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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 this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 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 the requirements . f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and study . I f u r t h e r agree that permiss ion f o r ex t e n s i v e copying 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 granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s 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 f i n a n c i a l ga in s h a l l not be a l lowed without 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 of B r i t i s h Columbia Vancouver 8, Canada Date TsVvy y i i ABSTRACT Results of drained and undrained t r i a x i a l compressions tests, on a sensitive clay are presented in this thesis. Contours of water content from both drained and undrained tests are compared, and i t appears that for the clay tested, there is not a unique relationship between effective 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 is 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 well. It indicates that for a s o i l which is yielding there is only one fundamental strength parameter, M, which is independent of both strain and strain rate. Methods of predicting stress-strain relationships are examined. The Roscoe method, which is based on the existence of a state boundary surface is not s t r i c t l y applicable, but does yield results which are of the same order as the measured relationships. The Landanyi method does not appear to apply to the clay tested. A method for predicting residual pore pressures and or permea b i l i t y in drained t r i a x i a l tests is derived. This enabled a l lowances to be made for the effect of residual pore pressures in drained tests. However, i t is f e l t that the method may have more application in the examination of s o i l structure, since a com parison of the permeability of samples at the same void ratio and temperature yields a measure of structural difference. TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1.1 Purpose 1 . 2 Scope CHAPTER 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 Field sampling and storing of block sampl *f.3 Description of test equipment k,h Testing technique CHAPTER 5 DISCUSSION OF TESTING TECHNIQUE 5.1 Introduction 5.2 Non-uniform stress and strain 5.3 Non-uniform pore pressures in undrained tests 5.^ Residual pore pressures in drained tests 5.5 Pore pressure measuring devices 5.6 Rate of testing 5.7 Pore pressures resulting from secondary- effects 5.8 Membrane leakage 5.9 Ram Friction CHAPTER 6 RESIDUAL PORE PRESSURES IN DRAINED TESTS 6.1 Introduction iv CHAPTER 6.2 Method 1 6.3 Method 2 CHAPTER 7 TEST RESULTS 7.1 Introduction 7.2 Characteristics of Haney clay 7.3 Comparison of contours of water content from drained and undrained tests 7<M- Energy corrections 7.5 Examination of methods for predicting stress-strain relations 7.6 Effect of strain rate on drained tests CHAPTER 8 CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 8.1 8.2 LIST OF SYMBOLS LIST OF REFERENCES APPENDIX I APPENDIX II Conclusions Suggestions for further research PAGE 75 76 85 85 86 96 107 115 122 125 125 126 128 131 135 lh2 V LIST OF TABLES PAGE TABLE I PHYSICAL PROPERTIES OF HANEY CLAY 31 TABLE II CHEMICAL PROPERTIES OF HANEY CLAY 3«f v i LIST OF FIGURES Figure Page 1. Rendulic Graphical Representation of Stresses in Triaxial Tests 5 2. Contours of Water Content for Normally Consolidated London Clay 8 3 . Stress Water Content Relations for Normally Consolidated Weald Clay 10 Roscoe et a l . Yield Surface 12 5. Roscoe et a l . energy balance 16 6. Method of Determining Stress-Strain Relationships for Kaolin 18 7. Strength Parameters 26 8. Grain Size Distribution Curve for Haney Clay 32 9. Standard Consolidation curve for Haney Clay 33 10. Block Samples of Haney Clay at Site 36 11. Triaxial Cell and Chamber Pressure System 37 12. Drainage and Pore Pressure Measuring System 38 13. Test Equipment 39 Ik-. Sample Trimming Equipment ^8 15. Sample in Place on Triaxial Base *+8 16. Sample During Shear " 53 17. Build-Up in Pore Pressure After Consolidation Haney Clay 69 18. Illustration of Method for Determining Drainage Rate During Shearing 79 19. Relationship Between Void Ratio and Permeability During Drained Shearing of Haney Clay 80 20. Relationship Between Measured Residual Pore Pressure and Shear Strain in Drained Tests 82 21. Comparison of Measured and Calculated Residual Pore Pressures in 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 for Undrained Tests on Haney Clay Principal Stress Ratio Versus Strain for Undrained Tests on Haney Clay Relationship Between Pore Pressure and Strain for Undrained Tests on Haney Clay Pore Pressure Parameter A. Versus Strain for Haney Clay S'tress-Strain Relationships for Drained Tests on Haney Clay Calculated Residual Pore Pressure Vs. Strain for Consolidated Drained Tests on Haney Clay Effect of Residual Excess Pore Pressure on the Principal Stress Ratio Vs. Shear Strain Relation, Test S-13 Relationships Between Principal Stress Ratio and Strain from Drained Tests on Haney Clay Comparison of Principal Stress Ratio Vs. Strain Relationships from Drained and Undrained Tests on Haney Clay Comparison of Contours of Water Content from Drained and Undrained Tests on Haney Clay Effective Stress Paths from Consolidated Undrained Tests on Haney Clay Effective 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) v i i i Figure Page 38. Comparison of State Boundary Surfaces from Drained and Undrained Tests on Haney Clay 106 39• Relationships Between Mean Normal Stress and Water Content for Haney Clay 109 ^0. Corrected and Uncorrected Stress Paths from Undrained Tests on Haney Clay (Roscoe et a l . Energy Eq.) I l l hi. Corrected and Uncorrected Stress Paths from Drained Tests on Haney Clay (Roscoe et a l . Energy Eq.) 112 h2. Roscoe M Parameter Versus Strain, Haney Clay 113 ^3. Contours of Water Content and Strain from Undrained Tests on Haney Clay 117 hh. Comparison of Measured and Calculated Stress- Strain Relations for Drained Tests on Haney Clay 119 1+5. Comparison of Theoretical and Experimental State Boundary Surfaces (Burland Plot) 121 ^6. Effect of Strain Rate on the Stress-strain Relations for Drained Tests on Haney Clay 123 U-7. Effect of Strain Rate on the Principal Stress Ratio Vs. Strain Relations for Drained Tests on Haney Clay 12*f h8. Effect of Strain Rate on the Water Content Vs. Strain Relations for Drained Tests on Haney Clay. 12h h9. Diagrams Showing Assumptions of Method 1 136 50. Stress-Strain Characteristics of Haney Clay 138 51. Relationship Between Coefficient of Consolidation and Effective Stress for Haney Clay IkO ix ACKNOWLEDGEMENT The investigation reported herein has been supported by- funds provided by the National Research Council of Canada. These funds also included financial support for the writer. Grateful appreciation is expressed for this assistance without which the graduate studies and this 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 for their guidance and con structive criticism during the preparation of this thesis. Drained tests results were obtained by Mr. T. J. Hirst with whom the task of developing suitable test equipment was shared. Dr. E. H. Gardner, Department of Soil Science kindly supplied data on the chemical properties of the clay tested. The technical assistance supplied by the staff of the C i v i l Engineer Department is gratefully 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 effective stresses and water content, or void ratio, for both drained and undrained t r i a x i a l tests on saturated remolded isotropically consolidated clay. The prime purpose of this testing program was to determine i f a similar relationship exists for a sensitive undisturbed clay. A secondary purpose was to compare the behaviour of the clay with that predicted by Roscoe and Schofield (1963) for an idealized "Wet-Clay" and in particular to compare stress-strain relations. 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. In s t a b i l i t y analysis, the structure is analyzed to insure that the sum of the.resisting forces on any potential failure surface is greater than the sum of the driving forces. No attempt is made to determine the magnitude of the deformations. The resisting forces are determined from strength tests on the s o i l . It is gen erally agreed that for most soi l s , the strength in terms of ef fective stresses is practically independent of the type of t r i a x i a l test performed, drained or undrained. However, for sensitive soils there is some disagreement on this. The testing program was undertaken jointly by Mr. T. J. Hirst and the writer. Hirst (1966) discusses the strength envelopes obtained from drained and undrained tests. Settlement analyses are concerned with the magnitude of 2 deformations. For many structures, such as foundations, i t is important that these be limited. Deformations are caused by volumetric strains due to changes in void ratio and by shear strains due to distortion.. If there is a unique relationship between stresses and water content or void ratio that is indepen dent of stress path, then the volumetric strain can be calculated for any stress path which lies between a drained and undrained path. The shear strains, however, are very much dependent on stress path. Poorooshasb and Roscoe (1963) determined a relation ship between volumetric and shear strains for normally loaded remolded clay and from their theory, i t is possible to estimate the shear strains for any stress path, A state boundary or yield surface is a fundamental part of their theory and this only exists i f there is a unique relationship between stresses and water content. It is realized that stress-strain relations and contours of water content may be dependent on strain rate, therefore, drained and undrained tests were performed at the same rate. Additional drained tests were performed at slower rates which allowed the effect of strain rate on drained relations to be examined. 1.2 Scope A review of pertinent literature is presented in Chapter 2 . A discussion of macroscopic components of shear resistance is presented in Chapter 3» The clay tested, test equipment and testing technique are discussed in Chapters h and 5<> Residual pore pressures of some magnitude are always present in drained tests. A method for predicting these pore pressures is presented 3 in Chapter 6. The results from drained and undrained t r i a x i a l compression tests on Haney clay are presented and discussed in Chapter 7. Conclusions and suggestions for further research are presented in Chapter 8. CHAPTER 2 REVIEW OF LITERATURE 2.1 Review of L i t e r a t u r e B a s i c e x p e r i m e n t a l r e l a t i o n s between t r i a x i a l s t r e s s c o n d i t i o n s , w a t e r c o n t e n t , and pore-water p r e s s u r e f o r n o r m a l l y con s o l i d a t e d c l a y s were f i r s t e s t a b l i s h e d by R e n d u l i c (1936, 1937). He performed b o t h d r a i n e d and u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n t e s t s on s a t u r a t e d remolded V i e n n a c l a y . T e s t specimens were d r a i n e d by a c e n t r a l c o r e of 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 i n the c o r e . No a l l o w a n c e was made f o r the e f f e c t of the change i n c r o s s s e c t i o n a l a r e a on the v e r t i c a l 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 are l i k e l y t o -be t o o h i g h . R e n d u l i c d e v i s e d a method f o r comprehensive g r a p h i c a l r e p r e s e n t a t i o n of the s t a t e of s t r e s s f o r any s t a g e i n a t r i a x i a l t e s t . C o n s i d e r F i g u r e l a ; s i n c e i n the t r i a x i a l t e s t <5~2 = 63 and (Jg = ^3? s t r e s s e s must p l o t on the shaded p l a n e . To p l o t p o i n t s on t h i s p l a n e the r a d i a l e f f e c t i v e s t r e s s (O^ or (3 )^ must f i r s t be m u l t i p l i e d by >/2. I s o t r o p i c c o n s o l i d a t i o n c o n d i t i o n s (O^ = CJ^ = O3) a r e r e p r e s e n t e d by t h e space d i a g o n a l or l i n e w h i c h 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 . F i g u r e l b shows 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 t e s t s p l o t t e d on t h i s p l a n e . Compression t e s t 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 t e s t s below. P l o t t e d p o i n t s r e p r e s e n t d i f f e r e n t s t a g e s i n a t e s t , and the l i n e j o i n i n g t h e s e p o i n t s r e p r e s e n t s the s t r e s s p a t h f o l lowed i n any one t e s t . I n an u n d r a i n e d t e s t on s a t u r a t e d n o r m a l l y l o a d e d c l a y , t he pore p r e s s u r e r i s e s and t h e s t r e s s p a t h which i s a l s o a l i n e of c o n s t a n t w a t e r c o n t e n t i s some curve as 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 drained test the r a d i a l e f f e c t i v e stress i s constant, and thus the stress path i s a v e r t i c a l l i n e . Curves of constant water content can also be obtained from drained tests where volume changes during shearing have been recorded. Contours of water content are shown in Figure 1c. The l i n e A D which makes an angle of 90 degrees with the i s o t r o p i c consolidation l i n e and a l l l i n e s p a r a l l e l to i t represent stress paths along which the value of the f i r s t e f f e c t i v e stress invariant (j{ = o]_ + O 2 + G 3 ) is con stant. For l i n e a r l y e l a s t i c material and f o r small s t r a i n s , J-|_ equal to a constant, represents a constant volume condition. It is seen that f o r normally loaded clay a J-[ = constant stress path would cause a volume decrease. Rendulic found f a i r l y good agreement between contours of water content determined from drained and undrained t e s t s , and he concluded that any point i n the diagram represents a unique r e l a t i o n between stresses and water content that i s independent of the stress path, provided the path does not cause a temporary decrease i n water content. If the contours are geometrically s i m i l a r , they w i l l plot on a single curve on the u n i f i e d Rendulic diagram, Figure Id, which is obtained by d i v i d i n g (J^ and <J^ by the e f f e c t i v e consolidation pressure (5"'. Rendulic found that the 0 curves were approximately geometrically s i m i l a r . Henkel (1958, 1959? I960) describes r e s u l t s of a comprehensive series of t r i a x i a l tests on saturated remolded Weald and London clayso The series included i s o t r o p i c a l l y consolidated drained and undrained compression and extension tests on both normally loaded and overconsolidated samples. A few tests were performed keeping 7 the mean effective stress p' (1/3 J^) constant, and some samples of Weald clay were anisotropically consolidated. Henkel found that there was a unique relationship between effective stresses and water content which was independent of the stress path whether the clay was isotropically or anisotropically consolidated, pro vided normally loaded and overconsolidated samples were considered separately. Maximum principal stress difference was considered to be failure and he found that the failure envelope was indepen dent of the stress path. Contours of water content from drained and undrained tests for normally consolidated London Clay are shown on the Rendulic diagram in Figure 2. It is seen that the contours are essentially independent of the effective stress path. Thus from undrained tests alone, the water content and deviator stress at failure for a drained test starting from a water content of 29.3 per cent and a consolidation pressure of 90 p.s.i. could be predicted to be 25.9 per cent and 82 p.s.i. respectively. If the average effective stress, p', were kept constant, then starting from the same water content and pressure as before, the water content and deviator stress at failure would be 27.h per cent and 62 p.s.i. respectively. It is seen that J-[ constant does not imply a zero volume change condition as i t does for linear elastic material and that change in water content is a function of both p' and the deviator stress q. Henkel (I960) suggests that similar relationships may also apply to undisturbed clays. However, for sensitive soils in which structure is an important factor and for clays in which the secon dary compression is 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 stresses and water content might be more complex than that sug gested f o r remolded s o i l s . Whitman, Ladd and P. da Cruz ( I 9 6 0 ) describe a series of tests on saturated remolded samples of backswamp clay from the lower M i s s i s s i p p i River v a l l e y . It was found that comparison of samples consolidated i s o t r o p i c a l l y and a n i s o t r o p i c a l l y did not produce a unique re l a t i o n s h i p between stresses and water content as sug gested by Henkel. For the same void r a t i o , the samples which were a n i s o t r o p i c a l l y consolidated had the higher strength, (CT^ - 0^ ) . The maximum p r i n c i p a l stress r a t i o appeared to be the same f o r both. Henkel and Sowa (1963) working with a new batch of Weald clay obtained results similar to Whitman. It was found that the water content a f t e r consolidation, whether the consolidation was i s o tropic or anisotropic was a function of p' only. This i s shown in Figure 3« The stress paths followed f o r samples of the same void r a t i o are also shown i n Figure 3 i n terms of p' and q (CJa - (5"r). A n i s o t r o p i c a l l y consolidated samples are seen to follow a markedly d i f f e r e n t stress path and i t can be seen that f o r the same void r a t i o they have a higher maximum deviator stress but that the strength envelope i s the same f o r both. They state that the results are quite d i f f e r e n t from the data presented by Henkel ( I 9 6 0 ) on an e a r l i e r batch of weald clay using similar t e s t i n g techniques, Roscoe et a l . have presented a number of papers since 1958 on the y i e l d i n g of s o i l s . They consider s o i l to be an e l a s t o - p l a s t i c i s o t r o p i c continuum material. Roscoe, Schofield and Wroth (1958) were primarily concerned with the establishment of a c r i t i c a l void r a t i o (C.V.R.) l i n e . It was suggested, however, that f o r saturated 10 0 e0 4-0 GO 80 IOO l£0 140 MEAN NORMAL EFFECTIVE STRESS, P' LBb./6<?.IN. Figure 3 — 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 in space which could be expressed in the form of an equation: w = f (p 1, q) where w = water content f = function of p' = 1/3 «5[ + 2C3) q = (C7]_ - (J3) corrected for boundary energy. This surface is shown in Figure ^f. It is seen that the envelope is comprised of two parts. Part A is a surface on which stress paths from a l l normally loaded samples l i e throughout the shearing process whether drained or undrained. Part B applies to over- consolidated samples, and stress paths l i e on this surface only at or near fai l u r e . Part A of the surface which is the portion of interest, suggests that there is a unique relation between stresses and water content which is independent of the stress path, provided that a correction for boundary energy is applied to the shear stress (C7-]_ - C3) in the case of drained tests to allow for the work done in changing volume. .The corrected deviator stress was given by the following equation: where = increment of volumetric strain = increment of major principal strain Poorooshasb and Roscoe (1961) presented data for normally loaded isotropically 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 of Const, LU Overconsolidoted Samples (Heavily) "Touch this Surface. Fig.4a — Isometric View of Roicoe efal. Yield Surface. ln1crb<?ttion o f Surface B uuifh U J Cons.t. Ptane. Intersection o f Surfqce. A. Ujiih uj Const Plane (Normally Consolidated Undroined Ptoth) Undrained Te&ts> uiith Varying Degrees of Overcons>o|idcfrion Fig. 4b—Constant UJ Plane. Figure 4 — Roscoe etal. Yield Surface.. 13 which indicated that there was a unique relation between stresses and water content provided no boundary energy correction was ap plied to the shear stresses. 