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Effective stress paths in a sensitive clay Byrne, Peter Michael 1966

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EFFECTIVE STRESS PATHS IN A. SENSITIVE CLAY by PETER MICHAEL BYRNE . E., University College Dublin, Ireland, 1959  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M. A. Sc. in the Department of C i v i l Engineering  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1966  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  f u l f i l m e n t of  requirements . f o r an advanced degree at the U n i v e r s i t y of Columbia, for  I agree t h a t the L i b r a r y  r e f e r e n c e and s t u d y .  s h a l l make i t  freely  the  British available  I f u r t h e r agree t h a t p e r m i s s i o n f o r  ex-  t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s  representatives.  understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r cial  is  finan-  g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . "  Department of  C/i//'/  tr/?j//2 itcrjrtty  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date  It  TsVvy  y  ii  ABSTRACT Results of drained and  undrained t r i a x i a l compressions tests,  on a sensitive clay are presented i n t h i s t h e s i s .  Contours of  water content from both drained and undrained tests are compared, and  i t appears that f o r the clay tested, there i s not a unique  relationship between e f f e c t i v e stresses and water content as found by Rendulic and Henkel for remolded s o i l .  The Roscoe concept of a  state boundary surface, which i s similar to the Rendulic concept is examined, and  i t also does not hold for the clay tested.  The Roscoe energy equation is applied to the results of a l l tests and  i t appears to hold quite w e l l .  It indicates that for  a s o i l which i s y i e l d i n g there i s only one fundamental parameter, M, which i s independent of both s t r a i n and  strength s t r a i n rate.  Methods of predicting s t r e s s - s t r a i n relationships are examined. The Roscoe method, which i s based on the existence of a state boundary surface  is not s t r i c t l y applicable, but does y i e l d r e s u l t s  which are of the same order as the measured r e l a t i o n s h i p s .  The  Landanyi method does not appear to apply to the clay tested. A method f o r predicting residual pore pressures and b i l i t y i n drained t r i a x i a l tests i s derived.  or permea-  This enabled a l -  lowances to be made f o r the e f f e c t of residual pore pressures i n drained t e s t s .  However, i t is f e l t that the method may  have more  application i n the examination of s o i l structure, since a comparison of the permeability  of samples at the same void r a t i o and  temperature yields a measure of s t r u c t u r a l difference.  TABLE OF CONTENTS  CHAPTER  1  INTRODUCTION  1.1  Purpose  1.2  Scope  2  REVIEW OF LITERATURE  2.1  Review of Literature  2.2  Discussion  CHAPTER  3  MACROSCOPIC COMPONENTS OF SHEAR STRENGTH  CHAPTER  If  TESTING PROCEDURES  ^.1  Description of s o i l tested  h.2  F i e l d sampling and storing of block sampl  *f.3  Description of test equipment  k,h  Testing technique  5  DISCUSSION OF TESTING TECHNIQUE  5.1  Introduction  5.2  Non-uniform stress and s t r a i n  5.3  Non-uniform pore pressures i n undrained tests  5.^  Residual pore pressures i n drained tests  5.5  Pore pressure measuring devices  5.6  Rate of testing  5.7  Pore pressures resulting from secondaryeffects  5.8  Membrane leakage  5.9  Ram F r i c t i o n  6  RESIDUAL PORE PRESSURES IN DRAINED TESTS  6.1  Introduction  CHAPTER  CHAPTER  CHAPTER  iv  PAGE CHAPTER  CHAPTER  6.2  Method 1  75  6.3  Method 2  76  7  TEST RESULTS  85  Introduction  85  7.1  CHAPTER  7.2  Characteristics of Haney clay  86  7.3  Comparison of contours of water content from drained and undrained tests  96  7<M-  Energy corrections  107  7.5  Examination of methods f o r predicting s t r e s s - s t r a i n relations  115  7.6  E f f e c t of s t r a i n rate on drained tests  122  8  CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH  125  8.1  Conclusions  125  8.2  Suggestions f o r further research  126  LIST OF SYMBOLS  128  LIST OF REFERENCES  131  APPENDIX I  135  APPENDIX II  lh2  V  LIST OF TABLES PAGE TABLE  I  PHYSICAL PROPERTIES OF HANEY CLAY  31  TABLE II  CHEMICAL PROPERTIES OF HANEY CLAY  3«f  vi  LIST OF FIGURES Figure 1.  Page Rendulic Graphical Representation of Stresses in T r i a x i a l Tests  5  2.  Contours of Water Content f o r Normally Consolidated London Clay  8  3.  Stress Water Content Relations f o r Normally Consolidated Weald Clay  10  Roscoe et a l . Y i e l d Surface  12  5.  Roscoe et a l . energy balance  16  6.  Method of Determining Stress-Strain Relationships f o r Kaolin  18  7.  Strength Parameters  26  8.  Grain Size D i s t r i b u t i o n Curve f o r Haney Clay  32  9.  Standard Consolidation curve f o r Haney Clay  33  10.  Block Samples of Haney Clay at Site  36  11.  T r i a x i a l C e l l and Chamber Pressure System  37  12.  Drainage and Pore Pressure Measuring System  38  13.  Test Equipment  39  Ik-.  Sample Trimming Equipment  ^8  15.  Sample i n Place on T r i a x i a l Base  *+8  16.  Sample During Shear  17.  Build-Up i n Pore Pressure A f t e r Consolidation Haney Clay  69  I l l u s t r a t i o n of Method f o r Determining Rate During Shearing  79  18.  " 53  Drainage  19.  Relationship Between Void Ratio and Permeability During Drained Shearing of Haney Clay  80  20.  Relationship Between Measured Residual Pore Pressure and Shear S t r a i n i n Drained Tests  82  21.  Comparison of Measured and Calculated Residual Pore Pressures i n Drained Tests  82  Relationship Between Water Content and Logarithm of Isotropic Consolidation Pressure, Haney Clay Relationship Between Undrained Strength and Isotropic Consolidation Pressure, Haney Clay Stress-Strain Relationships f o r Undrained Tests on Haney Clay P r i n c i p a l Stress Ratio Versus S t r a i n f o r Undrained Tests on Haney Clay Relationship Between Pore Pressure and S t r a i n for Undrained Tests on Haney Clay Pore Pressure Parameter A. Versus S t r a i n f o r Haney Clay S'tress-Strain Relationships f o r Drained Tests on Haney Clay Calculated Residual Pore Pressure Vs. S t r a i n for Consolidated Drained Tests on Haney Clay E f f e c t of Residual Excess Pore Pressure on the P r i n c i p a l Stress Ratio Vs. Shear S t r a i n Relation, Test S-13 Relationships Between P r i n c i p a l Stress Ratio and S t r a i n from Drained Tests on Haney Clay Comparison of P r i n c i p a l Stress Ratio Vs. S t r a i n Relationships from Drained and Undrained Tests on Haney Clay Comparison of Contours of Water Content from Drained and Undrained Tests on Haney Clay E f f e c t i v e Stress Paths from Consolidated Undrained Tests on Haney Clay E f f e c t i v e Stress Paths and Contours of Water Content from Drained Tests State Boundary Surface from Undrained Tests on Haney Clay (Burland Plot) State Boundary Surface from Drained Tests on Haney Clay (Burland Plot)  viii  Figure 38.  Page Comparison of State Boundary Surfaces from Drained and Undrained Tests on Haney Clay  106  39•  Relationships Between Mean Normal Stress and Water Content f o r Haney Clay  109  ^0.  Corrected and Uncorrected Stress Paths from Undrained Tests on Haney Clay (Roscoe et a l . Energy Eq.)  Ill  hi.  Corrected and Uncorrected Stress Paths from Drained Tests on Haney Clay (Roscoe et a l . Energy Eq.)  112  h2.  Roscoe M Parameter Versus S t r a i n , Haney Clay  113  ^3.  Contours of Water Content and S t r a i n from Undrained Tests on Haney Clay  117  Comparison of Measured and Calculated StressS t r a i n Relations f o r Drained Tests on Haney Clay  119  1+5.  Comparison of Theoretical and Experimental State Boundary Surfaces (Burland Plot)  121  ^6.  E f f e c t of S t r a i n Rate on the S t r e s s - s t r a i n Relations f o r Drained Tests on Haney Clay  123  U-7.  E f f e c t of S t r a i n Rate on the P r i n c i p a l Stress Ratio Vs. S t r a i n Relations f o r Drained Tests on Haney Clay  12*f  E f f e c t of S t r a i n Rate on the Water Content Vs. S t r a i n Relations f o r Drained Tests on Haney Clay.  12h  h9.  Diagrams Showing Assumptions of Method 1  136  50.  S t r e s s - S t r a i n Characteristics of Haney Clay  138  51.  Relationship Between C o e f f i c i e n t of Consolidation and E f f e c t i v e Stress f o r Haney Clay  IkO  hh.  h8.  ix  ACKNOWLEDGEMENT The  investigation reported herein has been supported by-  funds provided by the National Research Council of Canada. funds also included f i n a n c i a l support f o r the writer.  These  Grateful  appreciation is expressed f o r t h i s assistance without which the graduate studies and t h i s thesis could not have been accomplished. The writer wishes to express his thanks to Dr. W, D. Liam Finn and to Professor N. D. Nathan f o r their guidance and constructive c r i t i c i s m during the preparation of t h i s t h e s i s . Drained tests results were obtained whom the task of developing  by Mr. T. J . Hirst with  suitable test equipment was shared.  Dr. E. H. Gardner, Department of S o i l Science  kindly supplied  data on the chemical properties of the clay tested. The technical assistance supplied by the s t a f f of the C i v i l Engineer Department i s g r a t e f u l l y acknowledged.  1  CHAPTER 1 PURPOSE AND SCOPE 1.1  Purpose Rendulic (1936, 1937)  and Henkel (1958, 1959,  I960) have  shown that a unique relationship exists between e f f e c t i v e stresses and water content, or void r a t i o , for both drained and t r i a x i a l tests on saturated clay.  The  undrained  remolded i s o t r o p i c a l l y consolidated  prime purpose of t h i s testing program was  to determine  i f a s i m i l a r r e l a t i o n s h i p exists for a sensitive undisturbed clay. A secondary purpose was  to compare the behaviour of the clay with  that predicted by Roscoe and Schofield "Wet-Clay" and  (1963) for an idealized  i n p a r t i c u l a r to compare s t r e s s - s t r a i n r e l a t i o n s .  Most problems involving the design of earth structures  are  concerned with either s t a b i l i t y or settlement of a s o i l mass. s t a b i l i t y analysis, the structure sum  is analyzed to insure that  of t h e . r e s i s t i n g forces on any potential f a i l u r e surface  greater than the sum  of the driving forces.  It i s gen-  i n terms of ef-  is p r a c t i c a l l y independent of the type of t r i a x i a l  test performed, drained or undrained.  However, for sensitive  s o i l s there is some disagreement on t h i s . was  The  undertaken j o i n t l y by Mr. T. J . H i r s t and  testing program the writer.  Hirst  (1966) discusses the strength envelopes obtained from drained and  is  The r e s i s t i n g  tests on the s o i l .  e r a l l y agreed that f o r most s o i l s , the strength f e c t i v e stresses  the  No attempt i s made  to determine the magnitude of the deformations. forces are determined from strength  In  undrained t e s t s . Settlement analyses are concerned with the magnitude of  2  deformations.  For many structures, such as foundations, i t i s  important that these be l i m i t e d .  Deformations are caused by  volumetric strains due to changes i n void r a t i o and by shear strains due to distortion..  I f there i s a unique relationship  between stresses and water content or void r a t i o that i s independent of stress path, then the volumetric s t r a i n can be calculated f o r any stress path which l i e s between a drained and undrained path.  The shear s t r a i n s , however, are very much dependent on  stress path.  Poorooshasb and Roscoe (1963) determined a r e l a t i o n -  ship between volumetric and shear strains f o r normally loaded remolded clay and from t h e i r theory, i t i s possible to estimate the shear strains f o r any stress path,  A state boundary or y i e l d  surface i s a fundamental part of t h e i r theory and this only exists i f there i s a unique relationship between stresses and water content. It i s realized that s t r e s s - s t r a i n relations and contours of water content may be dependent on s t r a i n rate, therefore, drained and undrained tests were performed at the same rate.  Additional  drained tests were performed at slower rates which allowed the e f f e c t of s t r a i n rate on drained relations to be examined. 1.2  Scope A review of pertinent l i t e r a t u r e i s presented i n Chapter 2 .  A discussion of macroscopic components of shear resistance i s presented i n Chapter 3»  The clay tested, test equipment and  testing technique are discussed i n Chapters h and 5<> Residual pore pressures of some magnitude are always present i n drained tests.  A method f o r predicting these pore pressures i s presented  3  i n Chapter 6.  The results from drained and undrained  triaxial  compression  tests on Haney clay are presented and discussed i n  Chapter 7.  Conclusions and suggestions f o r further research are  presented i n Chapter  8.  CHAPTER 2 REVIEW OF LITERATURE 2.1  Review of L i t e r a t u r e Basic experimental relations  t i o n s , water  c o n t e n t , and pore-water  s o l i d a t e d c l a y s were f i r s t He  performed  tests  between t r i a x i a l  pressure f o r normally  e s t a b l i s h e d by R e n d u l i c  both d r a i n e d and undrained  on s a t u r a t e d remolded V i e n n a  stress condi-  compression  clay.  Test  con-  (1936, 1937). and e x t e n s i o n  specimens were  d r a i n e d by a c e n t r a l c o r e o f sand and mica m i x t u r e , and  pore-water  p r e s s u r e s were t h o s e e x i s t i n g  was made  i n the core.  No a l l o w a n c e  for  the effect  cal  s t r e s s , thus a t l a r g e s t r a i n s t h e v e r t i c a l s t r e s s e s a r e l i k e l y  to-be  o f t h e change i n c r o s s s e c t i o n a l a r e a on t h e v e r t i -  too high.  R e n d u l i c d e v i s e d a method f o r c o m p r e h e n s i v e  graphical representation of the state a triaxial test. <5~2 = 63 a n d (Jg  =  Consider Figure l a ; since i n the t r i a x i a l ^3? s t r e s s e s must p l o t  p l o t p o i n t s on t h i s must f i r s t  of s t r e s s f o r any stage i n  on t h e s h a d e d p l a n e .  plane the r a d i a l e f f e c t i v e  be m u l t i p l i e d b y >/2.  stress  test To  (O^ o r (3^)  Isotropic consolidation conditions  (O^ = CJ^ = O3) a r e r e p r e s e n t e d b y t h e s p a c e d i a g o n a l o r l i n e which  makes e q u a l a n g l e s w i t h t h e t h r e e a x e s .  t y p i c a l c o n s o l i d a t e d d r a i n e d and u n d r a i n e d plane.  Compression t e s t s  t e s t s below. and  the line  Plotted  l o a d e d c l a y , t h e pore also a line  tests  plotted  on t h i s  p l o t above t h e space d i a g o n a l , e x t e n s i o n  points represent d i f f e r e n t  j o i n i n g these  l o w e d i n a n y one t e s t .  F i g u r e l b shows  stages  i na test,  points represents the s t r e s s path  I n an undrained  fol-  t e s t on s a t u r a t e d n o r m a l l y  p r e s s u r e r i s e s and t h e s t r e s s path which i s  of constant water  content  i s some c u r v e a s i n d i c a t e d .  5  FAILURE ENVELOPE.  Fig. Ic  Fig. Id  Figure I - Pendulic Graphical Representation of Stresses in Trivial Tests  6  In a d r a i n e d t e s t the r a d i a l e f f e c t i v e and  thus the s t r e s s path i s a v e r t i c a l l i n e .  stress i s constant, Curves of constant  water content can a l s o be obtained from d r a i n e d t e s t s where volume changes d u r i n g s h e a r i n g have been r e c o r d e d . content are shown i n F i g u r e 1c.  The  Contours of water  l i n e A D which makes an  of 90 degrees w i t h the i s o t r o p i c c o n s o l i d a t i o n l i n e and  angle  a l l lines  p a r a l l e l to i t r e p r e s e n t s t r e s s paths along which the v a l u e of the f i r s t stant.  effective  stress  invariant  For l i n e a r l y e l a s t i c  ( j { = o]_ + O 2 + G 3 )  m a t e r i a l and  i s con-  f o r s m a l l s t r a i n s , J-|_  equal t o a c o n s t a n t , r e p r e s e n t s a constant volume c o n d i t i o n . i s seen t h a t f o r n o r m a l l y loaded c l a y a J-[ = constant would cause a volume  water content determined t h a t any  path  decrease.  R e n d u l i c found f a i r l y  concluded  stress  It  good agreement between contours  from d r a i n e d and  undrained  of  t e s t s , and  he  p o i n t i n the diagram r e p r e s e n t s a unique  r e l a t i o n between s t r e s s e s and water content t h a t i s  independent  of the s t r e s s path, provided the path does not cause a temporary decrease  i n water c o n t e n t .  I f the contours are g e o m e t r i c a l l y  s i m i l a r , they w i l l p l o t on a s i n g l e curve  on the u n i f i e d  Rendulic  diagram, F i g u r e Id, which i s obtained by d i v i d i n g (J^ and <J^ by 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 (5"'.  R e n d u l i c found  the  t h a t the  0  curves were approximately  geometrically similar.  Henkel (1958, 1959? I960) d e s c r i b e s r e s u l t s of a comprehensive s e r i e s of t r i a x i a l t e s t s on s a t u r a t e d remolded Weald and clayso  The  undrained and  London  s e r i e s included i s o t r o p i c a l l y consolidated drained  compression  and e x t e n s i o n t e s t s on both normally  o v e r c o n s o l i d a t e d samples.  A few  t e s t s were performed  and  loaded keeping  7  the mean e f f e c t i v e stress p' ( 1 / 3 J^) constant, and some samples of Weald clay were a n i s o t r o p i c a l l y consolidated. Henkel found that there was a unique relationship between e f f e c t i v e stresses and water content which was independent  of the stress path whether  the clay was 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, provided normally loaded and overconsolidated samples were considered separately.  Maximum p r i n c i p a l stress difference was considered  to be f a i l u r e and he found that the f a i l u r e envelope was independent of the stress path.  Contours of water content from drained  and undrained tests f o r normally consolidated London Clay are shown on the Rendulic diagram i n Figure 2 . I t i s seen that the contours are e s s e n t i a l l y independent  of the e f f e c t i v e stress path.  Thus from undrained tests alone, the water content and deviator stress at f a i l u r e f o r a drained test starting from a water content of 2 9 . 3 per cent and a consolidation pressure of 90 p . s . i . could be predicted to be 2 5 . 9 per cent and 82 p . s . i . respectively.  If  the average e f f e c t i v e stress, p', were kept constant, then s t a r t i n g from the same water content and pressure as before, the water content and deviator stress at f a i l u r e would be 27.h per cent and 62 p . s . i . respectively.  I t i s seen that J-[ constant does not  imply a zero volume change condition as i t does f o r linear e l a s t i c material and that change i n water content i s a function of both p' and the deviator stress q. Henkel  (I960) suggests  apply to undisturbed c l a y s .  that similar relationships may also However, f o r sensitive s o i l s i n which  structure i s an important factor and f o r clays i n which the secondary compression  i s large, he f e l t that the relationship between  6  Figure £ — Contours of Wafer Content for Normal]/ Consolidated London Cloy (After Henkel I9SO)  9  s t r e s s e s and water content might be more complex than t h a t gested f o r remolded  soils.  Whitman, Ladd and on s a t u r a t e d  P. da Cruz ( I 9 6 0 )  describe  a s e r i e s of t e s t s  remolded samples of backswamp c l a y from the  M i s s i s s i p p i River v a l l e y . consolidated  I t was  i s o t r o p i c a l l y and  lower  found that comparison of samples  a n i s o t r o p i c a l l y d i d not  produce a  unique r e l a t i o n s h i p between s t r e s s e s and water content as gested by Henkel.  For the same v o i d r a t i o , the  were 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 (CT^ - 0^)  .  The  sug-  had  the  sug-  samples which  higher  strength,  maximum p r i n c i p a l s t r e s s r a t i o appeared to be  the  same f o r b o t h . Henkel and  Sowa (1963) working w i t h a new  obtained r e s u l t s s i m i l a r to Whitman.  I t was  batch of Weald c l a y  found t h a t the water  content a f t e r c o n s o l i d a t i o n , whether the c o n s o l i d a t i o n was t r o p i c or a n i s o t r o p i c was in Figure  3«  The  a f u n c t i o n of p' o n l y .  s t r e s s paths f o l l o w e d  v o i d r a t i o are a l s o shown i n F i g u r e A n i s o t r o p i c a l l y consolidated d i f f e r e n t s t r e s s path and  envelope i s the  i s shown  f o r samples of the same  3 i n terms of p' and  q (CJ - (5" ). a  i t can be  seen that f o r the  same f o r both.  s t r e s s but  same v o i d that  the  They s t a t e that the  are q u i t e d i f f e r e n t from the data presented by Henkel ( I 9 6 0 ) e a r l i e r batch of weald c l a y using  results on  They c o n s i d e r  i s o t r o p i c continuum m a t e r i a l .  (C.V.R.) l i n e .  I t was  on  s o i l t o be an e l a s t o - p l a s t i c  Roscoe, S c h o f i e l d and Wroth (1958)  were p r i m a r i l y concerned w i t h the establishment of a c r i t i c a l ratio  an  s i m i l a r t e s t i n g techniques,  Roscoe et a l . have presented a number of papers s i n c e 1958 the y i e l d i n g of s o i l s .  r  samples are seen t o f o l l o w a markedly  r a t i o they have a higher maximum d e v i a t o r strength  This  iso-  suggested, however, t h a t f o r  void  saturated  10  0  Figure 3 —  e0  4-0 GO 80 IOO l£0 140 MEAN NORMAL EFFECTIVE STRESS, P' LBb./6<?.IN.  Stress Water Content Relations for Normally Consolidated WeqM Clqy (After Henkel ancj SouJ^lfifeS)  11  remolded clay tested under t r i a x i a l conditions, the envelope of a l l loading paths would form a unique surface i n space which could be expressed i n the form of an  equation:  w = f ( p , q) 1  where  w = water content f = function of p' = 1/3  «5[ + 2C3)  q = (C7]_ - (J3) This surface i s shown i n Figure ^f. is comprised of two parts. paths from a l l normally  corrected f o r boundary energy. It i s seen that the envelope  Part A i s a surface on which stress  loaded samples l i e throughout the  process whether drained or undrained.  shearing  Part B applies to over-  consolidated samples, and stress paths l i e on t h i s surface only at or near f a i l u r e .  Part A of the surface which i s the portion of  interest, suggests that there i s a unique r e l a t i o n between stresses and water content which is independent of the stress path, provided that a correction f o r boundary energy i s applied to the shear stress (C7-]_ - C3)  i n the case of drained tests to allow for the work done  i n changing volume. .The corrected deviator stress was following  where  given by the  equation:  = increment of volumetric  strain  = increment of major p r i n c i p a l s t r a i n Poorooshasb and Roscoe (1961) presented data for loaded  normally  i s o t r o p i c a l l y consolidated remolded samples of Weald clay  Undrained  P  a  t  h  —  ^  Surface. Common tb Both Drained and Undroiiied R»ths Drained Rsth Isotropic.  Consolidation  (Normally  Lo^deep  Plane o f Const, LU Overconsolidoted "Touch this  Samples  (Heavily)  Surface.  Fig.4a — Isometric View of Roicoe efal. Yield Surface. ln1crb<?ttion  o f Surface  B  uuifh U J Cons.t. Ptane. Intersection Ujiih  of  uj Const  (Normally  Surfqce. A. Plane  Consolidated  Undroined  Ptoth) Undrained Degrees  Fig. 4b—Constant UJ Plane.  Figure 4 — Roscoe etal. Yield Surface..  of  Te&ts> uiith Varying Overcons>o|idcfrion  13  which indicated that there was a unique r e l a t i o n between stresses and water content provided no boundary energy correction was plied to the shear stresses.  ap-  A two dimensional plot of the unique  surface was devised which allowed easy comparison of drained and undrained  tests.  Equation (1) above arises from the assumption  that a l l energy  transferred across the boundaries of the sample i s dissipated i n work done by the shear stresses. the case of a sand.  This may be reasonably true i n  However, i t i s l i k e l y that i n a clay, some  of t h i s energy w i l l be stored e l a s t i c a l l y (Hvorslev I960). Poorooshasb and Roscoe (1961) derived the following equation f o r the corrected deviator s t r e s s : ov  q  R  = «j[ - O 3 )  + (p»  -r ) - ^  (2)  where r i s a parameter expressing a measure of the energy stored. If r = p', then a l l the energy i s stored and q = (CJ^ - cj^). If r = 0, then no energy i s stored and q = (rj{ - a') +  .my 1  3 Sci,  which the authors f e e l should replace equation ( 1 ) .  