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Undrained response of saturated sands with emphasis on liquefaction and cyclic mobility Chern, Jin-Ching 1985

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UNDRAINED RESPONSE OF SATURATED SANDS WITH EMPHASIS ON LIQUEFACTION AND CYCLIC MOBILITY by JIN-CHING CHERN  B.S., National Taiwan University, 1968 M.E., Asian I n s t i t u t e of Technology, 1971 M.A.Sc, The University of B r i t i s h Columbia, 1981  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA January, 1985 ©Jin-Ching Chem, 1985  In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study.  I further  agree that permission for extensive copying of t h i s thesis for scholarly purposes may  be granted by the head of  department or by h i s or her representatives.  my  It i s  understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my permission.  Department of  C/u.'J  <g->^j» j ^ r - ,  The University of B r i t i s h Columbia 1956 Main Mall  Vancouver, Canada V6T  1Y3  Date  rLu*^^  /S" .  14 8-S~  written  ABSTRACT  An experimental i n v e s t i g a t i o n of the undrained monotonic and c y c l i c loading behaviour of a saturated angular sand and a rounded sand under t r i a x i a l conditions i s presented.  These studies are aimed at obtaining a  u n i f i e d approach to the undrained behaviour of sand spanning from s t r a i n softening (termed 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 ) to s t r a i n hardening  response and l i n k i n g the c y c l i c loading behaviour to the monotonic  loading behaviour.  It i s also aimed at i n v e s t i g a t i n g the differences In  undrained loading behaviour of sand with d i f f e r e n t p a r t i c l e a n g u l a r i t y . Under monotonic loading, the s t r a i n softening response i s i n i t i a t e d and terminated at two d i s t i n c t values of e f f e c t i v e s t r e s s r a t i o termed c r i t i c a l e f f e c t i v e s t r e s s r a t i o state (CSR) and phase  transformation  s t a t e (PT), regardless of the r e l a t i v e density and consolidation stress conditions.  For s t r a i n hardening response, the s t a r t of d i l a t i o n also  occurs at the same e f f e c t i v e s t r e s s r a t i o of PT f o r s t r a i n softening response.  It i s shown that the unique steady s t a t e l i n e concept f o r  l i q u e f a c t i o n Is a l s o v a l i d f o r l i m i t e d l i q u e f a c t i o n .  The PT states f o r  s t r a i n hardening response, however, form a s e r i e s of l i n e s , which are function of I n i t i a l void r a t i o , merging i n t o the unique steady state l i n e as the consolidation stresses increase. A 3-D  e f f e c t i v e s t r e s s state behavioural model i s developed, which  enables p r e d i c t i o n of the anticipated undrained loading behaviour ( s t r a i n softening or s t r a i n hardening) from the knowledge of the i n i t i a l state of the sand.  It Is shown that a complete s p e c i f i c a t i o n s of i n i t i a l state of  sand, i . e . , void r a t i o , confining pressure and s t a t i c shear, i s required to predict the type of undrained response, e s p e c i a l l y f o r angular sand.  - ii -  Under c y c l i c loading, i f l i q u e f a c t i o n develops, the CSR, e f f e c t i v e stress r a t i o at PT state and steady state l i n e are the same as those observed under monotonic loading.  If c y c l i c m o b i l i t y develops, the  e f f e c t i v e stress r a t i o at PT state i s also the same as that observed under monotonic loading.  Thus, the 3-D e f f e c t i v e stress state diagram  provides a l i n k between monotonic and c y c l i c loading behaviour, and i s used to develop the c r i t e r i a f o r the occurrence of l i q u e f a c t i o n and cyclic mobility.  The influences of void r a t i o and confining pressure on  the c y c l i c loading behaviour are s i m i l a r to those f o r the monotonic loading behaviour.  However, the influence of s t a t i c shear on c y c l i c loading  behaviour can be completely d i f f e r e n t depending on whether 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 i s developed. The undrained loading behaviour of rounded sand i s s i m i l a r to that of the angular sand.  However, for the range of consolidation stresses of  i n t e r e s t , the i n i t i a l r e l a t i v e density alone provides a good s i n g l e parameter c h a r a c t e r i z i n g the i n i t i a l state of the sand, and hence i t s a n t i c i pated response.  - i i i  TABLE OF CONTENTS  Chapter  Page  1  INTRODUCTION  1  2  GENERAL ASPECTS OF UNDRAINED BEHAVIOUR OF SAND  7  3  LABORATORY TESTING  21  3.1. Test Apparatus  21  3.1.1. T r i a x i a l Apparatus  21  3.1.2. Loading System  24  3.2. Testing Procedures  4  31  3.2.1. Sample Preparation and Saturation  31  3.2.2. Methods of Loading  34  3.3. Testing Program  38  3.4. Material Tested  41  3.4.1. S o i l Description  41  3.4.2. Consolidation C h a r a c t e r i s t i c s  43  UNDRAINED MONOTONIC LOADING BEHAVIOUR  48  4.1. Typical Undrained Monotonic Loading Behaviour  48  4.2. S t r a i n Softening and S t r a i n Hardening Responses  68  4.2.1. C l a s s i f i c a t i o n of Undrained Responses  69  4.2.2. C h a r a c t e r i s t i c s of S t r a i n Softening and Strain Hardening Responses 4.3. Undrained Strength Under Monotonic Loading  82 91  4.3.1. Peak Strength for States which Developed Liquefaction  94  4.3.2. Steady State Strength  104  4.3.3. Phase Transformation Strength f o r D i l a t i v e Response  107 - iv -  TABLE OF CONTENTS (cont'd)  Chapter  Page 4.4. 3-D E f f e c t i v e Stress State Diagram  109  4.5. Role of Void Ratio, Confining Pressure and S t a t i c Shear Stress on Undrained Monotonic Loading Behaviour  115  4.5.1. Void Ratio or Relative Density  115  4.5.2. Confining Pressure  116  4.5.3. S t a t i c Shear Stress or Consolidation Stress Ratio 5  118  UNDRAINED CYCLIC LOADING BEHAVIOUR  122  5.1. Liquefaction Induced Under C y c l i c Loading  123  5.1.1. Liquefaction During C y c l i c Loading  124  5.1.2. A p p l i c a b i l i t y of Steady State Concept to Liquefaction Under C y c l i c Loading Conditions  129  5.1.3. C r i t e r i a to Cause Liquefaction Under C y c l i c Loading  136  5.1.4. Test Results  145  5.2. C y c l i c Mobility Induced Under C y c l i c Loading 5.2.1. Strain Development Due to C y c l i c Mobility  157 157  5.2.2. C r i t e r i a to Cause C y c l i c M o b i l i t y Under C y c l i c Loading 5.2.3. Test Results  169 169  5.3. Resistance to Strain Development Under C y c l i c Loading  177  5.4. Influence of Certain Factors on the Undrained C y c l i c Loading Behaviour - v -  179  TABLE OF CONTENTS (cont'd)  Chapter  Page 5.4.1. Void Ratio or R e l a t i v e Density  179  5.4.2. Confining Pressure  181  5.4.3. S t a t i c Shear Stress or Consolidation Stress Ratio  6  185  5.5. Prediction of Undrained C y c l i c Loading Behaviour  194  5.6. Phenomenon of Spontaneous Liquefaction  197  CONCLUSIONS  206  REFERENCES  210  - vi-  LIST OF FIGURES Figure 2.1 2.2 2.3 2.4 2.5 2.6  Page Characteristic behaviour of saturated sand under undrained monotonic loading  8  Effective stress paths of contractive and dilative response ••  11  Characteristic behaviour of dilative sand after large deformation  11  Strain development on loading after the attainment of transient state of zero effective stress  14  Cyclic loading behaviour of contractive sand - true liquefaction and limited liquefaction  16  Cyclic loading behaviour of dilative sand - cyclic mobility  18  3.1  Schematic layout of t r i a x i a l apparatus  22  3.2  Schematic layout of loading system  25  3.3  Detailed layout of consolidation system  26  3.4 3.5  Anisotropic consolidation stress paths Undrained monotonic loading response with limited liquefaction using dead weight loading  30 36  Influence of the pneumatic loading system on the strain softening behaviour  37  3.7  Grain size distribution curves of sands tested  42  3.8  Consolidation characteristics of tailings sand  44  3.9  Consolidation characteristics of Ottawa sand  45  4.1 a-c  Undrained monotonic compression loading behaviour of i n i t i a l l y loose tailings sand under low, moderate and high confining pressure  50  Effective stress paths of monotonic compression loading response of i n i t i a l l y loose tailings sand  53  3.6  4.2  - vii -  LIST OF FIGURES (Continued)  Figure 4.3 a,b  Page Undrained monotonic compression loading behaviour of i n i t i a l l y dense t a i l i n g s sand under moderate and high confining pressure  55  E f f e c t i v e stress paths of monotonic compression loading response of i n i t i a l l y dense t a i l i n g s sand  57  Undrained monotonic extension loading behaviour of i n i t i a l l y loose t a i l i n g s sand  59  Undrained monotonic compression loading behaviour of i n i t i a l l y loose Ottawa sand under low and high confining pressure  60  E f f e c t i v e stress paths of monotonic compression loading response of i n i t i a l l y loose Ottawa sand  62  Undrained monotonic compression loading behaviour of i n i t i a l l y medium dense Ottawa sand under low and high confining pressure  64  E f f e c t i v e stress paths of monotonic compression loading response of i n i t i a l l y medium dense Ottawa sand  66  Undrained monotonic extension loading behaviour of i n i t i a l l y medium dense Ottawa sand  67  Relationship between e c and at PT state f o r t a i l i n g s sand at f i x e d e^ under undrained compression loading . . . .  70  Relationship between e c and at PT state f o r t a i l i n g s sand with various e^ under undrained compression loading  71  Relationship between e c and a 3 at PT state f o r Ottawa sand with various e^ under undrained compression loading  75  Comparison of steady state condition under compression and extension  77  Grain size d i s t r i b u t i o n of t a i l i n g s sand before and after test  79  4.16  Microphotograph of t a i l i n g s sand before and a f t e r test ..  81  4.17  Undrained monotonic loading response under various confining pressure  83  4.4  4.5  4.6 a,b  4.7  4.8 a,b  4.9  4.10  4.11  4.12  4.13  4.14  4.15  -  viii-  LIST OF FIGURES (Continued)  Figure 4.18  4.19  4.20  4.21  4.22  4.23  4.24  4.25  4.26  Page E f f e c t i v e stress conditions at the i n i t i a t i o n of s t r a i n softening response and s t a r t of d i l a t i o n of t a i l i n g s sand under undrained compression loading  85  Undrained monotonic loading behaviour of t a i l i n g s sand consolidated Into the region of contractive deformation  88  E f f e c t i v e stress conditions at the i n i t i a t i o n of s t r a i n softening response and s t a r t of d i l a t i o n of Ottawa sand under undrained compression loading  90  E f f e c t i v e stress conditions at the i n i t i a t i o n of s t r a i n softening response and s t a r t of d i l a t i o n of t a i l i n g s sand under undrained extension loading  92  E f f e c t i v e stress conditions at the i n i t i a t i o n of s t r a i n softening response and s t a r t of d i l a t i o n of Ottawa sand under undrained extension loading  93  Relationship between e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress for t a i l i n g s sand  95  Relationship between the r a t i o of e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress vs K c r a t i o for t a i l i n g s sand  96  Comparison of undrained monotonic loading response of t a i l i n g s sand under the same major consolidation stress but with d i f f e r e n t K c ratios  99  Undrained strengths of t a i l i n g s sand under monotonic compression loading  100  Relationship between e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress f o r Ottawa sand  102  Relationship between the r a t i o of e f f e c t i v e minor p r i n c i pal stress at CSR state and e f f e c t i v e minor consolidation stress vs K £ r a t i o for Ottawa sand  103  4.29  Steady state shear strength of t a i l i n g s sand  105  4.30  Steady state shear strength of Ottawa sand  106  4.31  (a) 3-D e f f e c t i v e stress state diagram f o r t a i l i n g s sand, and (b) A t y p i c a l section at constant e c  112  4.27  4.28  - ix -  LIST OF FIGURES (Continued) Figure A.32 5.1 a-c 5.2 a-c 5.3  5.4  5.5 5.6 5.7  Page Influence of static shear stress on the undrained monotonic loading behaviour  119  Undrained cyclic loading behaviour of contractive tailings sand under low, moderate and high confining pressure  125  Undrained cyclic loading behaviour of i n i t i a l l y loose Ottawa sand under low, moderate and high confining pressure  130  Effective stress conditions at the i n i t i a t i o n of strain softening response and start of dilation of tailings sand under undrained cyclic loading  134  Effective stress conditions at the i n i t i a t i o n of strain softening response and start of dilation of Ottawa sand under undrained cyclic loading  135  Comparison of steady state confining stress of tailings sand under monotonic and cyclic loading conditions  137  Comparison of steady state confining stress of Ottawa sand under monotonic and cyclic loading conditions  138  Comparison of steady state shear strength of tailings sand under monotonic and cyclic loading conditions  139  5.8  Comparison of steady state shear strength of Ottawa sand under monotonic and cyclic loading conditions 140  5.9  Cyclic shear stress conditions to cause liquefaction at fixed e c  142  Cyclic stress required to cause liquefaction or 2.5% axial strain for contractive tailings sand consolidated to various Kc ratios  14?  5.10  5.11  Typical undrained cyclic loading response for contractive tailings sand showing cyclic mobility 149  5.12  Typical undrained cyclic loading response for contractive tailings sand showing (a) liquefaction and (b) cyclic mobility 150  5.13  Typical strain development vs number of cycles for contractive tailings sand consolidated to various K ratios  - x -  1 5 2  LIST OF FIGURES (Continued)  Figure  Page  5.14  C y c l i c s t r e s s required to cause l i q u e f a c t i o n f o r i n i t i a l l y loose Ottawa sand consolidated to various Kc r a t i o s 153  5.15  Typical i l l u s t r a t i o n of l i q u e f a c t i o n of i s o t r o p i c a l l y consolidated Ottawa sand under c y c l i c loading  155  Typical s t r a i n development vs number of cycles f o r i n i t i a l l y loose Ottawa sand consolidated to various K c ratios  156  5.17 a-c  Typical undrained c y c l i c loading behaviour of i s o t r o p i c a l l y consolidated d i l a t i v e t a i l i n g s sand  159  5.18 a-c  Typical undrained c y c l i c loading behaviour of anisot r o p i c a l l y consolidated d i l a t i v e t a i l i n g s sand  162  5.19  Schematic i l l u s t r a t i o n o f monotonic and c y c l i c loading response of saturated sand i n 2-D state diagram  167  C y c l i c stress required to cause 2.5% a x i a l s t r a i n f o r d i l a t i v e t a i l i n g s sand consolidated to various K c ratios  171  5.21  Typical s t r a i n development vs number of cycles f o r d i l a t i v e t a i l i n g s sand consolidated to various K c r a t i o s  172  5.22  C y c l i c s t r e s s required to cause 2.5% a x i a l s t r a i n f o r medium dense Ottawa sand consolidated to various K c ratios  175  Typical s t r a i n development vs number of cycles f o r medium dense Ottawa sand consolidated to various K c ratios  176  Influence of confining pressure on the resistance to s t r a i n development under c y c l i c loading  183  Influence of s t a t i c shear s t r e s s on the resistance to s t r a i n development under c y c l i c loading: (a) d i l a t i v e t a i l i n g s sand; (b) medium dense Ottawa sand  186  Influence of s t a t i c shear s t r e s s on the resistance to s t r a i n development under c y c l i c loading: (a) contractive t a i l i n g s sand; (b) i n i t i a l l y loose Ottawa sand  137  Schematic i l l u s t r a t i o n showing the influence of s t a t i c shear stress on the resistance to l i q u e f a c t i o n under c y c l i c loading  192  5.16  5.20  5.23  5.24  5.25  5.26  5.27  - xi-  LIST OF FIGURES (Continued)  Figure 5.28  5.29  Page Flow chart f o r assessing the p o t e n t i a l of 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  196  Spontaneous l i q u e f a c t i o n induced by pore pressure increase i n i n i t i a l l y loose Ottawa sand  200  t  5.30  5.31  5.32  Spontaneous l i q u e f a c t i o n Induced by pore pressure increase i n contractive t a i l i n g s sand  201  Comparison of r e l a t i v e values of s t a t i c shear stress and steady state shear strength f o r t a i l i n g s sand at two Kc r a t i o s  203  Comparison of r e l a t i v e values of s t a t i c shear s t r e s s and steady s t a t e shear strength f o r Ottawa sand at two Kc r a t i o s  204  - xii -  NOTATIONS  A ^ a r e a  of top chamber and bottom chamber of air loading piston  Ar  area of the loading ram  A  sample area  s  a max  maximum ground surface acceleration  B  Skempton's pore pressure parameter  c  c r i t i c a l effective stress ratio constant = ( a * / c l )  CSR  c r i t i c a l effective stress ratio  CT  characteristic threshold  D  relative density  r  D  rc  D  relative density after consolidation i n i t i a l relative density of specimen as prepared (under 2  i n i t i a l effective stress of 0.2 kgf/cm ) e  void ratio  e  c  e^  void ratio after consolidation i n i t i a l void ratio of specimen as prepared (under i n i t i a l 2  effective stress of 0.2 kgf/cm ) g  gravitational acceleration  K  bias relay constant  K  c  consolidation stress ratio = o' fal l c 3c  m  magnification factor of pressure amplifier  N  number of stress cycles  p,p1,p2,p  air pressures  P*  = 1/2 (a* +  PT  phase transformation  ap  -  xii i  -  = 1/2 (a' - op magnification factor of ratio relay signal pressure steady state line undrained peak shear strength undrained steady state shear strength shear stress increment to peak shear strength under undrained monotonic loading pore pressure excess pore pressure axial strain angle of internal friction major and minor effective pricipal stresses major total principal stress major and minor effective prinpcipal stress increments major and minor effective principal consolidation stresses critical consolidation stress major and minor effective principal stresses at peak strength deviator stress cyclic deviator stress deviator stress increment cyclic shear stress = °(jCy./2 static shear stress  xiv  -  ACKNOWLEDGEMENTS  In presenting this t h e s i s , the author wishes to express his g r a t i tude to the University of B r i t i s h Columbia and National Research Council of Canada for f i n a n c i a l support which made t h i s i n v e s t i g a t i o n possible. The author would also l i k e to thank the following Individuals: • His supervisor, Dr. Y.P. Vaid, for h i s invaluable guidance and advice during the entire course of the research. • Dr. P.M. Byrne, Dr. R.G. Campanella and Dr. W.D.L. Finn for their valuable comments. • His colleagues for their valuable discussions, and Dr. P.K. Robertson for h i s suggestion i n the manner of presenting part of the test results. • The s t a f f of the C i v i l Engineering Department Workshop for t h e i r technical assistance i n f a b r i c a t i n g the t e s t i n g equipments. • Mrs. Brenda G i l l e s p i e for her assistance i n drafting the f i g u r e s , and Mrs. K e l l y Lamb for typing the manuscripts and f i n a l t h e s i s .  And f i n a l l y , the author deeply appreciates the support and consideration given to him by h i s wife during the entire course of his studies.  - xv -  1. CHAPTER 1 INTRODUCTION  Undrained loading behaviour of saturated sands i s of direct i n t e r e s t i n practice where deposits of such materials may  be subjected to rapid  shearing.  develop large deforma-  As a result of such loading, sand may  t i o n s , and f o r c e r t a i n I n i t i a l states may fluid.  even flow l i k e a f r i c t i o n a l  The undrained shearing could be due to c y c l i c earthquake loading  or rapidly applied s t a t i c loading such that p r a c t i c a l l y no drainage occurs• A large number of studies (e.g. , Finn et a l . , 1971; a l . , 1975;  Lee and Seed, 1967  1,2  ; Seed and Lee, 1966;  Ishihara et  Seed et a l . ,  1975)  have been reported i n l i t e r a t u r e concerning the large deformation developed i n saturated sands under c y c l i c loading.  The main emphasis i n these  studies has been on the resistance of sand to s t r a i n development, with l i t t l e attention paid as to the mechanism which i s responsible for t h i s s t r a i n development.  Most researchers attributed the developments of  large deformation under c y c l i c loading to l i q u e f a c t i o n . of developing  This phenomenon  large deformation under c y c l i c loading has apparently been  c a l l e d l i q u e f a c t i o n , because these deformations are developed when a condition of transient zero e f f e c t i v e stress occurs i n the sand at some stage of the c y c l i c loading. Large deformations can also occur i n saturated sands under rapidly applied s t a t i c loads.  The development of such deformations under s t a t i c  loading conditions, which i s a r e s u l t of s t r a i n softening (temporary or permanent decrease i n shear resistance with continued straining) undrained response of sand, has been treated separately as another  2.  category of problem (e.g., Casagran.de 1975, been termed l i q u e f a c t i o n .  Castro 1969), and has also  This type of l i q u e f a c t i o n response can not be  explained within the framework of l i q u e f a c t i o n as perceived under c y c l i c loading conditions. It i s now recognized, however, that the development of large deformation could be the result of transient zero e f f e c t i v e stress condition developed at c e r t a i n stage of the c y c l i c loading without any s t r a i n s o f t ening, or s t r a i n softening response developed under s t a t i c or even c y c l i c loading conditions (Castro 1969;. Seed, 1979).  These two phenomena have  been called c y c l i c mobility and l i q u e f a c t i o n , respectively (Castro, 1969; Casagrande, 1975; Seed, 1979) and w i l l also be referred to as such i n this t h e s i s . However, due to a lack of clear d i s t i n c t i o n as to which of the two phenomena i s responsible f o r development of s t r a i n , considerable controversies have arisen regarding the Influence of some f a c t o r s , most notably the l e v e l of s t a t i c shear, on the resistance to s t r a i n development i n l i q u e f a c t i o n and c y c l i c m o b i l i t y (Casagrande, 1975; Poulos, 1977).  Castro and  A proper recognition of the mechanism of s t r a i n develop-  ment ( l i q u e f a c t i o n or c y c l i c mobility) i s v i t a l for a r a t i o n a l explanat i o n of some of the c o n f l i c t i n g ideas regarding undrained response of 1  2  sand (Vaid and Chern, 1983 ' ). T r a d i t i o n a l l y , the study of the phenomenon of l i q u e f a c t i o n under monotonic loading has been c a r r i e d out on sand which developed s t r a i n softening response with unlimited deformation (Castro, 1969). The concept of an eventual steady state of deformation has been advanced i n r e l a t i o n to the sand during the state of l i q u e f a c t i o n .  The state of sand  i s characterized by i t s void r a t i o and the e f f e c t i v e stress conditions.  3. Liquefaction i s thus considered a phenomenon wherein a sand, which i s consolidated  to a state well above the steady state, develops large u n i -  d i r e c t i o n a l deformation associated with s t r a i n softening response on undrained shearing, ultimately ending at steady s t a t e .  Such a sand has  been c a l l e d contractive for which a unique steady state l i n e ,  independent  of the loading paths causing the steady state deformations, has been proposed (Castro, 1969; Castro and Poulos, 1977; Castro et a l , 1982). Based on this perception of l i q u e f a c t i o n , the development of large deformation i s exclusively due to the occurrence of s t r a i n softening leading to steady state deformation.  Liquefaction can not be induced i n sand  with i n i t i a l state below the steady state l i n e and such a sand i s c a l l e d dilative. During c y c l i c loading, the deformation can develop either due to the occurrence of l i q u e f a c t i o n or c y c l i c mobility (Castro, 1975; Vaid and 2 Chem, 19 83 ) .  In most c y c l i c loading s t u d i e s , however, predominant  focus has tended to be on the response of d i l a t i v e sand In which s t r a i n development occurs as a consequence of c y c l i c mobility (Seed and Lee, 1966; Lee and Seed, 1967).  For c e r t a i n i n i t i a l states and c y c l i c  s t r e s s e s , a sand may develop l i m i t e d l i q u e f a c t i o n ( s t r a i n softening response, but without unlimited s t r a i n ) under c y c l i c loading (Vaid and 1 2 Chern, 1983 ' ) .  In such cases, c y c l i c mobility can occur a f t e r the  occurrence of limited l i q u e f a c t i o n , when c y c l i c loading i s continued, which r e s u l t s i n additional accumulation of s t r a i n .  Thus, i t i s conceiv-  able that l i q u e f a c t i o n and c y c l i c mobility occur In d i f f e r e n t regimes of i n i t i a l sand s t a t e .  In between, both l i m i t e d l i q u e f a c t i o n and c y c l i c  mobility can occur, and limited l i q u e f a c t i o n always precedes c y c l i c mobility.  4.  In the steady state approach to l i q u e f a c t i o n (Castro, 1969; Castro et a l . , 1982), the void r a t i o and confining pressure have been used i n a 2-D  state diagram to separate the i n i t i a l sand state into regions of  l i q u e f a c t i o n and d i l a t i v e responses.  Tests on sand are performed  purposely f o r those I n i t i a l states which induce l i q u e f a c t i o n only.  For  states which develop d i l a t i v e response i n monotonic loading or c y c l i c mobility i n c y c l i c loading are considered of no concern.  Although the  general influence of s t a t i c shear stress on the occurrence of liquefact i o n has been i d e n t i f i e d , the s t a t i c shear stress has never been incorporated as a part characterizing the i n i t i a l state of sand i n order to predict the occurrence of l i q u e f a c t i o n . Only an a r b i t r a r y c r i t e r i o n , such as sand with an i n i t i a l state well above and to the right of the steady state l i n e i s susceptible to l i q u e f a c t i o n , has been proposed. clear quantitative boundary for separating  No  the I n i t i a l states into  regions of l i q u e f a c t i o n and d i l a t i v e response has been s p e c i f i e d , and thus the influence of several factors on the undrained behaviour of sand can not be explained r a t i o n a l l y .  At present, no comprehensive and  u n i f i e d approach exists which covers the undrained behaviour of sand i n both contractive (which includes l i m i t e d liquefaction) and d i l a t i v e regimes, and enables prediction of the undrained response from the knowledge of the I n i t i a l sand state together with the nature of loading applied. Most of the understanding i n the undrained behaviour of saturated sand has been obtained from tests performed on natural sands with genera l l y rounded p a r t i c l e s and under r e l a t i v e l y low confining pressures. Relative density has often been used as the sole c r i t e r i o n to separate the regions of development of l i q u e f a c t i o n and c y c l i c m o b i l i t y , without  5,  any reference as to the p a r t i c l e angularity and consolidation stress condition.  It i s generally believed that sand with low r e l a t i v e density  i s susceptible to l i q u e f a c t i o n , and that with high r e l a t i v e density can develop c y c l i c mobility only.  However, there Is a f a i r acceptance of the  fact that sand behaviour Is very much dependent on the p a r t i c l e charact e r i s t i c s and consolidation stress condition.  Thus, i t may not be  prudent to predict behaviour of a sand by extrapolating the results obtained on another sand under r e l a t i v e l y low consolidation stress and d i f f e r e n t consolidation stress conditions. The f i r s t purpose of these investigations i s to present a u n i f i e d approach f o r the undrained behaviour of sand which spans between liquef a c t i o n with unlimited deformation on one side and d i l a t i v e response on the other.  This i s done by an experimental study of the undrained mono-  tonic loading behaviour which covers the whole spectrum of undrained response, i . e . , from s t r a i n softening response associated with the development of unlimited s t r a i n on one end to s t r a i n hardening response on the other, using a wide range of i n i t i a l sand s t a t e s . behavioural  Then, a comprehensive  model f o r the sand Is attempted, which enables prediction of  the undrained monotonic loading behaviour from the knowledge of i n i t i a l state of the sand.  The l i n k between undrained s t a t i c and c y c l i c loading  response i s demonstrated within the framework of undrained monotonic loading behaviour, i . e . whether l i q u e f a c t i o n or c y c l i c mobility w i l l develop under c y c l i c loading conditions i n sand which i s characterized as contractive or d i l a t i v e under undrained monotonic loading condition. Furthermore, a d d i t i o n a l c y c l i c loading c r i t e r i a f o r l i q u e f a c t i o n under c y c l i c loading i s established even i f l i q u e f a c t i o n w i l l be expected under monotonic loading.  The behavioural model f o r the sand i s also used to  6.  explain the influence of factors (such as void r a t i o , confining pressure and s t a t i c shear) on the undrained behaviour of saturated sand under both s t a t i c and c y c l i c loading conditions i n an attempt to c l a r i f y some contradictory conclusions i n l i t e r a t u r e arisen primarily due to d i f f e r e n t perceptions of the phenomenon of l i q u e f a c t i o n . The second objective of the study i s the investigation of the differences i n the undrained response of sand with changes i n p a r t i c l e angularity.  This i s achieved by comprehensive experimental studies over  a large range of confining pressure on two sands having i d e n t i c a l gradation and mineral composition, one angular and the other rounded. Behaviour of angular sands under high confining pressure i s of utmost importance i n the design of t a i l i n g s dams where such sands are used. There i s a growing trend towards b u i l d i n g t a i l i n g s dams of increasing height.  Confining pressure up to 25.0 kgf/cm  encountered i n such dams of 200 m height.  2  (2450 kPa) could be  T a i l i n g s dams of this height  are either being constructed or under consideration i n the future.  The  undrained behaviour of t a i l i n g s sand under high confining pressure could have a dramatic difference from that of the rounded or subrounded sands.  7. CHAPTER 2 GENERAL ASPECTS OF UNDRAINED BEHAVIOUR OF SAND  Undrained response of saturated sand Is t r a d i t i o n a l l y considered separately under monotonic and c y c l i c loading conditions.  Interest i n  monotonic loading has generally been related to undrained f a i l u r e associated with flow s l i d e s .  The c h a r a c t e r i s t i c feature of such behaviour Is  extremely large deformation under very small shear resistance. Conditions which could bring about such a response from s o i l could be rapid increase i n stresses due to earthquake loading, shock loading or even s t a t i c loading.  Interest i n c y c l i c undrained loading behaviour has  been related to the s u s c e p t i b i l i t y of sand to accumulate undesirable deformation during earthquake shaking.  Monotonic Loading Behaviour The range of t y p i c a l undrained t r i a x i a l compression behaviour of i s o t r o p i c a l l y consolidated saturated sand under moderate confining pressure i s shown i n F i g . 2.1. The v a r i a t i o n s In s t r e s s - s t r a i n curves from type 1 to type 5 i s associated with Increasing r e l a t i v e density. These types of response have been reported by several i n v e s t i g a t o r s , such as Bishop, Webb and Skinner (1965), Bjerrum, Kringstad and Kummeneje (1961), Castro (1969), Castro et a l . (1982) and Lee and Seed (1970). The same type of c h a r a c t e r i s t i c behaviour i s also obtained i f the sand i s i n i t i a l l y a n i s o t r o p i c a l l y consolidated. Types 1, 2 and 3 are s t r a i n softening response - a behaviour associated with loss of shear resistance a f t e r the occurrence of a peak. Sand showing such behaviour i s c a l l e d c o n t r a c t i v e .  Type 1 response has  F i g . 2.1  Characteristic behaviour of saturated sand under undrained monotonic loading.  been c a l l e d l i q u e f a c t i o n by Castro (1969), Casagrande (1975) and Seed (1979).  It is. a s t r a i n softening response with unlimited u n i d i r e c t i o n a l  s t r a i n and w i l l be c a l l e d herein true l i q u e f a c t i o n .  The c h a r a c t e r i s t i c  feature of this type of response i s continued deformation at constant void r a t i o , confining stress and shear resistance, which has been c a l l e d steady state deformation or flow deformation, since i t resembles flow of f l u i d (Poulos, 1971; Castro, 1975; Vaid and Chern, 1 9 8 3 ) . However, the shear resistance during such deformation i s of a f r i c t i o n a l nature, instead of zero, as would be the case for a f l u i d . Type 2 and 3 responses were c a l l e d limited liquefacton by Castro (1969).  Such types of response i s thus s t r a i n softening with limited  unidirectional s t r a i n .  Instead of deforming continuously at reduced  constant shear resistance, the shear resistance of sand increases with further deformation after attaining a minimum, and simultaneously the pore pressure decreases after attaining i t s maximum v a l u e . However, over some f i n i t e range of s t r a i n prior to the commencement of increase i n shear resistance, the sand deforms at e s s e n t i a l l y constant void r a t i o , e f f e c t i v e confining stress and shear r e s i s t a n c e , which could be considered as the steady state condition of the case of true liquefaction.  The difference i n response represented by type 2 and type 3 i s a  lesser degree of s t r a i n softening and associated smaller s t r a i n u n t i l the start of increase i n shear resistance or decrease i n pore pressure i n type 3 compared to that i n type 2. The arrows i n F i g . 