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 is dissipated in work done by the shear stresses. This may be reasonably true in the case of a sand. However, i t is l i k e l y that in a clay, some of this energy w i l l be stored ela s t i c a l l y (Hvorslev I960). Poorooshasb and Roscoe (1961) derived the following equation for the corrected deviator stress: ov q R = «j[ - O 3 ) + (p» - r ) - ^ (2) where r is a parameter expressing a measure of the energy stored. If r = p', then a l l the energy is stored and q = (CJ^ - cj^). If r = 0, then no energy is stored and q = (rj{ - a') + . m y 1 3 Sci, which the authors feel should replace equation ( 1 ) . It is sug gested, therefore, that for normally loaded clays a l l energy trans ferred across the boundary is stored elastically and hence drained and undrained tests can be compared directly. Roscoe and Schofield ( 1 9 6 3 ) present a theory for the mechani cal behaviour of an ideal continuum referred to as "Wet Clay". The following equation is derived for the state boundary surface: q = *EL (F + A - K- e - l n p') ( 3 ) A -Iv where M,X , K,T are f o u r s o i l c o nstants M = r a t i o of q and p' at f a i l u r e r = v o i d r a t i o a t f a i l u r e f o r p' = 1 \ = slope of e vs In p' curve f o r both i s o t r o p i c and f a i l u r e c o n d i t i o n s K = slope of e vs In p curve f o r unloading and r e l o a d i n g . = increment of shear s t r a i n &V = increment of v o l u m e t r i c s t r a i n E q u a t i o n 3 expresses the unique r e l a t i o n s h i p between e f f e c t i v e s t r e s s e s and v o i d r a t i o or water c o n t e n t . A. new energy or work e q u a t i o n i s d e r i v e d which supersedes e q u a t i o n ( 2 ) : P'SV + qSe = 5$El + Mp'Se - — (if) 1 + e The terms used have a l r e a d y been d e s c r i b e d . The l e f t hand s i d e of E q u a t i o n U- expresses the energy t r a n s f e r r e d a c r o s s the boundaries of a u n i t volume of s o i l s u b j e c t t o s t r e s s e s p' and q on a p p l i c a t i o n of a probing s t r e s s incrementSp', oq. The terms on the r i g h t hand s i d e express to what use t h i s energy i s put. The term ^ p 1 1 + e r e p r e s e n t s the energy s t o r e d e l a s t i c a l l y and the term Mp 'S£ r e p r e s e n t s the energy d i s s i p a t e d by the shear s t r e s s e s . I t i s as sumed t h a t no energy can be s t o r e d by the shear s t r e s s e s . E q u a t i o n *f can be r e w r i t t e n as f o l l o w s : % - MP- = , * p- § - ^ | E l - - (5) T h i s means th a t i f a t any stage i n a d r a i n e d or undrained t r i a x i a l t e s t the d e v i a t o r s t r e s s q i s c o r r e c t e d f o r both energy due to 15 volume change and energy stored elastically, the corrected q = q w w i l l be on the failure envelope q = Mp1. Figure 5 shows how these corrections would be applied to both normally loaded drained and undrained tests. In an undrained test = 0 and since Sp' w i l l be negative because p' is decreasing, the elastic energy cor rection 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 for normally loaded remolded samples there is a unique relationship between stresses and water content provided no energy correction is applied. If an energy correction is applied in the form of equation 5» then the cor rected q w i l l l i e on the failure envelope for a l l points of the stress path, i.e. q w = Mp'. Roscoe has also predicted stress strain relations. Poorooshasb and Roscoe (1963) presented a graphical means of determining stress strain relations for normally loaded remolded clay where the stress paths l i e on the state boundary surface, which is the surface expressing the unique relation between stresses and water content (no energy corrections). Undrained tests were performed which show that for remolded spestone kaolin, contours of shear strain are radial lines. Consolidation tests were performed at different ratios of q to p' and relations between the shear strain and the volumetric strain were determined graphically. It is shown that volumetric strain also causes shear strain. The higher the ratio of q/p' the higher the shear strain for a given volumetric strain. It is stated that for any increment of applied stress the change in strain can be considered to be the sum of a change in strain at Figure 5 —Roscoe. etal. Energy Balance (After Roscoe eT al. '63) 17 constant volume, and a change in strain 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 in shear strain at constant volume is known, and also the change in volume t r i c strain due to the increment at constant q/p ' . The change in shear strain due to the change in volumetric strain is determined from the results of consolidation tests. The total change in shear strain is the sum of changes at constant volume and constant q/p ' . This method is shown for a stress increment AC on Figure 6 . Figure 6a shows stress paths from consolidated undrained'tests on t c kaolin. Contours of strain at constant volume are superimposed and are seen to be radial line from the or ig in . Figure 6b shows the relationship between increments of shear strain and volumetric strain as a function of q/p' derived from consolidation tests. A stress increment AC can be resolved into increments AB and BC. The shear strain increments arising from these are . 7 5 per cent at constant volume and 6.1+ per cent at constant q/p' thus the tota l shear strain increment is 8.2 per cent. In this manner a relation between shear stress and shear strain can be obtained for any stress path. Landanyi, La Rochelle, and Tanquay (1965) present a graphical method of predicting shear strains in saturated normally loaded and over-consolidated clays. It implies that contours of shear strain are independent of the stress path followed. Relationships between shear strain and princiapl stress ratio and shear strain Projection Of CS. Line Values of Contours of Shear strviin- (Con>t«nt VoL Tebts) UJ Contour 10 £0 SO 40 50 GO 70 60 Fig. £>a Stress* Paths and Contour*) o f Strain for Constant Volume. Tests on kaolin 2. o o" IfoT 141 IS+ 5,9 I0f 6+ 5 ° 4 + o o ""a t r 2 + •4 5 -Q> •6 For Increment BCjTj =-43 to S e - ° " i+e " I + UJQ- b v = g--3ye.-7 = 2 . S 6 % I O F ' c j . kb . Relqtion Between Increments of Shear and Volumetric Strains oft Constant r; Figure. Q> 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 this information the principal stress ratio versus strain relation was predicted for an undrained test and compared with an actual test. Agreement was quite reasonable. This theory would imply that i f there is a unique relation between stresses and water content that contours of shear strain are also unique. The unique relationship between stresses and water content implies a failure envelope which is independent of stress path. Casagrande and Wilson (1953) found that for both an organic clay and for Boston Blue clay the undrained strength envelope was higher than the drained strength envelope. Maximum principal stress ratio was considered as failure. The difference amounted to 9 degrees for the organic clay and between 2 and 5 degrees for the Boston Blue clay. In an undrained test on normally loaded clay, the pore pressure rises such that the normal effective stress on the failure plane f a l l s as shearing progresses. Thus at failure the s o i l could be considered to be overconsolidated. This over- consolidation is referred to as prestress effect and was consider ed responsible for the additional strength of the undrained tests. The strain rate in the undrained tests was considerably higher than the drained tests and i t has been argued by subsequent writers that this could account for the higher strength. However, undrain ed tests were performed as stress controlled and strain controlled and although the maximum deviator stress was higher for the stress controlled, the principal stress ratio was the same for both. It could therefore be implied that the strain rate affected the stress 20 path but not the strength envelope in terms of the principal stress ratio. Energy corrections were not considered. Bjerrum and Simons (i960) present data from drained and undrained tests on normally loaded undistrubed clays. The sensiti vity of these clays varied from 3 to 100. It was found that for almost a l l the Norwegian clays the pore pressure was s t i l l rising at maximum deviator stress and the maximum principal stress ratio was reached at higher strain. Kenney (1959) has suggested that this phenomenon is a function of the sensitivity of the clay. The greater the sensitivity the larger the difference in the strength envelope determined by both methods. Bjerrum and Simons found the undrained envelope to be slightly lower (about one degree) than the drained envelope, provided maximum principal stress ratio was taken as the criterion o f 1 f a i l u r e . This, they state, is opposite to the findings of Casagrande and Wilson. However, the writers have corrected their drained tests for boundary energy due to volume change, whereas Casagrande and Wilson did not. They suggest that the prestress effect is of secondary importance and state that i t is the overconsolidation ratio before application of the shear stresses that is important. Barron (i960) states that the volume change occurring in drained tests causes considerably more remolding than in undrained tests. He suggested that the undisturbed drained strength envelope and the remolded undrained envelope are only slightly different and that the undisturbed undrained strength envelope is higher because of structure and prestress effect. Scott (1963) considers that the prestress induced in the 21 undrained tests may or may not be important depending on the fai lure s tra in . If fai lure is occurring at large strains then the s o i l w i l l be fu l ly dispersed at fai lure and no memory of previous past pressure w i l l remain. On the other hand, i f fai lure occurs at low strains, as is l i ke ly with a s o i l i n i t i a l l y flocculated, memory of past pressure w i l l be retained and the s o i l w i l l exhibit a prestress effect. Thus, Scott suggests that the prestress ef fect w i l l be most pronounced for undisturbed soils and particularly for sensitive so i l s , these being highly flocculated. For compacted so i l s , and particularly for those soils compacted wet of optimum, with low salt concentrations in 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 fai lure envelope and the unique relationship between effective stresses and water content. It would appear that for normally loaded remolded material, the strength envelope is essentially independent of the stress path, and that the fai lure c r i te r ion , whether maximum principal stress rat io or maximum deviator stress makes l i t t l e difference. The volume change at fai lure in the case of drained tests is generally very small or zero so that a boundary energy correction i f ap pl ied, w i l l have negligible effect on the strength envelope. For undisturbed normally loaded material and particularly for sensi tive material, the maximum principal stress ratio occurs at a higher strain than the maximum deviator stress in undrained tests, leading to two possible fai lure envelopes. In drained tests, 22 maximum deviator stress and maximum principal stress ratio must occur at the same time. However, volume decrease at failure leads to a measurable boundary energy correction, and thus gives rise to two possible drained failure envelopes, i.e., one with a boundary correction and one without. It appears that i f maximum principal stress ratio is taken as the failure criterion, then drained and undrained tests have ap proximately the same failure envelope provided a correction for boundary energy be applied to drained tests. If no correction is applied, then the drained envelope w i l l l i e below the undrained. Evidence for the unique relationship between effective stresses and water content is rather conflicting, but suggests that for normally loaded remolded clays which have been isotro- pically consolidated, the relationship is approximately true. No data on sufficiently uniform undisturbed clay is available but i t has been suggested that a similar relationship might hold for undisturbed clays of low sensitivity. For sensitive clays i t was thought that the relationship would be more complex. The literature suggests that the relationship between effec tive stresses and water content determined from both drained and undrained tests may not be unique for any one clay for the following reasons: 1 . Rate of testing not identical for both drained and undrained tests; 2. Temperature not the same for a l l tests; 3 . Non-uniform distribution of stresses and water content due to end restraint; 23 h. Residual excess pore water pressure in drained tests; 5. Different structure arising from different stress paths followed in drained and undrained tests. The effects of 1. and 2 . may be eliminated by testing at the same strain rate and at constant temperature. Non-uniform stresses give rise to unequal pore pressures within undrained tests. If tests are run at suff ic iently slow strain 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 rise to non uniform water content. This aspect w i l l be considered in detai l in Chapter 5 . Residual excess pore pressures in drained tests cannot be completely eliminated, as theoretically i t would take an inf ini te time for one hundred per cent dissipation 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 in Chapter 6 . The prestress effect in undrained tests and the additional remolding effect of volume change in drained tests are macroscopic factors reflecting different microscopic struc ture in the clay. The macroscopic behaviour of a clay is very much dependent on the structure and this w i l l be considered in Chapter 3» 2lf CHAPTER 3 MACROSCOPIC COMPONENTS OF SHEAR STRENGTH The shear s t r e n g t h of a saturated c l a y i s of t e n considered t o comprise of a f r i c t i o n component, a cohesion component and a sur face or boundary energy component. The f r i c t i o n component i s tha t p o r t i o n of the shear r e s i s t a n c e which i s l i n e a r l y r e l a t e d to the normal e f f e c t i v e s t r e s s . Cohesion i m p l i e s a shear r e s i s t a n c e which i s independent of the normal e f f e c t i v e s t r e s s . The surface energy component of shear strength a r i s e s when a s o i l i s undergoing volume change. Taylor (19^8) demonstrated that the work done by the boundary s t r e s s e s during shearing could account f o r the d i f ference i n strengt h between a loose and a dense sand. Bishop (195!+) c a l c u l a t e d the energy component f o r t r i a x i a l c o n d i t i o n s (G^ = CJ^) at maximum d e v i a t o r s t r e s s as follows.: 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^, then the boundary energy t r a n s f e r r e d t o the sample, OW, w i l l be Sw = <J[ o£ x + 2 CJ^ 6 £ ^ now oV = tbE^ + 2 0 6 3 = volumetric 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 $ - | ^ - ff' ^ - - - - - (6) C3 i s the surface energy component of shear s t r e n g t h . I t i s p o s i t i v e f o r volume i n c r e a s e , negative f o r volume decrease and zero f o r constant volume or undrained c o n d i t i o n s . Although Bishop mentions that h i s equation would apply at 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), Gibson (1953) and others a p p l i e d the c o r r e c t i o n at other points on the s t r e s s path i n a d d i t i o n to 25 the point of maximum deviator stress. Hvorslev ( I960) suggested that part of the energy involved in volume change might be stored or released e la s t ica l ly and hence should not be considered in the term involving energy dissipated. Bishop (196^-) considered that the rate of change of elastic energy at maximum deviator stress would be small. Roscoe and Schofield (1963) developed an energy equation discussed in Chapter 2 which considered both boundary energy and elastic energy within the sample. Rowe, Oates and Skermer (1963) extended the stress dilatency theory to cohesive so i l s . The modified coulomb equation T f f •= c ' + CTj tan 0 ' (7) where Tff = shear stress on fai lure plane at fai lure c' = apparent cohesion Of = normal effective stress on failure plane at failure 0 ' = effective angle of internal f r i c t i on is often used to express the shear strength of clays. For satu rated normally loaded clays i t is generally found that c' = zero. If the clay has been overconsolidated, the strength in the over- consolidated region of interest may generally be expressed by Equation 7. However, the f r i c t i o n angle determined in 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. Fr ic t ion and cohesion in this form are now considered to be merely parameters expressing the slope and inter cept which best approximate the strength envelope in the region of interest (Figure 7 ) . Hvorslev, at the suggestion of Terza&hi, 2 f o • t I i Actual St&ngth Envelope Approximofed by bt l - i o e ^ ^ » nl O r—- NormaNv- Leaded <5n Figure 7q — Modified Coulomb Strength Parameters 2 7 performed direct shear tests on saturated remolded clay in such a manner that i t was possible to compare shear strength at the same void ratio but with different applied normal effective stresses. It was found that for the same void ratio, the shear strength was a linear function of effective normal stress and plotted with an intercept on the shear strength axis as shown in Figure 7 . Lower void ratios plotted as parallel lines with higher intercepts on the shear strength axis. The slope and intercept determined in this fashion were given the symbols 0Q and Cg and were thought to reflect true f r i c t i o n and true cohesion. Hvorslev ( I 9 6 0 ) prefer- red to refer to 0Q and c Q as effective f r i c t i o n and effective co hesion. The terms imply that at any one void ratio the cohesion is constant and independent of the effective stress. Hvorslev ( I 9 6 0 ) suggested that this would only be so i f there were no sig nificant differences in structure. Scott ( 1 9 6 3 ) stated that due to the irreversible nature of the compressibility of clay i t would not be possible to have two samples at the same void ratio with differing effective stresses and the same structure. The very fact that the stress is different signifies a different structure. Gibson (1953)> Bjerrum (195*+) and many others have determined the effective f r i c t i o n and effective cohesion components for remolded s o i l s . If the components were determined from drained tests, then the surface energy component was generally removed using the Bishop equation. Gibson found that application of the energy equation reduced c e and increased 0 e. Simons (I960) determined these parameters for an undisturbed s o i l . Bjerrum and Simons (I960) found that the effective f r i c t i o n component was 28 lower for a s o i l in the remolded than the undisturbed state. It is apparent that the same f r i c t i o n and cohesion components w i l l not be present for the same s o i l in the undisturbed and remolded states.. This is particularly true for sensitive s o i l s . Hvorslev (I960) considered that the components might only apply to re molded s o i l s . Schmertmann (1963) considered that the components as deter mined by Hvorslev' on remolded clay might be correct. The d i f fering consolidation ratios necessary to produce samples at the same failure void ratio but with differing effective stresses would result in samples which before shearing would have d i f ferent structures. However, he thought i t possible that the d i f fering failure strains could cause structures which were not i n i t i a l l y the same to be the same at failure, 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 identical samples at the same.strain under different effective stresses from which the friction-and cohesion, components.could be determined at any strain. These he termed the Dependent and Independent components. Noorany.and Seed (1965) proposed a.method of obtaining samples at the same void ratio and almost the same structure but with differing effective stresses. The method involved anisotropic consolidation of two samples to the same void ratio, after which time the deviator stress was removed from one, resulting in two samples at the same void ratio but with different effective stresses. The samples were then sheared at constant void ratio and 29 separation of Mohr circles at failure allowed the effective f r i c tion and cohesion components to be determined. The authors sug gested that the Mohr circles might plot quite close to each other for insensitive clays making separation of components quite d i f f i c u l t , whereas for sensitive material, considerable separation could be expected. However, this could also mean that the ob served separation in Mohr circles is due to structural