It is sug-  gested, therefore, that f o r normally loaded clays a l l energy transferred across the boundary i s stored e l a s t i c a l l y and hence drained and undrained tests can be compared d i r e c t l y . Roscoe and Schofield ( 1 9 6 3 )  present a theory f o r the mechani-  c a l behaviour of an i d e a l continuum referred to as "Wet  Clay". The  following equation i s derived for the state boundary surface: q = *EL (F + A - K- e - l n p') A -Iv  (3)  where M,X  , K,T  are four  M = ratio  o f q and  r  = void  \  = s l o p e of e vs  soil  constants  p' a t  failure  r a t i o at f a i l u r e  1  f o r p' =  I n p' c u r v e f o r b o t h  isotropic  and  failure  conditions K = s l o p e of e vs  &V  I n p c u r v e f o r u n l o a d i n g and  = increment  of s h e a r  = increment  of v o l u m e t r i c  Equation 3 expresses stresses  and  A. new equation  void  energy  strain  the unique  ratio  reloading.  strain  r e l a t i o n s h i p between  or water  effective  content.  or work e q u a t i o n i s d e r i v e d which  supersedes  (2):  + qSe  P'SV  = 5$El  (if)  - —  + Mp'Se  1 + e The  terms used  have a l r e a d y b e e n d e s c r i b e d .  E q u a t i o n U- e x p r e s s e s of  a u n i t volume  the energy  of s o i l  tion  of a probing s t r e s s  hand  side  express  transferred  incrementSp', this  represents  the energy  stored  represents  the energy  dissipated  sumed t h a t  no  c a n be  E q u a t i o n *f c a n be  % - MPThis  means t h a t  test  the d e v i a t o r  stage  p' and The  and  by  the  the  q  terms  i s put.  by t h e s h e a r  stored  = , * p- §  stress  energy  elastically  r e w r i t t e n as  i f a t any  oq.  left  hand s i d e  a c r o s s the  subject to stresses  t o what use  energy  The  boundaries on  applica-  on t h e  The  term  term  right ^p 1 + e 1  Mp'S£  stresses.  shear  of  I t is as-  stresses.  follows:  - ^  |El  - -  i n a d r a i n e d or u n d r a i n e d  q i s corrected  f o r both energy  due  (5) triaxial to  15  volume change and energy stored e l a s t i c a l l y , the corrected q = q w i l l be on the f a i l u r e envelope q = Mp . 1  w  Figure 5 shows how these  corrections would be applied to both normally loaded drained and undrained t e s t s .  In an undrained test  = 0 and since Sp'  will  be negative because p' i s decreasing, the e l a s t i c energy correction w i l l add to the measured q.  In a drained test the energy  due to volume decrease w i l l add to the measured q while the energy absorbed e l a s t i c a l l y w i l l subtract. Roscoe suggests therefore that f o r normally loaded remolded samples there i s a unique relationship between stresses and water content provided no energy correction i s applied.  I f an energy  correction i s applied i n the form of equation 5» then the corrected q w i l l l i e on the f a i l u r e envelope f o r a l l points of the stress path, i . e . q  w  =  Mp'.  Roscoe has also predicted stress s t r a i n r e l a t i o n s . and Roscoe  (1963)  Poorooshasb  presented a graphical means of determining stress  s t r a i n relations for normally loaded remolded clay where the stress paths l i e on the state boundary surface, which i s the surface expressing the unique r e l a t i o n between stresses and water content (no energy corrections).  Undrained tests were performed which  show that f o r remolded spestone kaolin, contours of shear s t r a i n are r a d i a l l i n e s .  Consolidation tests were performed at d i f f e r e n t  ratios of q to p' and relations between the shear s t r a i n and the volumetric s t r a i n were determined graphically. volumetric s t r a i n also causes shear s t r a i n .  It i s shown that  The higher the r a t i o  of q/p' the higher the shear s t r a i n f o r a given volumetric s t r a i n . It i s stated that f o r any increment of applied stress the change i n s t r a i n can be considered to be the sum of a change i n s t r a i n at  Figure 5  —Roscoe. etal. Energy Balance  (After Roscoe eT al. '63)  17  constant volume, and a change i n s t r a i n at constant q / p ' .  Thus,  i f the stress path is known, the applied stress can be considered to comprise of a number of stress increments and each increment can be subdivided into an increment at constant volume and an increment at constant q / p 1 .  From the undrained tests the change i n shear  s t r a i n at constant volume is known, and also the change i n volumet r i c s t r a i n due to the increment at constant q / p ' .  The change i n  shear s t r a i n due to the change i n volumetric s t r a i n i s determined from the results of consolidation t e s t s .  The t o t a l change i n shear  s t r a i n is the sum of changes at constant volume and constant q / p ' . This method i s shown for a stress increment AC on Figure 6 . Figure 6 a shows stress paths from consolidated undrained'tests on tc  kaolin.  Contours of s t r a i n at constant volume are superimposed  and are seen to be r a d i a l line from the o r i g i n .  Figure 6 b shows  the relationship between increments of shear s t r a i n and volumetric s t r a i n as a function of q/p' derived from consolidation t e s t s .  A  stress increment AC can be resolved into increments AB and BC. The shear s t r a i n increments a r i s i n g from these are . 7 5 per cent at constant volume and 6. + per cent at constant q/p' thus the t o t a l 1  shear s t r a i n increment is 8.2 per c e n t .  In this manner a r e l a t i o n  between shear stress and shear s t r a i n can be obtained for any stress path. Landanyi, La Rochelle, and Tanquay (1965) present a graphical method of predicting shear strains i n saturated normally loaded and over-consolidated c l a y s .  It implies that contours of shear  s t r a i n are independent of the stress path followed.  Relationships  between shear s t r a i n and p r i n c i a p l stress r a t i o and shear  strain  Contours of Shear strviin(Con>t«nt VoL Tebts)  Values  of  Projection Of C S . Line  UJ Contour  10  Fig. £>a  £0  SO  40  50  GO  70  60  Stress* Paths and Contour*) o f Strain for Constant Volume. Tests on kaolin  2.  o o"  For Increment B C j T j =-43  IfoT  141  to  IS+  °  "  bv = 5,9  Se  -  i+e " g--3ye.-7  I + UJQ=  2  .  S  6  I0f 6+  5°  4+ o o ""a  2+  tr  F'cj.kb.  Figure. Q>  •4  Relqtion  5 -Q>  •6  IO  Between Increments o f Shear and Volumetric Strains oft Constant r;  Method of Determining stress- Strain Relationships for kaolin (After Poorooshasb 4nd Roscoe  1963)  %  19  and water content were determined from drained tests at various confining pressures. Using t h i s information the p r i n c i p a l stress r a t i o versus s t r a i n r e l a t i o n was predicted for an undrained test and compared with an actual t e s t .  Agreement was quite reasonable.  This theory would imply that i f there i s a unique r e l a t i o n between stresses and water content that contours of shear s t r a i n are also unique. The unique relationship between stresses and water content implies a f a i l u r e envelope which i s independent of stress path. Casagrande and Wilson (1953) found that f o r both an organic clay and for Boston Blue clay the undrained strength envelope was higher than the drained strength envelope. stress r a t i o was considered as f a i l u r e .  Maximum p r i n c i p a l  The difference amounted to  9 degrees f o r the organic clay and between 2 and 5 degrees f o r the Boston Blue c l a y .  In an undrained test on normally loaded clay,  the pore pressure r i s e s such that the normal e f f e c t i v e stress on the f a i l u r e plane f a l l s as shearing progresses.  Thus at f a i l u r e  the s o i l could be considered to be overconsolidated. This overconsolidation i s referred to as prestress e f f e c t and was considered responsible f o r the additional strength of the undrained t e s t s . The s t r a i n rate i n the undrained tests was considerably higher than the drained tests and i t has been argued by subsequent writers that this could account f o r the higher strength. However, undrained tests were performed as stress controlled and s t r a i n controlled and although the maximum deviator stress was higher f o r the stress controlled, the p r i n c i p a l stress r a t i o was the same f o r both. I t could therefore be implied that the s t r a i n rate affected the stress  20  path but not the strength envelope i n terms of the p r i n c i p a l stress r a t i o .  Energy corrections were not considered.  Bjerrum and Simons (i960) present data from drained and undrained tests on normally loaded undistrubed clays. v i t y of these clays varied from 3 to 100.  The s e n s i t i -  I t was found that f o r  almost a l l the Norwegian clays the pore pressure was s t i l l r i s i n g at maximum deviator stress and the maximum p r i n c i p a l stress r a t i o was reached at higher s t r a i n .  Kenney (1959) has suggested that  this phenomenon i s a function of the s e n s i t i v i t y of the clay. The greater the s e n s i t i v i t y the larger the difference i n the strength envelope determined by both methods.  Bjerrum and Simons  found the undrained envelope to be s l i g h t l y lower (about one degree) than the drained envelope, provided maximum p r i n c i p a l stress r a t i o was taken as the c r i t e r i o n o f f a i l u r e . 1  This, they  state, i s opposite to the findings of Casagrande and Wilson. However, the writers have corrected t h e i r drained tests f o r boundary energy due to volume change, whereas Casagrande and Wilson did not.  They suggest that the prestress effect i s of  secondary importance and state that i t i s the overconsolidation r a t i o before application of the shear stresses that i s important. Barron (i960) states that the volume change occurring i n drained tests causes considerably more remolding than i n undrained tests.  He suggested that the undisturbed drained strength  envelope and the remolded undrained envelope are only s l i g h t l y different  and that the undisturbed undrained strength envelope  is higher because of structure and prestress  effect.  Scott (1963) considers that the prestress induced i n the  21  undrained tests may or may not be important depending on the failure strain.  If f a i l u r e is occurring at large strains then the  s o i l w i l l be f u l l y dispersed at f a i l u r e and no memory of previous past pressure w i l l remain.  On the other hand, i f f a i l u r e  occurs  at low s t r a i n s , as is l i k e l y with a s o i l i n i t i a l l y f l o c c u l a t e d , memory of past pressure w i l l be retained and the s o i l w i l l exhibit a prestress e f f e c t .  Thus, Scott suggests that the prestress  ef-  fect w i l l be most pronounced for undisturbed s o i l s and p a r t i c u l a r l y for  sensitive  soils,  soils,  these being highly f l o c c u l a t e d .  For compacted  and p a r t i c u l a r l y for those s o i l s compacted wet of optimum,  with low salt concentrations i n the pore f l u i d , the prestress effect w i l l be of minor importance. 2.2  Discussion It is seen that there is considerable difference  of opinion  both with regard to the unique f a i l u r e envelope and the unique relationship between effective  stresses and water content.  It  would appear that for normally loaded remolded material, the strength envelope i s e s s e n t i a l l y  independent of the stress path,  and that the f a i l u r e c r i t e r i o n , whether maximum p r i n c i p a l stress r a t i o or maximum deviator stress makes l i t t l e difference. volume change at f a i l u r e i n the case of drained tests is  The generally  very small or zero so that a boundary energy correction i f app l i e d , w i l l have negligible effect  on the strength envelope.  undisturbed normally loaded material and p a r t i c u l a r l y for  For  sensi-  t i v e material, the maximum p r i n c i p a l stress r a t i o occurs at a higher s t r a i n than the maximum deviator stress i n undrained t e s t s , leading to two possible f a i l u r e envelopes.  In drained t e s t s ,  22  maximum deviator stress and maximum p r i n c i p a l stress r a t i o must occur at the same time.  However, volume decrease at f a i l u r e leads  to a measurable boundary energy correction, and thus gives r i s e to two possible drained f a i l u r e envelopes, i . e . , one with a boundary correction and one without. It appears that i f maximum p r i n c i p a l stress r a t i o i s taken as the f a i l u r e c r i t e r i o n , then drained and undrained tests have approximately the same f a i l u r e envelope provided a correction f o r boundary energy be applied to drained t e s t s .  If no correction i s  applied, then the drained envelope w i l l l i e below the undrained. Evidence f o r the unique relationship between e f f e c t i v e stresses and water content i s rather c o n f l i c t i n g , but suggests that f o r normally loaded remolded clays which have been i s o t r o p i c a l l y consolidated, the relationship i s approximately true.  No  data on s u f f i c i e n t l y uniform undisturbed clay i s available but i t has been suggested that a similar relationship might hold f o r undisturbed clays of low s e n s i t i v i t y .  For sensitive clays i t was  thought that the relationship would be more complex. The l i t e r a t u r e suggests that the relationship between effective stresses and water content determined from both drained and undrained tests may not be unique f o r any one clay f o r the following reasons: 1 . Rate of t e s t i n g not i d e n t i c a l f o r both drained and undrained t e s t s ; 2 . Temperature not the same f o r a l l tests; 3 . Non-uniform  d i s t r i b u t i o n of stresses and water content  due to end r e s t r a i n t ;  23  h. Residual excess pore water pressure i n drained t e s t s ; 5. Different structure a r i s i n g from different  stress paths  followed i n drained and undrained t e s t s . The effects of 1. and 2 . may be eliminated by testing at the same s t r a i n rate and at constant temperature.  Non-uniform stresses  give r i s e to unequal pore pressures within undrained t e s t s .  If  tests are run at s u f f i c i e n t l y slow s t r a i n rates, these w i l l largely become equalized by migration of water within the sample. In drained tests non-uniform stresses w i l l give r i s e to nonuniform water content. i n Chapter 5 .  This aspect w i l l be considered i n d e t a i l  Residual excess pore pressures i n drained tests  cannot be completely eliminated, as t h e o r e t i c a l l y i t would take an i n f i n i t e time for one hundred per cent d i s s i p a t i o n of excess pore pressure.  A. method for estimating the excess pore pressure  at a l l stages of a drained test was devised and is presented i n Chapter 6 .  The prestress effect  additional remolding effect  i n undrained tests and the  of volume change i n drained tests  are macroscopic factors r e f l e c t i n g different microscopic structure i n the c l a y .  The macroscopic behaviour of a clay is very  much dependent on the structure and this w i l l be considered i n Chapter 3»  2lf  CHAPTER 3 MACROSCOPIC COMPONENTS OF SHEAR STRENGTH The  shear s t r e n g t h of a s a t u r a t e d c l a y i s o f t e n c o n s i d e r e d t o  comprise of a f r i c t i o n component, a c o h e s i o n component and a s u r f a c e or boundary energy component.  The f r i c t i o n component i s t h a t  p o r t i o n of t h e shear r e s i s t a n c e w h i c h i s l i n e a r l y r e l a t e d t o t h e normal e f f e c t i v e s t r e s s .  C o h e s i o n i m p l i e s a shear r e s i s t a n c e which  i s independent of t h e normal e f f e c t i v e s t r e s s .  The s u r f a c e  energy  component of shear s t r e n g t h a r i s e s when a s o i l i s undergoing volume change.  Taylor  (19^8) demonstrated t h a t t h e work done by  the boundary s t r e s s e s d u r i n g s h e a r i n g ference  c o u l d account f o r t h e d i f B i s h o p (195 +)  i n s t r e n g t h between a l o o s e and a dense sand.  !  c a l c u l a t e d t h e energy component f o r t r i a x i a l c o n d i t i o n s at maximum d e v i a t o r s t r e s s as f o l l o w s . :  (G^ = CJ^)  I f an element of m a t e r i a l  under s t r e s s e s CJ-^ and CJ3 undergoes changes i n s t r a i n <$£, and Sc^, t h e n the boundary energy t r a n s f e r r e d t o t h e sample, OW, w i l l be  Sw = <J[ o£ now  x  + 2 CJ^  6£^  oV = tbE^ + 2 0 6 3 = v o l u m e t r i c  s t r a i n increment, decrease  i n volume p o s i t i v e t h e r e f o r e oJ - 0 $ - | ^ C3  -  ff'  ^  ----- (6)  i s t h e s u r f a c e energy component o f shear s t r e n g t h .  i s p o s i t i v e f o r volume i n c r e a s e , n e g a t i v e zero f o r constant  It  f o r volume d e c r e a s e and  volume or u n d r a i n e d c o n d i t i o n s .  Although Bishop  mentions t h a t h i s e q u a t i o n would a p p l y a t maximum d e v i a t o r s t r e s s Roscoe, S c h o f i e l d and Wroth (1958), G i b s o n (1953) and o t h e r s  applied  the c o r r e c t i o n a t o t h e r p o i n t s on t h e s t r e s s p a t h i n a d d i t i o n t o  25 the point of maximum deviator s t r e s s .  Hvorslev ( I 9 6 0 )  suggested  that part of the energy involved i n volume change might be stored or released e l a s t i c a l l y and hence should not be considered i n the term involving energy d i s s i p a t e d .  Bishop (196^-) considered that  the rate of change of e l a s t i c energy at maximum deviator stress would be small.  Roscoe and Schofield (1963) developed an energy  equation discussed  i n Chapter 2 which considered both boundary  energy and e l a s t i c energy within the sample.  Rowe, Oates and  Skermer (1963) extended the stress dilatency theory to cohesive soils. The  modified coulomb equation Tff  where  •= c ' + CTj tan 0 '  (7)  Tff = shear stress on f a i l u r e plane at  failure  c' = apparent cohesion Of = normal effective 0'  = effective  stress on f a i l u r e plane at  failure  angle of internal f r i c t i o n  is often used to express the shear strength of c l a y s .  For satu-  rated normally loaded clays i t is generally found that c' = zero. If the clay has been overconsolidated, the strength i n the overconsolidated region of interest Equation 7 .  may generally be expressed by  However, the f r i c t i o n angle determined i n the over-  consolidated region w i l l be less than that of the normally loaded region.  Therefore, for the one clay there is more than one pos-  sible f r i c t i o n angle.  F r i c t i o n and cohesion i n this form are now  considered to be merely parameters expressing the slope and i n t e r cept which best approximate the strength envelope i n the region of interest  (Figure 7 ) .  Hvorslev, at the suggestion of Terza&hi,  2fo  •  t I  i  Actual St&ngth Envelope Approximofed by bt l - i o e ^ ^  r—-  NormaNv- Leaded  »O nl <5n  Figure 7q — Modified Coulomb Strength Parameters  27  performed d i r e c t shear tests on saturated remolded clay i n such a manner that i t was possible to compare shear strength at the same void r a t i o but with d i f f e r e n t applied normal e f f e c t i v e stresses. It was found that f o r the same void r a t i o , the shear strength was a l i n e a r function of e f f e c t i v e normal stress and plotted with an intercept on the shear strength axis as shown i n Figure 7 . Lower void r a t i o s plotted as p a r a l l e l lines with higher intercepts on the shear strength a x i s .  The slope and intercept determined i n  t h i s fashion were given the symbols 0Q and Cg and were thought t o r e f l e c t true f r i c t i o n and true cohesion. red to refer to 0  Q  hesion.  and c  Hvorslev ( I 9 6 0 )  as e f f e c t i v e f r i c t i o n and e f f e c t i v e co-  Q  The terms imply that at any one void r a t i o the cohesion  is constant and independent of the e f f e c t i v e s t r e s s . (I960)  prefer-  Hvorslev  suggested that t h i s would only be so i f there were no s i g -  n i f i c a n t differences i n structure.  Scott ( 1 9 6 3 ) stated that due  to the i r r e v e r s i b l e nature of the compressibility of clay i t would not be possible t o have two samples at the same void r a t i o with d i f f e r i n g e f f e c t i v e stresses and the same structure.  The very f a c t  that the stress i s d i f f e r e n t s i g n i f i e s a d i f f e r e n t structure. Gibson (1953)> Bjerrum (195*+) and many others have determined the e f f e c t i v e f r i c t i o n and e f f e c t i v e cohesion components f o r remolded s o i l s .  I f the components were determined from drained  t e s t s , then the surface energy component was generally removed using the Bishop equation. energy equation reduced c  e  Gibson found that a p p l i c a t i o n of the and increased 0 . Simons (I960) e  determined these parameters f o r an undisturbed s o i l .  Bjerrum and  Simons (I960) found that the e f f e c t i v e f r i c t i o n component was  28  lower f o r a s o i l i n the remolded than the undisturbed state. I t is apparent that the same f r i c t i o n and cohesion components  will  not be present f o r the same s o i l i n the undisturbed and remolded states..  This i s p a r t i c u l a r l y true f o r sensitive s o i l s .  Hvorslev  (I960) considered that the components might only apply to remolded s o i l s . Schmertmann (1963) considered that the components as determined by Hvorslev' on remolded clay might be correct.  The d i f -  f e r i n g consolidation ratios necessary to produce samples at the same f a i l u r e void r a t i o but with d i f f e r i n g e f f e c t i v e stresses would r e s u l t i n samples which before shearing would have d i f ferent structures.  However, he thought i t possible that the d i f -  f e r i n g f a i l u r e strains could cause structures which were not i n i t i a l l y the same to be the same at f a i l u r e , and hence the Hvorslev parameters could be correct.  He suggested that this  would not generally be the case and proposed a method of "curve hopping" to produce what he considered to be i d e n t i c a l samples at the same.strain under d i f f e r e n t e f f e c t i v e stresses from which the f r i c t i o n - a n d cohesion, components.could be determined at any s t r a i n . These he termed the Dependent and Independent  components.  Noorany.and Seed (1965) proposed a.method of obtaining samples at the same void r a t i o and almost the same structure but with d i f f e r i n g e f f e c t i v e stresses.  The method involved anisotropic  consolidation of two samples to the same void r a t i o , a f t e r which time the deviator stress was removed from one, resulting i n two samples at the same void r a t i o but with d i f f e r e n t e f f e c t i v e stresses.  The samples were then sheared at constant void r a t i o and  29 separation of Mohr c i r c l e s at f a i l u r e allowed the e f f e c t i v e f r i c t i o n and cohesion components to be determined.  The  authors sug-  gested that the Mohr c i r c l e s might plot quite close to each other for i n s e n s i t i v e clays making separation of components quite d i f f i c u l t , whereas f o r sensitive material, considerable could be expected.  separation  However, this could also mean that the  ob-  served separation i n Mohr c i r c l e s i s due to s t r u c t u r a l change caused by release of the anisotropic stress condition, and  as  would be expected, t h i s is more marked for sensitive material. The Roscoe concept discussed i n Chapter 2 indicates that a s o i l which is y i e l d i n g has only one strength parameter, M, which implies a linear r e l a t i o n between p' and the deviator stress corrected for both boundary energy and Internal energy. considered  M can be  as a f r i c t i o n component and the theory suggests that  the f u l l value of M i s mobilized at a l l s t r a i n s . tests i t is generally conceded that considerable sary to mobilize f u l l f r i c t i o n . indicates that t h i s conception  In undrained s t r a i n is neces-  However, the Roscoe concept is due to neglect of the release  of i n t e r n a l energy from the sample.  The  release of i n t e r n a l en-  ergy i s of course governed by the s o i l structure . Although i t i s of considerable  interest from t h e o r e t i c a l  considerations to t r y to i s o l a t e the components of shear strength, i n practice i t i s generally the measured combined value that i s required.  In addition, from the above discussion, i t appears that  the e f f e c t i v e f r i c t i o n and cohesion components may s i c a l meaning but arise from s t r u c t u r a l e f f e c t s .  have no phyIt may  be neces-  sary to t r y to isolate the surface energy component i f the  labora-  tory tests do not duplicate the f i e l d conditions with regard to volume changes.  3 0  CHAPTER If TESTING PROCEDURES k-.l  Description of s o i l tested. The clay used i n this testing program was taken from a de-  posit located i n the Fraser Valley, B r i t i s h Columbia.  The deposit  i s centred around the town of Haney which i s about t h i r t y miles from the mouth of the Fraser River, and is known l o c a l l y as Haney clay.  I t i s presently being used f o r the manufacture of bricks  and i t was from the p i t at the brick factory at Haney that samples were obtained. The clay i s thought to have been deposited i n a marine or brackish environment during or shortly after the l a s t g l a c i a t i o n of south-western B r i t i s h Columbia (Armstrong, 1957).  