2.1 indicate the arrest of s t r a i n softening response, i . e . , the start of increase i n shear resistance and decrease i n pore pressure with further s t r a i n i n g .  On e f f e c t i v e stress path, this  condition i s reflected by a sharp turnaround of the e f f e c t i v e stress  10. path.  Such a condition has been c a l l e d phase transformation (PT) state  by Ishihara et a l . (1975).  After the PT state has been reached, the  e f f e c t i v e stress path approaches the undrained f a i l u r e envelope rather quickly with further s t r a i n i n g .  A state of PT for true l i q u e f a c t i o n  (type 1 response) coincides with the attainment of steady s t a t e . The stress state then stays on the PT l i n e while steady state deformation continues I n d e f i n i t e l y . Type 4 response i s associated with a terminal case of s t r a i n softening  response i n which the degree of s t r a i n softening can be considered as  zero.  Such a behaviour i s represented by a f l a t plateau i n s t r e s s - s t r a i n  curve over a certain s t r a i n range before the shear resistance starts to increase and pore pressure starts to decrease with further s t r a i n i n g . Type 5 response represents the s t r a i n hardening behaviour with no loss of shear resistance. tive.  Sand showing such behaviour i s c a l l e d d i l a -  For such a response, a sharp turnaround i n the e f f e c t i v e stress  path i s not well defined (see F i g . 2.2).  However, the condition of start  of decrease i n pore pressure after i t s maximum value i s well defined. Such a condition has been c a l l e d c h a r a c t e r i s t i c threshold (CT) by Luong (1980), which i s the same as the PT state described before. Luong further showed that this threshold occurs at the same e f f e c t i v e stress r a t i o regardless of the r e l a t i v e density of sand.  I t represents the  boundary between contractive and d i l a t i v e regions of sand i n e f f e c t i v e stress space.  Luong's conclusions were based on tests on one sand under  low confining pressure only. It may be pointed out that a sand exhibiting s t r a i n hardening response can develop s t r a i n softening response but only after large straining.  Such type of response i s i l l u s t r a t e d schematically i n F i g .  F i g . 2.2  F i g . 2.3  E f f e c t i v e stress paths of contractive d i l a t i v e response.  and  C h a r a c t e r i s t i c behaviour of d i l a t i v e sand a f t e r large deformation.  12. 2.3.  After i n i t i a l s t r a i n hardening response (Type 5 ) , the sand d i l a t e s  u n t i l the e f f e c t i v e confining stress becomes high enough to cause cont r a c t i o n i n the sand.  The sand then develops a s t r a i n softening response  ultimately leading to a state of constant e f f e c t i v e confining stress and constant shear resistance.  This was also termed steady state by Poulos  (1981) and Castro et a l . (1982).  This type of s t r a i n softening response  however can be induced only after very large s t r a i n i n g , and the shear stress required to induce such response i s well above the levels of p r a c t i c a l interest and may even be greater than the drained strength. Moreover, the back pressure for the sand to sustain the negative excess pore pressure without causing c a v i t a t i o n i s very high, which may be encountered In p r a c t i c a l cases.  seldom  Therefore, this type of response Is  not considered i n this i n v e s t i g a t i o n . Predominant interest i n monotonic loading behaviour has been with the  occurrence of true l i q u e f a c t i o n .  Castro (1969), Castro et a l . (1982)  and Casagrande (1975) studied such behaviour i n r e l a t i o n to the problem of  flow s l i d e .  It has been shown by Castro (1969) that i f sand undergoes  true l i q u e f a c t i o n , the e f f e c t i v e confining stress and shear resistance during steady state deformation are uniquely related to void r a t i o , and that such r e l a t i o n s h i p i s independent of the i n i t i a l consolidation stress condition.  This unique l i n e r e l a t i n g the void r a t i o with effective con-  f i n i n g stress or shear resistance during steady state was called steady state l i n e .  T r i a x i a l tests on several sands with rounded to angular  p a r t i c l e s under a wide range of confining pressure and consolidation stress r a t i o have been shown to support these concepts (Castro, 1969; Castro et a l . 1982).  However, the studies have been limited to compres-  sion mode only, and possible influence of stress path, e.g., t r i a x i a l  13. extension, was not considered. Only true l i q u e f a c t i o n was considered and no attention was given to the treatment of range of behaviour described by response type 2 to type 5 ( F i g . 2.1).  Consideration was given only to  relate parameters during steady state deformation.  In p a r t i c u l a r , no  quantitative attempt was made to assess whether such a response couldN occur for a known i n i t i a l state of the sand. ion,  Only an a r b i t r a r y c r i t e r -  e.g., i n i t i a l state above and s i g n i f i c a n t l y to the right of steady  state l i n e w i l l cause true l i q u e f a c t i o n , was proposed.  Furthermore, In  t h e i r approach the deformation i s considered unlimited so that their design proposal are similar to a strength c r i t e r i o n .  Many cases of  l i m i t e d l i q u e f a c t i o n of p r a c t i c a l i n t e r e s t (response type 2 to type 3) may exist' where minimum strength available w i l l be s t i l l substantial but deformation to mobilize such strength could be excessive and therefore unacceptable.  Such cases were not considered by Castro within the frame-  work of l i q u e f a c t i o n .  C y c l i c Loading Behaviour I n i t i a l interest i n undrained c y c l i c loading behaviour of sand was triggered by the extensive f a i l u r e associated with saturated sand during Niigata and Alaska earthquakes of 1964. Consideration centered predominantly on the response of saturated sand under l e v e l ground, which w i l l be subjected to reversing shear stresses on h o r i z o n t a l planes (Seed and Lee, 1966).  The stress conditions on such s o i l elements are simulated i n  the laboratory by undrained c y c l i c simple shear or c y c l i c t r i a x i a l test on i s o t r o p i c a l l y consolidated samples.  The samples were subjected to  constant amplitude c y c l i c shear stresses on h o r i z o n t a l plane i n simple shear test or constant pulsating deviator loads i n the t r i a x i a l t e s t .  u. Continued c y c l i c loading r e s u l t s i n the development of large s t r a i n and s o i l i s said to have l i q u e f i e d .  C y c l i c shear stress or deviator  stress  amplitude which causes a s p e c i f i e d l e v e l of s t r a i n i n a fixed number of stress cycles i s c a l l e d the resistance to l i q u e f a c t i o n . L i q u e f a c t i o n i n c y c l i c loading has thus been defined as a s t r a i n c r i t e r i o n with no attention paid to the mechanism which i s responsible for the development of s t r a i n .  The phenomenon was c a l l e d l i q u e f a c t i o n  because during some stage of the c y c l i c loading with shear stress r e v e r s a l , a transient state of zero e f f e c t i v e stress i s reached when the applied shear stress i n sand i s zero.  Zero e f f e c t i v e stress i n sand  would imply zero shear resistance f o r a f r i c t i o n material and hence i t s equivalence with a l i q u i d and the corresponding phenomenon l i q u e f a c t i o n . The s t r a i n development during the increasing phase of the deviator  stress  i n a c y c l i c t r i a x i a l test a f t e r a state of zero e f f e c t i v e stress i s reached i s i l l u s t r a t e d i n F i g . 2.4.  F i g . 2.4  I t may be noted that large deforma-  S t r a i n development on loading a f t e r the attainment of transient state of zero effective stress.  15.  tion developed i s not associated with s t r a i n s o f t e n i n g . Undrained c y c l i c loading of sand causes a progressive increase i n pore pressure and c y c l i c deformation i n saturated sand with increasing number of c y c l e s , regardless of i t s r e l a t i v e density.  However, two  d i s t i n c t types of response may be obtained with regard to the development of  strain.  In the f i r s t type of response, at some stage during c y c l i c  loading the sample undergoes l i q u e f a c t i o n .  Castro (1969) has shown cases  in which true l i q u e f a c t i o n developed much i n the same manner as those 1 2 observed under monotonic loading ( F i g .  2.5a).  Vaid and Chem (1983 ' ) ,  however, have shown cases of c y c l i c loading of sand wherein limited l i q u e f a c t i o n developed In the same way as that observed i n type 2 and 3 response under monotonic loading ( F i g .  2.5b).  By making a detailed  observation of the development of pore pressure and s t r a i n not only at the end of cycles of loading but also within cycles of l o a d i n g , they c l a r i f i e d the possible mechanism of s t r a i n development during undrained c y c l i c loading. Vaid and Chem showed that s t r a i n softening associated with limited l i q u e f a c t i o n i s I n i t i a t e d at a c r i t i c a l value of e f f e c t i v e stress r a t i o (CSR) regardless of the void r a t i o or consolidation stress conditions of sand.  Following the arrest of l i q u e f a c t i o n (or s t r a i n softening), the  subsequent unloading from the peak amplitude of c y c l i c deviator stress causes large Increase i n pore pressure bringing the sample close to the state of zero e f f e c t i v e s t r e s s , but with very l i t t l e change i n deformation ( F i g .  2.5b,c).  Reloading In the extension region of the stress  cycle causes the sample to undergo large deformation with i t s stress state moving along the undrained f a i l u r e envelope. now,  Subsequent unloading  from the peak amplitude of deviator stress on extension s i d e , once  16.  F i g . 2.5  C y c l i c loading behaviour of contractive sand true l i q u e f a c t i o n and limited l i q u e f a c t i o n .  17. again brings the sample to a state of zero e f f e c t i v e s t r e s s , and further reloading into the compression region again causes the stress state moving along the f a i l u r e envelope with large deformation developed. Repetition of t h i s loading and unloading process causes a progressive increase i n c y c l i c deformation following l i m i t e d l i q u e f a c t i o n .  In such  type of response the accumulation of s t r a i n with loading cycle i s shown schematically i n F i g . 2.5d. In the second type of response, the sample develops progressive increase i n pore pressure and c y c l i c deformation but at no stage i s 1 2 deformation associated with s t r a i n s o f t e n i n g .  Vaid and Chern (1983 ' )  observed that such a sample develops very small deformation as long as i t s e f f e c t i v e stress state stays below the s t r e s s r a t i o corresponding to the phase transformaton l i n e ( F i g . 2.6a,b).  S i g n i f i c a n t amount of  deformation i s accumulated only when the s t r e s s state crosses the PT l i n e during the loading phase.  Unloading causes large increase i n pore  pressure bringing the sample close to the state of zero e f f e c t i v e s t r e s s , but with very l i t t l e change i n deformation.  Repetition of t h i s  phenomenon of s t r e s s state moving a l t e r n a t e l y into the region beyond the PT l i n e s with cycles of loading ultimately r e s u l t s i n a transient state of zero e f f e c t i v e s t r e s s , and i s responsible f o r further accumulation of deformation at a much f a s t e r r a t e .  S t r a i n accumulation with cycles of  loading In t h i s type of response i s shown i n F i g . 2.6c. In t h i s thesis the term l i q u e f a c t i o n w i l l be used only i f sand deforms i n a s t r a i n softening manner regardless of the nature of loading - monotonic or c y c l i c .  This d e f i n i t i o n i s consistent with that used by  Castro (1969) except that i t now encompasses l i m i t e d l i q u e f a c t i o n i n a d d i t i o n to true l i q u e f a c t i o n .  The second type of response described  18.  N F i g . 2.6  C y c l i c loading behaviour of d i l a t i v e sand cyclic mobility.  19. above, In which the deformation developed during c y c l i c loading i s not associated with s t r a i n softening, w i l l be c a l l e d c y c l i c mobility. d e f i n i t i o n of c y c l i c mobility i s also a f t e r Castro (1969).  This  Thus i n the  type of c y c l i c loading response i l l u s t r a t e d i n F i g . 2.5,  the accumulation  of deformation i s p a r t l y due  partly to c y c l i c  mobility following limited It may  to l i m i t e d l i q u e f a c t i o n and  liquefaction.  be pointed out that the progressive increase i n deformation  of serious magnitude can develop when there i s no shear stress i n sand with a c e r t a i n l e v e l of s t a t i c shear. such a sand, a state of transient and  the association  becomes ambiguous.  reversal  During c y c l i c loading of  zero e f f e c t i v e stress i s never r e a l i z e d  of term " l i q u e f a c t i o n " to the response of this sand Cyclic mobility i s a more appropriate term i n connec-  t i o n with the accumulation of a l l deformations under c y c l i c loading  not  associated with s t r a i n softening. Since a s p e c i f i e d s t r a i n development during c y c l i c loading could be due  to l i q u e f a c t i o n or c y c l i c mobility or the combination of two  2.5  and  2.6),  (Figs.  the term "resistance to l i q u e f a c t i o n " used to designate  resistance to c y c l i c loading w i l l herein be called resistance to s t r a i n development under c y c l i c loading.  However, i f the s p e c i f i e d s t r a i n  development during c y c l i c loading i s exclusively  due  to  liquefaction  only, then the term resistance to l i q u e f a c t i o n w i l l be used. s t r a i n development during c y c l i c loading i s due  If  the  to c y c l i c mobility o n l y ,  then resistance to c y c l i c mobility w i l l be used.  These d i s t i n c t i o n s  In  d e f i n i t i o n s are necessary because various factors affect l i q u e f a c t i o n c y c l i c mobility response d i f f e r e n t l y (Castro, 1969; 1975;  Vaid and  1  Castro and  Poulos,  2  Chern, 1983 ' ).  Attempts to l i n k the monotonic and  c y c l i c loading behaviour have  and  20. been confined only to the i l l u s t r a t i o n that s t r a i n softening occurs under c y c l i c loading much i n the same manner as under monotonic loading. Castro (1969) and Castro et a l . (1982) showed that the steady state l i n e i s unique under monotonic and c y c l i c loading conditions, which implies that the undrained stress paths have no e f f e c t on steady state l i n e .  A  1 2 study on one sand at one confining pressure by Vaid and Chern (1983  '.)  showed that the i n i t i a t i o n of s t r a i n softening under monotonic and  cyclic  loading occur at a unique value of e f f e c t i v e stress r a t i o .  Also  the  arrest of s t r a i n softening occurs at a stress r a t i o corresponding to the phase transformation  line.  No comprehensive studies have been made to  make general prediction of sand behaviour under c y c l i c loading from the known behaviour under monotonic loading.  The role of void r a t i o , confin-  ing pressure and s t a t i c shear on undrained c y c l i c loading behaviour are not clear and often contradictory, because of a lack of recognition of the mechanism of deformation under c y c l i c loading.  It i s the purpose of  these investigations to present a u n i f i e d approach for undrained response of sand, which w i l l enable prediction of the type of undrained monotonic and c y c l i c loading behaviour from the knowledge of the I n i t i a l state of the sand and the superimposed shear l o a d i n g .  It i s also intended to  c l a r i f y the role of various factors influencing the undrained response of saturated sand, including the e f f e c t s of p a r t i c l e  angularity.  21 .  CHAPTER 3 LABORATORY TESTING  3 .1  Test Apparatus  A l l tests were conducted using the t r i a x i a l apparatus.  The testing  system consists of an instrumented t r i a x i a l c e l l and a loading system. The loading system i s capable of monotonic consolidation under anisotropic stress conditions and c y c l i c loading under stress or s t r a i n controlled conditions.  3.1.1  T r i a x i a l Apparatus A schematic layout of the t r i a x i a l t e s t i n g apparatus and the asso-  ciated instrumentation i s shown i n F i g . 3.1.  The t r i a x i a l c e l l  was  designed to test specimen with 6.4 cm diameter and 12.7 cm height. It has long been recognized that f r i c t i o n l e s s end plattens cause more uniform deformation throughout the specimen and hence y i e l d more r e l i a b l e s o i l parameters.  Use of f r i c t i o n l e s s end plattens however, i s  often complicated by the development of non-uniform expansion i n the sample over i t s height, apart from the d i f f i c u l t sample preparation procedures involved and l a t e r a l s l i d i n g of sample o f f the platten during testing.  Green (1969) performed a comprehensive study on the deformation  modes of a Belgium sand by using f r i c t i o n l e s s end p l a t t e n s .  He found  that the sample did not develop uniform l a t e r a l expansion during shear. The sample expanded predominantly e i t h e r at the top or at the base, depending on the sample preparation procedures used.  This non-uniform  expansion was also obtained by Rowe and Barden (1964), Lee (1966) and by  22.  Cyclic  Input  ^Loading  Double  Acting  Frame  Air  Piston  $  CP  Trans  £ZZ3  •? Recorder  Legend: R)  F i g . 3.1  Schematic layout of t r i a x i a l  Pressure  Regulator  apparatus.  the writer i n preliminary t r i a l s using the f r i c t i o n l e s s ends.  The major  factor influencing the mode of deformation appears to be the difference i n the sand contact at the top and bottom sample-platten Interfaces (Green, 1969).  Although this may be reduced by forming a sample i n two  halves, as was done by Green, such a procedure i s not possible to use f o r sample formed by the sedimentation technique. Furthermore, most of the f r i c t i o n l e s s end plattens used have a s l i g h t l y higher central portion for the porous disk i n order to accommodate the thickness of the membranes and the grease on the outer portion. This technique serves to prevent the sample from s l i d i n g l a t e r a l l y off the end p l a t t e n .  Such a protrusion of stone into the sand sample may  result i n a complex stress and s t r a i n pattern within the sample, and hence may influence test results i n an unknown manner. Comprehensive studies have been made by Lee (1978) and Lee and Vernese (1978) on the influence of end r e s t r a i n t on the s t a t i c and c y c l i c strength of sand.  I t was found that end r e s t r a i n t could have a s i g n i f i -  cant e f f e c t on s t a t i c and c y c l i c strength, but only i n d i l a t i v e dense soil.  This effect appeared to be a d i r e c t function of d i l a t i o n tendency  of the s o i l .  For loose sand, l i t t l e or no e f f e c t of the type of end  restraint was found.  Such findings are also supported by recent studies  of Castro et a l . (1982) who investigated the e f f e c t of end r e s t r a i n t on the e f f e c t i v e confining stress at steady state for two types of loose sands.  No s i g n i f i c a n t difference i n r e s u l t s was found i f f r i c t i o n l e s s  ends were substituted for regular end plattens i n both sands.  Since the  major objective of the intended study i s the response of r e l a t i v e l y loose sand, the choice was made i n favour of regular end plattens for simplic i t y of test procedure.  Nevertheless, the end r e s t r a i n t was kept to a  24. minimum by using polished anodized plattens with a small central 2 cm diameter porous discs for drainage.  3.1.2  Loading System The loading system consists of two  and  the c y c l i c loading system.  described by Chern (1981) . were made to f a c i l i t a t e  parts: the consolidation system  This system i s b a s i c a l l y similar to that  However, considerable additional Improvements  testing under high confining pressure and  various  anisotropic consolidation stress c o n d i t i o n s .  Consolidation System In order to simulate the f i e l d consolidation stress condition more c l o s e l y , p a r t i c u l a r l y under the sloping ground, an anisotropic consolidation system was  developed.  In the conventional method, anisotropic  consolidation i s either carried out incrementally  In steps, or the sample  i s consolidated i s o t r o p i c a l l y f i r s t and then deviator stress applied under drained condition u n t i l the desired K c  = al /a' r a t i o i s obtained. l c 3c  The newly designed system enables the s o i l sample to be  consolidated  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 along any constant e f f e c t i v e stress r a t i o path.  This system i s I l l u s t r a t e d schematically i n the lower l e f t  part of F i g . 3.2, whereas the d e t a i l s are shown i n F i g .  3.3.  The consolidation system consists of a motorized pressure regulator, a pressure amplifier ( i f higher confining pressures are needed), a posit i v e and negative bias relay and an adjustable ratio r e l a y .  In operating  the system, an i d e n t i c a l signal pressure, s, from the motorized regulator i s fed Into the pressure amplifier and  the bias r e l a y .  The  pressure  a m p l i f i e r simply magnifies the s i g n a l pressure by a constant r a t i o m (=  Function  Elect.  Signal  Generator  I > I E / P Transducer  c  Ratio Relay  Volume Booster  Cyclic  Output  to Top Chamber of Air PiJfon  Precision Gage  ®  Regulated Air  Supply  Steady  F i g . 3.2  Schematic layout of loading system.  To  Bottom  of  Air  Output Chambe Piston  Pressure Regulator  To Triaxial  Motomatlc  Motor  Generator  Speed  Control  Unit  Chamber  M Pressure Amp Adjustable' Ratio Relay  Bios  P  To  Valve  or  Air  B Piston  Relay  P ' S P  F i g . 3.3  t  *  + RP  K '  R(S  +  K)  Detailed layout of consolidation system.  N)  4.167  i n system designed) before feeding the output pressure Into the  triaxial chamber as cell pressure O j , i.e.,  a3 = m s  The bias relay adds a constant K (continuously adjustable) to the signal pressure and outputs a pressure  p = s + K.  The pressure p when fed through the ratio relay gets multiplied by a factor R (continuously adjustable) and the output pressure  Pl  = R(s + K)  Is fed to the top chamber of the air loading piston, either directly or through a volume booster. For the given signal pressure s, the vertical stress  on the  sample Is given by (see Fig. 3.1)  a  l  = s  In which  A  [R(s + K)AX - p 2 A 2 - msAr] + m s  (3.1)  sample area, s  area of top chamber of air loading piston, area of bottom chamber of a i r loading piston,  A  area of the loading ram, r  P2  -  steady input to the bottom chamber of air loading piston.  28. If the consolidation is desired under a Kc value, incremental changes in a| and o*^ are related by  Now  1  Aa.'/Ao-; = K 1 3 c  (3.2)  Ao| = Lal  (3.3)  - Au  Ao^ = mAs - Au  (3.4)  Under drained conditions u = constant and thus Au = 0.  Therefore, from  Eqs. 3-2, 3-3 and 3-4,  AO,' = mAs K  1  (3.5)  c  Substituting for Ao^ from Eq. 3-1 into Eq. 3-5, we get  (RAsAj - A p A £ - mAsA^) + mAs = mAs K 2  (3.6)  s  If p2 is held constant, Ap2 = 0 and Eq. 3-6 reduces to  1 ^ - (RA, - mA ) + m = m K A r c s  (3.7)  from which the value of ratio relay R factor can be obtained in terms of the system constants for the desired  value.  In this Investigation,  the input pressure p2 in the bottom chamber of the air loading piston and the back pressure u were maintained constant.  Therefore, knowing R  factor of the ratio relay, the K factor of the bias relay can be obtained  29.  from the relationship a' = K 1  c  a'  i.e.,  J  ^— [R(s + K)AX - p2A2 - msA ] + ms - u = K (ms-u) s  (3.8)  For any value of signal pressure s. Once the constant R on the ratio relay and constant K on the bias relay are selected, the sample can be consolidated continuously along the desired constant  ratio path.  A cohesionless s o i l sample has to be set up with some finite confinement, which makes i t s i n i t i a l effective stress state hydrostatic. This hydrostatic stress was kept to a practical minimum of about 0.2 2  kgf/cm  (19.6 kPa) following the application of back pressure and prior  to initiating the consolidation phase of loading.  In order to avoid  sudden change of stress state from i n i t i a l hydrostatic stress of about 2  0.2 kgf/cm  (19.6 kPa) to the anisotropic stress condition, which may  cause sudden buildup of excess pore presure and cause collapse of loose sample, the consolidation stress path was brought to approach the desired K path during the i n i t i a l stage of consolidation (see Fig. 3.4). c  This  is done by opening the valve B slowly and admitting the pressure p^, to the air piston slowly.  Cyclic Loading System Cyclic loading i s applied by means of an electro-pneumatic (E/P) transducer driven by a function generator (Fig. 3.2).  Due to the limited  output pressure capability of the E/P transducers, an adjustable ratio relay was installed to magnify this pressure.  Any desired cyclic load  amplitude can be obtained by appropriate combination of piston size and multiplication factor of the ratio relay.  16.0  4 ^  t  0  /  4.0  _  ^  BO  .  12.0  .  16.0  1  20.0  1/2 ((J,'+ <%)  F i g . 3.4  +S 24.0  I  1  1  1  -»—  28.0  32.0  36.0  40.0  IkQf/cm*)  Anisotropic consolidation stress paths.  OJ  o  31. In order to maintain a constant c y c l i c load amplitude when large sample deformation develops, a 1:1 pressure r a t i o volume booster relay was i n s t a l l e d on both top and bottom chambers of the a i r p i s t o n .  A large  increase i n a i r flow rate and exhausting rate reduced greatly the degradation of c y c l i c load pulse when large deformation  developed.  After consolidation was completed, the pressure i n the top chamber of  the a i r piston was transferred to the c y c l i c loading system.  With  valve C closed, the pressure i n the c y c l i c loading system was increased to  the value equals to that i n the consolidation system using the DC-  o f f s e t on the function generator.  A smooth transfer was then made by  c l o s i n g valve B and opening valve C.  3.2  Testing Procedures  3.2.1  Sample Preparation and Saturation  Test samples were formed by p l u v i a t i n g sand i n deaired water which filled  the sample cavity formed by a membrane lined s p l i t mold.  While  depositing sand, the t i p of the pouring nozzle was always submerged and maintained at a constant height of about 1 cm above the sedimented sand surface.  The pouring t i p was traversed l a t e r a l l y over the plan area of  sample In order to form a loose uniform sand d e p o s i t . A l l samples were formed loose i n this manner. Higher i n i t i a l d e n s i t i e s , i f required, were obtained by d e n s i f i c a t i o n after the loading cap was i n place.  Densifica-  tion was achieved by tappings on the base of the t r i a x i a l c e l l with a soft hammer while maintaining a gentle pressure on the loading cap.  The  d e t a i l e d sample preparation techniques have been described previously by Chern (1981).  These techniques are believed to y i e l d samples of uniform  32. density throughout (Vaid and F i n n , 1979). During the process of sample set up i n the loading frame and checking  f o r saturation, the main emphasis was to f i r s t bring a l l samples to a  state of constant e f f e c t i v e stress p r i o r to consolidation. e f f e c t i v e stress was about 0.2 kgf/cm ing  2  This value of  (19.6 kPa), which was the confin-  pressure after the sample was formed.  The careful sample preparation  technique, which involved sedimentation by mutual transfer of sand with water without contacting a i r , resulted In v i r t u a l l y saturated samples with B value greater than 0.99. Other sample preparation techniques, e.g., moist or dry compaction, frequently give r i s e to nonuniformities i n density over the height of the sample (Castro, 1969). to  Moreover, they require a p p l i c a t i o n of f u l l vacuum  the sample i n order to remove the a i r trapped to f a c i l i t a t e  with high back pressure.  saturation  Such procedures r e s u l t i n unknown volume  changes i n the samples and hence an uncertainty i n the estimation of void r a t i o of the sample.  Furthermore, c e l l pressure has to be applied before  the sample i s percolated with water i n order to dissolve or drive out the a i r trapped i n the sample.  Thus, the sample f i r s t experiences an effec-  t i v e stress of more than 1.0 kgf/cm  2  (98 kPa) depending on the l e v e l of  c e l l pressure applied, followed by a loss of t h i s e f f e c t i v e stress when vacuum i s released at one end during the process of saturation.  Hence  the sample gets consolidated and then rebounded causing stress h i s t o r y effects i n addition to unknown volume changes.  This volume change may be  s i g n i f i c a n t when the water i s allowed to percolate into the sample.  Very  large volume change can take place e s p e c i a l l y i f the sand contains some fines.  In any case, the exact amount of volume change i s d i f f i c u l t to  estimate due to Inherent anisotropy of the pluviated samples even  33.  though the a x i a l deformation, i s monitored. The sample preparation technique adopted i n this i n v e s t i g a t i o n i s believed to y i e l d more uniform samples, the e f f e c t i v e stress p r i o r to initiating  consolidation was kept i d e n t i c a l i n a l l samples at a very low 2  value (0.2 kgf/cra ) and no a r b i t r a r y e f f e c t i v e stress h i s t o r y was imparted to the samples. e f f e c t i v e stress s t a t e . was  Consolidation was  started from this i n i t i a l  A complete record of volume changes of samples  kept and hence errors i n the estimation of void r a t i o at the end of  consolidation were eliminated.  Such e r r o r s , together with those associ-  ated with sample preparation by tamping, are e s p e c i a l l y Important In the study of undrained response of loose samples under r e l a t i v e l y consolidation  low  pressure.  A f t e r the sample had been saturated, the t r i a x i a l c e l l was on the loading platform, and the sample loading ram was loading piston rod.  The sample was  now  tropic consolidation, i f required, was sure and a x i a l load simultaneously Section 3.1.2.  2  connected to the  ready for consolidation.  Aniso-  achieved by r a i s i n g the c e l l pres-  i n a preset r a t i o as described i n  The c e l l pressure was  about 0.5 kgf/cm  centered  increased at a constant rate of  (49 kPa) per minute by the motorized regulator u n t i l  the desired c e l l pressure was  achieved.  During the process of consolida-  t i o n , the volume change, a x i a l deformation and a x i a l load were monitored at discrete levels of confining pressure. t i o n stress path f o r Kc 3.4.  r a t i o of 2.0  A t y p i c a l monotonic consolida-  i s i l l u s t r a t e d by path 3 i n F i g .  In the conventional procedure of anisotropic consolidation, the  sample would be f i r s t consolidated i s o t r o p i c a l l y and then sheared under drained condition to the desired value of K  r a t i o . This i s generally c carried out i n one step or i n multiple steps as i l l u s t r a t e d by paths 1  34. and 2 respectively i n F i g . 3.4.  A monotonic anisotropic consolidation Is  superior to the conventional technique, because of the possible influence of stress path during consolidation on the subsequent undrained behaviour. When the consolidation pressure reached the desired value, the drainage l i n e was  kept open for a period of time u n t i l the secondary  consolidation, i f any, was  complete.  The  time required for this phase  depends on the type and the l e v e l of consolidation stress used. rounded and angular sands consolidated this waiting period was  very short.  For both  to low consolidation pressure,  However, for angular t a i l i n g s sand  under high consolidation s t r e s s e s , a period of more than 20 minutes elapsed before the volume change got s t a b i l i z e d . the sample was  During consolidation,  always kept under stress c o n t r o l l e d condition u n t i l the  next stage of loading.  3.2.2  Methods of Loading Two  types of t e s t s , i . e . , monotonic and c y c l i c loading t e s t , were  performed i n order to study the undrained behaviour of sands.  In each  type of t e s t , either s t r a i n c o n t r o l l e d or stress controlled loading applied.  was  A l l tests were performed using the conventional t r i a x i a l stress  path, i . e . , the c e l l pressure was  maintained constant during shear.  Undrained Monotonic Loading Generally, undrained s t r a i n softening behaviour has been studied testing samples under stress c o n t r o l l e d conditions et a l . , 1982).  (Castro, 1969;  by  Castro  The dead weight system or a i r piston loading system can  be used for this purpose.  35.  It was  found that the dead weight system i s not suitable for  investigating behaviour of sand that developed limited l i q u e f a c t i o n . This i s due to the Impact on the sample a f t e r occurrence of steady state deformation and the sample moving beyond the state of PT with accompanied increase i n i t s r e s i s t a n c e . The impact force on the sample was the large i n e r t i a force i n dead weights at PT s t a t e .  due to  As an example, the  actual load acting on the sample during and a f t e r s t r a i n softening i s shown i n F i g . 3.5 tion.  together with pore pressure response and a x i a l deforma-  High frequency vibrations occurred i n the sample, causing a  complicated  s t r e s s - s t r a i n history a f t e r steady state deformation.  The  data for this test were recorded on an o s c i l l o g r a p h i c recorder. In contrast to the dead weight system, a i r piston loading i s a low i n e r t i a system.  Such a loading system was  found to influence the test  results If sand undergoes s t r a i n softening on account of i n t e r a c t i o n of sample c h a r a c t e r i s t i c s with that of the loading system.  