change caused by release of the anisotropic stress condition, and as would be expected, this is more marked for sensitive material. The Roscoe concept discussed in Chapter 2 indicates that a s o i l which is yielding has only one strength parameter, M, which implies a linear relation between p' and the deviator stress cor rected for both boundary energy and Internal energy. M can be considered as a f r i c t i o n component and the theory suggests that the f u l l value of M is mobilized at a l l strains. In undrained tests i t is generally conceded that considerable strain is neces sary to mobilize f u l l f r i c t i o n . However, the Roscoe concept indicates that this conception is due to neglect of the release of internal energy from the sample. The release of internal en ergy is of course governed by the s o i l structure . Although i t is of considerable interest from theoretical considerations to try to isolate the components of shear strength, in practice i t is generally the measured combined value that is required. In addition, from the above discussion, i t appears that the effective f r i c t i o n and cohesion components may have no phy s i c a l meaning but arise from structural effects. It may be neces sary to try 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 in this testing program was taken from a de posit located in the Fraser Valley, British Columbia. The deposit is centred around the town of Haney which is about thirty miles from the mouth of the Fraser River, and is known locally as Haney clay. It is presently being used for the manufacture of bricks and i t was from the pit at the brick factory at Haney that samples were obtained. The clay is thought to have been deposited in a marine or brackish environment during or shortly after the last glaciation of south-western British Columbia (Armstrong, 1957). Subsequent upli f t of the land relative to the sea has exposed the deposit and percolating rain water has since leached out much of the salt, 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 partially dry state, light and dark laminations of various thickness are evident. Standard laboratory identification 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 diffraction analysis to determine its mineral composition and the results are shown in Table II. It may be seen that the s i l t size particles are composed primarily of quartz and feldspar, while the clay size particles are mainly chlorite. TABLE I PHYSICAL PROPERTIES OF HANEY CLAY Specific gravity 2.80 Liquid Limit hh% Plastic Limit 26% Plasticity Index 18$ Natural Water content \2% ± 1% Per cent finer than 2 microns \6% Activity O.h Undisturbed unconfined compressive strength 1550 lbs./sq.ft. Remolded unconfined compressive strength 130 lbs./sq.ft. Sensitivity 12 Maximum past pressure 5500 lbs./sq.ft. 3£ Figure 8—Grain 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 MINERAL AMOUNT PRESENT Quartz Large S i l t Fraction Feldspar Large (greater than Chlorite Moderate - small 2 microns) Mica Moderate - small Amphibole Small Clay Fraction (less than 2 microns) Chlorite Feldspar Mica/chlorite Quartz Mica Amphibole Large Moderate - small Moderate - small Small Small Small - questionable 35 1+.2 Field Sampling and storing of block samples. Block samples were obtained by hand excavation from the clay deposit at Haney in 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 isolating 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 fine piano wire. These were trimmed to rough cubes of side 9 inches, and were coated with wax at the site as shown in Figure 10. The blocks were carefully trans ported to the laboratory and the next day were given further coatings of wax and then stored in a moist room until required. *+.3 Description of test equipment. The testing program was shared with Mr. T. J. Hirst. Drained tests were performed 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 equip ment, principally the installation of a de-aired water tank and a form of temperature control. At the end of the undrained series a further change was made. A transducer was introduced to measure pore pressure and an undrained test was run for comparison pur poses. Two very slow drained tests were then run with pore pres sure measurements in order to determine the magnitude of residual pore pressures in drained tests. These modifications w i l l be indicated in the description of the test equipment which follows. The test equipment used is shown in 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 Vertical Dial Crauop Proving Ring Machined Ram Machined Buthing 37 Saturation Spiral Sqmple porous Stona. Oiarilkd Drained Wafer Vacuum y& 1.0. Scran Tubing To P r a i s e Or Pore Pre* .~ — V6nT<y^ Electrical Transducer-' De-aired Water Tank To Drainage System I Strain 1 Controlled Axial 1 Drjva y& QO. Poly1hclcn&_ Tubinj yr-0-0. Copper Tubing | v ' / V ' / ^ — C o n t r o l Panel J •/4 O.D. Copper Tubing ~ J 1 \ Regulators Presiure. Supply vacuum Supply I Chamber Pre&sure -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. Distilled De - Aired • Water Supply Connections to Triaxial Cell (T) LouJer w Stone. £ ) Upper Stone © © Va o. D. Copper '/fe O P . Bi&hop and Henkel null Indicotor Pressure Corffro Cylinder 10 cc. Burette (Adjusti ble Height) Pore Pressure Gouge (o - loo 4 Ft. Mercu ry Manometer To Supply IOLb./S£j, Back Pressure L E G E N D (g) Hoke S a i l -Vblve (Mon - Displ.) X Hoke S t e m Va|ve (Displ.) ® Kliner A BIO Valves (Non-Displ.) N O T T O S C A L E Fioure 1 2 - Drainage on a! Pore Pressure Meas>urin^ System • Overflow e-s -Monomeicr •Saran Tubing -Mercury Over-Tlouj F i g u r e 13 - Test Equipment ko of stainless steel machined to a fine tolerance and were greased with "lubriplate" before each test. No significant leakage of water past the ram occurred. A loading cap which was free to rotate was used to minimize the lateral force and moment trans ferred 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 air 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 steel balancing tank under a vacuum and allowed to cool overnight. It was then fed into the chamber under a small air pressure. In the undrained series a d i s t i l l e d de-aired water tank was installed. 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 com pressed air from a house line and applying i t to the air-water steel balancing tank. The water in this tank was subject to a vacuum before each test, but during the test in the presence of air at a high pressure i t was expected that air would go into solution and find 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 in. O.D. polyethelene tubing. In the undrained series a 6 f t . length of 1/8 i n . I.D. Saran tubing was installed in the line to reduce the amount of air reaching the c e l l as suggested by Poulos (1961+). If leakage of water from the c e l l occurs then air is carried to the c e l l by the water instead of diffusing through the water along the length of the tube and the effect of the tubing is 1+1 then lost. The chamber pressure was measured by a 0-100 lbs./ sq.in. bourdon gauge graduated to 0.5 Ibs./sq.in., and f i t t e d with a mirror to reduce parallax. It was possible to estimate the pressure to 0.1 lbs./sq.in. The gauge was calibrated against a dead weight tester before each testing series and was found to creep under load. Variations of up to O.h Ibs./sq.in. were found to occur in successive calibrations. The balancing tank was f i t t e d with a transparent tube so that the water level in the tank was known and an elevation correction could be applied to deter mine the chamber pressure at the level of the centre of the sample. Drainage lines from the top and bottom of the sample led to a 10 cubic centimeter moveable burette, graduated to 0.1 cubic centimeters. Wherever possible 1/8 in. O.D. copper tube was used, but where movements were large relative to the length of tube, such as for the saturation spiral and the connection to the burette, flexible plastic tubing was used. The level of the water in the drainage burette was kept at the level of the mid height of the sample, so that as drainage proceeded i t was necessary to adjust the burette from time to time. To insure complete saturation of samplesa 10 Ibs./sq.in. back pressure was applied to the burette. This was accomplished by means of a mercury column and a 1200 cubic centimeter air balancing tank. The tank was sufficiently large that the change in the volume of air caused by drainage of 10 cubic centimeters of water would alter the back pressure by less than 0.1 Ibs./sq.in. Changes in temperature of + 1.0°c would alter the pressure by about + .05 Ibs./sq.in. However, changes in atmospheric pressure caused changes in the level of K2 the mercury which were not realized unt i l the el e c t r i c a l trans ducer was installed at the end of the testing program. The reason for this is as follows: A constant volume in the back pressure tank is maintained by a constant absolute pressure. If atmospheric pressure f a l l s then there is a tendency for the air in the tank to expand. This is prevented by rise of mercury in the standpipe equal to the change in atmospheric pressure (the small volume increase due to the rise of mercury can be neglected). The chamber pressure gauge reads pressures above atmospheric, the back pressure should therefore also be referenced to atmos pheric pressure. Errors in the back pressure may have occurred but i t is thought these amounted to no more than about 0.2 lbs./ sq.in., as the level of the mercury was corrected occasionally during a test by allowing air into or out of the tank. Later, when the transducer was present, the correct back pressure was attained by moving the drainage burette until the desired trans ducer reading was obtained. Pore water pressure was measured at the bottom stone only using the Bishop and Henkel null tube device (1 mm. I.D. tube). A 5 foot length of 1/8 In. outside diameter copper tube connected the null tube to the bottom stone. The compliance of this system produced a movement of 7/^ +0 in. in the null tube over a range of 100 Ibs./sq.in. that was f u l l y reversible. Bishop and Henkel (1962) suggest that the movement should not be more than 1/2 in. over a pressure range of 100 Ibs./sq.in. and the system was therefore considered satisfactory from the compliance point of view. During a test the position of the null point was varied >+3 w i t h t h e p r e s s u r e t o a c c o u n t f o r t h i s c o m p l i a n c e . The p r e s s u r e was measured w i t h a 0-100 I b s . / s q . i n . bourdon gauge s i m i l a r t o t h a t used f o r measuring the chamber p r e s s u r e . The gauge was c a l i b r a t e d u s i n g a dead w e i g h t t e s t e r t o a p p l y a chamber p r e s s u r e w h i c h was t h e n r e a d on the pore p r e s s u r e gauge. I n t h i s way no c a l c u l a t i o n was n e c e s s a r y to. account f o r the h e i g h t of mercury i n the n u l l tube or the change i n t h e h e i g h t of the mercury due t o change i n t h e n u l l p o i n t w i t h p r e s s u r e . A f t e r c a l i b r a t i o n , c a r e was t a k e n t o i n s u r e t h a t t h e h e i g h t of mercury f o r z e r o gauge r e a d i n g was always kept the same. Towards the end of t h e t e s t i n g program an e l e c t r i c a l t r a n s ducer of the bonded type and made by Data Sen s o r s I n c o r p o r a t e d was i n s t a l l e d . I t was p l a c e d as c l o s e as p o s s i b l e t o t h e c e l l t o m i n i m i z e the c o m p l i a n c e of t h e system. The t r a n s d u c e r had a range of 0 - 150 I b s . / s q . i n . a b s o l u t e and a r a t e d c o m p l i a n c e of 0.00027 c u b i c i n . f o r 100 I b s . / s q . i n . change i n p r e s s u r e . The r a t e d c o m p l i a n c e was checked w i t h t h e n u l l tube and found t o be c o r r e c t (9A0 i n . r i s e i n n u l l p o i n t f o r 100 I b s . / s q . i n . ) . T h i s c o u l d be compensated f o r d u r i n g a t e s t by u s i n g the n u l l tube d e v i c e t o add or remove water t o the t r a n s d u c e r system t o t a k e t h e p l a c e of the volume change caused by t h e e x p a n s i o n and c o n t r a c t i o n of t h e a c t i v e f a c e of the t r a n s d u c e r . I f t h i s were done i m m e d i a t e l y a f t e r a r e a d i n g was t a k e n , t h e n f l o w i n t o or out of the sample would a l l o w t h e s l i g h t p r e s s u r e surge t o d i s s i p a t e b e f o r e subsequent r e a d i n g s were t a k e n . The t r a n s d u c e r i s accompanied by an e l e c t r i c a l r e a d - o u t d e v i c e and the system was 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 e s t e r . The c a l i b r a t i o n was found t o be l i n e a r w i t h p r e s s u r e t o an a c c u r a c y kh of + 0.1 Ibs./sq.in., and pressure changes of 0.025 Ibs./sq.in. could be detected. The transducer measures pressure on an absolute scale and a barometer was i n s t a l l e d so that the pressure could be referred to gauge pressure. A l l tests were s t r a i n controlled. A. constant deformation rate was applied to the loading platform on which the c e l l was placed by means of a l/k- horse power e l e c t r i c motor and a system of gears. The gear system allowed t h i r t y deformation rates ranging from about 2 i n . per hour to 1 i n . per year. A. proving r i n g was used to measure the deviator force i n the ram. The force on the ram caused by the chamber pressure and by f r i c t i o n at the bushing was measured by moving the loading platform upward at the intended t e s t i n g rate without the ram being i n contact with the sample. The f r i c t i o n force may change during a test mainly because of induced l a t e r a l forces but no attempt was made to measure t h i s . The deformation of the sample was measured by a d i a l gauge placed such that the deformation of the sample only was measured. Hoke valves were used wherever leaks could not be tolerated. The stem type displacement valves were used where displacement was not a problem. Four Hoke non-displacement b a l l valves were used on the drainage and pore pressure lines where i t was e s s e n t i a l to have no volume change on opening and c l o s i n g valves. Klinger valves were used on the pore pressure device i n locations where small leaks were of no consequence. A.11 Klinger valves tested were found to leak. Four new Klinger valves were separately tested with the n u l l tube device and a l l were found to leak. Leakage ranged up to 0.003 cubic i n . per day under 100 Ibs./sq.in., which corresponds to a r i s e i n the n u l l point of about 2 inches. Poulos h5 (196k) found similar results, and this writer now understands that, where Klinger valves are used by other investigators in positions where leakage cannot be tolerated, either the valve linings have been replaced or the valve has been treated in some way. Hoke non-displacement valves were tested in the same manner as the Klinger valves and no leakage could be detected in 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 this was done from time to time. Subse quently, for other apparatus in the laboratory, Whitey non- displacement valves were used and were found to behave in a very satisfactory 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 lines. Due to the many problems encountered in getting the equipment 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 is re quired in de-airing the Hoke non-displacement valves as the sealing surface is not continuous and so an air space exists behind the seal. These valves must be held in the half open position while water is flushed through to remove this a i r . After de-airing, the system was allowed to cool and the null tube was then used to check the drainage system for compressibility and leakage. After the drained test series had been completed a form of temperature control was installed. 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 in. by h in. timber members and covered inside and outside with a layer of polyethelene to produce a h in. insulating air gap. A water cooled air conditioning unit of 9*4-00 B.T.U. capacity was used. It was capable of keeping about a 10°C difference in temperature between the room and the com partment but during the test series the difference was never more than 5°C* A. typical cycle was: air conditioner on for !-§• minutes, off for 3 minutes with a temperature variation within the com partment 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 tempera ture over most of the testing area. A thermometer placed in a 100 cubic centimeter flask did not record any noticeable variation in temperature due to the cyclic fluctuations of air temperature, and i t could be concluded that the sample which was surrounded by a considerably larger volume of water underwent negligable temperature variation. However, the air temperature variation did have a small effect on the Bishop and Henkel pore pressure measuring device. The effect on a closed system was for the pressure to f a l l on a rising temperature and rise on a f a l l i n g temperature. This is opposite to what one usually expects and may be explained as follows: On a rapidly rising air temperature the aluminum case of the pressure cylinder having a high conducti vity and low specific heat increases in temperature and expands allowing the water to increase in volume and hence reduce in pressure. The water having a low conductivity and high specific heat does not have time to heat and expand. The copper line to h7 the c e l l behaves In a similar way to the pressure cylinder although to a lesser extent. If, on the other hand, the temperature rise is slow then the water has time to heat and expand and water having a higher coefficient of thermal expansion than copper or aluminum tends to expand more, causing a pressure r i s e . This effect was essentially eliminated by binding the pressure cylinder and copper line by insulating tape. When the transducer was later installed, no variation in pore pressure in a closed system could be detected. h.h Testing technique Cylindrical samples 2.8 in. long and l.h in. in diameter were prepared in a moist room using a wire saw, miter box and trimming lathe. A trimmed sample and equipment is shown in Figure l ^ . Side and end trimmings were used for water content determinations. It was found that due to the laminated nature of the material, the. water content calculated from the end trimmings varied considerably from the side trimmings. These were not therefore used in 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 reliable 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 its side trimmings was found to be 0.-2 per cent and i t was concluded that the trimmings were a reliable measure of the average i n i t i a l water content of the sample. However, a precaution had to be observed in 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 ina l sample. Further trimming was necessary to allow for th i s . If this further trimming were not done, and i t was not always done by the writer, 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 in which i t was done the check was always within 0.2 per cent . The trimmed sample was measured and weighed. Three c i r cumferential measurements (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 in a l i i n . wide rubber s l ing to reduce stresses. Prior to the preparation of the sample the equipment was made ready. The porous stones were boiled for 10 minutes in d i s t i l l e d water and allowed to cool . Four 0-rings on ring expanders were fed over the top loading cap and down the saturation sp i ra l . These were followed by a rol led membrane. A, rol led membrane was also placed down over the pedestal. The cy l indr ica l surface of the pedestal was then covered with a f i lm of s i l i con grease and the membrane rol led to the top. Water was allowed to flow from the bottom drainage line to cover the top of the pedestal and form a convex meniscus. The bottom stone now cooled to room temperature was s l id into place. The sample was then s l id onto the bottom stone. 