Subsequent  u p l i f t of the land r e l a t i v e to the sea has exposed the deposit and percolating r a i n water has since leached out much of the s a l t , with the result that the clay now has a sensitive structure. Marine shells were found while sampling and attest to the depositional environment. Haney clay has a dark blue-gray colour when wet, and has the colour of neat cement when dry.  In the p a r t i a l l y dry state, l i g h t  and dark laminations of various thickness are evident.  Standard  laboratory i d e n t i f i c a t i o n tests were performed and the results are shown on Table I and Figures 8 and 9.  A. small dry sample of the  clay was subjected to X-ray d i f f r a c t i o n analysis to determine i t s mineral composition and the results are shown i n Table I I . I t may be seen that the s i l t size p a r t i c l e s are composed primarily of quartz and feldspar, while the clay size p a r t i c l e s are mainly c h l o r i t e .  TABLE I PHYSICAL PROPERTIES OF HANEY CLAY S p e c i f i c gravity  2.80  Liquid Limit  hh%  P l a s t i c Limit  26%  P l a s t i c i t y Index  18$  Natural Water content  \2% ± 1%  Per cent f i n e r than 2 microns  \6% O.h  Activity Undisturbed unconfined compressive Remolded unconfined compressive  strength 1550 l b s . / s q . f t .  strength  130 l b s . / s q . f t .  Sensitivity  12  Maximum past pressure  5500 l b s . / s q . f t .  3£  Figure 8 — G r a i n  Siae Distribution Curve for Haney Cloy  Figure 9 —"Typical Standard Consolidation Curve for Haney C l a y  3^  TABLE II CHEMICAL PROPERTIES OF HANEY CLAY  GRAIN SIZE S i l t Fraction (greater than 2 microns)  MINERAL  AMOUNT PRESENT  Quartz  Large  Feldspar  Large  Chlorite  Moderate - small  Mica  Moderate - small  Amphibole  Small  Chlorite  Large  Clay F r a c t i o n  Feldspar  Moderate - small  (less than  Mica/chlorite  Moderate - small  2 microns)  Quartz  Small  Mica  Small  Amphibole  Small - questionable  35  +.2  1  F i e l d Sampling and storing of block samples. Block samples were obtained by hand excavation from the clay  deposit at Haney i n an area that had recently been worked by the brick factory.  A. trench was dug around an area of about 12 square  feet to a depth of 3 feet, thus i s o l a t i n g a large block of s o i l . The top 18 inches or so of disturbed clay was removed and block samples were cut using f i n e piano wire.  These were trimmed to  rough cubes of side 9 inches, and were coated with wax at the s i t e as shown i n Figure 10.  The blocks were c a r e f u l l y trans-  ported to the laboratory and the next day were given further coatings of wax and then stored i n a moist room u n t i l required. *+.3  Description of test equipment. The testing program was shared with Mr. T. J . H i r s t .  tests were performed  Drained  by Hirst and undrained tests and some very  slow drained tests were performed  by the writer.  After completion  of the drained series some modifications were made to the equipment, p r i n c i p a l l y the i n s t a l l a t i o n of a de-aired water tank and a form of temperature  control.  a further change was made.  At the end of the undrained series A transducer was introduced to measure  pore pressure and an undrained test was run f o r comparison purposes.  Two very slow drained tests were then run with pore pres-  sure measurements i n order to determine pore pressures i n drained t e s t s .  the magnitude of residual  These modifications w i l l be  indicated i n the description of the test equipment which follows. The test equipment used i s shown i n Figures 11, 12 and 13. The t r i a x i a l c e l l was a clockhouse Engineering T.10 capable of receiving l.h  inch diameter samples.  The ram and bushing were  Figure 10 -  Block Samples of Haney Clay at Site  37  Proving Ring  Oiarilkd Drained Wafer Vacuum Vertical Dial  Machined Ram  Crauop  Machined Buthing  Saturation Spiral Sqmple  D e - a i r e d W a t e r Tank  porous Stona.  Regulators Presiure. Supply vacuum Supply  y& 1.0. Scran Tubing To P r a i s e Or Pore  Pre*.~ V6nT<y^  To Drainage System I  —  Electrical Transducer-'  |  Strain 11 CDonrtjrvoalled Axial  yr-0-0.  '/  v  V  I  '/^—Control  Panel  J  Copper Tubing Chamber  Pre&sure  •/4 O.D. Copper Tubing ~ J  y& QO. Poly1hclcn&_ Tubinj  1  \  -Steel  Balancing  TanK L E G E N D  0  Hoke.  Ball Val^e  (Non-Oisl.)  X  Hoke  Stem Volve  (Displ.).  NOT TO SCALE. Figure II — Triaxial Cell and Chamber Pressure  System.  e-s  • Overflow  Distilled De - Aired • W a t e r Supply  Connections to Triaxial Cell (T) w  £)  ©  Va  o. D.  Copper  LouJer Stone. Upper Stone  ©  Pore Pressure Gouge ( o - loo  '/fe O P .  -Monomeicr  Bi&hop and Henkel null Indicotor  Pressure Cylinder  •Saran Tubing  Corffro  10 c c . Burette (Adjusti ble Height)  -Mercury  Over-Tlouj  4 Ft. M e r c u r y Manometer To S u p p l y IOLb./S£j, Back P r e s s u r e  LEGEND (g)  Hoke S a i l -Vblve (Mon - Displ.)  X  Hoke S t e m (Displ.)  ®  Kliner A B I O  Va|ve  Valves  (Non-Displ.)  NOT  Fioure 1 2 - Drainage on a! Pore Pressure Meas>urin^ System  TO SCALE  Figure  13 -  Test Equipment  ko  of stainless s t e e l machined to a f i n e tolerance and were greased with " l u b r i p l a t e " before each t e s t . water past the ram occurred.  No s i g n i f i c a n t leakage of  A loading cap which was free to  rotate was used to minimize the l a t e r a l force and moment transferred to the ram and thus reduce f r i c t i o n at the bushing.  Dis-  t i l l e d de-aired water was used as a chamber f l u i d to reduce d i f fusion of a i r and water through the membranes into the sample. In the drained test series boiled d i s t i l l e d water was introduced into the air-water s t e e l balancing tank under a vacuum and allowed to cool overnight. a i r pressure.  It was then fed into the chamber under a small  In the undrained  tank was i n s t a l l e d .  series a d i s t i l l e d  de-aired water  D i s t i l l e d water was de-aired by sprinkling  i t into the tank under a vacuum.  The vacuum was removed and  water fed into the chamber under gravity. A constant chamber pressure was obtained by regulating compressed a i r from a house l i n e and applying i t to the air-water s t e e l balancing tank.  The water i n t h i s tank was subject to a  vacuum before each t e s t , but during the test i n the presence of a i r at a high pressure i t was expected that a i r would go into solution and f i n d i t s way into the c e l l .  In the drained series  the air-water tank was connected to the c e l l by a length of 3/8 i n . O.D. polyethelene tubing. length of 1/8  In the undrained  series a 6 f t .  i n . I.D. Saran tubing was i n s t a l l e d i n the line to  reduce the amount of a i r reaching the c e l l as suggested by Poulos  (196 +). 1  If leakage of water from the c e l l occurs then a i r i s  carried to the c e l l by the water instead of d i f f u s i n g through the water along the length of the tube and the e f f e c t of the tubing i s  1+1  then l o s t .  measured by a 0-100  The chamber pressure was  sq.in. bourdon gauge graduated to 0.5 with a mirror to reduce parallax. the pressure to 0.1  Ibs./sq.in., and  It was  l b s . / s q . i n . The  possible to  gauge was  lbs./ fitted  estimate  calibrated against  a dead weight tester before each t e s t i n g series and was found to creep under load.  Variations of up to O.h  to occur i n successive c a l i b r a t i o n s .  Ibs./sq.in. were found  The balancing tank was  f i t t e d with a transparent tube so that the water l e v e l i n the tank was  known and an elevation correction could be applied to deter-  mine the chamber pressure at the l e v e l of the centre of the sample. Drainage lines from the top and bottom of the sample led to a 10 cubic centimeter centimeters.  moveable burette, graduated to 0.1  Wherever possible 1/8  i n . O.D.  cubic  copper tube was  used,  but where movements were large r e l a t i v e to the length of tube, such as for the saturation s p i r a l and the connection to the burette, f l e x i b l e p l a s t i c tubing was drainage burette was  used.  The l e v e l of the water i n the  kept at the l e v e l of the mid height of the  sample, so that as drainage proceeded i t was the burette from time to time.  To insure complete saturation of  samplesa 10 Ibs./sq.in. back pressure was This was  necessary to adjust  applied to the burette.  accomplished by means of a mercury column and a  cubic centimeter a i r balancing tank.  The tank was  1200  sufficiently  large that the change i n the volume of a i r caused by drainage of 10 cubic centimeters less than 0.1  of water would a l t e r the back pressure  Ibs./sq.in.  Changes i n temperature of +  would a l t e r the pressure by about + .05  Ibs./sq.in.  by  1.0°c  However,  changes i n atmospheric pressure caused changes i n the l e v e l of  K2  the mercury which were not r e a l i z e d u n t i l the e l e c t r i c a l transducer was i n s t a l l e d at the end of the testing program. The reason f o r t h i s i s as follows:  A constant volume i n the back  pressure tank i s maintained by a constant absolute pressure. I f atmospheric  pressure f a l l s then there i s a tendency for the a i r  in the tank to expand.  This i s prevented by r i s e of mercury i n  the standpipe equal to the change i n atmospheric  pressure (the  small volume increase due to the r i s e of mercury can be neglected). The chamber pressure gauge reads pressures above atmospheric, the back pressure should therefore also be referenced to atmospheric pressure.  Errors i n the back pressure may have occurred  but i t i s thought these amounted to no more than about 0.2 l b s . / sq.in., as the l e v e l of the mercury was corrected occasionally during a test by allowing a i r into or out of the tank.  Later,  when the transducer was present, the correct back pressure was attained by moving the drainage burette u n t i l the desired transducer reading was obtained. Pore water pressure was measured at the bottom stone only using the Bishop and Henkel n u l l tube device (1 mm. I.D. tube). A 5 foot length of 1/8 In. outside diameter copper tube connected the n u l l tube to the bottom stone.  The compliance  of t h i s system  produced a movement of 7/^+0 i n . i n the n u l l tube over a range of 100 Ibs./sq.in. that was f u l l y r e v e r s i b l e .  Bishop and Henkel  (1962) suggest that the movement should not be more than 1/2 i n . over a pressure range of 100 Ibs./sq.in. and the system was therefore considered s a t i s f a c t o r y from the compliance view.  point of  During a test the position of the n u l l point was varied  >+3  w i t h the pressure t o account was  m e a s u r e d w i t h a 0-100  f o r t h i s compliance.  c a l i b r a t e d u s i n g a dead w e i g h t then read  c a l c u l a t i o n was  pressure  I b s . / s q . i n . b o u r d o n gauge s i m i l a r  t h a t u s e d f o r m e a s u r i n g t h e chamber p r e s s u r e .  w h i c h was  The  on t h e  necessary  The  gauge  was  t e s t e r t o a p p l y a chamber  pore p r e s s u r e gauge. to. a c c o u n t  to  pressure  I n t h i s way  no  f o r the h e i g h t of mercury  i n t h e n u l l t u b e or t h e c h a n g e i n t h e h e i g h t of t h e m e r c u r y t o change i n t h e n u l l c a r e was  always kept  T o w a r d s t h e end  installed.  I t was  rated compliance (9A0  system.  Incorporated  p o s s i b l e to the The  I b s . / s q . i n . a b s o l u t e and  was  cell  I b s . / s q . i n . change i n p r e s s u r e .  in null  p o i n t f o r 100  o f t h e a c t i v e f a c e of t h e t r a n s d u c e r . a f t e r a r e a d i n g was  s u b s e q u e n t r e a d i n g s were  The and  to  be This  tube  transducer  t h e s y s t e m was  c a l i b r a t i o n was  I f t h i s were done  pressure surge  to  taken.  c a l i b r a t e d a g a i n s t the dead w e i g h t t o be  of  dissipate  i s a c c o m p a n i e d by a n e l e c t r i c a l r e a d - o u t  found  the  and c o n t r a c t i o n  t a k e n , then f l o w i n t o or out  the sample would a l l o w t h e s l i g h t before  The  o r remove w a t e r t o t h e t r a n s d u c e r s y s t e m t o t a k e  p l a c e o f t h e v o l u m e c h a n g e c a u s e d by t h e e x p a n s i o n  immediately  of  Ibs./sq.in.).  c o u l d be c o m p e n s a t e d f o r d u r i n g a t e s t by u s i n g t h e n u l l d e v i c e t o add  a  a r a t e d compliance  found  was  to  t r a n s d u c e r had  c h e c k e d w i t h t h e n u l l t u b e and  in. rise  zero  program an e l e c t r i c a l t r a n s -  made by D a t a S e n s o r s  of t h e  0.00027 c u b i c i n . f o r 100  correct  calibration,  same.  p l a c e d as c l o s e a s  the compliance  r a n g e of 0 - 150  the  of t h e t e s t i n g  o f t h e b o n d e d t y p e and  minimize  After  t a k e n t o i n s u r e t h a t the h e i g h t of mercury f o r  gauge r e a d i n g was  ducer  point with pressure.  due  l i n e a r w i t h p r e s s u r e t o an  device  tester. accuracy  The  kh  of +  0.1  I b s . / s q . i n . , and  c o u l d be d e t e c t e d . s c a l e and  The  A. constant  deformation  by the chamber pressure  and  The  used t o  by f r i c t i o n at the bushing was  i n c o n t a c t with the  intended  sample.  deformation  made to measure t h i s .  The  The  measured  friction lateral  deformation  measured by a d i a l gauge placed such t h a t  of the sample only was  caused  testing rate  change d u r i n g a t e s t mainly because of induced  f o r c e s but no attempt was  gears.  f o r c e on the ram  by moving the l o a d i n g p l a t f o r m upward a t the being  rate  r a t e s ranging from about  A. proving r i n g was  measure the d e v i a t o r f o r c e i n the ram.  of the sample was  be  placed  motor and a system of  t h i r t y deformation  2 i n . per hour t o 1 i n . per y e a r .  f o r c e may  could  l o a d i n g p l a t f o r m on which the c e l l was  gear system allowed  the ram  absolute  pressure.  a p p l i e d to the  without  on an  i n s t a l l e d so t h a t the pressure  by means of a l/k- horse power e l e c t r i c The  Ibs./sq.in.  measures pressure  A l l t e s t s were s t r a i n c o n t r o l l e d . was  0.025  changes of  transducer  a barometer was  r e f e r r e d to gauge  pressure  the  measured.  Hoke v a l v e s were used wherever leaks c o u l d not be t o l e r a t e d . The  stem type displacement  v a l v e s were used where displacement  was  not a problem.  Four Hoke non-displacement b a l l v a l v e s were used  on the drainage  and  pore pressure  l i n e s where i t was  have no volume change on opening and v a l v e s were used on the pore pressure s m a l l leaks were of no consequence. were found to l e a k .  Four new  with the n u l l tube d e v i c e and ranged up to  0.003  closing valves.  e s s e n t i a l to Klinger  d e v i c e i n l o c a t i o n s where A.11  Klinger valves tested  K l i n g e r v a l v e s were s e p a r a t e l y t e s t e d a l l were found t o l e a k .  cubic i n . per day  under  100  Leakage  I b s . / s q . i n . , which  corresponds t o a r i s e i n the n u l l p o i n t of about 2 i n c h e s .  Poulos  h5  (196k) found similar r e s u l t s , and t h i s writer now understands that, where Klinger valves are used by other investigators i n positions where leakage cannot be tolerated, either the valve linings have been replaced or the valve has been treated i n some way.  Hoke  non-displacement valves were tested i n the same manner as the Klinger valves and no leakage could be detected i n a three day period. . However, after some usage i t was apparent that these valves also leaked. Tightening of the stem seals appeared to stop the leakage and t h i s was done from time to time.  Subse-  quently, f o r other apparatus i n the laboratory, Whitey nondisplacement valves were used and were found to behave i n a very s a t i s f a c t o r y manner.  Hoke displacement valves were also tested  and none was found to leak. The equipment was de-aired by drawing large quantities of boiled d i s t i l l e d water at a temperature of about 180°F through the  drainage l i n e s .  the  equipment  Due to the many problems encountered i n getting  operational, de-airing was done a number of times  and presented no particular d i f f i c u l t i e s .  However, care i s re-  quired i n de-airing the Hoke non-displacement valves as the sealing surface i s not continuous and so an a i r space exists behind the seal.  These valves must be held i n the half open position while  water i s flushed through to remove t h i s a i r . the  After de-airing,  system was allowed to cool and the n u l l tube was then used to  check the drainage system f o r compressibility and leakage. After the drained t e s t series had been completed a form of temperature control was i n s t a l l e d .  This was accomplished by  constructing an insulated compartment around the equipment  which  was kept below the general room temperature by a cooling unit.  he  The compartment comprised of a frame 15 feet long, 8 feet wide and 8 feet high constructed of 2 i n . by h i n . timber members and covered inside and outside with a layer of polyethelene to produce a h i n . i n s u l a t i n g a i r gap.  A water cooled a i r conditioning unit  of 9*4-00 B.T.U. capacity was used.  It was capable of keeping about  a 10°C difference i n temperature between the room and the compartment but during the test series the difference was never more than 5°C*  A. t y p i c a l cycle was:  a i r conditioner on f o r !-§• minutes,  off f o r 3 minutes with a temperature v a r i a t i o n within the compartment of 0.5°C.  The fan setting could be adjusted and i t was  found that the optimum adjustment gave a f a i r l y uniform temperature over most of the testing area.  A thermometer placed i n a  100 cubic centimeter f l a s k d i d not record any noticeable v a r i a t i o n in temperature due to the c y c l i c fluctuations of a i r temperature, and i t could be concluded that the sample which was  surrounded  by a considerably larger volume of water underwent negligable temperature v a r i a t i o n .  However, the a i r temperature v a r i a t i o n  did have a small e f f e c t on the Bishop and Henkel pore pressure measuring device.  The e f f e c t on a closed system was f o r the  pressure to f a l l on a r i s i n g temperature and r i s e on a f a l l i n g temperature.  This i s opposite to what one usually expects and  may be explained as follows:  On a r a p i d l y r i s i n g a i r temperature  the aluminum case of the pressure cylinder having a high conductiv i t y and low s p e c i f i c heat increases i n temperature and expands allowing the water to increase i n volume and hence reduce i n pressure.  The water having a low conductivity and high s p e c i f i c  heat does not have time to heat and expand.  The copper l i n e to  h7  the  c e l l behaves In a similar way to the pressure cylinder although  to a lesser extent.  I f , on the other hand, the temperature r i s e  is slow then the water has time to heat and expand and water having a higher c o e f f i c i e n t of thermal expansion than copper or aluminum tends to expand more, causing a pressure r i s e .  This  e f f e c t was e s s e n t i a l l y eliminated by binding the pressure cylinder and copper l i n e by insulating tape.  When the transducer was later  i n s t a l l e d , no v a r i a t i o n i n pore pressure i n a closed system could be detected. h.h  Testing technique C y l i n d r i c a l samples 2.8 i n . long and l.h i n . i n diameter  were prepared i n a moist room using a wire saw, miter box and trimming lathe.  A trimmed sample and equipment i s shown i n  Figure l ^ . Side and end trimmings were used f o r water content determinations. the  I t was found that due to the laminated nature of  material, the. water content calculated from the end trimmings  varied considerably from the side trimmings.  These were not  therefore used i n estimating the average i n i t i a l water content but  served to indicate the range of water content within the  sample.  Four tests were performed by Mr. Hirst with whom the  testing program was shared to determine i f the side trimmings were a r e l i a b l e measure of the average i n i t i a l water content of the sample.  The greatest water content difference between a sample  and i t s side trimmings was found to be 0.-2 per cent and i t was concluded that the trimmings were a r e l i a b l e measure of the average i n i t i a l water content of the sample.  However, a precaution had  to be observed i n taking side trimmings.  When side trimmings  Figure  15 -  Sample in Place on Triaxial Base  h9  were taken the sample had not been trimmed top and bottom and therefore the trimmings did not represent the f i n a l Further trimming was necessary to allow for t h i s .  sample. If this further  trimming were not done, and i t was not always done by the w r i t e r , the check between i n i t i a l and f i n a l water contents based on side trimmings was as poor as 1.5 per cent, whereas for those samples i n which i t was done the check was always within 0.2 per c e n t . The trimmed sample was measured and weighed. cumferential measurements  Three c i r -  (top, centre and bottom) and four length  measurements were obtained and averaged to determine the dimensions of the sample.  Samples were handled with extreme care and were  carried i n a l i i n . wide rubber s l i n g to reduce stresses. Prior to the preparation of the sample the equipment was made ready.  The porous stones were boiled for 10 minutes i n d i s t i l l e d  water and allowed to c o o l .  Four 0-rings on ring expanders were  fed over the top loading cap and down the saturation These were followed by a r o l l e d membrane. also placed down over the pedestal.  spiral.  A, r o l l e d membrane was  The c y l i n d r i c a l surface of  the pedestal was then covered with a f i l m of s i l i c o n grease and the membrane r o l l e d to the top.  Water was allowed to flow from  the bottom drainage l i n e to cover the top of the pedestal and form a convex meniscus. was s l i d into place. stone.  The bottom stone now cooled to room temperature The sample was then s l i d onto the bottom  The top cap was inverted and water allowed to flow out  and form a meniscus,.  The top stone was then placed and the cap  and stone righted and s l i d onto the top of the sample.  Silicon  grease was now smeared on the top cap and with one hand on the top  50 cap the lower membrane was r a p i d l y r o l l e d up, any excess water being pushed ahead  of the membrane.  This membrane was then covered  w i t h a f i l m of s i l i c o n grease and the second membrane r o l l e d down from the t o p . top  and bottom.  Two 0-rings were then placed over both membranes a t F i g u r e 15 shows a photograph of an i n s t a l l e d  sample d u r i n g a p r e l i m i n a r y t e s t s e r i e s when o n l y one membrane and two 0 - r i n g s were being used. The top of the c e l l was then placed i n p o s i t i o n and the a l i g n ment of the ram w i t h the b a l l b e a r i n g on the l o a d i n g cap was checked. the  T h i s was done by observing i f any l a t e r a l movement of  top cap o c c u r r e d when the ram c o n t a c t e d the b a l l .  The sample  was p o s i t i o n e d by t r i a l and e r r o r u n t i l no movement c o u l d be detected.  The ram was then brought i n t o contact w i t h the sample  and the v e r t i c a l d i a l s e t .  Water from the d i s t i l l e d d e - a i r e d  tank was f e d i n t o the chamber under g r a v i t y ,  water  A. 10 I b s . / s q . i n .  chamber pressure was a p p l i e d and the pore pressure measured.  In  those l a t e r t e s t s where the t r a n s d u c e r was used t o measure pore pressure, the pore pressure was measured as soon as the f i r s t membrane was i n p l a c e . the  The e f f e c t on the pore pressure of p l a c i n g  second membrane and a l i g n i n g the sample could be observed.  I t was found that the pore pressure f l u c t u a t i o n s of not more than 0.5  I b s . / s q . i n . occurred and were e l a s t i c .  The chamber pressure  was then a p p l i e d i n increments of 10 I b s . / s q . i n . a t f o u r  minute  i n t e r v a l s u n t i l the d e s i r e d chamber p r e s s u r e was a t t a i n e d .  The  pore pressure was r e c o r d e d before each increment was a p p l i e d a l l o w i n g the Skempton B parameter to be c a l c u l a t e d .  I t was found  t h a t B was equal t o u n i t y f o r a l l increments, i n d i c a t i n g that the  51  clay was  100 per cent  saturated.  Samples were allowed to consolidate f o r exactly 2k hours. Drainage from both top and bottom of specimens led to a burette to which a 10 Ibs./sq.in. back pressure was the time f o r *90 was  applied.  Since  never more than 200 minutes, i t was  that a l l pore pressure due to primary consolidation was dissipated at the end of the consolidation period.  