I t was  found  that the steady state strength and s t r a i n p o t e n t i a l (amount of s t r a i n from peak u n t i l PT state) could vary depending on the piston s i z e , position of the piston cylinder and the presence of volume booster.  An  example of such an Interaction Is i l l u s t r a t e d by the r e s u l t s of tests on two i d e n t i c a l sand samples i n F i g .  3.6.  The samples were loaded  i d e n t i c a l l y except that for one sample the volume of a i r i n the a i r piston prior to the occurrence of s t r a i n softening response was larger than for the other. I t was  found i n preliminary studies that the steady state strength  and s t r a i n p o t e n t i a l obtained under s t r a i n controlled conditions were comparable to those obtained using the dead weight system. observed by Castro et a l . (1982).  This was  For these reasons, a l l monotonic  also  36.  40.0  Time Fig. 3.5  Undrained monotonic loading response with limited liquefaction using dead weight loading.  37.  Ottawa Sand 2.0  e  c  A i r Volume in Piston  0.700 0.701 1.6  small large  C ' « 2.0 k g f / c m  2  3 c  E  .9 1.2  \ 3 0.8  0.4  2.0  F i g . 3.6  4.0  6.0  8.0  10.0  12.0  Influence of the pneumatic loading system on the s t r a i n softening behaviour.  38. loading tests were performed by using s t r a i n controlled loading system. However, i t should be noted that the Interaction of the sample with the stress c o n t r o l l e d loading system occurs i n samples which developed s t r a i n softening response only.  For samples which developedstrain hardening  response, both the stress c o n t r o l l e d and s t r a i n controlled tests should y i e l d the same r e s u l t . After consolidation was completed, the loading platform was raised or lowered u n t i l the piston rod contacted  the loading crosshead.  With  drainage l i n e closed, the sample was loaded monotonically under s t r a i n controlled conditions. used i n a l l t e s t s .  A x i a l s t r a i n rate of about 1.0% per minute was  During the process of loading, a x i a l load, pore  pressure, c e l l pressure and a x i a l deformation were monitored  continuously  by transducers and records obtained on a four pen chart recorder.  Undrained C y c l i c Loading C y c l i c loading tests were performed i n order to obtain the e f f e c t i v e confining stress and shear strength at PT state under c y c l i c loading condition, and also to assess the resistance to c y c l i c loading i n terms of s t r a i n development. For reasons described above, only s t r a i n c o n t r o l l e d loading was used to obtain the steady state strength parameters under c y c l i c loading.  It  was achieved manually by loading and unloading i n the s t r a i n controlled machine maintaining  constant stress amplitudes.  The s t r a i n rate used i n  these t e s t s was s i m i l a r to that used i n the monotonic loading t e s t s .  3.3  Testing Program Four types of t r i a x i a l tests were performed:  39, 1.  IC-U  - I s o t r o p i c a l l y Consolidated Undrained Monotonic Loading Tests.  2.  AC-U  - A n i s o t r o p i c a l l y Consolidated Undrained Monotonic Loading Tests.  3.  IC-U  - I s o t r o p i c a l l y Consolidated Undrained C y c l i c Loading T e s t s .  4.  AC-U  - A n i s o t r o p i c a l l y Consolidated Undrained C y c l i c Loading Tests.  Most of the monotonic loading t e s t s were performed i n the compression mode.  However, a,limited number of monotonic loading tests were  also c a r r i e d out i n the extension mode i n order to i l l u s t r a t e possible differences due to the two modes of loading.  The main purpose of this  t e s t i n g program was to e s t a b l i s h a u n i f i e d picture of the undrained behaviour of sand under monotonic and c y c l i c loading conditions, and the manner i n which the void ratio,, consolidation stress r a t i o , l e v e l of confining pressure and amplitude of c y c l i c loading influence this behaviour.  Tests were c a r r i e d out on samples having the same i n i t i a l  void r a t i o while varying the consolidation stress r a t i o K c and confining pressure l e v e l °-c»  Five series of test with i n i t i a l r e l a t i v e denstiy  varying from 15% to 70% for angular t a i l i n g s sand and three series of test with i n i t i a l r e l a t i v e density varying from 30% to 45% f o r rounded Ottawa sand were performed.  The consolidation stress r a t i o s were varied  from 1.0 to 2.0 under wide range of consolidation pressure from 2.0 kgf/cm  2  (196 kPa) to 25.0 kgf/cm  2  (2450 kPa).  Two types of c y c l i c loading t e s t were performed.  One type of tests  were carried out to examine, under c y c l i c loading conditions, the a p p l i c a b i l i t y of steady state concept established under monotonic loading condition.  In order to observe the steady state deformation under c y c l i c  40. loading condition, only i n i t i a l l y loose samples consolidated  to K  ratio c  of 2.0 and  subjected to consolidation pressure ranging from 2.0 kgf/cm  2  (196 kPa)  to 25.0  (2450 kPa)  explained  previously, these tests were carried out under s t r a i n  kgf/cm  were tested for both sands.  2  As  controlled conditions i n order to eliminate the influence of sample c h a r a c t e r i s t i c s - loading system i n t e r a c t i o n on test r e s u l t s .  The  other  type of tests were carried out to obtain the resistance to c y c l i c s t r a i n development or c y c l i c m o b i l i t y .  These tests were performed using  conventional stress controlled c y c l i c loading technique. two series of tests were performed.  In one  For each sand,  s e r i e s , the sample states  a f t e r consolidation were so chosen that steady state deformation expected under monotonic loading c o n d i t i o n .  was  These tests consisted of  sample with the same void r a t i o a f t e r consolidation and stress a l while the consolidation stress r a t i o K was 3c c 2.0.  the  consolidation varied from 1.0  to  In the second s e r i e s , the sample states a f t e r consolidation were  chosen such that they were well below the steady state l i n e from monotonic loading tests and hence no l i q u e f a c t i o n but the development of c y c l i c mobility was  anticipated.  Again, the samples were prepared with  the same void r a t i o after consolidation and consolidation stress a' 3c while the consolidation stress r a t i o K was varied from 1.0 to 2.0. c main purpose of these two series of tests was  The  to show the influence of  s t a t i c shear on resistance to l i q u e f a c t i o n and c y c l i c m o b i l i t y . In addition, several tests were performed to simulate the phenomenon of spontaneous l i q u e f a c t i o n . The d e t a i l s of such t e s t i n g w i l l be given i n Section  5.6.  41. 3.4  Material Tested  Two sands were used i n this laboratory testing program.  One was  Ottawa sand C-109, which has been used extensively i n the laboratory studies of undrained c y c l i c loading behaviour at UBC and elsewhere. other was a mine t a i l i n g s sand. screened.  The  The t a i l i n g s sand was s p e c i a l l y  The f r a c t i o n retained on #60 sieve was v i r t u a l l y a l l quartz  and the grain size d i s t r i b u t i o n almost i d e n t i c a l to that of Ottawa sand. Thus, the two sands represented sands which d i f f e r e d only i n t h e i r p a r t i c l e shape, and therefore provided a d i r e c t assessment of the i n f l u ence of p a r t i c l e angularity on the undrained behaviour.  3.4.1  S o i l Description  Ottawa Sand Ottawa sand i s a natural sand processed by Ottawa S i l i c a Company, Ottawa, I l l i n o i s .  It meets the ASTM Designation C-109.  uniform, medium sand with rounded p a r t i c l e s . of the sand i s shown i n F i g . 3.7.  It i s a c l e a n ,  The grain s i z e d i s t r i b u t i o n  The sand has a maximum and minimum  void r a t i o s of 0.82 and 0.50 r e s p e c t i v e l y , according to standard test method ASTM D2049.  The lowest r e l a t i v e density of water pluviated sand  a f t e r i s o t r o p i c consolidation to a^c  = 2.0 kgf/cm  2  (196 kPa) was about  32.0%.  Mine T a i l i n g s Sand Mine t a i l i n g s sand was obtained from a copper mining operation i n Peachland, B r i t i s h Columbia.  It constituted the coarse f r a c t i o n used i n  b u i l d i n g the embankment f o r t a i l i n g s impoundment. The sand consists of  & 100  m  sE  t  Z E •+ m  E  an  Sand  Gravtl  Coaua  n  o  E E , tm •<>• <  Medium  1  \  I *  \  80  \  y  Off  c-  iI I  CoifM  Fin*  *  a >anc  - J )9  Tai lit g ; - A» Washet thfou, 1 -it Sievi >  •  40  20  0 100 80  F i g . 3.7  40  20  10 8  4  2  1 0:8 Dumttcr (mm)  0.4  0.2  Grain s i z e d i s t r i b u t i o n curves of sands t e s t e d .  0.1  0.01  43. about 80-85% of quartz, 10-15% of mica, traces of chalopyrite and feldspar and has angular p a r t i c l e s . The t a i l i g n s sand was  washed through #60  the fines and mica presented.  sieve i n order to remove  Removal of these fines brought both the  mineral composition and the gradation curve of the f r a c t i o n retained on #60  sieve very s i m i l a r to that of the Ottawa sand C-109.  curve of the sand i s shown i n F i g . 3.7. size d i s t r i b u t i o n of the two  It may  The  gradation  be noted that the grain  sands are e s s e n t i a l l y i d e n t i c a l .  This  permits the influence of p a r t i c l e angularity on undrained behaviour to b isolated without introducing a d d i t i o n a l variables i n the form of gradat i o n and mineral content.  The maximum and minimum void r a t i o s of the  t a i l i n g s sand were found to be 1.060 standard test method ASTM D2049.  and 0.688 r e s p e c t i v e l y , according t  The loosest r e l a t i v e density of water  pluviated sand a f t e r Isotropic consolidation to kPa) was  3.4.2  =2.0  kgf/cm  2  (196  about 25.0%.  Consolidation C h a r a c t e r i s t i c s The consolidation c h a r a c t e r i s t i c s of sands were determined at  several i n i t i a l void r a t i o s e^ and consolidation stress conditions. The relationships between void r a t i o a f t e r consolidation e c and major consolidation stress  for t a i l i n g s sand are shown i n F i g .  3.8.  Similar r e s u l t s for Ottawa sand are shown In F i g . 3.9. It may  be noted that considerable  volume reduction occurs on a p p l i -  cation of high confining pressure during consolidation of angular t a i l ings sand ( F i g . 3.8).  However, the volume reduction i s much less for  rounded Ottawa sand under s i m i l a r stress l e v e l s .  Larger compressibility  of angular sand i s a consequence of easy breakage of sharp edges of  o  OTTAWA  0.80-  */  SAND  1.0  0.725 O O 700 A 0.673  0.75-  10  20 •  20  •  . 30  0.70-  •40 u Q  « O  30 c Q  0.65 60  D  o  a,  4)  0.6C-  70 a: 80  0.53 90  1  u  0.30  0.2  Fig.  3.9  1  0.4  I I  0.6  I  I  I  0.8 10  Consolidation  Consolidation  I  1_ 2.0  40  Stress,  60  2  8 0 10 0  0'lc (ka/cm )  characteristics of Ottawa sand.  200  40.0  60.0  L-  100  46. p a r t i c l e s under high consolidation s t r e s s e s , which makes the p a r t i c l e s to move into a more compact arrangement. for  As expected, the volume reduction  a given stress increment decreases with increasing i n i t i a l density.  However, the consolidation curves with various i n i t i a l void ratios tend to converge under high consolidation pressure. apparent i n the case of t a i l i n g s sand.  This i s p a r t i c u l a r l y  It appears that under very high  confining pressure the f i n a l void r a t i o may be more or l e s s independent of the i n i t i a l void ratio of the sample. It may also be noted i n F i g s . 3.8 and 3.9 that f o r a given  initial  void ratio the f i n a l void r a t i o a f t e r consolidation i s a function only of the major p r i n c i p a l consolidation s t r e s s Q^ > regardless of the c o n s o l i z  dation stress r a t i o K . c  Such consolidation behaviour of sand has also  been observed f o r Sacramento River sand over an even larger range of consolidation stress r a t i o and confining stress l e v e l by Lee and Seed (1970).  This c h a r a c t e r i s t i c behaviour may be used to estimate the f i n a l  void r a t i o of sand after consolidation once the i n i t i a l void r a t i o and consolidation stress conditions are known.  As w i l l be discussed i n  Section 5.1.4, the curves i n F i g s . 3.8 and 3.9 give a very good basis f o r preparing samples to a desired f i n a l void r a t i o under a wide range of consolidation stress conditions.  In this manner the f i n a l void r a t i o  could be reproduced with v a r i a t i o n of l e s s than 1.6% i n r e l a t i v e density. For a given e., the unique e v s . a' consolidation c h a r a c t e r i s t i c s of 1 c lc sand may also have s i g n i f i c a n t importance i n determining the i n - s i t u void r a t i o as construction proceeds i f the i n i t i a l placement void r a t i o can be estimated.  This i s e s p e c i a l l y true i f the sand i s loose.  Sampling of  loose sand i s known to always cause d e n s i f i c a t i o n and hence gives higher strength estimate, which could be unsafe f o r design purposes.  47,  It should be pointed out that the unique consolidation relationships of sand discussed above are restricted for water pluviated sand and under normal consolidation only. Other sample preparation procedures, e.g., moist tamping, dry compaction, etc., which may impart to the sample a complex stress history, may not result in such relationships. This will be especially critical for a sand with rounded particles in which the total volume change during consolidation is generally very small.  48.  CHAPTER 4 UNDRAINED MONOTONIC LOADING BEHAVIOUR I  Undrained t r i a x i a l compression tests were carried out on both sands using confining pressure  ranging from 2.0 to 25.0 kgf/cm  2450 kPa) and K£ values from 1.0 to 2.0.  2  (196 to  For each sand, samples were  formed at a fixed i n i t i a l void r a t i o e^ and a series of tests performed after consolidation to various l e v e l s of a' and K values. 3c c  Similar  series of tests were then repeated on samples formed at another f i x e d i n i t i a l void r a t i o .  In t h i s manner, f i v e i n i t i a l void r a t i o states f o r  t a i l i n g s sand and three i n i t i a l void r a t i o states f o r Ottawa sand were covered.  This enabled i n v e s t i g a t i o n of undrained behaviour which covered  v a f u l l spectrum of i n i t i a l states e , 0 ' » and K , of sand. c' 3c c  Only limited number of tests were performed under t r i a x i a l extension mode. The objective was to show possible influence of loading path on the undrained behaviour.  4.1  Typical Undrained Monotonic Loading Behaviour  Stress-strain and pore pressure response together with e f f e c t i v e stress paths f o r some selected tests on both sands incorporating a range of end of consolidation states are shown i n Figures 4.1 to 4.10.  It may  be noted that the range of observed undrained response covers the f u l l range of behaviour described by type 1 to 5 i n Chapter 2.  In the subse-  quent discussions, the magnitude of a x i a l s t r a i n from peak u n t i l the phase transformaton state ( s t a r t of pore pressure decrease) f o r s t r a i n softening response w i l l be designated as s t r a i n p o t e n t i a l . With this  49.  d e f i n i t i o n , true l i q u e f a c t i o n corresponds to an unlimited s t r a i n potential.  T a i l i n g s Sand Test Results T y p i c a l s t r e s s - s t r a i n and pore pressure response of i n i t i a l l y  loose  2  samples of t a i l i n g s sand consolidated to low (2.0 kgf/cm ), moderate (8.0 2  2  kgf/cm ), and high (25.0 kgf/cm ) confining pressures o' JC Fig. Fig.  4.1a,b,c.  The corresponding  are shown i n  e f f e c t i v e stress paths are shown i n  4.2. I s o t r o p i c a l l y consolidated sample under low confining pressure did  not develop s t r a i n softening response ( F i g . 4.1a) tive density was  only 25%.  even though the r e l a -  Instead, the sample developed a deviator  stress plateau over a small range of s t r a i n before the shear resistance started increasing once again due to d i l a t i o n with further s t r a i n i n g . may  It  also be seen that the s t r e s s - s t r a i n curve a f t e r the plateau was much  f l a t t e r than that i n the i n i t i a l stage of loading.  This i s the t y p i c a l  type 4 response described i n Chapter 2. A n i s o t r o p i c a l l y consolidated sample under the same confining pressure, on the other hand, developed a s l i g h t s t r a i n softening even though i t s r e l a t i v e density was sample ( F i g . 4.1a).  higher than that of i s o t o p i c a l l y consolidated  Small s t r a i n softening was  s t r a i n p o t e n t i a l of less than 2%.  associated with a small  The sample deformed i n a manner char-  acterized as l i m i t e d l i q u e f a c t i o n , except that the s t r a i n p o t e n t i a l was very small.  This i s the t y p i c a l type 3 response described i n Chapter 2.  When the confining pressure was  increased to 8.0 kgf/cm  2  (784  kPa),  both i s o t r o p i c a l l y and a n i s o t r o p i c a l l y consolidated samples developed s t r a i n softening response ( F i g . 4.1b)  even though r e l a t i v e densities were  50.  Tailings Sand  03c''2.0  kgf/cm  • e, =1.000 e =0.965 c  2  D =16.1% D = 25.5% rl  rc  &X =2.0 e  e, =0.997 e =0.948 c  D , =16.9% D =30./% r  rf:  12.0  Fig. 4 . 1 a  Undrained monotonic compression loading behaviour of i n i t i a l l y loose t a i l i n g s sand under low confining pressure.  10.0-  8.0 -  6.0 CM  E  u  \  oi  Tailings  4.0  Sand 2  O3J = 8.0 kgf/cm • KC * '.0 Dr) e; =0.999 ec =0.9/i Ore • Ke =2.0 e, --0.992 ec =0.87/ 0 rc  2.0  2.0  4.0  6.0  8.0  10.0  =16.4% =40.1% = 18.3% = 50.8%  _i 12.0  14.0  F i g . 4.1b Undrained monotonic compression loading behaviour of i n i t i a l l y loose t a i l i n g s sand under moderate confining pressure.  52.  Tailings Sand 0 > . 25.0  kgf/cm  3c  LO LOU e '0.827 • Kc -2.0  40.0"  ri *  J  e»*/.004 D e „ - 0,738  F i g . 4.1c  4.0  13.2%  ' 62.6 %  c  2.0  2  6.0  13.1 % Drc '86.6%  6,  8.0  /0.0  /2.0  14.0  16.0  Undrained monotonic compression loading behaviour of i n i t i a l l y loose t a i l i n g s sand under high confining pressure.  Tailings Sand e(- '1.00  Drj -16.1%  Kc -2.0  l/2(0,'+0 ') 3  (kgf/cm ) 2  OJ  F i g . 4.2  Effective stress paths of undrained monotonic compression loading response of i n i t i a l l y loose t a i l i n g s sand.  54. much higher than those under the lower confining pressure. Both samples deformed i n the same manner with steady state conditions over a moderate range of s t r a i n , before regaining strength due to d i l a t i o n with further straining.  These correspond to type 2 response described i n Chapter 2.  It may be noted that a n i s o t r o p i c a l l y consolidated sample, which simulates s o i l element with i n i t i a l shear b i a s , developed more severe loss of strength and larger s t r a i n p o t e n t i a l than the i s o t r o p i c a l l y consolidated one, even though i t s f i n a l r e l a t i v e density was higher.  Furthermore, i t s  shear resistance during steady state was s l i g h t l y less than the i n i t i a l s t a t i c shear stress after c o n s o l i d a t i o n . Under high confining pressure of 25.0 kgf/cm  2  (2450 kPa), both  samples behaved i n a manner s i m i l a r to those under moderate confining pressure (Fig.  4.1c).  Despite t h e i r much higher r e l a t i v e d e n s i t i e s ,  they developed a severe loss of shear resistance and larger s t r a i n p o t e n t i a l than samples at moderate confining pressure. The loss i n resistance was e s p e c i a l l y severe f o r a n i s o t r o p i c a l l y consolidated sample. Its  shear resistance  was reduced to a value considerably less than the  i n i t i a l s t a t i c shear s t r e s s , and the sample deformed continuously with unlimited s t r a i n p o t e n t i a l .  Although the r e l a t i v e density i s very high  (86.6%), i t s behaviour i s the same as the true l i q u e f a c t i o n developed i n very loose sand (type 1 response), with the difference that r e l a t i v e l y high shear resistance was s t i l l retained during steady state deformation. Typical s t r e s s - s t r a i n and pore pressure responses of i n i t i a l l y  dense  samples under moderate and high confining pressures i s shown i n F i g . 4.3a,b and the e f f e c t i v e stress paths i n F i g . 4.4. I s o t r o p i c a l l y consolidated sample under moderate confining pressure of 8.0 kgf/cm  2  (784 kPa) developed type 5 s t r a i n hardening response ( F i g .  55.  F i g . 4.3a  Undrained monotonic compression loading behaviour of i n i t i a l l y dense t a i l i n g s sand under moderate confining pressure.  Tailings Sand Cc  • 25.0 kgf/crn?  3  - LO e, "0.804 e '0.725  • K  c  c  D "68.8% D -90./% ri  rc  12.0  F i g . 4.3b  Undrained monotonic compression loading behaviour of i n i t i a l l y dense t a i l i n g s sand under high confining pressure.  Tailings Sand e  }  - 0 . 8 0 0  F i g . 4.4  Drl  *  70.0%  Effective stress paths of undrained monotonic compression loading response of i n i t i a l l y dense t a i l i n g s sand.  58. 4.3a), whereas a n i s o t r o p i c a l l y consolidated sample developed type 4 response.  When the confining pressure was increased to 25.0 kgf/cm  2  (2450 kPa), both I s o t r o p i c a l l y and a n i s o t r o p i c a l l y consolidated samples developed more contractive tendancy even though their r e l a t i v e densities were much higher than those under moderate confining pressure.  For iso-  t r o p i c a l l y consolidated samples, the response changed from type 5 under moderate confining pressure to type 4 under high confining pressure, while that of a n i s o t r o p i c a l l y consolidated samples transformed from type 4 to type 2 as the confining pressure increased by the same magnitude. Typical test results f o r an i n i t i a l l y loose sample under low confining  pressure of 1.84 kgf/cm  2  (180 kPa) subjected to monotonic extension  loading are shown i n F i g . 4.5. The sample developed s t r a i n softening response unlike s i m i l a r sample with the same i n i t i a l sample state but subjected to compression 4.1a).  loading, which developed  type 4 response ( F i g .  The sample loaded i n extension experienced severe loss of shear  resistance with accompanying large s t r a i n potential before i t regained i t s strength due to d i l a t i o n with further s t r a i n i n g .  Ottawa Sand Test Results Typical s t r e s s - s t r a i n and pore pressure response of i n i t i a l y  loose  samples of Ottawa sand consolidated to low and high confining pressures are shown i n F i g . 4.6a,b.  The corresponding e f f e c t i v e stress paths are  shown i n F i g . 4.7. In contrast to the behaviour of t a i l i n g s sand, a l l i n i t i a l l y loose samples of Ottawa sand developed s t r a i n softening response with cant s t r a i n p o t e n t i a l f o r the range of confining pressure and K c considered.  signifiratio  Strain softening i s p a r t i c u l a r l y severe under low confining  59.  Tailings Sand O' - 1.84 kgf/cm  2  12.0  l/2{6{+ 0  6"  1-0  0.5  o y ; 1.0  2  (kgf/cm ) 1.5  2.0  •  F i g . 4.5  Undrained monotonic extension loading behaviour of i n i t i a l l y loose t a i l i n g s sand.  60.  Ottawa Sand a 3c ' -2.0 kgf/cm •  K e;  e ®K e; e c  c  c  c  2  ' L O '0.725  Dri  -0.7/2 -2.0 -0.72/ -0.703  Drc  '29.7%  -33.8%  Dri - 3 0 . 9 % Drc =36.6%  i  i  i  i  i  i  i  2.0  4.0  6.0  8.0  /0.0  /2.0  /4.0  £0  (%)  S (%) a  F i g . 4.6a  Undrained monotonic compression loading behaviour of i n i t i a l l y loose Ottawa sand under low confining pressure.  61.  Ottawa Sand 25.0  °3c'  Kg/cm  2  LO e-, =0.728D =28.8% e =0.68/ D =43.4% © K -2.0 e; =0.723 D =30.3% e =0.667 D =47.8% ri  c  40.01-  rc  c  ri  c  rc  F i g . 4.6b Undrained monotonic compression loading behaviour of i n i t i a l l y loose Ottawa sand under high confining pressure.  Ottawa Sand e =0.725 D =30.0% }  ri  i/2(Oi'+03')  2  (Kgf/cm ) ON  N>  F i g . 4.7  E f f e c t i v e stress paths of monotonic compression loading response of i n i t i a l l y loose Ottawa sand.  63. pressure ( F i g .  4.6a).  The sand l o s t much greater percentage of i t s  resistance and developed much larger s t r a i n potential than those under high confining pressure. A l l samples developed type 2 response, which i s t y p i c a l of limited l i q u e f a c t i o n , and no type 1 response t y p i c a l of true l i q u e f a c t i o n was For  observed.  samples densified to I n i t i a l r e l a t i v e density of 45%, however,  completely d i f f e r e n t responses compared to those of the i n i t i a l l y loose states were obtained.  Instead of developing s t r a i n softening response,  a l l samples developed s t r a i n hardening or type 4 response, regardless of the confining pressure. T y p i c a l t e s t r e s u l t s f o r such response are shown i n F i g s . 4.8a,b and  4.9.  Typical test r e s u l t s for an i n i t i a l l y medium dense sample under a confining pressure of 8.0 kgf/cm  2  (784 kPa) and Kc  monotonic extension loading are shown i n F i g .  = 1.0 subjected to  4.10.  Similar to the  behaviour of t a i l i n g s sand, samples with states which developed s t r a i n hardening response i n compression developed s t r a i n softening response with s i g n i f i c a n t s t r a i n p o t e n t i a l under extension loading.  Comparison of T a i l i n g s and Ottawa Sand Response From the test results of t a i l i n g s and Ottawa sands presented above, i t may be noted that the s t r a i n softening and s t r a i n hardening behaviour are  s i m i l a r f o r both sands.  However, there are important differences i n  the factors which control the occurrence of s t r a i n softening or s t r a i n hardening response i n the two sands.  For t a i l i n g s sand, i t appears that  the confining pressure and consolidation stress r a t i o are the most important f a c t o r s .  Samples with low r e l a t i v e density can develop s t r a i n  hardening response under low confining pressure and low K „ r a t i o ,  6k.  Fig.  4.  8a  Undrained monotonic compression loading behaviour of i n i t i a l l y dense Ottawa sand under low confining pressure.  65.  e (%) a  Fig  4.8b  Undrained monotonic compression loading behaviour of i n i t i a l l y dense Ottawa sand under high confining pressure.  Ottawa Sand e; =0.676 D = 45% ri  1/2(a,'  + 0 ') 3  (kgf/cm ) 2  as  F i g . 4.9  Effective stress paths of monotonic compression loading response of i n i t i a l l y dense Ottawa sand.  67.  OffawQ Sand Tesf /C- U - # 4 5 0 ' =8.0 kgf/cm e, =0.667 Dr ; =47.8% s e =0.647 Drc 54,1% 2  3c  c  8.0  6.0 CM  E  o \  cn  4.0  < 2.0 eft  2.0  4.0  6.0  1/2(0,'+a ') 5  2.0  CM  E o  F i g . 4.10  4.0  8.0  10.0  2  (kgf/cm ) 6.0  8.0  10.0  Undrained monotonic extension loading behaviour of i n i t i a l l y medium dense Ottawa sand.  68. whereas samples even with high r e l a t i v e density can develop s t r a i n softening response under high confining pressure and high K c r a t i o .  On  the other hand, r e l a t i v e density seems to be the most important factor for  Ottawa sand.  A l l initially  loose samples developed s t r a i n softening  response over the range of confining pressure and Kc r a t i o considered, and a l l samples densified to an I n i t i a l r e l a t i v e density large than about 45% developed s t r a i n hardening response, regardless of the confining pressure and Kc r a t i o .  This difference i n the factors c o n t r o l l i n g the  undrained response of these two sands w i l l be discussed further i n Section 4.2. It may also be noted that the modes of loading influence the undrained behaviour of both sands.  Sand at given r e l a t i v e density may be  safe against l i q u e f a c t i o n (limited or true) under monotonic compression but may undergo l i q u e f a c t i o n under monotonic extension. The range of r e l a t i v e density over which l i q u e f a c t i o n can be induced i n extension i s larger than that i n compression under the s i m i l a r consolidation stress conditions.  Also the degree of s t r a i n softening i s more severe i n exten-  sion than that i n compression under s i m i l a r i n i t i a l sample states.  These  c h a r a c t e r i s t i c s are true for both sands.  4.2  Strain Softening and Strain Hardening Responses  T r a d i t i o n a l l y , s t r a i n softening and s t r a i n hardening responses are described by the shape of the s t r e s s - s t r a i n curve obtained.  In this way,  only q u a l i t a t i v e description as to the undrained behaviour, i . e . , softening  or hardening, can be obtained. Possible relationship of the type of  response either to the s o i l parameter during deformation or to i n i t i a l  69.  state (e , a' , K ) has not been Investigated c' 3c' c  comprehensively.  In the  investigations reported herein, d i f f e r e n t types of response w i l l be related to the sample state at phase transformation, and  and peak, strength  to the i n i t i a l sample s t a t e .  4.2.1  C l a s s i f i c a t i o n of Undrained Responses Test results r e l a t i n g void r a t i o a f t e r consolidation e c versus  e f f e c t i v e confining stress o"^ at phase transformation  state for t a i l i n g s  sand prepared at an i n i t i a l void r a t i o e^ of 0.90 are shown i n F i g . 4.11.  The r e l a t i o n s h i p between void r a t i o e c and consolidation stress  al which i s v a l i d for any value of K (see F i g . 3.8) i s also shown i n lc c the f i g u r e .  a  Samples under low consolidation stresses, [ c > developed  s t r a i n hardening response.  As the void r a t i o e c decreases as a result  of increasing consolidation stresses, the samples started to develop s l i g h t s t r a i n softening associated with small s t r a i n p o t e n t i a l . As the consolidation stresses are increased  f u r t h e r , the samples developed  s t r a i n softening response with s i g n i f i c a n t (>2%) s t r a i n potential or even true l i q u e f a c t i o n . It should be noted that data points In F i g . 4.11 contain results for samples consolidated  to various K c r a t i o s .  A  continuous unique relationship may be seen to exist between e^and a^ which describes  the f u l l spectrum of undrained response type 1 to type 5.  This continuous l i n e r e l a t i n g e and al c J  at PT state may be divided into  two d i s t i n c t regions of response, i . e . , s t r a i n hardening region and s t r a i n softening region ( F i g . 4.11).  Due to the unique e ^ o ^ r e l a t i o n -  ship, these two regions of response can also be related uniquely to consolidation stress al  lc  , regardless of the K  c  ratio.  In other words,  the undrained response i s uniquely related to consolidation stress a'  1.00  Tailings Sand 1.0 B  0.90"  Consolidation  1.5  20  a  Curve  (§0.80-  0.75-  Note • Steady Stale Transition transformation X State at phase tor dilative response  070-  0.2  0.4 Effective  0.6 0.8 1.0 Confining Stress  2.0 4.0 al PT State oy (kgf/cm )  6.0 8.0 10.0 20.0 or Effective Consolidation  40.0 Stress CJ| '  60.0  C  2  F i g . 4.11  Relationship between e c and at PT state for t a i l i n g s sand at fixed e^ under undrained compression loading.  o  I.OOt  Tailings  e, 0.95h  1.0  1.0  O  095  O  0.90  •  0.85  •  0.80  A  Sand  20  (.5 2 . 0  9  •  30  •  a  •  A  A  •  40  0.90\ Consolidation Curves ( e - Oj ') c  c  50  0.651  •  Critical Consolidation  Stress  I0, ) c  {60 Q c r i t  \70 «  0.801  a  4 ) V  Note0 Steady State Transition  u oo.TSf  {80 o "5  XSfofe af phase transformation for dilative response  490  0.70H  woo  0£5L  0.2 Effective  OA  06  Confining  F i g . 4.12  08  10  Stress  20 O 3 ' o r Effective  40  6.0  Consolidation  a t  _J L. 8.0 10 0  Stress  '110  20.0  400  Oj ' (kgf/cm ) 2  c  Relationship between e c and state f o r t a i l i n g s sand with various e^ under undrained compression loading.  60.0  72. which i s the product of K and al . c 3c Fig.  4.12 shows compilation of a l l test results r e l a t i n g e c and o\j  at PT state for t a i l i n g s sand with various i n i t i a l void r a t i o e^. The relationship between e figure.  v s . a' f o r various e. i s also shown i n the c Ic i It may be seen i n F i g . 4.12 that e - a l relationships for various C  -5  e^ form a series of curves which merge into a unique l i n e below a c e r t a i n e , depending on e. of the sand. c I  It i s found that t h i s unique l i n e  describes the behaviour of a l l samples which developed s t r a i n softening resulting i n true liquefaction or limited l i q u e f a c t i o n with s i g n i f i c a n t s t r a i n potential (greater than 2%), regardless of the e^ of the sand. Thus, for those samples that developed limited l i q u e f a c t i o n , the concept of a unique steady state l i n e proposed by Castro (1969) may be used i n the same manner as f o r samples that develop true l i q u e f a c t i o n . This steady state l i n e i s shown i n F i g . 4.12 by a darkened band. It should be emphasized that this steady state l i n e comprises of results f o r limited l i q u e f a c t i o n as well as true l i q u e f a c t i o n . If the sand developed s l i g h t s t r a i n softening with s t r a i n less than 2%, the & ~ 2 0  c  re  l a t i o n s h i p f o r each e^ starts to branch away  from the unique steady state l i n e . state l i n e , these relationships s t r a i n softening.  potential  Immediately to the l e f t of the steady  form a region characterized by s l i g h t  This i s shown by the dotted area i n F i g .  4.12 and Is  the region of t r a n s i t i o n from limited l i q u e f a c t i o n , which f i t s within the concepts of unique steady state l i n e , into the region of s t r a i n hardening response.  The dotted l i n e i n F i g . 4.12 which separates the regions of  s t r a i n hardening and s l i g h t s t r a i n softening response i s only approximate. A precise determination of t h i s l i n e would require a much more comprehensive testing program.  73. From F i g . 4.12,  i t may  be seeu that there e x i s t s a l i m i t i n g value of  consolidation stress cr! for each e, such that sand with consolidation lc i stress  greater than this value would always develop s t r a i n softening  response with s i g n i f i c a n t s t r a i n p o t e n t i a l and the relationships f i t s the unique steady state l i n e .  