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A plane strain apparatus for soils Vaid, Yoginder Pal 1968

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A PLANE STRAIN APPARATUS FOR SOILS by Y o g i n d e r P a l V a i d B . S c . E n g i n e e r i n g , P a n j a b U n i v e r s i t y , C h a n d i g a r h , I n d i a P o s t G r a d . D i p l o m a , U n i v e r s i t y o f R o o r k e e , R o o r k e e , I n d i a A THES I S SUBMITTED IN PART IAL FULF ILMENT OF THE REQUIREMENTS FOR THE DEGREE OF ' M . A . S c . i n t h e D e p a r t m e n t o f C i v i l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERS ITY OF BR IT ISH COLUMBIA O c t o b e r , 1968 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s . f o r a n . a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t 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 f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e . t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s , f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e Head o f my • D e p a r t m e n t • o r b y h.i's r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my. w r i t t e n , p e r m i s s i o n . D e p a r t m e n t o f O'vif *^'>Ketrirfr-The Up i v e r s i t y o f Br i t i s h Columb i a V a n c o u v e r 8, C a n a d a D a t e N"0Vlr*}>ZT 6y ( i i ) ABSTRACT. An a p p a r a t u s h a s b e e n d e s i g n e d t o i n v e s t i g a t e t h e m e c h a n i c a l b e h a v i o u r o f s o i l s u n d e r p l a n e s t r a i n . P r o v i s i o n h a s a l s o b e e n made t o c o n s o l i d a t e s p e c i m e n s u n d e r c o n d i t i o n o f no l a t e r a l y i e l d p r i o r t o t h e i r s h e a r ; t h u s s i m u l a t i n g t h e c o n s o l i d a t i o n s t a t e i n n a t u r a l s e d i m e n t a r y d e p o s i t s . The a p p a r a t u s i s s u i t e d f o r t e s t i n g b o t h s a n d s a n d c l a y s , i n c l u d i n g u n d i s t u r b e d c l a y s a m p l e s f r o m s t a n d a r d s i z e b o r e h o l e s a m p l e r s . The d e s i g n p e r m i t s a v a r i e t y o f s t r e s s p a t h s t o be f o l l o w e d d u r i n g s h e a r . An e x p e r i m e n t a l p r o c e d u r e f o r t e s t i n g b o t h s a n d s and c l a y s h a s b e e n d e v e l o p e d a n d some t e s t r e s u l t s a r e d e s c r i b e d . The r e s u l t s o b t a i n e d show a g e n e r a l c o n f i r m a t i o n o f e x i s t i n g i n f o r m a t i o n on t h e b e h a v i o u r o f s o i l s u n d e r p l a n e s t r a i n . ( i i i ) TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION . l CHAPTER 2 REVIEW OF L ITERATURE . . . . 6 F a i l u r e C r i t e r i a 6 T y p e s o f S h e a r T e s t s 13 T e s t R e s u l t s 16 Some S i g n i f i c a n t F e a t u r e s o f T y p e s . o f A p p a r a t u s E m p l o y e d i n t h e above I n v e s t i g a t i o n s . . . . . . . . . 24 CHAPTER 3 DESCRIPTION OF THE APPARATUS 3 0' S i z e 32 F r i c t i o n l e s s E n d P l a t e s 32 L a t e r a l P r e s s u r e D i a p h r a g m s . . . . . . . 34 Vo lume Change and P r e s s u r e M e a s u r e m e n t s 36 L o a d i n g E q u i p m e n t 36 CHAPTER 4 EXPERIMENTAL PROCEDURE . . . . . . . . . 40 P r e p a r a t i o n o f C l a y S amp l e s 4 0 P r e p a r a t i o n o f S a t u r a t e d Sand S a m p l e s . . kl CHAPTER 5 CHARACTER IST ICS OF THE APPARATUS . . . . 51 M e a s u r e m e n t o f A x i a l L o a d 51 M e a s u r e m e n t o f P r e s s u r e s . 52 ( i v ) TABLE OF CONTENTS ( C o n t ' d . ) Page M e a s u r e m e n t o f A x i a l D e f o r m a t i o n . . . . 53 K - C o n s o l i d a t i o n 53 o S a t u r a t i o n o f t h e S p e c i m e n s 6 0 U n i f o r m i t y o f D e f o r m a t i o n s 61 S h e a r S t a g e . 6 3 Measu remen t o f • ^ CHAPTER 6 SOME EXPERIMENTAL RESULTS 6 6 The T e s t P r o g r a m 6 6 T e s t R e s u l t s - c l a y 7 0 T e s t R e s u l t s - s a n d 8 5 CHAPTER 7 SUMMARY AND CONCLUSIONS 9 4 L I S T OF REFERENCES • 9 6 APPENDIX 1 P r o c e d u r e f o r M a k i n g R u b b e r , M e m b r a n e s . . 102 APPENDIX 2 M e a s u r e m e n t o f B - v a l u e s 104 ( v ) L I S T OF F.'GURES F i g u r e Page 2.1 R i g h t s e c t i o n s o f f a i l u r e s u r f a c e s by an o c t a h e d r a l p l a n e 11 3.1 P r i n c i p a l s t r e s s e s u n d e r p l a n e s t r a i n . . . . 31 3.2 E x p l o d e d v i ew o f t h e p l a n e s t r a i n a p p a r a t u s . 33 3.3 L a t e r a l p r e s s u r e d i a p h r a g m s . . . . . . . . . 35 3.4 S c h e m a t i c l a y o u t o f vo lume change and p r e s s u r e m e a s u r e m e n t s . . . . 37 3.5 S c h e m a t i c d i a g r a m o f t h e l o a d i n g e q u i p m e n t . . 3 8 4 .1 T r i m m i n g a p p a r a t u s f o r c l a y s p e c i m e n s . . . . 41 4 .2 R u b b e r membrane s t r e t c h e d on s l e e v e f o r i n s t a l l i n g c l a y s a m p l e s 43 4 . 3 A c l a y s amp le i n p a l c e 46 4 .4 Sample a s s e m b l y i n t h e l o a d i n g f r ame 46a 4 . 5 Sand s p e c i m e n u n d e r p r e p a r a t i o n 48 » 5.1 C o m p l i a n c e o f l a t e r a l p r e s s u r e d i a p h r a g m s . . 5 7 5.2 C o m p a r i s o n o f p r e s s u r e v o i d r a t i o r e l a t i o n s h i p f r o m p l a n e s t r a i n a p p a r a t u s and s t a n d a r d r i n g c o n s o l i d o m e t e r 5 8 5 .3 U n i f o r m v e r t i c a l s e c t i o n a l o n g t h e l e n g t h o f a d e f o r m e d p l a n e s t r a i n s p e c i m e n , (a ) i n a x i a l e x t e n s i o n , (b) i n a x i a l c o m p r e s s i o n .62 6.1 D e v i a t o r s t r e s s v s . a x i a l s t r a i n f o r c o n s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on Haney c l a y . . . . . . . . . . ?3 6 .2 P r i n c i p a l e f f e c t i v e s t r e s s r a t i o v s . a x i a l s t r a i n f o r c o n s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on Haney c l a y . . . . 74 ( v i ) L I S T OF FIGURES ( C o n t ' d . ) Page 6 .3 P o r e p r e s s u r e v s . a x i a l s t r a i n f o r c o n -s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on Haney c l a y 77 6 .4 P o r e p r e s s u r e p a r a m e t e r A v s . a x i a l s t r a i n f o r c o n s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on Haney c l a y 8 0 6 .5 E f f e c t i v e s t r e s s p a t h s f o r c o n s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on Haney c l a y 8 3 6 . 6 D e v i a t o r s t r e s s v s . a x i a l s t r a i n f o r d r a i n e d p l a n e s t r a i n t e s t s on d e n s e O t t a w a s a n d . . . . . . 86 6 . 7 E f f e c t i v e s t r e s s r a t i o v s . a x i a l s t r a i n f o r d r a i n e d p l a n e s t r a i n t e s t s on dense O t t a w a s a n d 87 6 .8 V o l u m e t r i c v s . a x i a l s t r a i n f o r d r a i n e d p l a n e s t r a i n t e s t s on d e n s e O t t a w a s a n d . . . . . 89 6 .9 E f f e c t i v e s t r e s s p a t h s f o r d r a i n e d s t r a i n t e s t s on dense O t t a w a p l a n e s a n d . . . . 91 ( v i i ) LIST OF TABLES Page Table I Results o f one dimensional c o n s o l i d a t i o n t e s t on undisturbed Haney c l a y . . . . 7 0 a. Table I I Results of c o n s o l i d a t e d undrained plane s t r a i n shear t e s t s on normally loaded undisturbed Haney c l a y 1J> a. Table I I I Results of drained plane s t r a i n shear t e s t s on dense Ottawa sand 9 I a Table A2-1 Measurement of B-values f o r an undisturbed specimen of Haney c l a y . . 104 ( v i i i ) LIST OF SYMBOLS ?oct °oct i f Shearing strength c" E f f e c t i v e cohesion <f)' E f f e c t i v e angle o f i n t e r n a l f r i c t i o n o" E f f e c t i v e normal s t r e s s on f a i l u r e plane 2 3 P r i n c i p a l t o t a l s t r e s s e s a£ 2 , 3 P r i n c i p a l e f f e c t i v e s t r e s s e s Octahedral t o t a l normal s t r e s s Octahedral e f f e c t i v e normal s t r e s s T . Octahedral shearing s t r e s s 'oct ° a Henkel pore pressure parameter Kg C o e f f i c i e n t of earth pressure at r e s t a-. Major p r i n c i p a l c o n s o l i d a t i o n pressure 03,-, Minor p r i n c i p a l c o n s o l i d a t i o n pressure c v C o e f f i c i e n t of c o n s o l i d a t i o n A£B Skempton's pore pressure parameters u Pore pressure e-^ 2 3 P r i n c i p a l s t r a i n s s u H a l f the major and minor p r i n c i p a l s t r e s s d i f f e r e n c e = (a^-ag)12 n A x i a l p r i n c i p a l t o t a l s t r e s s a" A x i a l p r i n c i p a l e f f e c t i v e s t r e s s cl a L a t e r a l p r i n c i p a l t o t a l s t r e s s L a t e r a l p r i n c i p a l e f f e c t i v e s t r e s s ( i x ) A_Y. Volumetric s t r a i n V . a Mean normal t o t a l s t r e s s m o" Mean normal e f f e c t i v e s t r e s s m (j)u Rowe1 s semi-empirical f r i c t i o n angle (x) ACKNOWLEDGEMENTS The i n v e s t i g a t i o n described h e r e i n has been p a r t l y supported by funds provided by the N a t i o n a l Research C o u n c i l of Canada. G r a t e f u l acknowledgement i s expressed f o r t h i s a s s i s t a n c e , which made these i n v e s t i g a t i o n s p o s s i b l e . The w r i t e r wishes to express h i s deepest thanks to h i s research s u p e r v i s o r , Dr. R.G. Campanella, f o r the continuous guidance during the development of the apparatus. Thanks are also due to Prof. P.M. Byrne f o r h e l p f u l suggestions. The t e c h n i c a l a s s i s t a n c e of the s t a f f o f the c i v i l engineering workshop, U.B.C, i n f a b r i c a t i n g the equipment, i s g r a t e f u l l y acknowledged. 