been conducted to assess the uniformity of samples prepared by moist tamping, often with c o n f l i c t i n g conclusions as to the success of the method (Castro, 1969,1982). Miura et. a l . , (1984) compare miniature cone penetration resistance within t r i a x i a l samples prepared by various methods. I t i s shown that a high degree of sample uniformity may be achieved by a i r p l u v i a t i o n while tamping r e s u l t s i n considerable non-uniformity i n cone penetration resistance. Due to water tension forces between grains, sand samples prepared by the moist tamping method may be prepared at much larger void r a t i o s than possible i n a dry or saturated state. Casagrande (1976) suggests that sand dumped i n a moist state i s p a r t i c u l a r l y prone to l i q u e f a c t i o n due to a "honeycomb structure because of c a p i l l a r y forces between moist grains"; Casagrande states that moist dumped sand remains a "bulked sand when saturated". Water tension forces between grains are larger i n f i n e r grained material, thus f i n e r grained s o i l i s more susceptible to bulking by water tension forces than coarse grained sand. I t has been observed that f i n e grained sand samples prepared by the moist tamping method may be assembled i n such a loose state that they may undergo large s t r a i n s during the saturation process due to the removal of water tension forces between grains. Other workers have observed s i m i l a r large s t r a i n s i n moist tamped s i l t y sands during the saturation process (Marcuson et. a l . , 1972, Chang et. a l . , 1982, Sladen et. a l . , 1985). I f a moist tamped s o i l specimen can be saturated with minor induced s t r a i n , i t i s often considerably less compressible during consolidation than a comparable water pluviated specimen, and thus may be consolidated to much larg e r void r a t i o s . Such incompressible specimens are often metastable and more susceptable to l i q u e f a c t i o n i n monotonic loading. 3.3.1.2 A i r Pluvi a t i o n The major factors that a f f e c t r e l a t i v e density of a i r pluviated sands are height of p a r t i c l e drop (Vaid and Negussey, 1986) and rate of deposition (Miura et. a l . 1982). A higher drop height or a higher rate of deposition r e s u l t s i n a higher energy of deposition and thus a denser s o i l specimen. Numerous workers who have used a i r p l u v i a t i o n have attempted to r e s t r i c t drop height and thus produce very loose sand samples. The a i r p l u v i a t i o n technique produces f a i r l y uniform specimens depending upon the technique used ( M u l i l i s et. a l . , 1975, Miura et. a l . , 1982, 1984). A i r p l u v i a t i o n best models the natural deposition process of wind blown aeolian deposits, which generally consist of ei t h e r well-sorted sand or well-sorted s i l t . A i r p l u v i a t i o n of well-graded sand i s not as successful as a i r p l u v i a t i o n of well-sorted sand. Well-graded sand may become segregated when deposited by p l u v i a t i o n through a i r , e s p e c i a l l y i f i t has a considerable f i n e s content. The process of sample saturation may disrupt i n i t i a l sand f a b r i c , and produce some s o i l segregation due to washing out of f i n e s from the sample. A i r pluviated dry s i l t y sands which have a large fines content are prone to bulking due to the fine s content. The extent of t h i s bulking i s i l l u s t r a t e d i n Figure 3 . 6 for s i l t y 2 0 / 2 0 0 Brenda sand. The figure shows that the ASTM maximum void r a t i o obtained by a i r p l u v i a t i o n i s v i r t u a l l y unaltered with s i l t content up to about 20%. The maximum void r a t i o obtained by the proposed s l u r r y deposition method, on the other hand, decreases s u b s t a n t i a l l y with increases i n s i l t content up to about 20%. A i r p l u v i a t i o n of s i l t y sand would neither simulate the deposition process nor the range of void r a t i o s possible i n hydraulic f i l l s or f l u v i a l deposits which are often comprised of s i l t y sands. Figure 3 . 6 also shows the v a r i a t i o n of sand skeleton void r a t i o of s i l t y sand i n the loosest state. By s l u r r y deposition t h i s void r a t i o may be noted to remain e s s e n t i a l l y constant with increasing s i l t content despite decrease i n o v e r a l l void r a t i o . This shows that sand deposits through a s i l t y s l u r r y i n much the same manner as i t does through clean water due to the large difference i n settlement v e l o c i t y of f i n e r s i l t and coarser sand through water. A i r p l u v i a t i o n on the other hand causes a r a d i c a l increase i n the void r a t i o of the sand skeleton with 68 increasing s i l t content, thus demonstrating large bulking of the sand matrix. A i r pluviated s i l t y sand which i s bulked would tend to be metastable and undergo very large s t r a i n s s i m i l a r to those found i n moist tamped s i l t y sands during saturation and consolidation. Large s t r a i n s induced within a sample during the preparation stage impart a s t r a i n h i s t o r y to the s o i l that i s much d i f f e r e n t from that produced i n a loose natural s i l t y sand which i s invari a b l y deposited through water and not appreciably bulked by s i l t content. Non- standardization of i n i t i a l s t r a i n during sample preparation has been i d e n t i f i e d by Tatsuoka et. a l . (1986) as one reason fo r the v a r i a t i o n i n t r i a x i a l behaviour of sand among various s o i l laboratories. Very loose a i r pluviated s i l t y sands bulked by s i l t content would tend to be more susceptible to l i q u e f a c t i o n under monotonic or c y c l i c loading than clean well-sorted sands at the same void r a t i o . Numerous studies have been conducted to explore the e f f e c t of sample preparation technique and the influence of sand f a b r i c upon undrained behaviour. Laboratory t e s t s conducted by Miura and Toki (1982) indicate that there i s a large difference i n behaviour of clean sands prepared by p l u v i a t i o n through a i r and by moist tamping or moist rodding. Tatsuoka et. a l . (1986) report s i m i l a r r e s u l t s , and f i n d that a i r pluviated and water pluviated clean sands have f a i r l y s i m i l a r c y c l i c strength which i s generally lower than the c y c l i c strength of comparable moist tamped or vibrated sand at the same void r a t i o . 3.3.1.3 Water Pl u v i a t i o n Sample preparation by the water p l u v i a t i o n technique has been described by several researchers, including Lee and Seed (1967), Finn et. a l . (1971), Chaney et. a l . (1978), and Vaid and Negussey (1984). The water p l u v i a t i o n technique ensures sample saturation. The terminal v e l o c i t y of sand f a l l i n g through water i s lower than that of sand f a l l i n g through a i r . This leads to a lower energy of deposition i n water pluviated samples and hence a looser deposit, as long as sedimentation currents are not set up within the water i n the deposition mold. The water p l u v i a t i o n technique simulates the deposition of sand through water found i n many natural environments and mechanically placed hydraulic f i l l s . Oda et. a l . (1978) report that natural a l l u v i a l sands and water pluviated sands have s i m i l a r f a b r i c and thus s i m i l a r s t r e s s - s t r a i n and strength behaviour. The water p l u v i a t i o n technique produces uniform samples of poorly-graded sand (Vaid and Negussey, 1984), but p a r t i c l e s i z e segregation i s a problem i n water p l u v i a t i o n of well-graded or s i l t y sands. Since laboratory t e s t s such as the t r i a x i a l t e s t are designed to model the stress conditions which e x i s t at a point and thus require uniform samples to ensure uniform stresses and s t r a i n s , the water 70 p l u v i a t i o n technique should only be used to t e s t poorly- graded sands. When a well-graded s o i l i s subjected to grain s i z e segregation during p l u v i a t i o n , the segregated s o i l generally has a larger average maximum void r a t i o than that of the unsegregated s o i l , and i t s mechanical properties are s i m i l a r to that of a more poorly-graded s o i l . The maximum possible void r a t i o a f t e r consolidation to a given stress state of a water pluviated sand i s generally lower than that of dry or moist tamped sand. This i s due to the e f f e c t s of bulking of fines i n the dry state or water tension forces i n the moist state. Water pluviated sands are generally more compressible during consolidation than moist tamped sands due to the higher r a d i a l compressibility of water pluviated sand f a b r i c (see Section 4.1.4). 3.3.2 The Slurry Deposition Method To overcome inherent problems of the methods of preparing reconstituted sand samples described i n Section 3.3.1 ( e s p e c i a l l y the problem of p a r t i c l e segregation i n poorly-graded or s i l t y sand samples) a new technique c a l l e d the s l u r r y deposition method was developed. The s l u r r y deposition method used i n the preparation of 63 mm diameter t r i a x i a l specimens i s described i n the following paragraphs. 3.3.2.1 Preparation of Sand A mass of t e s t sand s u f f i c i e n t to f i l l the sample preparation mold at minimum density i s poured into a fl a s k with s u f f i c i e n t water (see Figure 3.7(a)) and b o i l e d for f i f t e e n minutes to de-air the mixture. A f t e r cooling, more de-aired water i s added to the f l a s k to f i l l i t completely. I f the t e s t sample i s to contain s i l t or clay f i n e s , a separate f l a s k i s f i l l e d with the f i n e s and a volume of water approximately 60% of the f i n a l sample volume. The f i n e s s l u r r y i s also boiled to de-air and allowed to cool. 3.3.2.2 sample Preparation Mixing Tube The sample preparation tube i s a c l e a r p l e x i g l a s s c y l i n d r i c a l tube (see Figure 3.7(b)) 22.5 cm long, 6 cm i n diameter and with walls 5 mm thick. The preparation tube has a rubber membrane gasket seal glued to one end, and a number 11.5 rubber stopper which i s used to seal the other end. The f i n e s f r a c t i o n s l u r r y i s poured into the sample preparation tube and topped up with the de-aired water used to f l u s h clean the fines s l u r r y f l a s k . The f i n e s s l u r r y within the preparation tube i s allowed to s e t t l e to the bottom of the tube before the sand f r a c t i o n of the s o i l sample i s pluviated into the tube. For clean sand samples the preparation tube i s simply f i l l e d with de-aired water. The sand f l a s k opening i s constricted with a tapered rubber stopper which aids i n p l u v i a t i o n of the sand through water from the f l a s k to the preparation tube. Thus sample saturation i s maintained during a l l stages of preparation. Some s l u r r y fines which may move up into the sand f l a s k (<0 SAND BOILED IN WATER TO DE-AIR; SILT OR CLAY SLURRY BOILED SEPARATELY (b) SILT SLURRY OR CLAY SLURRY OR NAIER POURED INTO TRANSPARENT PLASTIC R U I N S TUBE; SAND PLUVIATED INTO R U I N S TUBE; SILT OR CLAY SLURRY LOST DURING SAND PLUVIATION IS COLLECTED TO BE NEISHED RUBBER HEHBRANE SEAL BLUED TO ONTO BASE PLATEN OF TRIAXIAL TEST APPARATUS FIGURE 3.1 SCHEMATIC DRAWING OF SLURRY DEPOSITION METHOD FOR PREPARATION OF WELL GRADED SILTY OR CLAYEY WELL MIXED SATURATED LOOSE TRIAXIAL TEST SAND SPECIMENS FIGURE 3.1 (continued) SCHEMATIC DRAWING OF SLURRY DEPOSITION METHOD FOR PREPARATION OF WELL GRADED SILTY OR CLAYEY WELL MIXED SATURATED LOOSE TRIAXIAL TEST SAND SPECIMENS (h) TOP CAP APPLIED CAREFULLY TO TOP OF SAMPLE; OVERSIZE CYLINDRICAL RING PLACED AROUND TOP CAP OHIO TOP OF FORHER TUBE. SAMPLE MEMBRANE PULLED UP OVER CYLINDRICAL RING; RUBBER 0-RIN6 ROLLED OVER RUBBER HEHBRANE AND CYLINDRICAL RING. EICESS RUBBER MEMBRANE ROLLED DONN TO O-RINfi TO ALLON REIOVAL CF CYLINDRICAL RING AND ACHIEVE UNDISTURBED SEALING OF TOP CAP NITH O-RINS 0) FIGURE 3.T (continued) SCHEMATIC DRAWING OF SLURRY DEPOSITION METHOD FOR PREPARATION OF WELL GRADED SILTY OR CLAYEY WELL MIXED SATURATED LOOSE TRIAXIAL TEST SAND SPECIMENS (j) RECONSTITUTED SOIL SAMPLE MAINTAINED UNDER VACUUM AFTER REMOVAL OF SPLIT SAMPLE FORMER TUBE 75 during p l u v i a t i o n are retained and weighed when dry to adjust the weight of fines retained within the sand sample. 3.3.2.3 Sealing of Sample Preparation Mixing Tube To mix the sand s l u r r y within the sample preparation mixing tube, the tube i s sealed i n the following manner. A t h i n 2 inch diameter rubber membrane i s r o l l e d onto the outside of the open end of the mixing tube and the tube i s placed i n a water bath as shown i n Figure 3.7(c). A bo i l e d and de-aired porous disk, which i s the bottom platen of the t r i a x i a l t e s t apparatus upon which the f i n i s h e d sample w i l l be seated, i s placed upon the open end of the mixing tube within the water bath, maintaining saturation of the porous disk within the water bath. The rubber membrane around the end of the mixing tube i s p u l l e d over the porous disk assembly, sealing the sides of the disk assembly. A t h i n round metal plate approximately the same diameter as the porous disk assembly i s placed upon the disk assembly and rubber membrane which seals i t , thus completely sealing the end disk assembly and sample mixing tube. The mixing tube i s then withdrawn from the water bath while maintaining a firm finger pressure upon the end disk assembly to keep i t sealed. The s l u r r y within the sample mixing tube i s then mixed by vigorously r o t a t i n g the mixing tube (see Figure 3.7(d)). The progress of sample mixing may be observed through the cl e a r p l a s t i c tube. Twenty minutes 76 of mixing was found s u f f i c i e n t to obtain completely homogeneous samples. 3.3.2.4 Placement of Mixing Tube Onto T r i a x i a l Base Platen Before the sand sample i s prepared i n the mixing tube, the t r i a x i a l t e s t base platen i s assembled within a water bath as shown i n Figure 3.7(e). A rubber membrane (generally 0.3 mm thickness, 59 mm diameter and 20 cm long) i s r o l l e d onto the base platen of the t e s t apparatus and sealed to the platen with a rubber o-ring. Once the sand s l u r r y i n the mixing tube has been mixed thoroughly as discussed i n the previous section, the tube i s held v e r t i c a l l y with the porous disk assembly downwards, and the s l u r r y i s allowed to s e t t l e . A f t e r the s l u r r y has sedimented to i t s loosest stable state, the basal metal plate i s removed from the disk assembly and the rubber membrane which holds the disk assembly i s pul l e d back to the sides of the porous disk which i s now held by water tension and the membrane on the sides of the porous disk. The porous disk end of the mixing tube i s then c a r e f u l l y placed upon the t r i a x i a l t e s t base platen as shown i n Figure 3.7(e). The rubber membrane which seals the porous disk i s now r o l l e d up o f f the mixing tube. The sample rubber membrane i s r o l l e d up from the base platen and o-ring seal which retains one end, over the porous disk and mixing tube towards the rubber stopper which seals the upper end of the mixing tube. The mixing tube i s thus sealed to the base platen and the whole apparatus may be removed from the water bath and taken to the f i n a l sample assembly s t a t i o n . 3.3.2.5 Deposition of « » m p i « A s p l i t sample former tube i s assembled around the base platen and sample mixing tube (see Figure 3.7(f)). The s o i l rubber membrane i s pulled r a d i a l l y outwards from the top of the sample mixing tube and folded over the top of the former. At t h i s point the s p l i t former completely seals the outside of the sample membrane. A c y l i n d r i c a l rubber membrane (75 mm diameter by 100 mm height, see Figure 3.7(f)) i s stretched over the top of the s p l i t sample former and the top of the sample membrane. Water i s poured into the c y l i n d r i c a l membrane to form a water bath above the s p l i t former. A vacuum applied to the inside of the former withdraws the sample membrane to the former walls and also draws water down from the membrane water bath above. The inside of the sample membrane i s now ready to accept the sand s l u r r y . The rubber stopper which plugs the end of the sample mixing tube i s removed. Excess s l u r r y f i n e s or water are withdrawn from within the top of the sample mixing tube and are weighed l a t e r when oven dry to determine the exact fines content i n the sand sample. The mixing tube i s then c a r e f u l l y and s t e a d i l y withdrawn to deposit the sand s l u r r y 78 within the membrane i n a very loose, homogeneous saturated state. The top of the sample i s c a r e f u l l y leveled, excess fines s l u r r y or water are withdrawn from the membrane water bath (to be weighed dry) and the water bath membrane i s removed from the top of the sample former tube (Figure 3.7(g)). 3 . 3 . 2.6 Application of «»mpie T O P Cap The upper t r i a x i a l t e s t platen i s c a r e f u l l y placed on the top surface of the sand sample. A small c i r c u l a r bubble l e v e l placed upon the top of the platen i s used to keep i t l e v e l at a l l times during placement. The s l i g h t e s t pressure upon or v i b r a t i o n of the upper platen causes settlement of the loose sample. Therefore a sp e c i a l technique f o r sealing the upper platen was developed. A c y l i n d r i c a l copper r i n g s l i g h t l y l a r g e r than the diameter of the platen (see Figure 3.7(h)) i s placed upon the top of the sample former. While pressure i s applied to the top of the copper r i n g to hold the sample membrane i n place against the top of the former, the folded portion of the membrane i s pulled up o f f the s p l i t former and onto the sides of the copper r i n g . A rubber o-ring i s r o l l e d downwards over the rubber membrane which covers the copper tube u n t i l the o-ring touches the top of the sample former. The excess rubber membrane which covers the copper tube i s r o l l e d down on top of the o-ring, and held down f i r m l y while the copper r i n g i s withdrawn. The o-ring snaps onto the top platen and over the sample membrane, sealing the sample with no disturbance. The top cap placement method described has been found to be very e f f e c t i v e i n the assembly of as deposited sand specimens of i n i t i a l l y loosest density. Once the sample has been sealed i n i t s rubber membrane, a 20 kPa vacuum i s applied to the pore pressure l i n e i n order to confine the specimen. A f t e r consolidation under the applied vaccuum the s p l i t former i s dismantled, and t r i a x i a l c e l l assembly completed i n the manner described i n Section 3 . 4 . 3.3.2.7 Preparation of Densified Band Samples Densified sand samples are prepared by placing the top platen upon the s o i l sample, applying a s l i g h t pressure upon the platen, and v i b r a t i n g the base of the t r i a x i a l c e l l with a mechanical v i b r a t o r or s o f t hammer u n t i l the desired r e l a t i v e density i s attained. Excess pore pressures caused by v i b r a t i o n are allowed to d i s s i p a t e through top and bottom drainage l i n e s . This technique y i e l d s samples of uniform density throughout (Vaid and Negussey, 1986). Densified s o i l samples are f i n a l l y sealed and confined i n the same manner as loose samples (see Section 3.3.2.6). 3.3.3 Evaluation of Slurry Deposition Method The a t t r a c t i v e features of the s l u r r y deposition method are as follows: 1) a sand sample remains f u l l y saturated 80 within de-aired water during preparation; 2) sample preparation i s normally completed within about 1.5 hours; 3) a sample i s mixed thoroughly as a lean saturated s l u r r y with l i t t l e excess pore water so as to minimize height of p a r t i c l e drop through water during deposition and thus control sedimentation currents and p a r t i c l e s i z e segregation during deposition; 4) the method forms i n i t i a l l y loose samples (poorly-graded unsegregated sand obtained by simple p l u v i a t i o n through water i s generally s l i g h t l y denser than s l u r r y deposited sand) which may be uniformly d e n s i f i e d by mechanical v i b r a t i o n ; 5) samples are exceptionally homogeneous with respect to void r a t i o and p a r t i c l e s i z e gradation, regardless of gradation and fines content; and 6) the deposition method models the s o i l f a b r i c found within natural f l u v i a l deposits or hydraulic f i l l s . 3 . 3 . 3 . 1 « * m p H o m o g e n e i t y To t e s t the uniformity of sand samples prepared using the s l u r r y deposition method, i d e n t i c a l samples of w e l l - graded 20/200 Brenda sand were prepared i n a loose state using the s l u r r y deposition method and the water p l u v i a t i o n method. The samples were set i n a 2.5% g e l a t i n solution under a confining pressure of 20 kPa (using the procedure described by Emery e t . a l . , 1973). When s o l i d i f i e d , the membrane was removed and the sample cut into four equal horizontal s l i c e s . Grain s i z e d i s t r i b u t i o n and void r a t i o 81 of each s l i c e was then measured. The t e s t r e s u l t s are shown i n Figure 3.8 and Figure 3.9. The s l u r r y deposited sample may be seen to be homogeneous with respect to p a r t i c l e s i z e gradation (Figure 3.9). In contrast, the water pluviated sample shows considerable p a r t i c l e s i z e segregation (Figure 3.8). Both water pluviated and s l u r r y deposited samples appeared v i s u a l l y quite uniform, although water pluviated samples may have v i s i b l e layers of f i n e r and coarser grained s o i l i f i n s u f f i c i e n t care i s taken to maintain v i s u a l sample homogeneity. Void r a t i o d i s t r i b u t i o n with sample height of both water pluviated and s l u r r y deposited samples i s f a i r l y uniform, although a tendency toward a s l i g h t l y better uniformity may be noted i n s l u r r y deposited samples. The water pluviated specimen deposited at a s l i g h t l y looser state due to p a r t i c l e segregation during deposition (compare void r a t i o s i n Figures 3.8 and 3.9). In contrast, poorly- graded sand, which by d e f i n i t i o n cannot segregate, was found to be s l i g h t l y denser when deposited by p l u v i a t i o n than when deposited by s l u r r y deposition. The r e s u l t s of a s i m i l a r t e s t to determine the uniformity of a s l u r r y deposited s i l t y sand specimen with 14% s i l t content are also i l l u s t r a t e d i n Figure 3.9. I t may be noted that the s i l t y sand specimen i s remarkably homogeneous with respect to p a r t i c l e s i z e gradation over i t s e n t i r e height, even though i t has previously been densified and c y c l i c a l l y loaded to i n i t i a l l i q u e f a c t i o n . F i g u r e 3.8 G r a i n s i z e d i s t r i b u t i o n c u r v e s f o r h o r i z o n t a l l y q u a r t e r e d s e c t i o n s o f a water p l u v i a t e d sand sample M.l.T. GRAIN SIZE CLASSIFICATION LD i— i UJ >- CD m LU UJ LD UJ L J r r UJ SAND SILT COARSE MEDIUM FINE COARSE MEDIUM FINE 100 90 80 70 60 50 40 30 20 10 0 40 60 100 140 200 _j i i i U.S. STANDARD SIEVE SIZE VOID RATIO DISTRIBUTION (BRENDA 20/200 SAND) SECTION VOID RATIO 1 O • A TOTAL 0. 893 0. 892 0. 908 0. 924 0. 904 CLEAN WELL-GRADED WATER PLUVIATED 20/200 BRENDA SAND (LOOSEST STATE) Gc = 20 kPa - i — r 0. 01 (mm) 00 ]ure 3.9 G r a i n s i z e d i s t r i b u t i o n c u r v e s f o r h o r i z o n t a l l y q u a r t e r e d s e c t i o n s o f s l u r r y d e p o s i t e d sands M. I. T. GRAIN SIZE CLASSIFICATION SAND SILT COARSE MEDIUM FINE COARSE MEDIUM FINE 20 40 BO 100 140 200 U.S. STANDARD S IEVE S I Z E 00 i I I I I VOID RATIO DISTRIBUTION 90 \ (BRENDA 20/200 SAND) 80 \ SECTION VOID RATIO 70 \ 1 2 0. 788 0. 780 60 - \ y 3 0. 787 50 Yv 4 0. 800 40 30 W TOTAL 0.798 20/200 SAND + 13.5% SILT CLEAN WELL GRADED \ \ (AFTER CYCLIC LOADING, 20 ~ 20/200 BRENDA S A N D \ \ 95% RELATIVE DENSITY) 10 _ (LOOSEST STATE) \ CTr = 350 kPa 0 LTC' = 20 kPa \ I I i i i i i i i i n M i l i i 11 i i i i i i 1. 0 0. 1 GRAIN SIZE 0. 01 (mm) 84 A major advantage of the s l u r r y deposition method i s that regardless of s i z e gradation, the method produces homogeneous well mixed samples. The extent of sample mixing obtained i n the sample mixing tube controls sample homogeneity (see Figure 3.7(d)). This may be co n t r o l l e d by the s k i l l and experience of the researcher. I t was found that the s l u r r y deposition method produces homogeneous samples with repeatable r e s u l t s i f the sand s l u r r y i s mixed fo r at l e a s t twenty minutes f o r the sample s i z e used. The homogeneity of s i l t y sand specimens was more e a s i l y c o n t r o l l e d because the well-graded material had to be completely mixed before a uniform s l u r r y consistency and c o l o r were obtained. Four factors a f f e c t the choice of dimensions f o r the s l u r r y deposition method mixing tube: 1) s o i l specimen dimensions at the loosest state of deposition, 2) mixing tube diameter should be only s l i g h t l y smaller than the diameter of the completed s o i l specimen to maintain homogeniety of the s o i l i n the o r i g i n a l well mixed state during the t r a n s f e r process, 3) the s l u r r y within the mixing tube should have a high enough water content to allow mixing, and 4) the s l u r r y should have a low enough water content such that p a r t i c l e settlement distance i s kept to a minimum and sedimentation currents do not segregate the s o i l during sedimentation. A mixing tube volume which i s 5 to 10% la r g e r than the volume of sand deposited i n the loosest state was found to be most e f f e c t i v e . The dimensions of the 85 s l u r r y mixing tube used for t h i s study are shown i n Figure 3.7(b). A longer mixing tube was used to deposit w e l l - graded sand with 20 percent s i l t content because of the higher v i s c o s i t y and larger segregated volume of the s i l t y sand. Better sample homogeneity and perhaps looser f i n e grained samples might be attained i f the sand s l u r r y were mixed d i r e c t l y within the sample former and deposited d i r e c t l y within the sample membrane without the need fo r a t r a n s f e r from the mixing tube. This i s because s l i g h t d e n s i f i c a t i o n or segregation may occur during t r a n s f e r from the mixing tube. Such a method would require construction of a s p e c i a l i z e d mixing apparatus. 3.3.3.2 Replication The degree to which the s l u r r y deposition technique i s able to r e p l i c a t e specimens at a desired density i s i l l u s t r a t e d i n Figure 3.10. Results of monotonic undrained compression response of two i d e n t i c a l specimens of uniform 20/40 Brenda sand i s o t r o p i c a l l y consolidated to 200 kPa are shown. Excellent r e p e a t a b i l i t y may be noted i n the t e s t r e s u l t s . S i m i l a r r e p l i c a t i o n of specimens was possible with s i l t y sands using up to 20% s i l t content. For a given s i l t y sand, the same loosest state void r a t i o was obtained following s l u r r y deposition. Since the uniformity of specimens was insured by the deposition technique, HALF DEVIATOR STRESS, CTd/2 PORE PRESSURE AU (kPa) 98 87 r e p l i c a t i o n of specimens was e a s i l y attained at any targeted density. 