considered essentially  Burette  readings were taken during consolidation so that the c o e f f i c i e n t of consolidation c  v  and the c o e f f i c i e n t of permeability k could  be calculated. In preliminary tests i t was  found that the sample would  generally not consolidate uniformly i n the v e r t i c a l d i r e c t i o n , so that at the end of consolidation the ram would no longer be aligned with the b a l l on the loading cap. ring i t was  necessary to bring the ram  To prevent this  into contact with the b a l l  from time to time during the consolidation period. stress involved i n this contact was O.k-  Ibs./sq.in.  It was  The  vertical  generally not more than about  important to have good alignment before  shearing otherwise there was buckling taking place.  occur-  a strong p o s s i b i l i t y of sample  In addition, poor alignment caused an  irregular i n i t i a l stress s t r a i n curve. About an hour before the end of the drainage period the loading platform was moved up at the intending testing rate without the ram being i n contact with the b a l l on the loading cap. this way  the force on the ram due to the chamber pressure  f r i c t i o n at the bushing was  determined.  This was  In and  l a t e r subtracted  from proving ring readings to determine the deviator f o r c e .  52  Samples were then sheared controlled conditions. The  s t r a i n r a t e was  under e i t h e r d r a i n e d or undrained  F i g u r e 16 shows a specimen d u r i n g s h e a r i n g .  about 0.5  f o r both d r a i n e d and  strain  per cent per hour and was the same  undrained t e s t s .  Some a d d i t i o n a l t e s t s were  run a t other r a t e s but were not used f o r the main purpose of the thesis.  V a r i a t i o n i n the s t r a i n r a t e occurred due  of the p r o v i n g r i n g .  The  The  chamber pressure was  a i r r e g u l a t i o n system was  fluctuations  In undrained t e s t s the v a r i a b l e s  pressure r e a d i n g .  Approximately  pore  50 s e t s of readings  the d u r a t i o n of any one t e s t .  d r a i n e d t e s t s were performed  Pore pressure was The  the excess  These were  analyzed. at one q u a r t e r the  transducer was  permitted.  a l s o used to measure the back pressure  l i n e so t h a t a v e r y a c c u r a t e measure of  pore pressure a t the bottom of the sample was  thought  general  measured with the t r a n s d u c e r at the bottom  a p p l i e d to the drainage  excess  recorded  proving r i n g deformation and  s t r a i n r a t e but drainage t o the top stone o n l y was  T h i s was  a l l tests.  I b s . / s q . i n . were recorded on the  l a t e r f e d to a d i g i t a l computer t o be  stone.  strain  In d r a i n e d t e s t s the drainage b u r e t t e r e a d i n g r e p l a c e d  were taken throughout  Two  un-  found t o work extremely w e l l and  were, time, sample deformation,  the pore  about onehalf the average  kept c o n s t a n t throughout  of not more than 0,1  chamber pressure gauge.  pressure.  deformation  In f a c t , d u r i n g the e a r l y part of the  d r a i n e d t e s t s the s t r a i n r a t e was rate.  to  obtained.  to g i v e a reasonable a c c u r a t e measure of the  pore pressure t h a t would e x i s t at the c e n t r e of a sample  d r a i n e d t o both top and bottom and  sheared at the u s u a l r a t e .  T h i s w i l l be d i s c u s s e d i n d e t a i l i n Chapter  6.  Figure 16 - Sample During Shear  5V  At the end  of the shearing process, s i n c e a check on the  water content was  r e q u i r e d , water was  first  allowed to back d r a i n  i n t o the sample before removing from t h e chamber. was  first  suggested  as f o l l o w s :  by Henkel and  This  procedure  Sowa (1963) and the reason i s  I f the e f f e c t i v e s t r e s s e s a t the end of the  test  are high, removal of the chamber pressure under undrained  condi-  t i o n s w i l l not change them and hence as the t o t a l s t r e s s e s go to zero, l a r g e t e n s i o n s are set up i n the pore p r e s s u r e .  I f these  are high enough they w i l l cause c a v i t a t i o n i n the drainage and water w i l l enter the ends of the sample.  lines  Even i f the t e n s i o n s  are not s u f f i c i e n t to cause c a v i t a t i o n , water may  be drawn i n t o  the sample form the porous stones d u r i n g d i s m a n t l i n g of the sample. S i n c e i t appears impossible to prevent water e n t e r i n g the sample the a l t e r n a t i v e i s to measure the amount t h a t e n t e r s . done by removing the d e v i a t o r s t r e s s and dropping  This  was  the chamber  pressure to 12 I b s . / s q . i n . while a l l o w i n g water t o f l o w from the at a back pressure of 10  drainage b u r e t t e which was  maintained  I b s . / s q . i n . a t a l l times.  Back drainage was  r a t e of f l o w was for  v e r y s m a l l or i n some cases i t was  the  continued  2h hours so t h a t a measure of the c o e f f i c i e n t s of c o n s o l i d a -  t i o n and way  continued u n t i l  p e r m e a b i l i t y a f t e r shearing c o u l d be o b t a i n e d .  the e f f e c t i v e s t r e s s was  reduced  to 2 I b s . / s q . i n .  In t h i s A f t e r back  d r a i n i n g the drainage v a l v e s were c l o s e d , the chamber pressure r e duced to zero and  the water removed from the c e l l .  The  rubber mem-  branes were cut and removed, the porous stones p u l l e d from the ends and  the whole sample was  then weighed.  I t was  not thought  that  much water would enter the sample from the porous stones s i n c e the t e n s i o n i n the pore water should not be more than 2 I b s . / s q . i n .  55  and the c a p i l l a r l y t e n s i o n of t h e s t o n e s was thought h i g h e r t h a n that. The water c o n t e n t of the whole sample was d e t e r m i n e d and from the known amounts of water d r a i n e d and back d r a i n e d t h e i n i t i a l water c o n t e n t c o u l d be c a l c u l a t e d .  T h i s was  t h e n checked  w i t h b o t h the i n i t i a l water c o n t e n t c a l c u l a t e d u s i n g the  initial  wet weight and f i n a l d r y weight of the whole sample and the i n i t i a l water c o n t e n t as determined f r o m s i d e t r i m m i n g s .  I t was  found t h a t the water c o n t e n t check was always w i t h i n Ooh per c e n t and g e n e r a l l y w i t h i n 0 . 2 for  per c e n t when t h e whole sample was  i n i t i a l water c o n t e n t and was always w i t h i n 0 . 2  used  per cent  when s i d e trimmings which were p r o p e r l y r e p r e s e n t a t i v e were used (see  discussion earlier i n this section).  I n t h o s e t e s t s which  were sheared a t one q u a r t e r the u s u a l r a t e t h e s h e a r i n g process t o o k about 10 days.  However, the water c o n t e n t check f o r t h o s e  two t e s t s was w i t h i n 0 . 1  per c e n t .  I t may t h e r e f o r e be c o n c l u d e d  t h a t the average water c o n t e n t a t the v a r i o u s s t a g e s of a t e s t was a c c u r a t e l y known and t h a t no s i g n i f i c a n t leakage o c c u r r e d . A f t e r removal of the sample, the d r a i n a g e l i n e s were f l u s h e d w i t h de-aired d i s t i l l e d water.  The c e l l ,  bottom  pedestal  and t o p l o a d i n g cap were t h o r o u g h l y washed w i t h d e t e r g e n t t o remove any grease w h i c h might l a t e r t r a p a i r . was t h e n ready f o r the n e x t t e s t .  The equipment  56  CHAPTER 5 DISCUSSION OF TESTING TECHNIQUE 3.1  Introduction The main purpose of the testing program was  to determine i f  for Haney clay a unique relationship exists between e f f e c t i v e stresses and the water content which is independent of the stress path, drained  or undrained.  It was  important that the drainage  condition should be the only variable i n the tests and  other  possible variables, such as temperature and s t r a i n rate, were therefore kept constant.  However, due  equipment errors arise which may  to the nature of t r i a x i a l  not a f f e c t drained and undrained  tests i n the same manner. In a t r i a x i a l t e s t the aim i s to subject a sample to homogeneous states of stress and  strain.  Due  to the presence of  f r i c t i o n forces at the top and bottom of a sample, the state of stress and consequently the state of s t r a i n is seldom uniform. In addition, i n undrained tests non-uniform stresses lead to non-uniform pore pressures and or migration sample.  of water within the  In drained tests residual pore pressures of some gen-  e r a l l y unknown value are present. uniform, errors may  Even i f the stress system were  arise i n measuring the applied pressures  and forces, p r i n c i p a l l y the pore pressure and deviator force, and are mainly caused by time lag i n the pore pressure measuring device and the presence of ram f r i c t i o n . w i l l be discussed 5.2  These errors  i n subsequent sections of this chapter.  Non-uniform stress and  strain  In the standard t r i a x i a l test f r i c t i o n a l resistance along  57 porous stones or end platens cause shear stresses to be applied at the top and bottom of a sample.  Even during consolidation  when no deviator stress i s applied, shear stresses are present and prevent diameter decrease at the top and bottom.  During shearing,  these shear stresses reverse i n d i r e c t i o n and e s s e n t i a l l y prevent the end diameters from increasing, resulting i n bulging of the sample.  When bulging occurs the cross sectional area at the  centre of the sample becomes greater than that at the ends and consequently the v e r t i c a l stress at the centre is less than that at the ends.  The shear stress at the ends has the a f f e c t of  increasing  at the ends and the overall r e s u l t i s that both  and  - fj^) i s  are higher at the ends than at the centre, but  higher at the centre (Bishop, Blight and Donald I 9 6 0 ) .  The devia-  tor stress i s generally calculated from a cross sectional area which i s determined r i g h t cylinder.  by assuming that the sample deformed as a  Roscoe, Schofield and Thurairajah ( 1 9 6 3 )  indicate  that at an a x i a l s t r a i n of 2 0 per cent, the area at the centre may be 1.*+ times the area calculated on the usual b a s i s . Casagrande and Wilson ( I 9 6 0 )  suggest that the r e l a t i o n between the v e r t i c a l  stress at the ends and centre of a t r i a x i a l specimen i s given by:  where  = v e r t i c a l stress at ends 0^ = v e r t i c a l stress at middle £]_ = a x i a l s t r a i n .  So that at 2 0 per cent s t r a i n the v e r t i c a l stress at the ends would be 50 per cent larger than at the middle.  58  The a x i a l s t r a i n i s generally calculated by d i v i d i n g the deformation  of the sample by the consolidated length, and i t i s  assumed that the s t r a i n i s uniform throughout the sample. Schofield and Thurairajah  (1963) showed  Roscoe,  that for drained compres-  sion tests on loose saturated sand, the a x i a l s t r a i n varies considerably throughout the depth of the sample.  In general, a x i a l  strains were found to be larger at the centre than at the ends. This would be i n agreement with Bishop's suggestion that the shear stresses are larger at the centre.  After about 10 per cent average  a x i a l s t r a i n , zones of maximum a x i a l s t r a i n occurred at about the t h i r d points and were thought due to the f a i l u r e zone moving towards the ends.  F a i l u r e f i r s t occurs around the c e n t r a l zone  followed by y i e l d i n g and bulging and reduced-stresses, and movement of the f a i l u r e zone towards the ends. normally  In compression tests on  loaded clay specimens, the s t r a i n d i s t r i b u t i o n is unlikely  to be the same as f o r sand.  However, a similar trend could be  expected, with maximum strains occurring near the centre followed possibly by the development of two zones of high s t r a i n between the centre and the ends at large average a x i a l s t r a i n . It i s apparent, therefore, that stresses and strains are not uniform throughout a sample.  At an average a x i a l s t r a i n of 20 per  cent, the stresses and strains within the sample may be as much as 50 per cent d i f f e r e n t from those calculated i n the conventional manner.  Since the actual stress and s t r a i n could not be r e l i a b l y  calculated for any element within the sample, the' conventional method was adopted.  I t was hoped that the errors would be similar  i n both drained and undrained  tests and that calculated average  59  values would provide r e l i a b l e comparisons. 5.3  Non-uniform pore pressures  i n undrained tests  Non-uniform stresses lead to a further problem i n the case of undrained t e s t s .  If the applied stresses are not uniform,  then either the pore pressure is not uniform, or i f the rate of testing is such that pore pressure equalization occurs by migration of water within the sample, then the f a i l u r e zone can hardly be considered to be undrained.  Undisturbed clays are not l i k e l y to  be homogeneous so that non-uniform pore pressures would probably occur to some extent even i n the absence of non-uniform stresses. It is generally agreed that for normally loaded and sensitive materials subject to undrained shear, the pore pressure at the centre of the sample w i l l be higher than at the ends (Whitman Bishop, Blight and Donald  I960,  I960,  and Blight  1963).  Hence,  flow of water w i l l take place from the central zone of higher shear towards the end zones.  In overconsolidated s o i l s where  shear stresses cause reduction i n pore pressure the reverse is true. If  the pore pressure is measured at one end of the sample as  is usual, then, i f the measured pore pressure is to have any meaning, the rate of testing must be such that the pore pressure throughout the sample is f a i r l y uniform.  To speed up equalization  of pore pressure, f i l t e r paper side drains may be used.  These  allow drainage to the c y l i n d r i c a l surface of the sample as well as to the top and bottom.  They are most effective i f the permea-  b i l i t y of the clay is very low compared to the permeability of the paper.  For clays of r e l a t i v e l y high permeability, considerable  head loss may occur i n the f i l t e r paper.  The calculated coef-  60  f i c i e n t of consolidation of the s o i l assuming no head loss i n the paper may be very much less than that measured i f no f i l t e r were present.  In the past, i n order to reduce hoop tension, f i l t e r  paper s t r i p s with alternating gaps were used. effectiveness  paper  This reduces  the  of the drainage surface and causes additional loss  in the f i l t e r paper due to the reduced cross sectional area of paper.  Bishop and Gibson (1963) suggested that continuous f i l t e r  paper with v e r t i c a l s l i t s to reduce hoop tension might be used to offset t h i s .  Campanella (1965) found that the use of s l i t s  rather  than slots i n the f i l t e r paper reduced the time for 100 per cent primary consolidation of bay mud by a factor  of about 5.  Bishop and Henkel (1962) and B l i g h t (1963) produced equations and  graphs from which the time to any r e l i a b l e reading can be  obtained for drained and undrained tests provided the of  consolidation c v or the apparent c v  loss i n the f i l t e r paper) is known.  coefficient  (obtained by assuming no  Their results were based on  95$ equalization of non-uniform pore pressures i n the case of undrained t e s t s , and 95$ d i s s i p a t i o n of excess pore pressure i n the case of drained t e s t s .  If i t is only required to have a re-  l i a b l e reading at f a i l u r e , then the time obtained is the time to failure.  If,  on the other hand, a stress path is required, the time  obtained w i l l be that to the f i r s t r e l i a b l e point on the stress path. Preliminary tests were conducted to determine i f the use of filter  paper would allow reduced testing times.  Isotropic c o n s o l i -  dation tests were performed on l.k- i n . by 2,8 i n . samples both with and without slotted f i l t e r drains compared. cm,2/  sec,  (Whatmans No. 5^) and the results  Without f i l t e r paper e v was found to be about 2 x 10"" 3 whereas with f i l t e r paper and assuming no head loss  61 in the paper the apparent c was about 5 x 10"^ cm. /sec. 2  v  Since  2 x 10~3 cm.^/sec. was the correct c and would have been measured v  had no loss occurred i n the paper (assuming k^ = ky), the eff i c i e n c y of the drains, which i s the r a t i o of the apparent c to v  the  actual c was about 2^ per cento  the  poor performance of the paper may have been due to smear on  the  l a t e r a l surfaces caused by sample trimming, but a similar  v  It has been suggested that  smear should then have been present at the top and bottom of the sample, and so i t seems very unlikely that smear could be responsible f o r such a poor e f f i c i e n c y .  Similar low e f f i c i e n c i e s  were obtained by Simons (1963) and Crawford (1963) on sensitive clays with c ' s i n the same range and were attributed to head v  loss i n the paper.  Based on the c values obtained, the times v  required to r e l i a b l e readings for undrained tests from Blight's chart are about h hours with or without drains. decided not to use drains.  It was therefore  Unfortunately, at the time of these  preliminary t e s t s , the concept of using s l i t s i n the f i l t e r paper instead of the usual s l o t s was not known to the writer.  It i s  very possible that s l i t paper would have been considerably more effective. 5.*+  Residual pore pressures i n drained tests Since f i l t e r paper side drains have a very low e f f i c i e n c y and  were not used, i t was necessary to have drainage top and bottom i n drained tests to reduce the testing time.  With a c  v  of 2 x 10"3  cm. /sec. and double-end drainage, a time of 11 hours to the f i r s t 2  s i g n i f i c a n t reading was calculated (Bishop and Henkel 1962).  Blight  (1963) suggests that the theoretical times for 95 per cent d i s sipation from which the Bishop and Henkel equation i s derived  62  predicts times considerably longer than those actually needed f o r 95 pe-r cent d i s s i p a t i o n .  He suggested that the time required f o r  a given degree of pore pressure d i s s i p a t i o n i n a drained test with double-end drainage would be the same as that required f o r the same degree of pore pressure equalization i n an undrained test without f i l t e r paper.  The time required for 95 per cent d i s s i p a t i o n of  excess pore pressure would therefore be h hours, the same as i t was f o r undrained t e s t s . The writer was concerned about the value of residual pore pressures i n drained tests because of the highly flocculated nature of sensitive c l a y s .  During shearing i t was expected that  large reductions i n permeability would take place due to struct u r a l change and decreased void r a t i o .  Hence i t was thought pos-  sible that residual pore pressures might be larger than usual. A. method was derived f o r c a l c u l a t i n g excess pore pressures from the rate of drainage of pore water from the sample.  This  was checked by running drained tests at T the normal speed but allowing drainage from the top only and measuring pore pressure at the bottom.  The method and results are discussed i n d e t a i l  i n Chapter 6. 5.5  Pore pressure measuring devices U n t i l quite recently pore pressures i n small test samples  have been measured by means of the n u l l - i n d i c a t o r .  This generally  comprises a water-mercury contact surface i n a small diameter tube which i s maintained at such a l e v e l that no flow from the sample to the system occurs. The pressure required t o maintain the l e v e l i s measured and gives the pore pressure at the centre  63  of the sample when the system is suitably c a l i b r a t e d .  More re-  cently e l e c t r i c a l transducers have been used to measure pore pressure.  Here very small deformations of a diaphragm produce  changes i n e l e c t r i c a l resistance of s t r a i n gauges allowing c a l culation of pore pressure. If the pore pressure within the sample is changing, and i f i t is assumed that the change would be uniform throughout the sample i n the absence of a pore pressure measuring device then the presence of one may lead to non-uniform pore pressures.  In  the n u l l tube device, movement of some observable amount must f i r s t occur before a pressure change can be applied, and hence a small flow of water into or out of the sample take place creating a gradient within the sample.  In the same way d e f l e c t i o n  of the  diaphragm i n the transducer causes a small volume change and similar gradients within the sample. Bishop and Henkel ( 1 9 6 2 ) defined the s e n s i t i v i t y of the n u l l indicator as the time required for a movement A X to occur i n the n u l l point under a small out of balance pressure Ap.  A. mathe-  matical expression was derived for this time, and for given values of A X and AP, i t depends on the nature of the s o i l tested ( c v and mv) and the r a t i o of the diameter of the n u l l tube to the d i a meter of the surface over which the pore pressure is measured raised to a power.  For Haney clay with Ap = 0 . 2 I b s . / s q . i n . and  Ax = 0 . 0 2 i n . and measurement at the bottom stone, the sensit i v i t y was about 30 seconds.  Had the area over which the pore  pressure was measured been very much smaller, say due to the use of a pore pressure probe, then the s e n s i t i v i t y time would have been very much greater.  61+  A. similar time lag occurs with the transducer due to i t s compliance.  When the transducer was  i n s t a l l e d towards the end  of the testing program, i t was found that for an ambient pressure increase of hO Ibs./sq.in. under undrained conditions, a time of about 2 minutes elapsed before 98 per cent of this i n crease was recorded on the transducer. of the compliance  This time i s a function  of the transducer system, the nature of the  sample material and the area over which the pore pressure i s measured.  Had the transducer been connected to a pore pressure  probe i n place of the bottom stone a very much longer time would have elapsed f o r 98 per cent equalization. In general the s e n s i t i v i t y time i s very much less than the time required for reasonable equalization of pore pressures due to non-uniform stresses and consequently sidered. diameter  However, i f pore pressures are measured with small probes inserted i n the sample, s e n s i t i v i t y may well be  an important 5.6  factor.  Rate of testing Since the drainage condition was  was  i t is not usually con-  to be the only variable, i t  necessary to have the rate of shearing the same for both  drained and undrained t e s t s .  In addition, stress paths were  required rather than just stresses at f a i l u r e and therefore the rate had to be such as would give r e l i a b l e values of stresses for a considerable portion of the stress path.  The approximate times  f o r 9 5 per cent d i s s i p a t i o n and equalization of pore pressures i n drained and undrained tests were 11 and U- hours respectively. If the more optimistic figure suggested  by Blight f o r drained  65  tests was taken, then the time for both was about h hours. Preliminary tests indicated that f o r undrained shear the maximum deviator stress occurred at about 3 per cent a x i a l s t r a i n while the maximum p r i n c i p a l stress r a t i o occurred at about 1 5 to 17 per cent a x i a l s t r a i n .  In drained tests both maximum deviator  stress and maximum p r i n c i p a l stress r a t i o occurred at about 30 per cent a x i a l s t r a i n .  A.n average shearing rate of 0 . 5 per cent  a x i a l s t r a i n per hour was selected. During the early portion of the t e s t , due to the rapid r i s e i n deviator stress, d e f l e c t i o n of the proving ring caused the s t r a i n rate to be considerably less than the average rate. was about 60 hours.  The time f o r 30 per cent a x i a l s t r a i n  In drained tests about one half of the stress  path occurred i n the f i r s t 11 hours while one quarter to one t h i r d occurred i n the f i r s t k hours.  Therefore at best two thirds of the  stress path would be r e l i a b l e and possibly only one half.  How-  ever, residual pore pressures were calculated and i t i s thought that the estimated stress path i s r e l i a b l e over almost i t s complete length. In undrained t e s t s , since the deviator stress rose very rapidly, with maximum deviator stress occurring after about 8 hours, a considerable portion of the stress path occurred within the f i r s t h hours.  In f a c t , one t h i r d of the readings were taken  within the f i r s t k hours and a c t u a l l y accounted for one half the stress path.  Therefore, one half the stress path might be con-  sidered unreliable.  However, Blight (1963) points out that errors  i n the measured values of the e f f e c t i v e stresses caused by nonuniform pore pressures depend on the overconsolidation r a t i o of the material tested.  For normally loaded material, errors are  6 6  l i k e l y to be small and consequently readings at a lower per cent equalization may be quite r e l i a b l e .  