1 CHAPTER 1 INTRODUCTION In the design of foundations and e a r t h s t r u c t u r e s the problems o f greatest concern are settlement and s t a b i l i t y . A proper assessment of these problems r e q u i r e s i n v e s t i g a t i o n s o f the s t r e s s - s t r a i n and strength character-i s t i c s of s o i l s i n v o l v e d . The most commonly used t e s t device f o r t h i s purpose i s the t r i a x i a l t e s t apparatus. In t h i s t e s t a c y l i n d r i c a l specimen of s o i l i s f i r s t i s o -t r o p i c a l l y c o n s o l i d a t e d arid then sheared under a state o f s t r e s s which i s a x i a l l y symmetric, i . e . , where two of the three p r i n c i p a l s t r e s s are always equal. Yet the r e s u l t s o f the t r i a x i a l t e s t are used i n s o l v i n g f i e l d problems, where the st a t e of i n i t i a l c o n s o l i d a t i o n i s a n i s o t r o p i c and shear occurs under nonsymmetrical s t a t e s o f s t r e s s , i . e . , where the three p r i n c i p a l s t r e s s e s are d i f f e r e n t . A common case i s that of plane s t r a i n , where there i s no change i n leng t h along the a x i s of the s t r u c t u r e . Problems of slope s t a b i l i t y , s t r i p f o o t i n g s , long excavations e t c . f a l l i n t o t h i s category. For many years engineers have been concerned w i t h the p o s s i b l e e f f e c t o f nonsymmetrical 2 s t a t e s o f s t r e s s and o f t h e s p e c i a l c a s e o f p l a n e s t r a i n , on t h e s h e a r i n g r e s i s t a n c e o f s o i l s . T h e r e s u l t s o f i n v e s t i -g a t i o n s i n t h i s d i r e c t i o n h a v e o f t e n b e e n c o n f l i c t i n g ( K j e l l m a n 1 9 3 6 , H a b i b 1 9 5 3 , K i r k p a t r i c k 1 9 5 7 , P e l t i e r 1 9 5 7 , H a y t h o r n t h w a i t e 1 9 6 0 , 1 9 6 3 , Broms and Ratnam 1 9 6 3 , Wu, L o h and M a l v e r n 196 3, L e u s s i n k a n d W i t t k e 196 3 , Broms and C a s b a r i a n 1 9 6 5 , Broms and J a m a l 1 9 6 5 , L e u s s i n k 1 9 6 5 , C o r n f o r t h 1 9 6 4 , M a r s a l 196 5, H e n k e l and Wade 1 9 6 6 , S h i b a t a and K a r u b e 1 9 6 5 , L o m i z e and K r y z h a n o v s k y 1 9 6 7 , Ko and S c o t t 1 9 6 8 , Whi tman and L u s c h e r 1 9 6 2 ) . H o w e v e r , t h e r e a p p e a r s t o be a g e n e r a l a g r e e m e n t t h a t t h e a n g l e o f s h e a r i n g r e s i s t a n c e o f s a n d s i s h i g h e r u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s t h a n t h a t f o u n d u n d e r c o n d i t i o n s o f a x i a l s ymmet ry o f t h e c o n v e n -t i o n a l ^ t r i a x i a l t e s t . The d a t a on c l a y s i s more l i m i t e d and t h e r e i s no g e n e r a l a g r e e m e n t on t h e i n c r e a s e i n s h e a r i n g r e s i s t a n c e u n d e r s t r e s s s t a t e s d i f f e r e n t f r o m t h a t o f t h e c o n v e n t i o n a l t r i a x i a l t e s t . S h e a r t e s t i n g o f s o i l s u n d e r n o n s y m m e t r i c a l s t a t e s i s t o o c o m p l i c a t e d f o r o t h e r t h a n s p e c i a l r e s e a r c h p u r p o s e s , w h e r e a s t h e c o n v e n t i o n a l t r i a x i a l t e s t h a s become a r o u t i n e t e s t i n many s o i l l a b o r a t o r i e s . I t seems t h a t t h e i n d i s c r i m i n a t e use o f t h e t r i a x i a l t e s t f o r a l l f i e l d p r o b l e m i s due t o i t s r o u t i n e n a t u r e a n d , r e s e a r c h h a s n o t p r o d u c e d c o n c l u s i v e e v i d e n c e t o p r o v e t h a t t h e m e c h a n i c a l b e h a v i o u r o f s o i l s d i f f e r s s i g n i f i c a n t l y u n d e r s t r e s s s t a t e s w h i c h c a n n o t be s i m u l a t e d i n t h i s t e s t . T h e r e i s a g r o w i n g f e e l i n g , h o w e v e r , t h a t a n i s o t r o p y i n c o n s o l i d a -3 t i o n and nonsymmetrical s t a t e s of s t r e s s may i n f l u e n c e the shear behaviour o f s o i l s to such a high degree so as to question the use of the conventional t r i a x i a l t e s t (Moretto 1965 ). To i n v e s t i g a t e the c o n s t i t u t i v e response of s o i l s an i d e a l piece of t e s t equipment would be one that produces a homogeneous st a t e of s t r e s s or s t r a i n i n the e n t i r e specimen. In a d d i t i o n , the apparatus must be able to f o l l o w the same s t r e s s path during c o n s o l i d a t i o n and subsequent shear, as i s l i k e l y to happen i n the f i e l d . When the s t a t e of s t r e s s or s t r a i n i s homogeneous throughout the e n t i r e specimen, i t can be considered as an i n f i n i t e s i m a l element of a continuum and the concept of s t r e s s o r s t r a i n at a p o i n t i s immediately a p p l i c a b l e . Then the measurement o f boundary s t r e s s e s and displacements provides the d e s i r e d i n f o r m a t i o n on the c o n s t i t u t i v e response of the m a t e r i a l . I t i s a formidable task to design an apparatus which imposes uniform s t r e s s e s or s t r a i n s -throughout the e n t i r e specimen. Consequently i n the various devices c u r r e n t l y used f o r s o i l t e s t i n g i t has been aimed to come as c l o s e as p o s s i b l e to the i d e a l device. The most s i g n i f i c a n t source of s t r e s s or s t r a i n ...inhomogenity a r i s e s from r e s t r a i n t imposed by r i g i d boundaries on a t e s t specimen. In a conventional t r i a x i a l t e s t , f r i c t i o n at the end caps does not permit the sample to s t r a i n l a t e r a l l y i n a uniform manner and, t h e r e f o r e , de-parture from homogeneous s t a t e of s t r e s s and s t r a i n occurs b o t h d u r i n g i s o t r o p i c c o n s o l i d a t i o n and d u r i n g s h e a r . To m i n i m i s e t h e r e s t r a i n i n g a c t i o n o f o r d i n a r y c a p s , l u b r i c a t e d end c a p s have b e e n s u c c e s s f u l l y u sed .CRowe and B a r d e n 1 9 6 4 , Lee a n d Seed 1 9 6 4 , B i s h o p and G r e e n 1 9 6 5 , B l i g h t 1 9 6 5 , B a r d e n and M c D e r m o t t 1 9 6 5 ) . H o w e v e r , t h e same c a p s were f o u n d i n e f f e c t i v e by o t h e r i n v e s t i g a t o r s ( C a s a g r a n d e and P o u l o s 1 9 6 4 , O l s o n and C a m p b e l l 1 9 6 4 ) . T h e m a i n p u r p o s e o f t h i s t h e s i s i s t o d e s c r i b e t h e d e v e l o p m e n t o f a t e s t a p p a r a t u s i n w h i c h s o i l s p e c i m e n s can be f i r s t a n i s o t r o p i c a l l y c o n s o l i d a t e d u n d e r c o n d i t i o n s o f no l a t e r a l y i e l d (K o r one d i m e n s i o n a l c o n s o l i d a t i o n ) , and t h e n s h e a r e d u n d e r t h e c o n d i t i o n s o f p l a n e s t r a i n . A r e v i e w o f t h e c u r r e n t l i t e r a t u r e on t h e b e h a v i o u r o f s o i l s u n d e r n o n -s y m m e t r i c a l s t a t e s o f s t r e s s , ha s been i n c l u d e d t o show c o n -f l i c t i n g r e s u l t s r e p o r t e d i n t h e l i t e r a t u r e and h e n c e t h e n e e d f o r f u r t h e r u n d e r s t a n d i n g i n t h i s f i e l d . D e s c r i p t i o n o f t h e a p p a r a t u s i s f o l l o w e d by a d e s c r i p t i o n o f t h e t e c h n i q u d e v e l o p e d f o r i n s t a l l i n g s a m p l e s i n t he a p p a r a t u s . T h i s i s f o l l o w e d by a s t u d y o f t h e s i g n i f i c a n t c h a r a c t e r i s t i c s o f t h e a p p a r a t u s d e s i g n e d a n d , o f i t s p o t e n t i a l i n p e r f o r m i n g v a r i o u s k i n d s o f t e s t s u s i n g d i f f e r e n t s t r e s s p a t h s t o f a i l u r e . One d i m e n s i o n a l c o n s o l i d a t i o n t e s t s a n d K -c o n s o l i d a t e d u n d r a i n e d p l a n e s t r a i n t e s t s on s p e c i m e n s o f a l o c a l u n d i s t u r b e d c l a y a r e d e s c r i b e d . A l s o d r a i n e d p l a n e s t r a i n t e s t s on d e n s e O t t a w a s a n d a r e d e s c r i b e d . An e v a l u -a t i o n o f t h e t e s t r e s u l t s i s made a n d , c o m p a r e d w i t h t h e 5 e x i s t i n g i n f o r m a t i o n on s o i l behaviour under plane s t r a i n . 