e c  ~o"^ at PT state  Hereinafter this type  of response w i l l be c a l l e d l i q u e f a c t i o n . In contrast, samples with consolidation stress  less than this c r i t i c a l value would always  develop either s t r a i n hardening or s l i g h t s t r a i n softening response and the  e c  T2  line.  a  a t  ^  st  a t e relationship does not f i t the unique steady state  This l i m i t i n g value of consolidation stress w i l l be c a l l e d  c r i t i c a l consolidation stress (al ) , . lc c r i t f i v e e^, a relationship betwen e^ and ( a ^ c ) c r ^ t may  be obtained.  From the results for test at  c r i t i c a l consolidation stress  This i s shown i n F i g . 4.12  by the dashed l i n e  to the right but more or l e s s p a r a l l e l to the steady state l i n e .  It  may  be noted that (al ) . Increases with decreasing e . lc c r i t c This c r i t i c a l consolidation stress (al ) . separates regions of lc c r i t ° I n i t i a l sample state (e , al ,'K ) which w i l l develop l i q u e f a c t i o n from c 3c c those which w i l l not. Any sample with a state a f t e r consolidation l y i n g on or to the right of (al ) . l i n e w i l l result i n l i q u e f a t i o n , otherlc c r i t ^ ' wise s l i g h t s t r a i n softening or s t r a i n hardening response w i l l be developed.  n (al ) . l i n e thus forms a quantitative criterion for lc c r i t  separating regions of l i q u e f a c t i o n from other types of response. eliminates  It  the a r b i t r a r i n e s s of c r i t e r i o n proposed by Castro (1969) and  Castro and Poulos (1977), which s p e c i f i e s that the i n i t i a l state of sand has to be well above and to the right of the steady state l i n e , i n order to develop l i q u e f a c t i o n . It should be noted that  tf^is  the major  consolidation s t r e s s , which i s the product of minor consolidation stress  74. 0 ' and K r a t i o , i . e . , a' and K do not influence the l i q u e f a c t i o n 3c c 3c c behaviour independently. a!  Therefore, a l l sample states along the constant  path w i l l show the same response as long as conditions at PT state  It w i l l be shown l a t e r that sand with a given e and al , ° c lc with al > (al ) . w i l l result In the same peak undrained strength and lc lc crit * are concerned.  steady state strength under monotonic loading, regardless of the individual value of al and K . 3c c The r e s u l t s of void r a t i o e versus e f f e c t i v e confining stress al at c J PT state for Ottawa sand are shown i n F i g . 4.13. The relationships between consolidation stress al and e f o r three i n i t i a l void ratios are lc c also shown i n the f i g u r e .  As discussed  i n Section 4.1, a l l i n i t i a l l y  loose samples (upper consolidation curve) developed s t r a i n softening response with s i g n i f i c a n t s t r a i n p o t e n t i a l (>2%).  The stress state at  steady state vs e^ f o r these samples may be seen to form a well defined steady state l i n e with s l i g h t scatter at around e c = 0.70. No i n i t i a l state gave r i s e to either s t r a i n hardening or s l i g h t l y s t r a i n softening response.  I n i t i a l l y somewhat denser samples (middle consolidation curve)  under low i n i t i a l stresses al  developed s t r a i n hardening response, but  lc s l i g h t s t r a i n softening response was obtained under higher al . For a' lc Jc 2 up to 25.0 kgf/cm (2450 kPa) and K =2.0 used i n this study, there was c no i n i t i a l stress state which led to s t r a i n softening with s i g n i f i c a n t s t r a i n p o t e n t i a l and hence no data point on the steady state l i n e . the sand was densified i n i t i a l l y  As  to i n i t i a l r e l a t i v e density of about  45%, a l l samples developed s t r a i n hardening response over the same range of a\ and K values. It may be noted i n F i g . 4.13 that the plots of Jc c void r a t i o versus a l at PT state f o r the two series of tests on i n i t i a l l y denser samples formed two l i n e s more or less p a r a l l e l to the steady state  085  Sand  OHawa  0.80-  10  Kc  i 1.0 0.725 2.0 0700 0.675  0.75  20 0^  Steady State  30,  Line Consolidation Curves lec -Olc ')  0.70-  40 ~ c «> Q 50  0.65-  o  o  60*  Stale at phase tranformation for dilative response  41  oloeo o >  2  NoteO Steady state f£ Transition State at phase transformation for dilative response  70  80  0.5590  0.50  L  0.2 Effective  1.0  0.5 Confining  F i g . A.13  Stress  Relationship various  2.0 OV  or  4.0  Effective  between e c  and  6.0  8.0 100  Consolidation  o^ a t PT  Stress  state  e^ under undrained compression  J  lc  40.0 20.0 (kal/cm )  f o r Ottawa sand  loading.  2  with  600  100  76. l i n e obtained from i n i t i a l l y loose samples.  These l i n e s tend to approach  and may eventually merge into the steady state l i n e at extremely high consolidation stress a' . lc  This c h a r a c t e r i s t i c s of Ottawa sand i s s i m i l a r  to that of the t a i l i n g s sand.  From the results presented i n F i g .  4.13 i t  appears that the PT state for e^ = 0.70 w i l l merge into the steady l i n e only when the consolidation stress considered here.  i s greater than the range  Similarly for I n i t i a l l y loose samples, i t appears that  s t r a i n hardening response can occur under very low consolidation stress 7 only.  Therefore, the c r i t i c a l consolidation stress (o*' ) . _ could not ' lc crit  be obtained for the range of consolidation stresses and i n i t i a l void r a t i o considered. However, as discussed i n Section 4.1, sample with i n i t i a l r e l a t i v e density greater than about 45% has l i t t l e p o s s i b i l i t y of developing s t r a i n softening response.  On the other hand, samples with  i n i t i a l r e l a t i v e density looser than about 40%, are highly susceptible to liquefaction. Only limited test data were obtained for both sands i n undrained extension loading.  Only those samples which led to the development of  steady state deformation were covered. ings sand are shown i n F i g .  4.14a.  Results of these tests for t a i l -  For Ottawa sand, more comprehensive  studies have been made by Chung (1984), and some of h i s test results are shown i n F i g .  4.14b.  From the limited data obtained, i t i s apparent that  the steady state l i n e i n extension i s not the same as that i n compression for  each sand.  Furthermore, the extension steady state l i n e for either  sand i s not as well defined as the compression steady state l i n e .  It i s ,  however, clear that for the same e c the steady state strength In extension i s always less than that i n compression because of smaller  at  steady state In extension. Moreover, the range of void ratio over which  77.  1.00  20  •  0.95  N  •  \  \  (a) Tailings \ \  •  \  40  \  / \  o  /  \  0.S5  Steady State Line in Compression 50  \  \  or  o  >  \  0.80  60  \ 70  \ \ \  0.75  80  \  \  \  0.70r--  1  _t_ ....  i  i  i  \  90  \  \  \  i  I/O  i  (b) Ottawa  /  0.70  a  Sand  H20  Steady State Line in C Compression in  o  30  vp o>  40  o w Q  50  0.65  in  Q:  60 >  CL)  or  H'o  0.75  D  0)  100  \  0.80  o  c  CD  Q  \  0£5  u Q  \ O  30  \  0.90  u  Sand  | 0)  0.60  70  *  80  ft  0)  0.55h  90 0.50  0.1  0.2  0.5  Effective Fig.  4.14  1.0  Confining  2.0  Stress,  5.0  CT^  10.0  2  20.0  100 50.0  (kgf/cm )  Comparison of steady state condition under compression and extension.  78. l i q u e f a c t i o n can be induced i n extension i s much larger than that i n compression for the same range of consolidation stresses considered. This difference i n compression and extension behaviour i s believed to be a consequence of the inherent anisotropy  i n pluviated sand samples.  However, these loading path differences may r e f l e c t c e r t a i n s i t u a t i o n s In nature, such as the s o i l elements at the crest and. near the toe of a p o t e n t i a l f a i l u r e surface.  If such a s i t u a t i o n occurs i n nature,  possible extension mode of loading should not be dismissed.  E f f e c t of P a r t i c l e  Angularity  It was pointed out i n Section 4.1 that Ottawa sand can not develop s t r a i n softening response once i t i s densified to an i n i t i a l r e l a t i v e density above 45% f o r the range of consolidation stresses considered. However, t a i l i n g s sand could develop s t r a i n softening response even though the f i n a l r e l a t i v e density was over 100%.  From the consolidation  c h a r a c t e r i s t i c s ( F i g . 3.8) I t may be noted that angular t a i l i n g s sand shows much larger compressibility under high consolidation s t r e s s .  Dur-  ing shear deformation angular sand shows stronger d i l a t i v e tendency under low consolidation stresses but stronger contractive tendency under higher consolidation stresses.  This increased contractive tendency i n shear and  higher compressibility during consolidation to high consolidation stress are believed to be due to the breakage of sharp edges of angular p a r t i c l e (Vaid et a l . , 1983).  It was found that the fines content (material pass-  ing No. 100 sieve) of angular sand a f t e r shearing increases with increasing consolidation stresses.  F i g . 4.15 shows the comparative grain size  d i s t r i b u t i o n curves of a fresh untested sample and a sample a f t e r undrained shearing.  An increase i n fines content from less than 1% to  about 6.5% may be observed when the confining pressure of 25.0 kgf/cm  2  Tailings Sand Test AQ - U - #6 05c ' =25.0 kgf/cm K -2.0  2  c  sm  Sand Coirs* E  r»>  c  i  C  -»  m •*  C H  I  O  •  Medium  8  Fin*  Coerse  I3 5i  t ^£  100  y  80  60  A 40  \V  - A rer  i est  F  /  / "  B ifOl  6  test  20  >» 0  Diameter (mm)  F i g . A. 15  G r a i n s i z e d i s t r i b u t i o n of t a i l i n g s sand before  and a f t e r  test.  Medium  80. (2450 kPa) and Kc ratio of 2.0 were used in undrained shear. From the grain size distribution, i t appears there was no major particle crushing. This may also be seen from the microphotographs of tailings sand samples before and after shear testing (Fig. 4.16). Very large amount of fines may be seen in the sample after testing, whereas there is hardly any particle with this size in the fresh sample.  For Ottawa sand, on the  other hand, no indication of particle breakage could be observed for the level of consolidation stresses considered.  Therefore, i t is conceivable  that strain softening response in sand of rounded particles is related to i n i t i a l loose structure.  Although consolidation of I n i t i a l l y loose  sample to high stresses can result in high relative density, strain softening response can s t i l l develop due to the I n i t i a l loose structure, which may be mostly preserved during consolidation.  This seems to be  true for other sands with rounded or subrounded particles, such as banding sand used in Castro's (Castro, 1969; Castro et a l . , 1982) studies. In such sands, liquefaction can develop only i n states of low relative density.  Thus, for sand with rounded particles, i n i t i a l relative density  provides a good single parameter defining its i n i t i a l state for a prediction of i t s anticipated undrained response as long as no particle breakage occurs. However, i f the consolidation stresses are high enough to cause particle breakage, i t is believed that the behaviour of rounded sand would be similar to that of the angular sand, due to the added potential compressibility due to particle breakage. It may also be noted in Fig. 4.12 and 4.13 that the steady state line for rounded Ottawa sand is much flatter than that of the angular tailings sand. This feature is another characteristic manifestation of the  differences in particle shapes.  Similar variations in slope of  81.  After Test F i g . 4.16  (AC-U-#6)  Microphotograph of t a i l i n g s sand before and a f t e r t e s t .  82. steady state l i n e with changing p a r t i c l e angularity have been reported by Castro et a l . (1982).  One important significance associated with the  f l a t steady state l i n e i s the extreme s e n s i t i v i t y to the magnitude of steady state strength with very small changes i n void r a t i o .  This aspect  of sand behaviour w i l l be discussed further i n l a t e r sections. While the discussions presented above are v a l i d f o r hard, c l e a n , uniform, medium quartz sand, p a r t i c l e c h a r a c t e r i s t i c s which increases the compressibility of sand, such as f r i a b l e p a r t i c l e or presence of f i n e s , w i l l increase the contractive tendency.  Sand with such p a r t i c l e  c h a r a c t e r i s t i c s w i l l have a steeper steady state l i n e which i s a d i r e c t r e f l e c t i o n of i t s c o m p r e s s i b i l i t y .  4.2.2  Characteristics of Strain Softening and Strain Hardening Responses It has been shown i n Section 4.2.1 that f o r any void r a t i o e c  there exists a c r i t i c a l consolidation stress (al ) . f o r t a i l i n g s sand. lc c r i t Sand consolidated to i n i t i a l states with void r a t i o e and consolidation c stress a I  equal to or greater than ( ° " ' c ) c r ^ t develops l i q u e f a c t i o n .  The  stress conditions at PT state then f i t the unique steady state l i n e when the sample i s loaded monotonically.  Otherwise only s t r a i n hardening  response or s l i g h t s t r a i n softening response can be developed.  This  c r i t i c a l consolidation stress separates the i n i t i a l sample state into regions which w i l l develop l i q u e f a c t i o n and other type of response. T y p i c a l undrained monotonic loading responses f o r samples consolidated to the same e  c  above and below the v(al ) . _ = constant l i n e are shown lc crit  schematically i n F i g . 4.17. For case A, i . e . , the i n i t i a l stress state (a^  c  a  or to the right of ( i c )  c r  j  = t  = K£ x a^ ) l y i n g on c  const, l i n e , the sand always develops type  2 response ( l i m i t e d liquefaction) or type 1 response (true liquefaction) i n the extreme case.  Many cases which f i t this type of response have  been shown by t y p i c a l test r e s u l t s i n Section 4.1.  I n i t i a l stress state  33.  .0o  Contractive TtVon  N  <T^ /c'W ( 7  6  °r^ ,\o<*  Region Consf.  1/2 (cr,'+ cr3';  4.17  Undrained monotonic l o a d i n g response under v a r i o u s confining pressures.  84, represented by Case B i s the l i m i t i n g case f o r this category.  The effec-  tive stress states at peak strength and PT state (same as steady state i n t h i s case) for a l l samples which show t h i s type of response f o r t a i l i n g s sand are shown i n F i g . 4.18. It may be seen that regardless of the void r a t i o , confining pressure and consolidation stress r a t i o , the peak stress states or the stress states at which s t r a i n softening i s i n i t i a t e d leading  to steady state deformation l i e e s s e n t i a l l y on a constant e f f e c t i v e  stress ratio l i n e .  This c h a r a c t e r i s t i c has also been reported by Vaid  2  and Chern (1983 ) based on r e s u l t s obtained f o r Ottawa sand under c y c l i c loading condition.  This stress r a t i o w i l l be called the c r i t i c a l e f f e c -  t i v e stress r a t i o (CSR) i n this t h e s i s .  The mobilized f r i c t i o n angle <f>'  at CSR (= 2.54) i s about 25.1° for t a i l i n g s sand.  F i g . 4.18 also shows  the e f f e c t i v e stress conditions at PT states f o r t a i l i n g s sand with i n i t i a l states which give r i s e to l i q u e f a c t i o n response.  It may be noted  that the PT states also l i e on a constant e f f e c t i v e stress r a t i o l i n e , regardless of the void r a t i o , confining stress and K c r a t i o of the sand.  The mobilized cf)' angle i s about 3 6 . 5 ° f o r this t a i l i n g s sand.  This implies that the steady state l i n e i s a space curve l y i n g on the phase transformation  plane.  If the i n i t i a l stress state l i e s to the l e f t of (al ) = const. lc c r i t (case C i n F i g . 4.17), the undrained response s t a r t s to move into a t r a n s i t i o n region, which i s characterized by the development of s l i g h t s t r a i n softening.  The e f f e c t i v e stress state at peak strength for such  I n i t i a l states was found to move c l o s e r and c l o s e r to the PT l i n e as the degree of s t r a i n softening became less and l e s s .  Case D i s the l i m i t i n g  case f o r t h i s type of response which i s t y p i c a l of the type 4 stresss t r a i n curve. for  The dotted l i n e j o i n i n g CSR state f o r Case B and PT state  case D ( F i g . 4.17) forms the locus of peak stress state i n t h i s  t r a n s i t i o n region at t h i s p a r t i c u l a r e c . The PT state f o r this type of response was found to have the same e f f e c t i v e stress r a t i o as that f o r  Failure Envelope  Tailings Sand 16.0 -  0 Initiation of Strain Softening Response • Sfeody State A Phase Transformation State for Strain H a r d e n i n g Response a n d Slight Strain S o f t e n i n g R e s p o n s e  Line  12.0  8.0  = 38.2°  ^ - ^ ^ - C S R Line  -  4.0 -  •  4.0  '  8.0  •  12.0  i  16.0  l/2(oy+oV) F i g . 4.18  L  20.0  »  24.0  i  28.0  i. 32.0  36.0  (kgf/cm ) 2  Effective stress conditions at the i n i t i a t i o n of s t r a i n softening response and start of d i l a t i o n of t a i l i n g s sand' under undrained compression loading.  40  86. i n i t i a l states which developed steady state deformation, regardless of the void r a t i o , confining pressure and K c shown i n F i g . 4.18  ratio.  The actual results  also include data points for test results character-  i s t i c of t r a n s i t i o n a l response. When the i n i t i a l stress state l i e s further to the l e f t of (cr' ) . lc crit = const, line (case E i n F i g . 4.17), the sand develops s t r a i n hardening response with no peak strength developed.  The PT state for this type of  response, which corresponds to the maximum pore pressure condition, was also found to have the same e f f e c t i v e stress r a t i o at PT states for states which developed l i q u e f a c t i o n or limited l i q u e f a c t i o n of the trans i t i o n region type.  The  test results shown i n F i g . 4.18  also  incorporate  results of samples which exhibited s t r a i n hardening response. From the i l l u s t r a t i o n i n F i g . 4.17, chosen e  c  the i n i t i a l stress state for the  to the l e f t of (a! ) . = const, l i n e may lc crit  tute e s s e n t i a l l y a d i l a t i v e region.  be seen to consti-  Sand with i n i t i a l stress states i n  this region w i l l develop s t r a i n hardening or s l i g h t s t r a i n softening only.  Region to the right of ( a ' ) . = const, l i n e including states on lc c r i t  this l i n e may  be regarded as the contractive region.  A l l i n i t i a l sample  states in this region w i l l develop steady state deformation.  The shaded  area i n F i g . 4.17  shearing  deformation may  where actual s t r a i n softening occurs during  be c a l l e d the region of contractive deformation.  the stress state reaches the CSR, developed (0.2 to 0.7%  Before  r e l a t i v e l y small deformation i s  for the sands tested) although considerable  pressure can be Induced and the sample i s e s s e n t i a l l y s t a b l e . once the stress state reaches the CSR,  pore  However,  preferred slippage between a  majority of p a r t i c l e contacts s t a r t s to occur.  Due  to the initial''loose  arrangement of p a r t i c l e s or breakage at sharp edges of p a r t i c l e In  87. angular sand under high confining pressure, the p a r t i c l e s tend to rearrange themselves  into a more compact form.  High pore pressure then  develops as a result of constant volume condition imposed with accompanying large deformation.  This process continues u n t i l the e f f e c t i v e  confining stress becomes low enough to cause a tendency to expand i n volume with further shearing deformation which occurs at the PT s t a t e . A l l discussion presented above are based on test r e s u l t s with i n i t i a l Kc  ratio less than CSR only.  It should be noted that the CSR  simply represents the s t a r t i n g of major rearrangement of p a r t i c l e s during shear.  Samples consolidated to K c values > CSR, i . e . , to a state within  the shaded area ( F i g . 4.17) would be p o t e n t i a l l y unstable and s t r a i n softening response could be induced by s l i g h t disturbance. This may seen from the results of the test shown i n F i g . sample was consolidated to a' of 8.0 kgf/cm Jc about 3.0 which was  greater than CSR.  2  4.19.  The  be  tailings  (784 kPa) and K  r a t i o of c  A s l i g h t increase i n shear stress  caused severe reduction i n shear resistance and the sand deformed i n a manner similar to the c h a r a c t e r i s t i c of true l i q u e f a c t i o n .  Thus, the  sand consolidated i n this shaded region of F i g . 4.17, although stable under drained conditions, i s p o t e n t i a l l y unstable under undrained conditions.  Such a region of contractive deformation exists f o r contrac-  t i v e sand only.  Luong (1980) designated the region below the CT l i n e  (same as PT l i n e ) as the contractive domain and the region beyond the CT l i n e as the d i l a t i v e domain i n the sense that positive pore pressure w i l l be induced i n contractive domain and d i l a t i o n (reduction i n pore pressure) w i l l start beyond the CT l i n e .  This i s consistent with the term  d i l a t i v e region used here, since the pore pressure reduction w i l l not occur u n t i l the PT l i n e i s reached even i f the sand develops  strain  88.  Tailings  Sand #33  Test AC-U-  <?3 ' - 8 . 0 k g f / c m Kc - 3 . 0 e -0.996 D -(7.2% 2  C  f  ec -0.328  r j  I/2(OI'+0 ') 3  DRZ ~62.4%  2  (kgf/cm )  F i g . 4.19 Undrained monotonic loading behaviour of t a i l i n g s sand consolidated i n t o the region of c o n t r a c t i v e deformation.  89. hardening response.  However, the terms contractive region and d i l a t i v e  region used herein refer to the type of response, i . e . , s t r a i n softening or s t r a i n hardening expected i n those regions of i n i t i a l state of sand p r i o r to undrained shear. For Ottawa sand, test results s i m i l a r to F i g . 4.18  f o r t a i l i n g s sand  representing the stress states at peak strength and steady state for those states that developed l i q u e f a c t i o n are shown i n F i g . 4.20.  Similar  to the behaviour of t a i l i n g s sand, two constant e f f e c t i v e stress r a t i o l i n e s , one corresponding to CSR and the other PT were obtained, irrespect i v e of the void r a t i o , confining pressure and K c  r a t i o of the sample.  The stress state at PT state of sample that developed s t r a i n hardening or s l i g h t s t r a i n softening are also shown i n F i g . 4.20.  As i n the case of  the t a i l i n g s sand, the PT state for s t r a i n hardening response may be seen to be the same as that of the s t r a i n softening response, regardless of the void r a t i o , confining pressure and K c  r a t i o of the sample.  The  mobilized cf)' angles for CSR and PT states f o r Ottawa sand are 2 3 . 5 ° and 29.5° respectively. It i s i n t e r e s t i n g to note that the slopes of CSR l i n e s f o r these two sands are nearly equal.  The mobilized  i n t e r p a r t i c l e f r i c t i o n angle ^  angles are very close to the  of the quartz sand, which varies from  2 2 . 8 ° to 27° according to Horn and Deere (1962).  It appears that  preferred s l i d i n g at a majority of contacts would occur when the effect i v e stress r a t i o reaches the value corresponding to cj>u and thus marks the I n i t i a t i o n of s t r a i n softening response. Similar to the behaviour i n compression, two d i s t i n c t e f f e c t i v e stress r a t i o lines corresponding to CSR and PT were found to exist i n extension mode f o r both sands, as i s c l e a r from the r e s u l t s shown i n  20.0  l/2(0,'  F i g . A.20  + a ') 3  2  (kgi/cm )  E f f e c t i v e s t r e s s c o n d i t i o n s at the i n i t i a t i o n of s t r a i n s o f t e n i n g response and s t a r t of d i l a t i o n of Ottawa sand under undrained compression l o a d i n g . o  ]  9 -  Figs. A. 21 and 4.22.  For tailings sand, i t appears that CSR may depend  somewhat on the i n i t i a l relative density of the sample, with mobilized <j>' angle varying from 18° to 2 3° from the limited data obtained.  Higher CSR  appears to be associated with higher i n i t i a l relative densities. For Ottawa sand, the mobilized $ ' angle at CSR i s about 15° (Fig. 4.22). The difference i n CSR i n compression and extension for each sand may be due to inherent anisotropy i n pluviated sand. The implication of different CSR in compression and extension on the cyclic loading behaviour will be discussed In the next chapter.  On the other hand, the PT line in exten-  sion has the same slope as that i n compression for both sands (Figs. 4.21 and 4.22). Since PT state i s a stress state after relatively large deformation, i t i s conceivable that inherent anisotropy may be erased as a consequence and hence the PT line w i l l be the same i n both deformation modes.  4.3  Undrained Strength Under Monotonic Loading  It has been shown i n the previous sections that a sand can develop either liquefaction or strain hardening response under monotonic loading depending on i t s state ( e c >  o ^ ) after consolidation.  For liquefac-  tion the major concern i s the strength loss and the associated excessive deformation, whereas for strain hardening response concern usually centres on limiting deformation to an acceptable level.  Therefore, i t  would be useful to have strength estimation for these two cases in order to avoid strength loss and excessive deformation i n contractive sand and excessive deformation in dilative sand.  92.  Tailings  Sand  1/2 (0','-ha ') 3  (kgf/cm ) 2  0 Initiation of Strain Softening Response a Steady State  F i g . 4.21  E f f e c t i v e stress conditions at the i n i t i a t i o n of s t r a i n softening response and start of d i l a t i o n of t a i l i n g s sand under undrained extension loading.  Ottawa Sand  F i g . 4.22  Effective stress conditions at the i n i t i a t i o n of strain softening response and start of d i l a t i o n of Ottawa sand under undrained extension loading.  OJ  94. 4.3.1  Peak Strength for States Which Developed Liquefaction  T a i l i n g s Sand The minor e f f e c t i v e confining stress at CSR s t a t e , a' , i s plotted r  against minor consolidation s t r e s s , 0 " ! ^ , f ° samples of t a i l i n g s sand that developed l i q u e f a c t i o n leading to steady state deformation i n F i g . 4.23.  It may be noted that the test r e s u l t s of samples with the same  ratio l i e on a straight line passing the void r a t i o of the sample.  through the o r i g i n , regardless of  This implies s i m i l a r i t y In e f f e c t i v e  stress path u n t i l the CSR i s reached for samples with the same K  ratio.  c Thus, the e f f e c t i v e confining stress at CSR state i s a function of i n i t i a l consolidation stress al and consolidation stress r a t i o K , and 3c c may be expressed as cr'  Jp  =  f(K ) a' c Jc  (4.1)  Plotting the slope of a' vs a' In F i g . 4.23 against K r a t i o , the -Jp Jc c function f(K ) can be obtained. Such a plot i s shown i n F i g . 4.24, which c indicates that f(K ) may be approximated as a l i n e a r function of K as c c follows: f(K ) = 0.412 K - 0.044 c c  (4.2)  It i s i n t e r e s t i n g to note that extension of the r e l a t i o n s h i p of K c vs  a' /al to al l a l = 1.0, I.e., the i n i t i a l consolidation stress condi3p 3c 3p 3c tion for which no excess pore pressure w i l l be induced during undrained shear at the instant of i n i t i a t i o n of s t r a i n softening corresponds to K c r a t i o approximately equal to CSR f o r the sand ( F i g . 4.24).  This  implies that s t r a i n softening response i s imminent, i f a sample i s consolidated at CSR state prior to undrained loading.  S l i g h t disturbance  35.  0 ' 3c  Fig  4.23  (kgf/cm ) 2  Relationship between e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress for t a i l i n g s sand.  F i g . 4.24  Relationship between the r a t i o of e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress vs K r a t i o for t a i l i n g s sand. ON  97-  could then cause the sample to develop strain softening, leading to steady state deformation. It should be emphasized that this is true for contractive sand only.  This phenomenon w i l l be discussed further in the  next chapter In conjunction with spontaneous liquefaction. It has been shown in previous sections that CSR for a given sand is a constant stress ratio, and  ratio.  regardless of the void ratio, confining stress  Therefore, the stress condition at CSR or peak strength  can be expressed as °ip  "  C 0  3p  4  3  <'>  where c is the CSR, which is a constant for the given sand (c = 2.54 for tailings sand) . Substituting Eqs. 4.1 and 4.2 into Eq. 4.3, the peak shear strength, S  up  = 1/2 (a' - ol ) , may be obtained as follows: lp 3p  S  up  = i (c-1) al 2 3p  (4.4a)  or S  up  = \ (c-1) (0.412 K i.  c  - 0.044) al Jc  (4.4b)  Hence the peak shear strength may be obtained as a function of i n i t i a l stress state, al and K . It was further noted that this function f(K ) 3c c c in Eq. 4.2 may be approximated by  f(K ) - 0.380 K c c  with error less than ±3.0%. F i g . 4.24.  (4.5)  This line (Eq. 4.5) is the dashed line in  Use of Eq. 4.5 instead of Eq. 4.2 in Eq. 4.4b yields  98.  up  j (c-1) 0.38 K a» Z c JC  0.19 (c-1) al lc  (4.4c)  Eq. 4.4c implies that the peak strength which occurs at CSR i s a function of major consolidation stress a^  only.  In other words, the peak stress  condition at CSR state would be the same regardless of the K r samples were consolidated to the same a' lc  ratio, i f  c but with d i f f e r e n t K  c  and a' . 3c  For a clearer i l l u s t r a t i o n of the above conclusions, results of three sets of t a i l i n g s sand samples each set consolidated  to i d e n t i c a l  al but samples within the set having d i f f e r e n t combinations of a' and lc * 3c K  c  are shown i n F i g . 4.25. It may be noted that, as postulated, S Is a up  function of a\ only at a l l three levels of al considered. lc lc  Thus, the  undrained behaviour i s mainly a function of °^c» which i s the product of K  c  and al . 3c  This may also be noted from e a r l i e r discussion i n Section  4.2.  Samples s t a r t i n g with the same e. w i l l r e s u l t In the same e and i c the same PT state i f the consolidation stresses al are the same. It has lc  now been shown further here that the peak stress state w i l l also be the same provided the samples r e s u l t i n s t r a i n softening response, leading to steady state deformation. Since f o r a given e^ the void r a t i o e c a f t e r consolidation i s a function of al only, regardless of the K r a t i o , the peak shear strength lc c in Eq. 4.4c can be expressed as a function of e instead of al . The c lc calculated peak shear strengths for f i v e e^ as a function of and hence e are shown by the peak strength l i n e s i n F i g . 4.26. The actual c peak strength test data are shown by the data points i n the f i g u r e . I t may be noted that the prediction of peak strength by using Eq. 4.4c i s  Tailings  Sand  e = 1.0 t  D - 16.4% ri  CvJ  E 6.0  o  K = c  cn  2.0  4.0  X 1  6" 2.0 CM  \  2.0  4.0  60  8.0  100  0  12  1/2 (0/4-03*) (Kgf/cm )  14.0  16.0  18.0  2  F i g . 4.25  Comparison of undrained monotonic loading response of t a i l i n g s sand under the same major consolidation stress but with different K r a t i o s . U3  F i g . 4.26  Undrained strengths of t a i l i n g s sand under monotonic compression loading.  101 . very good for i n i t i a l l y loose sample.  For i n i t i a l l y dense samples,  s t r a i n softening response leading to steady state deformation could develop only under high consolidation s t r e s s .  Very l i t t l e test data were  obtained i n this range of high consolidation s t r e s s e s .  The paired data  points connected by v e r t i c a l lines represent the peak strength (upper one) and steady state shear strength (lower one), which w i l l be discussed in the next s e c t i o n .  The PT shear strength l i n e s for s t r a i n hardening  response lying below the steady state l i n e w i l l also be discussed l a t e r .  Ottawa Sand For Ottawa sand, the relationship between al and a' as a function 3p 3c of K  c  r a t i o i s shown i n F i g . 4.27.  the t a i l i n g s sand may be observed.  Relationship similar to that for Much less pore pressure i s induced  u n t i l CSR state for samples with high K  r a t i o i n comparison to low K  c c This i s i l l u s t r a t e d i n F i g . 4.28 i n the plot of a' fal versus 3p 3c value. It i s again interesting to note that by assuming a l i n e a r  ratio. K  c  a  relationship between 3 p / ° 3 c  anc  * ^  c  r a t i o , the  r a t i o corresponding to  no pore pressure generation u n t i l CSR state was found to be approximately equal to CSR. ing  This also implies that the s t r a i n softening response lead-  to steady state deformation i s imminent when the sand i s consolidated  to a state close to CSR.  This i l l u s t r a t e s the s i m i l a r i t y i n undrained  behaviour of both sands i f l i q u e f a c t i o n i s developed. However, due to very small range of e^ over which l i q u e f a c t i o n can be induced, no attempt was made to relate peak strength to  (or e^) and hence no  comparison  made of predicted and observed S as a function of e , similar to F i g . up c 4.26. It may be pointed out that the peak strength w i l l be used l a t e r to  102.  24. Oh  03c'  F i g . 4.27  2  (kgf/cm )  Relationship between e f f e c t i v e minor p r i n c i p a l stress at CSR state and e f f e c t i v e minor consolidation stress for Ottawa sand.  0.2 .CSR  1.0  2.0  1.5  2.5  K, o  F i g . 4.28  Relationship between the ratio of e f f e c t i v e minor p r i n c i p a l stress at CSR state and effective minor consolidation stress vs K ratio for Ottawa sand.  V°  104.  construct the CSR plane In 3-D effective stress state diagram for a comprehensive illustration of the undrained behaviour of saturated sand only.  The effective stress condition at this state may offer an explana-  tion as to the influence of static shear or Kc ratio on the undrained response. Peak strength should not be used as a design parameter for sand which undergoes liquefaction since the sample Is not stable at this state.  