Simons (1963) suggests that  90 per cent equalization i n undrained tests i s quite adequate, the time f o r which would be 2 hours. path occurs i n the f i r s t 2 hours.  About one t h i r d of the stress Some preliminary tests were  also run at 0 . 2 5 per cent per hour average a x i a l s t r a i n or one half the rate a c t u a l l y used i n the testing program.  I t was found  that the stress path i n the early portion was very l i t t l e ferent to that obtained at the faster rate.  dif-  Thus about f i v e sixths  of the stress path i s known to be r e l i a b l e . Many investigators believe that considerably faster s t r a i n rates than those suggested by Bishop and Blight can be used and r e l i a b l e pore pressure measurements s t i l l obtained at the base of the sample.  Crawford (1963a) describes undrained tests on normally  loaded sensitive Leda clay i n which pore pressure probes i n add i t i o n to base measurements were used to determine pore pressures.  Specimens were l,h i n . diameter by 2.8 i n . i n length and  the c o e f f i c i e n t of consolidation was about 2 x 10~3-cm /sec., or 2  about the same as f o r Haney clay.  The s t r a i n rate was 0 . 5 per  cent per hour (same as used i n this testing program) and maximum deviator stress occurred at about 2 per cent a x i a l s t r a i n or after about h hours.  The t h e o r e t i c a l time f o r 95 per cent equalization  would be about h hours, thus, according to Bishop and Henkel (1962) a r e l i a b l e base measurement of pore pressure would only be obtained at f a i l u r e .  Crawford found that a pore pressure probe (0.12 cm  outside diameter) placed at the lower quarter l e v e l recorded ess e n t i a l l y the same pore pressure as that measured at the base of  67  the sample and that a similar probe placed at mid height recorded a lower pore pressure.  He concluded that pore pressure measure-  ments at the base give an accurate estimate of the pore pressure i n the f a i l u r e zone which he f e l t s t r a i n i n g effect  is near the base due to the re-  of the porous stone.  Higher pore pressures at the ends rather than at the centre for  normally loaded and sensitive material i s not i n agreement  with the general body of thought and evidence on this matter (Whitman I 9 6 0 , Bishop, Blight and Donald I 9 6 0 , and Blight 1 9 6 3 ) . The s e n s i t i v i t y time for a small diameter probe such as used by Crawford would be high.  Crawford (1963b) mentions that the res-  ponse of the pore pressure probes under ambient pressure changes could not be checked due to "plugging" of the needles.  Taylor  (1955) considered ambient pressure changes the best method of checking the response time of probes and considered a probe to be unsatisfactory  i f the delay i n reaching 95 per cent of the  applied ambient increment was more than about two minutes. The evidence for the r e l i a b i l i t y of base pore pressure readings at times which are less than that required for 95 per cent equalization may not always be trustworthy. and Donald ( i 9 6 0 )  Bishop, Blight  have stated that the onus should be on the  research worker to prove that his tests s a t i s f y reasonable for  accurate determination of pore pressure.  It is f e l t  criteria  that  the preliminary tests performed at the slower rate indicate that the pore pressures are only i n doubt for the f i r s t  one quarter  to one f i f t h of the stress path, 5.7  Pore pressures r e s u l t i n g from secondary effects  68  Samples were consolidating for a period of 2h hours after which time shearing was commenced immediately and i n undrained tests i t was assumed that a l l increase i n pore pressure was caused by applied stresses.  However, a later test series conducted by  Mr. Lou using the same test equipment and the same clay indicated that after consolidation, pore pressure r i s e w i l l take place i n the absence of any.applied deviator s t r e s s .  Figure 17 shows the  buildup i n pore pressure with time for a sample which was c o n s o l i dated to 75 I b s . / s q . i n .  for a period of 2k hours.  Since the time  for tgowas less than 200 minutes i t is f e l t that primary c o n s o l i dation was e s s e n t i a l l y complete after 2*+ hours and could not be responsible for the observed r i s e .  It was thought, at  first,  that part of the build up might have been caused by membrane leakage, or leakage past the 0-rings.  However, the rate of pore  pressure increase decreased with time and after two days had dropped to 0.3 I b s . / s q . i n .  per day.  Therefore, leakage could  account for only a small portion of the build-up. The pore pressure r i s e is thought to be due to structural re-arrangement after drainage.  It is closely associated with  secondary compression and i n fact could be described as the "converse" of secondary compression.  If further drainage is a l -  lowed secondary compression takes place due to s t r u c t u r a l rearrangement, while i f drainage is prevented pore pressure r i s e takes place. Therefore, some of the pore pressure measured during shearing is not due to applied deviator stresses and this influences the stress paths followed i n undrained t e s t s .  However, drained tests  were treated i n the same manner as undrained so that the pre-shear  NOTE". I.  Sample £4  \dlves  For  Allowed ft> Consolidate  Hours a | which Closed  and  Time Pore  Drainage Pressure  Observed. 2.  Time  Measured  Drainage  From  Close  of  Valves.  Figure 17 — Build-Up in Pore Pressure After Consolidation — Money Clay (After K. Lou)  70  conditions were the same for both.  The stress path i s not af-  fected i n the drained test but additional drainage takes place which a l t e r s the water content.  Since the object of the testing  program was to compare contours of water content obtained from drained and undrained t e s t s , i t may be that since the same procedures were observed i n both, that the water content contours are equally changed i n both types of t e s t s . 5,8  Membrane Leakage The o r i g i n a l testing procedure involved the use of glycerene  as a chamber f l u i d as suggested by Lambe (1958).  It was thought  that the use of glycerene would prevent migration of water from the chamber into the sample and allow the use of a single thin (.003 i n . wall thickness)  membrane.  the water content determined after  It was found, however, that shearing was always 1 to 2 per  cent below that calculated from i n i t i a l conditions. in the glycerene was always 20 I b s . / s q . i n .  The pressure  higher than the pore  pressure and i t was at f i r s t f e l t that pore water would not escape from the sample into the chamber against the pressure d i f f e r e n t i a l . After a series of check tests had been run, i t became apparent that high osmotic pressure differences  between glycerene and water  were responsible for the loss i n water from the sample. quently i t was discovered that previous investigators  Subse-  (Poulos,  190+) had found similar losses using glycerene and recommended that de-aired water be used as the chamber f l u i d .  With de-aired  d i s t i l l e d water as the chamber f l u i d and two membranes separated with a f i l m of s i l i c o n e grease and bound with two 0-rings top and bottom, no further leakage problems were observed.  71  5.9  Ram  friction  In most t r i a x i a l equipment the applied deviator force is measured outside the c e l l so that the f r i c t i o n force developed at the bushing where the ram i n the measured force.  passes out of the c e l l i s also included  To minimize t h i s f r i c t i o n force, b a l l  bushings, rotating rams or rotating bushings and c l o s e l y machined rams and bushings have been used.  The b a l l bushing type would  appear to be the most desirable of these because l a t e r a l forces on the ram would not produce any a d d i t i o n a l f r i c t i o n f o r c e .  A.  seal to prevent water escaping from the chamber i s necessary and w i l l give r i s e to some f r i c t i o n force which can be measured. A c e l l with a c l o s e l y machined ram and bushing was this test s e r i e s .  The ram was  used i n  greased with " l u b r i p l a t e " before  ea  test and very l i t t l e leakage occurred past the ram so that no additional seal was  necessary.  Ram  ram due to the chamber pressure was loading platform at the intended i n contact with the sample.  f r i c t i o n and  the force on the  measured by moving up the  testing rate with the ram  To determine i f the ram was  not  properly  machined and or i f the duration of the test affected the grease, a check test was  run where the loading platform was  moved up f o r  the duration of a test ( 7 0 hours) with no sample i n place. s i g n i f i c a n t change i n f r i c t i o n force occurred.  It was  that s i g n i f i c a n t f r i c t i o n forces might develop during  No  thought shearing  when the a x i a l force would be high and l a t e r a l forces might be present.  Bishop and Henkel  (1962)  suggest that a d d i t i o n a l f r i c -  t i o n forces only a r i s e because of l a t e r a l forces. College i t was  At  Imperial  found that with c e l l s similar to those used i n  72  this t e s t i n g program that the f r i c t i o n force was 1 to 3 per cent of the a x i a l load.  generally between  L a t e r a l forces were thought  to be small i n this test series because a loading cap which was free to rotate was  used.  If large horizontal forces were present  r o t a t i o n of the cap would occur followed by buckling. and Henkel suggest a f i x e d type loading cap f o r material to prevent buckling. moments may  undisturbed  However, large l a t e r a l forces and  be transferred to the ram  higher f r i c t i o n forces and may  Bishop  i n t h i s case causing  be responsible f o r the upper range  of f r i c t i o n forces quoted by Bishop and Henkel. Available evidence indicates that errors i n the deviator stress due to ram f r i c t i o n are not l i k e l y to be more than from 1 to 3 per cent and i t is quite possible that due to the of a rotating top cap, the errors may cent.  be even less than 1 per  use  73  CHAPTER 6 RESIDUAL PORE PRESSURES IN DRAINED TESTS 6.1  Introduction Residual pore pressures of some magnitude are always present  in drained shear t e s t s .  Flow of water to or from the drainage  boundaries i s caused by pore pressure gradients within the sample and the r e s u l t i n g pore pressures are referred to as residual pore pressures. The duration of drained tests i s generally chosen such that the average degree of pore pressure d i s s i p a t i o n i s at least 95 per cent at f a i l u r e , or i f a stress path i s required, at the time the f i r s t r e l i a b l e reading i s desired.  The time required for any  given degree of d i s s i p a t i o n i s usually calculated from the formulas t  F  h T\C (i-u) 2  (9)  v  where  tj> = time to f a i l u r e or a r e l i a b l e reading h = one half the height of sample T\ = factor depending on boundary drainage conditions c  v  = c o e f f i c i e n t of consolidation  U = average degree of d i s s i p a t i o n required The above formula was derived from t h e o r e t i c a l considerations by Gibson and Henkel (195^).  However, i t does not allow the c a l -  culation of average pore pressures.  An expression f o r pore pres-  sure was derived by Gibson and Henkel based on the assumption that the rate of pore pressure increase i n the undrained condition i s constant. This was then used to determine the upper bound f o r the average degree of d i s s i p a t i o n .  Since the rate of pore pres-  7h sure r i s e i n the undrained condition i s known not to be constant, their expression for excess pore pressure would"not be suitable f o r estimating residual pore pressures and was not intended to be so. Alternative methods f o r estimating pore pressures were therefore considered.  Since test data was  to be analyzed on the  computer, numerical methods of r e l a t i v e l y complex form could be tolerated.  Two  methods were developed and w i l l be referred to  as Method 1 and Method 2 .  The following common assumptions were  made: 1 . Homogeneous s o i l . 2 . Complete saturation. 3 . S o i l grains and water are not compressible. h. One dimensional flow. 5. V a l i d i t y of Darcy's 6 . k and c  y  law.  constant throughout the sample at any one time,  but vary with time, 7.  Sample deforms as a right c y l i n d e r .  It i s assumed f o r both methods that drainage top and bottom occurs. However, drainage from one end only i s obtained by simply replacing h by 2 h .  The average pore pressure rather than the maximum pore  pressure has been calculated.  The reason f o r t h i s i s that a  relationship between stresses and water content was being examined and since the water content was  the average water content, i t was  thought the stresses should be the average stresses.  It w i l l be  shown that when the degree of d i s s i p a t i o n i s high, as i t should be i n a drained test, the maximum pore pressure i s l£ times the  75 average.  So that the maximum pore pressure i s r e a d i l y obtained  from the average and vice versa. 6.2  Method 1 This method i s based on the superposition of pore pressures  (Terzaghi, 19^3» p. 2 8 6 ) . The deviator stress i s assumed to be applied i n increments, causing pore pressures which can be e s t i mated from the Skempton equation f o r change i n pore pressure under undrained conditions, namely: A U = B (A0" + A, (AcJ -A6 ) 3  x  (10)  3  Incremental pore pressures are assumed to dissipate independently and i n accordance with the one dimensional consolidation equation. The pore pressure at any time i s then the sum of the p a r t i a l l y dissipated incremental pore pressures at that time.  This method  i s discussed i n d e t a i l i n Appendix 1, Method 1 was found to predict zero residual pore pressure at maximum deviator stress for samples consolidated to k-0 Ibs./sq.in. However, drainage from the sample was s t i l l taking place at f a i l u r e , therefore excess pore pressures must be present.  I t was f e l t that  the quantity of water draining from samples could somehow be used to estimate excess pore pressure.  An examination of the work of  Gibson and Henkel (195*+) indicated that the basic equation of continuity could be used to y i e l d a much simpler expression f o r excess pore pressure i f one assumption were made.  This a l t e r -  native approach i s discussed i n the next section and i s considered to have more merit than Method 1.  76  6.3  Method 2 The equation of continuity for one dimensional flow leads  to the following p a r t i a l d i f f e r e n t i a l equation (Bishop and Gibson 1963) :  b?-  rw where  at  U 1 ;  k = permeability of the s o i l Yw = unit weight of water u = excess pore pressure z = distance or length measured from centre of sample = rate of loss of water per unit volume from any ot  element of s o i l . If i t i s assumed that the rate of loss of water from every element of a sample i s the same at any time ty, then q w i l l be a function of time only. sample was  Since the volume of water leaving a drained test  recorded during the shearing process, the rate of loss  per unit volume could be calculated,  u^, the pore pressure at  time t j i s a function of z only, hence for any one time the p a r t i a l d i f f e r e n t i a l equation (11) can be reduced to the ordinary differential  equation:  k  where  d u = _ dq = - R = constant ^ dt V R = rate of loss of water from the sample  (12)  V = volume of sample This can be integrated using the boundary conditions u = 0 at z = h and |^ = 0 at z = 0 to y i e l d the following expression f o r dt  77  the pore pressure at any time t j : j = 2 ^ § " — " And the average and maximum pore pressures are given by: U  (  h  2  z  2  )  Uj  (average) = I  YW R^h  Uj  (maximum) = A  " ^ j ^  (  1  3  )  (1>+)  2  (15)  2  •• ~ T i T  T  It i s seen from expression (13) that the theory predicts a parabolic d i s t r i b u t i o n of excess pore pressure, and consequently the average pore pressure i s two thirds the maximum pore pressure. Expression (ih)  i s very r e a d i l y programmed for the computer.  It i s much simpler than the expression involved i n Method 1 since i t involves no summation, and i n f a c t , could e a s i l y be calculated without a computer.  Only one unknown, the permeability of s o i l  appears i n the expression instead of the two occurring i n Method 1. However, an assumption was made that the rate of loss of water from a l l parts of the sample was constant at any one time.  This implies  that the change i n void r a t i o should be uniform throughout  a sample  between time i n t e r v a l s , which would probably be s t r i c t l y true only i f the rate of testing were i n f i n i t e l y  slow so that no excess pore  pressures developed and stresses were uniform throughout  the sample.  For slow testing rates, where the per cent pore pressure d i s s i pation i s high, this expression i s considered to give a good approximation of average r e s i d u a l pore pressures. The variables i n equations l*f and 15 are; the half height of sample, h; the volume of the sample, V; the rate of drainage, R;  78  and the permeability, k. readily calculated.  The height and volume of the sample are  The rate of drainage at time t j is the slope  of the volume drained versus time curve at time t j and since readings are not l i k e l y to be taken at equal time intervals was approximated as shown i n Figure 1 8 .  this  Since the permeabilities  calculated from isotropic consolidation prior to shearing and from swelling after  shearing were not considered r e l i a b l e , a method  based on measuring the pore pressure and assuming expression (15) to be correct was used.  Two slow drained tests were performed  at one quarter the normal speed, where drainage to the top only was allowed and pore pressures were measured at the bottom using the transducer.  Since the transducer Was also used to measure  the back pressure,  a very accurate measure of the maximum residual  pore pressure was obtained. and 70 I b s . / s q . i n .  Test samples were consolidated to *f0  respectively which was the range of consolida-  t i o n pressures used i n the drained test program. permeabilities are shown i n Figure 19.  The calculated  It is seen that the r e l a t i o n  between void r a t i o and permeability for both tests can be approximated by a straight  l i n e on the semi-log plot except for the  i n i t i a l portion of the test consolidated to ho I b s . / s q . i n .  It  w i l l be shown later that samples consolidated to kO I b s . / s q . i n . are not t r u l y normally loaded and t h i s i n i t i a l portion is due to an overconsolidation effect  reflected i n the permeability.  The  permeabilities calculated from i n i t i a l consolidation and from swelling after  shearing are also shown and i t appears that although  the permeabilities calculated from i n i t i a l consolidation are rel i a b l e , those obtained from swelling appear too low.  ure lfi>—Illustration of Method for Determining Drainage During Shea  80  LES-END  41  A  Dramed  Test  •»  Drained Test  S - 16 , <5 - 4 o Lbs/Sc^. InC  S-19,  1  = 70 Lb./ S^. In  j  4-0 Ini "l<* Inotropic Con»o idation  39  S-  ! ! j <  j j  •ia  |  1  Ii  1  1 0  [  i I  i !  \  i | j i ii i  36  !  57  A-lniti i l Ise frop c dons olic I s- IS  '  3fo  i  z ui u or  35  SI ieor Strain —  &  m 34CL  hZ Ul r-  33  O  52  u or: ul r<  /  t  i  1 / I  x  :  •  \/  A/  *)/  ; I  •  j  I  i  I  i  <  31  V  .  -7,  ' 0 ( 10  oJ*—<" SO  ! I  0757 I  .ECj  ~v  I  I i I  /*  Draimr 9 » - 19 o  £S  (  !^  ii  i iI i  i  z  £7  £fc £5  i  f•  •/  5  £.10'  6  7 8 9 I0"  2-  a  PERMEABILITY  lM  CM./SE.C.  NOTE: S - I B $ I 9 Sh<eqr&<=| a\ Vi, the Normal Pale but mith Drainage from Top Onl^. Excess Pore. Pr«S. From which Rermeobility Calculated . Measure«j at Botfofn Stone..  Figure 19 — Relationship  Between Void Ratio and Permeability During Shearing of-Haney- Clay.  Drained  ion  81  Since the tests to determine the permeability were run at one quarter the normal rate but with drainage from one end only, then t h e o r e t i c a l l y , i f secondary effects are not considered, the pore pressures measured at the bottom end of the slow tests should be i d e n t i c a l to those occurring at the centre of tests run at the normal speed.  The average pore pressure, equal to two thirds the  maximum measured pore pressure i s shown plotted versus shear s t r a i n in Figure 20 f o r both slow t e s t s .  Residual pore pressures calcu-  lated by Methods 1 and 2 are compared to the measured values i n Figure 21. Pore pressures calculated by Method 1 are seen to be quite d i f f e r e n t from the measured values.  For a consolidation  pressure of 70 Ibs./sq.in. the calculated pore pressures are genera l l y high by a factor of about two, while for a consolidation pressure of ^0 Ibs./sq.in. they are low, apart from an i n i t i a l peak at 1 to 2 per cent s t r a i n .  Pore pressures calculated by  Method 2 are seen to be quite similar to the measured values. They are s l i g h t l y below the measured values at strains up to about 10 per cent.  Since samples sheared at the slower rate  actually drained more than those sheared at the normal rate, due to additional time for secondary  consolidation, i t could be  ex-  pected that residual pore pressures would be s l i g h t l y higher f o r the slower rate. If i s f e l t that Method 2 gives a r e l i a b l e measure of excess pore pressure during a drained t e s t .  However, since the slow  drained tests were run at one quarter the normal speed, the measured pore pressures give r e l i a b l e values of the excess pore pressures generated at the centre of samples tested at the normal  NOTE • Avcnqge Residual pore Pres. A s s u m e d * ^ Max. Measured Pore. Pres. Ul  <r  a.  70 Lbs  I©J  ui oc o a  f  <  f/  a' iii cr  0  /  5  10 15 SO £5 SHEAR S T R A I N IN P E R C E N T Relationship Between Measured Residual Pore. Pressure Shear Strain in Drained Tests  O Fjg,£0-  3o and  II 10  1  \  a- 9 1 12  8  \  \  N  1. 1  « 70Lhs/S^-'f 1.  a 7 in  tr a a 6  f  II  j. < 5 ll O  Ul  or u  <  I  a  Of  Method 1  |.  \  1  70 P.S.I jM.ethi >eU  1  4.1 A S  ^ s ^ M e t h ?d  4-0 P.S.I  ui  7 ^ ^ ^ - S -  19 , ^ « 7 0 p.£.1. (Fig.eo)  — ^  \  \  \  aunsd  • 40 P.S.I. ^ ~ -  /-s-ia,j __(fj3.£0; hod  .  \ \  a  ^ "^ ' ^  <  ^ ^ ^ ^  S-17. &JeJfiod|  -  -  —  SO  io is ao SHEAR STRAIN IN PER C E N T NOTE:  S-IS &I3 Shear&d pt '/4- the. Normal f^afe ^ut uiith Stone o n l j .  Fig.  Pore  Pres.  21- Comparison of Measured and Drained Tests.  Droits?  from  Top  Measured a t bottom Stone  Calculated Residual Pore Pressures in  83  speed, so that these measured pore pressures could have been used to adjust the effective  stresses without any c a l c u l a t i o n s .  However,  i t may not be necessary to run check tests at such a slow r a t e . In fact the same permeability r e l a t i o n would most l i k e l y have been determined had the normal rate been used but with drainage from one end only. range,  For a drained test series i n the normally loaded  i t is probable that a few drained tests with pore pressure  measurement would be s u f f i c i e n t  to determine a relationship between  void r a t i o and permeability from which residual pore pressures in a l l other drained tests could be calculated. Method 2 also has the interesting alternative  of predicting  permeabilities under varying stress conditions when pore pressures are measured i n drained t e s t s .  If the permeability of a  s o i l is determined by the f a l l i n g head method, leaching of the s o i l may take place which i n i t s e l f may a l t e r the permeability, p a r t i c u l a r l y i n undisturbed s o i l s . takes place.  In Method 2 no such leaching  For any one s o i l at a given void r a t i o the permea-  b i l i t y is a measure of s o i l structure,  so that a measure of the  structural change caused by remolding could be obtained by comparing permeability versus void r a t i o relationships for the same clay i n the undisturbed and remolded states. Measurement of residual pore pressures and subsequent calcul a t i o n of permeabilities  i n drained tests would allow a very  simple check on the concept of Hvorslev's strength parameters 0Q and c e .  If samples at the same void r a t i o are to have the  same structure,  then their permeabilities  should be the same.  If  the void r a t i o versus permeability for normally loaded s o i l is a  straight l i n e on the serai-log plot as i t appears to be f o r Haney clay, then any overconsolidated sample i f i t i s to have the same structure at f a i l u r e as a normally loaded sample, must have i t s permeability on this normally loaded l i n e at f a i l u r e .  Samples of  Haney clay consolidated to kO Ibs./sq.in. are i n the overconsolidated range, but i t was seen from Figure 19 that after about 6 per cent shear s t r a i n the permeability lay on the straight l i n e and the sample thereafter behaved as normally loaded.  The  structure at f a i l u r e , which occurred at about 25 per cent shear s t r a i n could then be said to be the same as i f the sample had been normally loaded.  