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The effect of particle gradation on the undrained behaviour of sand Fisher, Jennifer M. 1987

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THE EFFECT OF PARTICLE GRADATION ON THE UNDRAINED BEHAVIOUR OF SAND by JENNIFER M. FISHER B.E.(Civil)(hons),  Canterbury  U n i v e r s i t y , N.Z. 1983  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING  We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER 1987 © JENNIFER M. FISHER, 1987  4  In  presenting  degree at  this  the  thesis in  University of  partial  fulfilment  of  of  department publication  this or of  thesis for by  his  or  her  representatives.  Engineering  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  &  October  for  an advanced  Library shall make  it  agree that permission for extensive  It  this thesis for financial gain shall not  Civil  that the  scholarly purposes may be  permission.  Department of  requirements  British Columbia, I agree  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  ABSTRACT  The  e f f e c t of p a r t i c l e gradation  on the undrained monotonic  and c y c l i c  l o a d i n g behaviour i s presented.  gradations  of E a r l s Creek sand w i t h v a r y i n g c o e f f i c i e n t s of  u n i f o r m i t y and  line  i d e n t i c a l mineralogy and D ^ Q were t e s t e d ,  using the t r i a x i a l t e s t . Improved sample techniques  Straight  preparation  were used to ensure sample u n i f o r m i t y . The  i n d i c a t e s t h a t , under monotonic l o a d i n g , the shear-induced c o m p r e s s i b i l i t i e s due  data  relative  to a v a r i a t i o n i n the  c o e f f i c i e n t of u n i f o r m i t y are a f u n c t i o n of the type of l o a d i n g . C y c l i c l o a d i n g t e s t s on  isotropically  consolidated  samples showed that the e f f e c t of p a r t i c l e g r a d a t i o n on the r e l a t i v e d e n s i t y . At low than about 45%),  depends  r e l a t i v e d e n s i t i e s , (less  the w e l l graded sand had  greater  cyclic  s t r e n g t h than the uniform  sand. At high r e l a t i v e d e n s i t i e s ,  (greater than about 60%),  t h i s t r e n d was  i i  reversed.  TABLE OF CONTENTS ABSTRACT  ii  TABLE OF CONTENTS  i i i  LIST OF TABLES LIST OF FIGURES  iv .  NOTATION  v vii  ACKNOWLEDGEMENTS 1. INTRODUCTION  ix 1  2. REVIEW OF PREVIOUS INVESTIGATIONS 5 2.1. GENERAL ASPECTS OF THE UNDRAINED BEHAVIOUR OF SANDS 5 2.2. MONOTONIC LOADING BEHAVIOUR 5 2.3. CYCLIC LOADING BEHAVIOUR 10 2.4. RELATIONSHIP BETWEEN MONOTONIC AND CYCLIC LOADING 16 2.5. THE EFFECT OF PARTICLE GRADATION 17 3..EXPERIMENTATION 3.1. TESTING PROGRAM 3.2. TESTING APPARATUS 3.3. MATERIAL TESTED 3.4. SAMPLE PREPARATION AND TESTING TECHNIQUES  21 21 22 24 28  4. TEST RESULTS 4.1. MONOTONIC LOADING BEHAVIOUR 4.1.1. Monotonic Compression R e s u l t s 4.1.2. Monotonic Extension R e s u l t s 4.1.3. Review of Monotonic Test R e s u l t s .... 4.2. CYCLIC LOADING BEHAVIOUR  38 38 38 52 58 62  5. CONCLUSION  72  REFERENCES  75  LIST OF 3.1  Material properties  TABLES 27  iv  LIST OF FIGURES 2.1  C h a r a c t e r i s t i c behaviour of s a t u r a t e d sand monotonic l o a d i n g  2.2  L i q u e f a c t i o n due t o c y c l i c  2.3  L i m i t e d l i q u e f a c t i o n due to c y c l i c l o a d i n g  13  2.4  C y c l i c m o b i l i t y due to c y c l i c  loading  14  3.1  Schematic  l a y o u t of t e s t i n g apparatus  23  3.2  G r a i n s i z e d i s t r i b u t i o n curves  26  3.3  R e l a t i o n s h i p between v o l u m e t r i c s t r a i n and mean normal s t r e s s d u r i n g c o n s o l i d a t i o n  29  3.4A  Sample P r e p a r a t i o n by The S l u r r y Method  31  3.4B  Sample P r e p a r a t i o n by the S l u r r y Method ..  32  4.1  Undrained monotonic Gradation 3  40  4.2  Undrained monotonic compression r e s u l t s f o r 50 kPa i n i t i a l confining stress  41  4.3  Undrained monotonic compression r e s u l t s f o r 200 kPa i n i t i a l c o n f i n i n g s t r e s s  42  Undrained monotonic compression r e s u l t s f o r 500 kPa i n i t i a l c o n f i n i n g s t r e s s  43  4.4  under  6  loading  12  compression r e s u l t s f o r  4.5  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r 50 kPa i n i t i a l c o n f i n i n g s t r e s s .  4.6  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r 200 kPa i n i t i a l c o n f i n i n g s t r e s s .  ..47  4.7  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r 500 kPa i n i t i a l c o n f i n i n g s t r e s s .  ..48  4.8  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r Gradation 1  49  4.9  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r Gradation 2  50  v  ...45  4.10  M o d i f i e d Mohr diagram f o r undrained monotonic compression f o r Gradation 3  4.11  M o d i f i e d Mohr diagram showing the phase transformation state  53  4.12  Undrained monotonic extension i n i t i a l confining stress  54  4.13  M o d i f i e d Mohr diagram f o r undrained monotonic extension f o r 200 kPa i n i t i a l c o n f i n i n g s t r e s s  4.14  M o d i f i e d Mohr diagram f o r undrained monotonic extension f o r Gradation 1 at 200 kPa c o n f i n i n g s t r e s s . 59  4.15  R e l a t i o n s h i p between i n i t i a l r e l a t i v e d e n s i t y , r e l a t i v e d e n s i t y a f t e r c o n s o l i d a t i o n and the s t r e n g t h a t phase t r a n s f o r m a t i o n  60  M o d i f i e d Mohr diagram f o r monotonic extension and compression l o a d i n g f o r 200 kPa i n i t i a l c o n f i n i n g stress  61  R e l a t i o n s h i p between r e l a t i v e d e n s i t y and no. of c y c l e s to l i q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c s t r e s s r a t i o s f o r Gradation 1  63  R e l a t i o n s h i p between r e l a t i v e d e n s i t y and no. of c y c l e s to l i q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c s t r e s s r a t i o s f o r Gradation 2  64  R e l a t i o n s h i p between r e l a t i v e d e n s i t y and no. of c y c l e s to l i q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c s t r e s s r a t i o s f o r Gradation 3  65  L i q u e f a c t i o n r e s i s t a n c e curves f o r N=10  68  4.16  4.17  4.18  4.19  4.20  vi  ....51  r e s u l t s f o r 200 kPa  55  NOTATION  B  Skempton's pore pressure parameter.  CSR  C r i t i c a l e f f e c t i v e stress r a t i o .  C  u  Coefficient of uniformity.  D  r  Relative  density.  D-  Relative  density after  Relative  density prior to consolidation.  DgQ  consolidation.  Mean p a r t i c l e diameter or e f f e c t i v e grain  size  of s o i l sample; 50 % by dry weight of sample i s smaller than t h i s grain e  Void r a t i o .  ec  Void r a t i o after  min  e„max„  size,  consolidation,  Minimum and maximum void ratios as determined,  N  Number of loading  cycles.  p'  1 / 2 ( 0 , ' + <x' ).  PT  Phase transformation.  s  l/2(a,' + a ' ) .  t  l/2(a,' - a ' ) .  u  Porewater pressure.  Au  Excess porewater pressure.  ea , ev 0'  Axial and volumetric s t r a i n , Angle of internal  0cv  Constant volume f r i c t i o n angle,  3  3  3  friction.  Deviator stress. o-£ y C  Cyclic deviator  stress. VI 1  0 1 a  3  '  o- ' 3c  Major and minor e f f e c t i v e p r i n c i p a l  E f f e c t i v e c o n s o l i d a t i o n p r e s s u r e i n the t r i a x i a l test.  r T  c y  /a, '  stresses.  Cyclic  shear s t r e s s  Cyclic  stress  ratio.  vi i i  =  ^  d c y  /2.  ACKNOWLEDGEMENTS  The  author  wishes t o express  her thanks t o her s u p e r v i s o r ,  Dr Y.P. V a i d , f o r h i s guidance d u r i n g t h i s  The  author  research.  a l s o wishes t o thank Dr D. Negussey f o r h i s  advice and support  throughout the course  of t h i s  research.  For a s s i s t a n c e i n the development of the equipment, Mr Fred Zurkirchen  The  i s thanked.  f i n a n c i a l support  of the J.R. Templin T r a v e l l i n g  Fund,  The N a t i o n a l Science and E n g i n e e r i n g Research C o u n c i l of Canada, and The U n i v e r s i t y of B r i t i s h Columbia acknowledged.  ix  i s gratefully  1. INTRODUCTION  During r a p i d s h e a r i n g , the development of l a r g e  deformations  in s a t u r a t e d c o h e s i o n l e s s s o i l s may occur. These deformations may be the r e s u l t of the l o s s of shear r e s i s t a n c e or p r o g r e s s i v e s t i f f n e s s degradation d u r i n g cyclic  loading, called  respectively.  l i q u e f a c t i o n and c y c l i c  (Castro 1969 & 1975, Seed 1979).  mobility Rapid  shearing may be the consequence of c y c l i c earthquake  loading  or monotonic i n c r e a s e s i n shear s t r e s s . The r a p i d nature of the l o a d i n g l i m i t s pore p r e s s u r e d i s s i p a t i o n , hence the behaviour i s c o n s i d e r e d undrained.  Liquefaction contractive  i s a s t r a i n s o f t e n i n g response, i n which h i g h l y (loose) sand l o s e s a l a r g e percentage of i t s  shear r e s i s t a n c e and deforms c o n t i n u o u s l y i n a s t a t e of constant normal e f f e c t i v e and shear s t r e s s e s , constant volume and constant v e l o c i t y termed (Casagrande  steady  state.  1976, C a s t r o 1969 & 1975, Seed 1979, Poulos  1981). E q u i l i b r i u m i s r e s t o r e d o n l y a f t e r enormous displacements or s e t t l e m e n t . ( N a t i o n a l Research C o u n c i l 1985).  With c y c l i c m o b i l i t y , the deformation i s accumulated cyclic  l o a d i n g momentarily  when  reduces the e f f e c t i v e s t r e s s to 1  2 zero at the i n s t a n t when the c y c l i c  shear s t r e s s  passes  through z e r o . F o l l o w i n g t h i s , deformation accumulates each c y c l e of l o a d i n g . Deformations e a r t h mass remains  with  are l i m i t e d and the  s t a b l e f o l l o w i n g shaking without great  changes i n geometry.  L i q u e f a c t i o n i s a s s o c i a t e d with c y c l i c or s t a t i c l o a d i n g whereas c y c l i c m o b i l i t y  i s a s s o c i a t e d with c y c l i c l o a d i n g  only. (Vaid & Chern 1985, C a s t r o 1975, Casagrande 1976, Seed 1979). The concern with l i q u e f a c t i o n with c y c l i c m o b i l i t y ,  is stability,  i t i s the accumulation  while  of u n d e s i r a b l e  deformation.  