3.3.3.3 Sand Fabric Since water pluviated sands have been shown to possess f a b r i c s i m i l a r to natural f l u v i a l sands (Oda, 1978), i t i s necessary to evaluate i f the s l u r r y deposition technique also gives r i s e to a s i m i l a r f a b r i c . This evaluation was done by comparing undrained monotonic response of specimens of Brenda 20/40 sand at i d e n t i c a l density, one prepared by water p l u v i a t i o n and the other by s l u r r y deposition technique. The r e s u l t s i l l u s t r a t e d i n Figure 3.11 show that water pluviated and s l u r r y deposited loose sands (near the loosest state possible by water p l u v i a t i o n and s l u r r y deposition methods) have s i m i l a r t r i a x i a l monotonic loading response. Both deposition methods produce considerably more d i l a t i v e response i n t r i a x i a l compression than i n extension loading. This i s t y p i c a l of a i r or water pluviated sands (Miura and Toki, 1982) and undisturbed natural sands (Miura and Toki, 1984). A s i m i l a r comparison of water pluviated and s l u r r y deposited ASTM Ottawa C-109 sand i s shown i n Figure 3.12. Sample preparation technique may be seen to a f f e c t behaviour of Ottawa C-109 sand shown i n Figure 3.12 more than that of poorly-graded Brenda 20/40 sand i l l u s t r a t e d i n Figure 3.11. The greater degree of v a r i a t i o n i s probably due to the fact that Ottawa sand, though considered uniform (Cu =1.5), i s Figure 3.11 Comparison of test results for slurry deposited and wate pluviated 20/40 Brenda sand 140 o Q_ CM ID 120- 100- 8 0 - 6 0 - 4 0 - 2 0 - 0 - 2 0 H - 4 0 EXTENSION COMPRESSION c -c(X) 1 2 1.011 35 0.995 39 1.009 35 1.009 35 0 40 80 120 160 (aVa;)/2 (kPa) 200 240 140 n 120 - 100 - 80 - o Q_ 60 - 40 - CM 20 - TD o - - 2 0 - - 4 0 - 2 SAMPLE PREPARATION 1 METHOD 1 SLURRY DEPOSITION 2 WATER PLUVIATION 1 2 • 1 " * V J - 1 0 - 5 0 AXIAL STRAIN (%) T 5 10 89 Fig. 3.12 Comparison of undrained response of slurry deposited and water pluviated Ottawa C—109 sand o o_ CM O a: LU OC o D \ f i in t-, in ~ LU \ cc ZJ °- < LU DC o a. tn C; LO ac C M 2 ^ 1.0 0.8 0.6 - 0.4 - 0.2 - 0 120 80 40 0 § a i % b° -40 100 200 300 (a; + LT;)/2 (KPa) 400 SAMPLE PREPARATION METHOD EXTENSION COMPRESSION D rc(*) Dr„ c 'cW 1 SLURRY DEPOSITION 0.689 27 0.707 21 2 WATER PLUVIATION 0.691 26 0.705 21 EXTENSION 1 COMPRESSION •15 -10 - 5 0 5 AXIAL STRAIN (%) 10 15 more well-graded than Brenda 20/40 sand and thus i s more subject to s i z e segregation during p l u v i a t i o n through water than Brenda 20/40 sand. Grain s i z e segregation was v i s u a l l y observed on water p l u v i a t i o n of Ottawa sand. Apparently, grain s i z e segregation produced by p l u v i a t i o n through water makes a more well-graded sand i n i t i a l l y s t i f f e r or more d i l a t i v e at low s t r a i n l e v e l , such that i t behaves as i f i t were a more poorly-graded material (see Section 5.2). In contrast, at larger s t r a i n l e v e l , water pluviated segregated sand i s apparently l e s s d i l a t i v e than s l u r r y deposited well mixed sand. 3.3.4 Rumfflwry of s l u r r y Deposition Method To overcome inherent problems of reconstituted sand sample preparation methods a new technique c a l l e d the s l u r r y deposition method has been developed. Slurr y deposition sand samples are prepared i n a f u l l y saturated state within de-aired water to ensure f u l l saturation. Samples are mixed thoroughly as a saturated s l u r r y with l i t t l e excess pore water so as to minimize height of sand p a r t i c l e drop through water during deposition and thus control sedimentation currents and p a r t i c l e s i z e segregation during deposition. Samples are formed i n an i n i t i a l l y loose state with an i n i t i a l void r a t i o which i s generally larger than that obtained i n a comparable unsegregated water pluviated sand. I n i t i a l l y loose samples may be uniformly densified by mechanical v i b r a t i o n to obtain a desired void r a t i o . Slurry deposited samples are exceptionally homogeneous with respect to void r a t i o and p a r t i c l e s i z e gradation, regardless of gradation and fines content. The s l u r r y deposition method simulates well the s o i l f a b r i c found within a natural f l u v i a l or hydraulic f i l l deposit, yet creates homogeneous samples that can be e a s i l y r e p l i c a t e d as required i n laboratory t e s t s f o r fundamental studies of material behaviour. 3 .4 ASSEMBLY OF TRIAXIAL TEST APPARATUS Once the sample has been deposited within the s p l i t former and the top platen positioned, i n i t i a l sample height i s recorded to determine maximum s l u r r y deposition void r a t i o . Sample height i s again recorded once the top platen i s sealed with the sample membrane. The former vacuum i s removed and a 20 kPa vacuum i s applied to the pore pressure l i n e to confine the s o i l specimen. The volume change during consolidation under t h i s 20 kPa e f f e c t i v e stress i s recorded together with sample height and circumference a f t e r removal of the sample former, to determine i n i t i a l dimensions and void r a t i o . The t r i a x i a l c e l l i s then assembled and an LVDT reaction bar bolted to the top platen loading rod (see Figure 3.1) before the f i n a l sample height and volume change data are recorded and the pore pressure l i n e closed to seal the consolidation vacuum. The t r i a x i a l c e l l i s f i l l e d with de-aired water and transfered to the loading frame. Transducers f o r the determination of a x i a l load, pore pressure, c e l l pressure, and a x i a l deformation are then set to t h e i r i n i t i a l zero l e v e l s , and data zeros f o r a l l transducers are recorded by s t r i p chart or computerized data a c q u i s i t i o n system. The c e l l pressure l i n e i s attached to the t r i a x i a l c e l l and c e l l pressure increased to 20 kPa to bring the sample pore pressure to zero. The pore pressure l i n e i s now attached to the sample, and the c e l l pressure applied undrained i n 25 kPa increments to 120 kPa. Increase i n pore pressure i s recorded to evaluate and thus check f o r saturation. The sample i s then consolidated incrementally to the desired e f f e c t i v e stress state i s o t r o p i c a l l y or a n i s o t r o p i c a l l y as described i n Section 3.1.1.1. A back pressure of 100 kPa was used during consolidation. Each consolidation increment was maintained f o r ten to twenty minutes i n order to allow most of the secondary consolidation to be completed (Negussey, 1984; Mejia et a l . , 1988). 3 . 5 UNIFORMITY OF SAMPLE STRAIN DURING MONOTONIC AND CYCLIC LOADING St r a i n during undrained t r i a x i a l compression and extension loading was observed to be uniform f o r a x i a l 93 s t r a i n l e v e l s below 10 to 15%, as shown i n Figure 3.13. At s t r a i n l e v e l s greater than 10 to 15%, samples loaded i n compression developed a uniform bulge at the mid section followed by the development of shear planes at very large s t r a i n . Samples loaded i n extension developed thinning of the x-sectional area at a random height within the sample, which l e d to the evolution of conjugate shear planes and r a d i c a l sample necking. Often sample s t r a i n uniformity i s better maintained i n extension loading than compression loading due to reduced end e f f e c t s i n extension loading. Only t e s t r e s u l t s from the uniform region of s t r a i n have been included i n t h i s t h e s i s . Results from the region of large non-uniform s t r a i n have been excluded. 3.6 TEST PROGRAM The range of undrained monotonic loading behaviour of several Brenda sand types was determined over a range of confining stresses. Both monotonic compression and extension t e s t s were conducted. Several poorly-graded sands, a well-graded sand, a poorly-graded s i l t y sand, and a well-graded s i l t y sand were tested. A l l samples were consolidated from loosest state of s l u r r y deposition, to determine the range of maximum contractive response f o r the various sands tested. Consolidation from loosest state of s l u r r y deposition was also chosen as a reference density to provide a method of comparing d i f f e r e n t sand properties 94 SAMPLE SHAPE UP TO 10 TO 1 5 % STRAIN COMPRESSION EXTENSION "7" / / / DEVELOPMENT OF NON-UNIFORM STRAIN AT LARGE STRAIN LEVEL > 1 5 % Figure 3.13 Uniformity of sample strain during loading 95 which takes into account the o r i g i n of the s o i l deposit. The concept of r e l a t i v e density attempts to c l a s s i f y s o i l density as a state between extremes of loosest and densest state obtained by standard laboratory t e s t techniques. This may not r e f l e c t the mechanism of placement of f i e l d s o i l s . When t e s t r e s u l t s are compared at loosest state of consolidation a f t e r s l u r r y deposition, two factors are automatically considered: (1) various s o i l gradations undergo the same deposition and loading h i s t o r y as would be expected to occur i n a f l u v i a l or hydraulic f i l l deposit; and (2) because samples are at loosest possible s l u r r y deposited state, the maximum possible contractive behaviour of sand deposited within water can be assessed. In summary, the objectives of the monotonic loading t e s t program are as follows: (1) To determine the e f f e c t which s o i l gradation and s i l t content have upon the undrained loading response of Brenda sand consolidated from loosest s l u r r y deposition state; (2) To determine the e f f e c t which s o i l gradation and s i l t content have upon the difference between extension and compression loading response; (3) To determine the e f f e c t which s o i l gradation and s i l t content have upon the v a r i a t i o n of undrained response with consolidation stress l e v e l . Consolidation data from a l l tests was compiled to determine the e f f e c t which s o i l gradation and s i l t content have upon the range of void r a t i o , r e l a t i v e density, sand skeleton r e l a t i v e density, and consolidation s t r a i n s obtained during consolidation from loosest state of s l u r r y deposition. A s e r i e s of undrained c y c l i c t r i a x i a l t e s t s were conducted on i s o t r o p i c a l l y consolidated samples of: (1) poorly-graded s i l t y sand; and (2) well-graded s i l t y sand. S i l t y sand samples were prepared i n a very loose to dense state. C y c l i c t e s t s were conducted to determine the e f f e c t of s i l t content upon the following features of sand c y c l i c loading behaviour: (1) s t r e s s - s t r a i n response; (2) pore pressure generation; (3) v a r i a t i o n of c y c l i c strength at constant void r a t i o , r e l a t i v e density, and sand skeleton r e l a t i v e density; and ( 4 ) v a r i a t i o n of c y c l i c strength a f t e r consolidation from loosest state of s l u r r y deposition. 97 CHAPTER 4 TRIAXIAL TEST CONSOLIDATION RESULTS 4 . 0 INTRODUCTION The following sections present i s o t r o p i c consolidation data f o r the various sand materials tested. Differences and s i m i l a r i t i e s i n consolidation behaviour are discussed, including 1) void r a t i o s and r e l a t i v e d e n s i t i e s at loosest state of s l u r r y deposition and subsequent consolidation, 2) compressibility and bulk modulus during consolidation, 3) s t r a i n paths during consolidation, and 4) incremental s t r a i n r a t i o s to demonstrate inherent anisotropy during i s o t r o p i c consolidation. 4.1 ACCURACY OF CONSOLIDATION DATA Inaccuracies i n calculated volumetric s t r a i n s r e s u l t mainly from membrane penetration e f f e c t s . Measured volume chnages were therefore corrected for membrane penetration according to method 2 described by Vaid and Negussey (1984) (see Appendix A). Two sands (Brenda 60/100, 100/140 gradations) required no membrane penetration correction to measured volume changes. This was consistent with the c r i t e r i o n that membrane penetration e f f e c t s are minimal i f average p a r t i c l e s i z e i s les s than h a l f the membrane thickness. Well-graded 98 20/200 sand samples required a small correction, while coarse grained 20/40 Brenda sand and Ottawa C-109 sand required r e l a t i v e l y large membrane penetration corrections (see Table 3.2). Although the consolidation data presented i s considered r e l i a b l e , samples consolidated from as deposited loosest state were generally subject to greater v a r i a t i o n i n consolidation response. The difference i n consolidated density between d i r e c t l y comparable t e s t s , such as complementary compression and extension t e s t s , on the same sand at i d e n t i c a l consolidation stress was kept to a minimum, and was generally l e s s than 0.01 void r a t i o or 2% r e l a t i v e density. 4.2 VOID RATIO AND RELATIVE DENSITY DURING CONSOLIDATION Figure 4.1 to Figure 4.4 display consolidation data (void r a t i o versus logarithm of e f f e c t i v e confining stress) f o r the various Brenda clean and s i l t y sands. As shown i n these diagrams, the void r a t i o attained by clean sands a f t e r s l u r r y deposition and a f t e r placement of the top platen (nominal consolidation stress of 1 kPa) i s approximately equal to the maximum void r a t i o attained by ASTM standard minimum density t e s t s (see Table 3.2). A l l loosest deposited sands possess s i m i l a r consolidation curves although there i s a large v a r i a t i o n i n absolute void r a t i o among various sand gradations, e s p e c i a l l y between the FIGURE 4.1 TRIAXIAL TEST ISOTROPIC CONSOLIDATION RESULTS FOR LOOSE COARSE GRAINED 2 0 / 4 0 BRENDA TAILINGS SAND F IGURE 4 .2 TRIAXIAL TEST ISOTROPIC CONSOL IDAT ION R E S U L T S FOR L O O S E MEDIUM GRAINED 6 0 / 1 0 0 B R E N D A TAILINGS S A N D < on o > 1.20 - i 1.10 -A 1.00 - 0.90 - 0.80 0.70 0.60 - 0.50 - 0.40 r ° - 2 0 40 60 80 100 120 140 160 180 "I 1—l—l l l I I | 10 T 1 1—I I I I I | 10 T 1 1—I I I I I 10 EFFECTIVE ISOTROPIC CONSOLIDATION STRESS 0 \ (kPa) CO z LU o LU > 1— LU rr < o o F IGURE 4 . 3 TRIAXIAL TEST ISOTROPIC CONSOL IDAT ION R E S U L T S FOR L O O S E U N I F O R M FINE GRA INED 1 0 0 / 1 4 0 B R E N D A TAIL INGS S A N D  103 uniform sands (Figure 4.1 through Figure 4 .3) and the we l l - graded sand (Figure 4.4). The r e l a t i v e l y low maximum void r a t i o of the well-graded sand i s interpreted to be the r e s u l t of f i n e r p a r t i c l e s f i l l i n g voids between coarser p a r t i c l e s i n the well mixed well-graded sand. 4.3 VOLUMETRIC STRAIN DURING CONSOLIDATION Figure 4.5 displays how volumetric s t r a i n changes with confining stress l e v e l for the various clean sands consolidated from loosest s l u r r y deposition state. I t i s in t e r e s t i n g to note that the various Brenda sands tested show l i t t l e difference i n volumetric compressibility with change i n gradation or mean grain s i z e , even though, as noted i n Section 4.2, there i s a large difference i n t h e i r absolute void r a t i o s . This s i m i l a r i t y i n volumetric compressibility between the various gradations of Brenda sand may be a consequence of t h e i r s i m i l a r f a b r i c i n the loose state. The compressibility of loose Ottawa sand i s also shown i n Figure 4.5 f o r comparison purposes. This rounded sand may be seen to be considerably l e s s compressible than the angular t a i l i n g s sand, even though both sands were i n i t i a l l y at t h e i r loosest s l u r r y deposition state. Figure 4 . 6 shows compressibility of loose s i l t y 20/200 sand. The t e s t r e s u l t s indicate that s i l t content has l i t t l e e f f e c t on the compressibility of sand prepared at the 0.05 Figure 4.5 Volumetric strains of various clean sands during isotropic consolidation from loosest state of slurry deposition ISOTROPIC CONSOLIDATION CHARACTERISTICS FROM LOOSEST STATE OF SLURRY DEPOSITION 0.04 > CO < I— Ul O LU 0.03 - 0.02 - 3 0.01 - _ J O > POORLY GRADED 60/100 BRENDA S A N D ^ POORLY GRADED 20/40 BRENDA SAND WELL GRADED 20/200 BRENDA SAND OTTAWA C-109 SAND, NORMAL PREPARATION -0.01 200 400 EFFECTIVE CONFINING STRESS O"' (kPa) 600 o Figure 4.6 Volumetric strains of silty 20/200 Brenda sand during isotropic consolidation from loosest state of slurry deposition 0.04 106 loosest state of s l u r r y deposition, even though absolute void r a t i o undergoes a d r a s t i c reduction with an increase i n s i l t content as shown i n Figure 4 . 4 . This i s c l e a r l y a consequence of e s s e n t i a l l y constant sand skeleton void r a t i o regardless of s i l t content. Figure 4 . 7 displays the v a r i a t i o n of bulk modulus with i s o t r o p i c consolidation stress f o r various clean t a i l i n g s sands. Bulk modulus i s seen to increase l i n e a r l y with confining stress for each gradation of sand tested, with a s l i g h t v a r i a t i o n i n slope f o r each type of sand. This i s i n contrast with the more commonly quoted l i n e a r v a r i a t i o n with square root of confining stress. The i n i t i a l bulk modulus of each sand i s approximately the same with B Q = 4 . 5 MPa. A s i m i l a r v a r i a t i o n i n bulk modulus with stress l e v e l was found f o r s i l t y well-graded 20/200 sand at several deposition r e l a t i v e densities (see Figure 4 . 8 ) . A summary of compressibility c h a r a c t e r i s t i c s of s i l t y 20/200 sand and i t s v a r i a t i o n with s i l t content and sand skeleton r e l a t i v e density i s shown i n Figure 4 . 9 and Figure 4 . 1 0 . The figures show how the parameters B Q and K B i n the bulk modulus expression B = B Q + K Ba 3' vary with s i l t content and sand skeleton r e l a t i v e density. The t e s t r e s u l t s show that s i l t content has l i t t l e e f f e c t upon the compressibility of s i l t y sand, although s i l t content d r a s t i c a l l y reduces absolute void r a t i o . The bulk modulus of very s i l t y sand or s i l t y sand at larger sand skeleton r e l a t i v e density may be seen to increase s l i g h t l y with increasing s i l t content. Figure 4.7 Bulk modulus of various clean Brenda sands during isotropic consolidation from loosest state of slurry deposition ISOTROPIC CONSOLIDATION CHARACTERISTICS FROM LOOSEST STATE OF S L U R R Y DEPOSITION 1 1 1 1 1 1 1 0 200 400 600 EFFECTIVE CONFINING STRESS CT̂  (kPa) Figure 4.8 Bulk modulus of silty 20/200 Brenda sands during isotropic consolidation from loosest state of slurry deposition 13.33±.15% SILT e c = 0.442+.002 = 9 4 . 9 1 0 . 6 % c ( ske l ) = 57 .510 .1% 13.67±.14% SILT e c = 0.4881.001 Dr c = 83.11 0.3% 13.94±.13% SILT e c = 0.5341 .007 Dr c = 7 1 . 0 1 2 % D r c ( s k e l ) = 2 0 - ° ± 2 % 200 400 600 ISOTROPIC CONSOLIDATION STRESS LT' FIGURE 4.9 SUMMARY OF COMPRESSIBILITY CHARACTERISTICS OF SILTY WELL-GRADED 2 0 / 2 0 0 BRENDA TAILINGS SAND INITIAL SAND SKELETON VOID RATIO e { ( s k e|) 0.86 0.82 0.78 0.74 0.70 0.66 0.62 130 120 1 0 0 - BULK MODULUS B A C T 3 cri + Bo + D e i (skel). D r i (skel) stress after sample taken at 20 preparation. kPa effective X % SILT BY WEIGHT X * 0 * 4.3 + 7.5 • 14 A 21 80 60 30 - 1 0 0 10 20 30 40 50 60 INITIAL SAND SKELETON RELATIVE DENSITY Drj ( s k e|) 70 FIGURE 4 . 1 0 SUMMARY OF INITIAL COMPRESSIBILITY CHARACTERISTICS OF SILTY WELL-GRADED 2 0 / 2 0 0 BRENDA TAILINGS SAND INITIAL SAND SKELETON VOID RATIO e; ( s k e | ) 12 11 10 9 8 7 6 5 A- 3 2 1 • 0 0 .86 0 .82 0 .78 0 .74 0 .70 0 .66 0 .62 J—i—i—I—i—i—i—I—l—i i I i i i I i i i I ' ' ' I ' l l BULK MODULUS B = = K0CT3 + Bo • e i (skel)- Drj (skel) taken at 20 k P a ef fect ive s t ress af ter s amp le p repara t ion . % SILT BY WEIGHT * 0 * 4.3 + 7.5 • 14 A 21 J 1 r—1 i 1 1 1 1 1 1 1 1 1 1 — r - 1 0 0 10 2 0 3 0 4 0 5 0 6 0 INITIAL SAND SKELETON RELATIVE DENSITY Drj ( s k e|) 70 I l l 4 . 4 AXIAL AND RADIAL STRAIN DURING CONSOLIDATION Although the magnitude of volumetric s t r a i n during consolidation i s s i m i l a r f o r the various loose clean t a i l i n g s sands tested, there i s a large v a r i a t i o n i n the d i s t r i b u t i o n of a x i a l versus r a d i a l s t r a i n f o r each sand, as shown i n Figure 4.11. A l l sands prepared using the s l u r r y deposition or water p l u v i a t i o n technique show much greater r a d i a l s t r a i n than a x i a l s t r a i n during i s o t r o p i c consolidation. This indicates that these r e c o n s t i t u t i o n techniques give r i s e to a f a b r i c that i s inherently more compressible i n the horizontal than i n the v e r t i c a l d i r e c t i o n . This type of behaviour has been observed by other workers including Negussey (1984), Ishihara and Okada (1982), and has been suggested as a method for the measurement of inherent anisotropy by El-Sohby (1969). The slope of the consolidation s t r a i n path (incremental s t r a i n r a t i o , see Figure 4.12) may be used as an i n d i c a t o r of the difference between r a d i a l and v e r t i c a l compressibility of a sand sample. I f a x i a l s t r a i n equals r a d i a l s t r a i n during i s o t r o p i c consolidation, the incremental s t r a i n r a t i o would be 1.0 and sand compressibility would be i s o t r o p i c . I f the incremental s t r a i n r a t i o i s not equal to 1.0, the compressibility of sand would be anisotropic. I t i s important to note that Figure 4.11 Strain paths of various clean sands during isotropic consolidation from loosest state of slurry deposition 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 AXIAL STRAIN £ a Figure 4.12 Incremental strain ratios of various clean sands during isotropic consolidation from loosest state of slurry deposition WELL GRADED 20/200 BRENDA SAND 1 1 1 1 1 1 1 0 200 400 600 EFFECTIVE CONFINING STRESS &'c (kPa) 114 i s o t r o p i c s t r a i n r a t i o s do not ensure i s o t r o p i c monotonic loading response. The incremental s t r a i n r a t i o of loose Ottawa sand i s shown to be e s s e n t i a l l y constant with increasing consolidation stress, as was also observed by Negussey (1984). Various gradations of clean t a i l i n g s sand show a consistent v a r i a t i o n of incremental s t r a i n r a t i o with consolidation stress. At low consolidation stess l e v e l s , incremental s t r a i n r a t i o i s low, i n d i c a t i n g that v e r t i c a l compressibility i s much lower than r a d i a l compressibility. With increasing consolidation stress, incremental s t r a i n r a t i o increases to an e s s e n t i a l l y constant value. Apparently, the process of i s o t r o p i c consolidation a l t e r s the anisotropic compressibility properties of t a i l i n g s sand samples, when consolidated from a very loose state. Figure 4.12 shows that f i n e poorly graded t a i l i n g s sand (100/140 gradation) has the greatest anisotropy i n compressibility, while well-graded t a i l i n g s sand (20/200 gradation) shows the le a s t anisotropy i n compressibility. A large difference between a x i a l and r a d i a l s t r a i n s occurs only during v i r g i n consolidation. I f the sand i s i s o t r o p i c a l l y unloaded and reloaded a f t e r v i r g i n consolidation, the s t r a i n path r e f l e c t s isotropy (axial s t r a i n = r a d i a l strain) below the maximum past pressure. This feature has been used to estimate membrane penetration correct i o n (Vaid and Negussey, 1984, Method 2). Researchers who use dry or moist tamping to prepare sand samples, which 115 must be saturated a f t e r deposition, generally observe e s s e n t i a l l y i s o t r o p i c behaviour during v i r g i n consolidation following saturation (Miura and Toki, 1982). I t has also been observed that sands which are saturated a f t e r deposition are much less compressible during v i r g i n consolidation than water pluviated sands. One may conclude that sands which are prepared i n a moist or dry state and must be resaturated display a form of overconsolidation behaviour. Consolidation s t r a i n paths shown i n Figure 4.11 are dependent upon many factors, including void r a t i o , stress l e v e l , s t r a i n history, time dependent creep behaviour, and perhaps most importantly the f a b r i c that r e s u l t s from sample preparation technique. The s t r a i n paths shown i n Figure 4.11 are average r e s u l t s for several t e s t s performed on each sand type. 116 CHAPTER 5 UNDRAINED MONOTONIC LOADING BEHAVIOUR 5.0 INTRODUCTION The r e s u l t s of undrained monotonic loading t e s t s on clean and s i l t y Brenda sands are presented and compared. Tests were conducted on poorly-graded sands with d i f f e r e n t D50 (gradations 20/40, 60/100 and 100/140), a well-graded sand (20/200) with a D 5 0 s i m i l a r to that of 60/100 poorly- graded sand, and well-graded 20/200 sand which contained various amounts of s i l t (see Section 3.2.1.2 fo r grain s i z e d i s t r i b u t i o n s ) . Samples of each sand were prepared at loosest state of s l u r r y deposition. Consolidation from t h i s state y i e l d s s o i l which displays the most contractive undrained loading response expected for each water deposited material. Samples were i s o t r o p i c a l l y consolidated. Both t r i a x i a l compression and extension t e s t were performed over a range of confining stresses. Samples were tested from an i n i t i a l state of i s o t r o p i c consolidation i n order to emphasize the e f f e c t s which d i r e c t i o n of loading have upon s o i l behaviour. The e f f e c t s of inherent anisotropy i n water pluviated sand are i d e n t i f i e d i n t e s t r e s u l t s . S o i l properties s p e c i f i c to water pluviated sand are i d e n t i f i e d and discussed, and various methods of sand behaviour categorization are assessed. 117 5.1 UNIQUENESS OF UNDRAINED RESPONSE For saturated s o i l at a given consolidation and density state, the undrained s t r e s s - s t r a i n response and e f f e c t i v e stress path are unique regardless of the t o t a l stress path, as long as the d i r e c t i o n of major p r i n c i p a l stresses remains the same i n r e l a t i o n to the sand deposition d i r e c t i o n (Bishop and Wesley, 1973; Vaid et a l . , 1988). This i s shown i n Figure 5.1 f o r coarse-grained Brenda 20/40 sand i n compression loading by two d i f f e r e n t t o t a l stress paths (denoted A and B). Results of a conventional t r i a x i a l compression t e s t (with r a d i a l t o t a l stress constant) and an active t r i a x i a l t e s t (with a x i a l t o t a l stress constant) are shown. E s s e n t i a l l y i d e n t i c a l s t r e s s - s t r a i n response and e f f e c t i v e stress path may be noted f o r the two t e s t s . The undrained extension response i s also unique, although the extension e f f e c t i v e stress path i s i n general not i d e n t i c a l to compression path, as discussed i n Section 2.1.3.1. At a given confining pressure, undrained e f f e c t i v e stress path depends on void r a t i o , but i t may also be affected at the same void r a t i o by (1) p r e s t r a i n h i s t o r y (Finn et a l . , 1970; Seed et a l . , 1975; Ishihara et a l . , 1978, 1982), (2) membrane penetration, and (3) sample preparation method ( M u l i l i s et a l . , 1975; Marcuson and Townsend, 1974; Tatsuoka et a l . , 1986). Uniqueness of e f f e c t i v e stress path f o r a given loading mode requires that pore pressure generated during undrained F i g u r e 5.1 V e r i f i c a t i o n o f i n d e p e n d e n c e o f e f f e c t i v e s t r e s s p a t h f r o m t o t a l s t r e s s p a t h in u n d r a i n e d m o n o t o n i c c o m p r e s s i o n l o a d i n g of B r e n d a 2 0 / 4 0 s a n d 119 loading be dependent upon t o t a l stress path. This i s shown for compression t e s t A and B i n Figure 5.1. Absolute pore pressure response i s c l e a r l y not unique. The f a c t that pore pressure response i s not unique makes i t a rather poor index property f o r the comparison of s o i l behaviour subject to d i f f e r e n t modes of loading. 5.2 BEHAVIOUR OF CLEAN SANDS Figure 5.2 through Figure 5.4 display the monotonic loading behaviour of various clean Brenda sand gradations. The sands were consolidated from loosest state of s l u r r y deposition, to various l e v e l s of consolidation s t r e s s . For comparison purposes, the response of clean sands at 200 kPa consolidation stress has been summarized i n Figure 5.5. 5.2.1 Stress-Strain Response The r e s u l t s presented i n Figure 5.2 through 5.5 show t y p i c a l undrained s t r e s s - s t r a i n response of Brenda sand. A l l gradations show a considerable difference or anisotropy between extension and compression loading response. This sort of anisotropy i n s o i l behaviour has been observed f o r natural and reconstituted sands by several workers, including Ishihara et a l . (1978,1982), Chang et a l . (1982), Miura and Toki (1982), and Chung (1985). Test r e s u l t s show that anisotropy i n undrained response i s affected by both grain s i z e and gradation. Poorly-graded gradations of sand 120 Figure 5.2 Undrained monotonic triaxial test results for 20/40 Brenda sand 1 00 —I—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—r 0 100 200 300 400 500 600 (LTj < )/2 (kPa) 1 . o - 0.8 - AXIAL STRAIN £ 0 (%) 121 Figure 5.3 Undrained monotonic triaxial test results for 60/100 Brenda sand 0 100 200 300 400 500 600 K < )/2 (kPa) AXIAL STRAIN £ a (%) 122 Figure 5.4 Undrained monotonic triaxial test results for 20/200 Brenda sand 0 100 200 300 400 500 600 (C7>LT;) /2 (kPa) 1 _ o -15 -10 - 5 0 5 10 15 AXIAL STRAIN £ 0 (%) 123 Figure 5.5 Undrained monotonic triaxial test results for various sand gradations (LTj+CT'Vz (kPa) AXIAL STRAIN £ o (%) (20/40, 60/100 and 100/140) exhibit considerably more anisotropy than the well-graded 20/200 sand. Finer grained uniform 60/100 and 100/140 sands have t y p i c a l l y d i l a t i v e s o i l response i n compression loading, yet almost steady- state l i q u e f a c t i o n response i n extension loading. Well- graded 20/200 sand has l i m i t e d l i q u e f a c t i o n response i n extension loading, with larger strength at phase transformation state than observed i n any of the poorly- graded sands. The various Brenda sands which have been consolidated from loosest state of s l u r r y deposition show s i m i l a r behaviour i n compression loading but rather d i f f e r e n t behaviour i n extension loading. These r e s u l t s suggest that although the behaviour of d i f f e r e n t s o i l s i n one p a r t i c u l a r mode of loading may be s i m i l a r , t h i s does not ensure s i m i l a r behaviour i n other modes of loading. These r e s u l t s also suggest that s o i l s with d i f f e r e n t f a b r i c s may have e i t h e r d i f f e r e n t or s i m i l a r s o i l properties. I t i s suggested that compression loading t e s t r e s u l t s are s i m i l a r only because each s o i l was deposited at loosest s l u r r y deposition state. The density of sands deposited by v e r t i c a l settlement through water i s governed by the v e r t i c a l load bearing capacity of the material at low stress l e v e l . Apparently the loosest state v e r t i c a l compressibility properties of the various s o i l gradations i s s i m i l a r , with t h i s s i m i l a r i t y being maintained at higher consolidation stress l e v e l . 