6 CHAPTER 2 L ITERATURE REVIEW T h i s r e v i e w i s p r e s e n t e d t o e m p h a s i z e t h e c o n -f l i c t i n g n a t u r e o f t h e r e s u l t s o f i n v e s t i g a t i o n s o f s h e a r b e h a v i o u r o f s o i l s u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s . The m a j o r i t y o f t h e s e i n v e s t i g a t i o n s have b e e n c o n c e r n e d w i t h t h e s t u d y o f s t r e s s c o n d i t i o n s a t f a i l u r e . The r e s u l t s o f s t r e n g t h t e s t s a r e e x p r e s s e d i n t e r m s o f a f a i l u r e c r i t e r i o n . T h e r e f o r e , b e f o r e d i s c u s s i n g any s u c h r e s u l t s , a b r i e f d e s c r i p t i o n o f t h e v a r i o u s f a i l u r e c r i t e r i a a p p l i -c a b l e t o s o i l s i s p r e s e n t e d b e l o w . F a i l u r e C r i t e r i a The f a i l u r e c o n d i t i o n s f o r a s o i l can be e x p r e s s e d i n t e r m s o f a l i m i t i n g s h e a r s t r e s s , c a l l e d s h e a r s t r e n g t h , o r a s a f u n c t i o n o f t h e p r i n c i p a l s t r e s s e s . T h e , m o s t w i d e l y u s e d e x p r e s s i o n f o r s h e a r s t r e n g t h i s o b t a i n e d on t h e a s s u m p t i o n t h a t t h e s o i l f a i l s a c c o r d i n g t o M o h r - r u p t u r e c r i t e r i o n . M o h r ' s c o n c e p t o f f a i l u r e a s sumes t h a t a t f a i l u r e a c r o s s a p l a n e , t h e n o r m a l a n d t h e l i m i t i n g s h e a r s t r e s s e s a c r o s s t h e p l a n e , a and Tf, a r e r e l a t e d by a 7 f u n c t i o n a l r e l a t i o n s h i p , T f = F(o) ( 2 . 1 ) Since shearing r e s i s t a n c e of s o i l s i s c o n t r o l l e d by the e f -f e c t i v e and not by t o t a l normal s t r e s s e s , equation ( 2 . 1 ) becomes T F = F(o') ( 2 . 1 a ) where a ' i s the e f f e c t i v e normal s t r e s s on the f a i l u r e plane. On the a" j •••/•T ^  s t r e s s plane, equation ( 2 . 2 ) represents a curve which i s the envelope o f a l l the Mohr-stress c i r c l e s corresponding to the c o n d i t i o n s at which f a i l u r e takes p l a c e . This curve i s known as the Mohr envelope. The a c t u a l Mohr envelopes f o r s o i l s are o f t e n s l i g h t l y curved but they are replaced by s t r a i g h t l i n e s . This i s eq u i v a l e n t to assuming that the s o i l s conform to the Coulomb f a i l u r e condi-t i o n . When the Mohr envelope i s a s t r a i g h t l i n e , the f a i l u r e c o n d i t i o n becomes T F = c* + cr"tan<f>/ ( 2 . 2 ) which i s known as the Mohr-Coulomb f a i l u r e c r i t e r i o n . In equation ( 2 . 2 ) , c" and <j>" are r e s p e c t i v e l y the apparent cohesion and angle o f i n t e r n a l f r i c t i o n o f the s o i l w i t h respect to e f f e c t i v e s t r e s s e s . When expressed i n terms o f p r i n c i p a l s t r e s s e s , the Mohr-Coulomb f a i l u r e c r i t e r i o n i s : 8 io'-a') = (a n-a.) = 2c'cos<j>' + (a_'+a*) s i n $ * ( 2 . 3 ) 1 3 x j 1 -3 where o£ and a r e r e s p e c t i v e l y t h e m a j o r and t h e m i n o r p r i n c i p a l e f f e c t i v e s t r e s s e s a t f a i l u r e . F o r g r a n u l a r s o i l s and n o r m a l l y l o a d e d c l a y s c o h e s i o n c" e q u a l s z e r o and e q u a t i o n ( 2 . 3 ) becomes ( 0 ^ - 0 - 3 ) = (a£+aj)sin(|) ( 2 . 3 a ) M o h r - C o u l o m b f a i l u r e c r i t e r i o n i m p l i e s t h a t t h e i n t e r m e d i a t e p r i n c i p a l e f f e c t i v e s t r e s s , 0 ^ , does n o t i n f l u e n c e t h e e x t r e m e v a l u e s o f t h e p r i n c i p a l s t r e s s e s 0 ^ and 0 3 a t t h e p o i n t o f f a i l u r e . Two o t h e r f a i l u r e c r i t e r i a c o n s i d e r e d a p p l i c a b l e t o s o i l s , f o l l o w the o c t a h e d r a l s h e a r t h e o r y . T h e s e a r e t h e e x t e n d e d T r e s c a and t h e e x t e n d e d von M i s e s c r i t e r i a , w h i c h t a k e a c c o u n t o f t h e i n f l u e n c e o f t h e i n t e r m e d i a t e p r i n c i p a l e f f e c t i v e s t r e s s , 0 ^ , on f a i l u r e s t r e n g t h . F o r c o h e s i o n l e s s s o i l s and n o r m a l l y l o a d e d c l a y s , i . e . , c o n -s i d e r i n g c" - 0 , t h e s e c r i t e r i a may be w r i t t e n as f o l l o w s : E x t e n d e d T r e s c a : o.'+o' + 0 o ( 0 f - 0 3 > = at-^-j £ ) = c t 0 o C t ( 2 . 4 ) E x t e n d e d von M i s e s : 9 T o c t 2 = ( a £ - a 2 ) 2 + ( c J 2 - ° 3 ) 2 + ( ( 7 3 ^ 1 ) 2 = 2 a 2 a o c t 2 ( 2 ' 5 ) 9 where a * o c t and T o c t a r e r e s p e c t i v e l y t h e o c t a h e d r a l n o r m a l e f f e c t i v e and s h e a r s t r e s s e s and a i s a s t r e n g t h p a r a m e t e r . mean n o r m a l e f f e c t i v e s t r e s s and d e s i g n a t e d by a". F o r an t e n d e d T r e s c a and e x t e n d e d von M i s e s c r i t e r i a c o i n c i d e . The f o r m o f E q u a t i o n s ( 2 . 4 ) and ( 2 . 3 a ) i s n o t a n a l y t i c ; i t v i o l a t e s t h e r u l e t h a t t h e manne r i n w h i c h t h e p r i n c i p a l e f f e c t i v e s t r e s s e s a r e l a b e l l e d 1, 2 , 3 s h o u l d n o t a f f e c t , t h e f o r m o f f a i l u r e c r i t e r i a ( Fung 19 6 6 ) . H o w e v e r , E q u a t i o n s ( 2 . 4 ) and ( 2 . 3 a ) c a n be made a n a l y t i c as f o l l o w s : i t i s o b s e r v e d t h a t any one o f t h e d i f f e r e n c e s j a £ — | > |a^-o^ | , | ^3 —cr£ 1 n a s a v a l u e otaoct ^ n e x t e n d e d T r e s c a a n d (,a^+a^) sin^" i n M o h r - C o u l o m b c r i t e r i a . Hence t h e s e two C r i t e r i a may be w r i t t e n a s , E x t e n d e d T r e s c a : O c t a h e d r c l n o r m a l e f f e c t i v e s t r e s s , i s a l s o c a l l e d t h e m [ ( a £ - a 2 - ) 2 - a 2 a 0 ' c t 2 ] x C ( a 2 ' - a 3 ) 2 - a 2 a ( ; c t 2 ] x x C ^ - a ^ - a 2 ^ 2 ] = 0 ( 2 . 4 a ) M o h r - C o u l o m b : ( 2 . 3 b ) 10 Equations (2.3b), (2.4a) and (2.5) represent pyramid shaped s u r f a c e s , with apex at the o r i g i n , i n the p r i n c i p a l e f f e c t i v e s t r e s s space w i t h coordinates a^, a^j a^• These surfaces are symmetrical with respect to the space d i a g o n a l , a£ = = a g • T n e r i g h t s e c t i o n s of pyramids formed by planes p e r p e n d i c u l a r to the space diagonal(the o c t a h e d r a l planes) are r e s p e c t i v e l y ( f i g . 2.1) i r r e g u l a r hexagons (equal s i d e s but not p a r a l l e l ) f o r the Mohr-Coulomb, r e g u l a r hexagons f o r the extended Tresca and c i r c l e s f o r extended von Mises c r i t e r i a . The s i z e of the r i g h t s e c t i o n s depends on the magnitude of the mean normal e f f e c t i v e s t r e s s and strength parameters of the s o i l , <j>' or a. A x i a l l y symmetric st a t e s of s t r e s s (a^ = c^ o r ^\ ~ which correspond r e s p e c t i v e l y to the conventional t r i a x i a l compression and extension t e s t s , y i e l d f a i l u r e p o i n t s which are l o c a t e d on the adjacent r a d i a l l i n e s of a 60° s e c t o r (points a and b or b" i n f i g . 2.1). The shape-of the f a i l u r e surface between these extreme l i m i t s of the magnitude of > can be i n v e s t i g a t e d o n l y under nonsymmetrical s t a t e s of s t r e s s . Because of the symmetry of the r i g h t s e c t i o n s of f a i l u r e s u r f a c e s , i t i s s u f f i c i e n t to e s t a b l i s h e x p e r i m e n t a l l y o n l y a 60° s e c t o r such as a to bb*. One obvious procedure to e s t a b l i s h the v a l i d i t y of any f a i l u r e c r i t e r i o n , i s to determine whether the values o f the r e l e v a n t s t r e n g t h parameters c", or a are i n f a c t dependent on the s t a t e of s t r e s s at f a i l u r e . Mohr-11 F ig . 