Many i n v e s t i g a t i o n s have been c a r r i e d out t o study the e f f e c t of v a r i o u s parameters cyclic  on the undrained monotonic and  response of s a t u r a t e d sands. These i n c l u d e  parameters  such as v o i d r a t i o , e f f e c t i v e c o n f i n i n g s t r e s s , s t a t i c  shear  s t r e s s , p a r t i c l e a n g u l a r i t y , s t r e s s path, and p r e s t r a i n history.  (Castro et a l 1982, Chern 1981, Chung 1985,  I s h i h a r a et a l 1975, Seed 1979, Tumi 1983, V a i d & Chern 1985). However no i n v e s t i g a t i o n has been done which  isolates  and c l e a r l y d e f i n e s the e f f e c t of c o e f f i c i e n t of u n i f o r m i t y on the undrained monotonic and c y c l i c s a t u r a t e d sand. The c l a r i f i c a t i o n  l o a d i n g behaviour of  of i t s e f f e c t w i l l  improve  the understanding of the undrained behaviour of s a t u r a t e d  sands. A l s o , knowledge of-those preclude  liquefaction  soil characteristics  i s important  c o n d i t i o n s where l i q u e f a c t i o n may  which  in i d e n t i f y i n g i n - s i t u not be a  concern.  S u b s t a n t i a l b e n e f i t s w i l l be d e r i v e d from a b e t t e r understanding  of the l i m i t s on g r a d a t i o n o u t s i d e which  dynamic l o s s of s o i l  s t r e n g t h and  need not be c o n s i d e r e d .  In t h i s study,  instability  ( N a t i o n a l Research C o u n c i l  1985).  the e f f e c t of the c o e f f i c i e n t of u n i f o r m i t y  on the undrained undrained  liquefaction  behaviour of sand i s i n v e s t i g a t e d using  monotonic and c y c l i c t r i a x i a l t e s t s ,  on  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 samples. Three medium sands with s t r a i g h t - l i n e gradations, DgQ  i d e n t i c a l mineralogy and  are t e s t e d . Although i d e a l i z e d s t r a i g h t - l i n e  are not  found i n nature,  as the use of remolded c l a y  s t u d i e s of c l a y  behaviour.  Straight-line  i s o l a t i o n of the e f f e c t of g r a d a t i o n  gradations, D^Q  ensure  f o r a given medium  ensures that membrane p e n e t r a t i o n  a cause of v a r i a t i o n gradations.  i n fundamental  i d e n t i c a l mineralogy and constant  sand. Constant D ^ Q  gradations  t h e i r use, h e r e i n , i s j u s t i f i e d for  the same reason  combined with  identical  between the r e s u l t s of the  i s not  different  (Frydman et a l 1973). Since w e l l graded sand  tends to segregate  during c o n v e n t i o n a l  improved sample p r e p a r a t i o n techniques  water  pluviation,  were developed to  ensure sample u n i f o r m i t y . T e s t i n g of uniform  specimens i s a  4 prerequisite  f o r fundamental s t u d i e s of m a t e r i a l behaviour.  2. REVIEW OF PREVIOUS INVESTIGATIONS  2.1.  GENERAL ASPECTS OF THE UNDRAINED BEHAVIOUR OF  SANDS  The undrained response of s a t u r a t e d sand i s t r a d i t i o n l y i n v e s t i g a t e d s e p a r a t e l y under monotonic and c y c l i c  loading  c o n d i t i o n s . The d e s i r e t o study each of these l o a d i n g c o n d i t i o n s i s s t i m u l a t e d from q u i t e d i f f e r e n t  concerns. Flow  s l i d e s , caused by undrained f a i l u r e , have generated the interest  i n monotonic l o a d i n g . The concern with c y c l i c  l o a d i n g of sand  i s mainly with the accumulation of  u n d e s i r a b l e deformation d u r i n g earthquake  2.2.  The  loading.  MONOTONIC LOADING BEHAVIOUR  three types of responses of an 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 s a t u r a t e d sand, s u b j e c t t o undrained compression  triaxial  under moderate c o n f i n i n g p r e s s u r e s , are shown i n  F i g u r e 2.1. The s t r e s s - s t r a i n  curves 1 through 3 represent  i n c r e a s i n g r e l a t i v e d e n s i t y . S i m i l a r behaviour m a n i f e s t s under i n i t i a l a n i s o t r o p i c  consolidation.  Types 1 and 2 represent the s t r a i n  s o f t e n i n g or c o n t r a c t i v e  response which i s a behaviour a s s o c i a t e d with a l o s s of shear r e s i s t a n c e a f t e r  a peak. The s t r a i n 5  softening  response  6  1/2{tfi'*03)  F i g u r e 2.1: C h a r a c t e r i s t i c behaviour of s a t u r a t e d sand under monotonic l o a d i n g . (Adapted from V a i d & Chern  1985).  7 i s i n i t i a t e d a f t e r attainment of a peak d e v i a t o r s t r e s s .  Type 1 response  i s l i q u e f a c t i o n as d e f i n e d by C a s t r o  Casagrande (1976), and Seed (1979). A f t e r an i n i t i a l  (1969), peak  s t r e n g t h , continuous deformation occurs a t constant c o n f i n i n g and shear s t r e s s and constant volume, i n a s t a t e termed steady s t a t e . In t h i s steady s t a t e , the sand mass flows as a f r i c t i o n a l the term  l i q u i d and hence the a s s o c i a t i o n of  'flow f a i l u r e ' .  Limited l i q u e f a c t i o n in which temporary liquefaction,  ( N a t i o n a l Research  C o u n c i l 1985).  i s represented by the type 2 response,  s t r a i n s o f t e n i n g , s i m i l a r to that of  i s i n i t i a t e d . T h i s t r a n s i t o r y l o s s of shear  r e s i s t a n c e i s regained with f u r t h e r s t r a i n i n g . The e f f e c t i v e stress ratio response Ratio  (o^'/o^')  is initiated  a t which the s t r a i n s o f t e n i n g i s d e f i n e d as the C r i t i c a l S t r e s s  (CSR) (Vaid & Chern 1983). The CSR has been shown by a  wide body of experimental data t o be a constant f o r a given sand  i r r e s p e c t i v e of the v o i d r a t i o and s t r e s s s t a t e  to the commencement of undrained deformation.  The a r r e s t of the s t r a i n s o f t e n i n g behaviour liquefaction  (Chern  prior 1985).  in limited  i s at the minimum d e v i a t o r s t r e s s . T h i s minimum  d e v i a t o r s t r e s s i s higher than the d e v i a t o r s t r e s s at steady s t a t e i n the l i q u e f a c t i o n case. At the minimum d e v i a t o r  s t r e s s i n l i m i t e d l i q u e f a c t i o n , d i l a t i o n occurs, the pore pressure begins to decrease, and the e f f e c t i v e s t r e s s path takes a sudden turnaround. The s t a t e at t h i s p o i n t of change has been d e s i g n a t e d as the Phase Transformation by I s h i h a r a et a l (1975). The e f f e c t i v e s t r e s s r a t i o at phase transformation  i s a m a t e r i a l constant f o r a s p e c i f i c  ( I s h i h a r a et a l 1975, V a i d & Chern  sand.  1985). A f t e r the phase  t r a n s f o r m a t i o n , the e f f e c t i v e s t r e s s path approaches the undrained f a i l u r e envelope deviatoric state.  with f u r t h e r s t r a i n i n g . At h i g h  s t r e s s e s , the sample may e v e n t u a l l y reach steady  ( C a s t r o 1982).  With l i q u e f a c t i o n , the e f f e c t i v e s t r e s s path terminates at steady s t a t e . F a i l u r e occurs as a r e s u l t of l a r g e deformations p r i o r t o and at steady s t a t e , without the s t r e s s path reaching the undrained  f a i l u r e envelope. The  f r i c t i o n angle at phase t r a n s f o r m a t i o n equals the f r i c t i o n angle at steady s t a t e .  (Vaid & Chern  1985).  Type 3 response d e p i c t s the s t r a i n hardening or d i l a t i v e response. No l o s s of shear r e s i s t a n c e  i s experienced. The  phase t r a n s f o r m a t i o n s t a t e e x i s t s f o r d i l a t i v e sand  also,  and corresponds to the p o i n t at which d i l a t i o n commences and the pore p r e s s u r e s t a r t s t o drop. The phase t r a n s f o r m a t i o n s t a t e f o r d i l a t i v e and c o n t r a c t i v e behaviour  i s a t the same  9 effective stress ratio.  (Vaid & Chern 1985). At the phase  t r a n s f o r m a t i o n , i n e f f e c t i v e s t r e s s space, a turnaround occurs i n the s t r e s s path although i t may for highly d i l a t i v e  not be  discernible  states.  Under monotonic l o a d i n g , the steady s t a t e l i n e has been proposed  by C a s t r o et a l (1977  & 1982)  as a boundary i n two  dimensional  (void r a t i o , e ,  pressure,  ', at steady s t a t e ) space between i n i t i a l  c  versus e f f e c t i v e  confining  p r i o r to undrained l o a d i n g that are l i q u e f i a b l e and  states  those  that are not. S t a t e s s u b s t a n t i a l l y to the r i g h t of the steady s t a t e l i n e l e a d to l i q u e f a c t i o n , while those below are n o n l i q u e f i a b l e .  Sladen, D'Hollander  and Krahn (1958) propose  the e x i s t e n c e  of a c o l l a p s e s u r f a c e i n p'-q-e space. They combine the concepts of steady s t a t e with the c r i t i c a l  s t a t e concept  forward by Roscoe et a l (1958). For a f i x e d e , c  p o i n t s on the s t r e s s paths i n p'-q  space  the peak  form a s t r a i g h t  l i n e that passes through the steady s t a t e p o i n t , not the o r i g i n as proposed  through  by V a i d & Chern (1985). A p o s s i b l e  reason f o r t h i s d i f f e r e n c e i s that Sladen's model was on a small number of t e s t  based  r e s u l t s . Sladen a l s o prepared h i s  samples u s i n g moist tamping. T h i s technique produces with nonhomogenieties.  put  (Castro 1969,  samples  C a s t r o et a l 1982).  10 Pluviation, the technique used by Vaid & Chern, forms more homogeneous samples, therefore their results are more r e l i a b l e . The position of t h i s collapse l i n e i s shown by Sladen et a l to s h i f t with changes in void r a t i o , while i t s slope remains constant. Drawn in p'-q-e space, these l i n e s combine to form a surface, termed a 'collapse surface'.  The  behaviour of a sand is stated in terms of i t s stress state r e l a t i v e to the collapse surface. For t h i s collapse  surface  concept to be used, contactive behaviour i s necessary for the d e f i n i t i o n of a peak in the stress path, and of the steady state l i n e .  2.3.  CYCLIC LOADING BEHAVIOUR  Sand liquefaction was  reported as long ago as 1783  (Hobbs  1907), but i t wasn't u n t i l i t caused severe damage in the form of building settlement and t i l t i n g and slope  failures  during earthquakes in Niigata, Japan and Alaska in 1964 the phenomenon was  begun to be  that  investigated.  