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. S i l i con grease was now smeared on the top cap and with one hand on the top 50 cap the lower membrane was rapidly r o l l e d up, any excess water being pushed ahead of the membrane. This membrane was then covered with 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 top. Two 0-rings were then placed over both membranes at top and bottom. Figure 15 shows a photograph of an i n s t a l l e d sample during a preliminary test series when only one membrane and two 0-rings were being used. The top of the c e l l was then placed i n position and the a l i g n ment of the ram with the b a l l bearing on the loading cap was checked. This was done by observing i f any l a t e r a l movement of the top cap occurred when the ram contacted the b a l l . The sample was positioned by t r i a l and error u n t i l no movement could be detected. The ram was then brought into contact with the sample and the v e r t i c a l d i a l set. Water from the d i s t i l l e d de-aired water tank was fed into the chamber under gravity, A. 10 Ibs./sq.in. chamber pressure was applied and the pore pressure measured. In those l a t e r tests where the transducer was used to measure pore pressure, the pore pressure was measured as soon as the f i r s t membrane was i n place. The ef f e c t on the pore pressure of placing the second membrane and al i g n i n g the sample could be observed. It was found that the pore pressure fluctuations of not more than 0.5 Ibs./sq.in. occurred and were e l a s t i c . The chamber pressure was then applied i n increments of 10 Ibs./sq.in. at four minute intervals u n t i l the desired chamber pressure was attained. The pore pressure was recorded before each increment was applied allowing the Skempton B parameter to be calculated. It was found that B was equal to unity for a l l increments, indicating that the 51 clay was 100 per cent saturated. Samples were allowed to consolidate for 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 applied. Since the time for *90 was never more than 200 minutes, i t was considered that a l l pore pressure due to primary consolidation was essentially dissipated at the end of the consolidation period. Burette readings were taken during consolidation so that the coefficient of consolidation c v and the coefficient of permeability k could be calculated. In preliminary tests i t was found that the sample would generally not consolidate uniformly in the vertical direction, so that at the end of consolidation the ram would no longer be aligned with the ball on the loading cap. To prevent this occur ring i t was necessary to bring the ram into contact with the ba l l from time to time during the consolidation period. The vertical stress involved in this contact was generally not more than about O.k- Ibs./sq.in. It was important to have good alignment before shearing otherwise there was a strong possibility of sample buckling taking place. In addition, poor alignment caused an irregular i n i t i a l stress strain 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 in contact with the ba l l on the loading cap. In this way the force on the ram due to the chamber pressure and f r i c t i o n at the bushing was determined. This was later subtracted from proving ring readings to determine the deviator force. 52 Samples were then sheared under either drained or undrained s t r a i n c ontrolled conditions. Figure 16 shows a specimen during shearing. The s t r a i n rate was about 0.5 per cent per hour and was the same for both drained and undrained t e s t s . Some additi o n a l tests were run at other rates but were not used for the main purpose of the t h e s i s . Variation i n the s t r a i n rate occurred due to deformation of the proving r i n g . In f a c t , during the early part of the un drained tests the s t r a i n rate was about onehalf the average s t r a i n rate. The chamber pressure was kept constant throughout a l l t e s t s . The a i r regulation system was found to work extremely well and fluctuations of not more than 0,1 Ibs./sq.in. were recorded on the chamber pressure gauge. In undrained tests the variables recorded were, time, sample deformation, proving ring deformation and pore pressure. In drained tests the drainage burette reading replaced the pore pressure reading. Approximately 50 sets of readings were taken throughout the duration of any one t e s t . These were l a t e r fed to a d i g i t a l computer to be analyzed. Two drained tests were performed at one quarter the general s t r a i n rate but drainage to the top stone only was permitted. Pore pressure was measured with the transducer at the bottom stone. The transducer was also used to measure the back pressure applied to the drainage l i n e so that a very accurate measure of the excess pore pressure at the bottom of the sample was obtained. This was thought to give a reasonable accurate measure of the excess pore pressure that would e x i s t at the centre of a sample drained to both top and bottom and sheared at the usual rate. This w i l l be discussed 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, since a check on the water content was required, water was f i r s t allowed to back drain into the sample before removing from the chamber. This procedure was f i r s t suggested by Henkel and Sowa (1963) and the reason i s as follows: If the e f f e c t i v e stresses at the end of the test are high, removal of the chamber pressure under undrained condi tions w i l l not change them and hence as the t o t a l stresses go to zero, large tensions are set up i n the pore pressure. If these are high enough they w i l l cause c a v i t a t i o n i n the drainage lines and water w i l l enter the ends of the sample. Even i f the tensions 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 into the sample form the porous stones during dismantling of the sample. Since i t appears impossible to prevent water entering the sample the alternative i s to measure the amount that enters. This was done by removing the deviator stress and dropping the chamber pressure to 12 Ibs./sq.in. while allowing water to flow from the drainage burette which was maintained at a back pressure of 10 Ibs./sq.in. at a l l times. Back drainage was continued u n t i l the rate of flow was very small or i n some cases i t was continued for 2h hours so that a measure of the c o e f f i c i e n t s of consolida t i o n and permeability a f t e r shearing could be obtained. In t h i s way the e f f e c t i v e stress was reduced to 2 Ibs./sq.in. After back draining the drainage valves were closed, the chamber pressure re duced to zero and the water removed from the c e l l . The rubber mem branes were cut and removed, the porous stones pulled from the ends and the whole sample was then weighed. It was not thought that much water would enter the sample from the porous stones since the tension i n the pore water should not be more than 2 Ibs./sq.in. 55 and the c a p i l l a r l y t e n s i o n of the stones was thought higher than t h a t . The water content of the whole sample was determined and from the known amounts of water drained and back drained the i n i t i a l water content could be c a l c u l a t e d . This was then checked w i t h both the i n i t i a l water content c a l c u l a t e d using the i n i t i a l wet weight and f i n a l dry weight of the whole sample and the i n i t i a l water content as determined from side trimmings. I t was found that the water content 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 per c e n t when the whole sample was used f o r i n i t i a l water content and was always w i t h i n 0 . 2 per cent when side trimmings which were pro p e r l y r e p r e s e n t a t i v e were used (see d i s c u s s i o n e a r l i e r i n t h i s s e c t i o n ) . In those t e s t s which were sheared at one quarter the usual r a t e the shearing process took about 10 days. However, the water content check f o r those two t e s t s was w i t h i n 0 . 1 per c e n t . I t may th e r e f o r e be concluded that the average water content at the v a r i o u s stages of a t e s t was a c c u r a t e l y known and that no s i g n i f i c a n t leakage occurred. A f t e r removal of the sample, the drainage 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 top loading cap were thoroughly washed w i t h detergent to remove any grease which might l a t e r t r a p a i r . The equipment was then ready f o r the next t e s t . 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 effective 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 in the tests and other possible variables, such as temperature and strain rate, were therefore kept constant. However, due to the nature of t r i a x i a l equipment errors arise which may not affect drained and undrained tests in the same manner. In a t r i a x i a l test the aim is to subject a sample to homo geneous 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 strain is seldom uniform. In addition, in undrained tests non-uniform stresses lead to non-uniform pore pressures and or migration of water within the sample. In drained tests residual pore pressures of some gen erally unknown value are present. Even i f the stress system were uniform, errors may arise in measuring the applied pressures and forces, principally the pore pressure and deviator force, and are mainly caused by time lag in the pore pressure measuring device and the presence of ram f r i c t i o n . These errors w i l l be discussed in subsequent sections of this chapter. 5.2 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 is applied, shear stresses are present and prevent diameter decrease at the top and bottom. During shearing, these shear stresses reverse in direction and essentially prevent the end diameters from increasing, resulting in 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 vertical stress at the centre is less than that at the ends. The shear stress at the ends has the affect of increasing at the ends and the overall result is that both and are higher at the ends than at the centre, but - f j^ ) is higher at the centre (Bishop, Blight and Donald I 9 6 0 ) . The devia tor stress is generally calculated from a cross sectional area which is determined by assuming that the sample deformed as a right cylinder. Roscoe, Schofield and Thurairajah ( 1 9 6 3 ) indicate that at an axial strain of 2 0 per cent, the area at the centre may be 1.*+ times the area calculated on the usual basis. Casagrande and Wilson ( I 9 6 0 ) suggest that the relation between the vertical stress at the ends and centre of a t r i a x i a l specimen is given by: where = vertical stress at ends 0^ = vertical stress at middle £]_ = axial strain. So that at 2 0 per cent strain the vertical stress at the ends would be 50 per cent larger than at the middle. 58 The axial strain is generally calculated by dividing the deformation of the sample by the consolidated length, and i t is assumed that the strain is uniform throughout the sample. Roscoe, Schofield and Thurairajah (1963) showed that for drained compres sion tests on loose saturated sand, the axial strain varies con siderably throughout the depth of the sample. In general, axial strains were found to be larger at the centre than at the ends. This would be in agreement with Bishop's suggestion that the shear stresses are larger at the centre. After about 10 per cent average axial strain, zones of maximum axial strain occurred at about the third points and were thought due to the failure zone moving to wards the ends. Failure f i r s t occurs around the central zone followed by yielding and bulging and reduced-stresses, and movement of the failure zone towards the ends. In compression tests on normally loaded clay specimens, the strain distribution is unlikely to be the same as for 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 strain between the centre and the ends at large average axial strain. It is apparent, therefore, that stresses and strains are not uniform throughout a sample. At an average axial strain of 20 per cent, the stresses and strains within the sample may be as much as 50 per cent different from those calculated in the conventional manner. Since the actual stress and strain could not be reliably calculated for any element within the sample, the' conventional method was adopted. It was hoped that the errors would be similar in both drained and undrained tests and that calculated average 59 values would provide rel iable comparisons. 5 . 3 Non-uniform pore pressures in undrained tests Non-uniform stresses lead to a further problem in the case of undrained tests. 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 fai lure zone can hardly be considered to be undrained. Undisturbed clays are not l ike ly to be homogeneous so that non-uniform pore pressures would probably occur to some extent even in 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 I960, Bishop, Blight and Donald 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 soils where shear stresses cause reduction in 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 cy l indr ica 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 re lat ively high permeability, considerable head loss may occur in the f i l t e r paper. The calculated coef-60 f ic ient of consolidation of the s o i l assuming no head loss in the paper may be very much less than that measured i f no f i l t e r paper were present. In the past, in order to reduce hoop tension, f i l t e r paper strips with alternating gaps were used. This reduces the effectiveness 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 ver t ica l s l i t s to reduce hoop tension might be used to offset th i s . Campanella (1965) found that the use of s l i t s rather than slots in 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 Blight (1963) produced equations and graphs from which the time to any reliable reading can be obtained for drained and undrained tests provided the coefficient of consolidation c v or the apparent c v (obtained by assuming no loss in the f i l t e r paper) is known. Their results were based on 95$ equalization of non-uniform pore pressures in the case of undrained tests, and 95$ dissipation of excess pore pressure in the case of drained tests . If i t is only required to have a re l iable reading at fa i lure , then the time obtained is the time to f a i lure . 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 rel iable point on the stress path. Preliminary tests were conducted to determine i f the use of f i l t e r paper would allow reduced testing times. Isotropic consoli 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 (Whatmans No. 5^) and the results compared. Without f i l t e r paper e v was found to be about 2 x 10"" 3 cm, 2 / s e c , whereas with f i l t e r paper and assuming no head loss 61 in the paper the apparent c v was about 5 x 10"^ cm.2/sec. Since 2 x 10~3 cm.^/sec. was the correct c v and would have been measured had no loss occurred in the paper (assuming k^ = ky), the ef ficiency of the drains, which is the ratio of the apparent c v to the actual c v was about 2^ per cento It has been suggested that the poor performance of the paper may have been due to smear on the lateral surfaces caused by sample trimming, but a similar 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 res ponsible for such a poor efficiency. Similar low efficiencies were obtained by Simons (1963) and Crawford (1963) on sensitive clays with c v's in the same range and were attributed to head loss in the paper. Based on the c v values obtained, the times required to reliable readings for undrained tests from Blight's chart are about h hours with or without drains. It was therefore decided not to use drains. Unfortunately, at the time of these preliminary tests, the concept of using s l i t s in the f i l t e r paper instead of the usual slots was not known to the writer. It is very possible that s l i t paper would have been considerably more effective. 5.*+ Residual pore pressures in drained tests Since f i l t e r paper side drains have a very low efficiency and were not used, i t was necessary to have drainage top and bottom in drained tests to reduce the testing time. With a c v of 2 x 10"3 cm.2/sec. and double-end drainage, a time of 11 hours to the f i r s t significant reading was calculated (Bishop and Henkel 1962). Blight (1963) suggests that the theoretical times for 95 per cent dis sipation from which the Bishop and Henkel equation is derived 62 predicts times considerably longer than those actually needed for 95 pe-r cent dissipation. He suggested that the time required for a given degree of pore pressure dissipation in a drained test with double-end drainage would be the same as that required for the same degree of pore pressure equalization in an undrained test without f i l t e r paper. The time required for 95 per cent dissipation of excess pore pressure would therefore be h hours, the same as i t was for undrained tests. The writer was concerned about the value of residual pore pressures in drained tests because of the highly flocculated nature of sensitive clays. During shearing i t was expected that large reductions in permeability would take place due to struc tural change and decreased void ratio. Hence i t was thought pos sible that residual pore pressures might be larger than usual. A. method was derived for calculating 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 in detail in Chapter 6. 5.5 Pore pressure measuring devices Until quite recently pore pressures in small test samples have been measured by means of the null-indicator. This generally comprises a water-mercury contact surface in a small diameter tube which is maintained at such a level that no flow from the sample to the system occurs. The pressure required to maintain the level is measured and gives the pore pressure at the centre 63 of the sample when the system is suitably calibrated. More re cently e lec t r i ca l transducers have been used to measure pore pressure. Here very small deformations of a diaphragm produce changes in e lec t r i ca l resistance of strain gauges allowing ca 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 in the absence of a pore pressure measuring device then the presence of one may lead to non-uniform pore pressures. In the nul 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 deflection of the diaphragm in the transducer causes a small volume change and similar gradients within the sample. Bishop and Henkel (1962) defined the sensi t iv i ty of the nul l indicator as the time required for a movement AX to occur in the nul 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 ratio of the diameter of the nul l tube to the dia meter of the surface over which the pore pressure is measured raised to a power. For Haney clay with Ap = 0 . 2 Ibs . / sq . in . and Ax = 0 . 0 2 i n . and measurement at the bottom stone, the sensi t 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 sensi t iv i ty time would have been very much greater. 61+ A. similar time lag occurs with the transducer due to its compliance. When the transducer was installed towards the end of the testing program, i t was found that for an ambient pres sure increase of hO Ibs./sq.in. under undrained conditions, a time of about 2 minutes elapsed before 98 per cent of this in crease was recorded on the transducer. This time is a function of the compliance of the transducer system, the nature of the sample material and the area over which the pore pressure is measured. Had the transducer been connected to a pore pressure probe in place of the bottom stone a very much longer time would have elapsed for 98 per cent equalization. In general the sensitivity time is very much less than the time required for reasonable equalization of pore pressures due to non-uniform stresses and consequently i t is not usually con sidered. However, i f pore pressures are measured with small diameter probes inserted in the sample, sensitivity may well be an important factor. 5.6 Rate of testing Since the drainage condition was to be the only variable, i t was necessary to have the rate of shearing the same for both drained and undrained tests. In addition, stress paths were required rather than just stresses at failure and therefore the rate had to be such as would give reliable values of stresses for a considerable portion of the stress path. The approximate times for 95 per cent dissipation and equalization of pore pressures in drained and undrained tests were 11 and U- hours respectively. If the more optimistic figure suggested by Blight for drained 65 tests was taken, then the time for both was about h hours. Preliminary tests indicated that for undrained shear the maximum deviator stress occurred at about 3 per cent axial strain while the maximum principal stress ratio occurred at about 15 to 17 per cent axial strain. In drained tests both maximum deviator stress and maximum principal stress ratio occurred at about 30 per cent axial strain. A.n average shearing rate of 0 . 