4.3.2  Steady State Strength It has been shown i n the previous section that the PT state coincide  with the unique steady state line provided the sample develops liquefaction.  Moreover, the minor effective confining stress  at steady state  is a function of e c only, regardless of the I n i t i a l void ratio and consolidation stress conditions.  Since the effective stress state at  steady state lies on the phase transformation line which i s a constant stress ratio line through the origin, the steady state shear strength S u g can be expressed as a function of e c only.  This predicted relationship  between e c and steady state shear strength based on the unique relationship between  and e c at steady state i s shown in Fig. 4.29 together  with actual test results.  The predicted values may be seen to be i n good  agreement with observed results.  Similar unique relationships between  steady state shear strength or steady state confining stress and void ratio e^ have also been reported by Castro et a l (1982). Relationship between e and S for Ottawa: sand Is shown i n Fig. c us 4.30.  It may be noted that the range of void ratio i n which steady state  deformation can be developed for Ottawa sand i s very small for the range of consolidation stresses considered.  The steady state shear strength  105.  1.00  Steady State Shear Strength, F i g . 4.29  S  u  s  (kgf/cm )  Steady state shear strength of t a i l i n g s sand.  2  0.75  Ottawa  Sand  0.725h  30 0> U  Q)  Q 0.70 h 40 >»  o  c  cr  TJ o >  CD  0.675H  Q  Q>  50  D a> cr  0.65  60  0.625 0 1  2.0  4.0 Steady  Fig.  4.30  Steady  state  6.0 State shear  8.0 Shear  strength  10.0 Strength,  of Ottawa  sand.  /2.0 S  J4.0 16.0  /8.0  (kgf/cm ) 2  u s  o  ON  107. Increases rapidly with decreasing e c when the r e l a t i v e l y density i s i n excess of about 40%. The steady state shear strength of sand may be regarded as the stable value of shear stress the sand can s u s t a i n .  Sand subjected to a  s t a t i c shear stress greater than I t s steady state shear strength, which i s substantially less than i t s drained shear strength, i s p o t e n t i a l l y unstable under undrained conditions.  Catastrophic f a i l u r e could be  induced i f any type of undrained loading brings the stress state of sand to the CSR s t a t e .  Therefore, the steady state shear strength should be  used as the design parameter against l i q u e f a c t i o n .  4.3.3  Phase Transformation Strength f o r D i l a t i v e Response For d i l a t i v e sand i t was shown that al at PT state versus e 3 c  form a  series of curves depending on the e^ of the sand, regardless of the consolidation stress condition ( F i g . 4.12).  Due to a constant stress  r a t i o at PT s t a t e , the phase transformation shear strength can be determined as a function of e c  and e.. i  The rpredicted results based on al and . 3  e f f e c t i v e stress r a t i o at phase transformation are shown by a series of l i n e s i n F i g . 4.26.  A l l these l i n e s l i e below the steady state l i n e .  The- data points correspond to actual test r e s u l t s .  I t may be noted that  for fixed e^ the phase transformation shear strength increases with decreasing e c and approaches the steady state shear strength as the sample becomes more contractive with increasing consolidation stresses. The lines f o r phase transformation shear strength merge into the steady state l i n e when the consolidation stress i s high enough to cause steady state deformation.  It should be pointed out that these l i n e s include  test data i n the t r a n s i t i o n region of sand, which r e s u l t s i n s l i g h t s t r a i n softening and associated very small s t r a i n p o t e n t i a l , and may be  108. considered to be the same category as the s t r a i n hardening region for design purposes. From the e a r l i e r discussion of s t r a i n hardening behaviour of sand, i t was noted that much f l a t t e r s t r e s s - s t r a i n curve develops after PT state ( F i g s . 4.3a and 4.8a,b).  From the e f f e c t i v e stress path ( F i g . 4.4)  i t may also be noted that the phase transformation shear strength i s much less than the corresponding drained shear strength.  Furthermore, the  phase transformation shear strength i s much less than the ultimate undrained shear strength which can be mobilized only a f t e r very large deformation.  Therefore, to design against large deformation for d i l a t i v e  sand, the phase transformation shear strength may be the more appropriate strength parameter to be used i f undrained condition p r e v a i l s .  It should  be pointed out that the strength estimation given here i s good f o r sand that are not very d i l a t i v e or are even s l i g h t l y contractive which would have the most p r a c t i c a l concern during undrained loading where l i m i t i n g deformation are s p e c i f i e d .  For highly d i l a t i v e sand, such as sand with  high r e l a t i v e density under low consolidation s t r e s s e s , the phase transformation shear strength i s very close to the drained shear strength. The ultimate undrained shear strength w i l l be very high and the s t r a i n involved i s very small.  Drained shear strength w i l l then be appropriate  for design purposes. From F i g . 4.12, It may be noted that the series of l i n e s which branch o f f the unique steady state l i n e are very similar i n shape. Therefore, r e l a t i v e l y small number of tests have to be performed i n order to establish the key aspects of undrained behaviour of sand; i . e . , steady state l i n e , branch o f f l i n e s , consolidation c h a r a c t e r i s t i c s and c r i t i c a l consolidation stress (o' )  line.  The undrained strength parameters,  109. i.e.,  steady state shear strength and phase transformation shear strength  can readily be obtained from e - o l plot and the e f f e c t i v e stress ratio of c J PT l i n e .  For sand with a given e^ and consolidation stress conditions,  the undrained response and i t s strength parameter can be determined. For  sand with known e  and consolidation stress condition, the undrained  c response, i . e . , l i q u e f a c t i o n or d i l a t i v e response, can be determined from the (al ) , d i r e c t l y . lc crit  If l i q u e f a c t i o n occurs, the steady state shear  strength can be determined from e c d i r e c t l y .  For d i l a t i v e response,  the e, can always be interpolated from the consolidation curves (e - a l ) i c lc as long as normal consolidation p r e v a i l s . always be interpolated from F i g . 4.12  Knowing e^, a^ at PT state can  and hence the PT shear strength  estimated.  4.4  3-D E f f e c t i v e Stress State Diagram  Experimental evidence presented previously has indicated that sand can develop either l i q u e f a c t i o n , s l i g h t s t r a i n softening or s t r a i n hardening response depending on i t s i n i t i a l state (e , al , K ) . Therefore, c Jc c i t would be of utmost importance to develop a method which would enable separation of the i n i t i a l states into regions susceptible to l i q u e f a c t i o n and s t r a i n hardening response, and explain the Influence of i n i t i a l  state  parameters on the occurrence of l i q u e f a c t i o n and s t r a i n hardening response. Since most of the studies on the undrained behaviour of sand have been performed on sands with rounded p a r t i c l e s , i t i s generally believed that the r e l a t i v e density i s the most important factor c o n t r o l l i n g the undrained response.  Sand with low r e l a t i v e density may be considered to  no. be susceptible to l i q u e f a c t i o n without any reference as to i t s consolidation stress conditions.  Based on the r e s u l t s of present study i t has  been shown i n Section 4.1 that this may be a s u f f i c i e n t guideline for sand with rounded p a r t i c l e s but may be completely Inadequate for sand with angular p a r t i c l e s .  Moreover, the use of r e l a t i v e density alone can  not explain the influence of confining pressure and s t a t i c shear on the occurrence of l i q u e f a c t i o n . Castro (1969, 1975) proposed the concept of steady state l i n e i n 2-D ^~2 c  a  space.  The concept of steady state deformation was used to explain  the phenomenon of l i q u e f a c t i o n . It was proposed that the i n i t i a l state of the sample has to be well above and to the right of the steady state l i n e i n order to have the p o s s i b i l i t y of l i q u e f a c t i o n occurring.  Atten-  tion was focussed only on the s o i l behaviour during steady s t a t e .  Speci-  f i c a l l y , no quantitative attempt was made to assess whether l i q u e f a c t i o n could occur for a known i n i t i a l state (e , a' , K ) . Also no r a t i o n a l c 3c c explanation as to the influence of s t a t i c shear on the occurrence of l i q u e f a c t i o n was o f f e r e d . A comprehensive understanding of the undrained behaviour of sand can be obtained only by looking at the undrained behaviour over a whole spectrum of responses from s t r a i n softening to s t r a i n hardening under various consolidation stress conditions on d i f f e r e n t types of sand. Moreover, not only the sample state during steady state deformation but also at the i n i t i a t i o n of l i q u e f a c t i o n has to be examined i n order to understand the influence of factors such as void r a t i o , confining stress and s t a t i c shear, on the occurrence of l i q u e f a c t i o n . This requires a 3-D e f f e c t i v e stress representation of the most important stages, i . e . , i n i t i a l state (e , o' , K ) and i n i t i a t i o n of l i q u e f a c t i o n and PT state  111.  during undrained response.  Although the type of undrained response can -  be predicted by using the e ( o  )  r e l a t i o n s h i p and the i n i t i a l  sample state i n a 2-D p l o t , as described i n Section 4.2, i t can not explain the r o l e of s t a t i c shear on the occurrence of l i q u e f a c t i o n . It w i l l be shown further i n the next chapter that a 2-D plot Is i n s u f f i c i e n t to predict the occurrence of l i q u e f a c t i o n under c y c l i c loading, even though i t s u f f i c e s to predict the occurrence of l i q u e f a c t i o n under monotonic loading.  Therefore, i t requires a 3-D e f f e c t i v e stress  representa-  t i o n of state at CSR, steady state f o r s t r a i n softening response and phase transformation state f o r s t r a i n hardening response.  This i s shown  schematically i n F i g . 4.31, and w i l l be c a l l e d 3-D e f f e c t i v e stress state diagram. The state of sand i s defined by a point i n 3-D space given by void r a t i o a f t e r consolidation e , p' = 1/2 (o ' + a') and q = 1/2 (a* - a ' ) . C 1 J L j Other combination, such as e , a ', a I, may also be used. The I n i t i a l  c  l  J  sample state i s given by the consolidation curve which l i e s on constant r a t i o plane.  For c l a r i t y of the diagram, the consolidation curves are  not shown i n the f i g u r e .  The main features of the 3-D diagram are the  existence of phase transformation  (PT) and c r i t i c a l e f f e c t i v e stress  r a t i o (CSR) planes which are shown i n the f i g u r e .  The PT plane l i e s  s l i g h t l y below the undrained e f f e c t i v e stress f a i l u r e plane which i s not shown i n the diagram. It was shown i n Section 4.2.2. that the steady state f o r liquefact i o n and PT state for s t r a i n hardening response occur at a unique value of e f f e c t i v e stress r a t i o corresponding to PT l i n e ( F i g . 4.18), regardl e s s of the void r a t i o of the sample.  Hence, the unique steady state  l i n e f o r l i q u e f a c t i o n and PT state l i n e s f o r d i l a t i v e response shown i n  Hydrostatic  Fig. 4.31  Plane  (a) 3-D effective stress state diagram for tailings sand and (b) a typical section at constant e .  113.  F i g . 4.12 are states on the PT plane. . Therefore, the unique steady state l i n e i s a space curve on PT plane, which r i s e s up above the hydrostatic plane as the void r a t i o decreases, as shown i n F i g . 4.3la.  The l i n e s  branching away from the steady state l i n e are a series of l i n e s corresponding to the l o c i of PT state f o r d i l a t i v e response f o r several e^.  A  small section of these curves near the eventual merger into the steady s t a t e l i n e l i e s i n the t r a n s i t i o n region (darkened area) of s l i g h t s t r a i n so ftening. On the CSR plane, there e x i s t another s e r i e s of peak strength l i n e s for various e^,, which are the l o c i of CSR states f o r those samples which developed l i q u e f a c t i o n . shown i n the 3-D diagram.  For c l a r i t y of the diagram, these l i n e s are not From the peak strength l i n e s shown i n F i g .  4.26, which are the projection of peak strength l i n e s on CSR plane on e^-q plane, these l i n e s terminate at a c e r t a i n s t a t e .  In other words,  CSR plane does not extend a l l the way to the o r i g i n as shown i n F i g . 4.18.  The state at which the of CSR plane ends are shown by the curve C  In F i g . 4.31a.  The construction of curve C w i l l be discussed i n the next  paragraph. As discussed i n Section 4.2.1, f o r a given e c r i t i c a l consolidation stress (a ' ) , lc c r i t to a t  there e x i s t s a c (Fig- 4.12). A sand consolidated  a  equal to or greater than ( { c ) c r ^ t w i l l develop l i q u e f a c t i o n under  monotonic loading.  Otherwise, s t r a i n hardening or s l i g h t s t r a i n soften-  ing responses w i l l be developed. with decreasing e^.  The ( ° { c ) c r ^ t  Any combination of  w a s  un  f° d  t o  increase  and a ' ^ which r e s u l t s i n  K ol = a' = ( a ' ) , i s the c r i t i c a l consolidation s t r e s s . c 3c lc lc crit  This Is  shown by the constant ( a ! ) . paths AB i n 3-D diagram ( F i g . 4.31a) and lc c r i t i n p'-q plot at constant e c ( F i g . 4.31b). It was also shown i n Section  114. 4.3.1  that a l l samples with state on path AB w i l l r e s u l t i n the same  peak stress state at C and steady state at S.  The peak stress state C path AB at which  also corresponds to the upper l i m i t of constant al lc  l i q u e f a c t i o n i s imminent.  This i s also i l l u s t r a t e d by the stress paths  s t a r t i n g from i n i t i a l states A , B and C i n F i g . 4.31b.  Therefore, the  c r i t i c a l consolidation stress condition i n 3-D diagram i s a curved surface generated by t r a n s l a t i n g the constant o| the void r a t i o changes ( F i g . 4.31a).  a  (= ^ [ c ^  c r  ^^  path as  The i n t e r s e c t i o n of t h i s curved  surface with the CSR plane forms a l i m i t i n g curve C which i s the lower bound of the CSR plane.  Below curve C the CSR plane does not e x i s t .  Liquefaction w i l l be i n i t i a t e d when the sample moves into CSR plane i n t h i s region from below, e.g., sample D, during monotonic loading.  The  shear stress corresponding to the lower bound of CSR plane (curve C i n Fig.  4.31a) has a very important implication i n the occurrence of l i q u e -  f a c t i o n under c y c l i c loading condition and w i l l be discussed i n the next chapter. From the 3-D  e f f e c t i v e stress state diagram, a c l e a r picture of the  undrained monotonic loading behaviour can be obtained based on the i n i t i a l state of the sand.  For samples with i n i t i a l states l y i n g on or  a  to the r i g h t of the ( ^ c ) c r £ t s u r f a c e , l i q u e f a c t i o n w i l l be developed. Sample state w i l l reach the CSR plane f i r s t and then undergo s t r a i n s o f t ening leading to steady state deformation, f i n a l l y ending at steady state S (samples A , B , C and D).  For i n i t i a l states l y i n g to the l e f t of  ( o ^ c ) c r ^ t surface, s t r a i n hardening response or s l i g h t s t r a i n softening response w i l l be developed.  The sample state w i l l reach the PT plane  d i r e c t l y (sample E ) or reach the peak strength i n the t r a n s i t i o n region and then undergo s l i g h t s t r a i n softening (sample F) depending on how  115. close Che i n i t i a l state i s to the (al It may 4.3,  ) . surface. lc c r i t  be noted that the undrained behaviour obtained i n Section  i . e . , steady state l i n e , phase transformation  state l i n e s and pore  pressure generation c h a r a c t e r i s t i c s , which are used to develop the e f f e c t i v e stress state diagram, are s i m i l a r for both sands. s i m i l a r 3-D  3-D  Therefore,  e f f e c t i v e stress state diagram as that of the t a i l i n g s sand  should e x i s t for Ottawa sand a l s o .  However, due to a rather small range  of r e l a t i v e density over which l i q u e f a c t i o n can be induced for the range of consolidation s t r e s s considered, no s i m i l a r 3-D for Ottawa sand.  diagram was  developed  Nevertheless, the r o l e of void r a t i o , confining pres-  sure and K r a t i o on the undrained behaviour were found s i m i l a r for both c sands with only minor d i f f e r e n c e s .  These differences w i l l be  discussed  i n the next s e c t i o n .  4.5  Role of Void Ratio, Confining Pressure and S t a t i c Shear Stress on Undrained Monotonic Loading Behaviour  4.5.1. Void Ratio or Relative Density Most of the understanding of the undrained behaviour of sand has come from tests on rounded sands.  It Is generally believed that r e l a t i v e  density i s the most important parameter d i c t a t i n g the undrained response with no reference as to the associated consolidation s t r e s s conditions and p a r t i c l e a n g u l a r i t y . From the consolidation c h a r a c t e r i s t i c s discussed i n Chapter 3, i t may  be seen that a sample with given void r a t i o e c ,can be achieved by  various combinations of e, and consolidation s t r e s s condition a' and K . i 3c c The i n i t i a l state of the sample can l i e e i t h e r to the l e f t or to the  116. right of the c r i t i c a l consolidation stress surface ( F i g . 4.31a).  The  response under these two conditions w i l l be completely d i f f e r e n t .  There-  fore, specifying void r a t i o or r e l a t i v e density alone without reference to i t s consolidation stress condition w i l l not give any i n d i c a t i o n as to the type of undrained response anticipated. Generally, decreasing e  w i l l increase the c r i t i c a l consolidation c s t r e s s l e v e l required to cause l i q u e f a c t i o n . This may be seen from the increasing c r i t i c a l consolidation stress ( a ! ) . as the void ratio lc c r i t decreases from the 3-D  e f f e c t i v e stress state diagram ( F i g . 4.31a).  seems to be true f o r Ottawa sand a l s o .  This  However, f o r the range of  consolidation s t r e s s considered, the i n i t i a l void r a t i o alone of Ottawa sand gives a good prediction as to the type of undrained response, as discussed i n the previous sections.  4.5.2. Confining Pressure Undrained behaviour i s normally studied by t e s t i n g 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 consolidated samples. pressure a o n  The Influence of confining  undrained response i s assessed by coupling  such as i n Castro's 2-D,  e  -a c  3 state diagram.  As shown i n the  with  o^ c ,  3-D  e f f e c t i v e stress state diagram, i t i s the complete sample s t a t e , i . e . , e , K and a I , which controls the undrained response. c c JC a !j  Specifying e  only i s not s u f f i c i e n t to predict the undrained response.  This  c  and  may  be explained c l e a r l y from the behaviour of sand along a constant a' path Jc GB i n F i g . 4.31b. ratio.  Samples G and B have the same a^  but d i f f e r e n t Kc  As explained i n Section 4.4.1, Sample B w i l l r e s u l t i n l i q u e f a c -  t i o n , whereas G w i l l r e s u l t i n s t r a i n hardening response or s l i g h t s t r a i n softening response.  117. The general influence of increasing confining pressure on undrained response with other two factors e c and  held constant i s Increasing  contractive tendency (e.g. Sample E to D i n F i g . 4.31b).  However, the  influences of a ^ c on the occurrence of l i q u e f a c t i o n i n the contractive region and the s t r e s s increment required to reach PT state i n the d i l a t i v e region have to be considered  separately due to d i f f e r e n t response  developed i n these two regions. In the contractive region, the shear stress increment required to reach the CSR increases with increasing 0 - c » but i s proportional to a l ^ due  to the s i m i l a r i t y of stress paths (with same K c ) .  However, the  potential to develop steady state deformation increases with Increasing a' .  This may be seen from the response of Samples B and D i n F i g .  JC  4.31b.  Sample D w i l l develop much severe strength loss and larger defor-  mation u n t i l steady state strength i s mobilized than Sample B.  Static  shear stress on Sample D could be greater than i t s steady state shear strength i f the confining stress i s high enough. state i s p o t e n t i a l l y unstable.  Sample under such a  This i s e s p e c i a l l y serious f o r cases of  high Kc r a t i o . In the d i l a t i v e region, the shear stress increment required to reach the PT state also increases with increasing al , but the r a t i o of shear 3c s t r e s s increment to a^  decreases with increasing a i ^ due to the  increased contractive tendency.  This w i l l be r e f l e c t e d by the decrease  i n resistance to c y c l i c mobility with increasing a^c i n c y c l i c loading, which w i l l be discussed i n the next chapter. For sand with rounded p a r t i c l e s a l s o , such as Ottawa sand, the sample w i l l develop s t r a i n hardening response under very low confining pressures.  As the confining stress increases, the sample develops s t r a i n  118.  softening response s i m i l a r to that f o r the angular sand.  However, as  stated i n the r o l e of void r a t i o , r e l a t i v e density i s the most important factor c o n t r o l l i n g the undrained response of rounded Ottawa sand for the range of consolidation s t r e s s considered h e r e i n .  4.5.3. S t a t i c Shear Stress or Consolidation Stress Ratio The increase i n s t a t i c shear or K  a' -3c  r a t i o while maintaining e and c c constant could transform a sample from s t r a i n hardening response to  l i q u e f a c t i o n as discussed before.  The influence of K  r a t i o on the c  undrained response f o r samples i n the contractive and d i l a t i v e regions could be quite d i f f e r e n t due to d i f f e r e n t types of deformation developed. This may be i l l u s t r a t e d by e f f e c t i v e stress paths f o r samples i n the' contractive and d i l a t i v e regions shown i n F i g .  4.32.  In the contractive region (Sample C^ and sample with higher K  having same-al ) , the  r a t i o develops higher peak shear strength.  This  c may also be seen from Eq. 4.4b.  However, the shear stress increment  required to reach the peak strength s t a r t i n g from the i n i t i a l s t a t i c value always decreases with increasing  ratio.  s u b s t i t u t i n g Eq. 4.4b i n t o the r e l a t i o n of AS  This may be shown by = S  up  -T up  where S s  = peak up  shear strength and T s = s t a t i c shear s t r e s s .  AS  up  = L[(1/2 (c-1)(0.412 K - 0.044) - 1/2 c  Equation 4.6 implies AS l i m i t i n g case, i . e . , K  J (K -1)] al c ic  decreases with increasing = CSR  ratio.  (4.6)  For the  (=c), the shear s t r e s s increment required  c to reach the peak strength i s p r a c t i c a l l y zero.  i n other words, the  s t r a i n softening response i s imminent when the sample i s consolidated  120. under t h i s e f f e c t i v e stress r a t i o .  This may also be seen; from the r e l a -  tionship between the pore pressure generated u n t i l l the CSR state and K c r a t i o as shown i n F i g . 4.24.  This case may correspond to: the phenomenon  of spontaneous l i q u e f a c t i o n , which w i l l be discussed further i n the next chapter.  Due to the unique steady state strength at constant void r a t i o  e^, the p o t e n t i a l to develop steady state deformation Increases with increasing K  c  r a t i o . . More severe loss of shear resistance accompanied by  l a r g e r deformation w i l l occur i n sand with high K  than with lower K c  ratios.  c  Therefore, not only l i q u e f a c t i o n i s easier to occur but also the  strength loss on l i q u e f a c t i o n i s more severe when the s t a t i c shear stress i s increased. From the pore pressure generation c h a r a c t e r i s t i c s and unique steady state l i n e observed, i t appears that the behaviour discussed above for t a i l i n g s sand are also true f o r rounded Ottawa sand. In the d i l a t i v e region (Samples D^ and D^) also the sand with higher K  c  r a t i o develops higher shear strength at PT state and the shear stress  increment required to reach the PT state i s smaller. that observed i n the contractive region.  This i s s i m i l a r to  However, t h i s s i m i l a r i t y i n  monotonic loading behaviour i n contractive and d i l a t i v e regions can not be applied to c y c l i c loading behaviour, as w i l l be shown i n the next chapter. The same conclusion concerning the influence of s t a t i c shear to reach the PT state In the d i l a t i v e region appears to be true f o r Ottawa sand also due to the s i m i l a r i t y of undrained behaviour i n the d i l a t i v e region i n both sands. From the discussions presented above, i t may be seen that using r e l a t i v e density or a 2-D e -o I representation i s i n s u f f i c i e n t for  121 . predicting the undrained response.  Undrained response i s mainly  c o n t r o l l e d by major consolidation stress o ^ f o r  a given sand.  e f f e c t i v e stress state diagram developed t i e s the e f f e c t s of  The  3-D  and a l  on the undrained response and also provides a method to predict the undrained response given the i n i t i a l state of the sand.  It also provides  a general understanding as to the r o l e s of void r a t i o , confining pressure and s t a t i c shear s t r e s s on the undrained monotonic loading behaviour.  122. CHAPTER 5 UNDRAINED CYCLIC LOADING BEHAVIOUR  It was discussed  i n Chapter 2 that s t r a i n development during  cyclic  loading could be either due to l i q u e f a c t i o n or c y c l i c mobility or a combination of two. Although both l i q u e f a c t i o n and c y c l i c mobility result i n large deformation which i s unacceptable for engineering purposes, the mechanisms of s t r a i n development as a consequence of l i q u e faction and c y c l i c mobility are quite d i f f e r e n t .  Therefore, the e f f e c t  of factors on the s t r a i n development due to these two mechanisms could be quite d i f f e r e n t too. In order to understand the influence of f a c t o r s , such as void r a t i o , confining pressure and s t a t i c shear stress l e v e l , on the s t r a i n development under c y c l i c loading thus requires a clear understanding as to the mechanism which i s responsible f o r the s t r a i n development. Moreover, It would be desirable to be able to predict whether liquefaction or c y c l i c mobility w i l l be induced under c y c l i c loading given the I n i t i a l state of the sand and the amplitude of c y c l i c load applied. 1  2  Although Vaid and Chern (1983 ' ) made clear d i s t i n c t i o n s between l i q u e f a c t i o n and c y c l i c mobility as the mechanisms of s t r a i n development during c y c l i c loading, the studies were limited to one sand and one confining pressure only.  Therefore, no general guideline was offered to  predict the occurrence of l i q u e f a c t i o n or c y c l i c mobility under c y c l i c loading given the i n i t i a l state of the sample and the c y c l i c  loads  applied. This chapter describes tests on samples of both sands consolidated to various i n i t i a l states to i l l u s t r a t e the mechanisms of l i q u e f a c t i o n  123. and c y c l i c mobility for s t r a i n development under c y c l i c loading.  The 3-D  e f f e c t i v e stress state diagram developed under monotonic loading tions i s then used, together with c y c l i c loading  condi-  results to develop a  comprehensive method for prediction of the occurrence of l i q u e f a c t i o n or c y c l i c mobility given the i n i t i a l state of the sand and the c y c l i c loads applied.  A r a t i o n a l explanation as to the influence of factors a f f e c t i n g  the resistance to s t r a i n development under c y c l i c loading i s presented i n an attempt to c l a r i f y some of the controversial aspects of c y c l i c  loading  response reported i n l i t e r a t u r e .  5.1  Liquefaction Induced Under C y c l i c Loading  In order to demonstrate occurrence of l i q u e f a c t i o n during c y c l i c loading, a series of tests were performed on i n i t i a l l y both sands.  loose samples f o r  A l l sand states (e , a l , K ) a f t e r consolidation were so c' 3c c  chosen that liquefactions were expected under monotonic loading  condi-  tions.  i n order  Tests were performed under s t r a i n controlled conditions  to avoid the influence of loading system on the post-peak s t r e s s - s t r a i n behaviour, as discussed i n Chapter 3. For i s o t r o p i c a l l y consolidated 2 a l c required  sand, the c y c l i c stress r a t i o  <J (  j C y/  to cause l i q u e f a c t i o n to occur Is very high and close to  the peak shear strength under monotonic loading.  Moreoever, under this  high c y c l i c stress r a t i o , l i q u e f a c t i o n occurs invariably i n the extension mode, which i s not the main focus of study i n these i n v e s t i g a t i o n s . Therefore, only samples consolidated series of t e s t .  to high K c r a t i o were used i n this  The results obtained i n this series of tests were used  to e s t a b l i s h c r i t e r i a for l i q u e f a c t i o n to occur under c y c l i c conditions.  loading  124.  Another series of c y c l i c loading tests were performed i n order to confirm the l i q u e f a c t i o n c r i t e r i a established by the e a r l i e r test s e r i e s . These test r e s u l t s are also used to I l l u s t r a t e the influence of various factors on the resistance to s t r a i n development under c y c l i c loading (Section 5.4).  5.1.1  Liquefaction During C y c l i c Loading Typical results I l l u s t r a t i n g s t r e s s - s t r a i n r e l a t i o n s and pore  pressure response of t a i l i n g s sand under various levels of confining pressure are shown In F i g . 5.1a,b,c, together with the e f f e c t i v e stress paths.  It may be seen that during the f i r s t few cycles of loading, pore  pressure accumulated progressively and the e f f e c t i v e stress path moved toward l e f t . Its  However, the sample accumulated  very small s t r a i n before  state reached a c e r t a i n e f f e c t i v e stress r a t i o .  Further straining  beyond this e f f e c t i v e stress ratio caused the sample to lose i t s shear resistance, which was accompanied by the development of large unidirect i o n a l deformation ( c h a r a c t e r i s t i c of liquefaction) and pore pressure increase.  The sample deformed continuously over a s i g n i f i c a n t range of  a x i a l deformation i n the same manner as the steady state observed under monotonic loading conditions.  This continuous deformation was arrested  in a l l samples after large straining except i n the case under high confining pressure ( F i g .  5.1c) which developed unlimited s t r a i n (true  l i q u e f a c t i o n ) without causing d i l a t i o n . showed a sudden turnaround.  The e f f e c t i v e stress path then  The sample kept on strengthening with  decreasing pore pressure while the e f f e c t i v e stress path moved toward the undrained f a i l u r e envelope u n t i l the peak c y c l i c load applied was reached.  125.  5.Oh  \/2 F i g . 5.1a  (a, '+(J ') 3  2  (kgf/cm )  Undrained c y c l i c loading behaviour of contractive t a i l i n g s sand under low confining pressure.  126.  l/2(0i'+03 ')  F i g . 5.1b  (kgf/cm ) 2  Undrained c y c l i c loading behaviour of contractive t a i l i n g s sand under moderate confining pressure.  127.  32.0\-  e  F i g . 5.1c  a  (%)  Undrained c y c l i c loading behaviour of contractive sand under high confining pressure.  tailings  Tailings  Sand  1/2  F i g . 5.1c  (Cont'd)  (oy + oy)  2  (kgf/cm )  Undrained c y c l i c l o a d i n g behaviour of c o n t r a c t i v e sand under high c o n f i n i n g p r e s s u r e .  tailings  129. For Ottawa sand, behaviour similar to that for t a i l i n g s sand was observed.  Typical test results i l l u s t r a t i n g s t r e s s - s t r a i n curves and  pore pressure  response are shown i n F i g . 5.2a,b,c, along with the effec-  tive stress paths.  Unlike the behaviour of the t a i l i n g s sand, a l l  samples of Ottawa sand developed limited s t r a i n s before the continuous deformations were arrested. high confining pressure.  No unlimited s t r a i n was developed even under  Such behaviour of Ottawa sand i s similar to  that observed under monotonic loading conditions. The e f f e c t i v e stress states at which s t r a i n softening response was i n i t i a t e d during c y c l i c loading are shown i n F i g s . 5.3 and 5.4 for t a i l ings sand and Ottawa sand r e s p e c t i v e l y . I t may be seen that for both sands a l l data points l i e e s s e n t i a l l y on the c r i t i c a l e f f e c t i v e stress r a t i o (CSR) l i n e obtained under monotonic loading conditions.  This  unique CSR line under monotonic and c y c l i c loading was also observed by 2  Vaid and Chern (1983 ) f o r Ottawa sand under low confining pressures.  5.1.2  A p p l i c a b i l i t y of Steady State Concept to Liquefaction Under C y c l i c Loading Conditions Test r e s u l t s In the previous sections showed that the l i q u e f a c t i o n  occurs during c y c l i c loading i n the same manner as observed under monotonic loading conditions.  In order to consider the a p p l i c a b i l i t y of the  steady state concept and the 3-D e f f e c t i v e stress state diagram developed under monotonic loading conditions to predict the occurrence of liquefaction under c y c l i c loading conditions, the uniqueness of steady state under monotonic and c y c l i c loading conditions has to be examined. The minor e f f e c t i v e confining stress loading condition versus void ratio e  at steady state under c y c l i c  are shown by data points i n F i g s .  