I n i t i a l research dealt purely with strain development during c y c l i c loading. This was  attributed to the development of  states of zero e f f e c t i v e stress during some stages of loading. (Seed & Lee  1966). Later i t was  recognised  that  there were two d i s t i n c t l y d i f f e r e n t mechanisms of strain  11 development : 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 .  (Castro  1969).  True l i q u e f a c t i o n , due t o c y c l i c  loading,  Figure  cyclic  2.2. At some stage d u r i n g  liquefaction  loading,  i s t r i g g e r e d and the sample undergoes u n l i m i t e d  deformation. (Castro  1969). T h i s occurs i n a manner s i m i l a r  to that observed under monotonic l o a d i n g .  Limited  i s i l l u s t r a t e d in  l i q u e f a c t i o n , shown i n F i g u r e  (See F i g u r e 2.1).  2.3, occurs with  cyclic  l o a d i n g as w e l l as with monotonic l o a d i n g a l s o , (cf  Figure  2.1). (Vaid & Chern 1985, Chern 1985). With l i m i t e d  l i q u e f a c t i o n , the sand develops a s t r a i n s o f t e n i n g  response  in a manner s i m i l a r t o l i q u e f a c t i o n but over a l i m i t e d s t r a i n range. The CSR, the phase t r a n s f o r m a t i o n  state  a s s o c i a t e d with l i m i t e d l i q u e f a c t i o n and the steady  state  a s s o c i a t e d with l i q u e f a c t i o n are the same f o r monotonic and cyclic  loading  f o r a given  sand. (Vaid & Chern 1985).  C y c l i c m o b i l i t y due to c y c l i c  loading  i s shown i n F i g u r e  2.4. C y c l i c m o b i l i t y i s caused by the p r o g r e s s i v e of pore pressure  b u i l d up  with c y c l e s of l o a d i n g . I f the c y c l i c  s t r e s s e s are higher  than the s t a t i c  s t a t e of s t r e s s r e v e r s a l occurs, l o a d i n g c y c l e s , the c y c l i c  shear  shear s t r e s s e s , i e . a  and there are s u f f i c i e n t  l o a d i n g can momentarily reduce  12  Figure  2.2: L i q u e f a c t i o n due to c y c l i c (After Vaid &  Chern  1985).  loading.  13  3: L i m i t e d l i q u e f a c t i o n due to c y c l i c ( A f t e r v a i d & Chern 1985).  loading.  15 the e f f e c t i v e s t r e s s e s to zero when the c y c l i c passes through z e r o . Deformation  shear  then accumulates  stress  with each  c y c l e of l o a d i n g , and a t t a i n s a f i n i t e magnitude with the completion of l o a d i n g .  If d u r i n g c y c l i c  l o a d i n g a s p e c i f i e d l e v e l of deformation  occurs, i t c o u l d be due to l i m i t e d l i q u e f a c t i o n , m o b i l i t y or a combination  cyclic  of the two. I t should be noted  that deformation due t o l i m i t e d l i q u e f a c t i o n always occurs before the r e a l i z a t i o n of momentary s t a t e s of zero e f f e c t i v e stress.  (Vaid & Chern 1985). I f 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 occurs, the concern  i s with s t a b i l i t y  because  the a s s o c i a t e d deformations w i l l be very l a r g e and unacceptable. I f c y c l i c m o b i l i t y o c c u r s , the concern the accumulation  The  i s with  of u n d e s i r a b l e deformation.  r e s i s t a n c e to c y c l i c  l o a d i n g i s d e f i n e d as the c y c l i c  s t r e s s r a t i o r e q u i r e d to cause c o n t r a c t i v e deformation or t o develop a s p e c i f i e d amount of a x i a l s t r a i n due to c y c l i c mobility  i n a f i x e d number of c y c l e s .  (Castro et a l 1982,  V a i d & Chern 1985). Development of l i q u e f a c t i o n a s s o c i a t e d with the accumulation  of a l a r g e  i s always  strain.  16 2.4.  RELATIONSHIP BETWEEN MONOTONIC AND  There  i s a close  l i n k between  CYCLIC  t h e type of monotonic  a n d t h e m e c h a n i s m by w h i c h s t r a i n d e v e l o p m e n t cyclic Chern  loading.  (Castro  LOADING  response  o c c u r s under  1969, C a s t r o e t a l 1982, V a i d  &  1985). F o r a sand t o d e v e l o p c o n t r a c t i v e b e h a v i o u r  under c y c l i c  loading  ( 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 ) ,  there are 3 requirements: 1.  The i n i t i a l  s t a t e o f t h e s a n d must l i e i n t h e r e g i o n  where c o n t r a c t i v e d e f o r m a t i o n w o u l d o c c u r monotonic 2.  loading,  under  i e . w e l l above t h e s t e a d y s t a t e  The maximum s h e a r s t r e s s must e x c e e d t h e s h e a r at phase  transformation  line.  strength  f o r l i m i t e d l i q u e f a c t i o n or a t  steady s t a t e f o r l i q u e f a c t i o n . 3.  T h e r e must be a s u f f i c i e n t  number o f l o a d i n g  cycles to  move t h e e f f e c t i v e s t r e s s s t a t e o f t h e s a n d t o t h e CSR state.  It  ( V a i d & Chern  h a s b e e n shown by V a i d  contractive  of the  i s i n i t i a t e d a t a constant value of the  (monotonic or c y c l i c ) .  initial  (1985) t h a t t h e  to l i q u e f a c t i o n or l i m i t e d  s t r e s s r a t i o , CSR, w h i c h  loading  confining  & Chern  response leading  liquefaction critical  1985).  s t a t e o f t h e sand  i s independent of the type I t i s also  independent of  (void ratio, effective  s t r e s s , and shear s t r e s s ) and of t h e a m p l i t u d e o f  17 cyclic  The  stress.  0 p'  m o b i l i s e d f r i c t i o n angle at phase t r a n s f o r m a t i o n ,  pP  f  for c o n t r a c t i v e or d i l a t i v e behaviour i s e q u i v a l e n t t o the constant  volume f r i c t i o n angle,  m o b i l i z e d f r i c t i o n angles  0  C V  *  at steady  s t a t e . The  at phase t r a n s f o r m a t i o n  s t a t e a r e independent of c o n f i n i n g pressure,  and steady  initial  packing  d e n s i t y , p a r t i c l e s i z e and p a r t i c l e shape. They are dependent only on the mineral c o n s t i t u e n c y and  are consequently  unique f o r a granular m a t e r i a l .  (Negussey et a l 1986, Wijewickreme  2.5.  of the m a t e r i a l  1986).  THE EFFECT OF PARTICLE GRADATION  Most r e s e a r c h on the undrained  response of sands to c y c l i c  and monotonic l o a d i n g has been done on uniform  and c l e a n  sands. Uniform c l e a n sands are r a r e l y encounted i n n a t u r a l s o i l d e p o s i t s and i t i s now known that l i q u e f a c t i o n can occur  i n a v a r i e t y of s i t u a t i o n s with s o i l s of d i f f e r e n t  properties. i s necessary  ( N a t i o n a l Research C o u n c i l  1985). T h e r e f o r e , i t  to determine the e f f e c t of other  factors,  such  as p a r t i c l e g r a d a t i o n , on the response of sand.  Lee  & Fitton  (1969) d i d a study  on the e f f e c t of g r a i n  size,  g r a i n s i z e d i s t r i b u t i o n , and g r a i n shape on the s t r e n g t h of  18 s o i l s under simulated earthquake performed  l o a d i n g c o n d i t i o n s . They  c y c l i c t r i a x i a l t e s t s on an a l l u v i a l  sand and  g r a v e l d e p o s i t from E l Monte, C a l i f o r n i a . They concluded that there was no s i g n i f i c a n t d i f f e r e n c e i n s t r e n g t h between the well-graded and the u n i f o r m l y graded sand. They ensured that the m i n e r a l types were the same f o r a l l s i z e  ranges,  although they d i d not i s o l a t e the e f f e c t of c o e f f i c i e n t of u n i f o r m i t y . The comparison  of samples f o r the e f f e c t of  g r a i n s i z e d i s t r i b u t i o n was done with samples of v a r y i n g mean diameter,  (D^Q).  A r e p o r t submitted to the N a t i o n a l Science  Foundation,  Washington DC, by G e o t e c h n i c a l Engineers I n c . (1982) looked at the e f f e c t of p a r t i c l e g r a d a t i o n on the steady l i n e . They concluded that r e l a t i v e l y  state  small d i f f e r e n c e s i n  g r a i n s i z e d i s t r i b u t i o n s i g n i f i c a n t l y a f f e c t e d the p o s i t i o n , but not the shape and s l o p e , of the steady s t a t e l i n e . They used  f i v e g r a d a t i o n s of Banding  so the e f f e c t of c o e f f i c i e n t  sand which had v a r y i n g D ^ Q ,  of u n i f o r m i t y was not i s o l a t e d .  Chang, Yeh and Kaufman (1982) s t u d i e d the e f f e c t of g r a d a t i o n and s i l t  content on l i q u e f a c t i o n p o t e n t i a l of  sand. They d i d undrained c y c l i c  t r i a x i a l t e s t s on a Denver  sand. They concluded that f o r coarse sand, D ^ Q g r e a t e r than 0.37 mm,  the r e s i s t a n c e to l i q u e f a c t i o n decreases with an  19  i n c r e a s e i n the c o e f f i c i e n t DgQ  smaller than 0 . 2 3 mm,  of u n i f o r m i t y . For  the r e s i s t a n c e i n c r e a s e s with  c o e f f i c i e n t of u n i f o r m i t y . The u n i f o r m i t y vanishes preparation  at C  f i n e sands,  u  e f f e c t of the c o e f f i c i e n t than about 8 .  greater  technique used was  moist tamping,  s a t u r a t i o n under back p r e s s u r e . Moist  The  sample  with  considerably  more non-uniform than other methods such as a i r and  Wong et a l  (Castro  (1974)  1969,  Castro  et a l  performed c y c l i c  of  tamping, however,  g i v e s r i s e to samples with d e n s i t i e s that are  pluviation.  the  water  1982).  t r i a x i a l t e s t s to  i n v e s t i g a t e the behaviour of " g r a v e l l y s o i l s " . They t e s t e d s o i l s of constant  D ^ Q at a r e l a t i v e d e n s i t y of 6 0 % and  that the w e l l graded g r a v e l l y m a t e r i a l r e q u i r e d a c y c l i c deviator 2.5  s t r e s s than the uniform  % axial strain  r e s u l t c o u l d be due  smaller  m a t e r i a l to develop  i n 1 0 c y c l e s . They proposed that to membrane compliance and  the w e l l graded m a t e r i a l has  found  the  this fact  some tendency to d e n s i f y as  that the  f i n e r p a r t i c l e s move i n t o the spaces between the l a r g e r p a r t i c l e s . They compared samples at a constant  D ^ Q , however  the mineralogy v a r i e d through the g r a i n s i z e s . Thus, some of the observed d i f f e r e n c e may t e s t s were a l s o r e s t r i c t e d  The  be due to one  to t h i s aspect. relative  N a t i o n a l Research C o u n c i l Report  i  Their  density.  ' L i q u e f a c t i o n of  Soils  20  d u r i n g Earthquakes', Nov. grain size d i s t r i b u t i o n liquefaction  1985,  i d e n t i f i e d the e f f e c t  on dynamic l o s s of s o i l  t h i s r e p o r t which  The  l i t e r a t u r e review, h e r e i n , suggests that no  i n i t i a t e d t h i s study.  study has been performed  factors  i n which the e f f e c t  of u n i f o r m i t y has been i s o l a t e d  which  straight-line  fundamental  of the from other  i n f l u e n c e the undrained behaviour of sand. In  t h i s study, sands of v a r y i n g C , but i d e n t i c a l g r a d a t i o n s and i d e n t i c a l D ^ Q  that the e f f e c t c o u l d be  s t r e n g t h and  as one of the areas which r e q u i r e d r e s e a r c h . I t  was  coefficient  of  mineralogy,  were t e s t e d such  of g r a d a t i o n on the undrained behaviour  identified.  3. EXPERIMENTATION  3.1. TESTING  In order  PROGRAM  to determine the e f f e c t of p a r t i c l e g r a d a t i o n ,  monotonic and c y c l i c  both  l o a d i n g t e s t s were performed on the 3  medium sands of v a r y i n g c o e f f i c i e n t s of u n i f o r m i t y . A l l t e s t s were undrained and were performed on i s o t r o p i c a l l y consolidated  samples.  S t r a i n c o n t r o l l e d monotonic l o a d i n g t e s t s were conducted to determine the v a r i a t i o n due to g r a d a t i o n  of the undrained  response of the sand t o monotonic l o a d . The monotonic l o a d i n g t e s t s a l s o g i v e an i n d i c a t i o n of the mechanism of s t r a i n response d u r i n g c y c l i c  l o a d i n g . These t e s t s were  performed on the 3 g r a d a t i o n s  a t a constant  relative  density  of 38.5 ± 1.5 %. T h i s d e n s i t y was the minimum d e n s i t y obtainable  f o r Gradation  3 under an i n i t i a l  confining  pressure  of 500 kPa. The lowest p o s s i b l e d e n s i t y s t a t e s were  selected  i n order  for  to provide  the most favourable  the occurence of c o n t r a c t i v e deformation. T e s t s  compression mode were c a r r i e d out f o r i n i t i a l pressures  of 50, 200 and 500 kPa. T e s t s  mode were performed f o r an i n i t i a l kPa  conditions  only.  21  i n the  confining  i n the extension  c o n f i n i n g pressure  of 200  Stress c o n t r o l l e d c y c l i c  l o a d i n g t e s t s were performed t o  determine t h e r e s i s t a n c e curves to c y c l i c gradations, cyclic  loading  so that the behaviour c o u l d be compared. A l l  t e s t s were c a r r i e d out f o r an i n i t i a l  pressure  f o r the 3  of 200 kPa. The c y c l i c  confining  stress ratio,  ( a y/  was v a r i e d between 0.123 and 0.23. The r e l a t i v e  a  of the sand being  3 ' )» C  d e n s i t y was  v a r i e d between 22 and 73 % depending on the c y c l i c r a t i o and the gradation  2 a  C  stress  tested.  3.2. TESTING APPARATUS  A schematic layout of the t e s t i n g apparatus f o r the s t r e s s controlled cyclic  The  cyclic axial  piston. I n i t i a l l y  loading  t e s t s i s given  i n Figure 3.1.  l o a d was a p p l i e d u s i n g a d o u b l e - a c t i n g the pressures  air  i n the two chambers of the  p i s t o n are equal and the l o a d i n g ram i s a t r e s t . The pressure  i n the bottom chamber of the p i s t o n i s c o n t r o l l e d  by a p r e s s u r e  r e g u l a t o r . Volume boosters  are connected t o  the top and bottom chambers of the p i s t o n t o ensure that there  i s no degredation of the l o a d pulse when l a r g e  deformations occur. The c y c l i c  l o a d i s a p p l i e d through the  top chamber of the p i s t o n . I t i s a p p l i e d by an electro-pneumatic transducer  which i s d r i v e n by the f u n c t i o n  generator. The maximum output of the electo-pneumatic  23  Double-acting Air Piston.  —  LVDT  'Volume Booster  ' Ratio Relay  llf (RV  Load Cell  ^Function Generator Electropneumatic Transducer To Recorder  Pressure Regulator  A i n TE  "ir" r- Cell Pressure (ft V Transducer  TT  Figure  3 . 1 : Schematic  —H  I  Pore Pressure Transducer  layout of t e s t i n g  apparatus.  24 transducer amplify  The  monotonic  piston  was  load,  during  to the  was  system,  by a s t r a i n  to  piston.  t e s t s were p e r f o r m e d loading  included  using  i n which  d r i v e . An  a  layout  the a i r  adjustable  controlled  speed  loading  tests.  Creek,  the  test.  in this British  study i s a n a t u r a l Columbia,  sand  i s used  the p r o d u c t i o n  locally  of a s p h a l t  sub-angular, with p a r t i c l e  river  deposit  o b t a i n e d from t h e  y a r d s h a v i n g been t r a n s p o r t e d  b a r g e . The  were  TESTED  sand u s e d  Municipal  in  relay  d e f o r m a t i o n , and p o r e p r e s s u r e i n t h e sample  MATERIAL  Earls  so t h e r a t i o  used t o p r o v i d e the s t r a i n  f o r the  recorded  The  replaced  motor was  3.3.  loading  to the c y c l i c  required  The  kPa,  the p r e s s u r e p r o v i d e d  similar  DC  i s 103  mix.  sizes  Vancouver  from E a r l s  for backfilling E a r l s Creek r a n g i n g from  from  Creek  by  t r e n c h e s and  sand i s 0.06  mm  to 5  mm.  The  sand  divided  fraction into  which  12 g r a i n  t o #200. T h e s e  grain  p a s s e d t h r o u g h t h e #8  size  r a n g e s by  sieves  sieve  was  r a n g i n g from  s i z e s were t h e n combined  t o form 3  #10  25  l i n e a r g r a d a t i o n s with a constant D^Q of 0 . 4 2 mm. 1, 2 ,  gradations 1.5,  3,  and  and  The  3 have c o e f f i c i e n t s of u n i f o r m i t y of  6 r e s p e c t i v e l y . The  linear grain size  d i s t r i b u t i o n curves of these g r a d a t i o n s are shown i n F i g u r e 3.2,  along with t h a t of the o r i g i n a l E a r l s Creek sand.  The m i n e r a l composition  of the sand i s approximately  3 0 % f e l d s p a r with the remaining  q u a r t z and  50 %  being  hornblende,  c l i n o p y r o x e n e , b i o t i t e mica, and  sphene. The  composition  i s uniform over the e n t i r e range of g r a i n s i z e s  which allows f o r the i s o l a t i o n of the e f f e c t of the c o e f f i c i e n t of u n i f o r m i t y . M a i n t a i n i n g a constant D^Q a l s o chosen to f u l f i l l  t h i s requirement.  The  membrane  p e n e t r a t i o n i n t o the v o i d s of a specimen of g r a n u l a r due  was  soil,  to a p p l i c a t i o n of a p a r t i c u l a r ambient p r e s s u r e , i s a  f u n c t i o n of the D^Q of the s o i l ,  and not i t s g r a d a t i o n .  (Frydman et al.1973). Consequently,  any d i f f e r e n c e s i n  behaviour  between the 3 g r a d a t i o n s i s not caused  variation  i n the membrane p e n e t r a t i o n .  by a  The minimum and maximum v o i d r a t i o s , c o e f f i c i e n t s of u n i f o r m i t y , and p a r t i c l e s i z e range f o r the 3 g r a d a t i o n s are given i n Table 3.1. The minimum and maximum v o i d r a t i o s , (e  •„ and e ), were obtained i n accordance with the min max ' standard t e s t method, ASTM D 2 0 4 9 . There i s a l a r g e v a r i a t i o n  27  Particle S i z e Range (mm)  Gradation  Cu  1  1 .5  0 .94  0.63  0.3-0.59  2  3  0.77  0.51  0.15-1.2  3  6  0.61  0.37  0.074-2.4  e  max  Table 3.1: M a t e r i a l  e  min  properties.  in e  „ and e •„ between the g r a d a t i o n s , however, there i s max mm ' ' not much v a r i a t i o n i n (e „ -e • „ ) . max min 5  m  The  s p e c i f i c g r a v i t y was  obtained using the method  recommended by Lambe (1951) and  i s constant  at 2.72  f o r the  3 gradations.  The  h y d r o s t a t i c c o n s o l i d a t i o n c h a r a c t e r i s t i c s of the 3  gradations,  f o r a r e l a t i v e d e n s i t y of 38.5%  c o n f i n i n g p r e s s u r e , are shown i n F i g u r e 3.3.  at 500  kPa  The  c o n s o l i d a t i o n c h a r a c t e r i s t i c s are given i n terms of  the  r e l a t i o n s h i p between volumetric s t r a i n and mean normal s t r e s s d u r i n g c o n s o l i d a t i o n . The compressible  than the uniform  w e l l graded sand i s more  sand, shown by the w e l l graded  sand d e v e l o p i n g higher volumetric  s t r a i n s than  the  uniform  sand at constant mean normal s t r e s s .  3.4.  SAMPLE PREPARATION AND  TESTING TECHNIQUES  Sample homogeneity, u n i f o r m i t y of d e n s i t y and s a t u r a t i o n were the prime requirements was  found  t h a t p l u v i a t i o n through a i r or water caused  s e g r e g a t i o n , t h e r e f o r e a new called  for sample r e c o n s t i t u t i o n . I t  method of sample p r e p a r a t i o n ,  'the s l u r r y method', was  developed  by Ralph  (1987). T h i s method r e s u l t e d in homogeneous and  Keurbis  uniform  *  Gradation  1  «  Gradation  2  o  Gradation  3  I  200  400  P ' (kPa) Figure 3.3: R e l a t i o n s h i p between volumetric normal s t r e s s during c o n s o l i d a t i o n .  s t r a i n and mean  30 specimens. U n i f o r m i t y grain  was  v e r i f i e d by an a n a l y s i s of  s i z e d i s t r i b u t i o n and  sample. A sample was porewater. When the sections  and  calculated  v o i d r a t i o throughout  formed using sample had  solidified,  the v o i d r a t i o and  s l i c e s was  1.5  i t was  the the cut  v a r i a t i o n between the  %, while f o r the g r a i n  2 %.  The  samples had  of  123  a diameter of 637  mm  and  an average height  mm.  p e r i o d of 3.4a). The  the  sand and  sand was  saturation,  The  c y l i n d e r has  fit  i n s i d e the  (see  Figure  then t r a n s f e r r e d by water p l u v i a t i o n  water i n a c y l i n d e r which was  (see F i g u r e  such that  the porous d i s k s were b o i l e d f o r a  10 minutes to insure  into deaired  of the  weight  (Keurbis 1987).  Initially,  end.  void  size  d i s t r i b u t i o n s , the v a r i a t i o n in the percent f i n e r by was  into 4  g r a i n s i z e d i s t r i b u t i o n were  f o r each s e c t i o n . The  r a t i o s of the  g e l mixed with  the  plugged at  one  3.4b).  an outside  diameter of 60 mm  sample former. The  there was  thus  can  of the c y l i n d e r  was  s u f f i c i e n t water present to allow mixing  sand-water s l u r r y , but  segregation d i d not  length  and  occur on  not  too much such that  inversion.  