5 per cent axial strain per hour was selected. During the early portion of the test, due to the rapid rise in deviator stress, deflection of the proving ring caused the strain rate to be considerably less than the average rate. The time for 30 per cent axial strain was about 60 hours. In drained tests about one half of the stress path occurred in the f i r s t 11 hours while one quarter to one third occurred in the f i r s t k hours. Therefore at best two thirds of the stress path would be reliable and possibly only one half. How ever, residual pore pressures were calculated and i t is thought that the estimated stress path is reliable over almost its complete length. In undrained tests, 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 fact, one third of the readings were taken within the f i r s t k hours and actually 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 in the measured values of the effective stresses caused by non uniform pore pressures depend on the overconsolidation ratio 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 reliable. Simons (1963) suggests that 90 per cent equalization in undrained tests is quite adequate, the time for which would be 2 hours. About one third of the stress path occurs in the f i r s t 2 hours. Some preliminary tests were also run at 0 .25 per cent per hour average axial strain or one half the rate actually used in the testing program. It was found that the stress path in the early portion was very l i t t l e d i f ferent to that obtained at the faster rate. Thus about five sixths of the stress path is known to be reliable. Many investigators believe that considerably faster strain rates than those suggested by Bishop and Blight can be used and reliable 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 in which pore pressure probes in ad dition to base measurements were used to determine pore pres sures. Specimens were l,h in. diameter by 2.8 in. in length and the coefficient of consolidation was about 2 x 10~3-cm2/sec., or about the same as for Haney clay. The strain rate was 0 .5 per cent per hour (same as used in this testing program) and maximum deviator stress occurred at about 2 per cent axial strain or after about h hours. The theoretical time for 95 per cent equalization would be about h hours, thus, according to Bishop and Henkel (1962) a reliable base measurement of pore pressure would only be obtained at failure. Crawford found that a pore pressure probe (0.12 cm outside diameter) placed at the lower quarter level recorded es sentially 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 in the fai lure zone which he fe l t is near the base due to the re straining effect of the porous stone. Higher pore pressures at the ends rather than at the centre for normally loaded and sensitive material is not in agreement with the general body of thought and evidence on this matter (Whitman I960, Bishop, Blight and Donald I 9 6 0 , and Blight 1963). The sensi t ivi ty 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 in 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. Bishop, Blight and Donald ( i960) have stated that the onus should be on the research worker to prove that his tests satisfy reasonable c r i t e r i a for accurate determination of pore pressure. It is f e l t that the preliminary tests performed at the slower rate indicate that the pore pressures are only in 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 resulting from secondary effects 68 Samples were consolidating for a period of 2h hours after which time shearing was commenced immediately and in undrained tests i t was assumed that a l l increase in 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 rise w i l l take place in the absence of any.applied deviator stress. Figure 17 shows the buildup in pore pressure with time for a sample which was consoli dated to 75 Ibs . / sq . in . for a period of 2k hours. Since the time for tgowas less than 200 minutes i t is fe l t that primary consoli dation was essentially complete after 2*+ hours and could not be responsible for the observed r i s e . It was thought, at f i r s t , 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 Ibs . / sq . in . per day. Therefore, leakage could account for only a small portion of the build-up. The pore pressure r ise is thought to be due to structural re-arrangement after drainage. It is closely associated with secondary compression and in fact could be described as the "converse" of secondary compression. If further drainage is a l lowed secondary compression takes place due to structural re arrangement, while i f drainage is prevented pore pressure rise 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 in undrained tests. However, drained tests were treated in the same manner as undrained so that the pre-shear NOTE". I. Sample Allowed ft> Consolidate For £4 Hours a | which Time Drainage \dlves Closed and Pore Pressure O b s e r v e d . 2. T i m e Measured From Close o f Drainage 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 is not af fected in the drained test but additional drainage takes place which alters the water content. Since the object of the testing program was to compare contours of water content obtained from drained and undrained tests, i t may be that since the same pro cedures were observed in both, that the water content contours are equally changed in both types of tests . 5,8 Membrane Leakage The original testing procedure involved the use of glycerene as a chamber f lu id 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. It was found, however, that the water content determined after shearing was always 1 to 2 per cent below that calculated from i n i t i a l conditions. The pressure in the glycerene was always 20 Ibs . / sq . in . 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 ferent ia 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 in water from the sample. Subse quently i t was discovered that previous investigators (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 lu id and two membranes separated with a f i lm of si l icone grease and bound with two 0-rings top and bottom, no further leakage problems were observed. 71 5.9 Ram f r i c t i o n 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 passes out of the c e l l is also included in the measured force. To minimize this f r i c t i o n force, ball bushings, rotating rams or rotating bushings and closely machined rams and bushings have been used. The ba l l bushing type would appear to be the most desirable of these because lateral forces on the ram would not produce any additional f r i c t i o n force. A. seal to prevent water escaping from the chamber is necessary and w i l l give rise to some f r i c t i o n force which can be measured. A c e l l with a closely machined ram and bushing was used in this test series. The ram was greased with "lubriplate" before ea test and very l i t t l e leakage occurred past the ram so that no additional seal was necessary. Ram f r i c t i o n and the force on the ram due to the chamber pressure was measured by moving up the loading platform at the intended testing rate with the ram not in contact with the sample. To determine i f the ram was 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 for the duration of a test ( 7 0 hours) with no sample in place. No significant change in f r i c t i o n force occurred. It was thought that significant f r i c t i o n forces might develop during shearing when the axial force would be high and lateral forces might be present. Bishop and Henkel (1962) suggest that additional f r i c tion forces only arise because of lateral forces. At Imperial College i t was found that with cells similar to those used in 72 this testing program that the f r i c t i o n force was generally between 1 to 3 per cent of the axial load. Lateral forces were thought to be small in this test series because a loading cap which was free to rotate was used. If large horizontal forces were present rotation of the cap would occur followed by buckling. Bishop and Henkel suggest a fixed type loading cap for undisturbed material to prevent buckling. However, large lateral forces and moments may be transferred to the ram in this case causing higher f r i c t i o n forces and may be responsible for the upper range of f r i c t i o n forces quoted by Bishop and Henkel. Available evidence indicates that errors in 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 use of a rotating top cap, the errors may be even less than 1 per cent. 73 CHAPTER 6 RESIDUAL PORE PRESSURES IN DRAINED TESTS 6.1 Introduction Residual pore pressures of some magnitude are always present in drained shear tests. Flow of water to or from the drainage boundaries is caused by pore pressure gradients within the sample and the resulting pore pressures are referred to as residual pore pressures. The duration of drained tests is generally chosen such that the average degree of pore pressure dissipation is at least 95 per cent at failure, or i f a stress path is required, at the time the f i r s t reliable reading is desired. The time required for any given degree of dissipation is usually calculated from the formulas t - h 2 F T\C v ( i - u ) (9) where tj> = time to failure or a reliable reading h = one half the height of sample T\ = factor depending on boundary drainage conditions c v = coefficient of consolidation U = average degree of dissipation required The above formula was derived from theoretical considerations by Gibson and Henkel (195^). However, i t does not allow the cal culation of average pore pressures. An expression for pore pres sure was derived by Gibson and Henkel based on the assumption that the rate of pore pressure increase in the undrained condition is constant. This was then used to determine the upper bound for the average degree of dissipation. Since the rate of pore pres-7h sure rise in the undrained condition is known not to be constant, their expression for excess pore pressure would"not be suitable for estimating residual pore pressures and was not intended to be so. Alternative methods for estimating pore pressures were therefore considered. Since test data was to be analyzed on the computer, numerical methods of relatively 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. Validity of Darcy's law. 6 . k and c y constant throughout the sample at any one time, but vary with time, 7. Sample deforms as a right cylinder. It is assumed for both methods that drainage top and bottom occurs. However, drainage from one end only is obtained by simply replacing h by 2 h . The average pore pressure rather than the maximum pore pressure has been calculated. The reason for this is 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 dissipation is high, as i t should be in a drained test, the maximum pore pressure is l£ times the 75 average. So that the maximum pore pressure is readily obtained from the average and vice versa. 6.2 Method 1 This method is based on the superposition of pore pressures (Terzaghi, 19^3» p. 286). The deviator stress is assumed to be applied in increments, causing pore pressures which can be e s t i mated from the Skempton equation for change in pore pressure under undrained conditions, namely: A U = B (A0"3 + A, (AcJx -A63) (10) Incremental pore pressures are assumed to dissipate independently and in accordance with the one dimensional consolidation equation. The pore pressure at any time is then the sum of the partially dissipated incremental pore pressures at that time. This method is discussed in detail in 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 failure, therefore excess pore pressures must be present. It 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 yield a much simpler expression for excess pore pressure i f one assumption were made. This alter native approach is discussed in the next section and is 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 partial d i f f e r e n t i a l equation (Bishop and Gibson 1963) : rw b ? - at U 1 ; where 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 o t element of s o i l . If i t is assumed that the rate of loss of water from every element of a sample is the same at any time ty, then q w i l l be a function of time only. Since the volume of water leaving a drained test sample was recorded during the shearing process, the rate of loss per unit volume could be calculated, u^, the pore pressure at time t j is a function of z only, hence for any one time the partial d i f f e r e n t i a l equation (11) can be reduced to the ordinary differential equation: k d u = _ dq = - R = constant (12) ^ dt V where R = rate of loss of water from the sample V = volume of sample This can be integrated using the boundary conditions u = 0 at z = h and |^ = 0 at z = 0 to yield the following expression for dt 77 the pore pressure at any time t j : U j = 2 ^ § ( h 2 " z 2 ) — " ( 1 3 ) And the average and maximum pore pressures are given by: U j (average) = I YW R^h2 (1>+) Uj (maximum) = A " ^ j ^ 2 (15) • • ~ T T T i It is seen from expression (13) that the theory predicts a para bolic distribution of excess pore pressure, and consequently the average pore pressure is two thirds the maximum pore pressure. Expression (ih) is very readily programmed for the computer. It is much simpler than the expression involved in Method 1 since i t involves no summation, and in fact, could easily be calculated without a computer. Only one unknown, the permeability of s o i l appears in the expression instead of the two occurring in 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 in void ratio should be uniform throughout a sample between time intervals, 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 is high, this expression is considered to give a good ap proximation of average residual pore pressures. The variables in 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. The height and volume of the sample are readily calculated. 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 ike ly to be taken at equal time intervals this was approximated as shown in Figure 18. Since the permeabilities calculated from isotropic consolidation prior to shearing and from swelling after shearing were not considered re l iab le , 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. Test samples were consolidated to *f0 and 70 Ibs . / sq . in . respectively which was the range of consolida tion pressures used in the drained test program. The calculated permeabilities are shown in Figure 19. It is seen that the relat ion between void rat io and permeability for both tests can be approxi mated by a straight line on the semi-log plot except for the i n i t i a l portion of the test consolidated to ho Ibs . / sq . in . It w i l l be shown later that samples consolidated to kO Ibs . / sq . in . are not truly normally loaded and this i n i t i a l portion is due to an overconsolidation effect reflected in 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 re l i ab le , those obtained from swelling appear too low. ure lfi>—Illustration of Method for Determining Drainage During Shea 41 4-0 39 36 57 3fo z ui 35 u or m 34-CL h- Z 33 Ul r- O 52 u or: ul 31 r-< SO £S £7 £fc £5 LES-END A Dramed Test S- 16 , <5C - 4o Lbs/Sc^. In- •» Drained Test S -19 , = 70 Lb./ S^. In 8 0 £.10' 1 j j j | 1 I 1 ! < ! j [ i Ini "l<* Inotropic Con»o idation S- i 1 •ia 0 i I i ! \ i | j i i ! i i A-lniti ' s- i l Ise IS frop c dons I olic i / t i & SI ieor Strain — x 1 / I • A / \/ : ; I i *)/ • j I i I < ! I V . -7, oJ*—<" '0 ( 10 0757 I .ECj ~v I I i I i i i i Draimr 9 » - 19 o /* !^ ( i I i z f • • / 5 6 7 8 9 I0" a 2- PERMEABILITY lM CM./SE .C . ion NOTE: Figure 19 — 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.. Relationship Between Void Ratio and Permeability During Drained Shearing of-Haney- Clay. 81 Since the tests to determine the permeability were run at one quarter the normal rate but with drainage from one end only, then theoretically, i f secondary effects are not considered, the pore pressures measured at the bottom end of the slow tests should be identical 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 is shown plotted versus shear strain in Figure 20 for both slow tests. Residual pore pressures calcu lated by Methods 1 and 2 are compared to the measured values in Figure 21. Pore pressures calculated by Method 1 are seen to be quite different from the measured values. For a consolidation pressure of 70 Ibs./sq.in. the calculated pore pressures are gener al 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 strain. Pore pressures calculated by Method 2 are seen to be quite similar to the measured values. They are slightly 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 slightly higher for the slower rate. If is f e l t that Method 2 gives a reliable measure of excess pore pressure during a drained test. However, since the slow drained tests were run at one quarter the normal speed, the measured pore pressures give reliable values of the excess pore pressures generated at the centre of samples tested at the normal Ul <r a. ui oc o a < a' iii cr NOTE • Avcnqge Residual pore Pres. Assumed*^ Max. Measured Pore. Pres. I©J 70 Lbs f/ f 0 / O 5 10 15 SO £5 SHEAR S T R A I N IN P E R C E N T Fjg,£0- Relationship Between Measured Residual Pore. Pressure and Shear Strain in Drained Tests 3o a- 12 a ui tr a a j. < O Ul or u < Of I II 10 9 8 7 6 5 4. S a 1 \ 1 \ \ N 1. 1 i n « 70Lhs/S^-'f 1. f Method 1 4-0 P.S.I ^ s ^ M e t h \ ?d |. II 1 ll 1 70 P.S.I jM.ethi >eU \ 1 A — ^ 7 ^ ^ ^ - S - 19 , ^ « 7 0 p.£ .1. (Fig .eo) \ \ aunsd . /-s-ia,j • 40 P.S.I. ^ ~ -__(fj3.£0; \ \ hod a ^ " ^ ' ^ ^ ^ ^ ^ < - S-17. &JeJfiod| - — io is ao SHEAR STRAIN IN PER CENT SO N O T E : S-IS &I3 Shear&d pt '/4- the. Normal f^afe ^ut uiith D r o i t s ? f rom Top Stone onl j . Pore Pres. Measured a t bottom Stone Fig. 21- Comparison of Measured and Calculated Residual Pore Pressures in Drained Tests. 83 speed, so that these measured pore pressures could have been used to adjust the effective stresses without any calculations. However, i t may not be necessary to run check tests at such a slow rate. In fact the same permeability relation would most l ike ly have been determined had the normal rate been used but with drainage from one end only. For a drained test series in the normally loaded range, i t is probable that a few drained tests with pore pressure measurement would be sufficient to determine a relationship between void ratio 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 pres sures are measured in drained tests. If the permeability of a s o i l is determined by the f a l l ing head method, leaching of the s o i l may take place which in i t s e l f may alter the permeability, part icularly in undisturbed so i l s . In Method 2 no such leaching takes place. For any one s o i l at a given void rat io 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 com paring permeability versus void rat io relationships for the same clay in the undisturbed and remolded states. Measurement of residual pore pressures and subsequent calcu lat ion of permeabilities in 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 rat io are to have the same structure, then their permeabilities should be the same. If the void ratio versus permeability for normally loaded s o i l is a straight line on the serai-log plot as i t appears to be for Haney clay, then any overconsolidated sample i f i t is to have the same structure at failure as a normally loaded sample, must have its permeability on this normally loaded line at failure. Samples of Haney clay consolidated to kO Ibs./sq.in. are in the overconsoli dated range, but i t was seen from Figure 19 that after about 6 per cent shear strain the permeability lay on the straight line and the sample thereafter behaved as normally loaded. The structure at failure, which occurred at about 25 per cent shear strain 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 , for Haney clay, a unique relationship exists between effective stresses and water content which is independent of effective stress path. The main body of the testing consisted of 7 consolidated undrained (C-U) tests and 6 consolidated drained (S) tests on undisturbed samples of Haney clay a l l of which were sheared at the same strain rate ( 0 . 5 per cent per hour). In addition, 2 consolidated drained tests were performed at one quarter the normal strain 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 analyzed on the I.B.M. 70*4-0 at the University of British Columbia. Results from a l l tests are shown graphically in the diagrams that follow. Typical test readings, computer programs and computer outputs are shown in Appendix II for C-U-2 and S - 1 7 . Stress-strain characteristics of Haney clay are presented in Section 7 . 