130.  2.5  2.0 0.43 kgf/cm  CM  6  2  (.5  CJ  \  >*D» -SC  LO Ottawa Sand Test AC - U  CO  as o  Y?  cy  -#55  0*3^ = 2.0 kgf/cm Kc =2.0 ej =0.722 Dri =30.6% = 366% er =0.703 're  0.5  2.0  4.0  a.o  6.0  /o.o  (2.0  14.0  CM  E  u 1.0  I  rj  0.5 h  C\J  1/2 (Cf,'-hCJ ') (kgf/cm') 3  F i g . 5.2a  Undrained c y c l i c loading behaviour of i n i t i a l l y loose Ottawa sand under low confining pressure.  131 .  Ottawa Sand  0  t  i  2.0  i  1  I  4.0  6.0  8.0  L  10.0  &a (%)  1/2  F i g . 5.2b  (0*,*-rd '; 3  ( k g f / c m  2  1—  12.0  )  Undrained c y c l i c loading behaviour of i n i t i a l l y loose Ottawa sand under moderate confining pressure.  F i g . 5.2c  Undrained c y c l i c loading behaviour of i n i t i a l l y loose Ottawa sand under high confining pressure.  Ottawa  Sand  2  1/2  F i g . 5.2c (Cont'd)  (Oi'+03 ')  (kgf/cm )  Undrained c y c l i c loading behaviour of i n i t i a l l y loose Ottawa sand under high confining pressure.  20.0  4.0  8.0  12.0  16.0  1/2 (Of'+O^)  F i g . 5.3  20.0  24.0  28.0  32.0  36.0  40.0  2  (kgf/cm )  Effective stress conditions at the i n i t i a t i o n of strain softening response and start of d i l a t i o n of t a i l i n g s sand under undrained c y c l i c loading.  O J  20.0 Ottawa Sand  1/2 (Of'+Oj)  F i g . 5.A  (kgf/cm ) 2  E f f e c t i v e s t r e s s c o n d i t i o n s at the i n i t i a t i o n of s t r a i n s o f t e n i n g response and s t a r t of d i l a t i o n of Ottawa sand under undrained cyclic loading.  UO Ul  136. 5.5 and 5.6 f o r t a i l i n g s sand and Ottawa sand r e s p e c t i v e l y .  The range of  a'^ covered under c y c l i c loading spans the f u l l range covered under monotonic loading. ing  Average steady state l i n e s obtained under monotonic load-  conditions are shown by s o l i d l i n e s , and i t may be noted that the  c y c l i c loading results f i t very c l o s e l y the results from monotonic loading  over the entire range of void ratio considered  for both sands.  Furthermore, the c y c l i c loading test data i n F i g s . 5.3 and 5.4 show that the effective stress states at steady state also l i e on the same PT line obtained under monotonic loading.  Therefore, the steady state i s not  affected by the loading paths which bring the sand to this state, and the steady state concept developed under monotonic loading conditions can be used for c y c l i c loading conditions a l s o . Due to the uniqueness of steady state l i n e and PT l i n e under monotonic and c y c l i c loading conditions, the steady state shear strength can be obtained as a function of e a l s o . c  The results f o r t a i l i n g s sand and  Ottawa sand are shown i n F i g s . 5.7 and 5.8 r e s p e c t i v e l y .  C y c l i c loading  and monotonic loading results may be seen to be defined by a unique curve for  each sand. It may be pointed out that the existence of steady state for a sand  with a given i n i t i a l state does not necessarily imply that l i q u e f a c t i o n w i l l develop under c y c l i c loading.  The c r i t e r i a whether a sand with a  given i n i t i a l state w i l l develop l i q u e f a c t i o n under c y c l i c loading i s discussed i n the next s e c t i o n .  5.1.3  C r i t e r i a to Cause Liquefaction Under C y c l i c Loading It has been shown that the c r i t i c a l  e f f e c t i v e stress r a t i o (CSR) at  which s t r a i n softening response i s i n i t i a t e d leading to l i q u e f a c t i o n  /.OOi  O.I  0.2  0.5  Steady  1.0  State  2.0  50  Confining Stress,  10.0  0' 3  20.0  50.0  1000  (kgf/cm ) 2  oj  F i g . 5.5  Comparison of steady state confining stress of t a i l i n g s sand under monotonic and c y c l i c loading conditions.  0 0.80-  -10  > -80 0.55 -  o Cyclic loading  fesf  result  -90 i  sol  '  0.1  i  l I 0.5 1.0 2.0 5.0 Steady State Confining Stress, 0 ' I  0.2  I  3  F i g . 5.6  1  I  100 20.0 (kgf/cm )  1  50.0  1100 100.0  2  Comparison of steady state confining stress of Ottawa sand under monotonic and c y c l i c loading conditions.  CO  139.  Fig. 5.7  Comparison of steady state shear strength of tailings sand under monotonic and cyclic loading conditions.  0.75 Ottawa Sand  -  0.725  30  0.70 Steady State Shear Strength obtained from monotonic loading tests.  / /  u  40  0.675 Rati  O ~0  "  50  Xi  1  06.5 o  06 .250 20 . 40 . 60 . i  i  i  i  Cycl/c  test result  .J40 100 . 120 . 1 . 160 .60 i  8.0 Steady State Shear Strength, S  Fig. 5 . 8  loading  i  2  u s  (kgf/cm )  Comparison of steady state shear strength of Ottawa sand under monotonic and c y c l i c loading conditions.  141. under c y c l i c loading conditions i s the same as that under monotonic loading  conditions.  Moreoever, the steady state concept developed under  monotonic loading conditions can also be applied to l i q u e f a c t i o n under c y c l i c loading conditions.  Therefore, the 3-D  diagram developed f o r monotonic loading may for  l i q u e f a c t i o n to occur under c y c l i c It was  e f f e c t i v e stress state  be used to develop c r i t e r i a  loading.  shown i n Chapter 4 that for a given void r a t i o e Q  there  exists a c r i t i c a l consolidation stress (al ) . above which the sand lc crit develops l i q u e f a c t i o n under monotonic loading, and below which only s t r a i n hardening response or s l i g h t s t r a i n softening can be induced ( F i g . 4.12).  Due  to the demonstrated uniqueness of steady state under mono-  tonic and c y c l i c loading, therefore, the f i r s t c r i t e r i o n for l i q u e f a c t i o n to occur under c y c l i c loading i s that the i n i t i a l state of the sand ( e c > al , K ) must be above the c r i t i c a l consolidation stress N(al ) 3c' c lc crit surface.  In other words, the sand must at an i n i t i a l state (e , al , K ) c' 3c' c  which has the p o t e n t i a l to develop steady state deformation.  Whether a  sand with such an. i n i t i a l state can develop l i q u e f a c t i o n or not then depends further on the c y c l i c loadings applied, which constitutes another c r i t e r i o n and i s discussed i n the next paragraph. l i e below the (al ) . s u r f a c e lc crit  (Fig. &  For i n i t i a l state that  J 4.31), the steady state can not '  be  achieved and hence l i q u e f a c t i o n can not be induced. As discussed i n the previous chapter, the CSR  plane exists only i n  the region above peak shear strength at c r i t i c a l consolidation stress (ol ) (state C i n F i g . 5.9 lc crit °  for the fixed void r a t i o e ) and c  the  e f f e c t i v e stress path CS i s the lowest stress path over which s t r a i n softening response i s developed leading to steady state deformation. Hence the peak shear strengh at (al  )  (strength at C) i s the lowest  143. l e v e l of shear s t r e s s to be applied i n order to develop l i q u e f a c t i o n . Due  to the uniqueness of CSR and steady s t a t e , the c y c l i c loading applied  must therefore result i n peak stress state above state C. CSR  Only then the  l i n e w i l l be reached i n order to have l i q u e f a c t i o n i n i t i a t e d .  Such a  s i t u a t i o n can be i l l u s t r a t e d by the e f f e c t i v e stress path plots of three samples at constant void r a t i o e^ and a^  in Fig.  5.9.  For sand with no s t a t i c shear stress (Sample A1 ) , although the p o t e n t i a l to develop steady state deformation e x i s t s ( f i r s t  criteria  s a t i s f i e d ) under monotonic loading, for the l e v e l of c y c l i c stress shown i n the f i g u r e , the stress state of the sand with continued c y c l i c loading w i l l reach the CSR  l i n e i n the region where CSR state does not exist  (dashed l i n e below C ) . case.  Hence, l i q u e f a c t i o n can not be Induced i n t h i s  C y c l i c loading w i l l move sample state progressively toward the PT  l i n e and only c y c l i c mobility w i l l develop, which w i l l be discussed i n Section 5.2.  Liquefaction f o r state A1  can be developed only by applying  c y c l i c load with shear stress amplitude equals to the peak shear strength (S  j_) under monotonic loading.  Under t h i s c o n d i t i o n , l i q u e f a c t i o n w i l l  be induced i n the f i r s t compression loading, which i s i d e n t i c a l to monotonic l o a d i n g . Increasing the s t a t i c shear stress l e v e l while holding a^ c to a value l e s s then the peak shear strength S  constant  ^ (Sample A 2 ) , two  condi-  tions can occur, depending on the amplitude of c y c l i c loading a p p l i e d . If the t o t a l shear stress i s less than S , , i . e . , x „ + T ' < S , , the upl s2 cy upl sample state with continued c y c l i c loading w i l l reach the CSR region where CSR developed.  i n the  state does not e x i s t , and hence l i q u e f a c t i o n can not  Under t h i s c o n d i t i o n , only c y c l i c mobility can be induced.  However, i f the amplitude of c y c l i c load i s large enough such that the  be  t o t a l shear stress i s greater than S , , i . e . , x „ + T > S , , the upl s2 cy upl sample state with continued c y c l i c loading w i l l reach the CSR region where CSR at CSR  state does e x i s t .  i n the  Liquefaction w i l l then be i n i t i a t e d  l i n e , provided that the number of stress cycles i s large enough to  move the e f f e c t i v e stress state of sample to the CSR state by  the  progressive development of residual pore pressure. For sand with I n i t i a l s t a t i c shear stress greater than the peak shear strength S  ^ at C (Sample Ag ) , the sand state w i l l always reach  the CSR i n the region where CSR state e x i s t s .  Hence l i q u e f a c t i o n w i l l  always be developed provided the number of stress cycles i s large enough to move the e f f e c t i v e stress state of sample to the CSR It should be noted that the peak shear strength S f o r the chosen e c  state.  , at (a' ) upl lc crit  Is s l i g h t l y greater than the steady state shear  strength (S  )•  Therefore, for p r a c t i c a l purpose the steady state shear  strength may  be used as the minimum value of t o t a l shear stress instead  of the peak shear strength value at C.  Thus, the second c r i t e r i o n for  l i q u e f a c t i o n to occur i s that the maximum shear stress ( s t a t i c + c y c l i c ) must be greater than the steady state shear strength.  That these two  conditions must be simultaneously s a t i s f i e d f o r l i q u e f a c t i o n to occur under c y c l i c loading w i l l be examined by actual tests In the l a t e r sections. It may  be pointed out that the two c r i t e r i a s p e c i f i e d above for  occurrence of l i q u e f a c t i o n under c y c l i c loading are the necessary conditions only.  Whether a c t u a l l i q u e f a c t i o n can be developed or not depends  on the number of s t r e s s cycles a p p l i e d .  If the number of stress cycles  i s not large enough to move the sample state to the CSR  s t a t e , no  l i q u e f a c t i o n can be induced, even though both c r i t e r i a s p e c i f i e d above  145. are s a t i s f i e d .  However, the combination of c y c l i c loading and pore  pressure increase due to pore pressure r e d i s t r i b u t i o n i n the s o i l mass following the termination of c y c l i c loading could move the sample state to  the CSR state and I n i t i a t e l i q u e f a c t i o n .  This i s e s p e c i a l l y important  i f the i n i t i a l s t a t i c shear stress i s greater than the steady state shear strength, since the pore pressure increase due to c y c l i c loading coupled with the pore pressure increase due to post c y c l i c pore pressure redist r i b u t i o n could lead to the occurrence of l i q u e f a c t i o n .  Therefore, an  i n i t i a l condition with T " > S should always be avoided i n order to s us eliminate the p o s s i b i l i t y of l i q u e f a c t i o n under c y c l i c loading. For Ottawa sand also the CSR i s unique, regardless of the loading paths which brings the sample state to the CSR, and the steady state Is unique after l i q u e f a c t i o n has been induced.  Therefore, the c r i t e r i a  specified above for angular t a i l i n g s sand can be applied to sand with rounded p a r t i c l e s a l s o .  However, i n order to examine the existence or  non-existence of steady s t a t e , the i n i t i a l r e l a t i v e density alone may be used for the range of consolidation stress considered h e r e i n , as discussed i n Chapter 4. It should be noted that the discussions presented above apply to compression deformation mode only. to extension mode a l s o .  However, similar concept should apply  I t w i l l be shown l a t e r by actual test results  that l i q u e f a c t i o n can be induced i n extension mode i f these two c r i t e r i a specified above are s a t i s f i e d i n extension mode.  5.1.4  Test Results A series of c y c l i c loading tests on samples consolidated to the same  e and o' but with various levels of K r a t i o were carried out to c 3c c  146. examine the v a l i d i t y of the c r i t e r i a established f o r l i q u e f a c t i o n to occur for both sands.  The i n i t i a l sample states were so chosen that the  sand would experience l i q u e f a c t i o n under monotonic loading.  These  results w i l l also be used l a t e r i n Section 5.4 to i l l u s t r a t e the influence of e , o l and K on the resistance to s t r a i n development unde c 3c c  cyclic  loading.  T a i l i n g s Sand For t a i2 l i n g s sand,, the minor e f f e c t i v e consolidation stress a^ c of 16.0 kgf/cm (1568 kPa) and r e l a t i v e density a f t e r consolidation D of rc 70% were used. Four series of tests with consolidation stress r a t i o K c of 1.0, 1.25, 1.5 and 2.0 were performed.  The i d e n t i c a l f i n a l void r a t i  under various consolidation stress conditions was achieved by consolidating samples prepared with i n i t i a l void ratios e^, obtained by interpolating between the consolidation curves ( F i g . 3.8). Extremely consistent f i n a l densities were obtained with variations i n r e l a t i v e density less than ±1.6%.  This also served as a check of the consolida-  t i o n c h a r a c t e r i s t i c s of sand discussed  i n Chapter 3.  The results of c y c l i c stress r a t i o a . /2a' (= x /a' ) versus dcy 3c cy 3c number of stress cycles to develop l i q u e f a c t i o n or c y c l i c mobility are shown In F i g . 5.10.  If c y c l i c m o b i l i t y developed, the number of cycles  refer to those needed to accumulate 2.5% a x i a l s t r a i n . develops, a x i a l s t r a i n i n excess of 2.5%  If liquefaction  develops u n t i l steady s t a t e .  It may be seen that not a l l samples developed l i q u e f a c t i o n , although p o t e n t i a l to develop l i q u e f a c t i o n i n monotonic loading existed f o r a l l i n i t i a l states.  A combination of i n i t i a l stress conditions and c y c l i c  loading amplitude dictated whether l i q u e f a c t i o n or c y c l i c mobility would  Tailings  Sand  0 " ' - 16.0 k g f / c m  2  3c  e Drc c  0.20-  - 0 8 0 0 t 0.006 '70.01 1.6%  •  o o  1.0 1.25 1.5 2.0  0.15  Cvj  0.10  u  Note- X indicates no liquefaction induced. 2.5% axial sfrafns  were used for cyclic mobility.  0.05-  5  Number F i g . 5.10  10  of cycles,  20  50  100  N  Cyclic stress required to cause liquefaction or 2.5% a x i a l s t r a i n for contractive t a i l i n g s sand consolidated to various ratios.  148. develop. Fig.  Both l i q u e f a c t i o n and c y c l i c mobility r e s u l t s are presented i n  5.10 to f a c i l i t a t e discussion of the c r i t e r i a to cause l i q u e f a c t i o n  under c y c l i c loading. For i s o t r o p i c a l l y consolidated states (K = 1.0) and a n i s o t r o p i c a l l y c consolidated states with lity.  = 1.25, a l l samples developed c y c l i c mobi-  T y p i c a l s t r a i n developments and pore pressure responses during  c y c l i c loading f o r such i n i t i a l states are i l l u s t r a t e d i n F i g . 5.11. Since the maximum shear stresses ( s t a t i c + c y c l i c ) were less than 2.4 kgf/cm  2  2  =1.0 and 1.25 respecc t i v e l y , which are s u b s t a n t i a l l y less than the steady state shear strength for  (235 kPa) and 4.7 kgf/cm  (461 kPa) for K  the e selected (about 5.6 kgf/cm c  2  lower bound), l i q u e f a c t i o n could  not develop. For a n i s o t r o p i c a l l y consolidated state with  = 1.5, however, both  l i q u e f a c t i o n and c y c l i c mobility could develop depending on the amplitude of c y c l i c load applied ( F i g . 5.10).  For c y c l i c stress r a t i o greater than  0.13, l i q u e f a c t i o n developed, whereas f o r c y c l i c stress r a t i o less than 0.13  c y c l i c mobility developed.  These two cases are i l l u s t r a t e d by the  s t r e s s - s t r a i n curves and pore pressure responses i n F i g . 5.12a,b. In Fig.  5.12a, the c y c l i c stress r a t i o r e s u l t s i n maximum shear stress of  6.10 kgf/cm  2  (598 kPa) which i s s l i g h t l y greater than the steady state  shear strength.  About 2.5% a x i a l s t r a i n was developed i n the 5th loading  cycle with accompanying pore pressure increase.  In F i g . 5.12b, however,  the maximum shear stress Is s l i g h t l y less than the steady state shear strength.  Consequently no sudden development of s t r a i n associated with  steady state deformation occurred. The s t r a i n developed progressively with number of stress cycles as a r e s u l t of c y c l i c m o b i l i t y .  This may  also be seen from the plot of s t r a i n development versus number of stress cycles i n F i g . 5.13.  149-  E  4.0  3.0  2.0  Ext. F i g . 5.11  1.0  0  £a(%)  /.0  2.0  Comp.  Tyipcal undrained c y c l i c loading response for contractive t a i l i n g s sand showing c y c l i c m o b i l i t y .  150.  Tailings O&-I6-0 Kc •  I6.0\-  Sand kgf/cm  /.5  ec  '0.805  (a)  0dcy /203c '  5th cycle  2  Drc ' 68.4% = 0.J53 6th cycle  13 th cycle  -  12.0]  /  Estimated Steady State Strength  8.0  4.0  2.0  4.0  6.0  e (%)  8.0  10.0  a  (6.0  (o)  CT  dcy  /2Cr ' - 0 . / 0 9 3c  Estimated Steady State Strength  I2.0\  / *d  8.0  4.0  66th cycle  36th cycle  2.0  4.0  6.0  8.0  10.0  e (%. a  F i g . 5.12 T y p i c a l undrained c y c l i c loading response f o r contractive t a i l i n g s sand showing (a) l i q u e f a c t i o n , and (b) c y c l i c mobility.  151.  From the two test examples shown above, both i n i t i a l states satisfy the first criterion. But, the occurrence of liquefaction depends in addition on whether the maximum shear stress condition in relation to steady state strength is satisfied. For anisotropically consolidated state with  = 2.0, a l l samples  developed liquefaction (Fig. 5.10). In this test series, the static 2  shear stress equals 8.0 kgf/cm  (784 kPa), which i s substantially higher  than the steady state shear strength.  Thus, both criteria are satisfied,  and hence liquefaction occurs in a l l samples.  Typical strain development  with number of stress cycles for such samples is shown in Fig. 5.13.  Ottawa Sand For Ottawa sand, minor effective consolidation stress a' of 2.0 3c 2  kgf/cm  (196 kPa) and relative density after consolidation D  were used.  of 35.5%  Three series of tests with Kc ratios of 1.0, 1.5 and 2.0  were carried out.  Similar method as used in preparing the tailings sand  sample was employed to achieve samples with identical f i n a l density. Again, very consistent final relative density was obtained, with variation less than ±1.0% from the desired target.  A l l i n i t i a l sample states  chosen would develop liquefaction under monotonic loading. The results showing cyclic stress ratio a, /2o' versus the number dcy 3c of stress cycles to develop liquefaction are shown in Fig. 5.14. results for  The  = 1.19 obtained from previous studies by Chern (1981) are  also shown in the figure.  In contrast to the behaviour of tailings sand,  a l l samples developed liquefaction, regardless of the K c ratio. For isotropically consolidated state, although the cyclic shear 2  stress applied (0.18 kgf/cm ) to one sample was less than the steady  No. of cycles, N F i g . 5.13  T y p i c a l S t r a i n development vs number of c y c l e s c o n s o l i d a t e d to v a r i o u s K ratios. c  for contractive  t a i l i n g s sand  OHawa  Sand  O^.» 2.0 kgf/cm e - 0 706 ± 0 0 0 3 D « 3 5 . 5 % 11.0 % efl - 2 . 5 % 8 5 . 0 % 2  c  r c  •  i.o 1.5 2.0  1.19 0.J5  u CVJ  u  0.05  10  20  50  100  200  No. of cycles, N  F i g . 5.14  Cyclic stress required to cause liquefaction for i n i t i a l l y loose Ottawa sand consolidated to various K r a t i o s .  154. 2  state shear strength In compression (about 0.35 kgf/cm ) at the chosen e c , this c y c l i c shear stress was greater than the steady state shear 2  strength i n extension (less than 0.1 kgf/cm ).  Therefore, l i q u e f a c t i o n  occurred i n extension mode. This i s i l l u s t r a t e d by the e f f e c t i v e stress paths i n F i g . 5.15. Typical s t r a i n development with the number of stress cycles i s shown i n F i g . 5.16, As the K r a t i o increased to 1.19 c  although the s t a t i c shear stress  was less than the steady state shear strength i n compression mode, the maximum shear stress ( s t a t i c + c y c l i c ) was s l i g h t l y larger than the steady state value.  Therefore, l l q u e f a t i o n occurred i n compression mode.  This Is shown by the dashed line i n F i g .  5.14. The corresponding s t r a i n  development with the number of stress cycles i s shown i n F i g . 5.16. For states with K  c  ratios of 1.5 and 2.0, the s t a t i c shear stresses  were equal to or greater than the steady state shear strength i n compression.  Therefore, l i q u e f a c t i o n occurred on the compression side i n a l l  cases. From the r e s u l t s for both sands presented above, I t may be concluded that both c r i t e r i a must be met i n order to develop l i q u e f a c t i o n under c y c l i c loading.  Liquefaction can not be induced i f the maximum shear  stress c r i t e r i o n i n r e l a t i o n to steady state shear strength Is not s a t i s fied even though the sample has the p o t e n t i a l to develop l i q u e f a c t i o n . It w i l l be shown i n Section 5.2 that l i q u e f a c t i o n can never be induced i f the f i r s t c r i t e r i o n i s not met, no matter what c y c l i c stress amplitude i s applied.  It should also be emphasized that these two c r i t e r i a hold for  l i q u e f a c t i o n i n compression as well as extension mode. Extension mode should be checked i f c y c l i c loading results i n s i g n i f i c a n t shear stress reversal.  In case both c r i t e r i a are met i n compression as well as  Ottawa Sand  Fig. 5.15  Typical i l l u s t r a t i o n of liquefaction of i s o t r o p i c a l l y consolidated Ottawa sand under c y c l i c loading.  No. of c y c l e s , N  F i g . 5.16  T y p i c a l s t r a i n development vs number of c y c l e s f o r i n i t i a l l y c o n s o l i d a t e d to v a r i o u s K ratios.  l o o s e Ottawa sand  157. extension, l i q u e f a c t i o n w i l l always occur i n extension mode due to a much lower CSR i n extension as shown by test results i n Section 4.2.2.  5.2  C y c l i c M o b i l i t y Induced Under C y c l i c Loading  It was shown i n the previous section that a sand develops c y c l i c mobility i f the shear stress c r i t e r i o n i s not s a t i s f i e d , even though the sand has the potential to develop l i q u e f a c t i o n .  In this section, i t w i l l  be shown that a sand can develop only c y c l i c mobility i f the steady state can not be achieved for the given i n i t i a l s t a t e . both sands consolidated  A series of tests on  to i n i t i a l sample states below the c r i t i c a l  consolidation stress (al ) . surface w i l l be used to i l l u s t r a t e t h i s lc c r i t mechanism of s t r a i n development during c y c l i c loading. These r e s u l t s w i l l also be used to i l l u s t r a t e the influence of various factors (e , c CT^c, K ) on the resistance to s t r a i n development under c y c l i c loading.  5.2.1  Strain Development Due to C y c l i c M o b i l i t y 2  It was shown by Vaid and Chern (1983 ) that dense Ottawa sand does not suffer l i q u e f a c t i o n under c y c l i c loading.  In such sand very small  deformations are developed u n t i l the e f f e c t i v e stress state of sand reaches the PT l i n e .  S i g n i f i c a n t amount of deformation i s developed  during the loading phase when the stress state crosses the PT l i n e . Unloading thereafter causes large increase i n pore pressure, bringing the sample close to the transient state of zero e f f e c t i v e s t r e s s , but with very l i t t l e change i n deformation.  Repetition of this phenomenon of  stress state moving a l t e r n a t e l y i n t o the region beyond the PT l i n e s with cycles of loading ultimately results i n a transient state of zero  158. e f f e c t i v e s t r e s s , which i s responsible f o r further accumulation of deformation.  For t a i l i n g s sand, t y p i c a l s t r e s s - s t r a i n and pore pressure  response and e f f e c t i v e stress paths f o r i s o t r o p i c a l l y and a n i s o t r o p i c a l l y consolidated samples are shown i n F i g s . 5.17 and 5.18. were consolidated to D  of 70% under  These two samples  of 2.0 kgf/cm  2  (196 kPa) , such rc Jc that t h e i r i n i t i a l states l i e w e l l below the ( a ' ) surface. Therelc crit  f o r e , the steady state can not be achieved, according to the r e s u l t s discussed i n Chapter 4. I s o t r o p i c a l l y consolidated sample ( F i g .  5.17), accumulated very  small deformation u n t i l i t s e f f e c t i v e stress state reached the PT l i n e . From the f i r s t cycle u n t i l 29th cycle of loading, the s t r a i n amplitude increased from 0.1% to 0.6% although the residual pore pressure reached 80% of the i n i t i a l consolidation pressure. However, the a p p l i c a t i o n of 30th cycle of loading produced a disproportionate e f f e c t . amplitude during t h i s stress cycle increased to about 1.0%. amplitude increased further from 1.0% stress c y c l e s . (Fig.  The s t r a i n The s t r a i n  to about 10% i n the next eleven  From the pore pressure response during the 30th cycle  5.17b), i t may be noted that sample showed a decrease i n pore  pressure when the maximum shear stress was reached (points 3 and 4 ) . This feature Is d i f f e r e n t from those observed i n the previous loading cycles (e.g.  points 1 and 2 ) .  The e f f e c t i v e stress state at which the  sample starts to d i l a t e (decrease i n pore pressure) was found to be e s s e n t i a l l y the same as the PT l i n e obtained under monotonic loading. Thus, the attainment of PT state also s i g n i f i e s the onset of s i g n i f i c a n t deformation of d i l a t i v e sample during c y c l i c loading.  It should be noted  that the stress state at PT l i n e moved closer and closer to the o r i g i n (Fig.  5.17c) as the c y c l i c loading continued.  This concept of stress  E o u  To/lings Sand Test IC-U - #27  u  cy  0 '"2.0 kgf/cm K -1.0 "0.814 D "66.1% "0.799 D "70.2% 2  3c c  rl  rc  .17a  Typical undrained c y c l i c loading behaviour of i s o t r o p i c a l l y consolidated t a i l i n g s sand.  dilative  Tailings  Sand  Test I C - I U -  Fig.' 5.17b  T y p i c a l undrained c y c l i c t a i l i n g s sand.  #27  l o a d i n g behaviour of i s o t r o p i c a l l y  consolidated  dilative P  Tailings Sand Test  I C-IW-#27  F i g . 5.17c  Typical undrained c y c l i c loading behaviour of consolidated d i l a t i v e t a i l i n g s sand.  isotropically  162.  Tailings  _i 1.0  F i g . 5.18a,b  Sand  i  i  i  — i  1  1  1—  2.0  3.0  4.0  5.0  6.0  7.0  8.0  Typical undrained c y c l i c loading behaviour of anisot r o p i c a l l y consolidated d i l a t i v e t a i l i n g s sand.  Tailings Sand  Fig. 5.18c  T y p i c a l undrained c y c l i c l o a d i n g behaviour of a n i s o t r o p i c a l l y c o n s o l i d a t e d d i l a t i v e t a i l i n g s sand.  164. path moving beyond the PT l i n e i n order to develop large deformation can s t i l l be applied when the transient state of zero e f f e c t i v e stress i s reached.  Reloading i n both the compression and extension regions caused  d i l a t i o n (points 5 to 6 and 7 to 8) with accompanying large deformation, p a r t i c u l a r l y a f t e r attainment of transient states of zero e f f e c t i v e stress.  Unloading resulted i n large increase i n pore pressure (points 6  to 7 and 8 to 9) but with very l i t t l e change i n a x i a l deformation. For  a n i s o t r o p i c a l l y consolidated sample ( F i g . 5.18), the c y c l i c  stress amplitude was selected so as to cause a s l i g h t amount of shear stress r e v e r s a l .  S i g n i f i c a n t amount of a x i a l deformation was observed  during the f i r s t cycle of loading. associated with l i q u e f a c t i o n .  However, this deformation i s not  The sample In fact d i l a t e d and showed a  turnaround i n e f f e c t i v e stress path ( F i g .  5.18c), a behaviour similar to  that observed for d i l a t i v e sand under monotonic loading.  The e f f e c t i v e  stress r a t i o at the s t a r t of d i l a t i o n (decrease i n pore pressure) was found to be approximately the same as that of the PT l i n e obtained before.  Unloading of shear stress during the stress cycle caused  increase i n pore pressure with very l i t t l e change i n a x i a l deformation (point 1 to 2). Reloading the sample beyond the PT l i n e again caused s i g n i f i c a n t amount of deformation and decrease i n pore pressure.  This  behaviour Is s i m i l a r to that observed f o r i s o t r o p i c a l l y consolidated sample once Its stress state reached the PT l i n e .  However, due to only  s l i g h t amount of shear stress reversal involved, the transient state of zero e f f e c t i v e stress was never r e a l i z e d .  Consequently, instead of  deformations increasing with number of stress c y c l e s , the accumulated deformations leveled o f f as the e f f e c t i v e stress path got v i r t u a l l y s t a b i l i z e d with increasing c y c l e s .  165, After 55 cycles of loading, the c y c l i c stress amplitude was Increased s l i g h t l y so as to cause 0.1 kgf/cm reversal.  2  (9.8 kPa) of shear stress  The r e s u l t s of such loading cycles are shown by the data  points i n f u l l dots i n F i g . 5.18.  In f i v e additional stress c y c l e s , the  a x i a l s t r a i n amplitude increased from 0.4% to 5.2% ( F i g .  5.18a) and  accumulated a x i a l s t r a i n increased from 5% to more than 7%.  Unloading of  shear stress during the stress cycle caused the sample to reach the transient state of zero e f f e c t i v e stress with very l i t t l e change i n deformation (points 5 to 6 and 7 to 8 ) .  On the other hand, loading  caused the sample to develop large deformation with accompanying drop i n pore pressure (points 6 to 7 and 8 to 9 ) .  This behaviour i s s i m i l a r to  that observed f o r the i s o t r o p i c a l l y consolidated case. From the r e s u l t s presented above, i t may be concluded that f o r d i l a tive sand the deformation during c y c l i c loading i s due to c y c l i c m o b i l i t y instead of l i q u e f a c t i o n associated with steady state deformation.  Signi-  ficant amount of s t r a i n can be developed only when the stress state reaches the PT l i n e .  Repetition of stress state moving into the region  beyond the PT l i n e i s responsible f o r further accumulation of deformation.  However, the rate of s t r a i n accumulation with number of stress  cycles Is generally slow i f no shear stress reversal i s involved.  This  has a very important implication on the e f f e c t of s t a t i c shear stress on the resistance to s t r a i n development under c y c l i c loading, and w i l l be discussed i n Section 5.4. The phenomenon of c y c l i c m o b i l i t y was often a t t r i b u t e d to the r e d i s t r i b u t i o n of water content within the test specimen during c y c l i c loading, e s p e c i a l l y i n the case with shear stress r e v e r s a l (Casagrande, 1975;  Castro, 1969 and 1975; Castro and Poulos, 1977).  I t has been  166. argued that near the top of the specimen, the void r a t i o of sand increases, and near the bottom i t decreases.  Appearance of necking  and  bulging of samples under the top loading cap during c y c l i c loading has been advanced In support of this view. deformations  The pore pressure buildup and  measured i n the laboratory were suggested to be due  to the formation of such loose zone within the specimen.  chiefly  Hence the  change i n e f f e c t i v e confining stress i n state diagram during c y c l i c loading, such as shown i n F i g . 5.19  for d i l a t i v e sample, i s considered  ficti-  tious i n the sense that i t represents average c o n d i t i o n s . Therefore, the state point may  not reach the condition of zero e f f e c t i v e confining  stress i f the specimen were to remain uniform. However, from the results shown above there i s good direct and i n d i r e c t evidence showing that this progressive softening may not be due to nonuniform deformation developed within the specimen.  It has been  shown i n previous sections that progressive increase i n pore pressure during c y c l i c loading causes very small s t r a i n u n t i l the stress, state reaches the PT state ( F i g . 5.17).  Under this s t r a i n l e v e l , there i s no  evidence that r e d i s t r i b u t i o n of water content can take place within the specimen.  Moreover, the progressive Increase i n pore pressure and  deformations  can also be induced i f c y c l i c loading does not result i n  shear stress r e v e r s a l , i n which case the condition of transient zero e f f e c t i v e stress ( F i g . 5.18)  never occurs - the condition which has been  considered responsible for development of nonuniformities.  Under this  stress condition, d e n s i f i c a t i o n i n bottom part of the specimen and loosening l n top part as suggested can not occur.  It appears that  necking can occur only l n sample with nonuniform sample density or a f t e r very large s t r a i n has developed.  By using the conventional procedures of  Effective  Fig.'5.19  Confining  Stress,  0*3'  Schematic i l l u s t r a t i o n of monotonic and c y c l i c loading response of saturated sand in 2-D state diagram.  