125 5.2.2 E f f e c t i v e Stress Path Response The various e f f e c t i v e stress path responses shown i n Figures 5.2 through 5.5 emphasize the e f f e c t of mode of loading on undrained behaviour. Figure 5.5 shows that uniform f i n e grained sands (60/100 and 100/140) have s i m i l a r behaviour, which i s considerably d i f f e r e n t from that of e i t h e r coarse grained 20/40 sand or well-graded 20/200 sand. The e f f e c t i v e stress path of coarse grained 20/40 sand i s probably affected by membrane penetration. Membrane penetration causes a c h a r a c t e r i s t i c s t i f f e n i n g of undrained response due to lower induced pore pressures. Membrane penetration e f f e c t s during undrained loading are believed to be minor f o r the f i n e r grained sands tested (see Table 3.2). A p e c u l i a r feature of the compression loading response of the well-graded 20/200 sand shown i n Figure 5.5 i s that at low deviator stress and s t r a i n l e v e l , t h i s sand i s s l i g h t l y s o f t e r than poorly-graded sand, yet at high deviator stress and s t r a i n l e v e l , well-graded sand i s s l i g h t l y s t i f f e r than poorly-graded sand. This behaviour i s probably a r e s u l t of the difference i n f a b r i c within w e l l - graded and poorly-graded water-pluviated sands. E f f e c t i v e stress path p l o t s show quite c l e a r l y that well-graded sand behaviour i s les s anisotropic than poorly- graded sand behaviour. 126 5.2.3 Pore Pressure Response As described i n Section 5.1, pore pressure response i s not unique, but dependent upon t o t a l stress path. Pore pressure data shown i n Figures 5.2 through 5.5 r e f l e c t s the influence of t o t a l stress path and mode of loading. Direct comparison of pore pressures generated i n compression and extension loading may lead to u n r e a l i s t i c conclusions, due to the difference i n t o t a l confining stress between compression and extension modes of loading. To separate shear induced pore pressure from changes i n pore pressure induced by changes i n mean normal stress, pore pressure data has been plotted using Henkel's (1960) pore pressure parameter 'a' (see Figure 5.6). Figure 5.6 shows c l e a r l y that shear induced pore pressures generated i n extension loading are considerably larger than those generated i n compression loading f o r a l l sand types tested. Fine grained uniform sands are shown to have the greatest anisotropy i n loading response, while well-graded sand i s shown to have the lea s t anisotropy i n loading response. Pore pressure parameter 'a' curves are normalized with respect to consolidation stress. The curves show that anisotropy i n s o i l response i s reduced by increasing i s o t r o p i c consolidation stress. There i s a general trend towards larger 'a' parameters i n compression loading and smaller 'a' parameters i n extension loading, at higher i s o t r o p i c consolidation stress. There i s also a general 127 Figure 5.6 Plot of Henkel's pore pressure parameter ' a ' versus s tra in for various gradations of undrained Brenda sand 16 oc LU s: < OC < a. oc CO to LU OC Q_ LU CC O a. co LU 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 5- 4 3 2 1 0 5- 4 3 2 1 0 -1 - 1 5 AU = A CF_ + a 3 ( A T o c t) AL7b - (ALTJ +Acrz +Acr 3 )/3 ?oct- CCLT,-0^).(0^-LT3)»cCr3-flri)]/3 60/100 BRENDA SAND (SEE FIGURE 5.3) 20/40 BRENDA SAND (SEE FIGURE 5.2) 20/200 BRENDA SAND (SEE FIGURE 5.4) -5 0 5 A X I A L STRA IN £ (%) 10 15 128 trend toward smaller v a r i a t i o n i n 'a' parameter with v a r i a t i o n i n s t r a i n l e v e l at higher consolidation stress. 5.2.4 E f f e c t of Consolidation Stress An increase i n i s o t r o p i c consolidation stress a f f e c t s extension and compression loading response d i f f e r e n t l y . A l l sand types show a tendency toward more contractive response i n compression loading at higher consolidation s t r e s s . This contrasts s i g n i f i c a n t l y with a tendency toward more d i l a t i v e response i n extension loading at higher consolidation s t r e s s . There i s a trend towards lessening difference between compression and extension response with increasing consolidation s t r e s s . This implies a change i n the nature of inherent anisotropy with changing l e v e l of consolidation s t r e s s . The observed tendency towards more i s o t r o p i c behaviour at higher consolidation stress i s s i m i l a r to that observed i n consolidation s t r a i n data (see Section 4.4). Consolidation stress l e v e l i s observed to have l e s s of an e f f e c t upon sample anisotropy than s o i l gradation. The observed increase i n dilatancy of extension loading response with increasing i s o t r o p i c consolidation stress may only be c h a r a c t e r i s t i c of lower stress range behaviour of water pluviated sand, due to the highly anisotropic nature of water pluviated sand a f t e r deposition. Different behaviour may be observed at much larger consolidation s t r e s s , or under anisotropic consolidation stress conditions. Anisotropic consolidation with v e r t i c a l stress 129 larger than horizontal stress has been observed to decrease dilatancy and strength i n extension loading. 5.2.5 E f f e c t of Grain Size and Gradation For loosest state s l u r r y deposited sands, compression loading response i s s i m i l a r regardless of gradation, while extension loading response i s apparently quite dependent upon gradation. The observed trend toward more d i l a t i v e behaviour i n extension loading i n more well-graded sand could be explained by the trend toward lower absolute void r a t i o within more well-graded sand. This explanation i s not completely convincing because i t cannot explain the small difference i n compression loading response between the various sands tested. Consolidation from loosest state of s l u r r y deposition i s observed to produce v a r i a b l e r e l a t i v e d e n s i t i e s , although a l l sands consolidated from loosest s l u r r y deposition state have s i m i l a r bulk modulus or volume change c h a r a c t e r i s t i c s (see Section 4.3). There does not appear to be a simple r e l a t i o n s h i p between the r e l a t i v e density of s o i l and i t s undrained loading response. The differences between responses of d i f f e r e n t s o i l gradations can be best explained as differences i n s o i l f a b r i c and inherent anisotropy which are the r e s u l t of differences i n s o i l gradation. Uniform sands show the greatest degree of anisotropy, while well-graded sands show a tendency toward more i s o t r o p i c behaviour. Coarse grained 20/40 sand shows a s l i g h t l y more d i l a t i v e response than other uniform sands, 130 which could be a consequence of membrane penetration e f f e c t s . Membrane penetration e f f e c t s are believed to be n e g l i g i b l e f o r other sands tested. 5.3 MATERIAL PARAMETERS Various material parameters, such as c r i t i c a l stress r a t i o , phase transformation angle, ultimate f r i c t i o n angle (or f r i c t i o n angle at maximum o b l i q u i t y ) , and steady-state concepts have been used by various researchers (see Section 2.0) to characterize undrained behaviour, with the assumption that the material parameters are constant for a s p e c i f i c type of sand. Test r e s u l t s of Brenda t a i l i n g s sand indicate that sand material parameters such as phase transformation angle and f r i c t i o n angle at maximum o b l i q u i t y are indeed f a i r l y consistent between various t e s t samples and st r e s s paths, while other parameters such as c r i t i c a l s tress r a t i o and steady-state concepts are not generally applicable. Table 5.1 presents a summary of the material properties. 5.3.1 Ultimate F a i l u r e Envelope F r i c t i o n angle at maximum o b l i q u i t y (Ishihara et. a l . , 1975), or boundary surface f r i c t i o n angle (Chang et. a l . , 1982), has been shown to be f a i r l y constant f o r various types of sands tested using the undrained t r i a x i a l t e s t . This angle has a general dependence upon s o i l mineralogy and 131 Table 5.1 Sand sample undrained friction angles Undrained friction angle (Degrees) Compression Extension 0 U.t 0CSR t t 0CSR Brenda Sand Gradation 20/40 WP 37.5 35.2 37.5 34.5 18 20/40 SD 35.6 34.2 26.4 33.0 31.7 17.0 60/100 SD 36.0 34.0 26.4 36.0 34.0 16.1 100/140 SD 35.3 33.0 12.0 20/200 SD 36.0 33.9 34.0 31.4 19.0 C-109 (Chem, 1985) 38.2 36.5 25.1 Ottawa C - 1 0 9 Sand SD 30.6 29.5 20.0 9.1 WP 30.9 30.1 21.5 31.5 29.5 10.7 (Chern, 1985) 31.5 29.5 23.5 (Chung, 1985) 31.5 29.5 23.0 31.5 29.5 13.5 WP = Loosest state water pluviated sand SD = Loosest state slurry deposited sand the i n t r i n s i c angle of f r i c t i o n between mineral grains. Some researchers have found s l i g h t v a r i a t i o n s i n t h i s angle f o r a si n g l e type of sand material as follows: (1) some v a r i a t i o n with stress and s t r a i n l e v e l , f i r s t increasing with increasing s t r a i n and then decreasing to phase transformation angle at very large s t r a i n (Castro et. a l . , 1982, see Figure 2.2), (2) some increase with an increase i n r e l a t i v e density (Chang et. a l . , 1982, Miura and Toki, 1982), (3) some v a r i a t i o n between t r i a x i a l extension and compression t e s t s (Chang et. a l . , 1982, Miura and Toki, 1982), and (4) some v a r i a t i o n with sample preparation technique or sand f a b r i c (Miura and Toki, 1982). As shown i n Table 5.1, a f r i c t i o n angle at maximum o b l i q u i t y of 36 degrees i s f a i r l y consistent f o r a l l Brenda sand gradations tested i n compression loading. Extension loading r e s u l t s are not as consistent as compression r e s u l t s , varying from 36 degrees f o r 60/100 sand to 34 degrees f o r 20/200 sand and 33 degrees f o r 20/40 sand. The s l i g h t v a r i a t i o n s i n extension f r i c t i o n angles at maximum o b l i q u i t y could be due to several factors, including the following: (1) v a r i a t i o n with e f f e c t i v e stress l e v e l , as extension loading stress paths reach ultimate f a i l u r e at much lower e f f e c t i v e confining stress than compression loading stress paths, (2) some natural v a r i a t i o n i n material properties between extension and compression loading for d i f f e r e n t sand gradations, (3) incomplete development of 133 ultimate f r i c t i o n angle i n the stress and s t r a i n range tested. Some extension t e s t r e s u l t s show a marked decrease i n maximum o b l i q u i t y f r i c t i o n angle at large s t r a i n (greater than 10 to 15%) due to the development of conjugate extension f a i l u r e planes. The development of non-uniform s t r a i n s i n extension t e s t r e s u l t s can be e a s i l y i d e n t i f i e d by t h i s marked decrease i n boundary envelope f r i c t i o n angle. The t e s t data derived from s t r a i n ranges which are non- representative of elemental s o i l behaviour have been omitted. I t may be that f r i c t i o n angles at maximum o b l i q u i t y of various sand gradations i n compression loading are s i m i l a r because s t r e s s - s t r a i n behaviour i n compression loading i s s i m i l a r (see Figure 5.5). S t r e s s - s t r a i n behaviour i n extension loading i s considerably d i f f e r e n t f o r the various gradations of loose sands tested. Sand f a b r i c e f f e c t s which produce the v a r i a t i o n of s t r e s s - s t r a i n behaviour i n extension t e s t s may also account for the v a r i a t i o n i n ultimate f r i c t i o n angles i n extension loading (see Section 2.1 and 2.2). 5.3.2 Angle of Phase Transformation Phase transformation angles f o r the various sands tested are summarized i n Table 5.1. Sand samples prepared by s l u r r y deposition have s i m i l a r phase transformation angles as samples prepared by water p l u v i a t i o n . Extension phase transformation angles generally show greater v a r i a t i o n with sand gradation than compression angles. Phase transformation angles are consistently 1 to 2 degrees less than the angles of maximum o b l i q u i t y . As with ultimate f r i c t i o n angles described i n the previous section, extension phase transformation angles may be s l i g h t l y d i f f e r e n t between d i f f e r e n t gradations due to differences i n sand f a b r i c s . 5.3.3 C r i t i c a l Stress Ratio C r i t i c a l stress r a t i o s of Brenda sand (see Section 2.1.1) are quite variable between compression and extension loading (Table 5.1), thus CSR values may be assumed to be a function of mode of loading. Compression loading CSR- f r i c t i o n angle values (obtained i n higher consolidation stress samples only) are f a i r l y constant at 26 degrees. Extension loading CSR values are much lower and have been shown to vary with (1) i n i t i a l sample preparation r e l a t i v e density before consolidation (Chung, 1985), and (2) factors such as sample preparation technique or sample s t r a i n h i s t o r y (see Section 2.1). Table 5.1 indicates that c r i t i c a l stress r a t i o i n extension loading also varies with s o i l gradation when consolidation from loosest state of s l u r r y deposition i s used as a s o i l density reference. Extension CSR values f o r a s p e c i f i c sand gradation and i n i t i a l preparation density are found to be constant with increasing confining stress over the consolidation stress 135 range tested, as has been found for Ottawa C-109 sand which i s i s o t r o p i c a l l y consolidated to various stress l e v e l s from the same i n i t i a l preparation density (Chung, 1985). As a generalization, one may state that more anisotropic poorly- graded sands are more l i k e l y to have lower CSR values than well-graded sands. From t e s t r e s u l t s , one may conclude that a compression loading CSR-friction angle value of 26 degrees i s a maximum value f o r Brenda sand, because i t i s observed i n samples which have only minor l i m i t e d l i q u e f a c t i o n behaviour and are generally d i l a t i v e i n t r i a x i a l compression loading. Lower CSR values are possible and depend upon the factors described above. Thus i t may be unconservative to assume a design CSR value based upon compression loading t e s t r e s u l t s , as lower CSR values are possible and indeed l i k e l y i n some f i e l d loading conditions. Sand micro-fabric factors which determine CSR values i n undrained loading are probably d i f f e r e n t i n compression and extension loading (see Section 2.2 and Section 7 . 0 ) . Generalizations made about compression loading CSR values (Castro, 1982, Sladen et. a l . , 1985, Mohamad and Dobry, 1986) may not apply to extension loading CSR values, CSR values determined from loading conditions other than the t r i a x i a l compression t e s t , or CSR values determined from samples which are prepared i n a d i f f e r e n t manner or have a s t r a i n h i s t o r y which d i f f e r s from that used i n the t e s t s e r i e s upon which the generalizations are based. 136 5.3.4 Steady-State Concepts The t r i a x i a l t e s t r e s u l t s show c l e a r l y that steady state concepts (Castro et a l . , 1982) do not apply to the undrained loading response of Brenda sand. Steady state concepts imply that undrained strength i s s o l e l y a function of s o i l void r a t i o , and i s not dependent upon the d i r e c t i o n of loading or the type of t e s t performed. Undrained t e s t s performed on water pluviated Brenda sands c l e a r l y do not f i t these c r i t e r i a (Chung, 1985 shows a s i m i l a r dependence of undrained strength upon d i r e c t i o n of loading i n water pluviated Ottawa C109 sand). I f only compression t e s t r e s u l t s up to 600 kPa e f f e c t i v e confining stress are considered, Brenda sand i s found to be non-susceptible to l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n . I f extension behaviour i s considered, Brenda sand i s found to be highly contractive and susceptible to l i q u e f a c t i o n , e s p e c i a l l y at low consolidation stress l e v e l s . Such dependence of s o i l dilatancy and undrained strength on d i r e c t i o n of loading would have serious implications i n the use of steady state concepts of design (Castro et a l . , 1982), wherein a unique steady state l i n e obtained from compression t e s t s i s the key assumption. I t would be negligent not to consider t r i a x i a l extension t e s t r e s u l t s i n an analysis of sand l i q u e f a c t i o n resistance. The difference i n the observed compression versus extension response of water pluviated sand i s a r e f l e c t i o n of the inherent anisotropy of the material with respect to 137 the d i r e c t i o n of maximum p r i n c i p a l stress of loading. The angle between the maximum p r i n c i p a l stress and the deposition d i r e c t i o n ( v e r t i c a l under gravity) i s designated a. Compression mode corresponds to a=0° while the extension mode corresponds to a=90°. Softer response under horizontal loading (as also noted i n consolidation s t r a i n data, Section 4.4) i s mainly responsible for contractive behaviour i n extension but d i l a t i v e behaviour i n compression loading. A s i m i l a r difference i n t r i a x i a l compression and extension undrained response has been reported by others (Bishop, 1971; Miura and Toki, 1982; Hanzawa, 1980; Chang et a l . , 1982; Chung, 1985). Recent undrained t e s t i n g using the hollow cyli n d e r t e s t apparatus which may induce a f u l l range of v a r i a t i o n of maximum p r i n c i p a l stress d i r e c t i o n from Q=0 to a=90 degrees shows that water pluviated sand undergoes systematic weakening under increasing a (Symes et a l . , 1985; Shibuya and Hight, 1987). These t e s t r e s u l t s indicate that water pluviated sand i s most contractive under a t r i a x i a l extension mode of loading, and l e a s t contractive or most d i l a t i v e under a t r i a x i a l compression mode of loading. The nature of inherent anisotropy i n moist tamped specimens appears to be s i m i l a r but possibly not as pronounced as that i n water deposited sands (Hedberg, 1977). This could be attributed to one-dimensional v e r t i c a l compression i n the forming mold s i m i l a r to that which occurs during water deposition. Consequently, moist tamped materials would also show d i r e c t i o n a l v a r i a t i o n i n undrained 138 behaviour. I t i s surp r i s i n g that researchers engaged i n the development and application of steady state concepts have remained oblivious to path dependence of undrained response, when such a dependence i n clay has been rou t i n e l y considered since the pioneering work of Bjerrum (1972). Although the undrained strengths at phase transformation or steady state i n compression and extension are d i f f e r e n t , the f r i c t i o n angle i s e s s e n t i a l l y i d e n t i c a l . Therefore, the phase transformation or steady state l i n e f or contractive response i n void r a t i o stress space (Vaid and Chem, 1985) i s not unique, though these l i n e s are e s s e n t i a l l y unique i n e f f e c t i v e stress space. These differences i n undrained steady state or phase transformation strength are due mainly to larger pore pressures induced i n extension on account on greater hor i z o n t a l compressibility. Under f i e l d loading conditions, one could expect a large v a r i a t i o n i n p r i n c i p a l stress d i r e c t i o n s , even within a simple s o i l embankment or foundation. Thus i t i s important that a d i r e c t i o n a l dependence of s o i l strength be considered i n the s t a b i l i t y assessment of s o i l structures. 5 . 4 EFFECT OF SILT CONTENT UPON UNDRAINED MONOTONIC LOADING RESPONSE The undrained e f f e c t i v e stress paths and s t r e s s - s t r a i n response of monotonically loaded s i l t y well-graded 20/200 sand samples deposited at loosest state by the s l u r r y deposition method and i s o t r o p i c a l l y consolidated to 350 kPa e f f e c t i v e stress are shown i n Figure 5.7. Since the loosest state void r a t i o obtained by s l u r r y deposition decreases s u b s t a n t i a l l y with increasing s i l t content (see Figure 4.4) the response shown i n Figure 5.7 represents a large range of void r a t i o s . The ASTM standard r e l a t i v e d e n s i t i e s of the loosest state samples are shown to increase s u b s t a n t i a l l y with increasing s i l t content (Figure 5.7), from 29% at zero s i l t content to 98% at 22.3% s i l t content. The sand skeleton void r a t i o of the samples (see Section 3.2.2.4 for a d e f i n i t i o n of sand skeleton void ratio) i s shown to vary l e s s with increasing s i l t content (Figure 5.7). Figure 5.7 shows that the compression loading behaviour of the s i l t y 20/200 sand i s d i l a t i v e with a trend towards increasing dilatancy as s i l t content i s increased. The behaviour i n extension loading i s contractive with l i m i t e d l i q u e f a c t i o n , and a trend towards le s s contractive behaviour as s i l t content i s increased. The compression behaviour appears to be more greatly affected by an increase i n s i l t content than the extension behaviour. Ishihara et. a l . (1980) suggest that r e l a t i v e density i s not a suit a b l e index f o r characterizing the behaviour of s i l t y sands. Instead they suggest the use of void r a t i o for comparing the behaviour of s i l t y sands. The void r a t i o and r e l a t i v e density data shown i n Figure 5.7 suggests that both r e l a t i v e density and void r a t i o are poor indices for characterizing the behaviour of s i l t y sands, because both 140 Figure 5.7 Undrained monotonic triaxial test results for silty 20/200 sand T i i i i i i i i i i i i i i i i — i i i i — i — i i i — i — i i—r 0 100 200 300 400 500 600 0Ja' < )/2 (kPa) 0.8 - AXIAL STRAIN Ea (%) 141 density parameters vary s u b s t a n t i a l l y with increasing s i l t content, yet s o i l behaviour i s not observed to vary a large amount with increasing s i l t content. The minor changes i n s o i l behaviour with increasing s i l t content suggest that the s i l t within the s i l t y sands may be occupying sand skeleton void space and f o r the most part have l i t t l e e f f e c t upon s o i l behaviour. To investigate the e f f e c t of s i l t content upon s i l t y sand behaviour, i t i s i n s t r u c t i v e to ignore the s i l t f r a c t i o n of the s o i l and compare s o i l properties i n terms of sand skeleton void r a t i o (see Section 3.2.2.4), as a l l s i l t y 20/200 sands tested have the same gradation and thus s i m i l a r sand skeletons. I t may be seen that consolidation of s i l t y 20/200 sand from loosest state of s l u r r y deposition produces samples which have s i m i l a r sand skeleton void r a t i o s (Fig. 5.7), i n contrast to t o t a l void r a t i o s which vary considerably with s i l t content. This may explain the observation that the sand behaviour does not change much as s i l t content i s increased. Figure 5.8 shows that phase transformation and angle of maximum o b l i q u i t y increase s l i g h t l y (up to 2 degrees) with increasing s i l t content. E f f e c t i v e f r i c t i o n angles of 20/200 sand i n extension and compression loading also become equal when s i l t i s added. As described i n Section 5.3, undrained f r i c t i o n angles have been found to vary s l i g h t l y with density and sand f a b r i c , thus i t i s not unexpected that they may also vary with s i l t content. Rowe (1962, 1971) shows t e s t r e s u l t s which indicate that the f r i c t i o n angle of Figure 5.8 Variation of near loosest state silty 20/200 sand undrained friction angles with silt content 4 0 - 3 9 - 3 8 - 3 7 - - ^ ~ - ~ - ^ B r ~ ^ ^ MAXIMUM OBLIQUITY ANGLE 36 J / / / / / 3 5 - PHASE TRANSFORMATION ANGLE ^ — 34-t 4 3 3 - B &— 3 2 - / B TRIAXIAL COMPRESS ION TEST 31 - _ TRIAXIAL EXTENSION TEST 3 0 - i i i i 1 i i i i l i i i i i i i i r ~ i — i — i — i — i — 0 5 10 15 2 0 2 5 SILT CONTENT BY WEIGHT (%) 143 a material increases with decreasing grain s i z e , which may account f o r the increase i n e f f e c t i v e f r i c t i o n angles of s i l t y 20/200 sand with increasing s i l t content. 144 CHAPTER 6 CYCLIC TRIAXIAL TEST RESULTS 6.0 INTRODUCTION C y c l i c t r i a x i a l t e s t s were conducted on samples of s i l t y Brenda 20/40 and 20/200 sand to determine the e f f e c t of s i l t content upon the resistance of s i l t y sand to l i q u e f a c t i o n . Both poorly-graded and well-graded sands showed s i m i l a r v a r i a t i o n i n c y c l i c strength with change i n s i l t content. Thus only the behavior of s i l t y well-graded 20/200 sand i s discussed i n d e t a i l , as natural s i l t y sands are i n general more well-graded. T r i a x i a l t e s t samples were i s o t r o p i c a l l y consolidated to 350 kPa e f f e c t i v e stress. The consolidation stress used i s within the range i n which l i q u e f a c t i o n of i n s i t u s o i l deposits i s generally encountered. Isotropic consolidation rather than anisotropic consolidation was chosen fo r the following reasons: (1) sample preparation i s simpler, (2) the e f f e c t of anisotropic consolidation upon undrained c y c l i c t r i a x i a l t e s t r e s u l t s i s complex and not well understood, with c o n f l i c t i n g views reported i n the l i t e r a t u r e (Lee and Seed, 1967, Lee et. a l . 1975, Seed et. a l . 1975, Seed, 1983, Castro, 1969, 1975, Casagrande, 1976, Castro and Poulos, 1977, and Castro et. a l . 1982), and (3) most co r r e l a t i o n s between f i e l d and laboratory behaviour of 145 s o i l s are based upon i s o t r o p i c a l l y consolidated t e s t samples. Anisotropic consolidation may increase or decrease the s u s c e p t i b i l i t y of a t r i a x i a l specimen to l i q u e f a c t i o n , depending upon many factors including degree of anisotropic consolidation, density, and sand type (Vaid and Chem, 1983, Mohamad and Dobry, 1986), and various factors which a f f e c t sand f a b r i c , such as method of specimen preparation. The e f f e c t of anisotropic consolidation has also been shown to be a function of method of loading. Seed (1979) shows that anisotropic consolidation a f f e c t s simple shear and t r i a x i a l t e s t r e s u l t s d i f f e r e n t l y . The c y c l i c t r i a x i a l t e s t does not, i n general, model a s p e c i f i c form of f i e l d c y c l i c loading. An element of f i e l d s o i l subject to c y c l i c loading may have p a r t l y stress and p a r t l y s t r a i n controlled boundaries, variable mechanisms of loading (from simple shear to plane s t r a i n ) , and v a r i a b l e d i r e c t i o n s of loading, a factor which i s important i f s o i l properties are anisotropic. The question then a r i s e s as to how one may best use the t r i a x i a l t e s t to determine c y c l i c strength of s o i l f o r c o r r e l a t i o n purposes. To address t h i s question, i t i s i n s t r u c t i v e to consider recent research on the undrained behavior of sand using the hollow cyli n d e r device, which can model the f u l l spectrum of loading conditions. Using the hollow cyli n d e r t e s t equipment, Symes et. a l . (1985) and Shibuya and Hight (1987) have shown that water pluviated sand i s l e a s t contractive and least 146 susceptable to l i q u e f a c t i o n i n a t r i a x i a l compression mode t o t a l stress path, yet most contractive and most susceptible to l i q u e f a c t i o n i n a t r i a x i a l extension mode t o t a l stress path. These t e s t r e s u l t s indicate that c y c l i c t e s t i n g of i s o t r o p i c a l l y consolidated t r i a x i a l specimens i n both extension and compression phases w i l l ensure that both most r e s i s t a n t and l e a s t r e s i s t a n t loading phases are included, such that one might hope to a t t a i n an average estimate of s u s c e p t i b i l i t y to l i q u e f a c t i o n which i s useful for c o r r e l a t i o n purposes. A factor to consider i n the s e l e c t i o n of a, c y c l i c loading t e s t technique i s stress and s t r a i n r e v e r s a l , which occurs i n t r i a x i a l t e s t loading between compression and extension phases. Stress and s t r a i n reversal has been shown by several workers (for example Vaid and Chem, 1983, Mohamad and Dobry, 1986, and others) to have a profound softening e f f e c t upon s o i l behavior, e s p e c i a l l y during the development of c y c l i c mobility due to the mechanical reorganization of s o i l p a r t i c l e s . The extent to which stress reversal and c y c l i c mobility may occur i n f i e l d loading i s disputed, but recent centrifuge studies (Lee and Schofield, 1988) indicate f i e l d loading conditions may induce the c y c l i c f l u c t u a t i o n of pore pressure and d i r e c t i o n a l hardening and softening of s t r e s s - s t r a i n response which i s generally associated with stress and s t r a i n reversal (see Figure 6.1). Thus for c o r r e l a t i o n 147 Figure 6.1a Typical undrained cyclic loading response of isotropically consolidated silty well-graded 20/200 Brenda sand 60- D — Q_ 40- 20- — \ 0- 1 - 2 0 - 1 - 4 0 - -60- C 150-i CYCLIC MOBILnY LOADING COMPRESSION EXTENSION 100 200 300 (0"^<)/2 (kPa) 400 D D. 100 - 50- 0 -50- -100- -150 SILTY 20/200 BRENDA SAND 4.55% SILT CONTENT e c= 0.673 Dr c= 46% ec(**r ° - 7 5 4 D rc(*..)