2 . It is f e l t that these curves are useful in interpreting the results discussed in subsequent sections. Con tours of water content from drained and undrained tests are compared in Siection 7 . 3 • Energy corrections, the possibility of predicting 86 stress -strain relations and the effect of strain rate on stress- strain relations in drained tests are discussed in Sections 7»U-, 5 and 6. 7.2 Characteristics of Haney clay The most d i f f i c u l t problem in attempting to determine rela tionships between effective stresses and water content for an undisturbed clay is to find a clay of sufficiently uniform com position that consolidated samples can be obtained which l i e on a single void ratio or water content versus logarithm of pressure line. The water content versus logarithm of isotropic consoli dation pressure relation is shown on Figure 22. It is seen that consolidated water contents from a l l drained tests l i e on a com mon straight line, whereas consolidated water contents from un drained tests show some scatter and appear to l i e on a straight line 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 speci mens could be obtained from any one block, but in fact the drained test specimens were taken from 3 different blocks. It is un fortunate, therefore, that the undrained test specimens taken from a fourth block do not l i e on the same straight line. Haney clay is laminated and i f care was not taken to insure specimens were taken from the same level within blocks, different water contents resulted. When comparing contours of water content from drained and un drained tests, i t is necessary to have samples which l i e on a com mon isotropic consolidation line. The scatter, in consolidated water contents for undrained tests (Figure 22) appears to have l i t t 67 LEGEND C - U - l Consolidated Undrained Test No.!". S - l £ Consolidated Drained Test No. I£ . Figure 22 — Relationship Between Void Ratio and Logarithm oF isotropic Consolidation Pressure.^ Haney Clay. 88 effect on the stress paths followed in undrained tests, as may be seen in Figure 33, Section 7 .3 . The scatter is such that C-U-6 has a consolidated water content that actually lies on the iso tropic consolidation line common to drained tests. Yet the ef fective stress path followed by C-U-6 is very similar to that followed by C-U-7. It appears that for the samples of Haney clay tested, the consolidation pressure determines the effective stress paths followed in undrained shear. It was concluded from this evidence that for the purpose of comparing contours of water con tent, i t would be reasonable to assume that undrained samples had consolidated water contents which lay on the isotropic consoli dation line obtained for drained samples. Stresses and principal stress ratios are plotted versus shear strain rather than axial strain. The shear strain or more correctly the principal shear strain, £, is given by £ = £ , _ - 1/3 AV = 2/3 (e x - £ 3) where £ = principal shear strain &L = axial strain AV - volumetric strain In undrained tests AV = 0 and the shear strain equals the axial strain. In drained tests AV ^ 0 and the shear strain is therefore not equal to the axial strain. Since the effects of distortion are being examined, i t appears more reasonable to compare shear strains from drained and undrained tests rather than axial strains. The maximum deviator stress versus consolidation pressure relationship for undrained tests is shown in Figure 23. It is 69 o ' 1 1 1 1 0 30 40 to < 80 100 ISOTROPIC CONSOLIDATION PRESSURE , RS.I Figure 23 — Relationship Between Undromed Strength and isotropic COHSOLIDATION Pressure j Haney Clay. 90 seen that while samples consolidated to 75 and 88.5 Ibs./sq.in. l i e on a straight line passing through the origin as would be expected for normally consolidated material, samples consolidated to60 Ibs./sq.in. show maximum deviator stress above this line, indicating overconsolidation. This is surprising as the water content versus logarithm of consolidation pressure relation ap pears to be a straight line for pressures greater than k-0 lbs./sq. in. It 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, principal stress ratio, pore pressure and the pore pressure parameter A. a l l plotted versus shear strain are shown in Figures 2h to 27 for a l l undrained tests. Each test is shown by a different symbol so that the reproduceability of results can be examined. It is seen that the maximum deviator stress occurs at about 3 per cent strain, while the maximum prin cipal stress ratio occurs at about 15 per cent strain (Figure 2h). Principal stress ratio versus shear strain curves are very similar for a l l tests and are represented by a single line (Figure 25). Pore pressures (Figure 26) continue to rise with strain, although the rise is very slight from 15 to 30 per cent strain. The A. value (Figure 27) increases throughout tests. At maximum devia tor stress i t is about 1.1, while at maximum principal stress ratio i t is about 1.7. At 30 per cent strain i t is about 2 .3 . Maximum deviator stress occurs at about 3 per cent shear strain in undrained tests, at which time the principal stress ratio is only 2.^5. The phenomenon of maximum deviator stress 50 40 Sso 02 if Iii o r » -tf> o Si i i i ,/ m *fl" fa T. • 11 i l • M C-U - 6 $7, <£ = 68-3 P.S.I. ^ - C - U - 5 , <SC • 75 P.S.L. • 1 1 ^Buckled "V ^ ^ ^ rBuck lod i i T I i i i O 9 C - U - l ^ . f i c * ^ 0 P.S.I. — ' 1 :> • . • i • •: 1 i l i 1 0 Figure £4- eo as 30 5 10 15 SHEAR STRAIN IN PER CENT Stress - Strain Relationship* for Undrained Tests on Haney Clay 3-2 3 0 o fl: c£ £-2 til or _i 9: 1-8 z 1 1-6 K 1-2 10 — - f ' 8 - q " ^ 3? A A • A CT , LEfirSND A C - U - 1 , ^ - 6 0 RS.I © c-u-a, »&o ps.i o C - U - & , 6'c "SS-5RS.1 • C-U -7 , cr.' »8a-5 P.5.I NOTE: C-U -a45,f iu«75 PS.I Ar« Not Shown For Clarity. i I • f 10 IS £0 SHEAR STRAIN IN PER C E N T £5 30 Ficj.2.5-— Principal Stress Ratio \ersus Strain for Undrained Tests o n Haney Clay 9 0 A © 0 LEG-END C - U - l , <£ - t o o p.c,.l. C-U-Z, C t ' « 6 0 - 0 P.S.I. C- U - 3 , C£ =• 75 -0 RS.I. C- U-3, < - 75-0 RS.I. C- U-&, C£'« SBS P.S.I. C- u - 7 . <rj* aa-5 P.S.I. 0"d' = 8S'5 R S.I. C"c'=75 Rs. 1. '• V f l 0^=60 PSi 1. - u £D ^ ! i ! 60 .70 cr 00 j 50 40 Ui CC ^ 3 0 Ul or W or 2 10 10 IS £0 SHEAR STRAIN IN PER CENT £ 5 SO Figure 2G»—Relationship Between Pore Pressure and Strain For Undrained "Tests on Haney Clq_y 3 0 6 * 3 ti < eo Ui £ 1-0 ui or a 0-5 a.- O*^ - CO P.S.I. P.S.I. 10 15 PER 20 £ 5 SO SHEAR STRAIN IN CENT, Figure 2 7 - Fbre Pressure fbrameler A Versus Strain for Haney Clay 93 occurring before maximum principal stress ratio appears to be a characteristic of sensitive clays and is caused by the pore pres sure continuing to rise after maximum deviator stress has been reached. Bjerrum and Simons (I960) found similar results from undrained tests on undisturbed sensitive Norwegian clays. They f e l t that the lower principal stress ratio 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 strain. It w i l l be shown in Section h of this chapter that in creasing pore pressures cause release of internal energy in un drained tests which when corrected for by the Roscoe energy equation suggests that the f u l l " f r i c t i o n angle" is being mobi lized at a l l strains. Deviator stress versus shear strain relations for a l l drained tests are shown in Figure 28. It may be seen that a marked kink occurs in the deviator stress at about 1% per cent strain for samples consolidated to hO Ibs./sq.in., a smaller kink occurs for those consolidated to 55 Ibs./sq.in. This is further evidence of • overconsolidation at the lower consolidation pressures, but the effect appears to be lost at about 6 per cent strain. Maximum deviator stress occurs at about 26 per cent strain. Residual pore pressures calculated by Method 2 and discussed in Chapter 6 are shown in Figure 29. Maximum average excess pore pressures occur at about 5 per cent strain and vary from 2 .5 Ibs./sq.in. for samples consolidated to ^ 0 Ibs./sq.in. to *+.l Ibs./sq.in. for 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 for samples consolidated to *+0 and 70 Ibs./sq.in. 34 LEG-END A S-I2,0"c» 40 Lbs./So,.In. V S - 13; Cc' = 55 Lbs./Sc|.ln. 0 S - 14, - 70 Lbs./S«|. In. • S - 15, G t' - 70 Lbs./S^.ln. e $> - 16, C c 's 55 Lbs./ 5^ .In. O S - 17, C"/ MO Lbs./ S T in I30 0 5 10 15 20 25 SO SHEAR STRAIN IN PER CENT Figure 26— Stress-Strain Relationships for Drained Tests on Haney Clay 3 5 A 0 • o s- L.E6-END 5.-IS, 0^ = 4 0 Lbs . /6^ ln. 3 - 14 , 6e' = 70 Lbs ./^. ln. ••£>- 15 , - 70 Lbs./6cj. In- 5 - 17 , <JC' » 40 Lbs./Sq,. In. I £ Consolidated Drained Te*t No. IE ~ Effective Isotropic Consolidation Pressure. • • ^»>^3 7- • • • Q \ 0 » ^^^^ • k ol4- 10" or h LI Q. Ll I * 0. _1 < 10 IS so S H E A R 5 T R A I N IN PER C E N T £5 50 N O T E 1. Exce&S Pore Pressutes C«|cu|cotee| By Method 2 2. Testa <it C t - a a p.s.i. NoT shown for the Sake «T Clarity Figure £ 9 - Calculated Residual Pons Pressure Vs. Strqin For Consolidated Drained Tests on Haney Clay 96 The effect of residual pore pressures on the principal stress ratio in drained tests is seen to be small (Figure 3 0 ) . The prin cipal stress ratio versus shear strain relations for a l l drained tests are shown in Figure 31* These have been corrected for re sidual pore pressures. It is seen that the curves are identical except at strains below about 7 per cent. It is thought that the separation of curves at low strain is due to an overconsolidation effect present at the lower confining pressures. Maximum princi pal stress ratio for drained tests occurs at about 25 per cent shear strain. A. comparison of principal stress ratio versus shear strain relationships from both drained and undrained tests is shown in Figure 32. It may be seen that the undrained material is much s t i f f e r than the drained. Maximum principal stress ratio equal to 3.05 occurs at about 15 per cent strain in undrained tests while the maximum principal stress ratio in drained tests is 2.82 and occurs at about 25 per cent strain. 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 in principal effective stress space in Figure 33• It may be seen that the contours of water content from drained and undrained tests have quite different shapes. Thus, for Haney clay, there does not appear to be a unique relationship between effective stresses and water content. The data shown in Figure 33 was prepared from the effective stress paths shown in Figures 3^ and 35. Stress paths from un-3-0; IO 1 ! '•• ! - 1 5 10 15 20 £5 SO SHEAR STRAIN IN PER CENT Figure 3 0 — E f f e c t of Residual Excess Pore Pressure on [He, Principal Stress Ratio Vs. Shear Strain Relqtion in "lest S—13 SHEAR S T R A I N iN PER C E N T Figure 3i — Relationships Between Principal Stress Ratio ancj Strain from Drained Tests on Haney Clay 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 c ' « & 0 PS.I. © C-U-£,<r c ' -60 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. |. Fgure 34 — Effective Stress Raths from Consolidated Undrained Tests on Haney Clay stress Ffa1h Assuming •Ro"Pfe*s]3uorPore Pres. II Siresi Rath Residual Horc (-"res. Considered IOI 20 30 100 UO 40 50 €.0 70 sJZGi IN R5.I. Figure 35 — Effective Stress Paths And Contours of Water-Content From Drained Tests 102 drained tests are shown in Figure 3*+ and these are also contours of water content. Stress paths from drained tests are shown in Figure 35. Generally drained stress paths plot as vertical 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 in Figure 35. It was stated in Section 7.2 that drained and undrained test specimens did not l i e on a common isotropic consolidation line. It was assumed for the purpose of comparing contours of water con tent that drained and undrained samples had consolidated water contents which lay on the isotropic consolidation line for drained samples. However, Figure 33 indicates that the shapes of water content contours determined from drained and undrained tests are quite different. 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 for Haney clay. Due to the small number of tests performed, the Rendulic diagram is not a very satisfactory method of checking the hypo thesis. The unique relationship between effective stresses and water content is identical to the Roscoe concept of a state boundary surface discussed in Chapter 2. Poorooshasb (1961) developed a method by which the three dimensional surface could be shown as a line in two dimensions. Burland (1965) suggested an even simpler method of showing this surface in two dimensions. His method is basically identical to that proposed by Rendulic in 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 is the pressure on the isotropic consolidation line corresponding to the particular void ratio of the sample at the time p' and q are measured. For undrained tests p e is constant and equal to the i n i t i a l consolidation pressure. 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 ratio. The surfaces for a l l undrained tests are shown in Figure 36. It is seen that tests consolidated to 75 and 88.5 Ibs./sq.in. l i e on the same line or surface, while tests consolidated to 60 lbs./ sq.in. are clearly on a separate line. It was mentioned earlier that samples consolidated to 60 Ibs./sq.in. behave in an over- consolidated manner, and i t is this overconsolidation effect that is thought responsible for the separation of curves shown. The state boundary surfaces for drained tests are shown in Figure 37. It is seen that drained tests from each consolidation pressure l i e on a different surface. This was to be expected since samples below a consolidation pressure of about 70 Ibs./sq.in. behave in an overconsolidated manner and hence would not l i e on the nor mally loaded surface. It may be seen that tests consolidated to 55 and 70 Ibs./sq.in. are reasonably similar, while tests consoli dated to hO Ibs./sq.in. are quite different. Since the overcon solidation effect is reducing with increased consolidation pres sure this result could be expected. In Figure 38 yield 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. Una1 mined Teste on Haney Clay (Bur land Plot) Gfc=4cps.l. P/ < _Net]>sci irg Residual & I Pore Pres. (40P-S.1) Figure 37-State Bouncjary Surfaces from Drained Tests on Haney Cloy (Burland Plot) O / - S ta te Bo Undary si i r f a c e s / \ Drained T< s f e , ^ 7( llecting Resii ) P-S.l. Jua| Pore Pr /fl / Undr lined Tests = 75$ r~\'~ f ^ \ \ \ 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 in a truly normally loaded manner. Residual pore pressures were allowed for in calculating drained yield surfaces (residual pore pressures are always allowed for unless otherwise stated) but the effect of neglecting them is also shown. It is seen that drained and undrained tests do not l i e on the same sur face and that neglecting the residual pore pressures in drained tests results in even poorer agreement. Since the drained tests at a consolidation pressure of 70 Ibs . / sq . in . also l i e outside the undrained tests at 60 Ibs . / sq . in . the effect of overconsolida- tion 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 in Chapters 2 and 3 and i t appears that the Roscoe and Schofield (1963) energy equation which considers both boundary and internal e last ic energy changes is the most log ica l . This energy equation has been applied 108 to the Haney clay test data and the results are in reasonable agreement with the predictions of the equation. The equation is as follows: p 'Sv + qo£ = K^P' + Mp'oc (16) 1 + e where oV = incremental volumetric strain S£ = incremental distortional strain K = slope of e Vs. Lnp' on rebound or reload and M = ratio 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 elastically, 1 + e while Mp'&£ represents energy dissipated by shearing stresses. Mp» = q w can be considered as the internal shear stress and by definition lies on the failure envelope q = Mp'. Equation (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 yielding or s l i p at grain contacts is occurring the relation between the corrected q (q w) and p' is always constant and therefore drained and undrained tests corrected for both boundary and internal energy should have stress paths which l i e on the straight line q = Mp'. This was shown diagramatically in Figure 5» Chapter 2. The isotropic consolidation and rebound lines for Haney clay are shown in Figure 3 9 . The coefficient of expansion, C e, was Line peviot&r Stress 4 ^ 6 7 6 3 10 £d ; 30 40 50 60 70 SO 100 £00. MEAN NORMAL STRESS p' IN RS.I. Figure39—Relationships Between Mean Normal Stress and VVater Content for Haney Clay O 110 calculated to be 0.11, and K, which is the slope of void ratio versus natural logarithm of pressure plot is therefore O.Oi+8. Since the computer was used to analyze test results q w was readily obtained for a l l readings. Hand calculations of incremental distortional and volumetric strains would have been very time consuming since the incremental strains at the times of readings cannot be directly calculated but must be estimated by averaging the adjacent increments. In addition, the length and volume of sample to be used when calculating strain increments are not the i n i t i a l ones but rather those existing at the time in question. The corrected stress paths for 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 for a l l tests and for 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. Figure *+l shows corrected stress paths for a l l drained tests. Here the points f a l l within a band rather than on a line. It appears that the M value is de creasing with strain. A. plot of M versus strain for a drained and an undrained test is shown in Figure *+2. M is seen to decrease with strain, slightly in the case of undrained tests and somewhat more in the case of drained tests. Considering that Haney clay is an extra-sensitive material and that the Roscoe energy equation was developed for an idealized continuum material, the results, especially those for undrained tests appear to be in reasonable agreement with the theory. Scatter in M values at low strain may be due to errors in readings at low strain at which time stresses are changing very rapidly and readings are closely spaced. Alter-I l l A 0 L E G E N D C - U - I , ^ ' - 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 Shewn at strqini Lsss t h a n o!5 % 40 :-J 60 ^ ao MEAN NORMAL STESS, PIN P.S.I. v Figun?40-Corrected and Uncorrected Stress Paths From Unclrainecj Tests On Honey Cloy ( Roscoe est, a|. Energy LE&END A S-12 , O;' *40 P.S.I. V S-13, 0;'^55 p.s.i. S- 14, O;' =70 P.S.I. • S-15, cr/=70 RS.I. © s-17, o;'*4o P.S.I. 0 ao 40 , feo e>o 100 lao P IN P.S.I. Figure41 - Corrected and Uncorrected .Stress Fbths from Drainec) Tests On Haney Cloj ( Roscoe' et q|. Eneraj ECJ.) L E G E N D A C - U - 8 , C T . ' - 6 0 p S . l 0 S- |4 ,0^'-7O PS. l 2.0 IS It 5 Sf 12 h- . Ul | ,0 It A > 35.