31  a SAND BOILED IN HATER TO DE-AIR;  b SAND PLUVIATED INTO MUINS TUBE  RUBBER HEHBRANE SEAL GLUED TO  ONTO BASE PLATEN OF TRIA1IAL TEST APPARATUS  Figure 3.4A: Sample p r e p a r a t i o n by 'The S l u r r y Method'. (Adapted from Keurbis 1987).  RUBBER ItENBRANE STRETCHED ONTO SAMPLE FORHER TUBE  T K I A I I M . U S ! BASE PLATEK  e  f  H U M S TUBE PLACED UPON TRIAIIAL TEST APPARATUS BASE PLATEN IN MATER BATH; RUBBER MEMBRANE IS ROLLED UP SIDES OF fill INS TUBE  5AHPLE FORHER TUBE ASSEMBLED AROUND M1XINB TUBE; SAMPLE MEMBRANE STRETCHED OVER SAMPLE FORMER TUBE; APPLICATION OF VACUUM TO FORMER TUBE EIPANDS MEMBRANE AND DRANS IN RESERVOIR MATER FROM ABOVE, MA1NIAININS SATURATION  g till INS TUBE WITHDRAWN LEAVINS LOOSE SATURATED UNIFORMLY MIIED SAMPLE IN FORMER TUBE; TOP OF SAMPLE CAREFULLY FLATTENED  F i g u r e 3.4B: Sample p r e p a r a t i o n by 'The S l u r r y Method'. (Adapted from Keurbis 1987).  co to  33 The  s a n d - f i l l e d c y l i n d e r was then immersed i n a water bath.  The  porous base d i s k , 637 mm i n diameter and 4.7 mm t h i c k ,  was t r a n s f e r r e d under water to the top of the c y l i n d e r and held  i n p l a c e by a s e c t i o n of membrane. I t was i n s u r e d  there was no a i r w i t h i n  that  the c y l i n d e r or trapped between the  membrane, stone, and c y l i n d e r such that water t e n s i o n would h o l d the stone i n place when the c y l i n d e r was i n v e r t e d . There was a rubber s e a l on the end of the c y l i n d e r so a good s e a l between the porous d i s k and the c y l i n d e r was maintained,  The  (see F i g u r e  3.4c).  c y l i n d e r was removed from the water bath. An aluminium  d i s k was then p l a c e d i t s desaturation  on t o p of the porous d i s k to prevent  during  thoroughly, (see F i g u r e  Preparation  mixing. The sample was then mixed 3.4d).  of the base of the c e l l was done i n a water  bath. The 0.012 inch t h i c k membrane was f i x e d to the base pedestal  with an 0 r i n g , and the a i r removed from between  the p e d e s t a l  and the membrane. The membrane was then  down such that  rolled  i t d i d not protrude above the top of the base  pedestal.  When the sand was mixed t o an homogeneous s t a t e , the c y l i n d e r was i n v e r t e d with care t o prevent  segregation,  34 porous disk down, the aluminium d i s k removed and the connective  membrane c a r e f u l l y p u l l e d away from the face of  the porous d i s k . The c y l i n d e r was then p l a c e d on the base p e d e s t a l , having  removed any a i r bubbles from the face of  the porous d i s k under water, (see F i g u r e 3.4e). A f i r m downwards pressure was then maintained connective  on the c y l i n d e r , the  membrane removed, and the t e s t membrane r o l l e d up  the o u t s i d e of the c y l i n d e r .  The  c e l l base was then removed from the water bath and the  sample former put i n p l a c e . The membrane was p u l l e d away from the c y l i n d e r , and h e l d i n p l a c e w i t h i n the former with a vacuum of about 7.5 cm of Hg. T h i s was done with the base drainage  open to a r e s e r v o i r and a supply  to the top of the base d i s k t o prevent porous d i s k , (see F i g u r e  The  of d e a i r e d water  d e s a t u r a t i o n of the  3.4f).  plug was removed from the top of the c y l i n d e r , and the  excess water on top of the sand e v i s c e r a t e d t o prevent overflow  on removal of the c y l i n d e r . The c y l i n d e r was then  removed with one slow continuous r e q u i r e d to prevent  segregation  movement. C o n t i n u i t y i s of the g r a i n s i z e s . (see  F i g u r e 3.4g).  The  top of the sample was l e v e l e d , then the top cap placed  35  and  l e v e l e d . Next the sample was  maintaining  double drainage  d e n s i f i e d by v i b r a t i o n  u n t i l the  d e n s i t y r e q u i r e d . A g e n t l e pressure  initial  was  maintained  top cap d u r i n g d e n s i f i c a t i o n to prevent formation  l i n e was  sample was  kPa), The  then c l o s e d and  c e l l was  top  the membrane s e a l e d to the  ring.  a p p l i e d a s u c t i o n of about 12 cm  the sample former removed, and  of Hg  the c e l l put  (17  together.  then f i l l e d with d e a i r e d water and placed  c e n t r e d on the l o a d i n g frame. A small c e l l pressure a p p l i e d to overcome s u c t i o n , and were then connected. The  the pore pressure  sample was  now  s a t u r a t i o n . Samples were only accepted pressure  the  the p o s s i b l e  of the l i q u e f a c t i o n r e s i s t a n c e . The  top cap with an 0  The  on  of a loose s u r f a c e l a y e r which would lead to an  underestimation drainage  placement  and  was lines  checked f o r i f a Skempton's pore  parameter, B, of at l e a s t 0.99  was  obtained.  C o n s o l i d a t i o n of the sample to the r e q u i r e d s t r e s s with basal drainage  only was  then performed. T h i s was  i n c r e a s i n g the c e l l p r e s s u r e ,  step-wise,  done by  such that  c o n s o l i d a t i o n c h a r a c t e r i s t i c s of the sample c o u l d  the be  monitored. At the f i n a l c o n s o l i d a t i o n s t r e s s , the e q u i l i b r i u m readings were taken a f t e r the consolidation,  i f any,  had  secondary  taken p l a c e . T h i s was  to ensure  36 •that pore pressure b u i l d up due to secondary d i d not e f f e c t the r e s u l t s during the  consolidation  the shearing  phase. For  sands t e s t e d , the secondary c o n s o l i d a t i o n phase took  approximately  Tests  10 minutes.  were performed to determine the membrane  f o r the 3 gradations  penetration  and the c o r r e c t i o n f o r each was a p p l i e d  to the volume changes i n the c o n s o l i d a t i o n phase. The corrections  f o r the 3 gradations  approximately equal. al  This  were found to be  i s i n accordance with Frydman e t  (1973) who concluded that membrane p e n e t r a t i o n  is a  f u n c t i o n of D ^ Q only and not of g r a d a t i o n .  After consolidation  the loading  ram was connected to the  l o a d i n g p i s t o n . An eyed connecting r i n g was used to minimize the d i s t u r b a n c e  t o the sample d u r i n g  prevent i t s premature  connection and to  loading.  The  sample was now ready t o be loaded.  The  mean g r a i n s i z e i s 0.42 mm and thus the p e r m e a b i l i t y of  the sand i s high. Consequently, the rate of t e s t i n g i n the monotonic l o a d i n g  t e s t s has no e f f e c t on the r e s u l t s on  account of p o s s i b l e end r e s t r a i n t . A constant r a t e of s t r a i n of 0.4 % a x i a l s t r a i n per minute was used f o r convenience.  37  During the monotonic t e s t s , the a x i a l  load,  porewater  p r e s s u r e , and a x i a l deformation were monitored  by e l e c t r o n i c  transducers and recorded u s i n g a data a c q u i s i t i o n  system,  coupled t o a computer.  Constant  shear s t r e s s amplitude  c y c l i c t e s t s were  performed.  A s i n e s o i d a l load pulse with a frequency of 0.1 Hz was used. The  low frequency l o a d i n g was used to be compatible with the  low frequency response c a p a b i l i t i e s of s t r i p c h a r t r e c o r d e r s . During each t e s t , the c y c l i c a x i a l l o a d , porewater  p r e s s u r e , and a x i a l deformation were c o n t i n u o u s l y  monitored  by e l e c t r o n i c t r a n s d u c e r s and recorded on a s t r i p  c h a r t r e c o r d e r . C o r r e c t i o n s were made to the data f o r rod f r i c t i o n , and membrane s t r e n g t h . (Bishop & Henkel  1962).  4. TEST  In t h i s chapter, of  RESULTS  the undrained  monotonic l o a d i n g  the 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 samples i s d i s c u s s e d  first,  s u b d i v i d e d i n t o the compression mode, the e x t e n s i o n  mode, and a d i s c u s s i o n of i s o t r o p y . The c y c l i c then  The  behaviour  r e s u l t s are  discussed.  b a s i s of comparison of the t e s t s i s i d e n t i c a l  d e n s i t y which i s the approach taken by other  relative  researchers.  4.1. MONOTONIC LOADING BEHAVIOUR  Undrained monotonic l o a d i n g t e s t s were performed on 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 samples at a constant  relative  d e n s i t y of 38.5 ± 1.5 %. T e s t s were performed i n both the compression and e x t e n s i o n modes. The compression modes w i l l be d i s c u s s e d  first.  4.1.1. M o n o t o n i c C o m p r e s s i o n  Results  Monotonic compression t e s t s were performed f o r i n i t i a l c o n f i n i n g pressures  of 50, 200 and 500 kPa, f o r a r e l a t i v e  d e n s i t y of 38.5 ± 1.5 %. A d d i t i o n a l t e s t s were c a r r i e d out at  each c o n f i n i n g pressure  f o r every g r a d a t i o n 38  i n order t o  ensure the r e p e a t a b i l i t y of the t e s t s . For Gradation an i n i t i a l  3, f o r  c o n f i n i n g pressure of 500 kPa, F i g u r e 4.1  p r e s e n t s the r e s u l t s of 2 t e s t s a t e s s e n t i a l l y  identical  r e l a t i v e d e n s i t y , given i n terms of the d e v i a t o r i c  stress  and excess porewater pressure as a f u n c t i o n of a x i a l  strain.  These r e s u l t s show e x c e l l e n t r e p e a t a b i l i t y of the t e s t s , reflected deviatoric  i n the s i m i l a r i t y s t r e s s developed.  i n porewater pressure and T h i s confirms the u n i f o r m i t y  and c o n s i s t e n c y of the samples prepared  by 'the s l u r r y  method.' The t e s t performed at a r e l a t i v e d e n s i t y of 39.9% i s s l i g h t l y more d i l a t i v e than the t e s t at 38.7% r e l a t i v e d e n s i t y , probably due to i t s s l i g h t l y higher d e n s i t y .  (Seed  & Lee 1966, Castro 1969, Casagrande 1976, V a i d & Chern 1985). The i n c r e a s e d d i l a t i v e n e s s i s shown by the s l i g h t l y higher d e v i a t o r i c s t r e s s e s and lower  porewater p r e s s u r e s  induced.  R e s u l t s of the d e v i a t o r i c  s t r e s s and the excess  p r e s s u r e as a f u n c t i o n of a x i a l s t r a i n ,  porewater  for i n i t i a l  c o n f i n i n g pressures of 50, 200, and 500 kPa, are given i n F i g u r e s 4.2, 4.3, and 4.4 r e s p e c t i v e l y . A l l samples t e s t e d in monotonic compression,  r e g a r d l e s s of the c o e f f i c i e n t of  u n i f o r m i t y , e x h i b i t e d s t r a i n hardening behaviour.  