= 3 2 % 0 V 2 0 % = 0.167 DEVELOPMENT OF CYCLIC MOBILITY STRAIN -15 -10 -5 0 AXIAL STRAIN £„(%) 10 NUMBER OF LOAD CYCLES N 148 Fig. 6.1b Comparison of the typical undrained cyclic loading response of poorly—graded 20/40 and well—graded 20/200 Brenda sand (both samples prepared at loosest state) POORLY-GRADED 20/40 SAND (analog data recorded on strip chart) <G'+(j')/2 CkPa) a r 149 purposes i t i s prudent to observe the e f f e c t s of c y c l i c loading with stress and s t r a i n r e v e r s a l . For the reasons described above, i t i s believed that i s o t r o p i c a l l y consolidated t r i a x i a l specimens which are symmetrically loaded i n extension and compression phases provide the most useful c y c l i c t r i a x i a l t e s t data for general c o r r e l a t i o n purposes. For the purposes of t h i s research, l i q u e f a c t i o n i n undrained t r i a x i a l loading i s defined as the development of 2.5% s i n g l e amplitude a x i a l s t r a i n (5% peak to peak a x i a l s t r a i n between extension and compression loading phases). I f steady-state l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n are not induced by c y c l i c loading, as i s the case for the majority of c y c l i c t e s t s performed on 20/200 sand, the development of 2.5% s t r a i n generally corresponds to the i n i t i a l occurrence of a transient 100% pore pressure r a t i o . The number of load cycles required to induce l i q u e f a c t i o n i s defined as N^. A representative example of data obtained from a sin g l e c y c l i c t r i a x i a l t e s t on s i l t y 20/200 sand i s shown i n Figure 6.1. The following sections present data obtained from 80 c y c l i c t r i a x i a l t e s t s performed on s i l t y 20/200 Brenda sand over a large range of densities, c y c l i c stress r a t i o s , and number of cycles to l i q u e f a c t i o n . The e f f e c t s of s i l t content upon e f f e c t i v e stress path, s t r e s s - s t r a i n response, pore pressure generation c h a r a c t e r i s t i c s , shear s t r a i n generation, and resistance to l i q u e f a c t i o n are discussed. 150 6.1 GENERAL RESPONSE Two d i f f e r e n t types of response are observed under c y c l i c loading: (1) c y c l i c loading which leads to the i n i t i a t i o n of steady-state l i q u e f a c t i o n or li m i t e d l i q u e f a c t i o n , with a very rapid generation of both pore pressure and shear s t r a i n below 100% pore pressure r a t i o , and (2) c y c l i c loading which produces a systematic increase i n pore pressure and s t r a i n with each load cycle, with the development of large c y c l i c mobility s t r a i n s only a f t e r a transient pore pressure r a t i o of 100% has been achieved. Steady-state l i q u e f a c t i o n or li m i t e d l i q u e f a c t i o n may only be i n i t i a t e d during c y c l i c loading i f i t i s possible under monotonic loading conditions. In addition, the sum of s t a t i c and c y c l i c stress must exceed phase transformation strength ( i n eithe r extension or compression phases). The development of large c y c l i c mobility s t r a i n i n r e l a t i v e l y few loading cycles may follow the occurrence of l i m i t e d l i q u e f a c t i o n . The c y c l i c loading response of s i l t y 20/200 Brenda sand shown i n Figure 6.1 i s generally c h a r a c t e r i s t i c of the w e l l - graded clean and s i l t y sands tested. The general character of the e f f e c t i v e stress path of well-graded sand under c y c l i c loading does not show a great deal of v a r i a t i o n with r e l a t i v e density, provided that l i m i t e d l i q u e f a c t i o n does not occur. Limited l i q u e f a c t i o n i n the well-graded sand was only observed to occur i n the extension phase of c y c l i c loading (as observed i n monotonic t e s t results) and only i n very loose well-graded sand samples which required l e s s than 10 cycles to achieve 2.5% s t r a i n . For the majority of samples which f a i l e d by the development of c y c l i c mobility s t r a i n , the difference i n loading response between loose and dense sands i s mainly the magnitude of deviator stress required to induce 2.5% s t r a i n i n a given number of cycles, and the ease with which c y c l i c mobility s t r a i n s are developed once a transient state of zero e f f e c t i v e stress has occurred. A x i a l s t r a i n s much les s than 1% were generally observed during pore pressure generation up to 60% pore pressure r a t i o . A x i a l s t r a i n s larger than 1% occurred with the development of l i m i t e d l i q u e f a c t i o n and/or with the development of c y c l i c mobility. Loose to medium dense sands generally developed large c y c l i c mobility s t r a i n s i n excess of 15% very quickly within a few load cycles a f t e r development of i n i t i a l zero e f f e c t i v e stress, even when a large number of load cycles were required to achieve i n i t i a l zero e f f e c t i v e stress (see Figure 6.2). Denser sands required a greater number of load cycles to achieve large c y c l i c mobility s t r a i n s a f t e r the occurrence of i n i t i a l zero e f f e c t i v e stress state, with very dense sands reaching a l i m i t e d c y c l i c mobility s t r a i n l e v e l before the development of conjugate shear planes i n the extension phase of loading. S t r a i n development was observed to be uniform as a rule, except a f t e r a large number of c y c l i c mobility loading cycles i n denser sands, or the development of conjugate Figure 6.2 Development of shear strain in wel l-graded 2 0 / 2 0 0 sand during cyclic loading 0 0 .2 0 . 4 0 .6 0 . 8 1 1.2 1.4 NORMALIZED NUMBER OF LOAD CYCLES N/N, shear planes i n extension loading a f t e r the development of large extension s t r a i n s . The development of extension phase shear planes i n a s o i l may be e a s i l y i d e n t i f i e d i n t e s t data, as e f f e c t i v e stress path on a modified Mohr diagram deviates from the boundary envelope during c y c l i c mobility loading. The major difference i n c y c l i c loading response between well-graded and poorly-graded sands i s the e f f e c t which gradation has upon steady-state l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n response. As observed i n monotonic t e s t r e s u l t s , poorly-graded sands are more susceptible to li m i t e d l i q u e f a c t i o n than well-graded sand. Thus well-graded sand i s more l i k e l y to f a i l by the development of c y c l i c mobility s t r a i n than poorly-graded sand. The range of c y c l i c strengths of well-graded and poorly-graded sands i s s i m i l a r , and within the range of c y c l i c strengths previously reported for other sands. This indicates that although more w e l l - graded sands are les s susceptible to l i m i t e d l i q u e f a c t i o n , both well-graded and poorly-graded sands are susceptible to pore pressure and c y c l i c mobility s t r a i n development under c y c l i c loading. Well-graded and poorly-graded sands show a marked difference i n the e f f e c t i v e stress path produced by the intermediate stages of c y c l i c loading. During intermediate loading cycles, with development of pore pressure i n the range from 20% to 60% of i n i t i a l e f f e c t i v e stress, the e f f e c t i v e stress path of well-graded sand appears to be more 154 symmetric between compression and extension loading phases on the modified Mohr diagram (see Figure 6.1b). The e f f e c t i v e stress path i s closer to v e r t i c a l on the modified Mohr diagram. This increased symmetry i n e f f e c t i v e stress path response i s s i m i l a r to that observed between monotonic compression and extension loading. The e f f e c t i v e stress path during intermediate cycles of loading could be considered to represent e s s e n t i a l l y e l a s t i c s o i l response. The recoverable changes i n pore pressure during loading are due e s s e n t i a l l y to e l a s t i c s o i l response and changes i n mean normal st r e s s . The observation that pore pressure response during t h i s stage of loading varies with gradation implies that pore pressure response i s not only a function of change i n mean normal stress, but also a function of the e l a s t i c volume changes induced during loading. The e l a s t i c s t r e s s - s t r a i n behaviour of a sand i s thus shown to be a function of gradation. More well-graded sand i s shown to have generally more contractive e l a s t i c s t r a i n s i n compression loading and more d i l a t i v e e l a s t i c s t r a i n s i n extension loading than poorly-graded sand. This v a r i a t i o n i n e l a s t i c loading response with gradation i s s i m i l a r to that observed i n p l a s t i c loading response (in monotonic t e s t r e s u l t s ) , where more well-graded sand shows le s s anisotropy i n dilatancy behaviour between compression and extension loading. The boundary surface f a i l u r e envelopes i n extension and compression loading phases were found to have e s s e n t i a l l y 155 the same f r i c t i o n angles, although with some v a r i a t i o n (plus or minus 1 degree) as observed i n monotonic t e s t r e s u l t s (Section 5.3.1). These f r i c t i o n angles were observed to change s l i g h t l y with a x i a l s t r a i n l e v e l , generally f i r s t increasing with increasing c y c l i c mobility s t r a i n , and then decreasing with larger s t r a i n , both i n extension and compression loading phases as shown i n Figure 6.3. F a i l u r e envelope f r i c t i o n angles were also observed to vary with trends i n c y c l i c mobility s t r a i n development. The development of a trend towards residual extension phase c y c l i c mobility s t r a i n was observed to coincide with larger extension and smaller compression phase boundary f r i c t i o n angles. S i m i l a r l y , the development of residual compression phase c y c l i c mobility s t r a i n was observed to coincide with lar g e r compression and smaller extension phase boundary envelope f r i c t i o n angles. The majority of t e s t samples generally developed larger extension s t r a i n s than compression s t r a i n s , thus extension phase boundary f r i c t i o n angles shown i n Figure 6.4 are generally l a r g e r than compression phase f r i c t i o n angles. The development of l a r g e r s t r a i n s i n the extension phase i s p a r t i a l l y due to s o i l anisotropy and s o f t e r extension loading response, and p a r t i a l l y due to the fact that s o i l samples were tested i n a load c o n t r o l l e d rather than a stress c o n t r o l l e d manner, and thus changes i n sample area produced larger extension and smaller compression maximum stresses at large s t r a i n s . The observed v a r i a t i o n i n f a i l u r e envelope f r i c t i o n angles with 156 Figure 6.3 Variation of boundary envelope friction angle during cyclic mobility loading 50 40 - 30 - 20 10 f- 0 - 1 5 50 40 30 ^ 5 a y 20 LU I—I Q_ ^ O £ 10 0 COMPRESSION SILTY 2 0 / 2 0 0 BRENDA SAND WITH 4.35% SILT BY WEIGHT TOTAL 59.7 0.627 SAND 47.1 0.701 SKELETON q& / 2 0 $ c - 0.251 0"c' = 350 kPa Ni = 5 CYCLES T - 5 0 5 AXIAL STRAIN (%) 10 15 COMPRESSION A n EXTENSION n ~~i i i i i " — i 1 1 1 1 1 1—'—r 0 2 4 6 8 10 12 NUMBER OF LOAD CYCLES N \ 14 Figure 6.4 Var iat ion of m a x i m u m boundary enve lope f r i c t ion angle of si lty 2 0 / 2 0 0 B renda sand with silt content and sand ske le ton relat ive dens i ty 158 c y c l i c mobility s t r a i n development may be an i n d i c a t i o n of change i n sand f a b r i c with a change i n c y c l i c mobility s t r a i n amplitude. The observed v a r i a t i o n s i n boundary envelope f r i c t i o n angles with d i r e c t i o n of loading and s t r a i n l e v e l may be q u a l i t a t i v e l y explained by considering the structures which control s o i l f a b r i c , as described i n Section 2.2. Maximum o b l i q u i t y f r i c t i o n angles were observed to increase with increasing sand skeleton r e l a t i v e density, as shown i n Figure 6.4. The f r i c t i o n angles shown i n Figure 6.4 generally have a scatter of plus or minus 1 degree. The scatter i n maximum o b l i q u i t y f r i c t i o n angles i s probably due to the v a r i a t i o n of f r i c t i o n angle with c y c l i c mobility s t r a i n development. Figure 6.4 also shows the v a r i a t i o n of maximum o b l i q u i t y f r i c t i o n angles with increasing s i l t content. The f r i c t i o n angles of loose sand (with a sand skeleton r e l a t i v e density le s s than 50 percent) was observed to increase somewhat with increasing s i l t content, as also observed i n monotonic t e s t r e s u l t s (Section 5.4). In contrast, maximum o b l i q u i t y f r i c t i o n angles of moderately dense to dense sands (with a sand skeleton r e l a t i v e density greater than 50 percent) were observed to change l i t t l e with increasing s i l t content. 159 6.2 STRESS-STRAIN RESPONSE WITHIN LOADING CYCLES Figure 6.5, Figure 6.6, and Figure 6.7 show t y p i c a l s t r e s s versus s t r a i n loops obtained during c y c l i c loading of clean and s i l t y well-graded 20/200 sands. Several researchers have reported s i m i l a r r e s u l t s f o r other sand types (for example Seed and Lee, 1966, Ishihara 1978). There are i n general three c h a r a c t e r i s t i c types of undrained c y c l i c loading s t r e s s - s t r a i n response: (1) p r e - l i q u e f a c t i o n response at low induced s t r a i n and pore pressure l e v e l such as shown i n Figure 6.5, (2) contractive response of the steady-state l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n types as shown i n Figure 6.6, and (3) c y c l i c mobility response as shown i n Figure 6.7, which develops with stress reversal following r e a l i z a t i o n of transient states of zero e f f e c t i v e s t r e s s . A singl e s o i l sample may undergo a l l three types of s t r a i n development, or ju s t types (1) and (3). In type (1) there i s a general f l a t t e n i n g of the hysteresis loops with increasing load cycles. Type (2) w i l l occur only i n c y c l i c loading i f sand i s contractive i n monotonic loading, and only i f c y c l i c stress exceeds phase transformation strength. In the well-graded sands tested, t h i s i s generally observed only i n moderately loose to very loose sand, or at higher e f f e c t i v e confining stress l e v e l . Type (1) and (2) s t r e s s - s t r a i n responses are i n general governed by (a) the i n i t i a l s o i l f a b r i c , and (b) the mode of loading. Figure 6.5 Typical cyclic loading stress—strain response at low strain level o D_ TO tn LU a: \-tn on o Lu 140 120 rod 80 60 40 20 0 - 2 0 - 4 0 - 6 0 - 8 0 -100 -120 -140 W E L L - G R A D E D 2 0 / 2 0 0 B R E N D A S A N D D r c = 4 5 % CTj = 3 5 0 k P a N, = 10 C Y C L E S CTd/2CT^c = 0 . 1 7 8 6 FIFTH LOAD CYCLE - 0 . 2 0 -0.15 - 0 . 1 0 - 0 . 0 5 0 AXIAL STRAIN (PERCENT) 0.05 0.10 o Figure 6.6 Cyclic loading stress—strain response of well—graded sand subject to limited liquefaction in extension loading 8 0 - 6 0 - 40 20-1 0 WELL GRADED 2 0 / 2 0 0 BRENDA SAND D r c = 2 2 % CTj = 350 kPa N| = 6 CYCLES Od/2LJic = 0 . 1 4 7 - 8 - 7 LIMITED LIQUEFACTION IN FIFTH LOAD CYCLE "i i r~ -3 - 2 -1 STRAIN HARDENING •5 - 4 - 3 - 2 -1 0 AXIAL STRAIN (PERCENT) Figure 6.7 Deve lopmen t of cyc l i c mob i l i t y s t ra in in l o o s e si l ty we l l—graded 2 0 / 2 0 0 B r enda s a n d -8 - 6 - 4 - 2 0 2 AXIAL STRAIN ( P E R C E N T ) CTi Type (3) response i s governed mainly by stress and s t r a i n reversal rather than stress l e v e l . When applied stre s s i s increased toward compression or extension during a si n g l e phase of loading, the s t r e s s - s t r a i n response i s characterized by s t r a i n hardening. I f stress reversal does not occur, c y c l i c mobility s t r a i n s are generally small and may quickly reach a l i m i t i n g value. I f c y c l i c stress reversal does occur, very large s t r a i n s may occur i n r e l a t i v e l y few load cycles, even though a large number of cycles of the same r e l a t i v e l y low deviator stress amplitude were required to achieve an i n i t i a l transient state of zero e f f e c t i v e s t r e s s . The development of s t r a i n hardening which i s observed i n each consecutive phase of mono-directional loading i s i n d i c a t i v e of a changing f a b r i c within the sample during the development of c y c l i c mobility s t r a i n . Sample f a b r i c becomes more d i l a t i v e under increasing stress, which causes the material to s t i f f e n i n the d i r e c t i o n of applied load. The s t i f f e n i n g of response i n the d i r e c t i o n of applied load i s contrasted by a softening of the response when p r i n c i p a l stresses are reversed. This indicates that the d i l a t i v e and stable f a b r i c established during loading i n one d i r e c t i o n i s also highly contractive and unstable with the onset of p r i n c i p a l stress reversal. The development of c y c l i c mobility s t r a i n occurs as a consequence of the f l u c t u a t i o n between s o i l f a b r i c s which are stable under each phase of compression and extension loading. The character of s t r e s s - 164 s t r a i n curves i n both phases of loading are s i m i l a r , which indicates that a s i m i l a r type of f a b r i c i s established i n each d i r e c t i o n of loading. The stable axis of the s o i l f a b r i c developed i n each phase of loading i s p a r a l l e l to the d i r e c t i o n of maximum p r i n c i p a l stress. The e f f e c t i v e (boundary envelope) f r i c t i o n angle mobilized during each phase of loading i s e s s e n t i a l l y the same, which also indicates a s i m i l a r i t y i n developed s o i l f a b r i c between each mode of loading. Incremental s t r e s s - s t r a i n loops i n progressive load cycles are s i m i l a r , although the magnitude of s t r a i n s generated i s s i g n i f i c a n t l y larger with each cycle. This f a c t suggests that the major difference between successive load cycles i s the amount of induced s t r a i n required to i n i t i a t e d i l a t a n t and hence s t r a i n hardening response. Type (3) s t r e s s - s t r a i n loops show only small recoverable s t r a i n during unloading of deviator stress. This means a great deal of hy s t e r e t i c work i s absorbed by the s o i l i n each cycle of loading. Perhaps the h y s t e r e t i c work absorbed by the s o i l during loading could be used to quantify the d i r e c t i o n a l s o i l f a b r i c produced by the loading. 6 . 3 PORE PRESSURE GENERATION DURING CYCLIC LOADING As i n monotonic loading r e s u l t s (Section 5.1) pore pressure generation during undrained c y c l i c loading i s a 165 function of t o t a l stress path. Figure 6.1 shows that there are generally large fluctuations i n pore pressure with changing mean normal stress. The magnitude of these fluctuations i s dependent upon t o t a l stress path. The c y c l i c e f f e c t i v e stress path i s , however, independent of t o t a l stress path i f the p r i n c i p a l stress d i r e c t i o n s remain constant. This dependence of induced pore pressure upon t o t a l stress path complicates the i n t e r p r e t a t i o n of pore pressure induced by c y c l i c loading. For laboratory t e s t i n g purposes, previous workers have defined the r e s i d u a l pore pressure induced by c y c l i c loading as the pore pressure l e v e l which remains a f t e r each loading cycle has been completed. The t o t a l stress l e v e l at t h i s point i s equivalent to the i n i t i a l t o t a l stress conditions. This d e f i n i t i o n of r e s i d u a l stress may not model c y c l i c loading conditions i n the f i e l d , because the residual t o t a l stress a f t e r c y c l i c loading i n the f i e l d has ceased may not correspond to the i n i t i a l t o t a l stress conditions. The standard d e f i n i t i o n of residual pore pressure i n laboratory t e s t samples i s adopted for the presentation of r e s u l t s i n t h i s t h e s i s . Residual pore pressure i s defined as the pore pressure at transient states of i s o t r o p i c t o t a l stress, as a l l samples were i n i t i a l l y consolidated under i s o t r o p i c s t r e s s . 166 6 . 3 . 1 E f f e c t of C y c l i c Stress Ratio Figure 6.8 shows how the residual pore pressure response of clean 20/200 sand (without s i l t ) v a r i e s with change i n c y c l i c stress r a t i o . The samples were i s o t r o p i c a l l y consolidated to 350 kPa e f f e c t i v e stress, with a r e l a t i v e density of 45% a f t e r vibratory d e n s i f i c a t i o n and consolidation. The number of cycles required to induce l i q u e f a c t i o n increases with decreasing c y c l i c stress r a t i o , as expected. Residual pore pressure generation curves i n Figure 6.8 have been normalized with respect to the number of cycles required to achieve l i q u e f a c t i o n , i n order to determine i f the character of normalized pore pressure generation curves i s s i m i l a r , as suggested by De Alba (1976). Normalized curves are often used to estimate pore pressure generation i n s i t u . This requires that the normalized curves have the same general shape. Figure 6.8 shows that the normalized pore pressure generation curves do not have the same shape. There i s a c l e a r trend i n the v a r i a t i o n of pore pressure generation with changing c y c l i c stress r a t i o . At low c y c l i c stress r a t i o , or a large number of cycles to i n i t i a l l i q u e f a c t i o n , normalized pore pressure apparently builds r e l a t i v e l y more quickly during i n i t i a l loading up to 30% pore pressure r a t i o , and r e l a t i v e l y more quickly a f t e r 70% pore pressure r a t i o . At higher c y c l i c stress r a t i o or few cycles to l i q u e f a c t i o n , normalized curves are almost l i n e a r over the Figure 6.8a Var ia t ion of pore pressure genera t ion in loose c lean 2 0 / 2 0 0 sand with change in cyc l ic s t ress rat io 1 1 1 1 1 1 1 1 1 1 i 1 1 0 0.2 0.4 0.6 0.8 1.0 1.2 NORMAL IZED N U M B E R OF LOAD C Y C L E S N / N | Figure 6.8b Var ia t ion of pore p ressure genera t ion in loose c l ean 20/200 sand with change in cyc l i c s t r e s s rat io NUMBER OF LOAD CYCLES N oo 169 range of loading cycles. Steady-state or l i m i t e d l i q u e f a c t i o n was not observed i n 45% r e l a t i v e density samples, regardless of the c y c l i c stress l e v e l . 6.3.2 E f f e c t of s i l t Content Figure 6.9 and Figure 6.10 show how the r e s i d u a l pore water pressure generated by c y c l i c loading i n s i l t y 20/200 sand v a r i e s with change i n s i l t content. The samples were prepared at near loosest state of s l u r r y deposition and i s o t r o p i c a l l y consolidated to 350 kPa, and thus have s i m i l a r sand skeleton void r a t i o s . The samples were subjected to a r e l a t i v e l y large c y c l i c stress r a t i o and thus required a small number of cycles to achieve l i q u e f a c t i o n . Residual pore pressure response may be noted to be e s s e n t i a l l y the same for sand with 0 to 15% s i l t content. These samples a l l developed l i m i t e d l i q u e f a c t i o n during the s i x t h load cycle. In contrast, the sand with 20% s i l t content required 9 cycles to develop l i q u e f a c t i o n without the occurrence of l i m i t e d l i q u e f a c t i o n , although the sand skeleton void r a t i o was bulked by the 20% s i l t content. Apparently a large s i l t content retards the development of l i m i t e d l i q u e f a c t i o n during c y c l i c loading. This was also observed i n monotonic t e s t r e s u l t s (Section 5.4) Figure 6.11 and Figure 6.12 also show how the residual pore pressure generated by c y c l i c loading i n s i l t y 20/200 sand v a r i e s with change i n s i l t content. As before, the samples were prepared at near loosest state of s l u r r y Figure 6.9 Variation of pore pressure generation with silt content in 20/200 sand subject to limited liquefaction D_ — 0.1 H r~ 1 1 1 1 1 1 1 1 1 1 0 2 4 6 8 10 12 NUMBER OF LOAD CYCLES N Figure 6.10 Variation of pore pressure generation with silt content in 20/200 sand subject to limited liquefaction — 0.1 -i 1 1 1 1 1 1 1 1 1 1 1 0 0.2 0.4 0.6 0.8 1 1.2 NORMALIZED NUMBER OF LOAD CYCLES N/N | Figure 6.11 Variation of pore pressure generation with silt content in 20/200 sand not subject to limited liquefaction NUMBER OF LOAD CYCLES N PORE P R E S S U R E RATIO A U / C X o o o o o o o o o o ^ O - ^ b u ^ u l C D N j O O C D CZ.T 174 deposition and i s o t r o p i c a l l y consolidated to 350 kPa, and thus have s i m i l a r sand skeleton void r a t i o s . The samples were subjected to a r e l a t i v e l y low c y c l i c stress r a t i o , and thus required a larger number of cycles to achieve l i q u e f a c t i o n . Figure 6.11 indicates that s u s c e p t i b i l i t y to l i q u e f a c t i o n and generation of residual pore pressure i s reduced by any addition of s i l t to the sand. The figure also indicates that the degree of increase i n c y c l i c strength with addition of s i l t i s not a d i r e c t function of percentage s i l t content. The v a r i a t i o n of c y c l i c strength with increasing s i l t content appears to be f a i r l y complex. In contrast to the normalized residual pore pressure generation curves of clean sand shown i n Figure 6.8, the normalized curves of s i l t y sand shown i n Figure 6.12 show l i t t l e v a r i a t i o n with increasing s i l t content. The s i l t y sand normalized curves are representative of one c y c l i c stress r a t i o (0.113) while the clean sand normalized curves represent v a r i a b l e c y c l i c stress r a t i o s . The shape of normalized curves appears to be more dependent upon magnitude of c y c l i c stress r a t i o and l e s s dependent upon s i l t content. 6 . 3 . 3 E f f e c t of Relative Density Figures 6.13 and 6.14 show how the residual pore pressure generated i n clean 20/200 sand during c y c l i c loading v a r i e s with r e l a t i v e density. There appears to be Figure 6.13 Variation of pore pressure development in clean well—graded 2 0 / 2 0 0 sand with change in relative density 0 -0.1 H 1 1 1 1 1 1——i 1 1 1 1 1 1 1 1 1 1 1 0 20 40 60 80 100 120 140 160 180 NUMBER OF LOAD CYCLES N Figure 6.14 Var ia t ion of pore pressure genera t ion in c lean wel l—graded 2 0 / 2 0 0 sand with change in relative dens i ty —0.1 H \ 1 1 1 1 1 1 1 1 1 1 0 0.2 0.4 0.6 0.8 1 1.2 NORMALIZED N U M B E R OF LOAD C Y C L E S N / N | 177 l i t t l e variation in normalized curves for sands with a relative density between 45% and 60%. The loosest sample at 22% relative density suffered limited liquefaction in extension loading during the sixth load cycle, thus the i n i t i a l part of the normalized curve suggests relatively lower pore pressure generation before the onset of liquefaction. The dense sample at 81% relative density shows a response which i s considerably different than that of looser samples, because the dense material i s generally dilative. A great deal of cyclic mobility strain must be developed before an i n i t i a l state of zero effective stress i s achieved. 6 . 3 . 