2-1 - R i ? M sections °-f jo.Wu.re. S U T ^ Q C « S by An 12 C o u l o m b c r i t e r i o n has o f t e n b e e n a d v o c a t e d f o r s o i l s and i t s p a r a m e t e r s c", <|>'are. d i r e c t l y a p p l i c a b l e t o t h e s o l u t i o n o f p r a c t i c a l p r o b l e m s o f s t a b i l i t y . T h i s c o n c l u s i o n has been drawn on t h e s t r e n g t h o f i n f o r m a t i o n f r o m t h e t r i a x i a l t e s t r e s u l t s , where t h e same <{>" i s o f t e n o b t a i n e d i n 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 . T h e r e f o r e , t h e r e s u l t s o f s t r e n g t h t e s t s u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s a l s o a r e o f t e n e x p r e s s e d i n t e r m s o f M o h r - C o u l o m b c r i t e r i o n and i t s p a r a m e t e r s c" and (J>'-. T h e n a c o m p a r i s o n o f t h e s e p a r a -m e t e r s w i t h t h e c o r r e s p o n d i n g p a r a m e t e r s u n d e r . t r i a x i a l c o m p r e s s i o n c o n d i t i o n s (a^ = a £ ) i n d i c a t e s w h e t h e r i n f l u e n c e s t h e f a i l u r e s t r e n g t h . An a l t e r n a t i v e way t o i n -v e s t i g a t e t h e v a l i d i t y o f any f a i l u r e c r i t e r i o n i s t o p l o t t e s t r e s u l t s on t h e o c t a h e d r a l p l a n e i n t h e p r i n c i p a l e f - ' f e c t i v e s t r e s s s p a c e and e x a m i n e w h i c h o f t h e r i g h t s e c t i o n s t h e y f i t mos t c l o s e l y . S p e c i f i c a t t e m p t s t o f o r m u l a t e c o n s t i t u t i v e r e l a t i o n s f o r s o i l s i n t h e s u b f a i l u r e r e g i o n have n o t met w i t h much s u c c e s s , b e c a u s e o f t h e c o m p l e x n a t u r e o f s o i l s i n v o l v i n g a n i s o t r o p y , n o n l i n e a r i t y , i n e l a s t i c i t y and t i m e d e p e n d e n c e . T h e s i m p l e r r e l a t i o n s h i p s t h a t m i g h t be a p p l i -c a b l e t o many m e t a l s ( i n w h i c h t h e v o l u m e t r i c s t r a i n i s a • f u n c t i o n o n l y o f mean n o r m a l s t r e s s , and o c t a h e d r a l s h e a r s t r a i n a f u n c t i o n o f o c t a h e d r a l s h e a r s t r e s s o n l y ) a r e n o t a p p l i c a b l e i n g e n e r a l t o s o i l s . S h e a r s t r e s s e s may c a u s e vo lume i n c r e a s e o r d e c r e a s e i n s o i l s a t c o n s t a n t mean n o r m a l 13 s t r e s s . S t u d y o f s t r e s s - s t r a i n r e s p o n s e o f s o i l s h a s , t h e r e f o r e , b e e n m a i n l y c o n f i n e d t o a g r a p h i c a l f o r m . Some s u c c e s s f u l a t t e m p t s , h o w e v e r , have been made ( H e n k e l S Wade 1 9 6 6 , S h i b a t a £ K a r u b e 1965 ) t o e x p r e s s p o r e p r e s s u r e change ( w h i c h a r e r e l a t e d t o t e n d e n c y t o vo lume c h a n g e ) i n c o n s o l i d a t e d u n d r a i n e d t e s t s on c l a y s , as a s i m p l e f u n c t i o n o f o c t a h e d r a l n o r m a l and s h e a r s t r e s s e s . T y p e s o f S h e a r T e s t s A n o n s y m m e t r i c a l o r t h r e e d i m e n s i o n a l s t a t e o f s t r e s s u n d e r p l a n e s t r a i n i s r e a l i s e d i n a d i r e c t s h e a r box t e s t . H o w e v e r , as a r e s e a r c h t o o l t h i s t e s t has many s h o r t -c o m i n g s w h i c h make t h e m e c h a n i c s o f s h e a r d i f f i c u l t t o i n t e r p r e t . I n d e t e r m i n a c y o f t h e s t r e s s f i e l d , n o n u n i f o r m i t y o f s t r a i n s l e a d i n g t o p r o g r e s s i v e f a i l u r e , p r e s e l e c t i o n o f t h e f a i l u r e p l a n e a n d r o t a t i o n o f p r i n c i p a l a x e s a r e some o f t h e s e r i o u s l i m i t a t i o n s o f t h e t e s t . The r e s u l t s f r o m t h i s t e s t , t h e r e f o r e , c a n n o t be m e a n i n g f u l l y u t i l i z e d t o i n v e s t i g a t e s o i l b e h a v i o u r u n d e r p l a n e s t r a i n c o n d i t i o n s . An i n d e p e n d e n t c o n t r o l o f a l l t h e t h r e e p r i n c i p a l s t r e s s e s on t h e f a c e s o f a p r i s m a t i c s p e c i m e n o f s o i l has been u s e d b y some i n v e s t i g a t o r s ( K j e l l m a n 1 9 3 6 , L o r e n z e t a l 1 9 6 5 , L o m i z e a n d K r y z h a n o v s k y 1 9 6 7 , and Ko and S c o t t 1 9 6 7 a ) . The t y p e s o f a p p a r a t u s e m p l o y e d f o r t h i s h a v e , i n g e n e r a l , a l l r i g i d o r . a l l f l e x i b l e b o u n d a r i e s t o t r a n s m i t s t r e s s e s t o 14 t h e s a m p l e . In mos t s o i l s , h o w e v e r , d e f o r m a t i o n s r e s u l t i n g b o t h d u r i n g c o n s o l i d a t i o n and d u r i n g s u b s e q u e n t s h e a r may be s u f f i c i e n t l y l a r g e t o c a u s e i n t e r f e r e n c e o f s u c h b o u n d a r i e s a t common e d g e s . C o n s e q u e n t l y , t h e use o f t h e s e a p p a r a t u s i s l i m i t e d t o t h o s e s o i l s w h i c h r e q u i r e v e r y s m a l l d e f o r m a t i o n s t o f a i l u r e . H o w e v e r , a p l a n e s t r a i n a p p a r a t u s i n w h i c h one s e t o f o p p o s i t e b o u n d a r i e s i s . f l e x i b l e (Wood 195 8 , C o r n f o r t h 1 9 6 4 , H e n k e l and Wade 1 9 6 6 , Duncan and S e e d 1966 ) h a s been s u c c e s s f u l l y u s e d t o s t u d y f a i l u r e c o n d i t i o n s u n d e r p l a n e d e f o r m a t i o n . The s i m p l e s h e a r a p p a r a t u s ( Roscoe 1953 ) a l s o i m p o s e s a p l a n e d e f o r m a t i o n b o u n d a r y c o n d i t i o n on a p r i s m a t i c s p e c i m e n o f s o i l . T h i s a p p a r a t u s has t h e a d v a n t a g e t h a t i t p r o d u c e s v e r y u n i f o r m d i s p l a c e m e n t s on t h e b o u n d a r i e s o f t h e s p e c i m e n , b u t t h i s u n i f o r m i t y i s o b t a i n e d a t t h e c o s t o f a v e r y c o m p l e x s t r e s s f i e l d . T h e t e s t ha s p r i m a r i l y been u s e d t o s t u d y t h e y i e l d i n g o f s o i l s . The r e s u l t s f r o m t h i s a p p a r a t u s h a v e n o t g e n e r a l l y b e e n i n t e r p r e t e d i n t e r m s o f t h e c o n v e n t i o n a l s t r e n g t h p a r a m e t e r s c T and (j>". A n o t h e r c l a s s o f t e s t s w h i c h a im a t s i m u l a t i n g a n o n s y m m e t r i c a l s t a t e o f s t r e s s on t h e s p e c i m e n , u t i l i z e s o l i d and h o l l o w c y l i n d r i c a l s a m p l e s , where f a i l u r e i s c a u s e d by a x i a l t o r s i o n c o u p l e d w i t h a x i a l l o a d . In t h e s e t e s t s a p a r t f r o m t h e i n h o m o g e n i t y o f s t r e s s - s t r a i n f i e l d s due t o r i g i d end c a p s , s t r e s s e s and s t r a i n s a r e n o t u n i f o r m i n t h e r a d i a l a n d t a n g e n t i a l d i r e c t i o n s , b e c a u s e where t o r s i o n a l 15 moment i s used to induce f a i l u r e , shear s t r a i n s vary with the distance from the centre o.- r o t a t i o n . In hollow c y l i n d e r s , however, the nonuniformity of t o r s i o n a l s t r a i n i s minimised. In hollow c y l i n d e r t e s t s f a i l u r e can a l s o be induced w i t h -out t o r s i o n i f independent c o n t r o l i s e x e r c i s e d on pressures i n s i d e and out s i d e of the bore. Stresses and s t r a i n s , how-ever, s t i l l remain nonuniform as the two p r i n c i p a l s t r e s s e s , r a d i a l and t a n g e n t i a l , vary throughout the th i c k n e s s of the c y l i n d e r . F a i l u r e s t a r t s at e i t h e r the i n s i d e or outside of the bore, depending on s t r e s s path t o f a i l u r e , and progresses towards the opposite side along the t h i c k n e s s . This leads to a progressive f a i l u r e . Hence i n t e r p r e t a t i o n of t e s t r e s u l t s from the above types of t e s t s appears d i f -f i c u l t with most s o i l s . Furthermore, hollow c y l i n d e r t e s t cannot be used w i t h undisturbed s o i l s . When e v a l u a t i n g the t e s t r e s u l t s of various i n -v e s t i g a t o r s i t i s , t h e r e f o r e , imperative to recognise the l i m i t a t i o n s o f the t e s t type i n respect of i t s producing a r e l a t i v e l y homogeneous s t a t e o f s t r e s s or s t r a i n i n the e n t i r e specimen. From the foregoing d i s c u s s i o n i t appears tha t t e s t s i n v o l v i n g p r i s m a t i c specimens may not s u f f e r from s t r e s s - s t r a i n inhomogenity to as la r g e an extent as the hollow c y l i n d e r t e s t s , o r sol-id c y l i n d e r t e s t s with t o r s i o n . 16 T e s t R e s u l t s Mos t o f t h e i n v e s t i g a t i o n s c o n c e r n i n g s o i l b e h a v i o u r u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s h a v e been c o n f i n e d t o c o h e s i o n l e s s s o i l s . I n f o r m a t i o n on c l a y s i s v e r y l i m i t e d and c o v e r s o n l y n o r m a l l y l o a d e d r e m o l d e d c l a y s . H a r d l y any r e s u l t s have been r e p o r t e d on u n d i s t u r b e d c l a y s . I t h a s been f o u n d by some i n v e s t i g a t o r s ( B i s h o p 8 E l d i n 195 3 , K i r k p a t r i c k 195 7 , C o m f o r t h 1 9 6 4 , Wu e t a l 1963 ) t h a t t h e v a l u e o f was t h e same u n d e r t r i a x i a l c o m -p r e s s i o n a n d e x t e n s i o n - t h u s s u p p o r t i n g t h e M o h r - C o u l o m b c r i t e r i o n . In c o n t r a s t H a b i b ( 1 9 5 3 ) , P e l t i e r ( 1957 ) and H a y t h o r n t h w a i t e (1960 ) showed l o w e r v a l u e s w h e r e a s Broms 8 C a s b a r i a n (1965 ) showed h i g h e r v a l u e s o f cf>' i n e x t e n s i o n . In a s e t o f t r i a x i a l 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 a s a n d i n w h i c h b o t h l o c a l a n d o v e r a l l d e f o r m a t i o n o f t h e s a m p l e s were m e a s u r e d , Roscoe e t a l ( 1963 ) c o n c l u d e d , t h a t a l t h o u g h t h e a n a l y s i s o f t h e t e s t r e s u l t s on t h e b a s i s o f o v e r a l l d e f o r m a t i o n s s u p p o r t s M o h r - C o u l o m b c r i t e r i o n , u s i n g t h e l o c a l s t r e s s e s i n t h e c e n t r a l p o r t i o n o f t h e s p e c i m e n s , t h e f a i l u r e c r i t e r i o n i s f o u n d t o a p p r o a c h t h e e x t e n d e d T r e s c a o r e x t e n d e d von M i s e s c r i t e r i o n . B i s h o p ( 1 9 6 6 ) , h o w e v e r , a r g u e d t h a t t h e e x t e n d e d T r e s c a o r e x t e n d e d von M i s e s c r i t e r i a c a n n o t r e p r e s e n t t h e b e h a v i o u r o f d e n s e c o h e s i o n -l e s s m a t e r i a l s ( o r c' - 0 m a t e r i a l s ) h a v i n g a c o m p r e s s i o n o f more t h a n 3 6 . 