The response  or d i l a t i v e  of a l l the samples was that of type  3, shown i n F i g u r e 2.1, i n that the samples at no time  Figure 4.2: Undrained monotonic i n i t i a l confining stress.  £  a  (V.)  compression r e s u l t s f o r 50 kPa  400  F i g u r e 4.4: Undrained monotonic i n i t i a l confining stress.  compression r e s u l t s f o r 500  kPa  44 experienced a l o s s of shear r e s i s t a n c e . I t was not p o s s i b l e to  e x p l o r e the region of c o n t r a c t i v e behaviour at other  r e l a t i v e d e n s i t i e s over the range of c o n f i n i n g p r e s s u r e s used, s i n c e specimens l o o s e r than a r e l a t i v e d e n s i t y of about 38 % c o u l d not be prepared by the s l u r r y  deposition  technique.  The d e v i a t o r i c  s t r e s s and the excess porewater  f u n c t i o n of a x i a l initial  strain  f o r the compression  pressure as a  test  f o r an  c o n f i n i n g p r e s s u r e of 50 kPa i s given i n F i g u r e 4.2.  The r e s u l t s show that an i n c r e a s e i n the c o e f f i c i e n t of u n i f o r m i t y causes the behaviour t o be l e s s d i l a t i v e . T h i s i s r e f l e c t e d by the f a c t that the w e l l graded sample s u s t a i n e d lower d e v i a t o r i c  s t r e s s e s and developed higher porewater  p r e s s u r e s than the uniform sample. T h i s r e l a t i o n s h i p can a l s o be observed f o r the compression kPa i n i t i a l  t e s t s at 200 and 500  c o n f i n i n g p r e s s u r e , F i g u r e s 4.3 and 4.4  respectively.  The s t r e s s paths f o r the monotonic compression 50 kPa i n i t i a l  loading f o r  c o n f i n i n g p r e s s u r e , p l o t t e d on the M o d i f i e d  Mohr diagram are given i n F i g u r e 4.5. As evidenced i n the deviatoric  s t r e s s and excess porewater  pressure vs a x i a l  s t r a i n p l o t , F i g u r e 4.2, the s t r e s s paths i n d i c a t e the s t r a i n hardening response, type 3, as shown i n F i g u r e 2.1.  100  6' 2c  90  H  80  70  = 50  kPa  Gradation  1  ,  D  r c  *  Gradation  2  ,  D  r c  0  Gradation  3  /  D  H  1  0  20  40  60  V (0^6 ) f  2  3  80  100  (kPa)  Figure 4.5: M o d i f i e d Mohr diagram f o r undrained monotonic compression at 50 kPa i n i t i a l c o n f i n i n g s t r e s s .  120  46 The  e f f e c t of the i n c r e a s i n g c o e f f i c i e n t of u n i f o r m i t y ,  c a u s i n g a l e s s d i l a t i v e tendency, can a l s o be seen i n t h i s F i g u r e . T h i s i s r e f l e c t e d by the w e l l graded sand g r e a t e r porewater pressure  than the uniform  developing  sand. T h i s i s  shown by the r e l a t i v e h o r i z o n t a l s h i f t s of the e f f e c t i v e s t r e s s paths from the d r a i n e d  l o a d i n g c o n d i t i o n . The  M o d i f i e d Mohr diagrams f o r the monotonic compression t e s t s at i n i t i a l c o n f i n i n g p r e s s u r e s  of 200 and 500 kPa, F i g u r e s  4.6 and 4.7 r e s p e c t i v e l y , show that t h i s t r e n d i s continued at higher  confining pressures,  i e . an i n c r e a s e i n the  c o e f f i c i e n t of u n i f o r m i t y causes the behaviour t o become less  The  dilative.  undrained  f r i c t i o n angle  to be constant  a t maximum o b l i q u i t y  i s found  at 37.2 ± 0.7 degrees r e g a r d l e s s of the  g r a d a t i o n as shown i n F i g u r e s 4.8, 4.9 and 4.10. The undrained  f r i c t i o n angle  at maximum o b l i q u i t y  i s a constant  f o r a given sand. (Seed & Lee 1967, Chern 1985). The d r a i n e d f r i c t i o n angle,  however, i s a f f e c t e d by the d i l a t a n c y of the  sand a t f a i l u r e , which i s c o n t r o l l e d by the l e v e l of c o n f i n i n g pressure  and r e l a t i v e d e n s i t y . (Lambe & Whitman  1 969) .  The  s t r e s s s t a t e at phase t r a n s f o r m a t i o n  f o r a l l monotonic  compression t e s t s performed, r e g a r d l e s s of r e l a t i v e d e n s i t y ,  Figure 4.6: M o d i f i e d Mohr diagram for undrained monotonic compression at 200 kPa i n i t i a l c o n f i n i n g s t r e s s .  500  1  / 2 ( a l ' * a 3 / ) (kPa)  F i g u r e 4.7: M o d i f i e d Mohr diagram f o r undrained monotonic compression at 500 kPa i n i t i a l c o n f i n i n g s t r e s s .  co  600  Gradation  0  2  200  400 V2W  600 / 1  *(J  / 3  )  (kPa)  Figure 4 . 9 : M o d i f i e d Mohr diagram f o r undrained compression f o r Gradation 2.  monotonic  500  0  200  400  600  V (CT ' 2  ure 4.10:  M o d i f i e d Mohr diagram  1  +  Cfj)  f o r undrained monotonic  800  (kPa) compression  for Gradation 3  52 i s shown i n F i g u r e 4.11. The data p o i n t s may be seen t o l i e on a s t r a i g h t  l i n e p a s s i n g through the o r i g i n . Hence the  f r i c t i o n angle m o b i l i z e d at phase t r a n s f o r m a t i o n constant  a t 32.9 degrees r e g a r d l e s s of g r a d a t i o n . T h i s would  have been expected full  particle  s i n c e the mineralogy  i s constant  over the  s i z e range. Negussey et a l (1986) determined  t h a t , f o r a given mineralogy, at  isa  the f r i c t i o n angle m o b i l i z e d  phase t r a n s f o r m a t i o n was independent of the p a r t i c l e  s i z e , c o n f i n i n g p r e s s u r e , porewater p r e s s u r e , and d e n s i t y . T h i s o b s e r v a t i o n can now be extended to i n c l u d e g r a d a t i o n .  4.1.2. Monotonic Extension  Results  Monotonic l o a d i n g t e s t s i n the extension mode on the 3 g r a d a t i o n s were performed f o r a constant  i n i t i a l confining  s t r e s s of 200 kPa. Comparative r e s u l t s at i d e n t i c a l density  relative  i n terms of the d e v i a t o r i c s t r e s s and excess  porewater pressure vs a x i a l s t r a i n and the s t r e s s paths on the M o d i f i e d Mohr diagram are given i n F i g u r e s 4.12, and 4.13 r e s p e c t i v e l y . The r e s u l t s ~ i n d i c a t e that as the c o e f f i c i e n t of u n i f o r m i t y i n c r e a s e s , the behaviour more d i l a t i v e under extension  becomes  l o a d i n g . T h i s i s r e f l e c t e d by  the f a c t that as the c o e f f i c i e n t of u n i f o r m i t y i n c r e a s e s , the sand s u s t a i n s higher d e v i a t o r i c s t r e s s e s as shown i n F i g u r e 4.12, and i t develops  lower porewater p r e s s u r e s as  es  150  E Q  (V.)  Figure 4.12: Undrained monotonic extension r e s u l t s for 200 i n i t i a l confining stress.  kPa  •160 -180  -  -200  -  -220 -240 H  CC =  200 k P a  A  Gradation  1  Drc =  36- 7  *  Gradation  2  Drc =  37- 9 V .  o  Gradation  3  Drc  -260  =  39-3  %  V.  100  200 1  /2(tf *<$ ) /  1  3  300  (kPa)  Figure 4.13: M o d i f i e d Mohr diagram f o r undrained monotonic extension f o r 200 kPa i n i t i a l c o n f i n i n g s t r e s s .  400  56 shown in F i g u r e s 4.12  and  4.13.  t r e n d i d e n t i f i e d when s i m i l a r  T h i s i s the r e v e r s e to the  samples are s u b j e c t to  compression l o a d i n g .  Gradation  1, the more uniform  behaviour.  The  response i s that of type 2, F i g u r e  l i m i t e d l i q u e f a c t i o n . The shear  sample, e x h i b i t s c o n t r a c t i v e  sample s u f f e r s a temporary l o s s of  r e s i s t a n c e which i s regained with f u r t h e r s t r a i n i n g .  Gradations  2 and  3, with c o e f f i c i e n t s of u n i f o r m i t y of 3 and  6 r e s p e c t i v e l y , on the other hand, show a s t r a i n response,  type  3, F i g u r e 2.1.  s t r e s s observed, axial  2.1,  s t r a i n , and  The  in F i g u r e 4.12, i n Gradation  hardening  p l a t e a u of d e v i a t o r i c i n Gradation  2 at 4.2  3 at 3.8  % axial strain is  caused by necking of the sample. T h i s necking  a l s o causes  the sharp t u r n around i n the s t r e s s paths i n F i g u r e Necking i n Gradation  1 occured  %  g r a d u a l l y , and  4.13.  i s shown by  the gradual change of the slope of the s t r e s s path a f t e r phase t r a n s f o r m a t i o n  The  state in Figure  the  4.13.  f r i c t i o n angle m o b i l i z e d at phase t r a n s f o r m a t i o n , under  extension l o a d i n g i s 32.9  degrees. Thus, t h i s angle  i s the  same under compression and e x t e n s i o n l o a d i n g . T h i s was observed  by Chern (1985) and Chung (1985) f o r other  also  sands.  I n i t i a l c o n d i t i o n s which give r i s e to a d i l a t i v e  response  under monotonic l o a d i n g , can  mobility  under c y c l i c  develop only c y c l i c  l o a d i n g . I f a c o n t r a c t i v e response i s  under monotonic l o a d i n g , c y c l i c  l o a d i n g can  give r i s e  l i q u e f a c t i o n , l i m i t e d l i q u e f a c t i o n , or c y c l i c Contractive  response was  under extension  obtained  obtained to  mobility.  only with Gradation  1  l o a d i n g at r e l a t i v e d e n s i t i e s of l e s s than  about 48 %. f o r the s e l e c t e d i n i t i a l c o n f i n i n g pressure 200  of  kPa.  In e x t e n s i o n ,  provided  c o n t r a c t i v e response ensues,  s t r e n g t h at phase t r a n s f o r m a t i o n , initial  r e l a t i v e density, D^,  S , p T  i s a f u n c t i o n of  as w e l l as the  density a f t e r consolidation, D  rc  the  relative  • (Chung 1985).  Consequently, f u r t h e r t e s t s were performed on Gradation under monotonic extension  l o a d i n g to determine  r e l a t i o n s h i p between D^,  D ,  rational respect  rc  and  S  p T  i n t e r p r e t a t i o n of the c y c l i c  the  to a s s i s t  in a  loading r e s u l t s in  of the mechanism of s t r a i n development.  Extension  t e s t s were performed on  samples f o r a constant  initial  c o n f i n i n g s t r e s s of 200  kPa,  density  before  c o n s o l i d a t i o n , D ^,  Figure  4.14  r  1  with the r e l a t i v e  v a r y i n g between 16.3  and  47.8  shows the s t r e s s paths on a M o d i f i e d Mohr  diagram f o r 2 of these t e s t s , f o r a constant  initial  %.  58 c o n f i n i n g s t r e s s of of 200  kPa.  The angle  of  f r i c t i o n m o b i l i z e d at phase t r a n s f o r m a t i o n a constant The  of 32.9  internal  can  be seen to be  degrees r e g a r d l e s s of r e l a t i v e  density.  