85  CHAPTER 7 TEST RESULTS 7.1  Introduction The main purpose of the testing program was  to determine i f ,  f o r Haney clay, a unique r e l a t i o n s h i p exists between e f f e c t i v e stresses and water content which is independent of e f f e c t i v e stress  path.  The main body of the testing consisted of 7 consolidated undrained  (C-U)  undisturbed  tests and 6 consolidated drained (S) tests on  samples of Haney clay a l l of which were sheared at  the same s t r a i n rate ( 0 . 5 per cent per hour).  In addition, 2  consolidated drained tests were performed at one quarter the normal s t r a i n rate but with drainage from the top only.  Undrained  test specimens were consolidated to pressures of 6 0 , 75 and 8 8 . 5 Ibs./sq.in., while drained test specimens were consolidated to pressures of *+0, 55 and 70 Ibs./sq.in.  A.t least two tests were  performed at each consolidation pressure so that the consistency of results could be checked.  Test data was  70*4-0 at the University of B r i t i s h Columbia.  analyzed on the I.B.M. Results from a l l tests  are shown graphically i n the diagrams that follow.  Typical test  readings, computer programs and computer outputs are shown i n Appendix II f o r C-U-2  and  S-17.  S t r e s s - s t r a i n c h a r a c t e r i s t i c s of Haney clay are in Section 7 . 2 .  presented  It i s f e l t that these curves are useful i n  interpreting the results discussed i n subsequent sections. tours of water content from drained and undrained in Siection 7 . 3 •  Con-  tests are compared  Energy corrections, the p o s s i b i l i t y of predicting  86  stress - s t r a i n relations and the effect of s t r a i n rate on stresss t r a i n relations i n drained tests are discussed i n Sections 7»U-,  5 and 6. 7.2  Characteristics of Haney clay The most d i f f i c u l t problem i n attempting to determine  rela-  tionships between e f f e c t i v e stresses and water content f o r an undisturbed clay is to f i n d a clay of s u f f i c i e n t l y uniform composition that consolidated samples can be obtained which l i e on a single void r a t i o or water content versus logarithm of pressure line.  The water content versus logarithm of isotropic c o n s o l i -  dation pressure r e l a t i o n i s shown on Figure 22.  It i s seen that  consolidated water contents from a l l drained tests l i e on a common straight l i n e , whereas consolidated water contents from undrained tests show some scatter and appear to l i e on a straight l i n e of about the same slope although with a water content about 1-g- per cent higher for the same consolidation pressure.  Block  samples of Haney clay were of such a size that 8 t r i a x i a l specimens could be obtained from any one block, but i n fact the drained test specimens were taken from 3 d i f f e r e n t blocks.  I t i s un-  fortunate, therefore, that the undrained test specimens taken from a fourth block do not l i e on the same straight l i n e .  Haney  clay i s laminated and i f care was not taken to insure specimens were taken from the same l e v e l within blocks, d i f f e r e n t water contents resulted. When comparing contours of water content from drained and undrained t e s t s , i t i s necessary to have samples which l i e on a common isotropic consolidation l i n e .  The scatter, i n consolidated  water contents f o r undrained tests (Figure 22) appears to have l i t t  67 LEGEND C-U-l  Consolidated  S-l£  Consolidated  Undrained Drained  Test No.!".  Test No. I£ .  Figure 22 — Relationship Between Void Ratio and Logarithm oF isotropic Consolidation Pressure.^ Haney Clay.  88 effect on the stress paths followed i n undrained t e s t s , as may be seen i n Figure 33, Section 7 . 3 .  The scatter i s such that C-U-6  has a consolidated water content that a c t u a l l y l i e s on the isotropic consolidation l i n e common to drained t e s t s .  Yet the e f -  f e c t i v e stress path followed by C-U-6 i s very similar to that followed by C-U-7.  I t appears that f o r the samples of Haney clay  tested, the consolidation pressure determines the e f f e c t i v e stress paths followed i n undrained shear.  I t was concluded from this  evidence that f o r the purpose of comparing  contours of water con-  tent, i t would be reasonable to assume that undrained samples had consolidated water contents which l a y on the isotropic consolidation l i n e obtained f o r drained samples. Stresses and p r i n c i p a l stress ratios are plotted versus shear s t r a i n rather than a x i a l s t r a i n .  The shear s t r a i n or more  c o r r e c t l y the p r i n c i p a l shear s t r a i n , £, i s given by  £ = £ , _ - 1/3 AV = 2/3 ( e - £ ) x  where  3  £ = p r i n c i p a l shear s t r a i n &L = a x i a l s t r a i n AV - volumetric s t r a i n  In undrained tests AV = 0 and the shear s t r a i n equals the a x i a l strain.  In drained tests AV ^ 0 and the shear s t r a i n i s therefore  not equal to the a x i a l s t r a i n .  Since the effects of d i s t o r t i o n  are being examined, i t appears more reasonable to compare shear strains from drained and undrained tests rather than a x i a l strains. The maximum deviator stress versus consolidation pressure relationship f o r undrained tests i s shown i n Figure 2 3 .  It is  69  o  ' 0  30  1  1  1  40 to < 80 100 ISOTROPIC CONSOLIDATION PRESSURE , RS.I  Figure 23 — Relationship Between Undromed Strength and COHSOLIDATION  1  Pressure j Haney Clay.  isotropic  90 seen that while samples consolidated to 75 and 88.5 Ibs./sq.in. l i e on a straight line passing through the o r i g i n as would be expected f o r normally consolidated material, samples consolidated t o 6 0 Ibs./sq.in. show maximum deviator stress above t h i s l i n e , indicating overconsolidation. This i s surprising as the water content versus logarithm of consolidation pressure r e l a t i o n appears to be a straight l i n e f o r pressures greater than k-0 lbs./sq. in.  I t w i l l later be shown that other c r i t e r i a also indicate that  samples consolidated to less than 70 Ibs./sq.in. do not behave as normally loaded samples. Deviator stress, p r i n c i p a l stress r a t i o , pore pressure and the pore pressure parameter A. a l l plotted versus shear s t r a i n are shown i n Figures 2h to 27 f o r a l l undrained t e s t s .  Each test  is shown by a d i f f e r e n t symbol so that the reproduceability of results can be examined.  I t i s seen that the maximum deviator  stress occurs at about 3 per cent s t r a i n , while the maximum princ i p a l stress r a t i o occurs at about 15 per cent s t r a i n (Figure 2h). P r i n c i p a l stress r a t i o versus shear s t r a i n curves are very similar for a l l tests and are represented by a single line (Figure 25). Pore pressures (Figure 26) continue to r i s e with s t r a i n , although the r i s e i s very s l i g h t from 15 to 30 per cent s t r a i n . value (Figure 27) increases throughout t e s t s . tor stress i t i s about 1.1, r a t i o i t i s about 1.7.  The A.  At maximum devia-  while at maximum p r i n c i p a l stress  At 30 per cent s t r a i n i t i s about 2 . 3 .  Maximum deviator stress occurs at about 3 per cent  shear  s t r a i n i n undrained t e s t s , at which time the p r i n c i p a l stress r a t i o is only 2.^5.  The phenomenon of maximum deviator stress  50  i i i  Si  •  11  i •  lM  C - U - 6 $7, <£ =68-3 P.S.I.  ,/ m *fl„ fa T.  40  ^ - C - U - 5 , <S • 7 5 P.S.L. C  ^Buckled  11  •  " V ^^ ^ r B u c k l o d  i i I  Sso  ii  T  02  i  O  if  1  C - U - l ^ . f i c * ^ 0 P.S.I. — '  9  :>  Iii  or »tf>  •  .  • o 0 Figure £4-  5  10 15 SHEAR STRAIN IN P E R C E N T  •  i  • : i  1  i  1 30  l  as  eo  Stress - Strain Relationship* for Undrained Tests  on  Haney Clay  3-2 —  30  - q " ^ 3?  A  -  f'  8  A • A  CT  ,  o fl: c£  til or  £-2  A  LEfirSND C - U - 1 , ^ - 6 0 RS.I  ©  c-u-a,  o  C - U - & , 6' "SS-5RS.1  •  C - U - 7 , cr.' »8a-5 P.5.I  c  NOTE:  _i 9: 1-8  z 1 1-6 K 1-2 10  iI  »&o ps.i  C-U-a45,fiu«75 PS.I Ar« Not Shown For Clarity.  •  f  10  SHEAR  IS £0 STRAIN IN PER C E N T  Ficj.2.5-— Principal Stress Ratio \ersus  £5  30  Strain for Undrained Tests o n Haney Clay  LEG-END C - U - l , <£ - t o o  A  p.c,.l.  C-U-Z, C t ' « 6 0 - 0 P.S.I. C- U - 3 , C£ =• 7 5 - 0 RS.I. C- U-3, < - 7 5 - 0 RS.I.  © 0  C- U-&, C£'« SBS P.S.I. C- u - 7 . <rj* aa-5 P.S.I. 90  0" ' = 8S'5 R S.I. d  60 C" '=75 Rs. 1. c  .70  '•  Vfl  0^=60 PSi 1.  cr  - u £D  ^  00 j 50 40 Ui CC  ^30 Ul  or W or  !  2 10  i  !  10 IS £0 SHEAR STRAIN IN PER CENT  SO  £5  Figure 2G»—Relationship Between Pore Pressure and Strain For Undrained "Tests o n Haney Clq_y  30  a.6*3 ti  O*^- CO P.S.I.  < eo P.S.I. Ui  £ 1-0 ui or  a 0-5  20 15 IN PER PER CENT, Figure 2 7 - Fbre Pressure fbrameler A Versus Strain for Haney 10  SHEAR  £5  STRAIN  Clay  SO  93  occurring before maximum p r i n c i p a l stress r a t i o appears to be a c h a r a c t e r i s t i c of sensitive clays and i s caused by the pore pressure continuing to r i s e a f t e r maximum deviator stress has been reached.  Bjerrum and Simons (I960) found similar results from  undrained tests on undisturbed  sensitive Norwegian c l a y s .  They  f e l t that the lower p r i n c i p a l stress r a t i o or f r i c t i o n angle at maximum deviator stress was due to the fact that not a l l the available shearing resistance was being mobilized at the low I t w i l l be shown i n Section h of this chapter that i n -  strain.  creasing pore pressures cause release of internal energy i n undrained tests which when corrected f o r by the Roscoe energy equation suggests that the f u l l " f r i c t i o n angle" i s being mobil i z e d at a l l s t r a i n s . Deviator stress versus  shear s t r a i n r e l a t i o n s for a l l drained  tests are shown i n Figure 28. I t may be seen that a marked kink occurs  i n the deviator stress at about 1% per cent s t r a i n for  samples consolidated to hO Ibs./sq.in., a smaller kink occurs f o r those consolidated to 55 Ibs./sq.in.  This i s further evidence of  • overconsolidation at the lower consolidation pressures, but the effect appears to be l o s t at about 6 per cent s t r a i n . deviator stress occurs at about 26 per cent s t r a i n . pressures  Maximum  Residual pore  calculated by Method 2 and discussed i n Chapter 6 are  shown i n Figure 29. Maximum average excess pore pressures  occur  at about 5 per cent s t r a i n and vary from 2.5 Ibs./sq.in. f o r samples consolidated to ^0 Ibs./sq.in. to *+.l Ibs./sq.in. f o r samples consolidated to 70 Ibs./sq.in.  A.t maximum deviator stress excess  pore pressures were about 0.9 Ibs./sq.in. and 1.2 Ibs./sq.in, respectively f o r samples consolidated to *+0 and 70 Ibs./sq.in.  34 LEG-END A  S - I 2 , 0 " c » 40  Lbs./So,.In.  V  S - 13  Lbs./Sc|.ln.  ;  C' = 55 c  S - 14,  - 70  Lbs./S«|. In.  15,  G ' - 70  Lbs./S^.ln.  e  $> - 16,  C 's 55  O  S-  0  •  S-  t  c  17, C"/ MO  Lbs./ 5^.In. Lbs./ S  T  in  I30  0  5  10 SHEAR  15 STRAIN  IN  20 PER  Figure 2 6 — Stress-Strain Relationships for Drained  25  SO  CENT  Tests on Haney Clay  35  L.E6-END  A  5.-IS, 0^ = 4 0  0  3 - 14 , 6e' = 70 L b s . / ^ . l n .  •  ••£>- 15 ,  o s-  ol410" or  ^»>^3  7• •  - 70 Lbs./6cj. In-  5 - 1 7 , <J ' » 40 C  I£  Consolidated Te*t  ~  •  Lbs./6^ln.  Lbs./Sq,. In. Drained  No. IE  E f f e c t i v e Isotropic Pressure.  Consolidation  •  • Q  \  0  h  »  LI Q. Ll ^^^^  I * 0. _1  •  <  k  10 SHEAR  5TRAIN  IS IN  so PER  50  £5  CENT NOTE  1. Exce&S By  Pore  Method  Pressutes  C«|cu|cotee|  2  2. T e s t a <it C t - a a p.s.i. NoT shown f o r the Sake «T Clarity  Figure £ 9 - Calculated Residual Pons Pressure Vs. Drained Tests on Haney Clay  Strqin For Consolidated  96  The e f f e c t of residual pore pressures on the p r i n c i p a l stress r a t i o i n drained tests i s seen to be small (Figure 3 0 ) .  The prin-  c i p a l stress r a t i o versus shear s t r a i n relations f o r a l l drained tests are shown i n Figure 31* sidual pore pressures.  These have been corrected f o r r e -  It i s seen that the curves are i d e n t i c a l  except at strains below about 7 per cent.  I t i s thought that the  separation of curves at low s t r a i n i s due to an overconsolidation e f f e c t present at the lower confining pressures.  Maximum p r i n c i -  pal stress r a t i o f o r drained tests occurs at about 25 per cent shear s t r a i n . A. comparison of p r i n c i p a l stress r a t i o versus shear s t r a i n relationships from both drained and undrained tests i s shown i n Figure 32.  I t may be seen that the undrained material i s much  s t i f f e r than the drained.  Maximum p r i n c i p a l stress r a t i o equal  to 3.05 occurs at about 15 per cent s t r a i n i n undrained  tests  while the maximum p r i n c i p a l stress r a t i o i n drained tests i s 2.82 and occurs at about 25 per cent s t r a i n . 7.3  Comparison of contours of water content from drained and undrained tests Contours  of water content determined from drained and undrained  tests on Haney clay are shown plotted i n p r i n c i p a l e f f e c t i v e stress space i n Figure 33•  It may be seen that the contours of water  content from drained and undrained tests have quite d i f f e r e n t shapes.  Thus, f o r Haney clay, there does not appear to be a  unique relationship between e f f e c t i v e stresses and water content. The data shown i n Figure 33 was prepared from the e f f e c t i v e stress paths shown i n Figures 3^ and 35.  Stress paths from un-  3-0;  IO  1  !  5  '••  10 SHEAR  !  -  15  20  STRAIN IN PER  1  £5  SO  CENT  Figure 3 0 — E f f e c t o f Residual Excess Pore Pressure on [He, Principal Stress Ratio Vs. Shear Strain Relqtion in "lest S—13  SHEAR  STRAIN  iN  PER  Figure 3i — Relationships Between Principal Stress Tests on Haney Clay  CENT  Ratio ancj Strain from Drained  9a  Figufg3£.-Compdrison of Principal Stress Ratio Vs. Strain. Relationships From Drained and Undrained Teste on Haney Clay  3 9  rigure 33—Comparison of Contours o f Water ContenT from Drained and Undrqined Tests on Haney Clay  100 LEGrEND A ©  C - U - 1 , C ' « & 0 PS.I. C - U - £ , < r ' - 6 0 p.5.1.  O  C - U - 3 , ^ ' - 7 5 P.S.I.  V • .  C- U-5, P.S.I. C - U - & , 0 ^ 8 6 - 5 P.S.I. C - U - 7 , ff '=6S-5 PS. |.  c  c  £  Fgure 34 — Effective Stress Raths from Consolidated Undrained Tests on Haney Clay  IOI  stress Ffa1h Assuming  20  30  Figure 35 — Effective Stress  40  50  €.0  sJZGi I N R5.I.  70  •Ro"Pfe*s]3uorPore Pres.  II  Siresi  100  UO  Rath Residual Horc (-"res. Considered  Paths And Contours of Water-Content From Drained  Tests  102  drained tests are shown i n Figure 3*+ and these are also contours of water content. Figure 35.  Stress paths from drained tests are shown i n  Generally drained stress paths plot as v e r t i c a l lines  in the Rendulic diagram, but due to the presence of residual pore pressure, the stress paths plot as curves.  Water contents were  known at a l l stages of drained tests allowing contours of water content to be drawn and these are also shown i n Figure 35. It was stated i n Section 7.2 that drained and undrained test specimens did not l i e on a common isotropic consolidation l i n e . It was assumed f o r the purpose of comparing contours of water content that drained and undrained samples had consolidated water contents which lay on the isotropic consolidation l i n e f o r drained samples.  However, Figure 33 indicates that the shapes of water  content contours determined from drained and undrained tests are quite d i f f e r e n t .  So that, even i f values of water content were  not assigned to the contours of water content from undrained tests, i t could be concluded from the shape alone that contours of water content are not unique f o r Haney clay. Due to the small number of tests performed,  the Rendulic  diagram i s not a very s a t i s f a c t o r y method of checking the hypothesis.  The unique relationship between e f f e c t i v e stresses and  water content i s i d e n t i c a l to the Roscoe concept of a state boundary surface discussed i n Chapter 2.  Poorooshasb (1961)  developed a method by which the three dimensional surface could be shown as a line i n two dimensions.  Burland (1965) suggested  an even simpler method of showing t h i s surface i n two  dimensions.  His method i s b a s i c a l l y i d e n t i c a l to that proposed by Rendulic i n developing the unified Rendulic diagram to compare the geometry  103  of constant water content curves.  The stresses p' and q at any  stage of drained or undrained tests are divided by p^, which i s the pressure on the isotropic consolidation l i n e  corresponding  to the p a r t i c u l a r void r a t i o of the sample at the time p' and q are measured.  For undrained tests p  i n i t i a l consolidation pressure.  i s constant and equal to the  e  In drained tests p  e  increases  from the i n i t i a l consolidation pressure to the pressure on the isotropic consolidation line corresponding  to the f i n a l void r a t i o .  The surfaces f o r a l l undrained tests are shown i n Figure 36. It i s seen that tests consolidated to 75 and 88.5 Ibs./sq.in. l i e on the same l i n e or surface, while tests consolidated to 60 l b s . / sq.in. are c l e a r l y on a separate  line.  It was mentioned e a r l i e r  that samples consolidated to 60 Ibs./sq.in. behave i n an overconsolidated manner, and i t i s this overconsolidation e f f e c t that is thought responsible f o r the separation of curves shown. The state boundary surfaces f o r drained tests are shown i n Figure 37. It i s seen that drained tests from each consolidation pressure l i e on a d i f f e r e n t surface.  This was to be expected since samples  below a consolidation pressure  of about 70 Ibs./sq.in. behave i n  an overconsolidated manner and hence would not l i e on the normally loaded surface.  I t may be seen that tests consolidated to  55 and 70 Ibs./sq.in. are reasonably  s i m i l a r , while tests c o n s o l i -  dated to hO Ibs./sq.in. are quite d i f f e r e n t .  Since the overcon-  s o l i d a t i o n e f f e c t i s reducing with increased consolidation pressure this result could be expected. In Figure 38 y i e l d surfaces from drained and undrained tests are compared.  Only drained tests at a consolidation pressure  of 70 Ibs./sq.in. are shown since these alone of the drained  Figure 36-Stale. Boundary Surfaces from. Una mined Teste o n 1  Haney Clay  (Bur land Plot)  Gfc=4cps.l.  P / _ N e t ] > s c i i r g Residual I Pore Pres. (40P-S.1) <  &  Figure 37-State Bouncjary Surfaces from  Drained Tests on Haney  Cloy  (Burland Plot)  O  / - State  Bo U n d a r y  si i r f a c e s  / Drained T< s f e , ^  \  7( ) P-S.l.  llecting Resii Jua| Pore Pr  \  Undr lined Tests  = 75$  /fl /  f  r~\'~ f  \  ^  \  p.s.i.-V  \  \ \ 1  1 i  //  / 0  /  -  / "I  \  2.  -3  4  -5  b ^, p  p  -7  S  -3 •  10  / II  12  Figure 3£> — Comparison oF State Boundary Surfaces from Drained and Undrained Tests on, Han<?y Ctay.  —  107  tests behave i n a t r u l y normally loaded manner.  Residual pore  pressures were allowed for i n c a l c u l a t i n g drained y i e l d surfaces (residual pore pressures are always allowed for unless stated) but the effect  otherwise  of neglecting them is also shown.  It  is  seen that drained and undrained tests do not l i e on the same surface and that neglecting the residual pore pressures i n drained tests results i n even poorer agreement.  Since the drained tests  at a consolidation pressure of 70 I b s . / s q . i n . the undrained tests at 60 I b s . / s q . i n .  also l i e  the effect  outside  of overconsolida-  t i o n cannot be responsible for the lack of agreement.  This sub-  stantiates the findings from the Rendulic diagram of Figure 33 and indicates that there is not a unique relationship between  effective  stresses and water content for Haney clay or that the state boundary surfaces are not the same for drained and undrained stress paths. It may be of interest to note that had drained tests been corrected for energy due to volume change as suggested by Roscoe, Schofield and Wroth (1958)? the drained surface would be even further removed from the undrained.  The concept of applying an  energy correction to determine the state boundary surface is no longer considered v a l i d .  Roscoe and Schofield (1963) indicate  that no energy correction should be applied to test data when determining the state boundary surface. 7.+ 1  Energy corrections Energy components of shear strength were discussed  i n Chapters  2 and 3 and i t appears that the Roscoe and Schofield (1963) energy equation which considers both boundary and i n t e r n a l e l a s t i c energy changes i s the most l o g i c a l .  This energy equation has been applied  108  to the Haney clay test data and the results are i n reasonable agreement with the predictions of the The  equation.  equation i s as follows: p'Sv  where  + qo£  = ^P' + Mp'oc 1 + e  (16)  K  oV = incremental volumetric  strain  S£ = incremental d i s t o r t i o n a l s t r a i n K = slope of e Vs. Lnp'  on rebound or reload  and M = r a t i o of q to p  1  at f a i l u r e .  The terms on the l e f t hand side of the equation refer to the energy transferred across the boundaries per unit volume and  the  terms on the right hand side determine to what use this energy is put.  K  ^p' represents energy stored or released 1 + e  while Mp'&£ represents Mp»  = q  w  elastically,  energy dissipated by shearing stresses.  can be considered  as the i n t e r n a l shear stress and  d e f i n i t i o n l i e s on the f a i l u r e envelope q = Mp'.  Equation  by (16)  can therefore be written i n the following form: q  w  =  Mp'  =  q  +  p»  ||  &  -  KSP«  (1 ) 7  (l+e)5£  This equation implies that whenever y i e l d i n g or s l i p at grain contacts  is occurring the r e l a t i o n between the corrected q  and p' i s always constant  w  and therefore drained and undrained  tests corrected f o r both boundary and  i n t e r n a l energy should have  stress paths which l i e on the straight l i n e q = Mp'. shown diagramatically i n Figure The  (q )  This  was  5» Chapter 2.  i s o t r o p i c consolidation and rebound lines f o r Haney clay  are shown i n Figure 3 9 .  The c o e f f i c i e n t of expansion, C , e  was  Line  peviot&r Stress  4  Figure39—Relationships  ^  6 7 6 3 10 £d ; 30 40 MEAN NORMAL STRESS p' IN RS.I.  Between Mean  50 60 70 SO  100  £00.  Normal Stress and VVater Content for Haney Clay  O  110  calculated to be 0.11, and K, which i s the slope of void r a t i o versus natural logarithm of pressure plot is therefore O.Oi+8. Since the computer was used to analyze test results q obtained f o r a l l readings.  w  was readily  Hand calculations of incremental  d i s t o r t i o n a l and volumetric strains would have been very time consuming since the incremental strains at the times of readings cannot be d i r e c t l y calculated but must be estimated by averaging the adjacent increments.  In addition, the length and volume of  sample to be used when c a l c u l a t i n g s t r a i n increments are not the i n i t i a l ones but rather those existing at the time i n question. The corrected stress paths f o r a l l undrained tests are shown in Figure k-0. It is seen that the corrected deviator stresses l i e close tc a straight line f o r a l l tests and f o r a l l strains greater than about 0 . 5 per cent.  Most of the point scatter shown occurs  at strains of less than 0 . 5 per cent. stress paths f o r a l l drained t e s t s . band rather than on a l i n e . creasing with s t r a i n .  Figure *+l shows corrected Here the points f a l l within a  I t appears that the M value i s de-  A. plot of M versus s t r a i n for a drained and  an undrained test i s shown i n Figure *+2.  M i s seen to decrease  with s t r a i n , s l i g h t l y i n the case of undrained tests and somewhat more i n the case of drained t e s t s .  Considering that Haney clay i s  an extra-sensitive material and that the Roscoe energy equation was developed f o r an idealized continuum material, the r e s u l t s , e s p e c i a l l y those f o r undrained tests appear to be i n reasonable agreement with the theory.  Scatter i n M values at low s t r a i n may  be due to errors i n readings at low s t r a i n at which time stresses are changing very r a p i d l y and readings are c l o s e l y spaced.  Alter-  Ill  L E G E N D A  C-U-I  0  , ^ ' - 6 0 p.S.I.  C - U - 2 , Q = 6>ops.l. C- U - 3 ,  0r>75pS.|  C-U-5.  <3t'«7Sp.S.|. s  66-5P.S.I.  C - U - 7 \ CQ=S8-5RS.I. of the Point Scatter at  40 :-J 60 ^ ao MEAN NORMAL STESS, PIN P.S.I.  Shewn  strqini Lsss t h a n o!5 %  v  Figun?40-Corrected and Uncorrected Stress Paths From Unclrainecj Tests On Honey Cloy ( Roscoe est, a|. Energy  LE&END  0  ao  40  A V  S-12 , O;' *40 P.S.I. S-13, 0;'^55 p.s.i.  •  S- 14, O;' =70 P.S.I. S - 1 5 , cr/=70 RS.I.  ©  s-17,  , feo e>o  o;'*4o  100  P.S.I.  lao  P IN P.S.I.  Figure41 - Corrected and Uncorrected .Stress Fbths from Drainec) Tests On Haney Cloj ( Roscoe' et q|. Eneraj ECJ.)  A  LEGEND C-U-8,CT.'-60 pS.l  0  S- |4 ,0^'-7O P S . l  2.0 IS It  A 35.-70 p.S.I.  5  >  S f 12 h- . Ul  |  i ffl  £  o  i C >  Q(j  L»—  ^_  ^  8 , $ > f c O f>S.  