9 ° . Above t h i s l i m i t i n g v a l u e o f t}»', 17 t h e r i g h t s e c t i o n s o f f a i l u r e s u r f a c e s f o r t h e s e c r i t e r i a p r o j e c t i n t o t h e n e g a t i v e o r t e n s i l e e f f e c t i v e s t r e s s s p a c e , w h i c h o b v i o u s l y i s m e a n i n g l e s s f o r a c " - 0 m a t e r i a l . S i m . M a r c o n c l u s i o n s were drawn by B a r d e n and K h a y a t t ( 1 9 6 6 ) . T e s t s on p r i s m a t i c s p e c i m e n s o f s a n d l o a d e d by a l l r i g i d b o u n d a r i e s and f a i l e d u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s have b e e n r e p o r t e d by K j e l l m a n ( 1 9 3 6 ) . He o b s e r v e d a s i z e a b l e i n c r e a s e (up t o 8 ° ) i n t h e v a l u e o f (J>'for a d e n s e s a n d u n d e r s t r e s s s t a t e s a £ > > compa red t o t h e t r i -a x i a l c o m p r e s s i o n s t a t e , = 0 3 . U s i n g K j e l l m a n ' s a p p a r a t u s J a c o b s o n (195 7) d rew s i m i l a r c o n c l u s i o n s ; he f o u n d t h a t t h e v a l u e o f <j>' f o r s a n d s i n c r e a s e d as t h e t e s t d e p a r t e d f r o m t h e s y m m e t r i c c o m p r e s s i o n (a^ = a^) s t a t e o f s t r e s s and became as much as 6 ° h i g h e r when t h e o t h e r l i m i t o f s y m m e t r i c e x t e n s i o n (a^ = cr£) was a p p r o a c h e d . In a s i m i l a r a p p a r a t u s L o r e n z e t a l ( 1965 ) made a s t u d y o f s t r e s s s t r a i n r e s p o n s e o f a d r y s a n d u n d e r p l a n e s t r a i n . - T h e y r e p o r t e d an a l m o s t c o n s t a n t v a l u e o f i r r e s p e c t i v e o f t h e i n i t i a l p o r o s i t y o f s a n d . F u r t h e r m o r e , t h e y d i d n o t o b s e r v e any v o l u m e e x -p a n s i o n d u r i n g s h e a r , e v e n f o r t h e l o w e s t i n i t i a l p o r o s i t y . The t e s t s r e p o r t e d were made a t m o d e r a t e p r e s s u r e s . T h e s e o b s e r v a t i o n s a r e a p p a r e n t l y i n c o n f l i c t w i t h t h o s e f r o m t h e c o n v e n t i o n a l t r i a x i a l t e s t s . A l l f l e x i b l e p r i n c i p a l s t r e s s b o u n d a r i e s on t h e f a c e s o f a p r i s m a t i c s p e c i m e n were u s e d by Ko and S c o t t (1967a ) a n d L o m i z e £ K r y z h a n o v s k y ( 1 9 6 7 ) , f o r t h e s t u d y o f 18 deformation and strength c h a r a c t e r i s t i c s o f sands, under nonsymmetrical s t a t e s of s t r e s s . Scott and Ko found l a r g e v a r i a t i o n i n the value o f 4)" obtained i n t h e i r t e s t device under s t r e s s s t a t e corresponding to = 0 g , when compared to that obtained i n the conventional t r i a x i a l t e s t . Un-f o r t u n a t e l y , an a r b i t r a r y d e f i n i t i o n o f f a i l u r e was used to analyse t e s t r e s u l t s , because t e s t s could not be c a r r i e d to the usual d e f i n i t i o n of f a i l u r e due to extremely l i m i t e d deformations p o s s i b l e i n the t e s t device. T h e i r r e s u l t s showed that the value o f increased by 4° to 8° (depending on i n i t i a l p o r o s i t y ) as the s t r e s s s t a t e s departed from symmetric compression, ~ o^> towards nonsymmetrical s t a t e s and f i n a l l y reached the other l i m i t , the symmetric e x t e n s i o n , °2 = a i a n c^ Scott 196 8). The shape of f a i l u r e surface on an o c t a h e d r a l plane was found to be curved and d i d not f i t any o f the f a i l u r e c r i t e r i a discussed above. Lomize and Kryzhanovsky a l s o found that the value of was s i g n i f i c a n t -l y i n f l u e n c e d by a^. An increase of as much as 9° to 22° i n the value of was observed when the state of s t r e s s was v a r i e d from that of symmetric compression to the intermediate nonsymmetrical s t a t e s and f i n a l l y taken to the other l i m i t of symmetry, = a£. Their experimental r e s u l t s d i d not . favour any o f the commonly accepted c r i t e r i o n of f a i l u r e . Consequently they formulated a new f a i l u r e c r i t e r i o n , which p o s t u l a t e d , t h a t at f a i l u r e TQ ^ i s not d i r e c t l y p r o p o r t i o n a l to a" (as assumed i n Extended von Mises c r i t e r i o n ) but i s oct 19 a c o m p o s i t e f u n c t i o n o f °QC^. ^nd ( a^a^a^ ) , t h e t h i r d i n -v a r i a n t o f t h e s t r e s s t e n s o r . " h i s s u g g e s t i o n f a v o u r s the p o s t u l a t e o f Newmark ( 1 9 6 0 ) , who c o n s i d e r e d t h a t t he f o r m u -l a t i o n o f f a i l u r e c o n d i t i o n m i g h t i n v o l v e a l l t h e t h r e e i n v a r i a n t s o f t h e s t r e s s t e n s o r : i . ^ . . , a ' . . . T +. and ' ' OCT' OCt S t u d i e s on t h e b e h a v i o u r o f c o h e s i o n l e s s m a t e r i a l s u n d e r p l a n e s t r a i n c o n d i t i o n s have been done u s i n g l o n g r e c t a n g u l a r s p e c i m e n s w i t h one p a i r o f f l e x i b l e l o a d i n g b o u n d a r i e s ( L e u s s i n k and W i t t k e 1 9 6 3 , L e u s s i n k 1 9 6 5 , C o r n f o r t h 1 9 6 4 , M a r s a l 1 9 6 5 ) . B o t h t h e o r e t i c a l and e x p e r i m e n t a l r e s u l t s show t h a t t h e s t r e n g t h u n d e r p l a n e s t r a i n e x c e e d s t h e c o r r e s p o n d i n g t r i a x i a l v a l u e . The d i f f e r e n c e i n e q u i -v a l e n t <j>" v a r i e s w i t h d i f f e r e n t i n v e s t i g a t o r s . C h r i s t e n s o n ( 1 9 6 1 ) , C o r n f o r t h (1964) and L e u s s i n k (1965 ) r e p o r t e d an i n c r e a s e i n t h e v a l u e o f <j>' f o r s a n d s f r o m 2 ° t o 4 ° , whe reas M a r s a l ( 1965 ) showed an i n c r e a s e o f as much as 1 3 ° f o r a c o m p a c t e d r o c k f i l l m a t e r i a l . U n d e r p l a n e s t r a i n , vo lume c h a n g e s and s t r a i n a t f a i l u r e were f o u n d t o be a b o u t one t h i r d o f t h o s e o b s e r v e d u n d e r t h e c o r r e s p o n d i n g t r i a x i a l c o n d i t i o n s ( C o r n f o r t h 19 6 4 , F i n n , Wade and Lee 1 9 6 7 ) . H o w e v e r , t h e r a t e o f v o l u m e c h a n g e a t f a i l u r e was o b s e r v e d t o be a l m o s t t h e same i n t h e two t y p e s o f t e s t s , f o r t h e same i n i t i a l p o r o s i t y ( C o r n f o r t h 1 9 6 4 ) . In t o r s i o n t e s t s on s o l i d s a n d c y l i n d e r s ( H a b i b 1953 ) and on h o l l o w c y l i n d e r s o f a r e m o l d e d s i l t 20 (Haythornthwaite I 9 6 0 , 1963 ) i t was found t h a t considerable departure from the Mohr-Coulomb c r i t e r i o n occurred under s t r e s s s t a t e s a-^ > >'O-^' ^ v a ^ u e °f <{>' w a s reported to be 1 1 ° higher than the t r i a x i a l compression value by Habib ( 1 9 5 3 ) . Using hollow c y l i n d r i c a l sand samples, K i r k p a t r i c k ( 1957 ) observed an increase of about 2 ° i n the value of under c o n d i t i o n s approximating plane s t r a i n , whereas Whitman and Luscher ( 1962 ) reported a 6 ° i n c r e a s e . S i m i l a r c o n c l u s i o n s were drawn f o r sands by Wu, Loh and Malvern (1963 ) , when f a i l u r e occurred under a^ ' > °2 > a3 s t a ' t e s °f s t r e s s . I t , t h e r e f o r e , appears t h a t the l i t e r a t u r e todate p o i n t s out a sense of disagreement on the v a l i d i t y of the Mohr-Coulomb f a i l u r e c r i t e r i o n . There does not appear to be a general acceptance o f t h i s c r i t e r i o n even under t h e r a x i a l l y symmetric compression and extension s t a t e s of s t r e s s i n the conventional t r i a x i a l t e s t . Under nonsymmetrical s t a t e s of s t r e s s i n c l u d i n g the case of plane s t r a i n there seems a general agreement on the strengt h o f sand being higher when compared to the conventional t r i a x i a l compression value. However, the magnitude of the d i f f e r e n c e v a r i e s g r e a t l y with d i f f e r e n t i n v e s t i g a t o r s . This could be a t t r i b u t e d p a r t l y to the p e c u l i a r i t i e s of the t e s t devices and a r b i t r a r y d e f i n i t i o n s of f a i l u r e i n some cases. Where attempts have been made to e s t a b l i s h f a i l u r e surface f o r sands, i t has been g e n e r a l l y found that the surface does not favour any one o f the f a i l u r e 21 c r i t e r i a d i s