r e l a t i v e d e n s i t y , however, governs the s t r e n g t h at phase  transformation.  The  angle  of i n t e r n a l f r i c t i o n m o b i l i z e d at the  S t r e s s R a t i o i s a l s o a constant  at  17.8  degrees,  of the r e l a t i v e d e n s i t y , as shown i n F i g u r e  The  r e l a t i o n s h i p between S , p T  F i g u r e 4.15.  The  = 34.5  r  was  c a r r i e d out and  As D  rc  and/or D ^  i s given in  r c  and  r c  regardless  4.14.  S  %. For a d d i t i o n a l i ' s » D  r  was  fc  one  test  the r e l a t i o n s h i p s were assumed p a r a l l e l .  i n c r e a s e s , the s t r e n g t h at phase  r  S , p T  increases.  4.1.3. Review of Monotonic Test  The  and D  r e l a t i o n s h i p between D  determined at D ^  transformation,  D^,  Critical  Results  e f f e c t i v e s t r e s s paths on a M o d i f i e d Mohr diagram f o r  the monotonic compression and extension ± 1.5  % and  f o r 200  in F i g u r e 4.16.  kPa  initial  t e s t s at D  f c  =  38.5  c o n f i n i n g pressure are shown  Under compression l o a d i n g , the w e l l graded  sand i s more c o n t r a c t i v e than the uniform  sand, as i t  develops higher porewater p r e s s u r e s . T h i s appears to be i n  *  D j = 47-8 7. r  I  0  I  40  , D  I  rc  = 52-3  V.  I  80  1  1  120  v (cr; • cr;) 2  1  1  160  1  1  200  !  —f—  240  (kPa)  Figure 4.14: M o d i f i e d Mohr diagram f o r undrained monotonic extension for Gradation 1 at 200 kPa i n i t i a l c o n f i n i n g s t r e s s .  vo  60  Figure 4.15: R e l a t i o n s h i p between i n i t i a l r e l a t i v e d e n s i t y , r e l a t i v e d e n s i t y a f t e r c o n s o l i d a t i o n and the strength at phase t r a n s f o r m a t i o n .  0  200  *  Gradation  2  °  Gradation  3  400 V2(0 *0 ) , / 1  /  3  (kPa)  Figure 4.16: M o d i f i e d Mohr diagram f o r monotonic e x t e n s i o n and compression l o a d i n g f o r 200 kPa i n i t i a l c o n f i n i n g s t r e s s .  600  62 conformity  with c o n s o l i d a t i o n t e s t r e s u l t s , F i g u r e  3.3, that  show that the w e l l graded sand i s more compressible than the uniform sand under h y d r o s t a t i c paths i n F i g u r e pressure loading  l o a d . The e f f e c t i v e s t r e s s  4.16 show that the r e l a t i v e porewater  development of the 3 gradations i s reversed  under e x t e n s i o n  under compression  l o a d i n g . Thus, r e l a t i v e  shear-induced c o m p r e s s i b i l i t i e s under monotonic l o a d i n g are not constant loading,  4.2.  extension.  BEHAVIOUR  l o a d i n g t e s t s were performed on i s o t r o p i c a l l y  consolidated 3 c  sand but a f u n c t i o n of the type of  i e . compression or  CYCLIC LOADING  Cyclic  a ',  f o r a given  samples a t a constant  of 200 kPa. The c y c l i c  initial  confining stress,  stress ratio  /a  3 c  ' ) , and  r e l a t i v e d e n s i t y were the v a r i a b l e s . The r e s u l t s are presented i n the p l o t s of r e l a t i v e d e n s i t y a g a i n s t  the no.  of c y c l e s to l i q u e f a c t i o n (or l i m i t e d l i q u e f a c t i o n ) or 2.5 % axial strain 4.17,  f o r constant  cyclic  4.18, and 4.19, G r a d a t i o n s  For gradations  stress r a t i o s in Figures 1, 2, and 3 r e s p e c t i v e l y .  2 and 3, a l l samples achieved  2.5 % a x i a l  s t r a i n through c y c l i c m o b i l i t y , f o l l o w i n g f i r s t  realization  of a s t a t e of t r a n s i e n t zero e f f e c t i v e s t r e s s . For the same initial  d e n s i t y and s t r e s s s t a t e s , the behaviour of  —i  r  1  Gradation 1 ^cy/oVc 20  °  0-124  *  0135  D  0-H8  A  0190  40 *  0-230  60  80  62c = 200 k P a  Liquefaction 100  I 2  4  6  o  10  No. of Cycles to Liquefaction  20  or  40  60  80  100  2-5% Axial Strain  F i g u r e 4.17: R e l a t i o n s h i p between r e l a t i v e d e n s i t y and no. of c y c l e s t o l i q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c s t r e s s r a t i o s f o r Gradation 1.  80  No. of Cycles to Liquefaction  100  or 2-5% Axial Strain  Figure 4.18: R e l a t i o n s h i p between r e l a t i v e d e n s i t y and no. of c y c l e s to l i q u e f a c t i o n or 2.5 % a x i a l s t r a i n at constant c y c l i c s t r e s s r a t i o s f o r Gradation 2.  i  r  Gradation 3 20  AO  £cy/03c 0-136  0  "  0H8  °  0-163 0-213  A  60  80 tf ' 3  100  200 kPa  z c  l 2  X  4  No. of Cycles  6  to  8  10  20  40  60  80 100  Liquefaction or 2-5% Axial Strain  Figure 4.19: Relationship between r e l a t i v e density and no. of cycles to liquefaction or 2.5 & axial strain at constant c y c l i c stress ratios for Gradation 3.  01  66  Gradations extension  2 and  3 under monotonic l o a d i n g was  d i l a t i v e in  and compression, t h e r e f o r e 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 ) under c y c l i c range c o u l d not  l o a d i n g in t h i s s t r e s s  occur.  Under monotonic extension  l o a d i n g , Gradation  1  was  c o n t r a c t i v e over a range of r e l a t i v e d e n s i t i e s f o r the s e l e c t e d 200 cyclic  kPa  initial  confining pressure.  l o a d i n g , Gradation  Thus under  1 can develop d i l a t i v e  or  c o n t r a c t i v e behaviour. C o n t r a c t i v e behaviour under c y c l i c l o a d i n g was  developed i f the 3 requirements l i s t e d i n  S e c t i o n 2.4  were met,  i e . the i n i t i a l  s t a t e would l e a d to  c o n t r a c t i v e behaviour under monotonic l o a d i n g , the s t r e s s was  shear  greater than the s t r e n g t h at phase  transformation, samples that met  and  there were s u f f i c i e n t c y c l e s . Those  these requirements, i e . developed  l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n , are marked by an in F i g u r e D  r  4.17.  'L'  If l i q u e f a c t i o n occured, the r e l a t i o n s h i p i n  vs l o g N space, f o r a f i x e d c y c l i c  stress ratio, i s  approximately l i n e a r . T h i s r e l a t i o n s h i p i s e x h i b i t e d by t e s t s at c y c l i c F i g u r e 4.17. by Castro  s t r e s s r a t i o s of 0.124, 0.135  and  0.148, in  T h i s behaviour i s s i m i l a r to o b s e r v a t i o n s  (1982) and V a i d & Chern  As the r e l a t i v e d e n s i t y  made  (1983).  i n c r e a s e s , the shear s t r e n g t h at  67 phase t r a n s f o r m a t i o n , cyclic  s  p » T  i n c r e a s e s . Consequently,  shear s t r e s s r e q u i r e d to i n i t i a t e  deformation a l s o i n c r e a s e s . Therefore density  increased,  d i l a t i v e behaviour i n c r e a s e d , and  contractive  as the  the range of i n i t i a l  the  relative  s t r e s s states for  the response of the  sand  t e s t e d changed from l i q u e f a c t i o n to c y c l i c m o b i l i t y . When l i q u e f a c t i o n occured, i t was phase i n a l l cases.  initiated  Gradation  i n the  1 portrayed  behaviour under monotonic extension  i n the extension  A comparison of the loading  i s given  contractive  o n l y . Consequently,  p o t e n t i a l f o r l i q u e f a c t i o n under c y c l i c s t r e s s range was  loading  in t h i s  r e s i s t a n c e of the 3 g r a d a t i o n s  i n F i g u r e 4.20.  The  to  cyclic  data i s presented i n  s t r e s s r a t i o r e q u i r e d to  l i q u e f a c t i o n or 2.5  % axial strain  induce  i n 10 s t r e s s c y c l e s f o r a  range of r e l a t i v e d e n s i t i e s . From F i g u r e  4.20,  certain  trends  can  At low  r e l a t i v e d e n s i t i e s , ( l e s s than about 45 % ) , the  identified.  uniform sand, Gradation cyclic  loading. This  Gradation  1 was  1, has  i s the  increase may  the l e a s t r e s i s t a n c e  be  to  range of d e n s i t i e s over which  c o n t r a c t i v e under extension  r e s i s t a n c e i n c r e a s e s as the The  the  phase.  terms of the c y c l i c  be  extension  loading.  The  sand becomes more w e l l graded.  r e l a t e d to both improved g r a d a t i o n ,  as  0.25 0.24  N = 10  0.23  A  Gradation  1  x  Gradation  2  o  Gradation  3  0.22 0.21 0.2 ^0.19  03 E  a  C  = 200 k P a = 2-5  %  "^0.18 o  I°  0.17 0.16 0.15 0.14 0.13 0.12 0.11  Liquefaction  ~T~  0.1 20  40  60  D  r c  (°/o  F i g u r e 4 . 2 0 : L i q u e f a c t i o n r e s i s t a n c e curves for N=10.  80  69 w e l l as the change i n the mechanism of deformation from liquefaction  The  to c y c l i c m o b i l i t y .  c y c l i c s t r e n g t h of every sand i n c r e a s e s with  r e l a t i v e d e n s i t y . As the c o e f f i c i e n t  of  uniformity  i n c r e a s e s , l e s s b e n e f i t appears to be d e r i v e d i n c r e a s i n g the r e l a t i v e d e n s i t y ,  i e . less  gained.  slopes of the  cyclic  T h i s i s evident  from the  increasing  from  strength i s l i n e s in  s t r e s s r a t i o - r e l a t i v e d e n s i t y space. ( F i g u r e 4.20).  T h i s trend causes the r e l a t i v e  strengths  of the  gradations  to be reversed at high r e l a t i v e d e n s i t i e s , (greater than about 60 % ) , with the w e l l graded sand s u s t a i n i n g a lower cyclic  s t r e s s r a t i o than the uniform  relative  sand at the same  density.  These r e s u l t s (1974), who  are g e n e r a l l y supported by those of Wong et a l  showed that at a r e l a t i v e d e n s i t y of 60 %, a  w e l l graded sand r e q u i r e d a smaller c y c l i c d e v i a t o r than a uniform  m a t e r i a l to develop 2.5  % axial  stress  strain  in  10  cycles.  The  b a s i s of the comparison of the undrained behaviour of  the 3 g r a d a t i o n s  of E a r l s Creek sand i s i d e n t i c a l  d e n s i t y . T h i s b a s i s , however, may satisfactory  due  not be  relative  completely  to the l a r g e range i n a b s o l u t e  density.  