-70 p.S.I. i ffl £ o i C > Q( j L » — _^ ^ GD 8,$>fcO f>S. • y o 04' oa 0 10 15 £0 SHEAR STRAIN IN PER CENT 25 SO figure 42. — Roscoe M Rarameter Versus Si rain Haney Cloy nately the scatter may be due to neglect of dlstortional elastic energy which is an assumption of the Roscoe equation. The Roscoe concept appears to answer many questions regarding the behavior of s o i l . If the Mohr-tCoulomb failure criterion is considered rather than the extended Von Mises criterion as implied by Roscoe, then for t r i a x i a l compression tests ffi/ff. - . . . . (18) J 1 - V 3 M If M = 1.27 is considered an average value of M, then Equation 18 yields O^/G^ =3.2 or a strength envelope of 0 = 31.6 degrees. Principal stress ratio curves of Figure 32 indicated that strains of 15 and 25 per cent were needed to mobilize maximum principal stress ratio or maximum f r i c t i o n for undrained and drained tests respectively. Figure k2 indicates that f u l l f r i c t i o n is mobilized at very low strains and remains reasonably constant with strain. It is only when the energy corrections are zero that the internal or corrected shear stress equals the applied shear stress and the s o i l is then said to be in the c r i t i c a l state. Haney clay never did reach this state. The Roscoe concept does not question the validity 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 British Columbia shows that the deviator stress, when corrected for release of internal energy due to pore pressure rise, lies on the q = Mp' line for a l l stages of tests, apart from readings in the f i r s t one per cent strain. Here again f u l l f r i c t i o n is 115 being mobilized at a very early strain. If the Roscoe concept is correct, then the "Dependent" and "Independent" components of shear resistance as defined by Schmertmann (1963) and mentioned in Chapter 3 have no physical meaning and arise from internal energy changes. The Energy equation applies where plastic deformation or s l i p at grain contacts is occurring. Overconsolidated material is assumed to remain rigid plastic under distortional stresses until the state boundary surface is reached. If maximum q/p ratio is reached before yielding occurs the energy equation does not apply. It is not clear, therefore, i f the same M value applies to normally loaded and highly overconsolidated samples of the same clay. 7.5 Examination of methods for predicting stress-strain relations Methods of predicting stress-strain relationships are exa mined in this section. Poorooshasb and Roscoe (1963), Roscoe and Schofield (1963) and Landanyi, La Rochelle and Tanguay (1965) have presented methods for predicting stress-strain relationships. These methods have been discussed in detail in Chapter 2. An attempt has been made to apply these methods to Haney clay but none yields results that are in satisfactory agreement with the measured relations. Poorooshasb and Roscoe (1963) presented a graphical method for normally loaded remolded clays by which stress-strain relations in drained tests could be predicted from the results of undrained tests and consolidation tests conducted such that the ratio of q/p' remained constant. The method presupposes a unique relation ship between effective stresses and water content. Since for Haney 116 clay the relationship could hardly be considered to be unique (Section 7.3) the method is not s t r i c t l y applicable. However, i f i t is assumed that the water content contours from undrained tests are unique, the shear strain for 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 similar. Contours were therefore extrapolated for lower water contents and are shown on Figure h3» Shear strains were also extrapolated and contours of undrained shear strain appear as straight lines radiating from the origin. A. drained stress path for a test consolidated to 70 Ibs./sq.in. (allowance made for residual pore pressure) has a stress path as shown. The method for determining strains was discussed in detail in Chapter 2. The stress path is idealized into increments of stress at constant volume and constant q/p' as shown in Figure V} for a typical increment CE. The increment of strain from constant volume is determined from the contours of strain and equals about 0 . 5 per cent for the increment shown. Since no tests were performed to determine the relation between shear strain and volumetric strain at constant q/p', the following relation (Roscoe and Schofield 1963) was used: 8v ( M -\ 1 - K A (19) where ov volumetric strain increment M ratio 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 virgin consolidation Values of Shear Strain O £0 40 CO , 8 0 IOO 120 140 P IN RS.I. Figure 43 - Contours of Water Content and Strain From Undrained Testa on Honey Cby 118 Sc = shear strain increment. The values of M, K and have already been determined and when substituted in (19) yield S£ = J** .... (2o) 1.2/-T\ and SV = Ji§_ = £4°iw (21) l+e 0 1.9*+ and &V are increments of natural strain, however, since engineering strain was desired, i t was assumed that equation. (20) also held for engineering strain. For an increment of stress at constant q/p, nr^ is constant and equals 0.737 for the increment DE shown. Sv = l.Mf for this increment, from which the shear strain due to volume change from equation 20 is 2.7 per cent. The total shear strain increment due to the increment CE is the sum of the strain increments at constant volume and constant f[ and equals 3.2 per cent. By summation of such increments the stress-strain relation was calculated and is shown in Figure kh along with the measured stress-strain relation. It is seen that although the predicted stress-strain relationship is of approximately the same shape as the measured relation, the correlation could not be considered as satisfactory. Since strains due to volume changes account for the major portion of the calculated strains, stress- strain relations for drained tests cannot be predicted from un drained tests unless contours of water content are independent of stress path. Roscoe and Schofield (1963) presented an equation from which stress-strain and pore pressure-strain relations can be predicted ~ f i l Measur 0 ^ ' « 7 O sd Relation P S . I. — w > S- 1461 See Fit 41k ilated Rebtion ,^'•70 RS.I. / / / / / / / 1 / ( / / / / J / / / / / / // 1 t 7 -' 10 15 20 SHEAR STRAIN IN PER CENT 25 30 Figure 44-Comparison of Measured and Calculated Stress-Strain ,c Relations for Drained Tests on Haney Clay 120 for undrained tests in terms of K/\ and M. However, the relation is based on the validity of their equation for the state boundary surface. The Roscoe state boundary surface for M = 1.27 and KA = 0.22 is shown on the two dimensional Bur land plot in Figure *+5. It is seen to differ from both the drained and undrained state boundary surfaces. Burland (1965) proposed a variation on the Roscoe state boundary surface and his equation is also shown. It is seen that the undrained state boundary surface lies reasonably close to the Roscoe surface, while the drained lies closer to Burland's surface. Since the Roscoe equation for the state boundary surface was not considered to be in satisfactory agreement with the measured relation, no stress-strain predictions were made. Landanyi, La Rochelle and Tanguay (1965) presented a method for predicting shear strains in undrained tests from the results of drained tests. This method was discussed in 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 is not in agreement with Henkel (I960) and Roscoe. However, since i t was found that the stress-water content rela tionship is not unique for Haney clay, Landanyi's concept was further examined. 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. However, Figure 31, Section 7.2 indicates that for drained tests i s essentially 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 line, and drained and undrained tests should have the same 0~T/CV versus strain relation^ / / ^ / ^ > •From Burl< . . . / Ul « drained Te; .'» 7S4SS-5 \ PS.l. \ < \ ^ 4 — Drainec * \ V * From Roscoe et E^ udtion ' \ V / / • K« 0 04S ^* dai7 K/A=oaa M - I-2L7 State fiounc sry Surfaces - t \ \ \ \ / A Tan 6- M» | / 0 i ~ 2 3 A -5 , , -7 - 8 "9 10 M P/Pe Figure 45-Comparison of Theoretical and Experimental State Boundary Surfaces (Burland Plot) 122 It is seen from Figure 32 that drained and undrained tests have quite different CJ^/fJ^ versus strain relation. Therefore there is not a unique relation between 0 J/G3, £ and 0"^ and Landanyi's con cept does not apply to Haney clay. 7.6 Effect of strain rate on drained tests Since two additional drained tests were performed at one quarter the normal strain rate, but with drainage from one end only as discussed in Chapter 6, the effect of rate of testing on the drained characteristics of Haney clay can be examined. In Chapter 6 i t was 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 principal stress ratio versus strain relationships for the normal and slow rates are compared in Figures 6^ and k-7. It is seen that both the deviator stress and the principal stress ratio are slightly higher for tests conducted at the slower rate. The water content versus strain curves shown in Figure kS indicate that the slow tests drained more due to additional time for secondary compression and this probably accounts for their higher strength. It is generally considered that faster testing rates give higher strength, yet here i t appears that slower rates give higher strength.However, undrained tests are usually being considered. In undrained tests i t is l i k e l y that slower rates would give reduced strength, because the additional time would lead to higher pore pressures due to the tendency for secondary compres sion. 123 I40 130 120 110 loo CL 111 a: fe or > UJ • 30 ao 70 6 0 50 4o 3o £o LEGEND a S - 18, CTt'- 40 pS.l. O S- 19, %S 70 p.S.I. s-i« Sfno'm \ Cc'*70 R5. Rat* = o ies fc -©-©-—0 €^ \__A d "JO Strain r R b J . } A^ra^e ate -0-5% f ©+ S- 14^ 15 »er Nr. . / V 9/ I _ CTC= 40 RS Strain Rafe .1, Average c « O S % fer f f S-12 4 17 r. _ S-IB, 0"e'= 4o ps.l. ( 25 30 0 5 10 15 20 SHEAR STRAIN IN PER CENT Figure 4fe-EFfect of Strain Rbte on the Stress-Strain Relations from Drained Tests on Haney Clay S a o cr < a 6? a 1-4. 1-2 K> (7k ff> — Strain I talc OS%Per Hr S J LEGEND _ . .'iv ' I strain Rote o-lE5% O S- IS,^* TO RSI. J par Hr. Strain Rate os%, ter Mr. 5trqm Rote 0-ies%, P c Hr. 40 PS.l. io : is eo SHEAR STRAIN IM PER CENT 23 30 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 125 CHAPTER 8 CONCLUSIONS A.ND SUGGESTIONS FOR FURTHER RESEARCH 8.1 CONCLUSIONS T e s t r e s u l t s presented i n the previous chapter lead t o the f o l l o w i n g c o n c l u s i o n s : 1. For s e n s i t i v e c l a y , t h e r e i s not a unique r e l a t i o n s h i p between e f f e c t i v e s t r e s s e s and water content which i s independent of s t r e s s path, or a l t e r n a t i v e l y , t h e r e i s not a unique s t a t e boundary s u r f a c e f o r normally loaded s e n s i t i v e c l a y . Henkel (I960) suggested t h a t the r e l a t i o n s h i p f o r s e n s i t i v e c l a y s might be more complex than the simple r e l a t i o n proposed f o r remolded s o i l . 2. The Roscoe energy e q u a t i o n appears to a p p l y q u i t e w e l l t o Haney c l a y . The equation i m p l i e s t h a t whenever p l a s t i c deformation of s o i l i s o c c u r r i n g , the r e l a t i o n s h i p between the mean normal e f f e c t i v e s t r e s s and the d e v i a t o r s t r e s s c o r r e c t e d f o r both energy due to volume change and i n t e r n a l energy i s a const a n t , M. T h i s was found t o be approximately t r u e f o r d r a i n e d and undrained s t r a i n c o n t r o l l e d t e s t s as w e l l as creep t e s t s , and f o r s t r a i n s v a r y i n g from one to t h i r t y per c e n t . T h i s suggests the p o s s i b i l i t y t h a t the H v o r s l e v 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 c o h e s ion parameters and the Schmertmann "Dependent" and "Independent" parameters a r i s e from n e g l e c t of i n t e r n a l energy changes and t h a t , i n f a c t , t h e r e i s onl y one fundamental s t r e n g t h parameter, M, which corresponds to a f r i c t i o n component, and i s independent of both s t r a i n and s t r a i n r a t e . The Roscoe equation f u r t h e r i m p l i e s t h a t , s i n c e M does not depend on s t r a i n , i t i s a l s o independent of p a r t i c l e o r i e n t a t i o n 126 or structure. However, the uncorrected deviator stress which is of interest in practical problems is very much dependent on s o i l structure, since i t is s o i l structure that determines internal energy changes. 3 . The Roscoe method for predicting stress-strain relations can not be applied to a sensitive clay as i t does not have a unique state boundary surface. h. The Landanyi method for predicting stress-strain relations does not apply to a sensitive clay. 5. Stress-strain relations for drained samples of Haney clay with approximately the same degree of residual pore pressure d i s s i pation are only slightly altered by decreased strain rate. De creased strain rates allow greater time for secondary compression and result in slightly higher strength at a l l strains. 8.2 Suggestions for further research During the course of the testing program and the subsequent preparation of this thesis interest developed in the following topics: 1. It was suggested in this thesis that the Roscoe M is 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 test, for which the maximum excess pore pressure has been measured, can be calculated. 1 2 7 Since permeability at any given void ratio is also a measure of s o i l structure, i t is f e l t that very useful information with regard to s o i l structure could be obtained from void ratio versus permeability plots determined from normally loaded and overcon solidated tests on undisturbed and remolded samples of the same clay. The Hvorslev concept of samples at the same void ratio having the same structure could be checked in this manner. LIST OF SYMBOLS - area of mineral to mineral contact - pore pressure parameter - stress due to e lec t r i ca l attractive forces between particles - pore pressure parameter - coefficient of consolidation - effective cohesion parameter - Hvorslev cohesion parameter - compression index - expansion index - consolidated undrained test - void rat io - half height of sample - f i r s t stress invariant - permeability - coefficient of unit volume decrease - s o i l strength parameter - mean normal effective stress - effective 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 lec t r ica l repulsive forces between particles 129 R - rate of drainage t - time t^Q - time f o r 90 per cent primary consolidation tj* - time to f a i l u r e T - time factor u - pore pressure u e - res i d u a l pore pressure A U - change i n pore pressure U - average degree of consolidation V - volume of sample AV - volumetric s t r a i n oV - change i n volumetric s t r a i n w - water, content Sw - change i n energy A X - small change i n l e v e l of n u l l point z - length Yw - unit weight of water Vs - c r i t i c a l void r a t i o when mean normal e f f e c t i v e stress equals unity £ - shear s t r a i n Ei - a x i a l s t r a i n o£ - increment of shear s t r a i n T\ - factor depicting boundary drainage condition T\ - r a t i o of deviator stress to mean normal stress K - slope of void r a t i o versus natural logarithm of pressure during rebound 130 A - slope of void rat io versus natural logarithm of pressure during v i r g i n consolidation 0" - to ta l stress Cj1 - effective stress 0*^ - a x i a l effective stress - effective consolidation pressure 0"f - effective stress on fa i lure plane fj" i p : - pr incipal t o t a l stresses 1,2,3 " pr incipal effective stresses 131 ARMSTRONG, J 6 E e , 1957° " Sur 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 Clays." Proc. Am. Soc. C i v i l Eng. , Research Conference on Shear Strength of Cohesive Soi ls , Boulder Colo . , 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 . 370- 371. BISHOP, A.W., BLIGHT, G . E . , and DONALD, I .B . , I960. Discussion, Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive Soi l s , Boulder, Colo. , I960 , 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 Conso l idat ion Characteristics of So i l Measured in the Tr iax ia l Appara tus." Proc.'NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. BISHOP, A.W., and HENKEL, D . J . , 1962. "The Measurement of So i l Properties in the Tr iax ia l Test ." 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 So 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 So i l s , " Norwegian Geotechnical Institute, Oslo, Bul let in No. 5, 112 p p . BJERRUM, L . , and SIMONS, N . E . , I960 . "Comparison of Shear Strength Characteristics of Normally Consolidated Clays." Proc. Am. Soc. C i v i l Eng. , Research Conference on Shear Strength of Cohesive Soi l s , Boulder, Colo. , I960, 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 Clay." Ph. D. Thesis, University of Cal i fornia , Berkeley. CASAGRANDE, A . , and WILSON, S .D. , 1953. "Prestress Induced in Consolidated Quick Tr i ax i a l Tests ." Proc. Third Int. Conference on So i l Mech. and Found. Eng. , 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 Soil Specimens in Tria 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 Friction in Clays." Proc. Third Int. Conference on S o i l Mech. and Found. Eng., Zurich, 1953, Vol. 1, pp. 126-130. GIBSON, R.E., and HENKEL, D.J., 195*+. Influence of Duration of Tests at Constant Rate of Strain on Measured Drained Strength." Geotechnique, Vol. 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, Vol. 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 Soils, Boulder, Colo. I960, pp. 535-551*. 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. "Triaxial Compression Tests on an Undisturbed Sensitive Clay." M.A. Sc. Thesis, University of British Columbia, Canada. KENNEY, T.C, 1959. Discussion on a paper by C.B. Crawford. ASTM Spec. Tech. Publ. No. 25V, pp. *+9-58. LAMBE, T.W., 1958. "Soil Testing for Engineers." John Wiley and Sons, Inc., 150 pp. LAMBE, T.W., I960 "A Mechanistic Picture of Shear Strength in Clay." Proc. Am. Soc. C i v i l Eng., Research Conference on Shear Strength of Cohesive Soils, Boulder, Colo., I960. LANDANYI, B., La ROCHELLE, P., and TANQUAY, L., 1965. "Some Factors Controlling the Predictability of Stress-Strain Behaviour of Clay.", Canadian Geot. Jour., Vol. 2, May, 1965. 133 NOORANY, I., and SEED, H.B., 1965. "A New Experimental Method for the Determination of Hvorslev Strength Parameters for Sensitive Clays." Proc. Sixth Int. Conf. Soil 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 Dilation." Proc. F i f t h Int. Conf. S o i l Mech., Vol. 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 in the Triaxial Test." Harvard Soil Mechanics Series No. 71, Cambridge, Mass., 230 pp. RENDULIC, L., 1936. "Relation Between Void Ratio and Effective Principal Stresses for a Remolded S i l t y Clay." Proc. First Int. Conference Soil Mech. Found. Eng., Cambridge, Vol. 3, PP. V8-51. RENDULIC, L., 1937. "Ein Grundgesetz der Tonraechanik und Sein Experimentetler Beweiss." Der Bauingenieur, Vol. 18, pp. l+59-1+67. ROSCOE, K.H., SCHOFIELD, A.N., and WROTH, CP., 1958. "On the Yielding of Soils." Geotechnique, Vol. 8, pp. 2 2 - 5 3 . 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., Vol. 1, pp V7-5l+. ROSCOE, K.H., SCHOFIELD, A.N., and THURAIRAJAH, A., 1963. "Yielding of Clays in States Wetter than C r i t i c a l . " Geotechnique, Vol. 8:3, Sept., 1963. ROSCOE, K.H.,- SCHOFIELD, A.N., and THURAIRAJAH, A., 1963. "An Evaluation of Test Data for Selecting a Yield Criterion for Soils." 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 So i l Mechanics." Addison- Wesley Publishing Co, Inc., 550 pp. 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 Soils, Boulder, Colo., I960, pp. 887-96V. SCHMERTMANN, J.H., 1963. "Generalizing and Measuring the Hvorslev Effective 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 Soils, Boulder, Colo., I960. SIMONS, N.E., 1963. "The Influence of Stress Path on Triaxial Test Results." Proc. NRC/ASTM Symposium on Laboratory Shear Testing, Ottawa, 1963. TAYLOR, D.W., 19V8. "Fundamentals of So i l Mechanics." John Wiley and Sons, New York, 700 pp. TERZAGHI, K. 19V3. "Theoretical Soil Mechanics." John Wiley and Sons Inc., 510 pp. 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 Soils, 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 Soils, Boulder, Colo., I960, pp. 10V9- 1056. 135 APPENDIX 1 RFiSIDUAL PORE PRESSURES IN DRAINED TESTS, METHOD 1 This method is based on the superposition of pore pressures (Terzaghi, 19*+3> p. 286). The deviator stress w i l l be some func tion (t) of time as shown in Figure H-9. It is assumed to be applied in instantaneous increments AfJ^ at times £ (tj_ + t ^ _ | ) where the subscript (i) refers to a particular increment, so that the assumed 6"(t) is the dashed line shown on Figure k-9. The change in pore pressure Aui due to an instantaneous increment of devia tor stress ACT^ can be obtained from the Skempton equation for change in pore pressure under undrained conditions A u i = B (A(5^ + AAG^ ) Since B = 1 for saturated s o i l and (j^ does not change in the standard drained testjAO"^ = 0 therefore AU^ = AAG^ (22) It is assumed that AUj_ dissipates independently of other pore pressure increments and in 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 is A U U * where superposition the average pore pressure at time t j is the sum of the average partially dissipated incremental pore pressures at time t-? caused by a l l the increments prior to t^ AUJLJ = AUI (1 - U J J ) and Ujj is the average degree of consolidation after a time tj^j = t j - -2- (t± + ti_]_) as shown in Figure *+9. By the principal of therefore (23) i=l CROSS SECTION Of SAMPLg EXCESS PORE PRESSURE Fig.49«i m a: o I observed Relation t0 t,t 4 t s t 4 Fig.49b TIME u tt 3 l/» <P Ul ar a. ul £ ALI^ * Pore Prs due ACT| (In&tarftaneous) Fig. 43c TIME f^ une 49 — Diagrams Showing Assumptions of Method 1 137 The average degree of consolidation U is a function of the time factor T and is 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£ T < .283 (2V) (1 - U) = 1 - f n fT+.0851 \ (1 - U) = 10 V .9332 ^ T ^ .283 (25) where T = £y_t h2 therefore 1 - U i ; j = f (T i ; J) = f ( C y t i j ) (26) h2 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 for the average excess pore pressure at any time t j i s : Ui = G^T, f (°v*ij) (27) This expression can be readily programmed for the computer. How ever, 4, c v and h w i l l vary throughout the test, therefore some assumptions must be made with regard to their values. The Skempton A used here is an incremental A rather than the A usually calculated. It 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 strain. Typical devia tor stress and pore pressure versus strain relationships for un drained tests are shown in Figure 50a. The incremental A values 136 to SO 40 z O-30 <n 10 o '— PORE PRESSURE ( i n i t i a l Pon P l B > . " IO Lbs. * | . I * ) - DEVIATOR STRESS UNDRAIh IED TEST io 15 eo SHEAR STRAIN IN PER CENT Fig.50a es 30 1 / inc'ns mental A &oe* to Infinity ot Mq*. DeV. STres s / • < z o y- Q . 