4 Relationship Between Induced S t r a i n and Residual Pore Pressure Figure 6.15 shows how the residual pore pressure generated in clean 20/200 sand during cyclic loading varies with the development of shear strain. The only parameter which i s varied in the figure i s cyclic stress ratio and hence the number of cycles required to achieve liquefaction. Strain level i s defined as the difference between peak extension and peak compression strain during a given load cycle. The figure shows that there i s no direct relationship between residual pore pressure and shear strain level induced by cyclic loading. In fact, estimates of pore pressure based upon strain level may be off by 60% depending upon the magnitude of cyclic stress ratio. F igure 6 .15 Var ia t ion of pore p r e s su re genera t ion in c l e an 2 0 / 2 0 0 s a n d with shea r s t ra in level dur ing cyc l i c l oad ing 179 6.3.5 Relationship Between Residual Pore Pressure and Hysteretic Work Some researchers have attempted to r e l a t e residual pore pressure to damage induced i n a s o i l sample during c y c l i c loading (Finn and Bhatia, 1981). The damage induced within a s o i l specimen may be quantified by the irrecoverable work absorbed by the specimen during c y c l i c loading. This work may be e a s i l y calculated from the s t r e s s - s t r a i n loops observed during c y c l i c loading (Figure 6.16). Irrecoverable work absorbed per u n i t volume of s o i l i s equal to the cumulative area within h y s t e r e t i c s t r e s s - s t r a i n loops. The h y s t e r e t i c work absorbed by a sand specimen during c y c l i c loading has been shown by Towhata and Ishihara (1985) to c o r r e l a t e well with induced residual pore pressure. Their hollow cyli n d e r t e s t r e s u l t s f o r Toyoura sand show that the c o r r e l a t i o n between hy s t e r e t i c work and r e s i d u a l pore pressure i s v a l i d regardless of stress path and mode of loading. The development of residual pore pressure i n clean 20/200 sand during c y c l i c loading i s p l o t t e d versus irrecoverable work absorbed by the s o i l (see Figure 6.17). A good c o r r e l a t i o n i s observed between the two parameters fo r samples which undergo l i q u e f a c t i o n i n l e s s than 60 cycles. The c o r r e l a t i o n i s not as good for samples which require a large number of cycles to achieve l i q u e f a c t i o n , possibly due to accumulation of error i n the c a l c u l a t i o n of area within s t r e s s - s t r a i n loops, which increases p r o p o r t i o n a l l y to the number of loading cycles. D CL to tn tn LU cr j— tn 01 o Lu Q Figure 140 120 100 80 60 40 20 0 - 2 0 - 4 0 - 6 0 - 8 0 - 1 0 0 - 1 2 0 - 1 4 0 6 .16 Ca l cu l a t i on of i r r ecove rab le work a b s o r b e d by a so i l s p e c i m e n f r o m s t r e s s — s t r a i n r e s p o n s e obse r ved dur ing cyc l i c l oad ing APPROXIMATION OF HYSTERETIC WORK WITHIN STRESS-STRAIN LOOP D r c = 4 5 % CTc = 3 5 0 kPa N, = 10 CYCLES l 1 1 1 1— .10 - . 0 8 - . 0 6 i 1 1 r -.04 - . 0 2 THIRD LOAD C Y C L E STRESS-STRA IN LOOP WELL GRADED 2 0 / 2 0 0 BRENDA SAND —i 1 1 1 1 1 1— 0 0 .02 0 .04 0 .06 0 .08 AXIAL STRAIN ( P E R C E N T ) co o F igure 6 .17 Var ia t ion of pore p r e s su re genera t ion in l oose c l ean 2 0 / 2 0 0 s a n d with hys te re t i c work a b s o r b e d dur ing cyc l i c l oad ing 1.0 o b ZD O h-< LY. LU Cri ZD CO Ul LU m o_ LU a: o 0.9 - 0.8 - 0.7 0.6 0.5 - 0.4 0.0 oV = 350 kPa TEST N L cTd/2o-3C A B C D E F G 233 54 43 16 10 7 4 0.1 1 14 0.1314 0.1386 0.1620 0.1786 0.1929 0.2214 i — i i 1 1 1 1 1 "1 1 I I I I 111 1 1 I I II ! l | 1 1 I I I I 11 1 0 -2 1 0 - 1 1 10 10 IRRECOVERABLE SHEAR WORK ABSORBED PER UNIT VOLUME OF SOIL (kN/rn ) CO 182 Figure 6.18 shows the r e l a t i o n s h i p between the development of residual pore pressure and irrecoverable h y s t e r e t i c work i n clean sand at various r e l a t i v e d e n s i t i e s . Again there i s a good c o r r e l a t i o n between the two parameters, even though r e l a t i v e density, which controls the mode of f a i l u r e of the various samples under c y c l i c loading, i s v aried from 20 to 80%. Hysteretic work could provide an e f f i c i e n t method for the p r e d i c t i o n of residual pore pressure, i f s t r e s s - s t r a i n behaviour can be modelled s u f f i c i e n t l y well to predict h y s t e r e t i c damping. 6 .4 CYCLIC RESISTANCE DATA C y c l i c t r i a x i a l t e s t s were conducted on clean and s i l t y well-graded Brenda 20/200 sand samples to determine the e f f e c t of s i l t content upon c y c l i c strength. To show trends i n c y c l i c resistance, raw t e s t data from a ser i e s of samples with constant s i l t content and density i s processed by i n t e r p o l a t i o n of curves into d i f f e r e n t forms to allow d i f f e r e n t methods of comparison. 6 .4.1 C y c l i c Resistance Curves at Constant S i l t Content T r i a x i a l samples were prepared by c o n t r o l l i n g s i l t content and density. Thus the v a r i a t i o n of c y c l i c strength with number of cycles to l i q u e f a c t i o n on constant density contours can be d i r e c t l y observed from t e s t data, as plotted i n Section 6.4.1.1. To further reduce c y c l i c resistance F igure 6 .18 Var ia t ion of pore p ressu re genera t ion in l oose to dense c l ean 2 0 / 2 0 0 s a n d with hys te re t i c work a b s o r b e d dur ing cyc l i c l oad ing 0.0 H 1—i i i 1111| 1—i i i 11111 1—i i i 1111| 1—i i i 1111 10 " 2 10 ~1 1 10 10 2 IRRECOVERABLE SHEAR WORK ABSORBED PER UNIT VOLUME OF SOIL ( k N / m 2 ) 184 data such that the e f f e c t s of r e l a t i v e density and s i l t content may be better understood, raw t e s t data from Section 6.4.1.1 i s interpolated to determine contours of constant number of cycles to l i q u e f a c t i o n on c y c l i c stress r a t i o versus r e l a t i v e density p l o t s presented i n Section 6.4.1.2. 6.4.1.1 Raw Test Data p i u m t i w r y - constant Density Contours Figures 6.19 through 6.23 show c y c l i c stress r a t i o versus number of cycles to l i q u e f a c t i o n f o r clean and s i l t y 20/200 Brenda sand, with each sand at various r e l a t i v e d e n s i t i e s . The range of c y c l i c strengths shown ( c y c l i c stress r a t i o from 0.08 to 0.30) i s t y p i c a l of loose to moderately dense sands and s i l t y sands reported by other workers (for example Seed and Lee, 1966, Ishihara, 1980). In general, c y c l i c resistance curves are concave upward or s t r a i g h t i f the mechanism of s t r a i n development i s by c y c l i c mobility (as i s the case f o r most of the curves presented), and concave downward i f the mechanism of s t r a i n development i s by l i m i t e d l i q u e f a c t i o n or steady-state l i q u e f a c t i o n . Only very loose sand samples which were subjected to a r e l a t i v e l y large c y c l i c s t r e s s r a t i o developed l i m i t e d l i q u e f a c t i o n i n extension loading, as described i n Section 6.1. The v a r i a t i o n of c y c l i c strength with s i l t content of samples prepared near loosest state of s l u r r y deposition and i s o t r o p i c consolidation to 350 kPa i s shown i n Figure 6.23. At near loosest state, any increase i n s i l t content may be Figure 6.19 Cyclic loading liquefaction resistance curves of clean 20/200 Brenda sand 1 i i i i i i i i | 1 1 1 — i — i i i i | 1 1 1 — i — i i i i | 1 10 10 * 10 5 i-1 NUMBER OF CYCLES TO LIQUEFACTION (2.5% SINGLE AMPLITUDE STRAIN) N| ™ Figure 6.20 Cyclic loading liquefaction resistance curves of silty (4.3% silt) 20/200 Brenda sand 0.28 i 0.26 - 0.24 - \5> CM 0.22 - b 0.20 - K 0.18 H CO cn LU P£ 0.16 cn o 0 . 1 4 H >-o 0.12 - 0.10 - 0.08 SILTY 20/200 BRENDA SAND 4.341.1 5% SILT e c = 0.6251 .002 Dr_ = 60.0± 0.5% CT - 350 kPa © LIMITED LIQUEFACTION D r c (skeleton) = 47.5+0.5% e Q = 0.674+ .003 Dr. = 46.0± 0.5% D r c (skeleton) = ^2.31 0.5% e c = 0.7101.008 Dr c = 35.012.1% Dr / , , i \ = 22.612.2% u'c (skeleton) 4.0 1.20% SILT 4.5 1.21% SILT n 1—i—i i i i i 1—i—i—i t i i—i i i r~i 10 10 1 1 0 3 NUMBER OF CYCLES TO LIQUEFACTION (2.5% SINGLE AMPLITUDE STRAIN) N| CO Figure 6.21 Cyclic loading liquefaction resistance curves of silty (7.5% silt) 20/200 Brenda sand SILTY 20/200 BRENDA SAND 7.6 ±.30% SILT e = 0.605-+- .005 c _ Dr c = 61.0± 1.0% D r c (skel) = 36.6±0.5% CTC = 350 kPa 7.3 ±.15% SILT e c = 0.5571 .003 Drc = 74.5±0.7% D r c (skeleton) = 5 3 - 2 ± 1 - 0 % ® LIMITED LIQUEFACTION 7.76±.30% SILT e c = 0.655+ .006 Dr c = 47.2± 1.5% D r c (skeleton) = 20.011.5% 7.71 ±.10% SILT e c = 0.643± .006 Dr = 50.1 ± 1.0% D r c ( s k e . r 2 3 - 5 ± 1 - 5 % 1 1 1—i—i i i i~| 1 1 1—i—i—i i i | 1 1 1—i—i i i i | 10 10* 10 NUMBER OF CYCLES TO LIQUEFACTION (2.5% SINGLE AMPLITUDE STRAIN) N| cn Figure 6.22 Cyclic loading liquefaction resistance curves of silty (13.5% silt) 20/200 Brenda sand 0.28 - i 0.26 - 0.24 - «N 0.22 T3 b 0.20 - o I— cr 0.18 to to U J £ 0.16 to C J rj 0.14 H LI 0.12 - 0.10 - 0.08 © LIMITED LIQUEFACTION D r c ( s k e l e t o n ) >±2% SILTY 20/200 BRENDA SAND 0"c' = 350 kPa 13.33±.15% SILT 0.4421 .002 Dr c = 94.9±0.6% ( s k e l e t o n ) = 5 7 - 5 ± 0 . 1 % 13.67±.14% SILT e c = 0.488± .001 Dr c = 83.110.3% Dr / i i i \ = 40.010.5% c ( s k e l e t o n ) "i 1—i—i i i i 10 l 1—i—i i i i |— 10 7 i i—i—i i i i | 10 3 NUMBER OF CYCLES TO LIQUEFACTION (2.5% SINGLE AMPLITUDE STRAIN) N| 03 OO Figure 6.23 Cyclic loading liquefaction resistance curves of silty 20/200 sand at near loosest state of slurry deposition 0.28 0.26 5 0.24 -D * CM v. 0.22 - \ -a b 0.20 - o RA TI  0.18 - rR ES S 0.16 - to o CY CL l 0.14 - 0.12 0.10 0.08 PERCENTAGE SILT CONTENT BY WEIGHT 0 4.3 7.5 13.5 21 SILTY 2 0 / 2 0 0 BRENDA SAND CT' = 3 5 0 k P a 21 ±1.6% SILT e c = 0 .4461 .006 Dr = 9 6 1 2 . 5 % c D r c ( s k e l ) " 8 ( _ 1 - 5 ' ° , 4 - 6 ) % "i 1—i—r i i i | 10 T 1 1 1 I I I "1 1 1—I—I I ' l l 10 ' 10 3 NUMBER OF CYCLES TO LIQUEFACTION (2 .5% SINGLE AMPLITUDE STRAIN) N| 00 190 seen to increase the c y c l i c resistance of the sand. In some cases, a small increase i n s i l t content may apparently increase c y c l i c strength more than a larger increase i n s i l t content. 6.4.1.2 Comparison of C y c l i c Strength i n Fixed Number of Cycles to Liquefaction Figures 6.24 through 6.27 show c y c l i c stress r a t i o versus standard r e l a t i v e density curves f o r several fixed number of cycles to l i q u e f a c t i o n . The curves were interpolated from raw data presented i n Section 6.4.1.1. Although the range of c y c l i c strength does not change with s i l t content, standard r e l a t i v e density i s shown to increase s u b s t a n t i a l l y with increase i n s i l t content. When compared i n terms of standard r e l a t i v e density (for the small range i n which some curves overlap), s i l t content i s shown to d r a s t i c a l l y reduce c y c l i c strength. This observation leads one to the conclusion made i n Section 3.2.2.4, Section 5.4 and by other researchers (Ishihara, 1980, and ASTM D-2049-69) that the standard ASTM r e l a t i v e density provides a r e l a t i v e l y poor basis f o r the comparison of mechanical properties of s i l t y sand. In Figure 6.25 and Figure 6.26 one can see that c y c l i c resistance drops o f f rapidly near loosest state of s l u r r y deposition. Bulked s i l t y sand samples with lower standard ASTM r e l a t i v e densities could be prepared by moist tamping or dry p l u v i a t i o n , as described i n Section 3.3.1. Such samples would tend to be metastable under monotonic or Figure 6.24 Cyclic loading liquefaction resistance curves of clean 20/200 Brenda sand 0 10 20 30 40 50 60 70 80 90 100 ASTM STANDARD RELATIVE DENSITY D r c (*) Figure 6.25 Cyclic loading liquefaction resistance curves of silty (4.3% silt) 20/200 Brenda sand 0.28 0.26 * CN b 0.20 2 0.18 - !< a: m m in a _i o 0.16 0.14 0.12 - 0.10 - 0.08 SILTY 2 0 / 2 0 0 BRENDA SAND 4 . 3 % SILT CONTENT BY WEIGHT 0C = 3 5 0 k P a N| = NUMBER OF CYCLES TO LIQUEFACTION ( 2 . 5 % SINGLE AMPLITUDE STRAIN) 10 2 0 N| = 5 0 N l = 1 0 0 10 T 20 30 40 50 60 70 ASTM STANDARD RELATIVE DENSITY Dr c (*) 80 90 100 Figure 6.26 Cyclic loading liquefaction resistance curves of silty (7.5% silt) 20/200 Brenda sand 0.28 100 ASTM STANDARD RELATIVE DENSITY Drc (s) Figure 6.27 Cyclic loading liquefaction resistance curves of silty (13.5% silt) 20/200 Brenda sand 0.28 0.26 - J"o 0.24 - A 0.22 H c j 0-20 H o 0.18 - < cc cn 0-16 cn UJ £ 0.14 cn § 0.12 o ° 0.10 - SILTY 2 0 / 2 0 0 BRENDA SAND 1 3 . 5 % SILT CONTENT BY WEIGHT G'c = 3 5 0 . k P a N, = NUMBER OF CYCLES TO LIQUEFACTION ( 2 . 5 % S INGLE AMPLITUDE STRAIN) N , N , N, N i 0.08 n 1 1 1 1 1 1 1 1 1 r 20 30 40 50 60 70 ASTM STANDARD RELATIVE DENSITY Dr c (*) 10 80 90 100 195 c y c l i c loading and would be subject to very low steady-state l i q u e f a c t i o n strength as described by Castro (1969). Unsegregated water pluviated clean and s i l t y 20/200 sand samples are possible only i n the range of r e l a t i v e d e n s i t i e s shown. The data shown i n Figures 6.24 through 6.27 i s replotted i n terms of sand skeleton r e l a t i v e density, as shown i n Figures 6.28 through 6.30. In terms of sand skeleton r e l a t i v e density i t i s observed that the c y c l i c resistance curves f o r d i f f e r e n t s i l t contents are very s i m i l a r . This indicates that c y c l i c strength i s governed mainly by the sand portion of s i l t y sand f o r up to about 20% homogeneous s i l t content. S i l t content tends to increase c y c l i c strength somewhat when sand skeleton r e l a t i v e density i s chosen as the basis for comparison. 6.4.2 E f f e c t of S i l t Content on C y c l i c Resistance Data presented i n Section 6.4.1 may be interpolated to form a set of curves which show the e f f e c t of s i l t content on the c y c l i c strength of s i l t y 20/200 Brenda sand. Such curves are presented i n the following sections. 6.4.2.1 V a r i a t i o n of C y c l i c Strength With Void Ratio Ishihara et a l . (1980) have suggested that i n the case of s i l t y sands, void r a t i o might be a better basis for the comparison of c y c l i c strength. Figure 6.31 through Figure 6.34 show such v a r i a t i o n of c y c l i c strength f o r a given number of load cycles to l i q u e f a c t i o n (10, 20, 50, and 100 Figure 6.28 Cyclic loading liquefaction resistance curves of silty (4.3% silt) 20/200 Brenda sand 0.28 0.26 u 0.24 * CM 0.22 \ b 0.20 o t . 0.18 < ir tn 0.16 cn 111 cc i - 0.14 cn u _ i 0.12 o >-o 0.10 0.08 SILTY 2 0 / 2 0 0 BRENDA SAND 4 . 3 % SILT CONTENT BY WEIGHT 0 c = 3 5 0 k P a y N , = 10 s N ( = 2 0 ^ N| = 5 0 N, = 1 0 0 N, = NUMBER OF C Y C L E S TO LIQUEFACTION ( 2 . 5 % S INGLE AMPLITUDE STRAIN) 10 20 30 40 50 60 70 80 SAND SKELETON RELATIVE DENSITY D r c ( s k e l e t o n ) (%) 90 100 Figure 6.29 Cyclic loading liquefaction resistance curves of silty (7 .5% silt) 2 0 / 2 0 0 Brenda sand 0.28 0.26 * CM b ° 0.20 2 0.18 - cc CO CO CO o _J CO 0.08 SILTY 2 0 / 2 0 0 BRENDA SAND 7 . 5 % SILT CONTENT BY WEIGHT , N . = 10 CTC = 3 5 0 k P a X 1 y N , = 2 0 ^ ^ N, = 5 0 ^S3? ^ N, = 1 0 0 N, = NUMBER OF C Y C L E S TO LIQUEFACTION ( 2 . 5 % S INGLE AMPLITUDE STRAIN) 0 10 20 30 40 50 60 70 SAND SKELETON RELATIVE DENSITY D r c ( s k e | e t o n ) (%) 80 90 100 Figure 6.30 Cyclic loading liquefaction resistance curves of silty (13.5% silt) 20/200 Brenda sand 0.28 0.26 - 0 10 20 30 40 50 60 70 80 90 100 SAND SKELETON RELATIVE DENSITY D r c ( s k e | e t o n ) ( % ) Figure 6.31 Variation of silty 2 0 / 2 0 0 sand resistance to l iquefaction in 10 load cycles with consolidation void ratio co LU _l CM \ Q fc) O O O I— *- 2 z CO CO LU o CO o O LU 33 >- _i o or o 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0 PERCENTAGE SILT CONTENT BY WEIGHT SILTY 2 0 / 2 0 0 BRENDA SAND 0'c = 3 5 0 k P a Loosest State 0.08 I I I 0.40 0.45 0.50 0.55 VOID RATIO 0.60 0.65 0.70 0.75 0.80 0.85 0.90 Figure 6.32 Variation of silty 2 0 / 2 0 0 sand resistance to l iquefaction in 20 load cycles with consolidation void ratio 0.28 UJ 0.26 H 0 I PERCENTAGE SILT CONTENT BY WEIGHT SILTY 2 0 / 2 0 0 BRENDA SAND (j'c = 3 5 0 k P a LY. o 0.10 H 0.08 0.40 Loosest State 1 1 r— 0.45 0.50 0.55 VOID RATIO 0.60 0.65 0.70 0.75 0.80 0.85 0.90 Figure 6.33 Variation of silty 20/200 sand resistance to liquefaction in 50 load cycles with consolidation void ratio CO LU CJ 1 o fc) CN C Y \ Q O A _ i O o 1— m < CO z LJ  O on \— CT  CO < LU- o LU _ i ZD o O >- _ l o cn o Lu 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0 J PERCENTAGE SILT CONTENT BY WEIGHT Loosest State SILTY 20/200 BRENDA SAND Gc = 350 kPa 0.40 0.45 0.50 0.55 VOID RATIO 0.60 0.65 0.70 0.75 0.80 0.85 0.90 Figure 6.34 Variation of silty 20/200 sand resistance to liquefaction in 100 load cycles with consolidation void ratio 0.28 in H 0.26 - 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 VOID RATIO e c 203 load cycles) for s i l t y 20/200 sand. The figures show that near loosest state of deposition (the lowest data point on each curve), s i l t y 20/200 sands have s i m i l a r c y c l i c strength regardless of s i l t content, although there i s a large dif f e r e n c e i n void r a t i o s . The resistance curves are seen to s h i f t h o r i z o n t a l l y toward lower void r a t i o s as s i l t content increases. At each s i l t content there appears to be an approximately s i m i l a r increase i n c y c l i c resistance f o r a given decrease i n void r a t i o . I f compared at constant void r a t i o , s i l t content i s shown to decrease severely the c y c l i c strength of a sand material, as observed i n the v a r i a t i o n of c y c l i c strength with standard ASTM r e l a t i v e density discussed i n Section 6.4.1.2. As discussed previously, higher void r a t i o s may be attained i f s i l t y sands are prepared by moist tamping or a i r p l u v i a t i o n . Such samples would tend to have very low c y c l i c and monotonic strength, which i s uncharacteristic of water pluviated s i l t y sand. 6.4.2.2 Va r i a t i o n of C y c l i c Strength With Relative Density Figure 6.35 through Figure 6.38 show how s i l t content a f f e c t s the c y c l i c strength of s i l t y 20/200 sand when sand skeleton r e l a t i v e density as opposed to ASTM standard r e l a t i v e density i s used as the basis f o r comparison. As described i n Section 6.4.1.2, i f c y c l i c strength of s i l t y sand i s considered i n terms of ASTM standard r e l a t i v e density, s i l t content i s shown to s u b s t a n t i a l l y reduce c y c l i c strength. In contrast, i f compared i n terms of sand Figure 6.35 Variation of silty 20/200 sand resistance to liquefaction in 10 load cycles with relative density co UJ _ j CN \ a -o < fc> O o o I— *- 2 s CO 2 CO < Lu O LU Zi => o g or o 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 PERCENTAGE SILT CONTENT BY WEIGHT 0 4.3 7.5 13 .5 21 21 LTC = 3 5 0 k P a - 21 4- SAND SKELETON RELATIVE DENSITY • ASTM RELATIVE DENSITY SILTY 2 0 / 2 0 0 BRENDA SAND Loosest State (7C = 3 5 0 k P a 10 20 30 40 50 60 RELATIVE DENSITY Dr c (%) 70 80 21 90 100 Figure 6.36 Variation of silty 20/200 sand resistance to liquefaction in 20 load cycles with relative density 1 I | i | I | l | l | l | I | l | I | i | 0 10 20 30 40 50 60 70 80 90 100 RELATIVE DENSITY Drc (*) Figure 6.37 Variation of silty 20/200 sand resistance to liquefaction in 50 load cycles with relative density CO Ld CN U o o P m £ z Ld 2 O CO < Lu O Ld • a g >- —i ° c o 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 PERCENTAGE SILT CONTENT BY WEIGHT 0 4.3 7.5 13.5 21 SILTY 20/200 BRENDA SAND 0'c = 350 kPa 21 + SAND SKELETON RELATIVE DENSITY • ASTM RELATIVE DENSITY CTC = 350 kPa Loosest State 11 ^ 10 20 ~r 30 40 50 60 70 80 RELATIVE DENSITY Dr. (*) 21 90 100 Figure 6.38 Variation of silty 20/200 sand resistance to liquefaction in 100 load cycles with relative density 0.28 tn LU 0.26 0.24 o § ° - 2 0 - 0.18 - 0.16 O O < LY tn 2 tn < 0.14 LL. O UJ ci O 0.12 ° LY. 0.10 O u. 0.08 21 — r PERCENTAGE SILT CONTENT BY WEIGHT 4.3 — 7.5 13.5 21 — SILTY 2 0 / 2 0 0 BRENDA SAND Oi = 3 5 0 k P a 21 4- SAND SKELETON RELATIVE DENSITY • ASTM RELATIVE DENSITY (Tc = 3 5 0 k P a Loosest State 10 20 30 40 50 60 70 RELATIVE DENSITY Dr c (*) 80 21 90 100 208 skeleton r e l a t i v e density, s i l t content i s shown to have l i t t l e e f f e c t upon c y c l i c strength, or i n f a c t s l i g h t l y increase c y c l i c strength. The s i l t e s s e n t i a l l y f i l l s void space within the sand without causing a large change i n c y c l i c strength properties. 6 .4.2.3 V a r i a t i o n of C y c l i c Strength With S i l t Content at Constant Sand Skeleton Relative Density Interpolation of Section 6.4.2.2 c y c l i c resistance curves y i e l d s Figure 6.39, which shows that the c y c l i c strength of s i l t y sand i s increased up to 15% by any increase i n s i l t content, when considered at constant sand skeleton r e l a t i v e density. A small addition of s i l t (4.3% by weight) may i n fact increase c y c l i c strength more than a large addition of s i l t (13.5% by weight). This indicates that the increase i n absolute density produced by an increase i n s i l t content i s not the only reason f o r an increase i n c y c l i c strength with increasing s i l t content at constant sand skeleton r e l a t i v e density. Test r e s u l t s i n F i g . 6.39 indicate that the c y c l i c strength of hydraulic f i l l or f l u v i a l s i l t y sand which has been deposited through water s u f f i c i e n t l y quickly to avoid deposition of segregated s i l t layers may be estimated conservatively by te s t s on clean sand of s i m i l a r gradation and sand skeleton void r a t i o . The major difference i n f i e l d loading behavior of clean and s i l t y sands would be the extent of drainage possible during and a f t e r c y c l i c loading, a f a c t o r which i s not considered i n elemental undrained Figure 6.39 Summary of the variation of silty 20/200 sand cyclic strength with variation of silt content at constant sand skeleton relative density 6° 0.26 0 .24 - " 0 .22 - XI b 0 .20 5 0 .18 or co co 0 .16 UJ LY. CO O 0 .14 - ^ 0 .12 o 0 .10 0 .08 PERCENTAGE SILT BY WEIGHT 0 4.3 - 7.5 - 13 .5 = 3 5 0 k P a SAND SKELETON RELATIVE DENSITY ( PERCENT) 5 5 4 0 2 5 i i i i i i i T 1 1—I I I I 1 1 1 1—I I I I 1 10 1 0 2 10 NUMBER OF CYCLES TO LIQUEFACTION ( 2 . 5 * SINGLE AMPLITUDE STRAIN) N, 210 laboratory t e s t i n g , because samples are maintained i n an undrained state throughout t e s t i n g . 6 . 4 . 2 . 4 Consistency of Interpolations Figure 6.40 has been drawn from interpolated data derived from a l l previous c y c l i c resistance p l o t s presented i n Section 6.4, to show the v a r i a t i o n of l i q u e f a c t i o n resistance at constant applied c y c l i c stress r a t i o , and to check the v a l i d i t y of the interpolated data. The v a l i d i t y of interpolated p l o t s i s checked by p l o t t i n g interpolated data from a l l other p l o t s on Figure 6.40 to determine i f the data form a set of smooth curves, as i s observed to be the case. The same trends i n c y c l i c resistance data as have been previously described are seen i n Figure 6.40. 211 Figure 6.40 Variation of silty 20/200 sand cyclic strength with silt content at constant cyclic stress ratio 10 < I— co UJ Q < Ld _J O CO in CN C J If U J o CO U J o U J m 10 10 - PERCENTAGE SILT CONTENT BY WEIGHT 0 4.3 7.5 13 .5 + SAND SKELETON RELATIVE DENSITY • ASTM RELATIVE DENSITY 0C = 3 5 0 k P a O-J20L = 0 . 1 6 n i i i i 1 i 1 1 1 10 20 30 40 50 60 70 80 90 100 1 RELATIVE DENSITY D r c (%) 212 CHAPTER 7 DISCUSSION AMD INTERPRETATION OF TEST RESULTS The following features of the observed monotonic and c y c l i c loading behaviour of clean and s i l t y sands deposited through water merit further discussion: 1) The monotonic compression loading behaviour of Brenda sand a f t e r consolidation from loosest state i s observed to be generally d i l a t i v e ( i . e . steady-state or l i m i t e d l i q u e f a c t i o n i s not observed during shear). This i s true f o r both clean and s i l t y sands regardless of t h e i r average grain s i z e , gradation and s i l t content. 2) For samples prepared at loosest state, monotonic compression behaviour i s d i l a t i v e , yet extension behaviour i s contractive ( i . e . steady-state or l i m i t e d l i q u e f a c t i o n i s observed during shear). A l l sands regardless of t h e i r gradation, average grain s i z e and s i l t content behave i n t h i s manner over a range of confining stress. The same sand at a given void r a t i o i s shown to be ei t h e r contractive or d i l a t i v e , depending upon d i r e c t i o n of loading. 3) A l l sands tested display an i n i t i a l decrease i n e f f e c t i v e confining stress under undrained loading, u n t i l a unique phase transformation or steady-state e f f e c t i v e f r i c t i o n angle i s mobilized. Once sheared past phase transformation state, the materials d i l a t e with consequent increasing e f f e c t i v e confining stress. An e s s e n t i a l l y constant e f f e c t i v e angle of f r i c t i o n i s maintained within the material during d i l a t i o n . This behaviour i s observed regardless of d i r e c t i o n of loading and the magnitude of maximum p o s i t i v e pore pressure developed. Some of these aspects of material behaviour present r a d i c a l departures from the generally accepted ideas regarding undrained behaviour of sands. Causes of these departures may l i e i n the sand type and the c h a r a c t e r i s t i c f a b r i c of the water deposited materials used i n t h i s study. For example, water deposited Ottawa C109 sand at loosest deposition state shows steady-state or l i m i t e d l i q u e f a c t i o n response i n both extension and compression loading (see Figure 3.12 and Chung, 1985), while Brenda sand shows steady-state or li m i t e d l i q u e f a c t i o n response only i n extension loading from an i s o t r o p i c consolidation stress below 500 kPa. Although Ottawa sand shows l i m i t e d l i q u e f a c t i o n response i n compression loading, extension response i s s t i l l considerably more contractive than compression response. This anisotropy i n loading response appears to be c h a r a c t e r i s t i c of water deposited sands, regardless of sand type. Chung (1985) has shown that the anisotropy of water deposited sand may be r a d i c a l l y altered by stress and s t r a i n h i s t o r y (see Figure 2.3). Thus the process of s o i l deposition must impart a s p e c i f i c f a b r i c to the s o i l which 214 may only be altered by induced s t r a i n . The anisotropy of s o i l i s shown to be only s l i g h t l y changed by increasing consolidation stress l e v e l (which generally only induces small s t r a i n ) . S o i l f a b r i c i s observed to be dependent upon stress r a t i o h i s t o r y (which may induce larger strain) and i s observed to be e s s e n t i a l l y independent of magnitude of confining s t r e s s . Most research on the undrained behaviour of sands, e s p e c i a l l y well-graded and s i l t y sands, has been conducted using moist tamped samples. These samples may possess an e n t i r e l y d i f f e r e n t f a b r i c than that of water pluviated samples. Radical differences i n the undrained behaviour of the two d i f f e r e n t types of reconstituted samples may be expected due to differences i n f a b r i c . In addition, most research has been concentrated on the study of s o i l strength behaviour under a single mode of loading, commonly t r i a x i a l compression loading and les s commonly under t r i a x i a l extension or simple shear loading. Thus the opportunity to i d e n t i f y anisotropy i n undrained response has most often been missed. The undrained behaviour of sands has been t a c i t l y assumed to be i s o t r o p i c . Some researchers have i d e n t i f i e d non-uniform s t r a i n s i n extension loading of moist tamped sands as the reason for not conducting t r i a x i a l extension t e s t s (Castro, 1975). As i n most laboratory t e s t i n g techniques, the development of larger s t r a i n i n t r i a x i a l samples invari a b l y produces non-uniform stress and s t r a i n conditions (either i n compression or extension loading directions) . This does not mean that the s t r e s s - s t r a i n behaviour observed before the development of non- uniform s t r a i n s i s i n v a l i d . The important factor to consider i s at what point does s t r e s s - s t r a i n behaviour become in v a l i d ? Moist tamped specimens may be predisposed to the development of non-uniform s t r a i n s i n extension loading due to sample non-uniformity. Water pluviated samples maintain s t r a i n uniformity well past phase transformation state i n extension loading (see Figure 3.13). Thus the s o i l strength behaviour obtained from extension t e s t r e s u l t s i s v a l i d i n the s t r a i n range which i s of p r a c t i c a l s i g n i f i c a n c e . 