The  70 stress-deformation  and  shear s t r e n g t h are not only a f f e c t e d  by the r e l a t i v e d e n s i t y , but a l s o by the a b s o l u t e i e . the g r a i n s i z e d i s t r i b u t i o n , gradations  density,  (de Beer 1965). For  the 3  of E a r l s Creek sand t e s t e d , the l a r g e v a r i a t i o n  i n absolute  d e n s i t y between the gradations  preclude  i t s use  as a b a s i s of comparison. On  examination of F i g u r e 4.20,  can  (greater than about 60 % ) , an  be seen that at high D , r  it  attempt to compare the l i q u e f a c t i o n r e s i s t a n c e curves at an i d e n t i c a l absolute  d e n s i t y , however, would push the curves  f u r t h e r a p a r t . T h i s i s due sand, Gradation  1, has  the lowest a b s o l u t e  to the f a c t that the  the h i g h e s t c y c l i c  uniform  shear s t r e n g t h  d e n s i t y . Consequently, n o r m a l i z a t i o n  the l i q u e f a c t i o n r e s i s t a n c e curves with respect d e n s i t y would exaggerate the t r e n d already  to  but of  absolute  shown at  high  relative densities.  The  s t a t e parameter has  been proposed as an a l t e r n a t i v e  i n i t i a l parameter to r e l a t i v e d e n s i t y . The  s t a t e parameter  d e f i n e s the s t a t e of the sand as a f u n c t i o n of i t s p o s i t i o n r e l a t i v e to the steady s t a t e l i n e Jefferies  i n e-log p' space. (Been &  1985). However the s t a t e parameter i s not  i n extension  and  compression.  parameter i s only d e f i n e d  unique  (Chern 1985). A l s o the  state  f o r sands which e x h i b i t  c o n t r a c t i v e behaviour, as f o r d i l a t i v e behaviour, the  steady  s t a t e l i n e does not e x i s t . The  be  s t a t e parameter cannot  used here a s , f o r the s t r e s s range considered, gradations  that were t e s t e d , only Gradation  uniform sand, t e s t e d i n e x t e n s i o n ,  1, the more  exhibited contractive  behaviour. The s t r e s s range c o n s i d e r e d most a p p l i c a t i o n s .  of the 3  here i s r e l e v a n t  5. CONCLUSION  In order to determine the effect of the c o e f f i c i e n t of uniformity on the undrained behaviour of sand, undrained monotonic and c y c l i c t r i a x i a l tests were performed on 3 sands of varying straight line gradations,  with i d e n t i c a l  mineralogy and i d e n t i c a l Dgg. Monotonic tests in compression and extension D  rc'  a n c  ^ "it*  1  were performed at constant r e l a t i v e density, i n i t i a l confining stresses varying up to 500  kPa. Undrained c y c l i c tests were performed from a constant isotropic e f f e c t i v e confining stress of 200 kPa, with varying r e l a t i v e density and c y c l i c stress r a t i o s . A l l the samples that were tested, were i s o t r o p i c a l l y Based on the test r e s u l t s , several conclusions  consolidated. can be drawn.  Under monotonic compression loading, the sand becomes less d i l a t i v e as the c o e f f i c i e n t of uniformity  increases, i e . as  the sample becomes more well graded. The compressibility of the sand increasing with gradation  i s also exhibited under  hydrostatic loading during consolidation. Under monotonic extension  , the opposite  trend i s observed, with the sand  becoming more d i l a t i v e as the gradation  increases. Thus, the  r e l a t i v e shear-induced compressibilities are a function of the undrained stress path.  72  73 Under c y c l i c  l o a d i n g , at low r e l a t i v e d e n s i t i e s , ( l e s s than  about 45 % ) , i n c r e a s e d c y c l i c  strength  i s obtained by  i n c r e a s i n g the c o e f f i c i e n t of u n i f o r m i t y . C y c l i c induced  loading  l i q u e f a c t i o n or l i m i t e d l i q u e f a c t i o n i n the uniform  sample, while  the deformation i n the more w e l l graded  samples accumulated by c y c l i c m o b i l i t y .  Increasing  the r e l a t i v e d e n s i t y causes a g r e a t e r  s t r e n g t h i n c r e a s e i n the more uniform  cyclic  samples. Thus at high  r e l a t i v e d e n s i t i e s , (greater than about 60 % ) , the w e l l graded samples show g r e a t e r p r o p e n s i t y  towards deformation  accumulation. At these h i g h r e l a t i v e d e n s i t i e s the deformation was caused by c y c l i c m o b i l i t y .  At low r e l a t i v e d e n s i t i e s , the uniformly found t o have a much lower c y c l i c  r e s i s t a n c e than the w e l l  graded sand. When compared a t low c y c l i c equivalent be  strength  r e l a t i v e d e n s i t y s t a t e s f o r the uniform  15 t o 20 % g r e a t e r  For uniform  graded sand was  levels, sand can  than f o r the w e l l graded sand.  sand, l i q u e f a c t i o n was experienced  over a range  of r e l a t i v e d e n s i t i e s , from the l o o s e s t s t a t e at 33 % to 43 % r e l a t i v e d e n s i t y . The more w e l l graded sands, even a t t h e i r l o o s e s t r e l a t i v e d e n s i t y s t a t e s , (approximately experienced  c y c l i c m o b i l i t y . T h i s i m p l i e s t h a t , at low  23 % ) ,  74  r e l a t i v e d e n s i t i e s , g r a d a t i o n might c o n t r o l the occurrence of  The  liquefaction.  e f f e c t i v e n e s s of f i e l d d e n s i f i c a t i o n  i s dependent on the  g r a d a t i o n of the sand at low r e l a t i v e d e n s i t i e s . The c y c l i c shear s t r e n g t h of a uniform  sand i s g r e a t l y improved by an  i n c r e a s e i n r e l a t i v e d e n s i t y . For a w e l l graded sand, similar  i n c r e a s e s i n r e l a t i v e d e n s i t y w i l l cause much  smaller c y c l i c  shear s t r e n g t h  increases.  At high r e l a t i v e d e n s i t i e s , there cyclic  i s not much improvement i n  shear s t r e n g t h with g r a d a t i o n . Consequently, the  e f f e c t of g r a d a t i o n on the undrained  response may not be  s i g n i f i c a n t a t high r e l a t i v e d e n s i t i e s .  REFERENCES  1.  B e e n , K. and J e f f e r i e s , M.G., ( 1 9 8 5 ) . "A S t a t e P a r a m e t e r f o r S a n d s , " G 6 o t e c h n i q u e , V o l . 35, No. 2, 1985, pp. 99-122.  2.  B i s h o p , A.W. and H e n k e l , D . J . , ( 1 9 6 2 ) . "The T e s t , " Edward A r n o l d L t d . , L o n d o n , 1962.  3.  C a s a g r a n d e , A., ( 1 9 7 6 ) . " L i q u e f a c t i o n and C y c l i c D e f o r m a t i o n of Sands, A C r i t i c a l Review," H a r v a r d S o i l M e c h a n i c s S e r i e s No. 88, H a r v a r d U n i v e r s i t y , C a m b r i d g e , M a s s . , 1976.  4.  C a s t r o , G., ( 1 9 6 9 ) . " L i q u e f a c t i o n o f S a n d s , " H a r v a r d S o i l M e c h a n i c s S e r i e s No. 8 1 , H a r v a r d U n i v e r s i t y , C a m b r i d g e , M a s s . , 1969.  5.  C a s t r o , G., ( 1 9 7 5 ) . " 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 S a t u r a t e d Sands," J o u r n a l of the G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 1, GT6, 1975, pp. 551-569.  6.  C a s t r o , G. and P o u l o s , S . J . , ( 1 9 7 7 ) . " F a c t o r s A f f e c t i n g 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 , " J o u r n a l o f t h e G e o t e c h n i c a l E n g i n e e r i n g D i v i s i o n , ASCE, V o l . 103, No. GT6, P r o c . P a p e r 12994, J u n e , 1977, pp. 501-516.  7.  C a s t r o , G., P o u l o s , S . J . , F r a n c e , J.W. and E n o s , J . L . , ( 1 9 8 2 ) . " L i q u e f a c t i o n I n d u c e d by C y c l i c L o a d i n g , " R e p o r t S u b m i t t e d t o N a t i o n a l S c i e n c e F o u n d a t i o n , M a r c h , 1982.  8.  C h a n g , N.-Y., Y e h , S.-T., K a u f m a n , L.P., ( 1 9 8 2 ) . " L i q u e f a c t i o n P o t e n t i a l o f C l e a n and Sands," P r o c . 3rd M i c r o z o n a t i o n C o n f e r e n c e , 1982, pp. 1017-1032.  9.  Triaxial  of  Silty Seattle,  C h e r n , J . C , ( 1 9 8 1 ) . " E f f e c t o f S t a t i c S h e a r on R e s i s t a n c e t o L i q u e f a c t i o n , " M.A.Sc. T h e s i s , The U n i v e r s i t y of B r i t i s h C o l u m b i a , V a n c o u v e r , C a n a d a .  10. C h e r n , J . C , ( 1 9 8 5 ) . " U n d r a i n e d R e s p o n s e o f S a t u r a t e d S a n d s w i t h E m p h a s i s on 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 , " Ph.D. T h e s i s , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , Vancouver, Canada. 11. C h u n g , E.K.F., ( 1 9 8 5 ) . " E f f e c t s o f S t r e s s P a t h and P r e s t r a i n H i s t o r y on t h e U n d r a i n e d M o n o t o n i c and C y c l i c L o a d i n g B e h a v i o u r o f S a t u r a t e d S a n d , " M.A.Sc. T h e s i s , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , C a n a d a . 75  76 12. de Beer, E., (1965). " I n f l u e n c e of the Mean Normal S t r e s s on the Shearing S t r e n g t h of Sand," Proc. 6th I n t e r n a t i o n a l Conference on S o i l Mechanics and Foundation E n g i n e e r i n g , Montreal, 1965, pp. 165-169. 13. Frydman, S., Z e i t l e n , J.G. and Alpan, I . , (1973). "The Membrane E f f e c t i n T r i a x i a l T e s t i n g of Granular S o i l s , " J o u r n a l of T e s t i n g and E v a l u a t i o n , V o l . 1, No. 1, Jan. 1973, pp 37-41. 14. G e o t e c h n i c a l Engineers Inc., (1982). " L i q u e f a c t i o n Induced by C y c l i c Loading," Report submitted to the N a t i o n a l Science Foundation, Washington, DC, March 1982. 15. Hobbs, W.H., York, N.Y.,  (1907). "Earthquakes," D. Appleton Co., 1907.  New  16. I s h i h a r a , K., Tatsuoka, F. and Yasuda, S., (1975). "Undrained Deformation and L i q u e f a c t i o n of Sand Under C y c l i c S t r e s s e s , " S o i l s and Foundations, V o l . 15, No. 1, 1975, pp. 29-44. 17. K e u r b i s , R.H., (1987). "The E f f e c t of Gradation and F i n e s Content on the Undrained Response of Sand," M.A.Sc. T h e s i s i n p r o g r e s s , The U n i v e r s i t y of B r i t i s h Columbia, Vancouver, Canada. 18. Lambe, T.W., (1951). 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C , (1985). " C y c l i c and Monotonic Undrained Response of S a t u r a t e d Sands," Session No. 52, Advances i n the A r t of T e s t i n g S o i l s Under C y c l i c C o n d i t i o n s , Annual Convention and E x p o s i t i o n , D e t r o i t , Michigan, 1985. 32. Wijewickreme, D., (1986). "Constant Volume F r i c t i o n Angle of Granular M a t e r i a l s , " M.A.Sc. T h e s i s , The U n i v e r s i t y of B r i t i s h Columbia, Vancouver, Canada.  Wong, R.T., Seed, H.B. and Chan, C.K., (1974). " L i q u e f a c t i o n of G r a v e l l y S o i l s Under C y c l i c Loading C o n d i t i o n s , " Earthquake E n g i n e e r i n g Research Centre, Report No. 74-11, 1974, U n i v e r s i t y of C a l i f o r n i a , Berkeley, 18 pp.  

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