168. sedimentation and moist compaction, there i s a tendency for reconstituted samples to achieve higher density i n the bottom portion and lower density i n the top. Consequently, i n such specimens, nonuniform deformation tends to occur and r e l i a b l e results may not be obtained.  Therefore, i t  i s very important to emphasize the sample formation techniques so as to y i e l d sample with uniform density throughout. By using the improved sample preparation techniques described In Chapter 3, the sample did not develop necking even when the transient state of zero e f f e c t i v e stress was reached. It has been further i n f e r r e d that d i l a t i v e sand, which develops negative pore pressure after reaching PT state under monotonic loading ( F i g . 5.19), can not develop progressive softening under c y c l i c loading s i m i l a r to that of the contractive sample, i f the specimen were to remain uniform (Castro and Poulos, 1977; Casagrande, 1975).  As discussed i n  Chapter 4 and this chapter, d i l a t i o n can occur only after the stress state reaches the PT l i n e .  Therefore, the development of negative pore  pressure under monotonic loading i s a behaviour after large deformation. However, c y c l i c loading behaviour i s a small s t r a i n phenomenon u n t i l the stress state reaches the PT l i n e .  Therefore, d i l a t i v e response a f t e r  large deformations under monotonic loading ( F i g .  5.19) does not imply  that the same behaviour w i l l occur under c y c l i c loading.  It i s well  known that dense sample, which develops volume expansion under monotonic loading, causes volume reduction under c y c l i c loading.  It has also been  shown by Luong (1980) that c y c l i n g a sample under PT l i n e causes volume reduction under drained conditions.  Volume expansion can occur only when  the sample i s cycled i n the region beyond PT l i n e .  Under undrained  condition, this volume reduction r e s u l t s i n rebound i n s o i l structure to  the extent required to keep the volume constant. by the schematic diagram i n F i g . 5.19 (1975).  This may  be i l l u s t r a t e d  proposed by Seed, Pyke and  Martin  This i n t e r p l a y of volume reduction and s o i l structure rebound  results i n build up of pore pressure as the c y c l i c stress a p p l i c a t i o n continues.  Therefore, c y c l i c mobility i s another c l a s s of problem under  c y c l i c loading, and can occur i n sand during earthquake loading.  5.2.2. C r i t e r i a to Cause C y c l i c M o b i l i t y Under C y c l i c Loading It has been shown i n Section 5.1.3  that sand with the p o t e n t i a l to  develop l i q u e f a c t i o n , i . e . , the steady state e x i s t s , w i l l develop c y c l i c mobility i f the maximum shear stress ( s t a t i c + c y c l i c ) i s less than the steady state shear strength.  It was  further shown i n Section 5.2.1  that  sand with i n i t i a l state l y i n g below the c r i t i c a l consolidation stress a  ( j _ c ) c r j t surface, i . e . , steady state can not be achieved, develops c y c l i c mobility only, regardless of the amplitude of c y c l i c load applied. Therefore, i t may  be concluded that sand with any condition that does not  s a t i s f y the c r i t e r i a to cause l i q u e f a c t i o n w i l l develop only c y c l i c mobility.  However, the c r i t e r i a for l i q u e f a c t i o n should be examined both  i n compression and extension regions i f shear stress reversal i s involved. The above c r i t e r i a for c y c l i c mobility to occur i s v e r i f i e d by performing a series of tests on both sands consolidated below the  (al )  surface.  These tests are discussed i n the following s e c t i o n .  5.2.3. Test Results A series of c y c l i c loading t e s t s on samples consolidated to the same  170. e and al but with various l e v e l s of K r a t i o were performed to examine c 3c c the c r i t e r i a for c y c l i c mobility to occur.  The i n i t i a l sample states  were so chosen that the steady state can not be achieved i n compression for  both sands.  For Ottawa sand, however, the steady state exists i n  extension mode at the chosen void r a t i o .  These tests also serve to  i l l u s t r a t e the importance of the mode of loading on undrained behaviour. Results  from these test results w i l l also be used l a t e r i n section 5.4 to  i l l u s t r a t e the influence of e , al and K on the resistance to s t r a i n c 3c c  development under c y c l i c  loading.  T a i l i n g s Sand For t a i l i n g s sand, the minor e f f e c t i v e consolidation stress ai of 3c 2 2.0 kgf/cm (196 kPa) and r e l a t i v e density after consolidation D of 70% rc were used.  Three series of test with K c r a t i o of 1.0, 1.5 and 2.0 were  performed. Under these conditions, a l l I n i t i a l sample states l i e well to the l e f t of the steady state l i n e s (compression and extension).  Hence  the steady state can not be achieved i n a l l cases. The r e s u l t s of c yJ c l i c stress r a t i o a, /2al versus number of stress dcy 3c cycles to develop 2.5% a x i a l s t r a i n f o r various K c r a t i o s are shown In Fig.  5.20. A l l samples developed c y c l i c m o b i l i t y , regardless of the  i n i t i a l state of., the sample and the amplitude of c y c l i c loads applied. Typical results of s t r a i n development versus number of stress cycles are also i l l u s t r a t e d i n F i g . 5.21. I s o t r o p i c a l l y consolidated  sample developed very small deformations  u n t i l the stress state reached the PT l i n e .  The deformation  increased  r a p i d l y thereafter due to development of transient state of zero effect i v e stress (see F i g . 5.21).  Fig..5.20  Cyclic stress required to cause 2.5% a x i a l strain for d i l a t i v e t a i l i n g s sand consolidated to various K r a t i o s .  5.0  Tailings 0* '»2.0 3c  "0.801  •  *c 1.0 1.5 2.0  A  c o  kgf/cm  ec  4.0  Q  3.0  Sand 2  Drc -69.5%  0.193 0.344 0509  c/) 2.0 o X  /.0  0  15  20  No. of cycles, N F i g . 5.21  Typical strain development vs number of cycles for d i l a t i v e t a i l i n g s sand consolidated to various K r a t i o s , c  173. For  a n i s o t r p i c a l l y consolidated samples with K c = 1.5, the s t r a i n  development i s s i m i l a r to that for the i s o t r o p i c a l l y consolidated case, except that the i n i t i a l s t r a i n accumulation u n t i l the stress state reached the PT l i n e i s larger ( F i g .  5.21).  This may be due to the  presence of i n i t i a l s t a t i c shear bias and much larger c y c l i c load applied.  A small amount of s t r a i n was induced whenever the t o t a l shear  stress approached  i t s maximum value causing a small s t r a i n accumulation  a f t e r each cycle of loading. For  sample with K  c  = 2.0, the s t r a i n accumulation i s quite d i f f e r e n t  from the other two cases.  Relatively large s t r a i n was developed during  the f i r s t cycle of loading.  This was due to the fact that the i n i t i a l  e f f e c t i v e stress r a t i o was high.  During the loading phase of the f i r s t  stress c y c l e , the stress state reached the PT l i n e and thus a rapid accumulation of s t r a i n was observed from the beginning of the t e s t . However, the rate of s t r a i n accumulation decreased gradually because states of transient zero e f f e c t i v e s t r e s s , necessary f o r rapid s t r a i n accumulation, did not occur due to no shear stress r e v e r a l .  The sample  accumulated 2.5% a x i a l s t r a i n i n 10 stress c y c l e s , and i t took another 45 cycles to accumulate additional 2.5% For  axial s t r a i n .  sample with the same e c but under higher confining pressure,  i t was shown i n Section 5.1.4  that only c y c l i c mobility i s developed when  the maximum shear stress i s less than the steady state shear strength. For  such I n i t i a l states the relationships between c y c l i c stress ratio  versus number of stress cycles to develop 2.5% a x i a l s t r a i n for and 1.25  were shown In F i g . 5.10.  low confining pressure ( F i g . increasing K  = 1.0  Trends similar to those observed under a  5.20), i . e . , increasing < j C y ^ ° 3 c with  r a t i o , may be observed even under higher levels of  174. confining pressure.  Ottawa Sand For Ottawa sand, minor e f f e c t i v e consolidation stress ai of 2.0 3c 2 kgf/cm (196 kPa) and r e l a t i v e density a f t e r consolidation D of 51.5% rc were used.  Three series of test with Kc r a t i o of 1.0, 1.5 and 2.0 were  performed.  Under these conditions, the i n i t i a l sample states l i e below  the steady state l i n e i n compression.  Therefore, the steady state can  not be reached i n compression mode f o r these samples.  However, i t w i l l  be shown l a t e r that steady state i n extension can be reached f o r these samples. It was found that a l l samples developed c y c l i c mobility except the one with K c = 1.0 which developed l i q u e f a c t i o n i n extension mode. The results of c y c l i c stress r a t i o a^C y^ 2 a  c  v  ersus number of stress cycles  to develope 2.5% a x i a l t r a i n due to c y c l i c mobility or l i q u e f a c t i o n i n extension mode are shown i n F i g . 5.22. The r e s u l t s f o r K c = 1.19, which are interpolated from a previous study by Chem (1981), are also presented In the f i g u r e .  The r e s u l t s f o r both l i q u e f a c t i o n and c y c l i c  mobility are presented here i n order to f a c i l i t a t e discussion of the c r i t e r i a f o r occurrence of c y c l i c m o b i l i t y and l i q u e f a c t i o n .  Typical  results of s t r a i n development versus number of stress cycles for these tests are shown i n F i g . 5.23. For I s o t r o p i c a l l y consolidated sample, the c y c l i c stress applied exceeded the steady state shear strength i n extension. Therefore, l i q u e f a c t i o n occurred i n extension mode. This i l l u s t r a t e s the importance of examining the existence of steady state both i n compression and extension  Ottawa  Sand  •2.0 kgf/cm •0.655 ± 0.003 -51.5 ± 1.0% 2  DTC 0.4  Q A  G  0.3  CM  *c 1.0 1.5 2.0 (.19  -2.5%  0.2  4 N o t * ' X ' ' ' * sampla d*v*lop*d liquefaction n d  0.1  5  F i g . 5.22  10 No. of c y c l e s ,  20  50  100  c a  e  200  N  Cyclic stress required to cause 2.5% a x i a l s t r a i n for medium dense Ottawa sand consolidated to various K r a t i o s .  ^4  No. of cycles, N F i g . 5.23  Typical strain.development vs number of cycles for medium dense Ottawa sand consolidated to various K r a t i o s . c —i ON  177. modes, i f significant amount of shear stress reversal is involved. A l l anisotropically consolidated samples (K^ = 1.19, 1.5 and 2.0) developed cyclic mobility (Fig. 5.22). The strain development versus number of stress cycles (Fig. 5.23) is similar to that for the tailings sand with similar Kc ratios.  Accelerated increase in axial deformation  was observed only i f transient state of zero effective stress occurred after the sample state crossed the FT l i n e . stress reversal (K  For the case with no shear  = 2.0), large deformation was developed In the f i r s t  loading cycle when the stress state reached the PT l i n e .  However, the  strain accumulation slowed down in the subsequent cycles because no transient state of zero effective stress developed for the cyclic load amplitude applied.  5.3  Resistance to Strain Development Under Cyclic Loading  It has been shown in the previous sections that large cyclic and residual strains are developed once the sand develops liquefaction or cyclic mobility particularly after reaching the transient state of zero effective stress.  In the case of no shear stress reversal, the sand can  never reach the condition of zero effective stress under cyclic loading. Nevertheless, large undesirable deformation could accumulate. faction develops, large deformations are inevitable.  If lique-  Hence, the accumu-  lated strain Is often used as the failure critierion against cyclic loading.  The strain level considered as failure depends on the type and  relative importance of the earth structure considered. The accumulation of strain during cyclic loading may be due to liquefaction or cyclic mobility or a combination of both. Because of  178. d i f f e r e n t s t r a i n development mechanism i n l i q u e f a c t i o n  and c y c l i c  m o b i l i t Jy , the influence of factors (e , ol , K ) on the resistance to ' c 3c c s t r a i n development under c y c l i c loading i s l i k e l y to be influenced by the mechanism of deformation as well as the s t r a i n l e v e l of i n t e r e s t . If liquefaction  occurs, r e l a t i v e l y large deformation (at least  2.5%  a x i a l s t r a i n for the sands tested) w i l l be developed, once the liquefaction i s induced.  Therefore, i f 2.5% a x i a l s t r a i n development were used  as the f a i l u r e c r i t e r i o n , occurrence of liquefacton could be considered as f a i l u r e .  However, i f higher s t r a i n l e v e l were s p e c i f i e d , then the  t o t a l s t r a i n to f i a l u r e could be the combination of l i q u e f a c t i o n c y c l i c mobility following l i q u e f a c t i o n .  and  Such a case may be seen from the  s t r a i n development versus number of stress cycles f o r the t a i l i n g s sample with K C = 1.5 and c y c l i c stress ratio of 0.157  i n F i g . 5.13.  The sand  accumulated about 3.5% a x i a l s t r a i n at the end of stress cycle i n which liquefaction and only l  1 / 2  developed. %  Further accumulation of s t r a i n was  slowed down  additional s t r a i n developed i n the next stress  cycle.  Similar features of s t r a i n accumulation due to c y c l i c mobility following liquefaction may be seen i n Figs. 5.1b and 5.2c.  Due  of these two mechanisms for development of specified  to the combination l e v e l of s t r a i n , the  influence of f a c t o r s , e.g., s t a t i c shear, on the resistance to s t r a i n development under c y c l i c loading may be d i f f e r e n t depending on whether liquefaction  only or c y c l i c mobility only develops.  that 2.5% a x i a l s t r a i n due to liquefaction  It should be noted  i s for the l i m i t i n g case when  t o t a l shear stress Is s l i g h t l y greater than the steady state shear strength.  When t o t a l shear stress i s considerably larger than the steady  state strength, much larger deformation w i l l be developed. seen from the s t r a i n development due to l i q u e f a c t i o n  This may  i n Figs.  5.13  be and  179.  5.16. For  sand with state i n the t r a n s i t i o n region ( F i g .  potential due to s t r a i n softening i s very small.  4.17), the s t r a i n  It i s conceivable that  the s t r a i n developed due to s t r a i n softening under c y c l i c loading would be very small as w e l l .  Thus, the s t r a i n development for such  initial  states may be regarded as due mainly to c y c l i c m o b i l i t y .  5.4  Influence of Certain Factors on the Undrained C y c l i c Loading Behaviour  The most Important 'factors which Influence the undrained c y c l i c loading behaviour of sand are void r a t i o , confining pressure and s t a t i c shear s t r e s s .  The role of these factors on the undrained c y c l i c loading  behaviour of sands w i l l be discussed i n this s e c t i o n .  5.4.1  Void Radio or Relative Density Most of the knowledge on undrained c y c l i c loading behaviour of  saturated sand has been derived from studies on natural rounded sands. It i s generally believed that r e l a t i v e density i s the most important factor controlling; occurrence of l i q u e f a c t i o n and c y c l i c m o b i l i t y .  Sand  with r e l a t i v e density less than about 40% has been suggested to always develop l i q u e f a c t i o n , whereas sand with r e l a t i v e density greater than about 45% c y c l i c m o b i l i t y , without reference to the p a r t i c l e characteri s t i c s and i n i t i a l stress condition of the sand.  It w i l l be shown In the  following that this may be a good approximation f o r rounded sand, but may not be true for angular sand. Consider the e f f e c t i v e stress state plot of the 3-D e f f e c t i v e stress  180. state diagram at a constant void r a t i o as shown i n F i g . 4.31b.  From the  consolidation c h a r a c t e r i s t i c s of sand, i t was noted that the sand can be consolidated to t h i s void r a t i o by various combination of i n i t i a l void ratios e, and consolidation stress conditions a' and K . i 3c c  The sand with  i n i t i a l state to the l e f t of the ( a ' ) . = constant l i n e has no lc crit p o s s i b i l i t y to develop l i q u e f a c t i o n . It can only develop c y c l i c mobility except i n a small t r a n s i t i o n region immediately to the l e f t of (aj ) K 6 } l c crit = constant l i n e which may develop s l i g h t s t r a i n softening followed by cyclic mobility.  On the other hand, sand with i n i t i a l state on or to the  right of (a I ) . = constant l i n e can develop l i q u e f a c t i o n i f the c y c l i c lc c r i t stress applied i s large enough to cause t o t a l shear stress greater than i t s steady state shear strength.  Occurrence of these phenomena was  i l l u s t r a t e d by c y c l i c tests on samples with the same void r a t i o i n F i g s . 5.10 and 5.20.  It may be noted that a l l samples under low confining  pressure ( F i g . 5.20) developed c y c l i c m o b i l i t y , whereas samples under high confining pressure could develop l i q u e f a c t i o n i f the shear stress criterion for liquefaction i s s a t i s f i e d .  It may also be noted from F i g .  5.1c that l i q u e f a c t i o n can be induced i n samples with very high r e l a t i v e density (more than 85%) i f the consolidation stresses are high enough. For  Ottawa sand with rounded p a r t i c l e s the r e l a t i v e density seems to  be the most Important factor c o n t r o l l i n g the undrained c y c l i c loading behaviour for the range of consolidation stresses considered herein.  For  sample with i n i t i a l r e l a t i v e density larger than about 45%, the steady state can not be achieved even under high confining pressure, and hence l i q u e f a c t i o n Is not expected under c y c l i c loading at least In the compression mode. However, for I n i t i a l l y looser samples, l i q u e f a c t i o n does occur under the same range of consolidation s t r e s s e s .  181.  Therefore, for sand with rounded p a r t i c l e s the r e l a t i v e density gives a good i n d i c a t i o n as to the undrained c y c l i c loading behaviour since a l i m i t i n g value of D ^ alone w i l l s u f f i c e to separate regions of l i q u e f a c t i o n and c y c l i c m o b i l i t y .  However, for sand with angular  p a r t i c l e s , specifying the void r a t i o or r e l a t i v e density alone without reference to the associated consolidation stress conditions i s not s u f f i c i e n t to ascertain whether l i q u e f a c t i o n or c y c l i c mobility w i l l develop during c y c l i c loading. The Influence of void r a t i o or r e l a t i v e density on the occurrence of l i q u e f a c t i o n Is that Increasing  the r e l a t i v e density increases  the  c r i t i c a l consolidation stress ( a ' ) . i n order to have the p o s s i b i l i t y lc c r i t to developv l in q u e f a c t i o n . This i s shown by the increasing of (al ) J lc crit with decreasing  void r a t i o i n the 3-D  e f f e c t i v e stress state diagram  ( F i g . 4.31).  5.4.2. Confining Pressure Even specifying  and a^  f o r a sand i s s t i l l i n s u f f i c i e n t f o r a  prediction of the undrained c y c l i c loading behaviour with repsect to development of 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 . by two  This may  be i l l u s t r a t e d  samples with the same void r a t i o and confining pressure but with  d i f f e r e n t Kc  r a t i o s (Samples G and B i n F i g . 4.31b).  For Sample G,  steady state can not be achieved, and hence l i q u e f a c t i o n can not developed.  the  be  For Sample B, however, the steady state can be achieved, and  l i q u e f a c t i o n can be developed i f the c y c l i c load Is large enough to cause maximum shear stress greater than the steady state shear strength f o r the void r a t i o under consideration.  This i s also true when the  sample state at G i s to the r i g h t of the (a' )  .  initial  = constant l i n e .  Such  182. a behaviour i s i l l u s t r a t e d by the test r e s u l t s shown i n F i g . C y c l i c mobility occurred i n samples with low K c f a c t i o n developed i n samples with high K  5.10.  r a t i o , whereas lique-  r a t i o even though they had c  i d e n t i c a l e^and 2 ' a  c  Furthermore, the occurrence of l i q u e f a c t i o n depends  on the amplitude of c y c l i c load applied.  This i s apparent from the  undrained behaviour of sand with K  i n F i g . 5.10  = 1.5  i n which the  c lowest l e v e l of c y c l i c stress amplitude caused c y c l i c mobility instead of l i q u e f a c t i o n at higher stress amplitudes. For Ottawa sand, however, as discussed  i n the previous s e c t i o n , the  i n i t i a l r e l a t i v e density appears to be the most important factor controll i n g the occurrence of l i q u e f a c t i o n and c y c l i c mobility f o r the range of consolidation stress considered h e r e i n . The e f f e c t of l e v e l of confining pressure on the undrained c y c l i c loading behaviour not only dictates the occurrence of l i q u e f a c t i o n or c y c l i c mobility as discussed above, but also Influences s t r a i n development under either type of response.  the resistance to  This may  be  illustra-  ted by the response of samples with the same void r a t i o and K^ratio  but  d i f f e r e n t confining pressures ( F i g . 5.24). For samples i n the d i l a t i v e region (D1 can be developed.  and D 2 ) , only c y c l i c mobility  An increase i n confining pressure always results i n  increasing contractive tendency.  Therefore, f o r the same c y c l i c stress  r a t i o applied, the sample under higher confining pressure w i l l show a f a s t e r pore pressure buildup with cycles of loading and reach the PT e a r l i e r than that under lower confining pressure.  Therefore, the  resistance to s t r a i n development w i l l always decrease with increasing confining pressure.  Evidence for this argument may  c y c l i c loading test r e s u l t s shown i n F i g s . 5.10  be seen from the  and 5.20.  For each K  line  5.24  I n f l u e n c e of c o n f i n i n g p r e s s u r e on the r e s i s t a n c e to s t r a i n development under c y c l i c l o a d i n g .  134. value for which c yJ c l i c mobility developed, the resistance curve a, /2a' dcy 3c vs N for lower confining pressure i s located higher than that for higher confining pressure.  This reduced resistance to s t r a i n development due to  increasing confining pressure has also been observed by Vaid, Chern and Tumi (1983) for both angular and rounded sands.  In their i n v e s t i g a t i o n ,  sands were tested under simple shear conditions with no s t a t i c shear and i n i t i a l sand states which gave r i s e to only c y c l i c m o b i l i t y . For samples In the contractive region (C^ and C l i q u e f a c t i o n w i l l be developed, as discussed before.  2  i n F i g . 5.24), In this region, two  aspects of the influence of the l e v e l of confining pressure may F i r s t l y , due to the uniqueness of CSR, required to reach the CSR stress r a t i o .  the pore pressure r a t i o s  be noted. Au/a^  line w i l l be the same under the same c y c l i c  However, due to the increased contractive tendency under  higher confining pressure i n Sample C2  than Sample C^, i t i s conceivable  that Sample C2 w i l l reach the CSR l i n e faster (less number of cycles) than Sample C^.  In other words, the resistance to l i q u e f a c t i o n  (a, /2a' required to reach CSR l i n e In a fixed number of cycles) w i l l dcy 3c be decreasing with increasing confining pressure.  Secondly, the poten-  t i a l to develop steady state deformation and the associated loss i n shear resistance for sample under higher confining pressure i s always higher than the one under lower confining pressure due to the uniqueness of steady state strength ( F i g . 5.24).  Therefore, for sand under higher  confining pressure not only the l i q u e f a c t i o n i s easier to be induced but also the deformation associated with l i q u e f a c t i o n and the loss i n shear resistance Is more severe than those under lower confining pressure.  185.  5.4.3  Static Shear Stress or Consolidation Stress Ratio For sand with a given e c  and a ' , increasing K r a t i o may 3c c  transform  the undrained c y c l i c loading behaviour of sand from c y c l i c mobility under low Kc  r a t i o to l i q u e f a c t i o n under high Kc  shown i n e a r l i e r F i g . 5.10.  ratio.  This has been  Therefore, i n order to predict the undrained  c y c l i c loading behaviour of a sand sample, the shear stress component at the end of consolidation has to be considered r a t i o and confining pressure.  i n addition to the void  In t h i s regard the 3-D  e f f e c t i v e stress  state diagram developed under monotonic loading conditions, together with the amplitude of c y c l i c loading imposed provides a complete d e s c r i p t i o n as to the expected mechanism of s t r a i n development during undrained c y c l i c loading of saturated sand. Similar concept can also be used f o r Ottawa sand with rounded p a r t i c l e s , with the difference that i n i t i a l r e l a t i v e density may  suffice  to predict the existence of steady state f o r the range of consolidation stress considered  herein.  The influence of s t a t i c shear or K c loading behaviour may  r a t i o on undrained c y c l i c  be i l l u s t r a t e d more c l e a r l y by p l o t t i n g the r e s i s t /  2a  ance to s t r a i n development (° < j C y' ' 3 c required to cause 2  1/2  %  and  5%  and al as a function rc Jc Such test r e s u l t s f o r t a i l i n g s sand are shown i n F i g .  a x i a l s t r a i n i n 10 cycles) at fixed values of D of K c  ratio.  5.25a at D r c D  rc  = 69.5%  and a I  = 70% and a l = 16.0 Jc  sand at a l =2.0 Jc  =2.0  kgf/cm  kgf/cm  2  35.5%) are shown i n F i g s .  2  kgf/cm  (1568  2  (196 kPa) and i n F i g . 5.26a at  kPa).  Similar r e s u l t s for Ottawa  but d i f f e r e n t r e l a t i v e densities (51.5% and 5.25b and 5.26b.  Because of the d i f f e r e n t  mechanisms of s t r a i n development, the Influence of s t a t i c shear on the undrained c y c l i c loading behaviour should be considered separately i n the  186.  0.6  (a) T a i l i n g s  Sand  a3c' = 2.0 k g f / c m e =0.80/ ± 0.002 D =69.5 ± 0 . 5 % 2  c  r c  0 0.4  (b) Offawo Sand O ^ ' =2.0 k g f / c m e = 0 6 5 5 ± 0.003 D » 5 / . 5 ± 1.0% 2  c  r c  0.3  - o  S = 5.0% a  >!?  2.5 %  OJ \ »> o  Liquefaction (in extension)  1.0  F i g . 5.25  N = 10  1.5  2.0  Influence of s t a t i c shear stress on the resistance to strain development under c y c l i c loading: (a) d i l a t i v e t a i l i n g s sand; (b) i n i t i a l l y medium dense Ottawa sand.  187.  Ol 1.0  Fig.  I  1.5  5.26  L_  2.0  Influence of s t a t i c shear stress on the resistance to s t r a i n development under c y c l i c loading: (a) contractive t a i l i n g s sand; (b) i n i t i a l l y loose Ottawa sand.  188. contractive and d i l a t i v e regions.  For t a i l i n g s sand under low confining  r v pressure, the i n i t i a l sample state was '  constant for the void r a t i o considered. of Kc may  to the l e f t of (al ) ._ = lc crit Therefore, samples at a l l l e v e l s  r a t i o being d i l a t i v e developed c y c l i c mobility ( F i g . 5.25a).  be seen that the resistance to c y c l i c mobility ( f o r 2.5%  i n 10 stress cycles) increased from 0.238 to 0.515 was  increased from 1.0  to 2.0.  ance to c y c l i c m o b i l i t y may  It  axial strain  when the Kc  ratio  Similar magnitude of increase i n r e s i s t -  be noted f o r s t r a i n l e v e l of 5%.  As  discussed i n Section 5^2.1, rapid accumulation of s t r a i n due to c y c l i c mobility i s possible only when transient state of zero e f f e c t i v e stress occurs during c y c l i c loading.  Therefore, the higher the s t a t i c shear,  the higher i s the c y c l i c stress amplitude required to cause t h i s condition to occur and hence a consequent Increase In resistance to cyclic mobility. For Ottawa sand with D  = 51.5%, a trend s i m i l a r to that for t a i l -  rc ings sand under low confining pressure may  be noted ( F i g .  5.25b).  However, unlike the t a i l i n g s sand, which developed c y c l i c mobility regardless of the ratio. low K c  r a t i o , Ottawa sand developed l i q u e f a c t i o n at low  This has also been discussed e a r l i e r i n Section 5.2.3.  For  this  r a t i o , although the i n i t i a l sample state i s i n d i l a t i v e region  In the compression deformation mode, i t i s contractive i n the  extension  deformation mode. Therefore, l i q u e f a c t i o n would be induced i n extension mode, i f the applied c y c l i c shear stress exceeds the steady state shear strength i n extension.  As the s t a t i c shear stress i n compression  increases, the c y c l i c stress amplitude required to cause l i q u e f a c t i o n i n extension mode also increases.  Thus the I n i t i a l increase i n resistance  to c y c l i c s t r a i n developments at low K c  r a t i o i n F i g . 5.25b i s due to a  189.  d i f f e r e n t s t r a i n development mechanisms. compression below which l i q u e f a c t i o n found to be around 1.10. c y c l i c m o b i l i t y , and  could be Induced i n extension  Beyond t h i s K c  hence the  l i m i t i n g value of Y.^ i n  The  was  r a t i o , a l l samples developed  resistance to c y c l i c mobility increased  with increasing s t a t i c shear s t r e s s , which i s s i m i l a r to the behaviour o t a i l i n g s sand that developed c y c l i c m o b i l i t y . It may  also be noted from the r e s u l t s shown i n F i g . 5.25  that  the  resistance to c y c l i c mobility i s influence by the s t r a i n l e v e l adopted. This i s more s i g n i f i c a n t i n the region of high s t a t i c shear. under high s t a t i c shear stress l e v e l may  develop the  Sample  lower l e v e l of  prescribed s t r a i n i n a s p e c i f i e d number of stress c y c l e , but may many more cycles to accumulate higher l e v e l of s t r a i n due  take  to the slow  down i n the rate of s t r a i n accumulation i n the case of non-stress reversal ( F i g s . 5.21  and  5.23).  Therefore, the resistance curves diverg  rapidly i n the region of non-stress For  reversal.  t a i l i n g s sand under high confining pressure, i . e . , i n i t i a l  stat  H i s to the right of (al ) ._ = const, l i n e for the D selected, lique° lc crit rc '  f a c t i o n can not be induced at low K c  r a t i o and  be developed, as discussed i n Section 5.1.4. mobility may  only c y c l i c mobility The  resistance to c y c l i c  be seen to increase with increasing K c  which i s similar to the behaviour of d i l a t i v e sands.  r a t i o ( F i g . 5.26a), From the trend of  the curve, this increase i n resistance to c y c l i c m o b i l i t y peaked at r a t i o of about 1.35.  At  this Kc  shear stresses approaches the f o r the Kc  considered.  values > 1.35  and  r a t i o , the sum  can  of s t a t i c and  Kc  cyclic  lower bound of steady state shear strength  Therefore, l i q u e f a c t i o n  s t a r t s to develop for  the resistance to l i q u e f a c t i o n decreases dramatic-  a l l y with increasing s t a t i c shear.  190. For Ottawa sand at low r e l a t i v e density, similar trend as that of the t a i l i n g s sand under high confining pressure may be noted ( F i g . 5.26b).  Relative values of the steady state shear strength and c y c l i c  shear stress applied were such that the i s o t r o p i c a l l y consolidated sample should not develop l i q u e f a c t i o n .  Therefore, the increase i n resistance  with i n i t i a l increase i n K c should be the r e s u l t of c y c l i c mobility developed.  It was, however, found that this increase i n resistance at  low Kc ratio was due to the occurrence of l i q u e f a c t i o n i n extension mode and not the development of c y c l i c m o b i l i t y .  Increasing the s t a t i c  shear i n compression increases the c y c l i c load amplitude required to exceed the steady state shear strength i n extension.  This trend  continues u n t i l the s t a t i c shear stress i s high enough to cause liquefaction i n compression mode. This l e v e l of s t a t i c shear was found to be corresponding  to Kc r a t i o of about 1.15. Beyond this s t a t i c shear  stress l e v e l , l i q u e f a c t i o n always developed In compression mode, and the resistance to l i q u e f a c t i o n decreased with increasing s t a t i c shear stress level. From the above r e s u l t s on both sands, i t may be concluded that the resistance to l i q u e f a c t i o n always decreases with increasing s t a t i c shear stress l e v e l . diagram.  This may be explained from the 3-D e f f e c t i v e stress state  As discussed i n Sections 5.1.1, occurrence of liquefaction i s  due to the e f f e c t i v e stress state of contractive sand reaching the CSR state and consequent i n i t i a t i o n of s t r a i n softening response leading to steady state deformation.  Therefore, the resistance to liquefaction, i s  nothing but the c y c l i c stress ratio required to move the sample state to the CSR state i n a fixed number of stress c y c l e s .  For easy v i s u a l i z a -  t i o n , this may be I l l u s t r a t e d by the e f f e c t i v e stress path plot of 3-D  191 • e f f e c t i v e stress state diagram at constant e c as shown i n F i g . Tt may  5.27.  be noted i n this figure that the stress space to be traversed  the l e f t tn order to reach the CSR  to  state i s less i n the case of sand with  higher s t a t i c shear stress (case 2) than the sand with lower s t a t i c shear stress (case 1) .  Therefore, the c y c l i c stress r a t i o or the number of  stress cycles required to move the sample state from the i n i t i a l state to the CSR  state i s less for higher Kc  faction i s l e s s . (Fig.  and hence the resistance to lique-  From the trend of the l i q u e f a c t i o n resistance curves  5.26), i t appears that the resistance to l i q u e f a c t i o n would be very  low when a sand sample i s i n i t i a l l y close to the CSR  state.  