2 Ll h or * - 6 io is eo SHEAR STRAIN IN P E R C E N T £5 30 Fig. 5 0 b 70 CO $ 5 0 u? (0 -•40 z i P Ul 30 Or or 20 o > 10 ui a • • • DRAINED 1 EST i 1 i i > 10 15 SO SHEAR STRAIN IN PER CENT S5 Figure50 — Stress-Strain Characteristics of Haney Cby so 139 calculated from Figure 50a are shown in 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 in negative incremental A. values. Increasing pore pressures after maximum deviator stress are caused by distort ion, despite fa l l ing deviator stress, rather than because of f a l l ing deviator stress. A typical deviator stress versus strain curve for a drained test is also shown in Figure 50. It is seen that the shape is quite different from the undrained test with maximum deviator stress occurring at high strain and therefore the incremental A values from undrained tests could not be used. It might be expected that the incremental A would increase with strain from approximately 1/3 at low strain where elastic behaviour .might occur to in f in i ty at high strain as maximum deviator stress is approached. However, no logica 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 in structure and change in void ra t io . Values of c v determined from both preliminary consolidation prior to shearing and from oedometer tests are plotted versus the average pressure p1 = 1/3 ( C | + 20^) a n d shown on Figure 51. For oedometer tests i t was assumed that k 0 was 0.75. The range of p1 for a l l drained tests was from hO to 110 Ibs . / sq . in . and the relat ion between p1 and c v in 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 Af ter Shednnj O Drain*d Teste, Pnsllminbgr Consoliddtii + Oedometer Tests iTion NOTE: I. C v Plotted N t e f M J S Average effective. Stress For Load Increment". E K 0 » o«8 /Assumed For Oedometer Teats. O ui it) u > z g 5 o <o z o u u. o r-7. UJ u u. U- HJ o C l • ooa •0O25 • •ooe •0015 •001 •0005 o G \ CV' IN \ 0 O 5 l - $ 0 3 l & LOCr p A R E A O F \ \ I NTT REST 10 20 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 v in the area of interest is lower than the figure of 2 x 10 cm2/sec. used in the previous chapter to determine testing rates. However, i t is understood from Bishop and Henkel (1962) that the c y mentioned in their expressions is the c v obtained during the preliminary consoli-. dation prior to shearing and not the c v that exists at the f i n a l consolidation pressure. The c y values shown in Figure 51 are plotted at the average p' during the consolidation increment. c v's obtained from t r i a x i a l consolidation vary between 1 x 10~3 cm2/sec. and 3 x 10"3 cm2/sec. and hence the figure of 2 x 10~3 cmvsec. was chosen. The height of the sample also varies throughout a test and since axial strain at failure was about 30 per cent, this could not be neglected. The height of the sample was known at a l l times that readings were taken.. 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 coefficient of consolidation existing at that time. In actual fact pore pressures due to earlier increments would have been dissipating under a gradually reducing height and coefficient of consolidation. However, pore pressures due to earlier increments w i l l be very small and the height and coefficient of consolidation w i l l be essentially 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 TRIAXIAL COMPRESSION TEST J 1 leacBggasgraagaB SOIL SAMPLE : H o n ^ y Clgy T E S T N0.:_£ SPECIFIC &RAYITY: £ S O DATE > July 19, 2,5 T E S T T Y P E : Consolidated Undrained T E S T E D RY: RM-6. INITIAL MEASURED DIMENSIONS Circ, in Cm. Dia. in Cm. Aneq in Cm? T o p 11-43 10-36 Centre H-40 3 6£5 10-33 Bottom 11-36 3-620 10-30 Height of Sample = 7-OSCrn. = 2 -77S| n , A r e q - A t + 2A c - r A B g | 0 , 3 4 C r n a , | . to S | n t 4- \b lume ( V t ) ° 7 3 0 C m a \ V s = = 32-75 Cm. 3 Average ui% (Side Trimmings) -=4fr5; e » ft^T^ » I -196 Degree of Saturation S - «• 39-3 for Cent A F T E R CONSOLIDATION Change in Vol. - fe 15 Cc ) Change in ^M\tt Content « » 6> 7 % ^ UJ70 = 3S6 Change in Hf. -o-14 Cm. , Consolidated Ht. «6-3iCm. » 272 In. V _ / > V - s-feacrn,8" = i - 5 o i n . a Consolidated Areq m W A T E R C O N T E N T S He Specimen Location Side Side Side Si'de Top 6ottolT1 v/hole 4t Initial!* Whole cxl. Finalla Container No. 1 2. 3 4- 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 3603 94-sa 144 78 Wt. Water in o/ns 6-64 4 9 5 7-6S « -o7 6,- li 7 47 39-54 3501 Wt- Container in gms. 17-44. 17-Si IT 17 17-29 l a s t 17-47 5-02 53-48 Wf. Dry 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 4&-SO 40-4 4o-£ 4 i £ 3S-3 W A T E R CONTENT CHECK Vol- Drained During Consolidation » 6 - l 5 c c , Vo| . Drained During Shear a — cc , V o l . BaoK Drained » l - 8 o c c , Tota| V o l . Change *4'3SCC } Change in V/ofer Content * 4 6 % , REMARKS Initial UJ% (Side Trimming*) ~ 42-5 Initial ujy0 from Initial wt. 4 Final bry Wt. = 4J£ Initial 111% -From FiHo| ui% and Change, m m% = 43-1 P , . j c Trimming* Mat Further Trimmed h> AlloUi for T o p tt Bottom Trimming 144- APPLICATION OF CHAMBER PRESSURE UNDRAINED CONDITIONS TEST NO.: a DATE: Jujy|3ja&5 TESTED BY: RM..B. TIME HRJ. EUW.E& TlMB Mttl CHAM»tt OAUOK CHAMBER COR. Pit. CMAMBW PRE*. P.%.1. PORE PR. BS.I. Pope f»s. con. f>».l PORE PRES. R6.|. SK6MPT -° NB 0 10 0 10 ft-5 4-1 i 99 S3 064 4 1 zo 1 -0-1 I9;9 170 -4-4» 12-4 ll io-o i l l Ml ao - 0 | ea-2 -4-7 C3-5 - 99 10-5 IE 40 -oa S9B - 4 7 54«0 9 9 IOO roi \<o 50 -ot 4-9-8 46 a -4 -8 4.4 0 IOO 9B o sa 2 0 GO -o-e. 59-B 567 -4-9 11-4 II 5 24 71-3 -O l 7 i a 70%3 -3-0 OVER ALL B » ^ -|- *IOO REMARKS: Thermostat Stuck Before Commencing) qnd th»> Mqy Account For The Variation in B 145 CONSOLIDATED TRIAXIAL T E S T PRELIMINARY CONSOLIDATION C H A M B E R PRES. GAU&E = 71-3 PS.l- T E S T N O : a G-AUcVE. CORRECTION = - O l RS-I. D A T E : JULY IS, l%5 E L E V A T I O N CORRECTION ar-l -2 RSI- TESTED &Y: PM.B C H A M B E R PRESSURE = 7 0 0 PS.l. BACK P R E S . » lO-O RS.I E F F E C T I V E STRESS CHAN6E 4-7 TO GOO RS.|. DATE T I M E HRS) ELAPS66 TIME MIN. TIME DIAL RD. IN. BUfi. RD. CC TEMP °C TULYI<1 '65 o.oo OOO •940O 171 0:04 0>ZG <] 5 5 0:15 0-50 9 4 8 0:34 0 -75 9- 3 6 IOO • IOO 9 26 i . i4 l ' 2S I S O 9 Ob 3:04 I7S 32.2A 4:00 £ 0 0 6-85 2-SO 6-64 3 . 0 0 a q o 8-43 12* 15 3-50 i t o o 4..00 6 0 0 2 S O 0 500 7 5 a 36:O0 6 0 0 0 ^ 7 0 7-eo 49:00 7 00 a 0 5 61:00 a 00 • 100:00 1000 &-oa 120.00 I 0 3 S 0*947 s a o 131:00 1 l-4a. 5-fc6 Tuuy to l £ : £ S 08635 15fc 146 CONSOLIDATED UNDRAINED TRIAXIAL TEST Consolidated Areq « I-5Q ln.a > Proving Rin^ No. Teat No: £ Consolidated Length « &7L In , Colibrdhon fi»ctbr « »3lfe7 ^ Date: July 2.o/6>5 Chamber Pressure » 70 O P S . l T e m p . - £ 4 °C Tested By: P.HB. Time Hn Por«. Pres. Gouge Cor. Pore Prv%. P.S.I. Vertical Dial in- Proviig Dial Time Hr Pore Pre*. CrtlLl^e Cor. Pbre Pres. RS-I. 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 - 4 4 . l l -o 86Z2. 5 O 0 2S-IO 5 5 7 -4 -8 5 0 - q •7557 206-3 15-717 16- C -4fe 1 2 0 610 25-18 55-1 -4 -« SI-1 •7414 2047 I5-&JS 17-7 -4-fo 13-1 700 2B-28 •56-3 -4-9 53*4 •7057 2017 15-1+0 l&B - 4 7 14-1 •8815 8 0 0 30-4S 5 ^ 5 -4-*) 54-fc '6676 16-08 -4-7 I S i •8S07 TI-0 33-00 60-2 - 4 H 55-3 •6 340 196-5 16-15 2a-o -4-7 17* •B80O 100-0 S5-42 60-Q -4-9 5 5 ^ •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 - 4 7 •8778 IC| 0 38-50 -4 -9 5-6-3 •5488 191-7 Ifc-fcO 26>& - 4 7 22-1 •67*7 I30-5 40-5& 617 - 4 - 9 S6-8 •5R5 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 iso - e 4708 427 -4 - -V 57-8 •4174 1717 31*7 -4-7 27-0 •«7IO Ifeoo 47'30 62.-7 -4-fl 5 7 8 •4114 1873 1742- 33-1 -47 2«T-Z -5682 I70-O 57-50 63-o 56-1 •2600 183-3 I7-7S "i&-3 -47 3l-6> •8643 l e o ^ 60-17 63-9 -4-n S8-<| •2I?8 I8Z--3 IV17 31-8 -47 35-1 •8S«lo Ho-o 62-io 64-0 •1765 te °7 18-17 42-5 - 4 7 37-8 •8501 IT* 2 65-00 642. -4 -T S<W • 1453 178-6 l<V33 44-5 "4-7 11-8 •&4£« e o s o 72-45 5°1'3 .0307 m-7 20-38 47-6> - 4 .B 42-8 <S2C6. 20^3 ai-2Z 50 5 -4.. 8 4S7 •8|3fc 210-0 £1-70 sn -4>* 4>ff •S062 20<V4r 147 TEST NO. 2 CONSOLIDATION PRES.= 60.0 CONSOLIDATED UNDRAINED TRIAXIAL TEST ELAPSED TI.ME STRAIN DEFORMATION SIGMA 1 EFF ROOT 2 SIGMA 3 DEVIATOR PRINCIPAL SKEMPTON A PORE PRESSURE HOURS PFR f.FNT IN._ PER DAY . PSI EFF I.N PS.I_ . SXRESS PS.l SJRE.S.S RAXID PSI . -0.00 0.00 -0.000 60.0 84.8 -0.0 1.00 0.00 10.0 0.05 0.01 0.144 60.6 83.4 1.6 1.03 0.63 11.0 0. 13 0.03 0.161 61.9 82.0 3.9 1.07 0.51 12.0 0.25 0.05 0.125 62.7 80.5 5.8 1.10 0.53 13.1 0.36 0.07 0.134 63.8 79.0 7.9 1.14 0.52 14. 1 Oi50 0. 10 0. 135 64.3 76.5 .1.0...2 1.19 0.58 . 15._9" _ _ 0.60 0.13 0.141 64.8 74.5 12.1 1.23 0.60 17.3 0.73 0.16 ' 0. 144 65.7 72.5 14.4 1.28 I 0.60 18.7 0.89 0.21 0.154 64.9 68.4 16.5 1.34 0. 70 21.6 1.02 0.25 0.160 66.4 67.7 18.5 1.39 0.65 22. 1 1.20 0.31 0.170 66.8 65.2 20.7 1.45 0.67 23.9 1. 38 0. 38 0.178 6X..2 6.2.9 22.7 1.51 0.68 25.5 1.58 0.46 0.190 67.7 60.8 24.7 1.57 • 0.69 27.0 1.84 0.56 0.200 67.6 57.7 26.8 1.66 0.72 29.2 2.17 0.71 0.213 67.3 54.3 28.9 1.75 0.75 31.6 2.59 0.90 0.227 65.8 49.3 30.9 1.88 f 2.02 1 0.81 35.1 3.19 1.20 0.245 64.9 45.5 32.7 0.85 37.8 3. 75 1.50 0.261 64..0 42.7 33.8 2.12 0.88 39.8 4;. 80 2.0.9 0.285 61.7 38.5 34.5 2.27 0.95 42.8 5.64 2.57 0.298 58.8 34.4 34.5 2.42 1.04 45.7 6. 12 2.84 0.303 57.8 33.2 34.3 2.46 1.06 46.5 7.25 3.46 0.312 56.0 31.4 33.8 2.52 1.12 47.8 8.00 3.87 0.316 54.2 29.4 33.4 2.61 1.17 49.2 9.52 4_.JjO_ 0.322 52.0 2.7_..0. . 32..J? _ 2 . 72 1.24 5.0,._9. 10.40 5.22 0.328 51.4 26.7 32.5 2.72 1.27 51.1 12.70 6. 54 0.336 48.0 23.5 31.4 2.89 1. 38 53.4 14.87 7.94 0.349 45.7 21.8 30.3 2.97 1.47 54.6 17.42 9.17 0.344 44.2 20.8 29.5 3.01 1.53 55.3 19.84 10.54 0.347 42.8 19.9 28.7 3.04 1.60 55.9 21 .75 11 .66 - 0.350 . - 4.L..8. L9...4 28...1 _ 3.05 1.65 56.3. .. 22.92 12.31 0.351 41.3 19.4 27.6 3.02 [ 1.68 56.3 24.92 13.38 0.351 40.2 18.7 27.0 3.04 I 1.73 56.8 25.42 13.67 0.351 40.1 18.7 26.9 3.04 1 1.74 56.8 31.50 17. 14 0.355 37.6 17.3 25.4 3.08 1.88 57.8 31*92 17.36 0.355 37.5 17.3 25.3 3.07 ! 1.89 57.8 41.92 22.92 "0..J3.5_7_ 3_4...8 16.8 . 22.."9. _ _ 2.93 _ 2. 10 58. 1. 44.58 24.44 0.358 33.4 15.7 22.3 3.01 2. 19 58.9 47.32 25.99 0.359 32.5 15.4 21.6 2.98 2.27 59.1 49.42 27. 14 0.359 31.6 15.1 20.9 2.96 2.35 59.3 56.87 31.35 0.360 30.3 15.1 19.6 2.83 2.52 59.3 CONSOLIDATED UNDRAINED TRIAXIAL TEST TEST NO. 2 CONSOLIDATION PRES.= 60.0 STRAIN P EFFECTIVE Q QW M UNIT P UNIT Q , ^ PER CENT ROSCOE PSI ROSCOE PSI ROSCOE PSI ROSCOE ROSCOE ROSCOE S 0.00 60.0 -0.0 0.0 " 0.00 1.00 -0.00 0.01 59. 5 1.6 77.8 1.31 0.99 0.03 0.03 59.3 3.9 59.1 1.00 0.99 0.07 0.05 58.8 5.8 64.0 1.09 0.98 0.10 0.07 58.5 7.9 61.4 1.05 0.98 0.13 0.10 57.5 10.2 87.0 1.51 0.96 0.17 0. 13 56.7 12. 1 71.9 1.27 0.95 0.20 0. 16 56.1 14.4 85.9 1.53 0.94 0.24 0.21 53.9 16.5 61.5 1.14 0.90 0.28 0.2 5 54.1 18.5 28.9 0.53 0.90 0.31 0.31 53.0 20.7 59.2 1.12 0.88 0.34 0.38 52. 1 22.7 52.9 1.02 0.87 0.38 0.46 51.2 24.7 53.0 1.03 0.85 0.41 0.56 49.7 26.8 58.7 1.18 0.83 0.45 0.71 48.0 28.9 59.6 1.24 0.80 0.48 0.90 45.2 30.9 58.2 1.29 0.;75 0.51 1.20 43.1 32.7 47.4 1.10 0.72 0.54 1.50 41.5 33.8 46.0 1.11 0.69 0.56 2.09 38.7 34.5 47.2 1.22 0.64 0.57 2.57 35.8 34.5 44.3 1.24 0.60 0.57 2.84 34.9 34.3 41.0 1.17 0.58 0.57 3.46 33.5 33.8 41.1 1.23 0.56 0.56 3.87 31.9 33.4 40.9 1.28 0.53 0.56 4.70 30.1 32.9 35.8 1.19 0.50 0.55 5.22 29.7 32.5 34.8 1.17 0.50 0.54 6.54 27.1 31.4 35.0 1.29 0.45 0.52_ 7.94 25.5 30.3 32.4 1.27 0.43 0.51 9.17 24.5 29.5 31.1 1.27 0.41 0.49 10.54 23.7 28.7 30.0 1.27 0.39 0.48 11.66 23.1 28. 1 28.9 1.25 0.38 0.47 12.31 22.9 27.6 28.5 1.24 0.38 0.46 13.38 22.2 27.0 27.4 1.24 0.37 0_.45 13.67 22.2 26.9 27.1 1.23 0.37 0.45 17. 14 20.7 25.4 25.7 1.24 0.34 0.42 17.36 20.6 25.3 25.6 1.24 0.34 0.42 22.92 19.5 22.9 23.9 1.23 0.33 0.38 24.44 18.5 22.3 23.2 1.25 0.31 0.37 25.99 18. 1 21.6 22.2 1.23"_ 0.30 0.36 27.14 17.7 20.9 21.5 1.21 0.29 • 0.35 31.35 17.2 19.6 0.0 0.00 0.29 0.33 CONSOLIDATED DRAINED TRIAXIAL TEST TEST NO.17 CONSOLIDATION PRES.= 4 0 . 0 NO ALLOWANCE MADE FOR RESIDUAL PORE PRESSURE ALLOWANCE MADE FOR RESIDUAL PORE PRESSURE SHEAR AXIAL DEFORMATION WATER DEVIATOR SIGMA 1 PRINCIPAL PORE SIGMA 3 ROOT 2 SIGMA 1PRINCIPAL STRAIN STRAIN IN.PER DAY CONTENT STRESS EFF. STRE.SS PRES. EFF. SIGMA 3 EFF. STRESS PER CENT PSI PSI RATIO PSI PSI EFF. PS I PSI RATIO -0.00 -0.00 -0.000 37.9 0.0 40.0 1.00 0.0 40.0 56.6 40.0 1.00 0.04 0.05 0. 146 37.9 4__1 44. 1 1. 10 0__5 39.5 55.9 43.6 1. 10 0.13 0.16 0.172 37.8 9.2 49.2 1.23 0.8 39.2 55.4 48.4 1-23 0.18 0.23 0.182 37.8 11.9 51.9 1.30 0.9 39.1 55.3 51.0 1.30 0. 2 5 0.31 0. 191 37. 8 J___._7 'S*t*3 1.37 ; UO 39.0 55.1 53.7 1.38 0.35 0.45 0.211 37.7 17.9 57.9 1.45 1.4 38.6 54.6 56.5 1.46 0.46 0.59 0.224 37.6 20.8 60.8 1.52 1.3 38.7 54.7 59.4 1.54 0.57 0.74 0.235 37.5 23.5 63.5 1.59 1^5 38.5 54.5 62.0 1.61 0.73 0.97 0.248 37.4 26.6 66.6 1.67 1.6 38.4 54.3 65.0 1.69 0.93 1.23 0.264 37.3 28.6 68.6 1.72 1.8 38.2 54.0 66.8 1.75 1.12 1.50 0.277 37. 1 29.9 69.9 1.75 2.1 37.9 53.6 67.7 1.79 1.42 1.92 0.288 36.8 30.8 70.8 1.77 2.0 38.0 53.7 68.7 1.81 1.85 2.51 0.298 36.4 31.5 71.5 1.79 2.2 37.8 53.5 69.3 1.83 2.61 3.57 0.312 35.8 33.2 73.2 1.83 ______ 37.7 53.4 70.9 1.88 3.40 4.60 0.321 35.2 34.6 74.6 1.87 2.4 37.6 53.2 72.3 1.92 3.87 5.21 0.326 34.9 35.7 75.7 1.89 2.5 37.5 53.0 73.2 1.95 4.29 5.77 0.330 34.6 36.8 76_-J 1.92 ______ 37.5 53.0 74.2 1__98 4.77 6.40 0.331 34.3 37.7 77.7 1.94 2.5 37.5 53.0 75.2 2.00 5.25 7.03 0.331 34.0 38.8 78.8 1.97 2.5 37.5 53.1 76.3 2.03 8.07 10.50 0.338 32.5 46.9 86.9 2. 17 ; 2___3 37.7 53.3 84.6 2.24 8.72 11.28 0.338 32.2 48.3 88.3 2.21 2.3 37.7 53.3 86.0 2.28 9.34 12.03 0.338 32.0 50.4 90.4 2.26 2.4 37.6 53.2 88.0 2.34 10.50 13.39 0.J39 31 .5 53. 3 93.3 2.33 . 2_.2_ 37.8 53.4 91. 1 2.41 11.22 14.21 0.341 31.3 54.8 94.8 2.37 2.2 37.8 53.4 92.6 2.45 11.91 15.02 0.342 31.0 56.2 96.2 2.40 2.2 37.8 53.5 94.0 2.49 12.38 15.56 C.34I 30.9 57.0 97.0 2.42 ______ 37.9 53.6 94.9 2.50 12.95 16.21 0.341 30.7 58.6 98.6 2.46 2.1 37.9 53.6 96.4 2.55 13.69 17.05 0.341 30.5 60.2 100.2 2.51 1.8 38.2 54.0 98.4 2.58 _14_._16 17.58 0.3 42 30.4 61.1 101.1 2.53 1.7 38.3 5 4_._1 - 9_9_- 4 2.60 14.68 18.14 0.343 30.2 62.1 102.1 2.55 1.8 38.2 54.0 100.3 2.63 15.20 18.72 0.344 30.1 62.8 102.8 2.57 1.8 38.2 54.0 101.0 2.64 19.29 23.20 0.345 29.3 68.3 108.3 2.71 1__5 38.5 . 54.4 106.7 2.77 20.04 24.01 0.345 29.1 68.8 108.8 2.72 1.4 38.6 54.6 107.5 2.78 20.78 24.81 0.344 29.0 69.9 109.9 2.75 1.2 38.8 54.9 108.7 2.80 2_1._9.3_ 26.03 _0.345 28.8. 70.5 110.5 2_._76.__. i.JL 3_j3_._9 55.0 109.4 2.81 22.70 26.84 0.346 28.7 71.0 111.6 2.78 1.3 38.7 54.7 109.7 2.84 23.26 27.44 0.346 28.6 71.3 111.3 2.78 1.1 38.9 55.1 110.2 2.83 23.59 27.79 0.346 28.6 71.3 111.3 2.78 0__9 39.1 55.3 110.4 2.82 24.25 28.49 0.346 28.5 71.3 111.3 2.78 1.0 39.0 55.2 110.4 2.83 25.05 29.33 0.345 28.4 71.8 111.8 2.80 1.0 39.0 55.2 110.8 2.84 25.42 . 29.72 0.346 28.4 71.9 111.9 2.80 " 1.0 39.0. . 55..X. 1.1.0...9 2.85 25.96 30.29 0.346 28.3 72 .6 112.0 2.80 0.7 39.3 55.5 111.2 2.83 26.55 30.90 0.347 28.3 72.0 112.0 2.80 0.7 39.3 55.6 111.3 2.83 27. 17 31.54 0.347 28.2 72.0 112.0 2.80 0__7 39.3 55.6 111.3 2.83 27.69 32.08 0.348 28.2 71.9 111.9 2.80 0.7 39.3 55.5 111.1 2.83 28.03 32.44 0.348 28.2 71.6 111.6 2.79 - 0.8 39.2 55.4 110.8 2.83 28.77 3 3_. 2 0 0.347 2_8__1 J j L . 4 111.4 2.79 _0_._5.. 39-A _._ _5 5^ . 7 110...8 2 ._8_1 29.62 34.08 0.347 28.0 71.8 111.8 2.79 0.5 39.5 55.9 111.3 2.82 30.65 35.13 0.348 28.0 71.7 111.7 2.79 0.0 40.0 56.6 111.7 2.79 I S O CONSOLIDATION PRES.= 40.0 TEST NO.17 SHEAR P P MINUS Q QW QW(PP) M M(PP ) P/PE P/PE Q/PE STRAIN PSI PP. PSI PSI PSI PSI ( PP) -0.00 40.0 40.0 0.0 -49.7 28.1 -1.24 0.70 1.00 1.00 0.00 < 0.04 41.3 40.8 4.1 -36.8 30.0 -0.89 0.73 1.03 1.02 0. 10 0.13 _43.0 42.2 9.2 ._rP.8 47_9 -0.02 1.14 1.07 1.05 0.23 0.18 43.9 43. 1 11.9 4.8 46.0 0. 11 1.07 1.09 1.07 0.29 0.25 44.9 43.8 14.7 22. 1 56.1 0.49 1.28 1. l l 1.08 0. 36 0.35 45.9 44.5 17.9 36.9 63.8 0.80 1.43 I. 12 1.08 0.44 0.46 46.9 45.5 20.8 42.2 64.4 0.90 1.42 1.13 1.10 0.50 0.57 47.8 46.3 23.5 55.0 73.6 1. 15 1.59 1.14 1.10 0.56 0.73 _48.8 47.2 26.6 59.8 72.9 1.23 1.54 1. 14 1. 10 0.62 0.93 49.5 47.7 28.6 76. 1 83.6 1.54 1.75 1. 14 1. 10 0.66 1.12 49.9 47.8 29.9 81.1 85.5 1.63 1.79 1.12 1.07 0.67 1.42 50.2 48.2 30.8 85.2 87.4 1.70 1.81 1.09 1.04 0.67 1.85 50.4 48.3 31.5 86.3 87.4 . 1.71 1.81 1.04 1.00 0.65 2.61 51.0 48.7 33.2 84.4 84.6 1.66 1.74 0.97 0.93 0.63 3.40 51.5 49. 1 34.6 82.4 82.1 1.60 1.67 0.91 0.87 0.61 3.87 51.8 49.4 35.7 83. 1 82.7 1.60 1.68 0.88 0.83 0.60 4.29 52.2 49.7 36.8 84.8 84. 1 1.62 1.69 0.85 0.81 0.60 4.77 52.5 50.0 37.7 84.1 83.6 1.60 1.67 0.82 0.78 ' 0.59 5.25 52.9 50.4 38.8 83.7 83.3 1.58 1.65 0.79 0.75 0.58 8.07 55.6 53.3 46.9 79.7 79.9 1.43 1.50 0.68 0.66 0.58 8.72 56.0 53.7 48.3 80.1 80.8 1.43 1.50 0.67 0.64 0.57 9.34 56.7 54.4 50.4 80.4 81.1 1.42 1.49 0.65 0.62 0.58 10.50 57.7 55.5 53.3 78.9 79.6 1.37 1.43 0.62 0.60 0.58 11.22 58.2 56.0 54.8 80.0 80.6 1.37 1.44 0.61 0.59 0.57 11.91 58.7 56.5 56.2 80.8 81.2 1.38 1.44 0.59 0.57 0.57 12.38 58.9 56.8 57.0 80.9 81.6 1.37 1.44 0.59 0. 56 0. 57 12.95 59.5 57.3 58.6 81.3 82.0 1.37 1.43 0.58 0.56 0.57 13.69 60.0 58.2 60.2 78.6 79.4 1.31 1.37 0.56 0.55 0.57 14. 16 60.3 58.6 61.1 78.2 79.1 1.30 1.35 0.56 0.54 0.57 14.68 60.6 58.9 62.1 .78.6 79.3 1.30 1.35 0.55 0.54 0.57 15.20 60.9 59.1 62.8 79.2 79.8 1.30 1.35 0.55 0.53 0.56 19.29 62.7 61.2 68.3 82.8 83.0 1.32 1.36 0.50 0.49 0.55 20.04 62.9 61.5 68.8 81.9 82_._t 1 ._30 1 jJ34 0.49 0.48 0.54 20.78 63.2 62.0 69.9 81.4 81.8 1.29 1.32 0.49 0.48 0.54 21.93 63.4 62.3 70.5 80.3 80.6 1.27 1.29 0.48 0.47 0.53 22.70 63.6 62. 3 71.0 82.0 82.2 1.29 1.32 0.48 0.47 0.53 23.26 63.7 62.6 71.3 79.6 79.7 1.25 1.27 0.47 0.46 0.53 23.59 63.7 62.8 71.3 80.3 80.3 1.26 1.28 0.47 0.46 0.53 24.25 63.7 62.8 71.3 79.5 79.6 1.25 1.27 0.46 0.46 0.52 25.05 63.9 62.9 71.8 79.7 79.8 1.25 1.27 0.46 0.45 0.52 25.42 63.9 62.9 71.9 79.9 80.0 1.25 1.27 0.46 0.45 0.51 25.96 63.9 63.2 72.0 77.9 78.0 1.22 1.2 3 0.45 0.45 0.51 26.55 63.9 63.3 72.0 78.6 78.5 1.23 1.24 0.45 0.45 0.51 27.17 63.9 63.2 72.0 77.4 77.2 1.21 1.22 0.45 0.44 0.50 27.69 63.9 63.1 71.9 79.2 78.8 1.24 1.25 0.45 0.44 0.50 28.03 63.8 63.0 71.6 78.2 77.9 1.23 1.24 0.44 0.44 0.50 28.77 63.7 63.1 71.4 77.5 77.4 1.22 1.23 0.44 0.43 0.49 29.62 63.9 63.4 71.8 76.0 76.0 1.19 1.20 0.44 0.43 0.49 30.65 63.9 63.9 71.7 0.0 0.0 0.00 0.00 0.43 0.43 0.49 151 TEST NO.17 CONSOLIDATION PRES.= 4 0 . 0 SHEAR PORE PRESSURE STRAIN CV.H,A A CONSTANT K.H CONSTANT CV,H VARY VARY -0.00 0.0 0.0 0.0 _J0.,Q4 3_2 3._2 0.5 0.13 5.8 5.9 0.8 0.18 6.7 6.9 0.9 0.25 7____ 7_8 l__0_ 0.35 7.8 8.4 1.4 0.46 7.8 8.6 1.3 _ 0..J57 7 ._7 8.J. Ls5_ 0.73 7.0 8.2 1.6 0.93 5.8 7.1 1.8 1.12 4___5 5__J5 2.1 1.42 2.7 3.7 2.0 1.85 1.3 1.9 2.2 _ 2.61 0.8 1.1 2.3 3.40 0.6 0.8 2.4 3.87 0.8 0.9 2.5 4.29 0___? 1.0 2.5 4.77 0.7 0.9 2.5 5.25 0.7 0.9 2.5 8.07 0.4 0._5 2_3_ 8.72 0.7 0.8 2.3 9.34 l . l 1.2 2.4 10.50 0___9 UO 2.2 11.22 0.9 1.0 2.2 11.91 0.8 0.9 2.2 12.38 J3_7 0.8 2.1 12.95 0.9 1.0 2.1 13.69 0.9 1.0 1.8 14.16 0__9 0__9 1.7 14.68 0.9 0.9 1.8 15.20 0.7 0.8 1.8 19.29 _ 0.1 0..1. 1.5. 20.04 0.2 0.2 1.4 20.78 0.5 0.4 1.2 21.93 0__3 0_2 1.1 22.70 0.3 0.3 1.3 23.26 0.2 0.2 1.1 2 3...59 0,. 2 _0 .JL 0..9. 24.25 0.1 0.0 1.0 25.05 0.2 0.2 1.0 25.42 0__2 0.2 U0_ 25.96 0.1 0.1 0.7 26.55 0.1 0.0 0.7 _2 7_._17 0_._0 QL._0 JDL._7_ 27.69 -0.1 -0.1 0.7 28.03 -0.2 -0.2 0.8 28.77 -Q. 1 -0.1 0.6 29.62 0.1 0.1 0.5 30.65 0.0 0.0 0.0
UBC Theses and Dissertations
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UBC Theses and Dissertations
Effective stress paths in a sensitive clay Byrne, Peter Michael 1966-12-31
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