GD  ,0  It  y o  •  04'  oa 0  10 SHEAR  15 STRAIN  £0 IN P E R  25  CENT  figure 42. — Roscoe M Rarameter Versus Si rain  Haney Cloy  SO  nately the scatter may be due to neglect of d l s t o r t i o n a l e l a s t i c energy which i s an assumption  of the Roscoe equation.  The Roscoe concept appears to answer many questions regarding the behavior of s o i l .  I f the Mohr-tCoulomb f a i l u r e c r i t e r i o n i s  considered rather than the extended Von Mises c r i t e r i o n as implied by Roscoe, then f o r t r i a x i a l compression  ffi/ff. J  If M = 1.27  1 -  tests  . . . . (18) V3M  i s considered an average value of M, then Equation 18  yields O^/G^ = 3 . 2  or a strength envelope of 0 = 31.6  degrees.  P r i n c i p a l stress r a t i o curves of Figure 32 indicated that strains of 15 and 25 per cent were needed to mobilize maximum p r i n c i p a l stress r a t i o or maximum f r i c t i o n f o r undrained and drained tests respectively.  Figure k2 indicates that f u l l f r i c t i o n i s mobilized  at very low strains and remains reasonably constant with s t r a i n . It i s only when the energy corrections are zero that the i n t e r n a l or corrected shear stress equals the applied shear stress and the s o i l i s then said to be i n the c r i t i c a l state. did reach this state.  Haney clay never  The Roscoe concept does not question the  v a l i d i t y of the curves of Figure 35 but helps to explain their shape. Application of the Roscoe energy equation to the results of undrained creep tests on normally loaded samples of Haney clay presently being conducted by Mr. D. E. Snead at the University of B r i t i s h Columbia shows that the deviator stress, when corrected for release of i n t e r n a l energy due to pore pressure r i s e , l i e s on the q = Mp' l i n e f o r a l l stages of t e s t s , apart from readings in the f i r s t one per cent s t r a i n .  Here again f u l l f r i c t i o n i s  115  being mobilized at a very early s t r a i n . If the Roscoe concept i s correct, then the "Dependent" and "Independent" components of shear resistance as defined by Schmertmann (1963) and mentioned i n Chapter 3 have no physical meaning and a r i s e from i n t e r n a l energy changes.  The Energy  equation applies where p l a s t i c deformation or s l i p at grain contacts is occurring.  Overconsolidated material  i s assumed to remain  r i g i d p l a s t i c under d i s t o r t i o n a l stresses u n t i l the state boundary surface  i s reached.  I f maximum q/p r a t i o i s reached before  y i e l d i n g occurs the energy equation does not apply. clear, therefore, and 7.5  I t i s not  i f the same M value applies to normally loaded  highly overconsolidated samples of the same clay. Examination of methods f o r predicting s t r e s s - s t r a i n relations Methods of predicting s t r e s s - s t r a i n relationships are exa-  mined i n this section. Schofield  Poorooshasb and Roscoe (1963), Roscoe and  (1963) and Landanyi, La Rochelle and Tanguay (1965)  have presented methods f o r predicting s t r e s s - s t r a i n relationships. These methods have been discussed i n d e t a i l i n Chapter 2. An attempt has been made to apply these methods to Haney clay but none yields results that are i n s a t i s f a c t o r y agreement with the measured r e l a t i o n s . Poorooshasb and Roscoe (1963) presented a graphical method for normally loaded remolded clays by which s t r e s s - s t r a i n relations i n drained tests could be predicted from the r e s u l t s of undrained tests and consolidation tests conducted such that the r a t i o of q/p'  remained constant.  The method presupposes a unique r e l a t i o n -  ship between e f f e c t i v e stresses and water content.  Since for Haney  116  clay the relationship could hardly be considered to be unique (Section 7.3) the method i s not s t r i c t l y applicable.  However, i f  i t i s assumed that the water content contours from undrained tests are  unique, the shear s t r a i n f o r a drained path can be predicted  by the Poorooshasb and Roscoe method.  In Figure 36 i t was shown  that contours of water content from undrained tests consolidated to 75 Ibs./sq.in. or higher are geometrically s i m i l a r .  Contours  were therefore extrapolated for lower water contents and are shown on Figure h3»  Shear strains were also extrapolated and contours  of undrained shear s t r a i n appear as straight lines radiating from the o r i g i n . 70  A. drained stress path f o r a test consolidated to  Ibs./sq.in. (allowance made f o r residual pore pressure) has a  stress path as shown.  The method f o r determining strains was  discussed i n d e t a i l i n Chapter 2.  The stress path i s idealized  into increments of stress at constant volume and constant q/p' as shown i n Figure V} f o r a t y p i c a l increment CE.  The increment of  s t r a i n from constant volume i s determined from the contours of s t r a i n and equals about 0 . 5 per cent f o r the increment shown. Since no tests were performed to determine the r e l a t i o n between shear s t r a i n and volumetric s t r a i n a t constant q/p', the following r e l a t i o n (Roscoe and Schofield 1963) was used:  8v  (  M  where  ov M  -\  - A volumetric s t r a i n increment 1  K  (19)  r a t i o of q to p' at c r i t i c a l state q/p'  K  slope of e Vs. Ln. p' rebound curve  A  slope of e Vs. Ln. p* for v i r g i n consolidation  Values  O  £0  40  CO  P  ,  80  IN RS.I.  IOO  120  of Shear Strain  140  Figure 43 - Contours of Water Content and Strain From Undrained Testa on Honey Cby  118  Sc = shear s t r a i n increment. The values of M, K and  have already been determined and when  substituted i n (19) y i e l d  S£ = J**  ....  ( o) 2  1.2/-T\  and  SV = Ji§_  = £4°iw  l+e  1.9*+  0  (21)  and &V are increments of natural s t r a i n , however, since engineering s t r a i n was desired, i t was assumed that equation. (20) also held f o r engineering s t r a i n .  For an increment of stress at  constant q/p, nr^ i s constant and equals 0.737 f o r the increment DE shown. Sv = l.Mf for t h i s increment, from which the shear s t r a i n due to volume change from equation 20 i s 2.7 per cent.  The t o t a l  shear s t r a i n increment due to the increment CE i s the sum of the s t r a i n increments at constant volume and constant f[ and equals 3.2 per cent.  By summation of such increments the s t r e s s - s t r a i n  r e l a t i o n was calculated and is shown i n Figure kh along with the measured s t r e s s - s t r a i n r e l a t i o n .  It i s seen that although the  predicted s t r e s s - s t r a i n relationship i s of approximately the same shape as the measured r e l a t i o n , the c o r r e l a t i o n could not be considered as s a t i s f a c t o r y .  Since strains due to volume changes  account f o r the major portion of the calculated strains, s t r e s s s t r a i n relations f o r drained tests cannot be predicted from undrained tests unless contours of water content are independent of stress path. Roscoe and Schofield (1963) presented an equation from which s t r e s s - s t r a i n and pore pressure-strain relations can be predicted  ~ f i l Measur sd Relation 0^'«7O  PS.I.  — w >  S- 1461 See Fit ilated Rebtion ,^'•70 RS.I. 41k  /  / / / / /  / /  1  (J  //  / //  /  //  // // 1 t  7  -'  10 15 20 SHEAR STRAIN IN PER CENT Figure  ,c  25  44-Comparison of Measured and Calculated Stress-Strain Relations for Drained Tests on Haney Clay  30  120  for undrained tests i n terms of K/\ and M.  However, the r e l a t i o n  is based on the v a l i d i t y of t h e i r equation f o r the state boundary surface.  The Roscoe state boundary surface for M = 1.27 and  KA  = 0.22 i s shown on the two dimensional Bur land plot i n Figure *+5. It i s seen to d i f f e r from both the drained and undrained state boundary surfaces. Burland (1965) proposed a v a r i a t i o n on the Roscoe state boundary surface and his equation i s also shown.  It  is seen that the undrained state boundary surface l i e s reasonably close to the Roscoe surface, while the drained l i e s closer to Burland's surface. Since the Roscoe equation f o r the state boundary surface was not considered to be i n s a t i s f a c t o r y agreement with the measured r e l a t i o n , no s t r e s s - s t r a i n predictions were made. Landanyi, La Rochelle and Tanguay (1965) presented a method for predicting shear strains i n undrained tests from the results of drained t e s t s .  This method was discussed i n Chapter 2.  It  appeared to predict that i f the relationship between stresses and water content was unique, then the shear strains would also be unique, which i s not i n agreement with Henkel (I960) and Roscoe. However, since i t was found that the stress-water content r e l a tionship i s not unique for Haney clay, Landanyi's concept further examined.  was  The method assumes that the relationship be-  tween ^{/o^, £ and CJ3 form a three dimensional surface which i s unique for both drained and undrained paths and paths between these limits. tests  However, Figure 31, Section 7.2 indicates that f o r drained i s  e s s e n t i a l l y independent  of  (apart from an i n i t i a l  kink for samples consolidated to hO Ibs./sq.in.).  Therefore, the  3 dimensional surface would reduce to a l i n e , and drained and undrained tests should have the same 0~T/CV versus s t r a i n r e l a t i o n ^  /  / /  ...  *  /  ^ >  •From Burl<  ^  Uldrained Te; «  .'» 7S4SS-5 PS.l.  From Roscoe et E^udtion  A  /  0  /  i  ~  /  2  6- M»  |  3  ^ 4 — Drainec  *  '\  State fiounc sry Surfaces -  K« 0 04S ^* dai7 K/A=oaa  •  Tan  \  \ <  V  /  \  \  V  \  t  \  \ \  M - I-2L7  A  -5  , ,  -7  -8  "9  10  P/Pe  Figure 45-Comparison of Theoretical and Experimental State Boundary Surfaces (Burland Plot)  M  122  It i s seen from Figure 32 that drained and undrained quite d i f f e r e n t CJ^/fJ^ versus s t r a i n r e l a t i o n . not a unique r e l a t i o n between  0J/G3,  tests have  Therefore there is  £ and 0"^ and Landanyi's con-  cept does not apply to Haney c l a y . 7.6  E f f e c t of s t r a i n rate on drained tests Since two a d d i t i o n a l drained tests were performed at one  quarter the normal s t r a i n rate, but with drainage from one  end  only as discussed i n Chapter 6, the effect of rate of testing on the drained c h a r a c t e r i s t i c s of Haney clay can be examined. Chapter 6 i t was  In  shown that residual pore pressures are approxi-  mately the same for these tests as for those performed at the normal rate but with drainage top and bottom.  Deviator and  p r i n c i p a l stress r a t i o versus s t r a i n relationships for the normal and slow rates are compared i n Figures ^6 and k-7. I t i s seen that both the deviator stress and the p r i n c i p a l stress r a t i o are s l i g h t l y higher for tests conducted at the slower rate.  The water  content versus s t r a i n curves shown i n Figure kS indicate that the slow tests drained more due to a d d i t i o n a l time for secondary compression and this probably accounts for t h e i r higher strength. It i s generally considered that faster t e s t i n g rates give higher strength, yet here i t appears that slower rates give higher strength.However, undrained In undrained  tests are usually being  considered.  tests i t is l i k e l y that slower rates would give  reduced strength, because the a d d i t i o n a l time would lead to higher pore pressures due to the tendency f o r secondary compression.  123  LEGEND a S - 18, CT'- 40 pS.l. O S- 19, %S 70 p.S.I. t  I40  130  s-i«  c  Sfno'm Rat* = o i e s f c  120  110  "JO R b J . A^ra^e ©+ S- 14^15 Strain r ate -0-5% f »er Nr. .  /  30  a:  }  V  70  fe or  60  > UJ  50  •  d  9/  ao  111  €^  \__A  loo CL  -©-©-—0  \ C'*70 R5.  I  _ CT= 4 0 RS.1, Average c f S-12 4 Strain Rafe « O S %ferfr. C  4o  _ S-IB, 0"'= e  4o  17  ps.l.  3o £o  ( 0  5  10  15  20  25  30  SHEAR STRAIN IN PER CENT Figure 4fe-EFfect of Strain Rbte on the Stress-Strain Relations from Drained Tests on Haney Clay  (7k ff>  —  S Sao  cr < a  J 40 PS.l.  talc O S % P e rHr Strain I LEGEND  _ S. .'iv ' I strain Rote o-lE5% IS,^* TO RSI. J par Hr.  O  Strain  Rate o s % ,terMr.  5trqm  Rote  0-ies%, P c Hr.  6?  a 1-4. 1-2 K>  io : is eo S H E A R STRAIN IM PER C E N T  23  Figure 4 7 - Effect of Strain Rate on the Principal Stress Ratio Vs. Strain Relations for Drained Tests on Haney Clay  Fgure 46-Effed of Strain Rate . on the, Water Content VS. Strain Relations for Drained Tests on Haney Clay  30  125  CHAPTER 8 CONCLUSIONS 8.1  A.ND SUGGESTIONS FOR FURTHER RESEARCH  CONCLUSIONS Test  results  following  effective  that  clay,  stresses  there  and water  2. The R o s c o e clay.  there  f o r sensitive  than the simple r e l a t i o n  stress  the r e l a t i o n s h i p  and the d e v i a t o r  varying lity  from  that  tests  as w e l l  one t o t h i r t y  energy  f o r drained  as c r e e p t e s t s , This  friction  which  i s only  of i n t e r n a l  one f u n d a m e n t a l  corresponds to a f r i c t i o n  b o t h s t r a i n and s t r a i n The depend  Roscoe  energy This  and u n d r a i n e d and f o r s t r a i n s  and e f f e c t i v e  "Independent"  energy changes  strength  cohesion  and t h a t ,  parameter,  M,  component, a n d i s i n d e p e n d e n t o f  rate.  equation further  on s t r a i n ,  f o r both  suggests the p o s s i b i -  arise  there  deformation of  i s a c o n s t a n t , M.  parameters fact,  complex  soil.  plastic  and t h e Schmertmann " D e p e n d e n t " and  in  (I960) suggested  t o a p p l y q u i t e w e l l t o Haney  parameters  from n e g l e c t  boundary  between t h e mean n o r m a l e f -  per c e n t .  the Hvorslev e f f e c t i v e  state  be more  stress corrected  was f o u n d t o be a p p r o x i m a t e l y t r u e controlled  Henkel  might  t h a t whenever  t o volume c h a n g e a n d i n t e r n a l  strain  clay.  clays  between  i s independent of  i s not a unique  energy e q u a t i o n appears  i s occurring,  relationship  proposed f o r remolded  The e q u a t i o n i m p l i e s  fective due  content which  f o r normally loaded s e n s i t i v e  the r e l a t i o n s h i p  soil  i s not a unique  p a t h , or a l t e r n a t i v e l y ,  surface  to the  conclusions:  1. F o r s e n s i t i v e  stress  presented i n the previous chapter lead  i t i s also  implies  independent  that,  since  of p a r t i c l e  M does n o t orientation  126  or structure.  However, the uncorrected deviator  stress which i s  of interest i n p r a c t i c a l problems i s very much dependent on s o i l structure, since i t i s s o i l structure that determines i n t e r n a l energy changes. 3 . The Roscoe method for predicting s t r e s s - s t r a i n relations cannot be applied to a sensitive clay as i t does not have a unique state boundary surface. h. The  Landanyi method for predicting s t r e s s - s t r a i n relations does  not apply to a sensitive clay. 5. S t r e s s - s t r a i n relations for drained samples of Haney clay with approximately the same degree of residual pore pressure d i s s i pation are only s l i g h t l y altered by decreased s t r a i n rate.  De-  creased s t r a i n rates allow greater time f o r secondary compression and 8.2  result i n s l i g h t l y higher strength at a l l s t r a i n s . Suggestions for further research During the course of the testing program and  the subsequent  preparation of this thesis interest developed i n the  following  topics: 1. It was  suggested i n t h i s thesis that the Roscoe M i s a funda-  mental strength  parameter.  This concept could be checked by  t r i a x i a l tests on both overconsolidated undisturbed and  remolded  samples of Haney clay. 2. In Chapter 6 i t was  shown that the average permeability  of a  t r i a x i a l specimen at a l l stages of a drained t e s t , for which the maximum excess pore pressure has been measured, can be  calculated.  127  Since permeability at any given void r a t i o i s also a measure of s o i l structure, i t i s f e l t that very useful information with regard to s o i l structure could be obtained from void r a t i o versus permeability plots determined from normally loaded and overconsolidated tests on undisturbed and remolded samples of the same clay.  The Hvorslev concept of samples at the same void r a t i o  having the same structure could be checked i n t h i s manner.  LIST OF SYMBOLS - area of mineral to mineral contact - pore pressure parameter - stress due to e l e c t r i c a l a t t r a c t i v e forces  between  particles - pore pressure parameter - coefficient - effective  of consolidation  cohesion parameter  - Hvorslev cohesion parameter - compression index - expansion index - consolidated undrained test - void r a t i o - half height of sample - first  stress invariant  - permeability - coefficient  of unit volume decrease  - s o i l strength  parameter  - mean normal effective - effective  stress  stress on isotropic consolidation  - increment of mean normal effective  stress  - deviator stress - deviator stress corrected for energy - deviator stress corrected for energy - increment of deviator stress - stress due to e l e c t r i c a l repulsive forces particles  between  129  R  - r a t e of drainage  t  - time  t^Q  - time f o r 90 per cent primary c o n s o l i d a t i o n  tj*  - time t o f a i l u r e  T  - time f a c t o r  u  - pore pressure  u  e  - r e s i d u a l pore pressure  AU  - change i n pore pressure  U  - average degree of c o n s o l i d a t i o n  V  - volume of sample  AV  - volumetric  strain  oV  - change i n v o l u m e t r i c  strain  w  - water, content  Sw  - change i n energy  AX  - s m a l l change i n l e v e l of n u l l  z  - length  Yw  - u n i t weight of water  V  s  point  - c r i t i c a l v o i d r a t i o when mean normal e f f e c t i v e s t r e s s equals  unity  £  - shear  strain  Ei  - axial  strain  o£  - increment of shear  T\  - f a c t o r d e p i c t i n g boundary drainage  T\  - r a t i o of d e v i a t o r  K  - slope during  strain condition  s t r e s s t o mean normal s t r e s s  of v o i d r a t i o versus n a t u r a l l o g a r i t h m rebound  of pressure  130  A  - slope of void r a t i o versus natural logarithm of pressure during v i r g i n consolidation  0"  - t o t a l stress  Cj  - effective stress  0*^  - a x i a l effective stress  1  - effective consolidation pressure 0"f  - effective stress on f a i l u r e plane  fj"i p :  - p r i n c i p a l t o t a l stresses  1,2,3  " p r i n c i p a l effective stresses  131  ARMSTRONG, J 6 E e , 1957° " S u r f i c i a l Geology of New Westminster Map-Area,' B r i t i s h Columbia." Geological Survey, of Canada, paper 57-5, 25 pp.. BARRON, R-.A„, I 9 6 0 . "Prestress Effects on the Strength of C l a y s . " P r o c . Am. Soc. C i v i l E n g . , Research Conference on Shear Strength of Cohesive S o i l s , Boulder C o l o . , I 9 6 0 , p p . 163-168. BISHOP, A.W., 195*+. Correspondence on a paper by A.D.M. Penman, Geotechnique, V o l . V, pp. V3-V5. BISHOP, A.W.,196V. Correspondence on a paper by P.W. Rowe, L. •Barden, and I.K. Lee, Geotechnique, V o l . I V , s e c , 196V, p p . 370371. BISHOP, A.W., BLIGHT, G . E . , and DONALD, I . B . , I 9 6 0 . Discussion, Proc. Am. Soc. C i v i l E n g . , Research Conference on Shear Strength of Cohesive S o i l s , Boulder, C o l o . , I 9 6 0 , p p . 1027-10V2. BISHOP, A.W., and GIBSON, R . E . , 1963. "The Influence, of the Provision of Boundary Drainage on the Shear Strength and Consol i d a t i o n Characteristics of S o i l Measured i n the T r i a x i a l Apparatus." Proc.'NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. BISHOP, A.W., and HENKEL, D . J . , 1962. "The Measurement of S o i l Properties i n the T r i a x i a l T e s t . " Edward Arnold L t d . , 200 p p . BLIGHT, G . E . , 1963. "The Effect of Non-uniform Pore Pressures on Laboratory Measurements of the Shear Strength of S o i l s . " Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963, p p o 173-18V. BJERRUM, L . , 195V. "Theoretical and Experimental Investigations on the Shear Strength of S o i l s , " Norwegian Geotechnical I n s t i t u t e , Oslo, B u l l e t i n No. 5, 112 p p . BJERRUM, Strength Am. Soc. Cohesive  L . , and SIMONS, N . E . , I 9 6 0 . "Comparison of Shear Characteristics of Normally Consolidated C l a y s . " Proc. C i v i l E n g . , Research Conference on Shear Strength of S o i l s , Boulder, C o l o . , I 9 6 0 , p p . 711-726.  BURLAND, J . 3 . , 1965. Correspondence, Geotechnique, V o l . 15, June, 1965. CAMPANELLA, R t G . , 1965. "Effect of Temperature and Stress on the Time-Deformation Behaviour of Saturated C l a y . " Ph. D. Thesis, University of C a l i f o r n i a , Berkeley. CASAGRANDE, A . , and WILSON, S . D . , 1953. "Prestress Induced i n Consolidated Quick T r i a x i a l T e s t s . " Proc. Third Int. Conference on S o i l Mech. and Found. E n g . , Zurich, 1953, V o l . 1, p p . 106-110.  132  CASAGRANDE, A., and WILSON, S.D., I960. Moderators' Report, Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l , Boulder, Colo., I960, pp. 1123-1130. CRAWFORD, C.B., 1963a. "Pore Pressures within S o i l Specimens i n T r i a x i a l Compression". Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963, p p . 192-199. CRAWFORD, C.B,, 1963b. Discussion of paper by C.B. Crawford. Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa,  1963, pp. 209-211.  GIBSON, R.E., 1953. "Experimental Determination of the True Cohesion and True Angle of Internal F r i c t i o n i n Clays." Proc. Third Int. Conference on S o i l Mech. and Found. Eng., Zurich,  1953, V o l . 1, pp. 126-130.  GIBSON, R.E., and HENKEL, D.J., 195*+. Influence of Duration of Tests at Constant Rate of S t r a i n on Measured Drained Strength." Geotechnique, V o l . 195^, pp. 6-15. HENKEL, D.J., 1958. The Correlation between Deformation, Pore Water Pressure and Strength Characteristics of Saturated Clays." Thesis, University of London, A p r i l 1958. HENKEL, D.J., 1959. "The Relationships Between Strength, Pore Water Pressure and Volume Change of Saturated Clays." Geotechnique, V o l . 9, pp. 119-135. HENKEL, D.J., I960. "The Shear Strength of Saturated Remolded Clays." Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo. I960, pp. 535-55 *. 1  HENKEL, D.J., and SOWA, V.A., 1963. Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963, pp. 280-291. HIRST, T.J., 1966. " T r i a x i a l Compression Tests on an Undisturbed Sensitive Clay." M.A. Sc. Thesis, University of B r i t i s h Columbia, Canada. KENNEY, T . C , 1959. Discussion on a paper by C.B. Crawford. Spec. Tech. Publ. No. 25V, pp. *+9-58. LAMBE, T.W., 1958. " S o i l Testing for Engineers." and Sons, Inc., 150 pp.  ASTM  John Wiley  LAMBE, T.W., I960 "A Mechanistic Picture of Shear Strength i n Clay." Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo., I960. LANDANYI, B., La ROCHELLE, P., and TANQUAY, L., 1965. "Some Factors Controlling the P r e d i c t a b i l i t y of Stress-Strain Behaviour of Clay.", Canadian Geot. Jour., V o l . 2, May, 1965.  133  NOORANY, I., and SEED, H.B., 1965. "A New Experimental Method for the Determination of Hvorslev Strength Parameters f o r Sensitive Clays." Proc. Sixth Int. Conf. S o i l Mech. and Found. Eng., Canada, 1965, pp. 318-322. POOROOSHASB, H.B., and ROSCOE, K.H., 1961. "The Correlation of the Results of Shear Tests with Varying Degrees of D i l a t i o n . " Proc. F i f t h Int. Conf. S o i l Mech., V o l . 1, pp. 297-30*+. POOROOSHASB, H.B., and' ROSCOE, K.H., 1963. "A Graphical Approach to the Stress-Strain Relationships of Normally Consolidated Clays." Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. POULOS, S.J., 196V. "Report on Control of Leakage i n the T r i a x i a l Test." Harvard S o i l Mechanics Series No. 71, Cambridge, Mass., 230 pp. RENDULIC, L., 1 9 3 6 . "Relation Between Void Ratio and E f f e c t i v e P r i n c i p a l Stresses for a Remolded S i l t y Clay." Proc. F i r s t Int. Conference S o i l Mech. Found. Eng., Cambridge, V o l . 3, PP. V8-51. RENDULIC, L., 1937. "Ein Grundgesetz der Tonraechanik und Sein Experimentetler Beweiss." Der Bauingenieur, V o l . 1 8 , pp. +59-+67. l  ROSCOE, K.H., SCHOFIELD, A.N., and WROTH, C P . , 1958. Yielding of S o i l s . " Geotechnique, V o l . 8, pp. 2 2 - 5 3 .  1  "On the  ROSCOE , K.H., and SCHOFIELD, A.M.,"1963. "Mechanical Behaviour of an Idealized 'Wet-Clay'." European Conf. S o i l Mech. and Found. Eng., V o l . 1, pp V7-5l+. ROSCOE, K.H., SCHOFIELD, A.N., and THURAIRAJAH, A., 1963. "Yielding of Clays i n States Wetter than C r i t i c a l . " Geotechnique, V o l . 8:3, Sept., 1963. ROSCOE, K.H.,- SCHOFIELD, A.N., and THURAIRAJAH, A., 1963. "An Evaluation of Test Data f o r Selecting a Yield C r i t e r i o n for S o i l s . " Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. ROWE, P.W., OATES, D.B., and SKERMER, N.A., 1963. Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. SCOTT, R.F., 1963. "Principles of S o i l Mechanics." Wesley Publishing Co, Inc., 550 pp.  Addison-  SEED, H.B., MITCHELL, J.K., and CHAN, C.K., I960. "The Strength of Compacted S o i l . " Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo., I960, pp. 887-96V. SCHMERTMANN, J.H., 1963. "Generalizing and Measuring the Hvorslev E f f e c t i v e Components of Shear Resistance." Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963.  13V  SIMONS, "N.E., I960. ""Comprehensive Investigation of the Shear Strength of an Undisturbed Dramman Clay." Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo., I960. SIMONS, N.E., 1963. "The Influence of Stress Path on T r i a x i a l Test Results." Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. TAYLOR, D.W., 19V8. "Fundamentals and Sons, New York, 700 pp.  of S o i l Mechanics."  TERZAGHI, K. 19V3. "Theoretical S o i l Mechanics." Sons Inc., 510 pp.  John Wiley  John Wiley and  WHITMAN,"R.V., I960. "Some Considerations and Data Regarding the Shear Strength of Clays." Proc."Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo., I960, pp. 561-61V,  WHITMAN, R.V., LADD, C.C., and PAULO da CRUZ., I960, Discussion, Session 3 . Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive S o i l s , Boulder, Colo., I960, pp. 10V9-  1056.  135 APPENDIX  1  RFiSIDUAL PORE PRESSURES IN DRAINED TESTS, METHOD 1 This method i s based on the superposition of pore pressures (Terzaghi, 19*+3> p. 286). tion  The deviator stress w i l l be some func-  (t) of time as shown i n Figure H-9.  I t i s assumed to be  applied i n instantaneous increments AfJ^ at times £ (tj_ + t ^ _ | ) where the subscript ( i ) refers to a particular increment, so that the assumed 6"(t) i s the dashed l i n e shown on Figure k-9. The change in pore pressure A u i due to an instantaneous increment of deviator stress ACT^ can be obtained from the Skempton equation for change i n pore pressure under undrained conditions A u i = B (A(5^ + AAG^) Since B = 1 f o r saturated s o i l and (j^ does not change i n the standard drained testjAO"^ = 0 therefore A U ^ = AAG^  (22)  It i s assumed that AUj_ dissipates independently of other pore pressure increments and i n accordance with the one dimensional consolidation equation, so that at time t j where j s= i , the average pore pressure due to A U J AUJLJ  = AUI  i s A U U * where  (1 - U J J )  and Ujj i s the average degree of consolidation after a time tj^j = t j - -2- (t± + ti_]_) as shown i n Figure *+9.  By the p r i n c i p a l of  superposition the average pore pressure at time t j i s the sum of the average p a r t i a l l y dissipated incremental pore pressures at time t-? caused by a l l the increments prior to t^ therefore  (23)  i=l  CROSS SECTION Of SAMPLg  EXCESS PORE PRESSURE  Fig.49«i  observed Relation  m  a: o  I t  0  t,t t 4  s  t  TIME 4  Fig.49b  u tt  3 l/» <P Ul  ALI^ * Pore P r s due  ACT| (In&tarftaneous)  ar a. ul  £ TIME  Fig. 4 3 c  f^une 49 — Diagrams Showing Assumptions of Method 1  137  The average degree of consolidation U i s a function of the time factor T and i s usually determined from a plot of T versus U, However, since a numerical procedure was required the following relations were used (Taylor 19V8, p. 2 3 V ) . /V£ (1 - U) = 1  T < .283  (2V)  T ^ .283  (25)  - f n  fT+.0851 \ (1 - U) = 10 V .9332 ^ where  T = £y_t h2 therefore 1 - U = f (T ) = f ( C y t i j ) h2 i;j  (26)  i;J  where f (T) may be obtained from equation (2k-) or (25) depending on the value of T calculated.  Combining equations ( 2 2 ) , (23) and  (26) the complete solution f o r the average excess pore pressure at any time t j i s : Ui =  (27)  ^GT, f (°v*ij)  This expression can be r e a d i l y programmed f o r the computer. ever, 4, c  v  How-  and h w i l l vary throughout the test, therefore some  assumptions must be made with regard to t h e i r values. The Skempton A used here i s an incremental A rather than the A usually calculated.  I t was at f i r s t thought i t could be  estimated from the results of undrained tests by taking the ratios of.increments of pore pressure to increments of deviator stress and possibly expressing A as a function of s t r a i n .  T y p i c a l devia-  tor stress and pore pressure versus s t r a i n relationships f o r undrained tests are shown i n Figure 50a.  The incremental A values  136 to '— PORE  SO  (initial  PRESSURE  Pon  P l B > . " IO Lbs.  *|.  I*)  40  z  - DEVIATOR  O-30  STRESS  <n  UNDRAIh IED T E S T 10  o  io  es  eo  15  SHEAR STRAIN IN PER CENT  30  Fig.50a 1  /  < z o yQ. 2  inc'ns mental A  &oe* to Infinity ot  Mq*. DeV. STress  /  Ll  h or *  •  -6  io  is  SHEAR STRAIN  IN  eo PER  £5  CENT  30  Fig. 5 0 b 70 • CO  $50 u?  •  •  (0 -•40 z iP  Ul 30 Or  or 20 o > 10 ui  a  DRAINED i  1  i  i >  15 SO SHEAR STRAIN IN PER CENT  10  1 EST  Figure50 — Stress-Strain Characteristics of Haney Cby  S5  so  139 calculated from Figure 50a are shown i n Figure•50b.  It is  seen  that at maximum deviator stress, since the rate of change of deviator stress is zero A. = Q±  goes to i n f i n i t y .  After maximum  AO  deviator stress, pore pressures continue to increase resulting i n negative incremental A. values.  Increasing pore pressures  after  maximum deviator stress are caused by d i s t o r t i o n , despite f a l l i n g deviator stress, rather than because of f a l l i n g deviator s t r e s s . A t y p i c a l deviator stress versus s t r a i n curve for a drained test i s also shown i n Figure 50.  It is seen that the shape is  quite  different from the undrained test with maximum deviator stress occurring at high s t r a i n and therefore the incremental A values from undrained tests could not be used.  It might be expected that  the incremental A would increase with s t r a i n from approximately 1/3 at low s t r a i n where e l a s t i c behaviour .might occur to  infinity  at high s t r a i n as maximum deviator stress is approached.  However,  no l o g i c a l basis for varying A could be determined and so a constant value of A = 1 was chosen. The coefficient  of consolidation, c v , varies during a test  due to change i n structure and change i n void r a t i o .  Values of  c v determined from both preliminary consolidation prior to shearing and from oedometer tests are plotted versus the average pressure p 1 = 1/3 ( C | + 20^)  a  n  d  shown on Figure 51.  tests i t was assumed that k 0 was 0.75.  For oedometer  The range of p 1 for a l l  drained tests was from hO to 110 I b s . / s q . i n .  and the r e l a t i o n  between p 1 and c v i n this area was approximated by the  straight  line on the semi-log plot shown, from which c v = .0051 - .002^3 log  1 0  p'  cm 2 /sec.  ( 2 8 )  140 L  E  &  E  N  O  •  Undrained Tests j Pnsiiminoiy Consolidation  +  Undrained Test, Consolidation A f t e r Shednnj  O  Drain*d  +  Oedometer  Teste, Pnsllminbgr Consoliddtii  iTion  Tests  NOTE: I. C Plotted N t e f M J S Average effective. Stress For Load Increment". v  E  K » o«8 0  /Assumed For Oedometer Teats.  • ooa  o  •0O25 •  O ui it)  u  •ooe  >  z g  •0015  G  5 o  < zo o u  u. o  CV' 0 O 5 l - $ 0 3 l & L O C r p I N A R E A O F I NTT REST  •001  r-  \  7.  UJ  u  u. U-  HJ  o  C l  \ •0005  \  20  10  30  40  SO  60  70  \  60 90 100  MEAN NORMAL. EFFECTIVE STRESS IN LBS./SQ.IN.  Figure 51 — Relationship, Between-Coefficient of Conadidotion and Effective Stn»as for Honey  Clay.  It appears from Figure 51 that c lower than the figure of 2 x 10  v  i n the area of interest i s cm /sec. used i n the previous 2  chapter to determine testing rates.  However, i t is understood  from Bishop and Henkel (1962) that the c expressions i s the c  v  y  mentioned i n t h e i r  obtained during the preliminary consoli-.  dation prior to shearing and not the c consolidation pressure.  The c  y  v  that exists at the f i n a l  values shown i n Figure 51 are  plotted at the average p' during the consolidation increment. obtained from t r i a x i a l consolidation vary between 1 x  10~3  cm /sec. and 3 x 10"3 cm /sec. and hence the figure of 2 x  10~3  c 's v  2  2  cmvsec. was  chosen.  The height of the sample also varies throughout a test and since a x i a l s t r a i n at f a i l u r e was about 30 per cent, this could not be neglected.  The height of the sample was  that readings were taken..  known at a l l times  It was assumed that at any time t j  the pore pressures due to a l l prior increments  dissipated under  the constant sample height and c o e f f i c i e n t of consolidation existing at that time.  In actual fact pore pressures due to  e a r l i e r increments would have been d i s s i p a t i n g under a gradually reducing height and c o e f f i c i e n t of consolidation. However, pore pressures due to e a r l i e r increments w i l l be very small and the height and c o e f f i c i e n t of consolidation w i l l be e s s e n t i a l l y correct for those increments  applied immediately  prior to the  time of interest and which undoubtly cause the major portion of the pore pressure.  APPENDIX I I  143  COMPRESSION TEST  TRIAXIAL J  SOIL  SAMPLE :  SPECIFIC TEST  Hon^y  &RAYITY:  Undrained  Height of Areq  -  AFTER  B  g | 0  ,  = 2-77S| , n  3 4 C r n  a  V =  a  t  ,|.to | t S  = 32-75 Cm.  s  in Hf.  Consolidated WATER  ;  of  Saturation  «• 39-3 for Cent  S -  Change in  )  ^M\tt Content «  -o-14 Cm. , Consolidated Areq  V  m  _  /  >  0  Ht. «6-3iCm. » 272 In.  - s-feacrn, " = i - 5 o i n .  V  8  He  » 6> 7 % ^ UJ7 = 3S6  a  CONTENTS  Specimen  Location  Container  Si'de  Side  Side  Side  1  2.  3  4-  No.  Top  v/hole 4tWhole x . Initial!* Finalla c  6ottolT1  l  5  Wt- C o n t a i n e r {Wet Soil  3>9 S3  34-11  42-76  44-37  4o-49 4VS0 133-88 171-71  wT. Container 4 Dry ^*>l  3S'I9  29- It  35-11  36-30  3.4- IB  6-64  495  7-6S  «-o7  17-44.  17-Si  IT 17  17-29  last  17-47  Soil m grn*  15-73  II 63  1794  19-01  15-62  I6-5C  9|>30 91-30  Water Content ( U J ) %  4e-«*  44.50 4270  40-4  4o-£  4i£  Wt. Water  in o/ns  Wt-  Container  Wf.  Dry  i n gms.  CONTENT  3603  94-sa  144 78  6,- 7 li 47 39-54 3501  4&-SO  5-02 53-48  3S-3  CHECK  Vol- Drained During Consolidation » 6 - l 5 c c , Vo|. Drained During Shear — cc , Vol. BaoK Drained »l-8occ , Tota| V o l . Change *4'3SCC Change in V/ofer Content * 46 %,  Initial UJ% (Side Trimming*)  a  Initial ujy from 4 Final bry W t .  Initial wt.  Initial  FiHo| ui%  0  = 4J£  111% -From  Change, m m%  REMARKS Trimming* Mat Further  ~ 42-5  }  and P,.jc  3  CONSOLIDATION  Change in Vol. - fe 15 Cc  WATER  n  ui% (Side Trimmings) -=4fr5 e »ft^T^» I -196  Average Degree  Change  c  \blume ( V ) ° 7 3 0 C m \  3-620 10-30  Bottom 11-36  Sample = 7-OSCrn.  A t + 2A -r A 4-  10-36  H-40 3 6£5 10-33  Centre  RY: RM-6.  TESTED  DIMENSIONS  Dia. Aneq in Cm. in Cm?  11-43  N0.:_£  TEST  DATE > July 19, 2,5  Consolidated  MEASURED  Circ, in Cm. Top  Clgy  £SO  TYPE :  INITIAL  leacBggasgraagaB  1  Trimmed h> AlloUi f o r T o p tt Bottom Trimming  = 43-1  144APPLICATION OF CHAMBER PRESSURE UNDRAINED CONDITIONS TEST  NO.: a  D A T E : Jujy|3ja&5 TESTED BY: RM..B.  TIME HRJ.  EUW.E& CHAM»tt CHAMBER CMAMBW PORE PR. Pope f»s. PORE TlMB OAUOK COR. Pit. PRE*. con. f>».l PRES. Mttl BS.I. P.%.1. R6.|.  0  10  0  10  ft-5  SK6MPT  -° B N  4-1 S3  99  064  i  4  1  zo  -0-1  ll  -0|  -4-4»  -4-7  -oa  S9B  -47  -ot  4-9-8 46 a  -4-8  IOO 20  GO  -o-e.59-B  71-3  -Ol  7ia  OVER ALL  54«0  567  roi  4.4 0 9B  o sa  -4-9  11-4 24  C3-5  IOO  9 9  \<o 50  Ml  10-5  99 40  12-4  ill ea-2  -  IE  170  io-o  1  ao  I9;9  II  5  70%3 -3-0  B » ^-|- *IOO  REMARKS: Thermostat Stuck Before Commencing) qnd th»> Mqy Account For The Variation in B  145 CONSOLIDATED  TRIAXIAL  TEST  P R E L I M I N A R Y CONSOLIDATION CHAMBER  PRES.  GAU&E =  TEST  7 1 - 3 PS.l-  NO:  - O l  RS-I.  DATE :  JULY  ELEVATION  CORRECTION a r - l - 2  RSI-  TESTED  &Y:  CHAMBER  PRESSURE  G-AUcVE.  CORRECTION  EFFECTIVE  DATE  =  =  7 0 0 PS.l. STRESS  TIME HRS)  TULYI<1 '65  BACK  CHAN6E  ELAPS66  TIME TIME MIN.  PRES. »  4-7  DIAL  RD. IN.  TO  BUfi.  RD. CC  o.oo  OOO  0:04  0>ZG  <] 5 5  0:15  0-50  948  0:34  0-75  9- 3 6  IOO  9 26  IOO •  i.i4  •940O  171  l'2S 9 Ob  ISO  32.2A  3:04  I7S  4:00  £00  6-85  2-SO  6-64  3.00  aqo  8-43  12* 15  3-50  itoo  4..00  600  2SO0  500  75a  36:O0  600 0 ^ 7 0  7-eo  49:00  7 00 a 05  61:00 •  100:00 1000  &-oa  120.00 I 0 3 S 0 * 9 4 7  sao  131:00  Tuuy to  l£:£S  a 00  1 l-4a.  5-fc6 08635  15fc  GOO  TEMP  °C  lO-O RS.I RS.|.  a IS,  l%5  PM.B  CONSOLIDATED Consolidated Consolidated Chamber  Time Hn  Por«. Pres. Gouge  UNDRAINED  Areq « I-5Q ln. Length « &7L  > Proving  a  In  TRIAXIAL  Cor.  TEST  Rin^ No.  Teat  , Colibrdhon fi»ctbr « »3lfe7  Pressure » 70 O P S . l T e m p .  Vertical Pore Prv%. Dial P.S.I. in-  Proviig  146  ^  - £ 4 °C  Dial  Time Hr  Pore Pre*.  No:  £  Date: July 2.o/6>5 Tested By: P.HB.  Cor.  Pbre Pres. RS-I.  CrtlLl^e  Di'c,| in.  Proving Dial  15-583  -4-6.  |0-0  •8835  42-5  2358  540  -4 8  49-2  •77*3 207-3  15-633 iS-(b  -44.  ll-o  86Z2. 5O0  2S-IO  557  -4-8  50-q  •7557 206-3  15-717  16- C  -4fe  120  610  25-18  55-1  -4-«  SI-1  •7414 2 0 4 7  I5-&JS  17-7  -4-fo  13-1  700  2B-28  •56-3  -4-9  53*4  •7057 2017  15-1+0  l&B  -47  14-1  •8815  800  30-4S 5 ^ 5  -4-*)  54-fc  '6676  16-08  -4-7  ISi  •8S07 TI-0  33-00 60-2  -4H  55-3  •6 340 196-5  16-15  2 a - o -4-7  17*  •B80O 100-0  S5-42  60-Q  -4-9  55^  •5%7 194-7  23-4  -4-7  167  •87=11 lll'O  1733  (*\>B- 4 1  56-3  •S66J 1932  16-47  25-3  -47  •8778 IC| 0  38-50  -4-9  5-6-3  •5488 191-7  Ifc-fcO  26>& - 4 7  •67*7 I30-5  40-5& 617  -4-9  S6-8  • 5 R 5 iqo-o  16-78  -4-7  •&750 1407  4|-0  617  -4-q  56-8  •5H6. 1 9 0 0  16-^6  -4-7  25-5  •8733 i s o - e  4 7 0 8 427  -4--V  57-8  •4174  -4-fl  578  •4114 1873  56-1  •2600 183-3  S8-<|  •2I?8  22-1  1717  31*7  -4-7  27-0  •«7IO Ifeoo  4 7 ' 3 0 62.-7  1742-  33-1  -47  2«T-Z  -5682 I70-O  57-50 63-o  I7-7S  "i&-3 -47  3l-6>  •8643  leo^  60-17  63-9  IV17  31-8  -47  35-1  •8S«lo  Ho-o  62-io  64-0  18-17  42-5  -47  37-8  •8501 IT* 2  65-00 6 4 2 .  l<V33 44-5  "4-7  11-8  •&4£« e o s o  72-45  42-8  <S2C6. 2 0 ^ 3  20-38 47-6> - . B 4  ai-2Z  50 5 -4.. 8  4S7  •8|3fc 210-0  £1-70  sn  4>ff  •S062 20<V4r  -4>*  -4-n  I8Z--3  •1765 t e ° 7 -4-T  S<W 5°1'3  • 1453 178-6 .0307  m-7  147 TEST NO. 2 CONSOLIDATION PRES.= 60.0 CONSOLIDATED UNDRAINED TRIAXIAL TEST ELAPSED TI.ME HOURS -0.00 0.05 0. 13 0.25 0.36 Oi50 0.60 0.73 0.89 1.02 1.20 1. 38 1.58 1.84 2.17 2.59 3.19 3. 75 4;. 80 5.64 6. 12 7.25 8.00 9.52 10.40 12.70 14.87 17.42 19.84 21 .75 22.92 24.92 25.42 31.50 31*92 41.92 44.58 47.32 49.42 56.87  STRAIN PFR f.FNT 0.00 0.01 0.03 0.05 0.07 0. 10 0.13 0.16 ' 0.21 0.25 0.31 0. 38 0.46 0.56 0.71 0.90 1.20 1.50 2.0.9 2.57 2.84 3.46 3.87 4_.JjO_ 5.22 6. 54 7.94 9.17 10.54 11 .66 12.31 13.38 13.67 17. 14 17.36 22.92 24.44 25.99 27. 14 31.35  DEFORMATION IN._ PER DAY . -0.000 0.144 0.161 0.125 0.134 0. 135 0.141 0. 144 0.154 0.160 0.170 0.178 0.190 0.200 0.213 0.227 0.245 0.261 0.285 0.298 0.303 0.312 0.316 0.322 0.328 0.336 0.349 0.344 0.347 - 0.350 0.351 0.351 0.351 0.355 0.355 „0..J3.5_7_ 0.358 0.359 0.359 0.360  SIGMA 1 EFF PSI 60.0 60.6 61.9 62.7 63.8 64.3 64.8 65.7 64.9 66.4 66.8 6X..2 67.7 67.6 67.3 65.8 64.9 64..0 61.7 58.8 57.8 56.0 54.2 52.0 51.4 48.0 45.7 44.2 42.8 . - 4.L..8. 41.3 40.2 40.1 37.6 37.5 3_4...8 33.4 32.5 31.6 30.3  ROOT 2 SIGMA 3 EFF I.N PS.I_ . 84.8 83.4 82.0 80.5 79.0 76.5 74.5 72.5 68.4 67.7 65.2 6.2.9 60.8 57.7 54.3 49.3 45.5 42.7 38.5 34.4 33.2 31.4 29.4 2.7_..0. 26.7 23.5 21.8 20.8 19.9 L9...4 19.4 18.7 18.7 17.3 17.3 16.8 15.7 15.4 15.1 15.1  DEVIATOR SXRESS PS.l -0.0 1.6 3.9 5.8 7.9 .1.0...2 12.1 14.4 16.5 18.5 20.7 22.7 24.7 26.8 28.9 30.9 32.7 33.8 34.5 34.5 34.3 33.8 33.4  PRINCIPAL SJRE.S.S RAXID 1.00 1.03 1.07 1.10 1.14 1.19 1.23 1.28 I 1.34 1.39 1.45 1.51 1.57 • 1.66 1.75 1.88 f 2.02 2.12 2.27 2.42 2.46 2.52 2.61 2 . 72 . 32..J? _ 32.5 2.72 2.89 31.4 2.97 30.3 29.5 3.01 28.7 3.04 28...1 _ 3.05 27.6 3.02 [ 27.0 3.04 I 26.9 3.04 1 25.4 3.08 25.3 3.07 _ 2.93 . 22..„9. _ 3.01 22.3 2.98 21.6 2.96 20.9 2.83 19.6 1  !  SKEMPTON A 0.00 0.63 0.51 0.53 0.52 0.58 0.60 0.60 0. 70 0.65 0.67 0.68 0.69 0.72 0.75 0.81 0.85 0.88 0.95 1.04 1.06 1.12 1.17 1.24 1.27 1. 38 1.47 1.53 1.60 1.65 1.68 1.73 1.74 1.88 1.89 _ 2. 10 2. 19 2.27 2.35 2.52  PORE PRESSURE PSI . 10.0 11.0 12.0 13.1 14. 1 . 15._9„ _ _ 17.3 18.7 21.6 22. 1 23.9 25.5 27.0 29.2 31.6 35.1 37.8 39.8 42.8 45.7 46.5 47.8 49.2 5.0,._9. 51.1 53.4 54.6 55.3 55.9 56.3. .. 56.3 56.8 56.8 57.8 57.8 58. 1. 58.9 59.1 59.3 59.3  CONSOLIDATED UNDRAINED TRIAXIAL  ^  STRAIN PER CENT 0.00 0.01 0.03 0.05 0.07 0.10 0. 13 0. 16 0.21 0.2 5 0.31 0.38 0.46 0.56 0.71 0.90 1.20 1.50 2.09 2.57 2.84 3.46 3.87 4.70 5.22 6.54 7.94 9.17 10.54 11.66 12.31 13.38 13.67 17. 14 17.36 22.92 24.44 25.99 27.14 31.35  P EFFECTIVE ROSCOE PSI 60.0 59. 5 59.3 58.8 58.5 57.5 56.7 56.1 53.9 54.1 53.0 52. 1 51.2 49.7 48.0 45.2 43.1 41.5 38.7 35.8 34.9 33.5 31.9 30.1 29.7 27.1 25.5 24.5 23.7 23.1 22.9 22.2 22.2 20.7 20.6 19.5 18.5 18. 1 17.7 17.2  Q ROSCOE PSI -0.0 1.6 3.9 5.8 7.9 10.2 12. 1 14.4 16.5 18.5 20.7 22.7 24.7 26.8 28.9 30.9 32.7 33.8 34.5 34.5 34.3 33.8 33.4 32.9 32.5 31.4 30.3 29.5 28.7 28. 1 27.6 27.0 26.9 25.4 25.3 22.9 22.3 21.6 20.9 19.6  TEST  QW ROSCOE PSI 0.0 " 77.8 59.1 64.0 61.4 87.0 71.9 85.9 61.5 28.9 59.2 52.9 53.0 58.7 59.6 58.2 47.4 46.0 47.2 44.3 41.0 41.1 40.9 35.8 34.8 35.0 32.4 31.1 30.0 28.9 28.5 27.4 27.1 25.7 25.6 23.9 23.2 22.2 21.5 0.0  M ROSCOE 0.00 1.31 1.00 1.09 1.05 1.51 1.27 1.53 1.14 0.53 1.12 1.02 1.03 1.18 1.24 1.29 1.10 1.11 1.22 1.24 1.17 1.23 1.28 1.19 1.17 1.29 1.27 1.27 1.27 1.25 1.24 1.24 1.23 1.24 1.24 1.23 1.25 1.23„_ 1.21 0.00  TEST NO. 2 CONSOLIDATION PRES.= 60.0 UNIT P UNIT Q ROSCOE ROSCOE 1.00 -0.00 0.99 0.03 0.99 0.07 0.98 0.10 0.98 0.13 0.96 0.17 0.20 0.95 0.94 0.24 0.90 0.28 0.90 0.31 0.88 0.34 0.87 0.38 0.85 0.41 0.45 0.83 0.80 0.48 0.;75 0.51 0.54 0.72 0.69 0.56 0.57 0.64 0.60 0.57 0.57 0.58 0.56 0.56 0.53 0.56 0.50 0.55 0.50 0.54 0.45 0.52_ 0.51 0.43 0.41 0.49 0.39 0.48 0.47 0.38 0.46 0.38 0.37 0_.45 0.37 0.45 0.34 0.42 0.34 0.42 0.33 0.38 0.37 0.31 0.36 0.30 0.29 • 0.35 0.29 0.33  , S  TEST NO.17 CONSOLIDATION PRES.= 4 0 . 0 CONSOLIDATED DRAINED TRIAXIAL NO ALLOWANCE MADE FOR RESIDUAL PORE PRESSURE SHEAR AXIAL DEFORMATION WATER DEVIATOR STRAIN STRAIN IN.PER DAY CONTENT STRESS PER CENT PSI -0.00 -0.00 -0.000 37.9 0.0 0.04 0.05 0. 146 37.9 4__1 0.13 0.16 0.172 37.8 9.2 0.18 0.23 0.182 37.8 11.9  0. 2 5  0.31  0. 191  37. 8  J___._7  0.35 0.46 0.57 0.73 0.93 1.12 1.42 1.85 2.61 3.40 3.87 4.29 4.77 5.25 8.07 8.72 9.34 10.50 11.22 11.91 12.38 12.95 13.69 _14_._16 14.68 15.20 19.29 20.04 20.78 2_1._9.3_ 22.70 23.26 23.59 24.25 25.05 25.42 25.96 26.55 27. 17 27.69 28.03 28.77 29.62 30.65  0.45 0.59 0.74 0.97 1.23 1.50 1.92 2.51 3.57 4.60 5.21 5.77 6.40 7.03 10.50 11.28 12.03 13.39 14.21 15.02 15.56 16.21 17.05 17.58 18.14 18.72 23.20 24.01 24.81 26.03 26.84 27.44 27.79 28.49 29.33 29.72 30.29 30.90 31.54 32.08 32.44 3 3_. 2 0 34.08 35.13  0.211 0.224 0.235 0.248 0.264 0.277 0.288 0.298 0.312 0.321 0.326 0.330 0.331 0.331 0.338 0.338 0.338 0.J39 0.341 0.342 C.34I 0.341 0.341 0.3 42 0.343 0.344 0.345 0.345 0.344 _0.345 0.346 0.346 0.346 0.346 0.345 0.346 0.346 0.347 0.347 0.348 0.348 0.347 0.347 0.348  37.7 37.6 37.5 37.4 37.3 37. 1 36.8 36.4 35.8 35.2 34.9 34.6 34.3 34.0 32.5 32.2 32.0 31 .5 31.3 31.0 30.9 30.7 30.5 30.4 30.2 30.1 29.3 29.1 29.0 28.8. 28.7 28.6 28.6 28.5 28.4 28.4 28.3 28.3 28.2 28.2 28.2 2_8__1 28.0 28.0  17.9 20.8 23.5 26.6 28.6 29.9 30.8 31.5 33.2 34.6 35.7 36.8 37.7 38.8 46.9 48.3 50.4 53. 3 54.8 56.2 57.0 58.6 60.2 61.1 62.1 62.8 68.3 68.8 69.9 70.5 71.0 71.3 71.3 71.3 71.8 71.9 72.6 72.0 72.0 71.9 71.6 JjL. 4 71.8 71.7  .  SIGMA 1 EFF. PSI 40.0 44. 1 49.2 51.9  'S*t*3  57.9 60.8 63.5 66.6 68.6 69.9 70.8 71.5 73.2 74.6 75.7 76_-J 77.7 78.8 86.9 88.3 90.4 93.3 94.8 96.2 97.0 98.6 100.2 101.1 102.1 102.8 108.3 108.8 109.9 110.5 111.6 111.3 111.3 111.3 111.8 111.9 112.0 112.0 112.0 111.9 111.6 111.4 111.8 111.7  TEST ALLOWANCE MADE FOR RESIDUAL PORE PRESSURE PORE SIGMA 3 ROOT 2 SIGMA 1PRINCIPAL PRES. EFF. SIGMA 3 EFF. STRESS PSI PSI E F F . PS I PSI RATIO 0.0 40.0 56.6 40.0 1.00 0__5 39.5 55.9 43.6 1. 10 0.8 39.2 55.4 48.4 1-23 0.9 39.1 55.3 51.0 1.30  PRINCIPAL STRE.SS RATIO 1.00 1. 10 1.23 1.30  1.37  1.45 1.52 1.59 1.67 1.72 1.75 1.77 1.79 1.83 1.87 1.89 1.92 1.94 1.97 2. 17 2.21 2.26 2.33 2.37 2.40 2.42 2.46 2.51 2.53 2.55 2.57 2.71 2.72 2.75 2_._76.__. 2.78 2.78 2.78 2.78 2.80 2.80 „ 2.80 2.80 2.80 2.80 2.79 2.79 2.79 2.79  ;  UO  ;  .  -  1.4 1.3 1^5 1.6 1.8 2.1 2.0 2.2 ______ 2.4 2.5 ______ 2.5 2.5 2___3 2.3 2.4 2_.2_ 2.2 2.2 ______ 2.1 1.8 1.7 1.8 1.8 1__5 1.4 1.2 i.JL 1.3 1.1 0__9 1.0 1.0 1.0 0.7 0.7 0__7 0.7 0.8 _0_._5.. 0.5 0.0  39.0  38.6 38.7 38.5 38.4 38.2 37.9 38.0 37.8 37.7 37.6 37.5 37.5 37.5 37.5 37.7 37.7 37.6 37.8 37.8 37.8 37.9 37.9 38.2 38.3 38.2 38.2 38.5 . 38.6 38.8 3_j3_._9 38.7 38.9 39.1 39.0 39.0 39.0. . 39.3 39.3 39.3 39.3 39.2 39-A _._ 39.5 40.0  55.1  54.6 54.7 54.5 54.3 54.0 53.6 53.7 53.5 53.4 53.2 53.0 53.0 53.0 53.1 53.3 53.3 53.2 53.4 53.4 53.5 53.6 53.6 54.0 5 4_._1 54.0 54.0 54.4 54.6 54.9 55.0 54.7 55.1 55.3 55.2 55.2 55..X. 55.5 55.6 55.6 55.5 55.4 _5 5^. 7 55.9 56.6  53.7  56.5 59.4 62.0 65.0 66.8 67.7 68.7 69.3 70.9 72.3 73.2 74.2 75.2 76.3 84.6 86.0 88.0 91. 1 92.6 94.0 94.9 96.4 98.4 9_9_- 4 100.3 101.0 106.7 107.5 108.7 109.4 109.7 110.2 110.4 110.4 110.8 1.1.0...9 111.2 111.3 111.3 111.1 110.8 110...8 111.3 111.7  1.38  1.46 1.54 1.61 1.69 1.75 1.79 1.81 1.83 1.88 1.92 1.95 1__98 2.00 2.03 2.24 2.28 2.34 2.41 2.45 2.49 2.50 2.55 2.58 2.60 2.63 2.64 2.77 2.78 2.80 2.81 2.84 2.83 2.82 2.83 2.84 2.85 2.83 2.83 2.83 2.83 2.83 2 ._8_1 2.82 2.79  ISO  SHEAR STRAIN -0.00 0.04 0.13 0.18 0.25 0.35 0.46 0.57 0.73 0.93 1.12 1.42 1.85 2.61 3.40 3.87 4.29 4.77 5.25 8.07 8.72 9.34 10.50 11.22 11.91 12.38 12.95 13.69 14. 16 14.68 15.20 19.29 20.04 20.78 21.93 22.70 23.26 23.59 24.25 25.05 25.42 25.96 26.55 27.17 27.69 28.03 28.77 29.62 30.65  P PSI 40.0 41.3 _43.0 43.9 44.9 45.9 46.9 47.8 _48.8 49.5 49.9 50.2 50.4 51.0 51.5 51.8 52.2 52.5 52.9 55.6 56.0 56.7 57.7 58.2 58.7 58.9 59.5 60.0 60.3 60.6 60.9 62.7 62.9 63.2 63.4 63.6 63.7 63.7 63.7 63.9 63.9 63.9 63.9 63.9 63.9 63.8 63.7 63.9 63.9  P MINUS PP. PSI 40.0 40.8 42.2 43. 1 43.8 44.5 45.5 46.3 47.2 47.7 47.8 48.2 48.3 48.7 49. 1 49.4 49.7 50.0 50.4 53.3 53.7 54.4 55.5 56.0 56.5 56.8 57.3 58.2 58.6 58.9 59.1 61.2 61.5 62.0 62.3 62. 3 62.6 62.8 62.8 62.9 62.9 63.2 63.3 63.2 63.1 63.0 63.1 63.4 63.9  Q PSI 0.0 4.1 9.2 11.9 14.7 17.9 20.8 23.5 26.6 28.6 29.9 30.8 31.5 33.2 34.6 35.7 36.8 37.7 38.8 46.9 48.3 50.4 53.3 54.8 56.2 57.0 58.6 60.2 61.1 62.1 62.8 68.3 68.8 69.9 70.5 71.0 71.3 71.3 71.3 71.8 71.9 72.0 72.0 72.0 71.9 71.6 71.4 71.8 71.7  QW PSI -49.7 -36.8 ._rP.8 4.8 22. 1 36.9 42.2 55.0 59.8 76. 1 81.1 85.2 86.3 84.4 82.4 83. 1 84.8 84.1 83.7 79.7 80.1 80.4 78.9 80.0 80.8 80.9 81.3 78.6 78.2 .78.6 79.2 82.8 81.9 81.4 80.3 82.0 79.6 80.3 79.5 79.7 79.9 77.9 78.6 77.4 79.2 78.2 77.5 76.0 0.0  QW(PP) PSI 28.1 30.0 47_9 46.0 56.1 63.8 64.4 73.6 72.9 83.6 85.5 87.4 87.4 . 84.6 82.1 82.7 84. 1 83.6 83.3 79.9 80.8 81.1 79.6 80.6 81.2 81.6 82.0 79.4 79.1 79.3 79.8 83.0 82_._t 81.8 80.6 82.2 79.7 80.3 79.6 79.8 80.0 78.0 78.5 77.2 78.8 77.9 77.4 76.0 0.0  M -1.24 -0.89 -0.02 0. 11 0.49 0.80 0.90 1. 15 1.23 1.54 1.63 1.70 1.71 1.66 1.60 1.60 1.62 1.60 1.58 1.43 1.43 1.42 1.37 1.37 1.38 1.37 1.37 1.31 1.30 1.30 1.30 1.32 1 ._30 1.29 1.27 1.29 1.25 1.26 1.25 1.25 1.25 1.22 1.23 1.21 1.24 1.23 1.22 1.19 0.00  M(PP ) 0.70 0.73 1.14 1.07 1.28 1.43 1.42 1.59 1.54 1.75 1.79 1.81 1.81 1.74 1.67 1.68 1.69 1.67 1.65 1.50 1.50 1.49 1.43 1.44 1.44 1.44 1.43 1.37 1.35 1.35 1.35 1.36 1 jJ34 1.32 1.29 1.32 1.27 1.28 1.27 1.27 1.27 1.2 3 1.24 1.22 1.25 1.24 1.23 1.20 0.00  P/PE 1.00 1.03 1.07 1.09 1. l l I . 12 1.13 1.14 1. 14 1. 14 1.12 1.09 1.04 0.97 0.91 0.88 0.85 0.82 0.79 0.68 0.67 0.65 0.62 0.61 0.59 0.59 0.58 0.56 0.56 0.55 0.55 0.50 0.49 0.49 0.48 0.48 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.43  P/PE ( PP) 1.00 1.02 1.05 1.07 1.08 1.08 1.10 1.10 1. 10 1. 10 1.07 1.04 1.00 0.93 0.87 0.83 0.81 0.78 0.75 0.66 0.64 0.62 0.60 0.59 0.57 0. 56 0.56 0.55 0.54 0.54 0.53 0.49 0.48 0.48 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.43 0.43 0.43  CONSOLIDATION PRES.= 40.0 TEST NO.17 Q/PE  '  0.00 0. 10 0.23 0.29 0. 36 0.44 0.50 0.56 0.62 0.66 0.67 0.67 0.65 0.63 0.61 0.60 0.60 0.59 0.58 0.58 0.57 0.58 0.58 0.57 0.57 0. 57 0.57 0.57 0.57 0.57 0.56 0.55 0.54 0.54 0.53 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.51 0.50 0.50 0.50 0.49 0.49 0.49  <  151  CONSOLIDATION SHEAR STRAIN -0.00 _J0.,Q4 0.13 0.18 0.25 0.35 0.46 _ 0..J57 0.73 0.93 1.12 1.42 1.85 _ 2.61 3.40 3.87 4.29 4.77 5.25 8.07 8.72 9.34 10.50 11.22 11.91 12.38 12.95 13.69 14.16 14.68 15.20 19.29 _ 20.04 20.78 21.93 22.70 23.26 2 3...59 24.25 25.05 25.42 25.96 26.55 _2 7_._17 27.69 28.03 28.77 29.62 30.65  PORE P R E S S U R E CV.H,A A CONSTANT K.H CONSTANT CV,H VARY VARY 0.0 0.0 0.0 3_2 3._2 0.5 5.8 5.9 0.8 6.7 6.9 0.9 7____ 7_8 l__0_ 7.8 8.4 1.4 7.8 8.6 1.3 7 ._7 8.J. Ls5_ 7.0 8.2 1.6 5.8 7.1 1.8 4___5 5__J5 2.1 2.7 3.7 2.0 1.3 1.9 2.2 0.8 1.1 2.3 0.6 0.8 2.4 0.8 0.9 2.5 0___? 1.0 2.5 0.7 0.9 2.5 0.7 0.9 2.5 0.4 0._5 2_3_ 0.7 0.8 2.3 l . l 1.2 2.4 0___9 UO 2.2 0.9 1.0 2.2 0.8 0.9 2.2 J3_7 0.8 2.1 0.9 1.0 2.1 0.9 1.0 1.8 0__9 0__9 1.7 0.9 0.9 1.8 0.7 0.8 1.8 0.1 0..1. 1.5. 0.2 0.2 1.4 0.5 0.4 1.2 0__3 0_2 1.1 0.3 0.3 1.3 0.2 0.2 1.1 0,. 2 _0 .JL 0..9. 0.1 0.0 1.0 0.2 0.2 1.0 0__2 0.2 U0_ 0.1 0.1 0.7 0.1 0.0 0.7 0_._0 QL._0 JDL._7_ -0.1 -0.1 0.7 -0.2 -0.2 0.8 -Q. 1 -0.1 0.6 0.1 0.1 0.5 0.0 0.0 0.0  TEST NO.17 PRES.= 4 0 . 0  

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