c u s s e d a b o v e . I t seems r e a s o n a b l e t o e x p e c t t h e vo lume c h a n g e and s t r a i n a t f a i l u r e u n d e r p l a n e d e f o r m a t i o n t o be s m a l l e r t h a n the c o r r e s p o n d i n g t r i a x i a l v a l u e s . U n d e r p l a n e s t r a i n , t h e s a n d g r a i n s h a v e a more r e s t r i c t e d movement u n d e r i m p o s e d s h e a r s t r e s s e s c o m p a r e d t o t h e s y m m e t r i c s t a t e s o f s t r e s s , t h e r e b y c a u s i n g l e s s s l i p p a g e p a s t e a c h o t h e r a n d c o n s e q u e n t l y l e s s vo lume change a t any s t a g e o f s h e a r i n g p r o c e s s . H o w e v e r , t h e r e i s a d i s a g r e e m e n t on t h e s i g n o f vo lume c h a n g e s d u r i n g s h e a r . L o r e n z e t a l ( 1965 ) d i d n o t o b s e r v e any n e t e x p a n s i o n i n s h e a r u n d e r p l a n e d e f o r m a t i o n i r r e s p e c t i v e o f t h e i n i t i a l p o r o s i t y i n c o n t r a s t t o t h e p a r a l l e l o b s e r v a t i o n s by C o r n f o r t h (1964 ) a n d F i n n , Wade and Lee ( 1 9 6 7 ) . F o r a dense s a n d u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s e s , Ko and S c o t t ( 1 9 6 7 b ) d i d n o t o b s e r v e any c o m p r e s s i o n i n t h e e a r l y s t a g e s o f s h e a r i n c o n t r a s t t o t h e c o n v e n t i o n a l t r i a x i a l c o m p r e s s i o n t e s t . Thus t h e r e i s a n e e d t o f u r t h e r c l a r i f y t h e s t r e s s - s t r a i n r e l a t i o n s and f a i l u r e c o n d i t i o n s f o r s a n d s u n d e r s t r e s s s t a t e s o t h e r t h a n t h o s e i n t h e c o n v e n t i o n a l t r i a x i a l t e s t . O t h e r f e a t u r e s o f s i g n i f i c a n t i n t e r e s t may be t h e i n f l u e n c e o f s t r e s s p a t h t o f a i l u r e , a n i s o t r o p y i n c o n s o l i d a t i o n and r o t a t i o n o f p r i n c i p a l a x e s . T h e s e v a r i a b l e h a v e r e c e i v e d l i t t l e a t t e n t i o n u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s . B e h a v i o u r o f s a t u r a t e d , r e m o l d e d n o r m a l l y l o a d e d c l a y s i n n o n s y m m e t r i c a l s t r e s s f i e l d u s i n g p r i s m a t i c 2 2 s p e c i m e n s was s t u d i e d by S h i b a t a and K a r u b e ( 1965 ) and i n p l a n e s t r a i n by H e n k e l £ Wade (196 6 ) , U s i n g i s o t r o p i c c o n s o l i d a t i o n and s t r e s s p a t h t o f a i l u r e as (o^-cfg) = c o n s t , S h i b a t a £ K a r u b e (1965) showed t h a t t he r e l a t i v e v a l u e o f o"2 i n f l u e n c e d t h e s t r e s s - s t r a i n r e s p o n s e ; an i n c r e a s e i n (o^-cfg) r e s u l t e d i n a l i n e a r d e c r e a s e i n f a i l u r e s t r a i n . T h e i r r e s u l t s showed t h a t Moh r-Cou lomb c r i t e r i o n u n d e r -e s t i m a t e d t h e s t r e n g t h o f c l a y s u n d e r n o n s y m m e t r i c a l s t r e s s s t a t e s . H e n k e l and Wade (1966 ) p e r f o r m e d t e s t s on K 0 -c o n s o l i d a t e d s a m p l e s , a n d f o u n d t h a t <j>" was l a r g e r by a b o u t 1 . 2 ° and f a i l u r e s t r a i n o n l y a t h i r d when c o m p a r e d to t h e c o r r e s p o n d i n g t r i a x i a l c o n d i t i o n s . M e a s u r e m e n t o f showed t h a t t h e r a t i o c r a £ s t a y s c o n s t a n t d u r i n g s h e a r a t t h e e n d o f K Q - c o n s o l i d a t i o n v a l u e . B o t h S h i b a t a £ K a r u b e (1965) and H e n k e l £ Wade (1966) f o u n d t h a t p o r e p r e s s u r e s d u r i n g s h e a r were g o v e r n e d by o c t a h e d r a l s t r e s s e s a n d s u g g e s t e d t h e f o l l o w i n g r e l a t i o n s : Au = A a o c t + a o c t f ( A T o c t V A a o c t ) ( 2 . 6 ) S h i b a t a £ K a r u b e •: . ,. ( 2 . 7 ) H e n k e l £ Wade A u = A a o c t + a A x o c t where Au i s t h e c h a n g e i n p o r e p r e s s u r e and A T o c ^ - and A a o c t a r e c n a n S e s i- n o c t a h e d r a l s h e a r and n o r m a l s t r e s s r e s p e c t i v e l y ; f s t a n d s f o r " f u n c t i o n o f " a n d " a " i s a p o r e p r e s s u r e p a r a m e t e r . S h i b a t a £ K a r u b e (1965 ) f o u n d t h a t b e l o w a c e r t a i n c r i t i c a l v a l u e o f A t _ _ t , Au was a f u n c t i o n 23 o f A°" + o n l y and h e n c e i n d e p e n d e n t o f Ax OCX j - x o c t F o r r e m o l d e d n o r m a l l y c o n s o l i d a t e d c l a y s , h o l l o w c y l i n d e r t e s t s by Wu, L o h , and M a l v e r n (1963 ) s u p p o r t t he v a l i d i t y o f Moh r-Cou lomb f a i l u r e c r i t e r i o n i n t h r e e d i m e n -s i o n a l e f f e c t i v e s t r e s s s p a c e . In c o n t r a s t , i n s i m i l a r t e s t s by Broms and C a s b a r x a n ( 1 9 6 5 ) , t h e r e l a t i v e v a l u e o f o"^  was shown t o i n f l u e n c e t h e v a l u e o f cb' t o a c o n s i d e r -a b l e e x t e n t . S t a r t i n g f r o m t h e s y m m e t r i c c o m p r e s s i o n s t a t e o f s t r e s s , i n c r e a s i n g t h e v a l u e o f r e s u l t e d i n an i n c r e a s e i n t h e v a l u e o f cb" w h i c h a p p r o a c h e d 7 ° h i g h e r a t t h e o t h e r e x t r e m e l i m i t o f cr^* x n e s y m m e t r i c e x t e n s i o n s t a t e . F o r a n o r m a l l y c o n s o l i d a t e d r e m o l d e d k a o l i n i t e , Broms and Ratnam (1963 ) a l s o n o t e d an i n c r e a s e i n cb** v a l u e by a b o u t 4- 1/2 ° u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s when c o m p a r e d t o t h e t r i a x i a l c o m p r e s s i o n v a l u e . T h u s , f o r r e m o l d e d n o r m a l l y c o n s o l i d a t e d c l a y s a g r e e m e n t on t h e . v a l i d i t y o f M o h r - C o u l o m b f a i l u r e c r i t e r i o n i s l a c k i n g . U n f o r t u n a t e l y , t h e e x i s t i n g i n f o r m a t i o n i s e x t r e m e l y l i m i t e d and i t i s n o t p o s s i b l e t o draw e v e n a g e n e r a l p i c t u r e o f t h e s t r e s s - s t r a i n and s t r e n g t h c h a r a c t e r -i s t i c s o f c l a y s u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s . A g a i n , t h e i n f l u e n c e o f a n i s o t r o p y i n c o n s o l i d a t i o n , s t r e s s p a t h t o f a i l u r e and r o t a t i o n o f p r i n c i p a l a x e s have been g i v e n l i t t l e c o n s i d e r a t i o n , a l t h o u g h i n t h e f i e l d t h e s e s i t u a t i o n s a r e o f t e n e n c o u n t e r e d . 24 Some S i g n i f i c a n t F e a t u r e s o f T y p e s o f A p p a r a t u s E m p l o y e d i n t h e Above I n v e s t i g a t i o n s S o i l t e s t i n g u n d e r t h r e e d i m e n s i o n a l s t a t e s o f s t r e s s c o n s t i t u t e s a h i g h l y s p e c i a l i s e d r e s e a r c h f i e l d . The m e c h a n i c a l d i f f i c u l t i e s e n c o u n t e r e d i n t h e d e s i g n o f s u i t a b l e t e s t i n g e q u i p m e n t a r e numerous and t h e o p e r a t i o n o f a p p a r a t u s g e n e r a l l y i n v o l v e d . Such t y p e s o f t e s t s a r e e v i d e n t l y n o t s u i t e d f o r r o u t i n e p u r p o s e s , y e t t h e y a r e e s s e n t i a l t o c l a r i f y c e r t a i n a s p e c t s o f t h e m e c h a n i c a l b e h a v i o u r o f s o i l s w h i c h c a n n o t be a t t e m p t e d i n t h e c o n v e n -t i o n a l t y p e s o f a p p a r a t u s . I t i s n o t i n t e n d e d h e r e t o p r e s e n t t h e d e t a i l s a b o u t t h e v a r i o u s t y p e s o f e q u i p m e n t so f a r e m p l o y e d f o r s o i l t e s t i n g u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s . The e m p h a s i s o f d i s c u s s i o n w i l l be p l a c e d on the p r i n c i p l e s i n v o l v e d i n s u c h t y p e s o f t e s t i n g and on t h e m a j o r d i f f i -c u l t i e s i n h e r e n t i n t h e t e c h n i q u e . I t i s p r o p o s e d ; t o d i s c u s s o n l y t h o s e a p p a r a t u s w h i c h a r e d e s i g n e d t o t e s t p r i s m a t i c s p e c i m e n s . F o r r e a s o n s s t a t e d e a r l i e r , use o f p r i s m a t i c s p e c i m e n s i n i n v e s t i g a t i n g s o i l b e h a v i o u r u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s a p p e a r s s u p e r i o r t o t h e use o f h o l l o w o r s o l i d c y l i n d r i c a l s p e c i m e n s . K j e l l m a n (1936 ) and L o r e n z e t a l (1965 ) u s e d c u b i c s a m p l e s • ' l o a d e d on a l l f a c e s by r i g i d b o u n d a r i e s . Such an a r r a n g e m e n t p u t s s e r i o u s r e s t r i c t i o n s on t h e p e r m i s s i b l e d e -f o r m a t i o n s . As a c o n s e q u e n c e o n l y dense c o h e s i o n l e s s 25 m a t e r i a l s r e q u i r i n g s m a l l f a i l u r e s t r a i n c o u l d be t e s t e d t o f a i l u r e . L o r e n z e t a l ( 1965 ) e m p l o y e d s t r a i n gauge b l o c k s t o measu re t h e i n t e r m e d i a t e p r i n c i p a l s t r e s s i n t h e i r p l a n e s t r a i n t e s t s , b u t were n o t s u r e o f t h e m e a s u r e d v a l u e s , a p -p a r e n t l y due t o i m p e r f e c t i o n s o f t h e t e s t d e v i c e . The use o f a l l f l e x i b l e l o a d i n g b o u n d a r i e s on c u b i c s a m p l e s o f s a n d , as r e p o r t e d by Ko and S c o t t ( 1967a ) and L o m i z e and K r y z h a n o v s k y ( 1 9 6 7 ) , ha s t h e a d v a n t a g e o f p r o v i d i n g p r a c t i c a l l y t r u e p r i n c i p a l s t r e s s l o a d i n g b o u n d a r -i e s , and as a r e s u l t s h o u l d a p p r o a c h a homogeneous s t a t e o f s t r e s s a n d s t r a i n t h r o u g h o u t t h e e n t i r e s p e c i m e n . How-e v e r , s o i l s r e q u i r i n g l a r g e d e f o r m a t i o n s d u r i n g c o n s o l i d a t i o n and s u b s e q u e n t s h e a r c a n n o t be t e s t e d t o f a i l u r e b e c a u s e o f t h e i n t e r f e r e n c e o f f l e x i b l e b o u n d a r i e s a t common e d g e s , w h i l e u n d e r d i f f e r e n t p r e s s u r e s . The d e v i c e s , t h e r e f o r e , a p p e a r t o h a v e a l i m i t e d p o t e n t i a l . . Ko and S c o t t (196 7a) made u s e o f a r i g i d s e p a r a t i n g f r ame t o k e e p t h e f l e x i b l e membrane b o u n d a r i e s f r o m i n t e r f e r i n g w i t h e a c h o t h e r . A s i g n i f i c a n t p o r t i o n o f t h i s f r a m e ( a b o u t 1/4 " ) p r o j e c t s i n t o a p p r o x i m a t e l y 3.5 i n c h c u b i c s a m p l e a l o n g a l l t h e e d g e s . I t c a n be e x p e c t e d , t h e r e f o r e , t h a t t h e f r a m e m i g h t c a r r y a s i g n i f i c a n t p o r t i o n o f t he a p p l i e d s t r e s s e s , c a u s i n g t h e s t r e s s and s t r a i n f i e l d s t o be f a r f r o m homogeneous ( G r e e n 1 9 6 7 , B e l l 1 9 6 8 , A r t h u r 6 M e n z i e s 1 9 6 8 ) . : T h i s may a l s o e x p l a i n t h e u n u s u a l l y h i g h v a l u e s o f s a n d , Ko and S c o t t o b t a i n e d i n t h e i r t e s t d e v i c e , f o r s y m m e t r i c c o m p r e s s i o n 26 s t a t e o f s t r e s s , when c o m p a r e d t o t h o s e o b t a i n e d i n a c o n -v e n t i o n a l t r i a x i a l c o m p r e s s i o n t e s t . In f a c t , t h e s t r e s s -s t r a i n c u r v e s r e p o r t e d a r e s t e e p l y r i s i n g e v e n a t t h e p o i n 1 ; o f d e f i n e d f a i l u r e and show no s i g n o f f l a t t e n i n g o u t a t t h e s t r a i n s t h e t e s t s were t e r m i n a t e d . L o m i z e and K r y z h a n o v s k y ( 1 9 6 7 ) , on t h e o t h e r h a n d , d i d n o t s t a t e how t h e y g o t o v e r t h e p r o b l e m o f k e e p i n g f l e x i b l e r u b b e r membrane b o u n d a r i e s f r o m i n t e r f e r i n g w i t h e a c h o t h e r w h i l e u n d e r d i f f e r e n t p r e s s u r e s . In t h e t e s t i n g d e v i c e s e m p l o y e d f o r i n v e s t i g a t i n g s o i l b e h a v i o u r u n d e r p l a n e s t r a i n , l o n g r e c t a n g u l a r s p e c i m e n s a r e o f t e n u s e d . In g e n e r a l one p a i r o f l o a d i n g b o u n d a r i e s was made f l e x i b l e (Wood 195 8, C o r n f o r t h 1 9 6 4 , H e n k e l and Wade 1 9 Q 6 , L e u s s i n k and W i t t k e 1 9 6 3 , M a r s a l 1 9 6 5 , Duncan and Seed 1 9 6 6 ) . T h e s e r e c t a n g u l a r s p e c i m e n s h a d t h e h e i g h t -w i d t h r a t i o b e t w e e n 2 and 3 , as i n a c o n v e n t i o n a l t r i a x i a l s p e c i m e n , and l e n g t h much l a r g e r -than t h e w i d t h . C o n d i t i o n o f z e r o d e f o r m a t i o n was m a i n t a i n e d i n t h e l o n g i t u d i n a l d i r e c t i o n o f t h e s p e c i m e n by means o f one p a i r o f r i g i d e n d p l a t e s h e l d a t a f i x e d d i s t a n c e a p a r t . F r i c t i o n a l d r a g be tween t h e s e p l a t e s and t h e s p e c i m e n was k e p t t o a min imum by u s i n g p o l i s h e d p l a t e s w i t h a t h i n l a y e r o f s i l i c o n e g r e a s e be tween p l a t e and s a m p l e membrane . I f l e n g t h t o w i d t h r a t i o o f t h e s a m p l e i s l a r g e , a c o n d i t i o n o f p l a n e d e f o r m a t i o n i s c l o s e l y a p p r o a c h e d n e a r t h e c e n t r e o f t h e s p e c i m e n . Thus t he end e f f e c t s o f f r i c t i o n b e t w e e n p l a t e 27 and samp le membrane a r e m i n i m i s e d . . H o w e v e r , t h e e n d f r i c t i o n d o e s i n f l u e n c e t h e m e a s u r e d v a l u e o f v e r t i c a l s t r e s s on h o r i z o n t a l f a c e s , and s h o u l d be c o r r e c t e d a c c o r d i n g l y . No a t t e m p t s were made t o measu re f r i c t i o n d i r e c t l y . C o r r e c t i o n t o t h e v e r t i c a l d e v i a t o r s t r e s s was a p p l i e d on t h e b a s i s o f work done i n m o v i n g t h e s p e c i m e n a l o n g t h e e n d p l a t e s (Wood 1 9 5 8 ) . G e n e r a l l y a p r e s s u r e c e l l was u s e d t o e n c l o s e t h e s p e c i m e n ( s i m i l a r t o t h a t f o r a t r i a x i a l t e s t ) and t h e f l u i d p r e s s u r e f u r n i s h e d one o f t h e p r i n c i p a l s t r e s s e s . F o r d r y c o h e s i o n l e s s m a t e r i a l s , vacuum o n p o r e s p a c e s e r v e d t o p r o v i d e t h e c o n f i n i n g p r e s s u r e and no s e p a r a t e c e l l was n e c e s s a r y . ^ - c o n s o l i d a t i o n was a c h i e v e d ( C o r n f o r t h 1964 , H e n k e l a n d Wade 1966 ) t h r o u g h t h e use o f a n u l l d e v i c e s i m i l a r t o t h e l a t e r a l s t r a i n i n d i c a t o r ( B i s h o p and H e n k e l 1 9 6 2 ) . F o r c l a y s , t h i s t e c h n i q u e n e c e s s i t a t e d i n t e r m i t t e n t and s l o w i n c r e a s e o f b o t h c e l l and d e v i a t o r p r e s s u r e , a n d , b e c a u s e o f t h e l a r g e s i z e s p e c i m e n s ( 1 6 " x 4 " x 2 " ) , t o o k as l o n g a s one t o t h r e e weeks t o c o n s o l i d a t e . The s h e a r s t a g e o f t h e t e s t s u n d e r p l a n e s t r a i n c o n d i t i o n s , c o n s i s t e d o f i n c r e a s i n g t h e v e r t i c a l l o a d on t h e r e c t a n g u l a r l o a d i n g c a p . I t i s e s s e n t i a l t o p r e v e n t c o m p l e t e l y t h e r o t a t i o n o f t h e l o a d i n g c a p t o k e e p i t f r o m i n t e r f e r i n g w i t h t h e r i g i d e n d p l a t e s d u r i n g i t s v e r t i c a l movement . T h i s was a c h i e v e d by Wood ( 1 9 5 8 ) , C o r n f o r t h (1964 ) and H e n k e l and Wade ( 1 9 6 6 ) , by l o a d i n g t h e c a p a t t h e two 28 q u a r t e r p o i n t s . No s u c h a r r a n g e m e n t a p p e a r s t o have been a d o p t e d by Duncan and Seed ( 1 9 6 o ) . I n p l a n e s t r a i n a p p a r a t u s t h e m e a s u r e m e n t o f i n t e r m e d i a t e p r i n c i p a l s t r e s s , , i n t he l o n g i t u d i n a l d i r e c t i o n o f s p e c i m e n was done by t h e use o f a n u l l t e c h n i q u e s i m i l a r i n p r i n c i p l e t o t h a t u s e d i n p o r e w a t e r p r e s s u r e m e a s u r e m e n t s (Wood 195 8, C o r n f o r t h 1 9 6 4 , H e n k e l £ Wade 1 9 6 6 , L e u s s i n k and W i t t k e 1 9 6 3 ) . The r i g i d end p l a t e s m a i n t a i n i n g p l a n e d e f o r m a t i o n were c o n n e c t e d t h r o u g h f o u r s y m m e t r i c a l l y p l a c e d t i e b a r s . One o f t h e end p l a t e s i n c o r p o r a t e d a w a t e r p r e s s u r e c e l l , w i t h a f l e x i b l e r u b b e r d i a p h r a g m w h i c h was c o n n e c t e d t o t h e n u l l i n d i c a t o r . T h i s t y p e o f a r r a n g e m e n t has a f i n i t e f l e x i b i l i t y and t h e c o n d i t i o n o f z e r o s t r a i n had t o be m a i n t a i n e d by c o n t i n u o u s l y a d j u s t i n g t h e m e r c u r y t h r e a d o f t h e n u l l i n d i c a t o r t o a c c o u n t f o r t h e e l o n g a t i o n o f t i e r o d s , l e a d s e t c . u n d e r p r e s s u r e c h a n g e s . T h i s i s a t e d i o u s p r o c e d u r e when t h e s h e a r t e s t i s o f a l o n g d u r a t i o n (12 d a y s f o r 1 6 " x 4 " x 2 " c l a y s a m p l e ; H e n k e l and Wade 1 9 6 6 ) . I t a p p e a r s , t h e r e f o r e , t h a t s o i l t e s t i n g i n a n o n s y m m e t r i c a l s t r e s s f i e l d may i n v o l v e some f o r m i d a b l e p r o b l e m s . . S p e c i a l box s h a p e d membranes a r e n e e d e d t o e n c l o s e t h e s p e c i m e n s i f e d g e s o f t h e s p e c i m e n a r e t o be r e a s o n a b l y s h a r p . The a p p a r a t u s p r e f e r a b l y s h o u l d be a d a p t a b l e f o r t e s t i n g t o f a i l u r e b o t h s a n d s and c l