7.1 BAND FABRIC Moist tamped sand samples have been shown to have steady-state or l i m i t e d l i q u e f a c t i o n response i n compression loading over a range of void r a t i o s (Castro et a l . , 1985) regardless of gradation, s i l t content, sand type or p a r t i c l e shape. Castro et a l . (1982) present t e s t r e s u l t s f o r Lornex t a i l i n g s sand which has a s i m i l a r mineralogy and angularity as Brenda t a i l i n g s sand. Moist tamped Lornex sand i s shown to be highly contractive i n compression loading over a range of void r a t i o s . Since a l l the water deposited angular sands tested i n t h i s study are generally d i l a t i v e i n compression loading, even i n the loosest deposition state, the moist tamping technique must be imparting a f a b r i c to the sand 216 which promotes contractive behaviour. Conversely, p l u v i a t i o n of sand through water must be imparting a f a b r i c that promotes more d i l a t i v e behaviour, at l e a s t under compression loading. When moist sand i s placed before tamping, i t i s generally i n a bulked state with a r e l a t i v e density l e s s than zero percent. Tamping i s used to achieve any desired density. A moist sand i s i n i t i a l l y bulked and r e s i s t a n t to d e n s i f i c a t i o n due to c a p i l l a r y tensions between grains. Casagrande (1976) has i d e n t i f i e d moist dumped sands to be p a r t i c u l a r l y prone to l i q u e f a c t i o n due to t h e i r "metastable honeycomb structure" which i s induced by " c a p i l l a r y forces between moist grains". The magnitude of c a p i l l a r y tensions within a s o i l varies with grain s i z e . Finer grained s o i l s generate larger c a p i l l a r y tensions and thus may be subject to greater bulking and an increased resistance to d e n s i f i c a t i o n by tamping. At low stress l e v e l , c a p i l l a r y tensions control p a r t i c l e i n t e r a c t i o n within a moist s o i l . The e f f e c t s of c a p i l l a r y forces upon s o i l f a b r i c may be expected to p e r s i s t i n some form even a f t e r tamping to densities higher than the ASTM minimum. This i s suggested by some laboratory studies, where loose moist tamped specimens of f i n e r grained s o i l s have been shown to experience large s t r a i n s during the saturation process, even while being maintained under a consolidation vacuum (Marcuson, 1972; Chang et a l . , 1982; Sladen et a l . , 1985). This c o l l a p s i n g c h a r a c t e r i s t i c on 217 mere removal of c a p i l l a r y tensions suggests a f a b r i c which i s metastable. This f a b r i c i s l i k e l y to r e s u l t i n contractive behaviour during shear. In contrast to moist tamped sands, water pluviated sands are deposited under g r a v i t a t i o n a l forces and drag forces during settlement through water. Upon deposition, p a r t i c l e i n t e r a c t i o n i s governed by i n t e r p a r t i c l e f r i c t i o n , and not c a p i l l a r y tension forces. Deposition of dry coarse sand through a i r could be expected to y i e l d a s i m i l a r f a b r i c as deposition through water, because upon deposition, p a r t i c l e i n t e r a c t i o n i s governed by i n t e r p a r t i c l e f r i c t i o n . This i s indicated by the s i m i l a r i t y between ASTM and s l u r r y deposition maximum void r a t i o s shown i n Table 3.2. In contrast to coarse grained sands, a i r versus water pluviated f i n e and s i l t y sands may give r i s e to d i f f e r e n t f a b r i c s , as indicated by the loosest state void r a t i o s shown i n Figure 3.5 and Figure 3.6. The large increase i n maximum sand skeleton void r a t i o with increase i n s i l t content i n dry a i r pluviated s i l t y sands i s due to the pronounced e l e c t r o s t a t i c forces between fi n e s i l t grains i n the dry state. In the dry state, e l e c t r o - s t a t i c forces between s i l t grains may be considered to bulk the sand i n much the same manner as c a p i l l a r y tension forces i n moist sand. Thus both a i r pluviated and moist tamped samples may neither duplicate the f a b r i c nor the accessible range of void r a t i o s possible i n water deposited s o i l s . 218 7.2 INTERPRETATION OF FACTORS WHICH PRODUCE AND CONTROL FABRIC OF WATER PLUVIATED SAND Water pluviated sands show a c h a r a c t e r i s t i c trend i n strength behaviour and anisotropy. Thus the f a b r i c of water pluviated sand must have s p e c i f i c features which are derived from the process of p l u v i a t i o n through water. For the purposes of explaining and possibly p r e d i c t i n g the behaviour of water pluviated sands, i t i s important to i d e n t i f y the factors which produce and control t h e i r f a b r i c . Much of the behaviour observed i n the t e s t r e s u l t s reported can be explained i n terms of Rowe's two dimensional p a r t i c u l a t e model as described i n Section 2 . 2 . Rowe's model can be used to show that the dilatancy and s t r e s s - s t r a i n response of a p a r t i c u l a t e material i s co n t r o l l e d by i n t e r p a r t i c l e contact angle fi and p a r t i c l e dimension factor a. Dilatancy i s also shown to be a function of d i r e c t i o n of loading and s t r a i n l e v e l (see Section 2 . 2 ) . The physical parameters a and fi of Rowe's model are applicable to the desc r i p t i o n of sand f a b r i c i n a general manner because sand i s simply an assemblage of p a r t i c l e s . The difference between Rowe's model and a natural assemblage of sand p a r t i c l e s i s that a sand has a s t a t i s t i c a l d i s t r i b u t i o n or population of p a r t i c l e contact angles (fi) and structure dimension factors (a). As long as the deformation i n a sand i s c o n t r o l l e d mainly by the f r i c t i o n a l resistance between 219 p a r t i c l e s , Rowe's model may be expected to provide a reasonable simulation of deformation behaviour. S t r a i n behaviour i n a sand i s c o n t r o l l e d by the combinations of a and 0 which are rendered unstable and produce s l i p between p a r t i c l e contacts as stress r a t i o i s increased. Figure 7.1 shows the range of stable population of a and 0 f o r various l e v e l s of stress r a t i o . A comparison of Figure 7.1a and Figure 7.1b shows how the i n t r i n s i c angle of f r i c t i o n on p a r t i c l e surfaces a f f e c t s the range of stable population of p a r t i c l e contacts. The actual population of a and 0 within a sand may vary within the stable zone, depending upon s t r e s s - s t r a i n h i s t o r y and method of sample preparation, as described i n the following paragraphs. 7.2.1 Sample Preparation During p l u v i a t i o n through water, sand p a r t i c l e s are subjected to g r a v i t a t i o n a l forces and viscous drag forces. F l a t t e r shaped p a r t i c l e s may tend to orient themselves with t h e i r longer axes i n a horizontal d i r e c t i o n , and shortest axis i n the v e r t i c a l d i r e c t i o n , due to water drag forces. Upon sedimentation, the p a r t i c l e s would tend to s e t t l e upon the deposition plane with t h i s preferred orientation, i n addition to having p a r t i c l e contact normals which are preferably oriented closer to v e r t i c a l i n order to support self-weight. Both of these factors would tend to induce a concentration of lower a values and higher 0 values i n the p a r t i c l e contact population. Thus the p a r t i c l e contact F i g u r e 7.1a S t a b i l i t y contours f o r Rowe's p a r t i c u l a t e model as a f u n c t i o n of p a r t i c l e dimension f a c t o r « and i n t e r p a r t i c l e c ontact angle JS I N T E R P A R T I C L E CONTACT ANGLE ft (DEGREES) F i g u r e 7.1b S t a b i l i t y contours f o r Rowe's p a r t i c u l a t e model as a f u n c t i o n of p a r t i c l e dimension f a c t o r « and i n t e r p a r t i c l e c o n t a c t angle j8 I N T E R P A R T I C L E CONTACT ANGLE H (DEGREES) F i g . 7.2 Constant incremental s t r a i n r a t i o contours f o r Rowe's p a r t i c u l a t e model as a f u n c t i o n of p a r t i c l e dimension f a c t o r « and i n t e r p a r t i c l e c ontact angle |8 I N T E R P A R T I C L E CONTACT ANGLE j8 (DEGREES) 223 population would tend to be concentrated i n the lower r i g h t hand corner of Figure 7.1 and Figure 7.3. 7.2.2 Sample Consolidation Following the settlement of p a r t i c l e s , a state of K D consolidation i s established under self-weight within the material. This produces and maintains a stress r a t i o of approximately 2.0 within the material, which implies a range of stable p a r t i c l e contacts as shown i n Figure 7.3. As laboratory samples are i s o t r o p i c a l l y consolidated from as deposited K Q state, the range of stable p a r t i c l e contacts i s transformed to the population shown i n Figure 7 .4. The p a r t i c u l a t e model implies that mode B contractive volumetric s t r a i n s are induced during the transformation from K Q consolidation to i s o t r o p i c consolidation, because a zone of previously stable contacts i s exposed to the mode B s t r a i n unstable zone, as shown i n Figure 7.5. Mode B s t r a i n implies s l i p against the d i r e c t i o n of external maximum p r i n c i p a l stress (see Section 2.2). In a K Q consolidated t r i a x i a l specimen, t h i s would imply an increase i n sample height when r a d i a l stress i s increased to the magnitude of v e r t i c a l stress i n order to induce i s o t r o p i c consolidation. This form of s t r a i n development was observed and v e r i f i e d at low confining stress during the preparation of t a i l i n g s sand samples. Saturated samples were K Q consolidated a f t e r deposition by maintaining an 80 kPa vacuum between the former tube and the outside surface of the sample membrane, F i g u r e 7 .3 Range o f s t a b l e p a r t i c l e c o n t a c t s a f t e r Ko c o n s o l i d a t i o n 0 10 20 30 40 50 50 70 80 90 I N T E R P A R T I C L E CONTACT ANGLE jS (DEGREES) Figure 7.4 Range of stable particle contacts after isotropic consolidation I N T E R P A R T I C L E CONTACT ANGLE jS (DEGREES) Figure 7.5 Range of p a r t i c l e c o n t a c t s which undergo Mode B s l i p i n the trans f o r m a t i o n from Ko to i s o t r o p i c c o n s o l i d a t i o n 0 10 20 30 40 50 60 70 80 90 I N T E R P A R T I C L E CONTACT ANGLE |8 (DEGREES) 227 while a 20 kPa vacuum was applied i n increments to the sample. Thus the v e r t i c a l stress on the sample was 20 kPa, and r a d i a l stress a lower amount corresponding to K Q consolidation, because zero r a d i a l s t r a i n was imposed on the sample. Now, without disturbing the sample, the external 80 kPa vacuum on the outside surface of the sample was released, so that the sample would be transformed from K Q consolidation to i s o t r o p i c consolidation without a change i n v e r t i c a l s t r e s s . Sample height was observed to increase, while large contractive volumetric s t r a i n s indicated the occurrence of large compressive r a d i a l s t r a i n s . The predicted range of incremental s t r a i n r a t i o induced by a change i n population of stable p a r t i c l e contacts due to a change i n stress r a t i o can be determined from Figure 7.2. During the transformation from K Q to i s o t r o p i c consolidation, contractive mode B deformation i s predicted to occur. Incremental v e r t i c a l to horizontal s t r a i n r a t i o i s estimated to be greater than -0.4, which indicates a considerably larger r a d i a l than a x i a l s t r a i n , as has been observed i n t r i a x i a l t e s t r e s u l t s . Test r e s u l t s thus confirm that mode B st r a i n s are indeed possible within a sand, and that Rowe's p a r t i c u l a t e model can be e f f e c t i v e l y used to explain otherwise unexplainable observed behaviour. Rowe's p a r t i c u l a t e model assumes that s t r a i n within a p a r t i c u l a t e material may only be induced by s l i p between p a r t i c l e contacts. Individual p a r t i c l e s are assumed to be completely r i g i d . The r e s u l t of these assumptions i s that 228 s t r a i n i s only predicted to be induced by a change i n stress r a t i o , and not by a change i n the magnitude of s t r e s s . The model suggests that when a p a r t i c u l a t e material i s stable at one magnitude of consolidation stress, i t w i l l remain stable under increasing or decreasing consolidation stress ( i . e . s l i p at p a r t i c l e contacts w i l l not be induced) as long as s t r e s s r a t i o i s held constant. This contention i s reasonable f o r completely r i g i d p a r t i c l e s whose i n t r i n s i c angle of surface f r i c t i o n i s not a function of normal stress l e v e l . The r e l a t i v e l y small amount of s t r a i n induced i n sand during consolidation at constant stress r a t i o must then be due to factors other than s l i p between r i g i d p a r t i c l e s . The majority of s t r a i n induced i n sand during i s o t r o p i c consolidation i s expected to be due to p a r t i c l e contact crushing and the e l a s t i c s t r a i n of non-rigid p a r t i c l e s . These two mechanisms of s t r a i n development are not considered i n Rowe's p a r t i c u l a t e model. The s t r a i n induced by these two mechanisms could also induce unstable changes i n a and fi p a r t i c l e contact populations, which could i n turn, induce s l i p at p a r t i c l e contacts. The magnitude of p a r t i c l e contact s l i p during i s o t r o p i c consolidation i s expected to be coupled to the magnitude of s t r a i n developed by crushing at p a r t i c l e contacts and the magnitude of e l a s t i c s t r a i n . The r e l a t i v e l y small consolidation s t r a i n s observed i n crush r e s i s t a n t Ottawa C109 sand (see Figure 4.5) and the s u b s t a n t i a l l y larger s t r a i n s observed i n angular Brenda sand, which i s considerably l e s s r e s i s t a n t to p a r t i c l e crushing, confirm that p a r t i c l e crushing i s an important fact o r i n the development of s t r a i n during i s o t r o p i c consolidation. The proportion of recoverable or e l a s t i c s t r a i n i n loosest state Ottawa sand a f t e r v i r g i n i s o t r o p i c consolidation from 50 kPa to 550 kPa and unloading again to 50 kPa (see Figure A.3) i s approximately 97% a x i a l s t r a i n and 51% r a d i a l s t r a i n , while that of Brenda sand i s much les s at 36 to 32% a x i a l s t r a i n and 21 to 23% r a d i a l s t r a i n (see Figure A.2). This c o r r e l a t i o n of greater p a r t i c l e crushing resistance i n Ottawa sand with lower magnitude of consolidation s t r a i n and a high percentage of recoverable e l a s t i c s t r a i n tends to support the interpreted mechanism of coupled s t r a i n development under i s o t r o p i c consolidation. The s t r a i n s observed under v i r g i n i s o t r o p i c consolidation are always compressive or p o s i t i v e i n both a x i a l and r a d i a l d i r e c t i o n s (see Figure 4.11). This indicates that the st r a i n s induced by p a r t i c l e contact crushing and e l a s t i c deformation predominate during i s o t r o p i c consolidation, because the st r a i n s induced by mode A or mode B p a r t i c l e contact s l i p require that there be a combination of both compressive and extensional s t r a i n components which r e s u l t i n a negative s t r a i n r a t i o (see Figure 2 .4) . The e l a s t i c component of s t r a i n s induced during v i r g i n consolidation may be estimated from the st r a i n s induced during i s o t r o p i c unloading. The str a i n s 230 recovered during i s o t r o p i c unloading are e s s e n t i a l l y i s o t r o p i c and e l a s t i c (see Section 4.4, Appendix A, and Vaid and Negussey, 1984). When the e l a s t i c component of s t r a i n i s subtracted from v i r g i n s t r a i n , the remaining component of irrecoverable a x i a l s t r a i n i s s t i l l compressive but considerably l e s s compressive than the remaining component of irrecoverable r a d i a l s t r a i n . The irrecoverable s t r a i n component must be due to p a r t i c l e contact crushing, and induced s l i p between p a r t i c l e contacts which have been made unstable by e l a s t i c and crushing s t r a i n . I f p a r t i c l e crushing s t r a i n i s assumed to be i s o t r o p i c , then the remaining s t r a i n component due to p a r t i c l e contact s l i p i s in f e r r e d to be of the mode B type, s i m i l a r to that observed during sample preparation when switching from K Q consolidation to i s o t r o p i c consolidation. Since induced p a r t i c l e crushing and e l a s t i c s t r a i n s are r e l a t i v e l y small during v i r g i n i s o t r o p i c consolidation, only small changes i n the p a r t i c l e contact population a and p may be expected during v i r g i n i s o t r o p i c consolidation. Thus only the p a r t i c l e contact population which i s close to s l i p f a i l u r e (a s t a b i l i t y boundary i n Figure 7.4) could be expected to become unstable during i s o t r o p i c consolidation. The inference that p a r t i c l e s l i p during v i r g i n consolidation i s of the Mode B type implies that the majority of p a r t i c l e contacts which become unstable during v i r g i n i s o t r o p i c consolidation are close the mode B s t a b i l i t y boundary shown i n Figure 7.4. This might be expected because of the 231 previous K Q consolidation stress h i s t o r y . This previous stress h i s t o r y has insured that stable p a r t i c l e contacts have never been f a i l e d close to the node B s t r a i n boundary, while the mode A s t r a i n boundary has only recently been s h i f t e d into a previously unstable zone, and thus one would not expect a large population of stable p a r t i c l e contacts close to t h i s boundary (between the stress r a t i o of 1.0 and 2.0 contours as shown i n Figure 7.5). Thus the p a r t i c u l a t e model may also be used to explain the r e l a t i v e l y larger irrecoverable horizontal s t r a i n component of water pluviated sand under v i r g i n i s o t r o p i c consolidation. 7.2.3 Compression Loading Response A f t e r i s o t r o p i c consolidation, a t e s t sample i s expected to have a population of p a r t i c l e contacts as shown in the middle zone of Figure 7.5. As v e r t i c a l stress i s increased i n compression loading, the zone of stable p a r t i c l e contacts s h i f t s to the r i g h t of Figure 7.5 or 7.1, thus exposing previously stable p a r t i c l e contacts to mode A s t r a i n . Because of the K Q consolidation stress h i s t o r y a f t e r sample preparation (see Section 7.2.2) there i s a deficiency of stable p a r t i c l e contacts below the 2.0 stress r a t i o contour. Thus only minor mode A s t r a i n i s generated below a stress r a t i o of 2.0. In addition, because of settlement through water, the majority of p a r t i c l e contacts i s concentrated i n the bottom r i g h t hand corner of Figure 7.5, with higher fi value and lower a value. Under 232 compression loading, t h i s zone remains stable up to very large stress r a t i o (see Figure 7.1) thus one could again predict f a i r l y small mode A s t r a i n s . A pr e d i c t i o n of the incremental s t r a i n r a t i o and dilatancy induced by an increase i n stress r a t i o may be made from Figure 7.2. Under i n i t i a l increases i n stress r a t i o from 1.0, the model indicates that v e r t i c a l s t r a i n i s greater i n magnitude than horizontal s t r a i n , thus induced s t r a i n i s predicted to be contractive (e.g., to show a reduction i n e f f e c t i v e confining stress during undrained loading), as observed i n a l l s o i l t e s t s i n the low stress r a t i o range. As stress r a t i o i s increased, the p a r t i c u l a t e model predic t s that contractant response w i l l be transformed into d i l a t a n t response. The stress r a t i o at which t h i s occurs cannot be d i r e c t l y determined from the p a r t i c u l a t e model, as one stress r a t i o contour (Figure 7.1) i s crossed by several s t r a i n r a t i o contours (Figure 7.2). Strains induced by an increase i n stress r a t i o are governed by the population of a and p p a r t i c l e contacts which e x i s t within the s o i l . Due to the previous K Q consolidation stress h i s t o r y i n water pluviated sands, and the r e s u l t i n g deficiency i n p a r t i c l e contacts which may s l i p below a stress r a t i o of 2.0, the t r i g g e r i n g of steady-state or l i m i t e d l i q u e f a c t i o n response i s not expected below a stress r a t i o of 2.0. In undrained loading of water pluviated sands, the t r i g g e r i n g of steady-state or l i m i t e d l i q u e f a c t i o n i s expected i n the contractive range of loading response from a stress r a t i o of 233 2.0 to the phase transformation state. This i s indeed observed in the undrained loading response of Ottawa sand, which has a constant CSR of approximately 2 .0 (mobilized f r i c t i o n angle of 20 degrees) . Thus CSR i s shown to correlate well with the i n i t i a t i o n of increased particle contact s l i p predicted in water pluviated sand by the particulate model. The essentially constant ultimate f r i c t i o n angle maintained on the undrained failure envelope i s interpreted to represent the state where a similar population of particle contacts i s both created and destroyed under increasing strain. Such a mechanism could explain the observed increase in ultimate f r i c t i o n angle with increasing sand density (see Figure 6 .4 ) , because one could expect a greater resistance to particle rearrangement in a denser sand. 7.2.4 Extension Loading Response If the particle contact population which is interpreted to exist within an isotropically consolidated water pluviated sand (the same sand as that described in the previous section) i s subjected to extension loading, the values of a and fi must be transformed to a' = 90-a and fi' = 90- /9. This transformation accounts for the reversal of principal stress direction in loading (see Figure 2 . 4 ) . The resulting i n i t i a l population of particle contacts i s shown in Figure 7 . 6 . F i g u r e 7.6 Range o f p a r t i c l e c o n t a c t s which are s u b j e c t e d to s l i p i n e x t e n s i o n l o a d i n g , a f t e r a Ka and i s o t r o p i c c o n s o l i d a t i o n s t r e s s h i s t o r y i n UJ L U cr LD LU a 8 cr o i— CJ < a i—i L O L U U J cr ZD I— C_) ZD cr i— L O 90 80 70 60 50 40 30 20 10 0 ZONE OF PROBABLE PARTICLE CONTACT POPULATION DUE TO THE Ko STRESS HISTORY AND ISOTROPIC CONSOLIDATION 1.0 REVERSED STRESS DIRECTION: «' = 90 - °< jS' = so - J3 LX>LT n v ZONE OF MODE A S L I P WHEN LTh/LT> tanCP+^manCo*') ZONE OF MODE B SLIP WHEN LT h/LT< tan(]8 1 ( i)*t an (°< ) PARTICLE CONTACT POPULATION WHICH BECOMES STABLE UNDER ISOTROPIC CONSOLIDATION. BUT WHICH IS RELATIVELY DEPLETED DUE TO Ko STRESS HISTORY 10 20 30 40 50 60 70 I N T E R P A R T I C L E CONTACT ANGLE fT (DEGREES) 80 90 to CO Due to the sample preparation and i s o t r o p i c consolidation stress history, there i s a large population of p a r t i c l e contacts which are exposed to mode A s l i p i n extension loading as stress r a t i o i s increased. This contrasts with the sparse population of p a r t i c l e contacts which are exposed to mode A s l i p i n compression loading as stress r a t i o i s increased from 1.0 to 2.0. The population of contacts i n extension loading which are subject to s l i p i n the same stress r a t i o range (1.0 to 2.0) have never been subjected to s l i p during sample preparation. Thus a large amount of p l a s t i c contractive s t r a i n i s induced even at low stress r a t i o during extension loading. This difference i n s o i l f a b r i c between extension and compression loading o f f e r s a reasonable explanation for the observed differences i n c r i t i c a l s tress r a t i o (CSR) behaviour between extension and compression loading (see Sections 2.1 and 5.3). CSR i s observed to be e s s e n t i a l l y constant i n compression loading, which i s believed to be due to the sparcity of p a r t i c l e contacts which may undergo s l i p below a K Q consolidation stress r a t i o , due to the previous K Q consolidation stress h i s t o r y . P a r t i c l e contacts which are subject to s l i p by an increase of stress r a t i o above 2.0 have never been caused to s l i p by previous stress history, thus when stress r a t i o i s increased close to 2.0, large contractive s t r a i n s are induced. I f these contractive s t r a i n s are s u f f i c i e n t to produce a reduction i n sand strength, a CSR of close to 2.0 i s observed. In contrast to compression loading CSR, extension loading CSR i s observed to be a function of deposition void r a t i o (Chung, 1985). CSR i s generally much lower than observed i n compression loading (see Table 5.1), with loosest state samples having the lowest CSR, and denser samples showing a gradual increase i n CSR. The behaviour of CSR i n extension loading can be attributed to the reduced contractive behaviour of sand with increasing density. Although there i s a tendency toward volume contraction of sand during shear up to phase transformation stress r a t i o regardless of density, the magnitude of contraction i s diminished with increasing density. In undrained loading, the p o t e n t i a l f o r a s u f f i c i e n t amount of pore pressure generation to t r i g g e r l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n i s reduced with increasing sand density, thus CSR i s increased with increasing density, unless i t i s f i x e d by previous stress r a t i o h i s t o r y as observed i n compression t e s t r e s u l t s . Greater contraction i s observed i n extension loading because a larger number of p a r t i c l e contacts are subjected to contractive s l i p under extension loading. This population of contacts e x i s t s within the sand because they have not been rendered unstable by previous stress h i s t o r y . A second factor which y i e l d s greater contractive s t r a i n i n extension loading i s the i n i t i a l concentration of p a r t i c l e contacts produced by deposition through water (see Section 7.2.1) which r e s u l t s i n generally lower a and higher fi values. When these values are transformed to t h e i r equivalent i n the extension loading d i r e c t i o n , generally higher a' and lower fi' values r e s u l t . Thus the major concentration of p a r t i c l e contacts produced by deposition through water i s i n the upper l e f t hand corner of Figure 7 . 6 . This zone of p a r t i c l e contacts i s subject to s l i p under extension loading, while the same population was not subject to s l i p under compression loading. Due to t h i s concentration of p a r t i c l e contacts produced by p l u v i a t i o n of p a r t i c l e s through water, more contractive s t r a i n s are again predicted i n extension loading. 7.2.5 Stress Reversal As stress r a t i o i s increased i n one d i r e c t i o n of loading, the stable zone of p a r t i c l e contact population i s sh i f t e d , as shown i n Figure 7 . 7 for compression loading. A l l newly established p a r t i c l e contacts which are induced by s t r a i n must e x i s t within the new stable zone, i n order for the p a r t i c u l a t e material to remain stable. A peak stress r a t i o i s achieved when the mode A s t r a i n stable zone boundary can no longer be pushed to a higher stress r a t i o contour. In other words, the stable p a r t i c l e contact population produced by s l i p i s the same as that before s l i p occurred. I f stress r a t i o i s reduced following loading, the zone of stable p a r t i c l e contacts i s s h i f t e d again. One could expect mode B s t r a i n s as the previously stable zone i s exposed to the mode B s t r a i n unstable zone. Because the STRUCTURE DIMENSION FACTOR c x (DEGREES) mode B s t r a i n stable zone boundary above the 1 . 0 stress r a t i o contour has only recently been made stable by increasing stress r a t i o , one could not expect a large concentration of p a r t i c l e contacts within t h i s zone. Thus one could expect unloading s t r a i n s to be small i n comparison to loading s t r a i n s . The mode B s t r a i n s which do occur on unloading are predicted by the p a r t i c u l a t e model to be contractive, as observed i n c y c l i c loading t e s t r e s u l t s (see Section 6 . 0 ) . In contrast, the reduction of mean normal stress which generally accompanies a reduction i n stress r a t i o i n undrained loading implies that e l a s t i c s t r a i n s on unloading should be d i l a t i v e . The contractive s t r a i n s observed i n the unloading of undrained t e s t samples thus indicates that the mode B s t r a i n s induced by a reduction of stress r a t i o are larger than the e l a s t i c s t r a i n s induced by the reduction of mean normal stress. Figure 7 .8 displays what happens to the stable population shown i n Figure 7 .7 with the occurrence of stress r e v e r s a l . Compression loading a and fi values have been transformed to extension loading a' and fi' values. The majority of the previously stable zone produced by compression loading i s shown to f a l l i nto the mode A s t r a i n unstable zone under extension loading. Thus one would pre d i c t large contractive s t r a i n s to occur upon stress reversal and extension loading. This behaviour i s indeed observed i n undrained t e s t s , and leads to the development of large c y c l i c mobility s t r a i n s i n sands which are generally g u r e 7. 8 E x p l a n a t i o n o f t h e l a r g e c o n t r a c t i v e s t r a i n s a s s o c i a t e d w i t h p r i n c i p a l s t r e s s r e v e r s a l f o l l o w i n g l o a d i n g t o a h i g h s t r e s s r a t i o 80 70 60 H 50 40 30 -I 20 - ZONE OF MODE A SLIP WHEN (J/0" > t a n (]3+ ft,) * t a n («') 0 10 20 T T ZONE OF MODE B SLIP WHEN 0~h/LT < t a n (jS1 ft,) * t a n («') THE PARTICLE CONTACT POPULATION WHICH WAS PREVIOUSLY STABLE AT A STRESS RATIO OF 4.0 (SEE PREVIOUS FIGURE) SUBJECT TO UNLOADING AND REVERSAL OF PRINCIPAL STRESS DIRECTION. THE PARTICLE CONTACT DISTRIBUTION IS VERY UNSTABLE UNDER THE NEW DIRECTION OF LOADING. AND LARGE CONTRACTIVE STRAINS OCCUR UNTIL A MORE STABLE MATERIAL FABRIC IS REESTABLISHED. ORIGINAL STRESS DIRECTION: LT >CT ( 0" /CT )max = 4.0 v h v h REVERSED STRESS DIRECTION: cx' = 9Q - ex. |B' - 90 - J8 or >LT h v 30 40 50 INTERPARTICLE CONTACT ANGLE 60 70 JS' (DEGREES) 80 90 241 d i l a t i v e under monodirectional loading. The development of c y c l i c mobility s t r a i n i s considered to be due to the fl u c t u a t i o n of sand f a b r i c between extremes generated i n d i f f e r e n t d i r e c t i o n s of loading. With each extreme f l u c t u a t i o n of sand f a b r i c , the tendency f o r volume contraction i s increased. Thus greater d i l a t i v e s t r a i n s must be produced i n each load cycle i n order to increase e f f e c t i v e stress and s o i l strength to carry the applied load. 7.2.6 The E f f e c t of Stress History Upon CSR A K Q consolidation stress h i s t o r y which induces a stress r a t i o of 2.0 during sample preparation has been interpreted as the reason why water pluviated sand has a CSR of 2.0 i n compression loading (see Sections 7.2.3 and 7 . 