consolidated  to an i n i t i a l  state  Slight shear disturbance or even a pore pressure  increase could cause the sand to develop l i q u e f a c t i o n . This would correspond to the phenomenon of spontaneous l i q u e f a c t i o n , and w i l l be discussed  further in Section  5.6.  Comparing the stress states at CSR i t may  f o r Samples 1 and 2 i n F i g .  5.27,  further be noted that the potential to develop steady state  deformation i n Sample 2 i s much higher than that i n Sample 1.  Much  severe loss of resistance and larger deformation w i l l be developed In Sample 2, once l i q u e f a c t i o n i s i n i t i a t e d . s t r a i n development due  This may  to l i q u e f a c t i o n i n F i g .  5.13.  Behaviour of sand a n i s o t r o p i c a l l y consolidated not within the scope of this i n v e s t i g a t i o n .  also be seen from the  i n extension mode was  Chung (1984) found that  increasing the s t a t i c shear i n extension mode also causes decrease i n resistance to l i q u e f a c t i o n for Ottawa sand.  The  resistance curve i n F i g .  5.26b can thus be extended in the extension region.  Chung's findings are  consistent with those reported herein and could be explained framework of steady state concepts.  within  the  192.  1/2  F i g . 5.27  (oy+ oy)  Schematic i l l u s t r a t i o n showing the influence of s t a t i c shear stress on the resistance to l i q u e f a c t i o n under c y c l i c loading.  193. From che examination of results for both sands i n the contractive and d i l a t i v e regions, completely different trends i n l i q u e f a c t i o n and c y c l i c mobility response may be noted.  Increasing the s t a t i c shear  stress to the same l e v e l , e.g., Kc = 2.0, the resistance to c y c l i c mobility ( f o r 2.5% e ) increased from 0.238 to 0.515 f o r t a i l i n g s sand a and from 0.167 to 0.308 f o r Ottawa sand ( F i g . 5.25a,b), whereas the resistance to l i q u e f a c t i o n decreased from 0.176 to 0.074 for t a i l i n g s sand and from 0.114 to 0.056 f o r Ottawa sand ( F i g . 5.26a,b).  Therefore,  i t may be concluded that the resistance to s t r a i n development could decrease or increase depending on whether l i q u e f a c t i o n or c y c l i c mobility i s involved.  2  It Is often believed (Lee and Seed, 1967 , 1970) that s o i l  element i n slope i s more resistant to c y c l i c s t r a i n development than that under the l e v e l ground and suggestion i s made that c r i t i c a l i n i t i a l state would correspond to i s o t r o p i c consolidation, which represent an I n i t i a l l y zero s t a t i c shear.  This w i l l be true for s o i l elements which develop  c y c l i c mobility o n l y .  On the contrary, according to Castro and Poulos  (1977) and Casagrande (1975), the resistance to s t r a i n development for s o i l element i n the slope i s always less than that under the l e v e l ground and the suggestion  i s made that tests be performed on a n i s o t r o p i c a l l y  consolidated samples simulating appropriate i n i t i a l s t a t i c shear.  Again,  this w i l l be true for s o i l elements which develop l i q u e f a c t i o n only. Therefore, a clear understanding of the mechanism responsible f o r s t r a i n development i s necessary for a r a t i o n a l assessment of influence of c e r t a i n factors on the undrained c y c l i c loading response of sand. It i s also i n t e r e s t i n g to note that the Influences of s t a t i c shear stress on the undrained monotonic and c y c l i c loading behaviour are similar.  Increasing the s t a t i c shear stress l e v e l for fixed e  and a'  194. can transform a sand from s t r a i n hardening response to l i q u e f a c t i o n under monotonic loading conditions, and from c y c l i c mobility to l i q u e f a c t i o n under c y c l i c loading conditions.  The resistance to l i q u e f a c t i o n (stress  increment u n t i l peak i n monotonic loading) was found to decrease with Increasing s t a t i c shear stress l e v e l under both loading conditions. However, this s i m i l a r i t y can not be applied to monotonic s t r a i n hardening response and c y c l i c m o b i l i t y .  Under monotonic loading conditions, the  shear stress increment (Aa,/2al ) required to reach the PT state i s of d Jc a  concern, whereas the c y c l i c stress ( ^C y^°2c ^  re  iuired  to accumulate a  specified amount of s t r a i n i s of i n t e r e s t under c y c l i c loading conditions.  The former constitutes a strength c r i t e r i o n , while the l a t t e r i s  a deformation c r i t e r i o n .  The shear stress increment required to reach  the PT l i n e under monotonic loading was found to decrease with increasing s t a t i c shear which i s the reverse of the resistance to c y c l i c m o b i l i t y .  5.5  Prediction of Undrained C y c l i c Loading Behaviour  It was shown i n Section 4.4.2 that 3-D e f f e c t i v e stress state diagram gives a complete d e s c r i p t i o n of undrained behaviour under monotonic loading conditions, given the i n i t i a l state (e , a' , K ) of the c Jc c sand.  Under c y c l i c loading conditions, i t has further been shown i n  Sections 5.1 and 5.2 that the undrained behaviour depends i n addition on the amplitude of c y c l i c loads a p p l i e d .  The necessary c r i t e r i a for l i q u e -  f a c t i o n to occur under c y c l i c loading conditions are 1) the sand must have the p o t e n t i a l to develop steady state deformation, i . e . , the steady state can be achieved, and 2) the c y c l i c load amplitude applied must be large enough to cause the maximum shear stress ( s t a t i c + c y c l i c )  greater  195.  than i t s steady state shear strength and 3) s u f f i c i e n t number of load cycles are applied to move e f f e c t i v e stress state of sand to the line.  CSR  Otherwise, only c y c l i c mobility or very small deformation can be  developed. From the consolidation c h a r a c t e r i s t i c s of sand and the mentioned above, a flow chart may  criteria  be drawn to examine whether l i q u e f a c -  t i o n can be developed i n a sand with a given i n i t i a l state and loads.  This i s shown i n F i g .  applied  5.28.  In order to examine the f i r s t c r i t e r i o n , the i n i t i a l state of the sand Is located l n the 3-D  e f f e c t i v e stress state diagram.  This i n i t i a l  state of the sand i s obtained d i r e c t l y from the known void r a t i o e  and  the stress conditions i n the ground or from the known I n i t i a l void r a t i o  ej_ and the consolidation stress c o n d i t i o n s .  For sand elements with  i n i t i a l states below the c r i t i c a l consolidation stress (a! ) . ^ surface lc crit ( F i g . 4.31), i . e . , steady state can not he achieved, only c y c l i c mobility (together with s l i g h t s t r a i n softening for states s l i g h t l y below (al  ) . surface) can be induced, regardless of the c y c l i c lc crit  applied.  loads  For sand elements with i n i t i a l state on or above the  ( a l c ) c r ^ t s u r f a c e , i . e . , steady state can be achieved, p o t e n t i a l to develop l i q u e f a c t i o n always e x i s t s . a  For Ottawa sand with rounded p a r t i c l e s , the ( ] ^ c r i t *  S  difficult  At loose e., (al ) .^ i s extremely small (see Figure 4.13). J 1' lc crit In fact the s t r a i n softening and d i l a t i v e branch o f f does not appear even to obtain.  at  values as small as 0.13  kgf/cm  2  e., (al ) . i s exceptionally l a r g e . I' lc crit J O  (12.7  kPa).  And  at s l i g h t l y denser  However, the i n i t i a l r e l a t i v e »  density alone gives a good p r e d i c t i o n as to the p o t e n t i a l to develop liquefaction.  196.  3-D Effective Stress State Diagram  J  ±±  Steady State Exist?  T  s  >  S ? us  Cyclic Mobility  z  —  1  Yes Liquefaction  F i g . 5.28  Flow chart for assessing the p o t e n t i a l of 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 .  197. Once the p o t e n t i a l to develop l i q u e f a c t i o n i s determined and i s found to e x i s t , the second c r i t e r i o n has to be examined.  Liquefaction i  p o s s i b l e , regardless of the i n t e n s i t y of the c y c l i c loads applied, i f th i n i t i a l s t a t i c shear stress i s greater than the steady state shear strength of the s o i l element, which i s a unique function of i t s e c . This condition should always be avoided because combinations of pore pressure generated from c y c l i c loading and possible r e d i s t r i b u t i o n of pore pressure i n the surrounding s o i l elements during and a f t e r c y c l i c loading may cause l i q u e f a c t i o n and associated large deformations. However, i f the s t a t i c shear stress i s less than the steady state shear strength, l i q u e f a c t i o n i s possible only when the maximum shear stress ( s t a t i c + c y c l i c ) i s greater than the steady state shear strength. Otherwise, only c y c l i c mobility can be developed. It may be pointed out that very l i m i t e d amount of monotonic loading tests have to be c a r r i e d out i n order to e s t a b l i s h the 3-D e f f e c t i v e stress state diagram of sand.  The key aspects of the undrained c y c l i c  loading behaviour of a l l s o i l elements i n the earth structure can then b predicted from the 3-D e f f e c t i v e stress state diagram and c y c l i c load applied, i . e . , whether l i q u e f a c t i o n or c y c l i c mobility w i l l develop, thu enabling a f i r s t hand i d e n t i f i c a t i o n of the mechanism responsible f o r s t r a i n development under c y c l i c loading conditions. 5.6  Phenomenon of Spontaneous L i q u e f a c t i o n  As discussed i n the l a s t two chapters, l i q u e f a c t i o n i s the r e s u l t o occurrence of s t r a i n softening response leading to steady state deformat i o n when the e f f e c t i v e stress state of sands i s brought to the CRS state.  This s t r a i n softening response can occur i f p o t e n t i a l for l i q u e -  198.  faction exists and when the total shear stress acting on the s o i l element is greater than i t s steady state shear strength. occur on account of some shear disturbance  The change i n state can  applied to the s o i l element,  which can be either s t a t i c or c y c l i c i n nature.  If this disturbance i s  very small, the phenomenon Is called spontaneous l i q u e f a c t i o n . The  shear disturbance  under s t a t i c conditions can be caused by  increases In shear stress due to erosion of toe of slope or surcharge applied on slope.  It was shown by Eq. 4.6 i n Section 4.4.2 that for  t a i l i n g s sand the shear stress increment to reach the CSR state under monotonic loading conditions decreases as the s t a t i c shear stress acting on the sand increases.  When the i n i t i a l sample state i s close to the CSR  state, the shear stress increment required to I n i t i a t e l i q u e f a c t i o n i s very small.  This may also be seen from the r e l a t i o n s h i p of pore pressure  1  generated u n t i l the CSR state due to monotonic loading versus K c r a t i o in F i g s . 4.24 and 4.28 for both sands.  For sand consolidated  to even  higher Kc r a t i o , I.e., i n the region of contractive deformation ( F i g . 4.17), a s l i g h t increase i n shear stress can trigger s t r a i n softening response leading to steady state deformation.  Such a phenomenon was  i l l u s t r a t e d by the example i n F i g . 4.19. By an Increase In shear stress less than 8% of the s t a t i c shear s t r e s s , catastrophic f a i l u r e was Induced. From the trend of resistance to l i q u e f a c t i o n versus K c r a t i o curves shown i n F i g . 5.26, i t appears that the resistance to l i q u e f a c t i o n i s very small when the sand i s consolidated state.  to a state close to the CSR  For Ottawa sand consolidated to K c r a t i o of 2.0, the resistance  to l i q u e f a c t i o n i s about 0.056.  The shear stress disturbance  magnitude corresponds to earthquake with a  of this  of 0.05g according  to the  199. s i m p l i f i e d procedure proposed by Seed and I d r i s s (1971).  Such a small  change i n shear stress required to cause i n s t a b i l i t y i s indeed a case of spontaneous l i q u e f a c t i o n .  For K c  r a t i o higher than 2.0, the shear  disturbance required to cause l i q u e f a c t i o n i s even lower.  For t a i l i n g s  sand, however, due to r e l a t i v e l y high confining pressure Involved, the c y c l i c stress r a t i o under this confining pressure corresponds to a r e l a t i v e l y strong earthquake even though the c y c l i c stress r a t i o Is very low. Besides the shear stress disturbance discussed above, the change In sample state can also occur due to r i s e i n pore pressure.  This r i s e of  pore pressure could be the result of f l u c t u a t i o n of ground water l e v e l or r e d i s t r i b u t i o n of excess pore pressure during or a f t e r earthquake from the surrounding s o i l elements.  shaking  To i l l u s t r a t e this mechanism of  i n i t i a t i o n of l i q u e f a c t i o n , s p e c i a l tests were performed on both sands. An i n i t i a l l y loose sample was consolidated a n i s o t r o p i c a l l y to K c of 2.0, and a i  =2.0  kgf/cm  (980 kPa) f o r t a i l i n g s sand.  2  ratio  (196 kPa) f o r Ottawa sand and 10.0 kgf/cm Back pressure was  then increased slowly  while maintaining the s t a t i c shear stress constant.  By doing so the  e f f e c t i v e stress state of sand was moved h o r i z o n t a l l y toward the CSR line.  After the e f f e c t i v e stress state reached the state corresponding  to the CSR s t a t e , the drainage l i n e was closed. pore pressure was  observed which was  A s l i g h t Increase i n  followed by a catastrophic f a i l u r e  i n a manner s i m i l a r to that observed during l i q u e f a c t i o n . results for both sands are shown i n F i g s . 5.29  and  Typical  5.30.  Thus spontaneous l i q u e f a c t i o n w i l l be triggered as soon as the sample state reaches the CSR  state under undrained conditions due to a  very small disturbance at which s t r a i n softening response leading to steady state deformation i s i n i t i a t e d .  This phenomenon can, however,  2  200.  F i g . 5.29  Spontaneous l i q u e f a c t i o n induced by pore pressure increase in i n i t i a l l y loose Ottawa sand.  201 .  2.0  4.0  6.0  8.0  to/  1/2 (oy+oy) F i g . 5.30  10.0  12.0  (kgf/cm ) 2  Spontaneous liquefaction induced by pore pressure increase in contractive t a i l i n g s sand.  202.  occur only i f the sand i s subjected to s t a t i c shear stress greater than i t s steady state shear strength.  For t a i l i n g s sand, this s i t u a t i o n can  e x i s t only when an i n i t i a l l y loose sample i s consolidated to high confining pressure and high K c r a t i o .  This i s shown i n F i g .  5.31.  It may  be seen that for i n i t i a l l y loose sample with K c = 2.0 the confining pressure o l ^ has to be greater than 7.0 kgf/cm  2  (686 kPa) i n order to  have s t a t i c shear stress greater than i t s steady state shear strength. For  sand with K c = 1.5, the s t a t i c shear stress i s always less than i t s  steady state shear strength for the range of consolidation stress considered.  Therefore, under this K c (= 1.5) r a t i o , sand i s always  safe against such kind of f a i l u r e .  Due to very high confining pressure  required to have the condition discussed above to e x i s t f o r K c = 2.0, a very large pore pressure Increase Is required In order to bring about such a f a i l u r e .  In the example shown i n F i g . 5.30, an increase i n pore  pressure by about 3.0 kgf/cm  2  (294 kPa), which corresponds to a r i s e of  30 m i n water head, i s necessary to t r i g g e r spontaneous l i q u e f a c t i o n . Therefore, i t appears there i s rare p o s s i b i l i t y f o r such f a i l u r e to be induced i n t a i l i n g s sand unless the sand i s consolidated to K c  ratio  close to or greater than the CSR. Rounded Ottawa sand, however, behaves quite d i f f e r e n t l y compared to the angular t a i l i n g s sand.  For i n i t i a l l y loose sample under K c  ratio  of 1.5 and 2.0, as shown i n F i g . 5.32, the s t a t i c shear stress i s higher than i t s steady state shear strength under low confining pressure. The r a t i o of s t a t i c shear stress to the steady state shear strength decreases with increasing confining pressure. The l e v e l of confining pressure below which the s t a t i c shear stress i s greater than i t s steady state shear strength depends on the K c r a t i o of the sand.  For i n i t i a l l y  0.95Consolidation Curve (ej =1.0}  Tailings Sand  Static Shear Sfress (Kc= 1.5, ej =100) Steady  State Shear  Strength  Static Shear Stress (Kc = 2 0, e, = 1.00, 0.70- 100  0 1  0.2  0.5  Static Fig. 5.31  Shear  1.0  Stress  2.0  5.0  10 0  20.0  T or Steady Stare Shear Strength S s  U 3  50.0  100.0  (Kgf/cm )  Comparison of r e l a t i v e v a l u e s of s t a t i c shear s t r e s s and steady s t a t e shear f o r t a i l i n g s sand at two K ratios.  2  strength  0  0.80Ottawa  10  Sand  20  0.75 Consolidation C u r v e (e; = 0.725)  30  0.70-  40  o <D  Static  Shear  Stress  ( K c = l.5, ej = 0.725) o  Steady  0.65  "a  Stale Shear  50  Strength  Stotic Shear Stress (K c =2.0, e, - 0.725)  D  o  £  60  0.60  70  > 80 0.55 90  0.50 0.1  100 0.2  0.5  Static F i g . 5.32  Shear  1.0  Stress  2.0  T  s  5.0  10.0  20.0  or Steady State Shear Strength  50.0  S  U 3  100.0  (kgf/cm )  Comparison of r e l a t i v e v a l u e s of s t a t i c shear s t r e s s and steady s t a t e shear f o r Ottawa sand a t two K ratios. c  2  strength o  205. loose sand, i t i s about 5.0 and 20.0 kgf/cm r a t i o of 1.5 and 2.0  respectively.  2  (490 and 1960 kPa) f o r K c  Therefore, sand with rounded  p a r t i c l e s i s more susceptable to spontaneous l i q u e f a c t i o n .  Relatively  small pore pressure increase has to occur i n order to reach the CSR and consequently trigger l i q u e f a c t i o n .  state  206.  CHAPTER 6 CONCLUSIONS  Undrained monotonic and c y c l i c loading behaviour of a saturated angular and a rounded sand has been studied under t r i a x i a l conditions over a confining pressure ranging up to 25.0 kgf/cm i s o t r o p i c and anisotropic consolidation h i s t o r i e s .  2  (2450 kPa) and both The fange of beha-  viour under monotonic loading spanned between s t r a i n hardening at one end to various degrees of s t r a i n softening (termed l i q u e f a c t i o n or l i m i t e d liquefaction) at the other.  S i m i l a r l y , the range of behaviour respons-  i b l e for development of s t r a i n under c y c l i c loading consisted of liquefaction or c y c l i c mobility or a combination of both.  C y c l i c mobility  refers to the development of s t r a i n during c y c l i c loading which i s not due to the occurrence of s t r a i n softening response.  These d e f i n i t i o n s of  l i q u e f a c t i o n and c y c l i c mobility now enjoy a general acceptance among researchers.  Based on test results on angular sand, the following  conclusions may be drawn. 1)  Under monotonic loading, the s t r a i n softening response i s i n i t i -  ated at a c r i t i c a l value of e f f e c t i v e . s t r e s s r a t i o (CSR), regardless of the r e l a t i v e density and consolidation stress conditions of the sand. 2)  The termination of s t r a i n softening response, which i s charac-  terized by the s t a r t of d i l a t i o n (PT S t a t e ) , also occurs at a unique value of e f f e c t i v e stress r a t i o , regardless of the r e l a t i v e density and consolidation stress conditions of the sand.  When s t r a i n hardening  response develops, the start of d i l a t i o n , characterized by a decrease i n pore pressure a f t e r a p o s i t i v e maximum value, also occurs at the same e f f e c t i v e stress r a t i o as the PT state of s t r a i n softening response.  207. 3)  Under extension loading, the CSR i s less than that i n compres-  s i o n , but the e f f e c t i v e stress ratios at PT state i n compression and extension are the same. 4)  Under monotonic loading, the stress conditions at PT state f o r  s t r a i n hardening response form a series of l i n e s i n void r a t i o - e f f e c t i v e confining pressure p l o t .  These l i n e s are function of i n i t i a l void r a t i o  only, regardless of the consolidation stress conditions.  With  Increasing  consolidation s t r e s s e s , these l i n e s f o r various i n i t i a l void r a t i o merge into a unique steady state l i n e representing s t r a i n softening response, characterized as l i m i t e d or true l i q u e f a c t i o n .  This implies that the  concept of unique steady state l i n e can be used even when the sand develops s t r a i n softening response with s i g n i f i c a n t s t r a i n p o t e n t i a l (greater than about 2% f o r the sand tested) and i s not necessarily r e s t r i c t e d to unlimited s t r a i n c h a r a c t e r i s t i c s of true l i q u e f a c t i o n . 5)  From the consolidation c h a r a c t e r i s t i c s and stress conditions at  PT s t a t e , a r e l a t i o n s h i p between void r a t i o  e^  and c r i t i c a l  consolida-  tion stress (al ) . emerges. Sand at a void r a t i o e under consolidaa lc c r i t c tion stress al > (al ) . f o r e w i l l develop l i q u e f a c t i o n , regardless lc lc crit c of the i n d i v i d u a l magnitudes of K and £  F  o  r  °i  a  c  ^ ^ lc^crit'  o  s t r a i n hardening or s l i g h t s t r a i n softening response w i l l develop. ( l ) a  c  C T  l  t  n  ^ ec -  l i n e thus provides a quantitative d i v i s i o n of i n i t i a l states  i n t o regions of l i q u e f a c t i o n and s t r a i n hardening response on undrained loading. 6)  A 3-D e f f e c t i v e stress state diagram f o r the sand characterizes  comprehensively the anticipated monotonic loading response of sand from the knowledge of i t s end of consolidation state e , a' and K . ° c 3c c a  This  state diagram i n e c > l/2(cj+a^), l/2(aj-a^) space features a ( [ c ) c r £ t  208. surface which separates end of consolidation states of sand into regions of l i q u e f a c t i o n and s t r a i n hardening response or s l i g h t s t r a i n softening response. for  A knowledge of the complete i n i t i a l state of sand i s necessary  assessment of the anticipated monotonic loading response.  This  response can not be predicted by s p e c i f y i n g r e l a t i v e density alone or even the combination of r e l a t i v e density and confining pressure.  The 3-D  e f f e c t i v e stress state diagram also o f f e r s a r a t i o n a l explanation as to the influence of r e l a t i v e density, confining pressure and s t a t i c shear stress on the monotonic loading behaviour. 7)  Under c y c l i c loading, the s t r a i n development could be due to  l i q u e f a c t i o n or c y c l i c mobility or the combination of both.  If l i q u e f a c -  tion develops, the CSR, e f f e c t i v e stress r a t i o at PT state and steady state l i n e are the same as those observed under monotonic loading. If c y c l i c mobility develops, the e f f e c t i v e stress r a t i o at PT state i s also the same as that observed under monotonic loading.  Therefore, the stress  conditions which characterize the key features of s t r a i n softening and s t r a i n hardening response are not influenced by the type of load (monotonic or c y c l i c ) applied, and thus the 3-D e f f e c t i v e stress state diagram provides a l i n k between monotonic and c y c l i c loading behaviour. 8)  The 3-D e f f e c t i v e stress state diagram developed for monotonic  loading can be used to develop the c r i t e r i a f o r the occurrence of liquef a c t i o n and c y c l i c m o b i l i t y . f a c t i o n are: (a! ) . lc c r i t  The c r i t e r i a f o r the occurrence of l i q u e -  ( 1 ) the i n i t i a l sand state must l i e on or above the  surface, (2) the maximum shear stress ( s t a t i c + c y c l i c ) i s '  greater than the steady state shear strength, and ( 3 ) s u f f i c i e n t number of load cycles are applied to move the e f f e c t i v e stress state of sand to the CSR l i n e .  Otherwise, only cycTic moblity or very small deformation  209. can be developed. 9)  The  influences of r e l a t i v e density and confining pressure on  the  c y c l i c loading behaviour are s i m i l a r to those on the monotonic loading behaviour.  However, the influence of s t a t i c shear stress on c y c l i c load-  ing behavior could be quite d i f f e r e n t depending on whether l i q u e f a c t i o n or c y c l i c mobility i s developed.  If the sand develops l i q u e f a c t i o n , an  increase i n s t a t i c shear stress always r e s u l t s i n a decrease i n r e s i s t ance to l i q u e f a c t i o n . On the other hand, i f i t develops c y c l i c m o b i l i t y , increasing s t a t i c shear stress always r e s u l t s i n an increase i n r e s i s t ance to c y c l i c m o b i l i t y .  These conclusions  are i n agreement with those  suggested by Castro and Seed i f a proper recognition of the mechanism of s t r a i n development under c y c l i c loading i s made. The conclusions angular sand.  drawn above are based on the r e s u l t s of tests on  These conclusions  are also true for rounded sand.  However, for the range of consolidation stress considered herein range of  al Jc  (the  considered i s larger than what would be encountered In  most p r a c t i c a l s i t u a t i o n s ) , the i n i t i a l r e l a t i v e density alone provides a good single parameter for characterizing this i n i t i a l state of rounded sand.  For i n i t i a l l y loose s t a t e s , the sand always develops l i q u e f a c t i o n ,  regardless of the i n i t i a l stress conditions.  The response, however,  changes to s t r a i n hardening or s l i g h t l y s t r a i n softening i f i n i t i a l r e l a tive density exceeds a certain minimum value (about 40% tested).  for the sand  It appears that the l i q u e f a c t i o n response i n rounded sand i s  related to an i n i t i a l loose s t r u c t u r e , which i s not altered even a f t e r the application of large confining pressure.  210.  REFERENCES  Bishop, A.V., Webb, D. and Skinner, A.E. (1965). " T r i a x i a l Tests on S o i l s at Elevated C e l l Pressure," Proc. 6th ICSMFE, Montreal, V o l . 1, pp. 170-174. Bjerrum, L., Kringstad, S. and Kummeneje, 0. (1961). "The Shear Strength of Fine Sand," Proc. 5th ICSMFE, P a r i s , V o l . 1, pp. 29-37. Casagrande, A. (1936). "Characteristics of Cohesionless Soils Affecting the S t a b i l i t y of Slopes and Earth F i l l s , " J o u r , of the Boston Society of C i v i l Engineers, Jan. 1936. Casagrande, A. (1975). "Liquefaction and C y c l i c Deformation of Sands, A C r i t i c a l Review," Proc. 5th Pan American Conf. on S o i l Mech. and Found. Engng., Buenos A i r e s , V o l . 5, pp. 79-133. Castro, G. (1969). "Liquefaction of Sands," Ph.D. Thesis, Harvard S o i l Mech. Series, No. 81, Harvard U n i v e r s i t y . Castro, G. (1975). "Liquefaction and C y c l i c Mobility of Saturated Sands," Jour, of the Geot. Engng. D i v . , ASCE, V o l . 101, No. GT6, Proc. Paper 11388, pp. 551-569. Castro, G. and Poulos, S.J. (1977). "Factors Affecting Liquefaction and C y c l i c Mobility," Jour, of the Geot. Engng. Div., ASCE, V o l . 103, No. GT6, Proc. Paper 12994, pp. 501-516. Castro, G., Poulos, S.J., France, J.W. and Enos, J . L . (1982). "Liquefaction Induced by Cyclic Loading," Report Submitted to National Science Foundation, March, 1982. Chern, J.C. (1981). "Effect of S t a t i c Shear on Resistance to Liquefaction," M.A.Sc. Thesis, The University of B r i t i s h Columbia, Vancouver, Canada. DeAlba, P., Seed, H.B. and Chan, C K . (1976). "Sand Liquefaction i n Large-Scale Simple Shear Tests," Jour, of the Geot. Engng. Div., ASCE, V o l . 102, No. GT9, Proc. Paper 12403, pp. 909-927. Dobry, R. and Alvarez, L . (1967). "Seismic Failures of Chilean T a i l i n g s Dams," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 93, No. SM6, Proc. Paper 5582, pp. 237-260. Finn, W.D.L. (1981). "Liquefaction P o t e n t i a l : Developments Since 1976," I n t . Conf. on Recent Advances In Geot. E a r t h . Engng. and S o i l Dynamics, St. Louis, M0, pp. 655-681. Finn, W.D.L. and Byrne, P.M. (1976). "Liquefaction Potential of Mine Tailings Dams," Proc. 12th I n t . Conf. on Large Dams, Mexico C i t y , V o l . 1, pp. 153-177.  211 . Finn, W.D.L., Pickering, D.J. and Bransby, P.L. (1971). "Sand Liquefaction i n T r i a x i a l and Simple Shear Tests," Jour, of the Soil Mech. and Found. Div., ASCE, V o l . 97, No. SM4, Proc. Paper 2039, pp. 639-659. Finn, W.D.L. and Vaid, Y.P. (1977). "Liquefaction Potential from Drained Constant Volume Cyclic Simple Shear Tests," Proc. 6th World Conf. on Earth. Engng., New Delhi, Session 6, pp. 7-12. Green, G.E. (1969). "Strength and Compressibility of Granular Materials Under Generalized Strain Conditions," Ph.D. Thesis, University of London, Imperial College of Science and Technology. Gueze, E . (1948). " C r i t i c a l Density of Some Dutch Sands," P r o c , 2nd ICSMFE, Rotterdam, V o l . 3, pp. 125-130. Horn, H.M. and Deere, D.U. (1962). " F r i c t i o n a l Characteristics of Minerals," Geotechnique, V o l . 12, No. 4, pp. 319-335. Ishihara, K., Tatsuoka, F. and Yasuda, S. (1975). "Undrained Deformation and Liquefaction of Sand Under Cyclic Stresses," S o i l s and Foundations, V o l . 15, No. 1, pp. 29-44. Klohn, E.J., Maartman, C.H., Lo, R.C.Y. and Finn, W.D.L. (1978). "Simplified Seismic Analysis for T a i l i n g s Dams," P r o c , ASCE Specialty Conf. on Earth. Engng. and S o i l Dynamics, Pasadena, CA., pp. 540-556. Koppejan, A.W., Wamelen, B.M. and Weinberg, L . J . (1948). "Coastal Flow Slides i n the Dutch Province of Zeeland," P r o c , 2nd ICSMFE, Rotterdam, V o l . 5, pp. 89-96. Lee, I.K. (1966). "Stress-Dilatancy Performance of Feldspar," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 92, No. SM2, Proc. Paper 4734, pp. 79-108. Lee, K.L. (1978). "End Restraint E f f e c t s on Undrained Static T r i a x i a l Strength of Sand," Jour, of the Geot. Engng. Div., ASCE, V o l . 104, No. GT6, Proc. Paper 13838, pp. 687-704. 1  Lee, K.L. and Seed, H.B. (1967 ). " C y c l i c Stress Conditions Causing Liquefaction of Sand," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 93, No. SMI, Proc. Paper 5058, pp. 47-70. 2  Lee, K.L. and Seed, H.B. (1967 ). "Dynamic Strength of A n i s o t r o p i c a l l y Consolidated Sand," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 93, No. SM5, Proc. Paper 5451, pp. 169-190. Lee, K.L. and Seed, H.B. (1970). ' "Undrained Strength of A n i s o t r o p i c a l l y Consolidated Sand," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 96, No. SM2, Proc. Paper 7136, pp. 411-428. Lee, K.L. and Vernese, F . J . (1978). "End Restraint Effects on Cyclic T r i a x i a l Strength of Sand," Jour, of the Geot. Engng. Div., ASCE, V o l . 104, No. GT6, P r o c Paper 13839, pp. 705-719.  212. Lindenberg, J . and Koning, H.L. (1981). " C r i t i c a l Density of Sand," Geotechnique, V o l . 31, No. 2, pp. 231-245. Luong, M.P. (1980). "Stress-Strain Aspects of Cohesionless Soils Under C y c l i c and Transient Loading," I n t . Symp., Swansea, U.K. Poulos, S.J. (1971). "The Stress-Strain Curves of S o i l s , " Geotechnical Engineers Inc., Winchester, Mass., pp. 1-80. Poulos, S.J. (1981). "The Steady State of Deformation," Jour, of the Geot. Engng. Div., ASCE, V o l . 107, No. GT5, Proc. Paper 16241, pp. 553562. Rowe, P.W. and Barden, L . (1964). "Importance of Free Ends i n T r i a x i a l Testing," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 90, No. SMI, Proc. Paper 3753, pp. 1-27. Sangrey, D.A. Castro, G., Poulos, S.J. and France, J.W. (1978). "Cyclic Loadings of Sands, S i l t and Clays," P r o c , ASCE Specialty Conf. on Earthquake Engng. and S o i l Dynamics, Pasadena, CA., V o l . 2, pp. 836-851. Seed, H.B. (1979). " S o i l Liquefaction and Cyclic Mobility Evaluation for Level Ground During Earthquakes," Jour, of the Geot. Engng. Div., ASCE, V o l . 105, No. GT2, Proc. Paper 14380, pp. 201-255. Seed, H.B. (1981). "Earthquake-Resistant Design of Earth Dams," I n t . Conf. on Recent Advances i n Geot. Earthquake Engng. and S o i l Dynamics, St. Louis, MO, V o l . 3, pp. 1157-1173. Seed, H.B. and I d r i s s , I.M-. (1971). "Simplified Procedure for Evaluating S o i l Liquefaction Potential," Jour, of the S o i l Mech. and Found. Div., ASCE, V o l . 97, No. SM9, Proc. Paper 8371, pp. 1249-1273. Seed, H.B. and Lee, K.L. (1966). "Liquefaction of Saturated Sands During C y c l i c Loading," Jour, of the Sol Mech. and Found Div., ASCE, Vol 92, No. SM6, P r o c Paper 4972, pp. 105-134. Seed, H.B. and Lee, K.L. (1969). "Pore Water Pressure i n Earth Slopes Under Seismic Loading Conditions," Proc. 4th World Conf. on Earth. Engng., Santiago, V o l . 3, A-5, pp. 1-11. Seed, H.B., Lee, K.L., I d r i s s , I.M. and Makdisi, F . l . (1975). "The Slides i n the San Fernando Dams During the Earthquake of February 9, 1971," Jour, of the Geot. Engng. Div., ASCE, V o l . 101, No. GT7, Proc. Paper 11449, pp. 651-688. Seed, H.B., Pyke, R. and Martin, G.R. (1975). "Analysis of the Effect of M u l t i - D i r e c t i o n a l Shaking on the Liquefaction C h a r a c t e r i s t i c s of Sands," Report No. EERC 75-41, Earthquake Engineering Research Center, University of C a l i f o r n i a , Berkeley, C a l i f o r n i a . 1  Vaid, Y.P. and Chern, J.C. (1983 ). "Effect of S t a t i c Shear on Resistance to Liquefaction," Soils and Foundations, V o l . 23, No. 1, pp. 47-60.  • 213. 2  Vaid, Y.P. and Chern, J.C. (1983 ). "Mechanism of Deformation During Cyclic Undrained Loading of Saturated Sands," I n t . Jour, of S o i l Dynamics and Earthquake Engng., V o l . 2, No. 3, pp. 171-177. Vaid, Y.P., Chern, J.C. and Tumi, H. (1983). "Effect of Confining Pressure and P a r t i c l e Angularity on Resistance to Liquefaction," Proc. 4th Canadian Conf. on Earthquake Engng., Vancouver, pp. 341-351. Vaid, Y.P. and Finn, W.D.L. (1979). "Effect of Static Shear on Liquefaction Potential," Jour, of the Geot. Engng. Div., ASCE, V o l . 105, GT10, Proc. Paper 14909, pp. 1233-1246. Yoshimi, Y. and Oh-Oka, H. (1975). "Influence of Degree of Shear Stress Reversal on the Liquefaction Potential of Saturated Sand," S o i l s and Foundations, V o l . 15, No. 3, pp. 27-40.  

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