2 . 4 ) . This i n t e r p r e t a t i o n implies that CSR may be changed to a given stress r a t i o by simply p r e s t r a i n i n g a contractive sand to t h i s given stress r a t i o . Data presented by Chung (1985) on the e f f e c t s of sample p r e s t r a i n upon CSR and l i m i t e d l i q u e f a c t i o n response show that CSR may indeed be increased to a s p e c i f i c value by pr e s t r a i n i n g to an equivalent stress r a t i o value. As long as l i m i t e d l i q u e f a c t i o n behaviour i s maintained a f t e r p r e s t r a i n i n g and reconsolidation, and the d i r e c t i o n of preloading and reloading are the same, the CSR value obtained during reloading i s very close to the maximum stress r a t i o achieved during preloading. This i s true i n both compression and 242 extension loading d i r e c t i o n s . The observed e f f e c t of pre s t r a i n upon measured CSR values i s consistent with the pa r t i c u l a t e i n t e r p r e t a t i o n of factors which contribute to the f a b r i c and behaviour of water pluviated sands. 7 . 3 INTERPRETATION OF FACTORS WHICH PRODUCE AND CONTROL MOIST TAMPED SAND FABRIC At low confining stress, the in t e r n a l structure within a moist sand sample i s controlled by c a p i l l a r y tensions between grains. This i s because c a p i l l a r y tension forces are considerably larger than self-weight forces. Thus one could expect p a r t i c l e contacts to be e s s e n t i a l l y random within the sample, because the water tension forces which control s o i l structure are independent of d i r e c t i o n . The process of compaction by tamping may tend to induce a less random structure i n higher density samples. In loose samples, the random structure may have a and /3 p a r t i c l e contact values which are unbounded by stress r a t i o contours, because water tension forces and not f r i c t i o n a l resistance between p a r t i c l e s maintain the sample i n a stable state. One could thus expect r e l a t i v e l y large and contractive s t r a i n s i n a moist sand as an external stress which exceeds i n t e r p a r t i c l e c a p i l l a r y tensions i s applied to the sample. One might also expect large s t r a i n s during the saturation process, as c a p i l l a r y tension forces are removed from within the sample. Such large s t r a i n s induced during saturation while the moist sand i s maintained under a consolidation 243 vacuum have been reported by Marcuson et a l . (1972), Chang et a l . (1982) and Sladen et a l . (1985). The i n i t i a l stress h i s t o r y applied to a moist sand sample could be expected to e s t a b l i s h the i n i t i a l f a b r i c and anisotropic character of the sample. Under normal conditions, an i s o t r o p i c stress i s applied by creating a vacuum within the sample. This might be expected to create a population of a and p p a r t i c l e contacts which ex i s t s within the stress r a t i o = 1.0 contours of Figure 7.1. Within the stable zone, p a r t i c l e contacts could be expected to be e s s e n t i a l l y random, unlike that of water pluviated sand which has been subjected to i s o t r o p i c consolidation stress a f t e r preparation at a K Q consolidation state (see Section 7.2.). Depending upon the s t r a i n allowed i n the moist sample during i n i t i a l a p p l i c a t i o n of a confining vacuum, the stresses induced within the sample may not be i s o t r o p i c . Castro et a l . (1969, 1982) describes the standard method employed by himself and many other researchers f o r the preparation of moist tamped s o i l specimens. This method requires that the loading platens on each end of the sample be v e r t i c a l l y supported by the s p l i t former tube which r a d i a l l y encases the sample. As an i n i t i a l vacuum i s applied to the inside of the sample, the rubber membrane on the sides of the sample i s drawn i n , and the sample i s free to contract i n the r a d i a l d i r e c t i o n . Thus the r a d i a l stress on the sample equals the vacuum pressure. But because the loading platens at e i t h e r end of the sample are separated by the r i g i d former tube, e s s e n t i a l l y zero s t r a i n may occur i n the a x i a l d i r e c t i o n . The reaction due to the vacuum on the end platens i s c a r r i e d by the former tube, and only the K Q component of stress generated i n the a x i a l d i r e c t i o n of the sample due to the higher r a d i a l s tress. As t h i s i s equivalent to K Q consolidation i n the ground but with reversed d i r e c t i o n s of p r i n c i p a l stress, the a x i a l stress on the sample could be expected to be only h a l f the r a d i a l stress, u n t i l the s p l i t former tube i s removed. Upon removal of the former tube, a state of i s o t r o p i c stress would be established within the sample. This stress h i s t o r y would r e s u l t i n a f a b r i c which i s preloaded i n the r a d i a l d i r e c t i o n , but not preloaded i n the a x i a l d i r e c t i o n . Thus subsequent s t r a i n s induced by extension loading would be predicted to be r e l a t i v e l y small i n comparison to subsequent s t r a i n s induced by compression loading. This i s opposite to the trend predicted and observed i n water pluviated sands (see Section 7.2). I f the moist tamped sand were t r u e l y i s o t r o p i c a l l y consolidated during i n i t i a l sample preparation, one could expect shear induced pore pressures under subsequent undrained loading to be e s s e n t i a l l y independent of d i r e c t i o n of loading. In comparison to water pluviated sands, one could again predict greater shear induced pore pressures i n the compression loading response of moist tamped sand. 245 The predicted differences i n sand f a b r i c between water pluviated and moist tamped sands o f f e r s a reasonable explanation f o r differences i n CSR behaviour of the two sand types. In water pluviated sands, CSR i s observed to be constant i n compression loading, but variable and generally lower i n extension loading (see Section 2.1 and Section 5.3). CSR behaviour i n water pluviated sand i s interpreted to be a consequence of the s o i l f a b r i c produced by settlement of p a r t i c l e s through water (see Section 7.2.3 and 7.2 . 4 ) . In compression loading, water pluviated sand i s interpreted to have a CSR equal to the K Q stress r a t i o of approximately 2.0 because the K Q consolidation stress h i s t o r y following sand deposition has ensured that there i s a d e f i c i t of p a r t i c l e contacts which may s l i p and cause contractive deformation below a stress r a t i o of 2.0. In extension loading, no such stress h i s t o r y has occurred, thus the p a r t i c l e s l i p and induced contraction which t r i g g e r s l i q u e f a c t i o n may occur at lower and variable CSR values. CSR behaviour of moist tamped sand i n compression loading has been described by Castro (1982), Sladen et a l . (1985) and Mohamad and Dobry (1986). CSR has been shown to be v a r i a b l e , generally increasing with increasing density. Very low CSR values have also been reported i n compression loading. Thus the CSR behaviour of moist tamped sand i n compression loading i s more l i k e that observed i n water pluviated sand under extension loading. This i s explained by the difference i n interpreted sand f a b r i c between the two 246 sand types. Moist tamped sand i s interpreted to have a compression stress h i s t o r y only due to the tamping h i s t o r y during sample preparation, thus the p a r t i c l e contact population which may f a i l under compression loading i s c o n t r o l l e d by the degree and method of tamping. In r e l a t i v e l y loose sands, there i s no d e f i c i t of p a r t i c l e contacts which may f a i l during compression loading, thus CSR may be low and tend to increase with increasing density. In general, one could predict that moist tamped sands could be more contractive than water pluviated sands i n compression loading, and possibly l e s s contractive than water pluviated sands i n extension loading. The difference i n behaviour of the two sand types i s due to differences i n f a b r i c produced by sample preparation. 247 CHAPTER 8 PRACTICAL IMPLICATIONS The mechanism of placement of a sand and i t s s t r e s s - s t r a i n h i s t o r y invariably induces an inherent f a b r i c which imparts anisotropic strength properties to the sand. The v a r i a t i o n of strength properties with d i r e c t i o n of maximum p r i n c i p a l stress i s i n d i r e c t c o n f l i c t with the basic premise of the steady-state theory, which states that steady-state s o i l strength i s s o l e l y dependent upon void r a t i o . Test r e s u l t s presented i n t h i s t h e s i s indicate that at a given consolidation state, a sand may be e i t h e r contractive or d i l a t i v e , depending upon the o r i e n t a t i o n of p r i n c i p a l stresses during shear. Thus the use of steady- state theory may lead to e i t h e r conservative or unconservative estimates of s o i l strength, depending upon the procedure employed to determine s o i l strength. In order to determine the undrained strength c h a r a c t e r i s t i c s of natural f l u v i a l or hydraulic f i l l sands, we must e i t h e r obtain representative undisturbed samples from an i n s i t u deposit, or i f t h i s i s not possible, the deposition process and stress h i s t o r y expected i n the f i e l d must be simulated i n reconstituted laboratory t e s t specimens. Water pluviated sand has a c h a r a c t e r i s t i c behaviour under loading; i t has r e l a t i v e l y low compressibility under v e r t i c a l loading and r e l a t i v e l y high compressiblity under 248 horizontal loading. This anisotropy i n compressibility r e s u l t s i n an undrained loading response which i s dependent on the i n c l i n a t i o n a of the maximum p r i n c i p a l stress with the deposition d i r e c t i o n . An a value of 0 degrees r e s u l t s i n r e l a t i v e l y less contractive response (as i n t r i a x i a l compression loading), while an a value of 90 degrees r e s u l t s i n r e l a t i v e l y more contractive response (as i n t r i a x i a l extension loading). Hollow cyli n d e r t e s t s performed by Symes et a l . (1985) and Shibuya and Hight (1987) show a systematic weakening (increasing contractiveness and reduction i n phase transformation strength) i n water pluviated sand with increase i n a from 0 to 90 degrees, which suggests that compression and extension t e s t s provide the extremes of behaviour possible i n a given water pluviated sand. Although the trend i n inherent anisotropy i s s i m i l a r f o r a l l water pluviated sands which have been tested, the degree of anisotropy i s dependent upon sand type. For example, water pluviated Ottawa sand i s shown to have l i m i t e d l i q u e f a c t i o n behaviour i n both extension and compression loading when loaded at loosest state, while i n the same stress range, angular t a i l i n g s sand i s shown to have l i m i t e d l i q u e f a c t i o n behaviour only i n extension loading. Figure 8.1 shows that although Ottawa sand i s subject to l i m i t e d l i q u e f a c t i o n i n compression loading over a range of void r a t i o s , the material i s s t i l l subject to substantial d i l a t i o n once i t i s strained past phase transformation state. The contrast i n loading behaviour of Fig. 8.1 Undrained loading response of water deposited Ottawa Sand C109 at various densities 2.5 1.5 1.0 0.5 1.0 1.5 " Cr3"c = 2.0 k g f / c m 2 K c = 1.0 - • SAMPLE SET Drj(%) Drc(*) • 1 32.5 36 A 2 36.0 40.5 O 3 39.0 43.0 O 4 43.5 46.5 + 5 60 62.5 ! 1 < t < < r / / * + o J / + O / A 1 P o / F // ® n O A 7 > ] ) \ > > O-O-COO^g , cr + / + I I l l I I 1 1 1 1 1 1 - 7 - 5 - 3 - 1 1 3 5 7 AXIAL STRAIN £ tt) 250 Ottawa sand and Brenda sand indicates that i t i s well worth while to conduct laboratory t e s t s on representative samples of a given sand i n order to characterize i t s properties. The anisotropic properties of water pluviated sands may lead to modes of f a i l u r e and mechanisms of t r i g g e r i n g f a i l u r e i n a s o i l mass which are both unexpected and d i f f i c u l t to predict using presently a v a i l a b l e a n a l y t i c a l methods. S o i l masses which are subject to any form of l a t e r a l loading, such as i n offshore islands and harbour f a c i l i t i e s which are subject to i c e , wave or boat loading, may be highly susceptable to l i q u e f a c t i o n . In contrast, a s o i l mass which i s subject to mainly v e r t i c a l loading may be r e l a t i v e l y r e s i s t a n t to l i q u e f a c t i o n . Problems with current methods of evaluation a r i s e i n the majority of p r a c t i c a l cases where a s o i l mass may be subjected to a combination of loading conditions. The following paragraphs attempt to i d e n t i f y and explain some of the p r a c t i c a l implications of water pluviated sand f a b r i c and properties upon the performance of a common structure, a s o i l embankment. An embankment constructed of water pluviated sand should be r e l a t i v e l y r e s i s t a n t to l i q u e f a c t i o n under s t a t i c loading conditions, due to the r e l a t i v e l y low compressibility and high undrained strength of water pluviated sand under v e r t i c a l loading. Terzaghi and Peck (1967) state that "A clean sand deposited under water i s stable, although i t may be loose, because the grains r o l l down into stable positions. In a sand capable of 251 spontaneous l i q u e f a c t i o n , some agent must i n t e r f e r e with t h i s process". The r e l a t i v e l y small number of reported l i q u e f a c t i o n f a i l u r e s of hydraulic f i l l embankments under s t a t i c loading conditions tends to support the idea that most of these embankments are r e s i s t a n t to l i q u e f a c t i o n under normal conditions. The f a c t that some hydraulic f i l l embankments have been observed to f a i l under s t a t i c loading suggests that some s p e c i f i c features of ei t h e r the sand used or the method of construction has resulted i n f a i l u r e . Test r e s u l t s presented i n t h i s t h e s i s indicate that d i f f e r e n t sands at loosest state a f t e r deposition may indeed have varying degrees of resistance to l i q u e f a c t i o n under v e r t i c a l loading. A comparison of the properties of Ottawa C109 sand and Brenda t a i l i n g s sand suggests that rounded quartz sand which has a lower angle of i n t r i n s i c f r i c t i o n on p a r t i c l e surfaces i s more susceptable to the development of flow f a i l u r e under v e r t i c a l loading than angular f e l s i c sand which has on average a higher angle of i n t r i n s i c f r i c t i o n on p a r t i c l e surfaces. The amount of a i r entrapped within a hydraulic f i l l sand may also i n t e r f e r e with the development of a stable sand f a b r i c during deposition. A sand s l u r r y which i s deposited below water l e v e l may be expected to have a small percentage of entrapped a i r , which would have very l i t t l e e f f e c t on water pluviated sand f a b r i c due to small c a p i l l a r y tension forces. A sand which i s deposited into water may 252 contain r e l a t i v e l y more entrapped a i r , while a sand s l u r r y which i s deposited above water may contain a large amount of entrapped a i r , and thus develop a f a b r i c which i s more l i k e that of moist tamped sand. A sand which has a large content of entrapped a i r i s generally more unstable under v e r t i c a l loading than sand which i s deposited i n a saturated state, due to the bulking e f f e c t and influence of c a p i l l a r y tension forces between grains. I f a sand which i s deposited above water i s re-graded by a bulldozer without s i g n i f i c a n t compaction, the sand may be bulked and i t s f a b r i c altered further to produce a material which i s considerably less stable under v e r t i c a l loading. The mechanism of hydraulic f i l l placement may have a s i g n i f i c a n t a f f e c t upon i t s performance, thus i t i s very important to specify and control the mechanism of f i l l placement. The mechanism of hydraulic f i l l placement i n a f u l l y saturated state may also a f f e c t the i n s i t u f a b r i c and material performance. Laboratory prepared s l u r r y deposited t e s t specimens of sand and s i l t y sand are homogeneous and thus represent elemental material properties. Natural f l u v i a l and hydraulic f i l l sands, i n practice, w i l l undergo some degree of p a r t i c l e segregation. The e f f e c t of p a r t i c l e segregation may be assessed from the r e s u l t s of tests performed on Ottawa sand C109 (see Figure 3.12). One set of compression and extension t e s t s was performed on homogeneous s l u r r y deposited sand specimens (with no segregation) and another set of t e s t s was conducted on water pluviated sand specimens (some v i s i b l e segregation - Ottawa sand has C u = 1.5). A l l t e s t s were conducted on e s s e n t i a l l y loosest state specimens at s i m i l a r density. Segregation i s shown to increase both the peak strength as well as the phase transformation strength i n compression. The same e f f e c t , though to a smaller extent, i s observed i n extension loading. The e f f e c t of p a r t i c l e s i z e segregation upon undrained compression response i s s i m i l a r to the e f f e c t of gradation upon compression response i n Brenda sands (see Figure 5.5). When compared at loosest state a f t e r deposition, the compression loading response of homogeneous poorly-graded sand (Figure 5.5) and segregated sand (Figure 3.12) i s shown to be i n i t i a l l y s t i f f e r at small s t r a i n l e v e l and somewhat so f t e r at large s t r a i n l e v e l than the compression response of homogeneous well-graded sand (Figure 5.5) or unsegregated sand (Figure 3.12). In addition, both segregated sands and poorly-graded sands are shown to have lower density at loosest state than unsegregated or w e l l - graded sand (see Figure 3.8, Figure 3.9 and Table 3.2). One may conclude from these observations that p a r t i c l e segregation tends to make an otherwise well-graded sand behave as i f i t were more poorly-graded. This would be true i f loading response i s compared at e i t h e r loosest state a f t e r s l u r r y deposition, or at constant density. Since poorly-graded sands are more susceptible to l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n i n extension loading than well-graded sands, when consolidated from loosest state a f t e r deposition, some segregated sands could also be expected to be more contractive than unsegregated sands under extension loading at loosest state. In s i t u sands which invar i a b l y have some degree of p a r t i c l e s i z e segregation could be expected to be s l i g h t l y more susceptible to l i q u e f a c t i o n under horizontal loading and s l i g h t l y l e s s susceptible to l i q u e f a c t i o n under v e r t i c a l loading than unsegregated samples of equivalent gradation which are also consolidated from loosest state. In laboratory studies, the deposition of sand through water occurs i n the v e r t i c a l d i r e c t i o n , with settlement of p a r t i c l e s upon a horizontal deposition plane. This r e s u l t s i n the v e r t i c a l loading d i r e c t i o n having the l e a s t and horizontal loading the most contractive response. The axis of l e a s t contractive response i n a hydraulic f i l l sand deposited on a slope may s h i f t from v e r t i c a l towards a d i r e c t i o n normal to the slope. This could have the damaging e f f e c t of decreasing the resistance to l i q u e f a c t i o n along a pot e n t i a l f a i l u r e surface i f the slope was constructed outwards from the central core. An opposite e f f e c t , or an increase i n resistance to l i q u e f a c t i o n could occur i f the embankment was constructed by f i l l i n g on a slope that dips from the outer s h e l l towards the central core. Such a technique of construction could also l i m i t the damaging e f f e c t of f i n e r grained or s i l t y beds and lenses within the embankment slope, because these l e s s permeable beds would be dipping downwards towards the central core, opposite the dip of the embankment slope and a poten t i a l f a i l u r e surface. This o r i e n t a t i o n of f i n e r grained beds would cause fa s t e r d i s s i p a t i o n of pore pressures from within the embankment, and would also l i m i t the e f f e c t which any p a r t i c u l a r weaker or impermeable bedding layer might have upon the ori e n t a t i o n of a f a i l u r e surface. The r e s u l t s presented i n t h i s study show that water deposited s i l t y sands could be s l i g h t l y l e s s susceptable to li q u e f a c t i o n than clean sand. The permeability of s i l t y sands, however, decreases with increase i n s i l t content. Thus, under f i e l d conditions, a condition of s t r i c t l y undrained loading could occur more r e a d i l y i n s i l t y sands than i n clean sands, which could make s i l t y sands more vulnerable to l i q u e f a c t i o n . The stress conditions on a pot e n t i a l f a i l u r e surface through an embankment vary from the condition of a v e r t i c a l maximum p r i n c i p a l stress at and below the crest of the embankment, towards horizontal maximum p r i n c i p a l stress at the toe of the embankment. The d i r e c t i o n of maximum p r i n c i p a l stress undergoes continuous r o t a t i o n from the crest towards the toe of the embankment. In order to cal c u l a t e a Factor of Safety for a given slope, i t i s important to determine t h i s v a r i a b i l i t y of s o i l strength with d i r e c t i o n of loading. This i s e s p e c i a l l y important i n analyzing the s t a b i l i t y of hydraulic f i l l embankments, because hydraulic f i l l properties are highly anisotropic. A consequence of the r e l a t i v e l y lower strength of hydraulic f i l l sand with the rotation of maximum p r i n c i p a l stress toward the horizontal d i r e c t i o n i s that one could expect a r e l a t i v e l y deep seated f a i l u r e surface within an embankment. A major portion of the f a i l u r e surface would be predicted to be f a i r l y f l a t , as observed i n the f a i l u r e zone of the lower San Fernando hydraulic f i l l dam (Castro et a l . , 1985; Seed et a l . , 1975). On the r e l a t i v e l y f l a t f a i l u r e zone of the lower San Fernando Dam, the undrained strength would correspond to loading with a = 45 + <j>s/2, where ^ s i s the f r i c t i o n angle at steady-state. With ^ s = 37°, a = 63°, which i s c l o s e r to a horizontal d i r e c t i o n than a v e r t i c a l d i r e c t i o n of maximum p r i n c i p a l s t ress. I f s u i t a b l e a dependent values of steady-state strength were used i n the analysis of the s t a b i l i t y of the dam, i t would probably not be necessary to apply a reduction factor of 20 to the measured t r i a x i a l compression t e s t steady-state strength i n order to obtain back-analysed strength at f a i l u r e (as reported by Castro et a l . , 1985). Den s i f i c a t i o n of sand samples taken from the dam could be blamed fo r an overestimate of i n s i t u steady-state strength, but i t s e f f e c t s are probably overstated due to a neglect of a dependence of steady-state strength. An estimate of the magnitude of anisotropy between compression and extension loading modes may be obtained from the r e s u l t s reported i n t h i s t h e s i s . Loose Ottawa sand C109 has extension phase transformation strength that i s at most 10% of that i n 257 compression (Figure 3.12, Figure 8.1), while angular t a i l i n g s sands do not even show contractive behaviour i n compression (Figure 5.2 through Figure 5 . 4 ) . The low strength of water pluviated sands under horizontal loading may play a r o l e i n the i n i t i a t i o n of contractive flow i n a hydraulic f i l l embankment. Once l a t e r a l stresses at the toe of an embankment are large enough to i n i t i a t e s t r a i n softening, the toe region may develop very low strength. The development of low strength at the toe of the embankment i s e s s e n t i a l l y equivalent to unloading the toe of the embankment. As would be observed i n unloading the toe of any embankment, t h i s reduction of s o i l strength at the toe would cause a r e d i s t r i b u t i o n of the d r i v i n g stresses deeper within the embankment, which may be s u f f i c i e n t to i n i t i a t e progressive or e n t i r e f a i l u r e of the embankment. Any factors which contribute to increased l a t e r a l loading of the toe of the embankment may cause i n i t i a t i o n of toe f a i l u r e and subsequent progressive f a i l u r e of the en t i r e slope. Increased l a t e r a l load may be induced by external c y c l i c loading due to seismic loading, or an increase i n porewater pressure under the conditions of ei t h e r s t a t i c of c y c l i c loading. The mechanism whereby increased pore pressure may induce an increase i n l a t e r a l stress i s described i n the following paragraphs. Increased pore pressure within an embankment may be induced by rapid rates of construction, by seepage through an embankment which retains water, by the i n i t i a t i o n of 258 s t r a i n softening contractive response, or by c y c l i c loading. Beneath the crest of an embankment, v e r t i c a l t o t a l stress d i s t r i b u t i o n i s a function of s o i l u n i t weight and depth within the embankment. The d i s t r i b u t i o n of v e r t i c a l t o t a l stress below the embankment crest i s e s s e n t i a l l y constant, and may only be altered by a change i n embankment height. V e r t i c a l e f f e c t i v e stress i s i n addition a function of porewater pressure. In contrast, both horizontal t o t a l and e f f e c t i v e stresses are a function of porewater pressure and the mobilized angle of f r i c t i o n within each s o i l element. Assuming that v e r t i c a l t o t a l stress d i s t r i b u t i o n i s constant ( i . e . that the embankment height i s not changed) one may derive Equation 8.3 which rel a t e s the v a r i a t i o n of horizontal t o t a l stress on a s o i l element beneath the crest .of an embankment with the mobilized f r i c t i o n ( e f f e c t i v e mobilized stress r a t i o R) and pore pressure within the s o i l element. Equation 8.3 shows that an increase i n pore pressure within a s o i l element beneath the crest of an embankment would probably also induce an increase i n horizontal t o t a l s t r e s s . Horizontal t o t a l stress within these s o i l elements could be expected to vary from a minimum corresponding to K Q consolidation state, up to a maximum when v e r t i c a l and horizontal t o t a l stress are equal at a state of zero e f f e c t i v e s t r e s s . The horizontal t o t a l stress generated within these s o i l elements beneath the crest of an embankment must be transfered and c a r r i e d by adjacent s o i l elements within the embankment slope. This spreading of l a t e r a l stress would tend to rotate the d i r e c t i o n of maximum p r i n c i p a l stress away from v e r t i c a l and towards horizontal within s o i l elements i n the embankment slope. Within these elements, horizontal t o t a l stress would not be l i m i t e d by the magnitude of i n i t i a l v e r t i c a l stress, as beneath the cr e s t of the embankment. Horizontal t o t a l stress may i n fact exceed i n i t i a l v e r t i c a l t o t a l stress, g i v i n g r i s e to a t r i a x i a l extension type of loading towards the toe of the embankment slope. I f pore pressure i s increased within an embankment, t h i s may also lead to a spreading of l a t e r a l t o t a l stress i n the embankment, which could t r i g g e r s t r a i n softening at the toe of the embankment. I f strength at the toe i s reduced, t h i s would simulate unloading of the toe, which may produce progressive or complete f a i l u r e of the embankment. This mechanism of t r i g g e r i n g flow deformation i s p a r t i c u l a r l y relevant to hydraulic f i l l embankments, due to the c h a r a c t e r i s t i c strength anisotropy of water pluviated sand. For a s o i l element beneath the embankment crest: R = (ow - U) / (a n - U) (8.1) where R e f f e c t i v e mobilized p r i n c i p a l stress r a t i o a. V v e r t i c a l t o t a l stress 260 a h = horizontal t o t a l stress U = porewater pressure Then oh = U + ( a v - U ) / R (8.2) D i f f e r e n t i a t i n g Equation (8.2): d a h = d U + d ( a v / R ) - d ( U / R ) d a h = d U + d a v / R - < 7 vdR/R 2 - dU/R + U d R / R 2 A a h = (1-1/Ri) ( U 2 - U 1 ) + ( a v 2 - a v l ) / R 1 + ( U 2 - a v 2 ) ( l / R j - l / R ^ when a v = constant: Aah = (1-1/Ri) ( U 2 - U 1 ) + ( U 2 - a v ) ( l / R ^ l / R j ) (8.3) where: = i n i t i a l mobilized stress r a t i o R 2 = f i n a l mobilized stress r a t i o A a n = change i n horizontal t o t a l stress = i n i t i a l pore pressure U 2 = f i n a l pore pressure (see Figure 8.2) F ig . 8.2 Change in lateral total s t ress with change in ef fect ive s t r e s s s ta te for a soi l e lement beneath the crest of an e m b a n k m e n t 262 CHAPTER 9 SUMMARY AND CONCLUSIONS In the past, our knowledge of the fundamentals of sand l i q u e f a c t i o n behaviour has been derived from laboratory t e s t s and observations. To ensure that fundamental material strength properties determined i n the laboratory are applicable to p r a c t i c a l f i e l d problems, two basic questions must be considered: (1) i s the s o i l sample tested i n the laboratory representative of the i n s i t u s o i l being modelled, and (2) does the laboratory t e s t i n g technique employed simulate the loading conditions that occur i n s i t u . Previous studies have shown that sand l i q u e f a c t i o n behaviour i n the laboratory i s controlled by both method of sample preparation and mode of s o i l t e s t i n g . A majority of loose sandy s o i l s which are prone to l i q u e f a c t i o n and of p r a c t i c a l concern i n geotechnical designs are deposited by natural f l u v i a l deposition or a r t i f i c i a l hydraulic f i l l placement. These deposits are often well-graded with some fines content. A majority of laboratory t e s t i n g i n the past has been conducted on poorly- graded sands i n order to ensure sample uniformity, which i s required i n most laboratory t e s t s i n order to measure elemental s o i l properties. The study of well-graded sands and sands with some fines content has been r e l a t i v e l y l i m i t e d . Since these sands are r e l a t i v e l y common i n the f i e l d , the study of the e f f e c t of gradation and fines 263 content upon sand behaviour has been i d e n t i f i e d as a major research objective by the U.S. N.R.C. (1985) report on earthquake engineering. Most sands which have been tested i n the past have been reconstituted i n the laboratory using the moist tamping or dry p l u v i a t i o n techniques of sample preparation. These techniques may not simulate e i t h e r the density range or strength behaviour possible i n a sand which i s pluviated through water, as i n a f l u v i a l or hydraulic f i l l sand deposit. In order to model the behaviour of f l u v i a l and hydraulic f i l l sands i n the laboratory, the s l u r r y deposition method of sample preparation has been developed. This method simulates the mechanism of hydraulic f i l l or f l u v i a l sand deposition through water very well, yet y i e l d s homogeneous well-mixed samples which are e s s e n t i a l l y unsegregated, regardless of gradation and fines content. A comparison of the s o i l strength properties of poorly-graded water pluviated and s l u r r y deposited sand samples indicates that both sample preparation techniques y i e l d s i m i l a r t e s t r e s u l t s . In order to observe the e f f e c t which gradation and fines content have upon the properties of sands which have been pluviated through water, a seri e s of undrained t r i a x i a l t e s t s have been conducted on samples of poorly-graded, w e l l - graded and s i l t y angular t a i l i n g s sands derived from the Brenda Mine, B r i t i s h Columbia. This t a i l i n g s sand i s representative of generally more well-graded and s i l t y sands found i n se i s m i c a l l y active mountainous areas, and t a i l i n g s sands which are derived from g r a n i t i c rock. The use of t a i l i n g s sand derived from crushed rock ensures that sand mineralogy i s e s s e n t i a l l y independent of grain s i z e . Both t r i a x i a l compression and extension t e s t s were employed, i n order to show the e f f e c t of d i r e c t i o n of loading upon strength behaviour. The f a b r i c of water pluviated sand i s shown to produce a c h a r a c t e r i s t i c anisotropy i n undrained loading response. Water pluviated sand i s s u b s t a n t i a l l y more contractive when loaded under a horizontal maximum p r i n c i p a l s t r e s s , and s u b s t a n t i a l l y l e s s contractive when loaded under a v e r t i c a l maximum p r i n c i p a l s tress. The substantial d i r e c t i o n a l dependence of sand strength at constant void r a t i o c o n f l i c t s with the main premise of steady-state concepts, which states that the ultimate undrained strength of sand i s only a function of s o i l void r a t i o , and independent of factors such as s o i l f a b r i c , d i r e c t i o n of loading and consolidation state. The use of steady-state concepts and t r i a x i a l compression t e s t r e s u l t s to characterize the behaviour of water pluviated sand would r e s u l t i n high estimates of sand strength. The use of such estimates i n design could r e s u l t i n designs which are highly unconservative. In water pluviated sands consolidated from loosest state of deposition, as might be expected i n a hydraulic f i l l deposit, t r i a x i a l compression s t r e s s - s t r a i n response i s e s s e n t i a l l y the same for various gradations of sand. In 265 contrast, t r i a x i a l extension response i s highly dependent upon s o i l gradation. Well-graded sand i s shown to be su b s t a n t i a l l y l e s s contractive than poorly-graded sand i n extension loading. Well-graded sand thus shows less anisotropy, or less of a difference between extension and compression t e s t response than poorly-graded sand. One may conclude that well-graded sand i s i n general more r e s i s t a n t to l i q u e f a c t i o n than poorly-graded sand. In poorly-graded sand, smaller grain s i z e tends to produce s l i g h t l y more d i l a t i v e response i n compression loading, yet more contractive response i n extension loading. Strength anisotropy of i s o t r o p i c a l l y consolidated sand i s shown to be greatest at low consolidation stress and l e a s t at high consolidation s t r e s s . The process of i s o t r o p i c consolidation i s thus observed to s l i g h t l y a l t e r strength anisotropy, or s o i l f a b r i c . Gradation generally has a greater e f f e c t upon material properties of sand than non-cohesive fines content, e s p e c i a l l y i f the sand portion i s coarser grained. An increase i n s i l t content up to 20% i n loosest state s l u r r y deposited 20/200 sand makes monotonic compression loading behaviour somewhat more d i l a t i v e and extension loading behaviour somewhat less contractive. The rather small change i n loading behaviour with increasing s i l t content can be explained by the fact that sand skeleton void r a t i o remains v i r t u a l l y unaltered with increasing s i l t content. S i l t e s s e n t i a l l y f i l l s sand skeleton void space and does not greatly a f f e c t s o i l behaviour. On the other hand, s i l t y sands need not have a large void r a t i o to be susceptible to li q u e f a c t i o n , as long as sand skeleton void r a t i o and s i l t p ortion void r a t i o are high. S i l t y 20/200 sands at loosest state show only a s l i g h t increase i n c y c l i c strength with increasing s i l t content, despite a large reduction i n void r a t i o . When compared at constant sand skeleton void r a t i o , c y c l i c strength i s shown to increase s l i g h t l y with increasing s i l t content. I f the s i l t f r a c t i o n of a s o i l i s segregated into s i l t y lenses, as often i s the case i n hydraulic f i l l or f l u v i a l s o i l deposits, c y c l i c strength of the material may be expected to be lower than i f the material i s well mixed (when considered at loosest state of consolidation), simply because elements of the segregated s o i l are more poorly- graded. I f a segregated sand and a well mixed sand with the same grain s i z e gradation and void r a t i o are compared, the segregated s o i l would tend to be more r e s i s t a n t to li q u e f a c t i o n , because i t i s e f f e c t i v e l y more poorly-graded and thus at an e f f e c t i v e l y denser state. For p r a c t i c a l purposes i t i s conservative to ignore s i l t content i n a hydraulic f i l l s i l t y sand, when considering undrained s o i l strength, as long as the water pluviated reconstituted s i l t free material tested i n the laboratory has a s i m i l a r sand gradation and sand skeleton void r a t i o as the s i l t y sand being modelled. 267 The conclusion that s i l t content generally makes a laboratory s o i l sample more r e s i s t a n t to l i q u e f a c t i o n (when compared at both loosest state or constant sand skeleton void r a t i o ) does not take into account drainage and migration of porewater as may occur i n a f i e l d embankment. In general, a s i l t y sand embankment of s i m i l a r sand skeleton density and gradation as a clean sand embankment may be more susceptible to s t r a i n development due to: (1) greater retension of pore pressure during loading, and (2) migration and build-up of pore pressure at s i l t y layer b a r r i e r s . The c h a r a c t e r i s t i c loading response and anisotropy of water pluviated sand may be explained by considering the mechanics of f r i c t i o n a l resistance to p a r t i c l e contact s l i p during loading. For an assembly of r i g i d p a r t i c l e s , dilatancy during loading i s shown to be a function of p a r t i c l e structure or f a b r i c (the s p a c i a l d i s t r i b u t i o n and o r i e n t a t i o n of p a r t i c l e contacts), d i r e c t i o n of loading, stres s r a t i o l e v e l and s t r a i n l e v e l . The f a b r i c of a sand i s interpreted to be a function of sample preparation and stres s r a t i o h i s t o r y . The s o i l f a b r i c and properties derived from a s p e c i f i c method of deposition may be explained by considering the physical processes which are a c t i v e during deposition. The method selected for s o i l placement i n the f i e l d may influence the s t a b i l i t y of a s o i l mass considerably. The method of s o i l deposition has been shown to have a large e f f e c t upon: (1) the range of void r a t i o s possible within a 268 s o i l deposit, (2) the range, of undrained loading response possible, (3) the range of s o i l anisotropy possible, and (4) the magnitude of s o i l strength at a given void r a t i o . Moist or dry s o i l may be prepared at much larger void r a t i o s than possible i n s i m i l a r water pluviated s o i l . Thus much lower strengths may be obtained by moist or dry preparation of a sand, simply because much higher void r a t i o s are possible. At the same void r a t i o , water pluviated sand may be weaker or stronger than a i r pluviated or moist tamped sand, depending upon s o i l f a b r i c and d i r e c t i o n or mode of loading. Laboratory observations concerning the e f f e c t of s o i l deposition method upon s o i l properties may be used i n evaluating and perhaps designing better f i e l d construction techniques. The hydraulic f i l l form of construction i s shown to be f a i r l y good i n that lower depositional void r a t i o s can generally be attained with no compactive e f f o r t , as long as the hydraulic f i l l technique ensures saturation of the f i l l material. In addition, hydraulic f i l l i s r e l a t i v e l y l e s s compressible under v e r t i c a l loading, which i s often b e n e f i c i a l under f i e l d loading conditions. The c h a r a c t e r i s t i c properties of water pluviated sand would r e s u l t i n c h a r a c t e r i s t i c modes of f a i l u r e and t r i g g e r i n g f a i l u r e within a s o i l mass which may be d i f f i c u l t to p r e d i c t . The v a r i a t i o n of material properties with d i r e c t i o n of loading should be considered during design. The method of s t a b i l i t y analysis employed i n design should be able to account f o r the v a r i a t i o n of undrained strength 2 6 9 with the i n c l i n a t i o n of maximum p r i n c i p a l stress to the f i l l deposition d i r e c t i o n . The r e l a t i v e l y low strength of water pluviated sand under l a t e r a l loading conditions would tend to induce a deep seated f a i l u r e surface i n an embankment. In addition, undrained f a i l u r e of an embankment i s l i k e l y to be triggered by i n i t i a l l i q u e f a c t i o n f a i l u r e at the toe, which i s induced by increased l a t e r a l stress i n the embankment. Liquefaction at the toe under a maximum p r i n c i p a l stress which i s close to horizontal would simulate unloading of the embankment toe, which could lead to progressive or complete f a i l u r e of the embankment. 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"A C r i t i c a l Assessment of Membrane Penetration i n the T r i a x i a l Test," Geotechnical Testing Journal, Vol. 7, No. 2, pp. 70-76. Vaid, Y.P. and Negussey, D. (1986). "Preparation of Reconstituted Sand Specimens," U.B.C. S o i l Mechanics Series No. 98, The University of B r i t i s h Columbia, 26p. Vaid, Y.P., Negussey, D. and Zergoun, M. (1988). "A Stress- and Strain-Controlled Monotonic and C y c l i c Loading System," ASTM STP 977. 278 Appendix A: Membrane Penetration Correction Volumetric and radial strains during consolidation have been corrected for membrane penetration errors using Method 2 described by Vaid and Negussey (1984). Method 2 membrane penetration corrections are determined by conducting an isotropic consolidation load and unload test on a single soil sample. In isotropic consolidation loading, soil specimen strains need not be isotropic due to soil anisotropy, but in isotropic consolidation unloading, soil specimen strains have been found to be isotropic. The deviation of triaxial test soil specimen unloading strain from isotropy with respect to axial strain is shown to be due to membrane penetration effects in the radial direction of loading. The correction to radial strain required to maintain isotropic unloading strain is the correction required to account for membrane penetration effects. The unit membrane penetration correction £ m is calculated as shown in Equation A.1: v̂tu = £ m ASA>+ ^ o u Eqn. A.1 Where: £ = unit membrane penetration correction or membrane penetration m volume per unit surface area of membrane cT V t u = total volumetric strain measured in an unloading step cl = axial strain measured in an unloading step au 3cTou = true volumetric strain in the unloading step if there is no membrane penetration (top and bottom platens must be rigid) A s = surface area of soil sample covered with rubber membrane V 0 = initial volume of soil sample within membrane Equation A.1 may be rewritten in terms of soil sample diameter, Equation A.2: £ m = £ v t u - 3 c : a u ) D e / 4 Eqn. A.2 Where: D0 = soil sample diameter 279 Unit membrane penetration £ m varies approximately linearly with logarithm of effective consolidation stress (see Figure A.1, after Vaid and Negussey, 1984). The slope (m, Equation A.3) of unit membrane penetration with logarithm of effective stress is essentially constant, and may be used in Equation A.4 to calculate true volumetric strain within a soil specimen whose m value is known. m Eqn. A.3 Eqn. A.4 Where: m membrane penetration function slope (see Figure A.1) consolidation effective stress on membrane initial consolidation effective stress on membrane true volumetric strain corrected for membrane penetration FIGURE A.1 Unit membrane penetration of various Brenda sand gradations determined by the single specimen method After Vaid and Negussey (1984) 0.007 - i , 2 8 1 Figure A.2 Strain in Various Gradat ions of Brenda Sand Under Virgin Isotropic Consol idat ion and Unloading AXIAL STRAIN £ q (%) 282 Figure A.3 Strain in Ottawa sand C109 during isotropic virgin consolidation and unloading 283 Appendix B: Calculation of Membrane Stress Correction Various methods for calculating the stresses applied to a soil sample by its confining rubber membrane have been described in soil mechanics literature. These corrections are based on a number of assumptions which may or may not be true, depending upon test conditions. There are three general types of membrane correction assumptions as follows (from Fukushima and Tatsuoka, 1984): Method 1) the membrane is assumed to maintain the shape of a thin wall cyclindrical shell, such that elastic thin shell compression theory can be used; Method 2) it is assumed that axial deformation occurs independently of radial and circumferential deformations; and Method 3) it is assumed that the resistance of a membrane against axial deformation is negligible due to membrane buckling, and only membrane "hoop stresses" are applied to the soil sample. Method 2 is thought to be unreliable because it neglects elastic theory. Method 3 is useful for compression test corrections at larger strain level if buckling can be visually observed, especially in the testing of soft clay samples which are prone to large consolidation strains and are generally tested with very thin membranes. Method 1 is generally preferable to the other methods of correction at smaller strain levels as long as membrane buckling is not observed and if soil samples are tested in both compression and extension loading. Method 1 is particularly useful for testing sandy materials for susceptability to liquefaction, as low stress levels are encountered, larger membrane thicknesses which are less susceptable to buckling are used to overcome membrane penetration and damage problems, consolidation strains which may increase susceptability to buckling are small, and samples may be loaded in both extension and compression directions. Method 1 type corrections have been derived and used by numerous workers, for example Henkel and Gilbert (1952), Duncan and Seed (1967). Berre (1982), Ponce and Bell (1971), Molenkamp and Luger (1981) and DeGroff et. al. (1988). Although the same general method of evaluation has been used, different researchers have used different formulations which may or may not take into account the following factors which should be considered: 1 ) stress and strain induced in the membrane during sample preparation, 2) change in soil membrane thickness during strain, 3) 284 change in membrane modulus with strain level, 4) change in membrane stress and strain during sample saturation and consolidation, and 5) change in membrane stress with axial and radial strain during loading; it is important to note that according to elasticity theory, axial and radial membrane strains have an effect upon both axial and radial stresses, depending upon Poisson's ratio. In addition to theoretical formulation of membrane stress corrections, experimental verification of corrections should be undertaken to validate their reliability. A formal derivation of Method 1 corrections which takes into account all of the factors described above and which simplifies the calculation of membrane stress correction is presented in the following pages. Experimental verification of the derived membrane stress correction factors is provided by a strain controlled undrained extension and compression test upon a triaxial test sample membrane filled with water. Calculation of membrane stress correction by Method 1 (elastic shell theory): The elastic strains in an elastic membrane cylindrical shell are as follows: ^MO= ( ^ . - V O ^ - V O J / E M Eqn. 1 £MC= (-^a+^c-^U/ E M Eqn. 2 £ M t = (-VOJ-VLJ^+GJ/ E M Eqn. 3 Where: ^ua= axial strain in cylindrical membrane £ U c = circumferential strain in cylindrical membrane £ u t = radial strain, or strain in thickness of the cylindrical membrane E u = Young's modulus of membrane rubber 1/ = Poisson's ratio of membrane rubber 0y a= axial stress in membrane tT U c= circumferential stress in membrane Oyt==LTr «= radial stress in cylindrical membrane 285 From the cylindrical dimensions of the membrane and radial stress upon the inside of the membrane, a relationship between LT U c and 0"ul may be determined: Figure B.1 Rubber membrane shell D*H* a = t X *2*t*H r MC ffr=t7Me*2*t/D H i If t << D (for a thin cylindrical elastic shell) CT << ( J , thus one can assume that CT = (JUi= 0, and may be ignored; from Equations 1 and 2: 'Ma 'Mc ( O M a - ^ M c ) / E M (-^ a4 - C T M c ) / E M Hence: C L o = ( ^ 0 + ^ ^ C ) * E M / ( I - T / 2 ) ° M c = ( V E M ^ M > E M / ( 1 - V a ) Eqn. 4 Eqn. 5 Eqn. 6 Eqn. 7 Corrected stresses on a cylindrical soil sample within a confining membrane are O a ^ O a ' - 4 * ^ ) * ^ ff> q ' -2 * ( t / D ) * o ; Mc Eqn. 8 Eqn. 9 286 Where: CT = corrected axial stress on soil sample GT = corrected radial stress on soil sample CT = axial stress on soil sample CT = radial stress on soil sample t = present membrane thickness D = present sample diameter Thus membrane corrected sample stresses are: (6) +(8) a a >CT '-4* ( t /D ) *E u * ( c T M Q + VEj/O-V2) Eqn. 10 (7) +(9) . = j / - 2 * ( t / D ) * E M * ( V E M t E M B ) / ( 1 - v y a ) Eqn. 11 (Compression stress and strain is positive) With a membrane rubber Poisson's ratio of V = 0.5 as is commonly measured (which implies that the membrane rubber undergoes zero volume change when strained): from (10) a a > a ; - 8 < t / D ) * E M < 2 £ M a + c i M o ) / 3 Eqn. 12 from (11) arrl = CT '-4* ( t/D)*E M * ( £Mo+2 £ M c )/3 Eqn. 13 With no volume change in rubber during strain ( V = 0.5): Where: = volumetric strain in rubber Considering circumferential strain in membrane: S = 7 T D AS = 7 T A D Eqn. 15 287 Where: S = circumference of cylindrical membrane S = nominal unstretched membrane circumference 0 D = diameter of cylindrical membrane D = nominal unstretched membrane diameter 0 EUc = A S / 5 0 = 7 T A D / 7 r D 6 = A D / D 0 = £ r Eqn. 16 £ r = (DL - D)/D e D = ( 1 - E r )*D o Eqn. 17 Where: £ r = radial strain of cylindrical membrane dimensions referenced to initial unstretched membrane diameter Considering radial strain in membrane (or change in membrane thickness): = ( t o " 0/t o= - ( £ r + £ M a ) Eqn. 18 t = t.(1+ ciM a+ Er ) Eqn. 19 Where: t 0 = nominal undisturbed membrane thickness Considering volume contained within membrane: ^v = (Ve - V)/V 0 = ( £ M o +2Er ) Eqn. 20 ^ R = ( ^ V - ^ M O )/2 Eqn. 21 from (21) + (17) D = D (2+ £ M a - £ v )/2 E q n > 2 2 V = 7 T D 2 H /4 Where: V 0 = nominal volume within unstretched cylindrical membrane H q = nominal height of unstretched membrane which contains sample cTv = volumetric strain of volume within the stretched membrane referenced to unstretched membrane volume 288 Considering axial stress on soil sample: C T a > C T ; - 8 < t / D ) * E M < 2 £ M o + c i M c ) / 3 Eqn . 12 (12)+(19) CTm = C T ' - S * ^ / D ) * E M *(1 + £ r + £ M a )(2 £ M o + £ r ) /3 + ( 2 D CT̂  = GT ' -2*a / D ) * E M *(2+ £ v + £ M q )(3 £M a+ E v )/3 , , 4 * t 0 *E M ( 2 4 - £ v + e U o )(3 £ M a + £ v ) +(22) CT = CT — — - ^—^ ^ lJ. E a n 0 3 Considering radial stress on soil sample: <L = L T ' - 4 * ( t / D ) * E M * ( £ M a + 2 c i M c ) / 3 Eqn . 13 from (l3) + (l9) + (22) + (2l) 8 * E M * t o ( i + e M a 4 - £ r ) £ v CT = a 3*D 0 (2- £ v + O 3 * D 0 ( 2 - £ v + O E ^ 2 4 Thus soil stresses corrected for axial and radial membrane loading are: n - ^ 4 « t 0 * E u ( 2 + £ v + £ u J ( 3 £ u „ + £ v ) ff"" ^ 3 * 0 . ( 2 - £ v + £ U o ) E ^ 2 3 (2+ £„ + £ „ „ )£ „ a - = C f - 3*D„(2- £ v + £„„ ) E q n - 2 4 Note: All strains are measured with respect to nominal unstretched membrane dimensions. 289 Determination of membrane Young's modulus E M : In the previous derivation of membrane stress corrections, present membrane thickness and dimensions are used in the calculation of membrane stresses. The experimental technique for the determination of membrane Young's modulus described by Bishop and Henkel (1962), which requires that a strip of rubber membrane be hung between two glass rods and loaded with known mass to measure induced deformation in the membrane, is adequate for the determination of membrane Young's modulus as long as stretched membrane area is used in the calculation of induced membrane stress and thus Young's modulus. The original method of Young's modulus calculation described by Bishop and Henkel does not account for changes in stretched membrane dimensions. If stretched membrane area is used in the calculation of membrane stress. Young's modulus is found to be constant from 0 to 25% extension loading strain (see Table B.1). If initial membrane area is used to calculate induced stress and thus Young's modulus, Young's modulus is shown to decrease up to 25% with 25% extension strain. Thus the calculation of Young's modulus using present induced membrane stress is also preferable because calculated modulus is found to be constant with changing stress and strain level. Poisson's ratio can also be verified to be 0.5 when Bishop and Henkel's experimental method is used to determine Young's modulus, by simply measuring the width and thus lateral strain in the test membrane as load is applied. Calculation of membrane stress corrections: To use Equations 23 and 24 to calculate membrane stresses on a soil sample, the following procedure is employed during sample preparation: 1) Initial membrane unstretched thickness t and nominal diameter D„ are determined. 2) Horizontal lines 10 cm apart are drawn with a marker pen on the unstretched membrane, so that initial axial sample preparation strain in the membrane may be determined by measuring the distance between 290 Determination of membrane Young's modulus E u for a Geotest membrane (2.36" diameter by 0.012" thick by 8" high): Figure B.2 Measurement of membrane modulus after Bishop and Henkel (1962): I — length between marks on membrane W = load on membrane E u = Young's Modulus by Bishop and Henkel method of calculation, using initial dimensions of sample membrane. E u = Young's Modulus using loaded thickness and width of membrane to calculate stress on membrane. f W Table B.1 Calculation of a Geotest membrane modulus Load W Length I Width £ , EL E u (kg) (cm) (cm) (kg/cm 2) (kg/cm 2) 0 7.85 5.05 0 0 0.25 8.26 0.0522 15.46 16.31 0.5 8.70 0.1083 14.91 16.66 0.75 9.26 0.1796 13.48 16.28 1.0 9.92 4.38 0.2637 0.1327 12.25 16.25 V = 0.1327/0.2637 = 0.503 (used to calculate membrane area and stress) Use E u = 16.3 kg/cm 2 = 1600 kPa Note: One should use present membrane dimensions to calculate stress in membrane and thus membrane modulus. 291 pen marks after sample preparation has been completed. 3) The length of membrane which covers the sample after sample preparation has been completed is adjusted for axial strain induced in the membrane during sample preparation to determine the unstretched height H0 which covers the soil sample. 4) The unstretched volume of membrane which contains the sample is determined from H and D,. . 0 0 5) The axial and volumetric strains used in Equation 23 and 24 are calculated from unstretched membrane dimensions, and updated every time the soil sample within the membrane undergoes axial or volumetric strain. It should be noted that the probability of membrane buckling can be reduced or completely avoided by prestretching the membrane during sample preparation. If a membrane is axially prestretched 5 to 10% during sample preparation, which is not uncommon if the membrane is initially of smaller diameter than the soil sample and stretched to the sides of a sample former tube by an external vacuum, then the membrane will be under axial tension up to 5 to 10% soil sample compression strain and maintain an unbuckled shape at higher compression strain level. The initial load on the soil sample due to the sample membrane is not a problem as it may be accurately calculated using Equations 23 and 24. Equations 23 and 24 have been validated by assembling a rubber membrane within a triaxial test cell with only de—aired water filling it to its initial cylindrical sample shape. The water filled membrane was loaded undrained in a strain controlled testing apparatus, to determine the load—strain response of the membrane experimentally as shown in Figure B.3. The predicted load—strain response calculated using Equation 23, as also shown in Figure B.3, provides a good estimate of membrane load—strain response. The membrane does not buckle until compression strain is greater than 5%; buckling resistance is better in a soil test because membrane shape is maintained by the soil sample within the membrane. .3 Cylindrical rubber membrane stress correction verification by triaxial test constant rate of strain loading of a Geotest membrane filled with water Geotest membrane specifications 2.36" Dia. x 0.012" x 8" E u = 1600 kPa = 16.3 kg/cm Membrane state before loading: •= 413.8 cm1 13.00 cm £ = 0.008 Ma, Cy," -0-119 Unstretched membrane dimensions: H = 13.104 cm V = 369.77 cm 3 0 0 t = 0.0305 cm Rod area = 0.3167 cm Cap buoyant weight = 0.2412 kg Cell pressure = 142 kPa Compression Predicted load versus strain using elastic shell theory Friction on rod = 0.22 kg Extension Measured undrained load versus strain response of a rubber membrane filled with water (corrected for LVDT spring) S a m p l e a x i a l s t r a i n £ = H, — H 0 5 ( p e r c e n t ) 10

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