a y s . In p l a n e s t r a i n a p p a r a t u s l o n g s p e c i m e n s a r e p r e f e r a b l e t o o f f s e t t h e e f f e c t o f e n d f r i c t i o n , b u t t o o b i g a s i z e i s 29 d i f f i c u l t to handle, makes the t e s t i n g times u n n e c e s s a r i l y long and i s i m p r a c t i c a l f o r undisturbed c l a y because o f l i m i t a t i o n on s i z e o f tube samplers. S e t t i n g up a satu-r a t e d r e c t a n g u l a r c l a y specimen i f always a problem, as i t i s d i f f i c u l t to get a i r out from between the sample and the membrane. Very close t o l e r a n c e s are needed i n machin- .. ing the moving boundaries to prevent t h e i r i n t e r f e r e n c e w i t h other r i g i d boundaries. Use o f water pressure c e l l s and t i e rods to ho l d end p l a t e s at f i x e d distance apart i n a plane s t r a i n apparatus, n e c e s s i t a t e s a cumbersome manual c o n t r o l with a p r e c a l i b r a t e d n u l l device. K Q c o n s o l i d a t i o n stage i s unusually prolonged as the st r e s s e s have to be brought on the sample g r a d u a l l y . In the plane s t r a i n device to be described h e r e i n , an attempt has been made to incor p o r a t e some improvements over the devices c u r r e n t l y i n use. Some s i g n i f i c a n t innova-t i o n s aimed at were: the use o f no n r o t a t i n g l o a d i n g cap, f a s t e r K - c o n s o l i d a t i o n , d i r e c t measurement o f f r i c t i o n o ' between the end p l a t e s and the deforming sample, measurement of through the use o f end p l a t e s with b u i l t i n lo a d c e l l s and f l e x i b i l i t y i n l o a d i n g path to f a i l u r e . A reasonably convenient sample s i z e was employed which reduced t e s t i n g time f o r c l a y s o f even low p e r m e a b i l i t y to l e s s than 3 days. 30 CHAPTER 3 DESCRIPT ION OF THE APPARATUS The a p p a r a t u s t o be d e s c r i b e d was d e s i g n e d t o i m p o s e a c o n d i t i o n o f p l a n e s t r a i n d u r i n g s h e a r o f a r e c -t a n g u l a r s p e c i m e n o f s o i l ( f i g . 3 . 1 ) . P r i v i s i o n was a l s o made t o c o n s o l i d a t e t h e s p e c i m e n s a n i s o t r o p i c a l l y u n d e r c o n d i t i o n s o f no l a t e r a l y i e l d (K o r one d i m e n s i o n a l c o n -s o l i d a t i o n ) . No p r e s s u r e c e l l was u s e d ; i n s t e a d , f l e x i b l e w a t e r f i l l e d r u b b e r d i a p h r a g m s s e a l e d on p e r s p e x p l a t e s were e m p l o y e d ' t o f u r n i s h t h e l a t e r a l p r i n c i p a l s t r e s s . The f l e x i b l e d i a p h r a g m s u p p o r t p l a t e s were c l a m p e d t o t h e r i g i d e n d p l a t e s w h i c h m a i n t a i n z e r o d e f o r m a t i o n i n t h e l o n g i t u d i n a l d i r e c t i o n o f t h e s p e c i m e n . B o t h l o n g i t u d i n a l and l a t e r a l d e f o r m a t i o n s d u r i n g c o n s o l i d a t i o n were c o m p l e t e l y p r e v e n t e d by t h e end p l a t e s and by m a i n t a i n i n g a c o n s t a n t vo lume o f w a t e r i n t h e l a t e r a l p r e s s u r e d i a p h r a g m s . P e r s p e x was u s e d f o r m a k i n g t h e e n d p l a t e s and the f l e x i b l e d i a p h r a g m s u p p o r t p l a t e s i n t h e i n i t i a l d e s i g n i n o r d e r t o o b t a i n a c l e a r v i e w o f t h e . s p e c i m e n d u r i n g a l l s t a g e s o f t e s t a n d , h e n c e t o be a b l e t o d e t e c t any u n u s u a l h a p p e n i n g l i k e i n t e r f e r e n c e o f b o u n d a r i e s o r r u b b e r membranes . 31 °1 =o e,= o F»g- 3 1 — P-rinci'^al s+T«sses u n d e r JJ lane de-foTrncxH ton 32 S i z e The s p e c i m e n i s 4 i n c h e s l o n g , 1 i n c h w ide and 2 t o 2 1/2 i n c h e s h i g h . The l e n g t h - w i d t h r a t i o was c h o s e n t o m i n i m i s e t h e e f f e c t o f e n d f r i c t i o n on s a m p l e b e h a v i o u r . The h e i g h t - w i d t h r a t i o was t h e same as t h a t u s e d , i n t h e c o n -v e n t i o n a l t r i a x i a l s p e c i m e n s . S p e c i m e n s o f u n d i s t u r b e d c l a y s c o u l d be c o n v e n i e n t l y t r i m m e d f r o m s t a n d a r d 5 i n c h d i a m e t e r t h i n ' w a l l e d t u b e s a m p l e r s . F r i c t i o n l e s s End P l a t e s T h e s e p l a t e s f o r c e p l a n e d e f o r m a t i o n on t h e s p e c i m a n , b o t h d u r i n g t h e c o n s o l i d a t i o n and s h e a r s t a g e s o f t h e t e s t . T h e y were made o f p e r s p e x and t h e f a c e s i n c o n t a c t w i t h t h e s p e c i m e n e n d s were h i g h l y p o l i s h e d . A t h i n l a y e r o f s i l i c o n e g r e a s e was u s e d on t h e p o l i s h e d f a c e s t o r e d u c e f r i c t i o n a l d r a g be tween t h e s a m p l e membrane and t h e p l a t e s . The c o e f f i c i e n t o f f r i c t i o n b e t w e e n t h e s amp l e and t h e e n d p l a t e s i s t h e n q u i t e s m a l l ( C o r n f o r t h 1 9 6 4 , B l i g h t 196 3 , Wood 1 9 5 8 , Duncan a n d S e e d 1 9 6 6 ) , u s u a l l y o f t h e o r d e r o f 0 . 0 2 . The end p l a t e s were h e l d i n p o s i t i o n a t f i x e d d i s t a n c e a p a r t by h o l d i n g them t o t h e f l e x i b l e d i a p h r a g m s u p p o r t p l a t e s ( f i g . 3 . 2 ) . -4-02»-end fifties assembly-34 L a t e r a l Pressure Diaphragms I t was proposed to e x e r c i s e a completely inde-pendent c o n t r o l over the v e r t i c a l and l a t e r a l s t r e s s e s a c t i n g on the specimen, L a t e r a l pressure diaphragms p r e s s i n g against the side s o f the specimen were used to provide the l a t e r a l p r i n c i p a l s t r e s s . These diaphragms c o n s i s t e d of shallow, box shaped, water f i l l e d , t h i n rubber membranes (0.012" to 0.015" t h i c k ) sealed by rubber 0-rings on the faces o f perpex p l a t e s ( f i g . 3.2). The diaphragms were connected through short 1/8" outside diameter saran tubes to a volume change and pressure measuring device. In order to prevent the p r e s s u r i s e d diaphragms from squeezing out past the opening between the diaphragm p l a t e s and the l o a d i n g cap or base p e d e s t a l , the clearance between the diaphragm p l a t e s and cap or base was kept at 0.00 8 inches on each s i d e . Pressures up to 100 p . s . i . were used i n these diaphragms but there was no tendency f o r them to squeeze i n between the sample and end p l a t e s o r out of the opening between the diaphragm support p l a t e s and cap or base. To reduce t h e i r volume compliance (Volume change under u n i t pressure change) the l a t e r a l pressure diaphragms were s t i f f e n e d by H-shaped m i l d s t e e l s t i f f n e r s , on faces away from, the sample ( f i g . 3.3). 35 ® o ® o ® o ® s d t-t-Jl-1-OH U-36 Vo lume Changes and P r e s s u r e ' M e a s u r e m e n t s A s c h e m a t i c l a y o u t o f t h e e q u i p m e n t f o r vo lume c h a n g e s and p r e s s u r e m e a s u r e m e n t s i s shown i n f i g . 3 . 4 . S h o r t 1/8" o u t s i d e d i a m e t e r s a r a n t u b i n g d r a i n a g e l i n e s f r o m t o p and b o t t o m o f t h e s amp l e l e d t o a vo lume c h a n g e and p r e s s u r e m e a s u r i n g d e v i c e w h i c h h a d a c a l i b r a t e d p i p e t t e f o r m e a s u r i n g vo lume c h a n g e s and a s t r a i n gauge t r a n s d u c e r f o r m e a s u r i n g p r e s s u r e . D r a i n a g e l e a d s f r o m t h e l a t e r a l p r e s s u r e d i a p h r a g m s l e d t o a n o t h e r s i m i l a r d e v i c e . Vo lume c h a n g e s were m e a s u r e d by o b s e r v i n g t h e movement o f t h e c o l o u r e d k e r o s e n e - w a t e r i n t e r f a c e i n t h e c a l i b r a t e d p i p e t t e , g r a d u a t -ed t o r e a d t o t h e n e a r e s t 0 . 0 1 - c c . To a c h i e v e s a t u r a t i o n o f t h e s a m p l e s a b a c k p r e s s u r e was a p p l i e d by r e g u l a t i n g t h e a i r p r e s s u r e on t h e B e l l o f r a m s e a l w h i c h was u s e d t o p r e v e n t d i f f u s i o n o f a i r t h r o u g h t h e d r a i n a g e l i n e s . A s i m i l a r s e a l was u s e d a t t h e a i r - w a t e r i n t e r f a c e where l a t e r a l d i a p h r a g m p r e s s u r e was a p p l i e d . A l l p r e s s u r e s were m e a s u r e d on the w a t e r s i d e o f t he B e l l o f r a m s e a l s u s i n g t h e t r a n s d u c e r s . L o a d i n g E q u i p m e n t A s c h e m a t i c a r r a n g e m e n t o f t h e l o a d i n g e q u i p m e n t i s shown i n f i g . 3 . 5 . The r e c t a n g u l a r s a m p l e l o a d i n g cap was s c r e w e d t o t h e l o a d i n g r o d w h i c h was g u i d e d i n i t s 37 38 A n t i To+c?-!'('oin guide •0 r »i 0 T O L o a d i n g b l a i ^ o r m &TacKef -for dial gauge - T h o m p s o n l i n e a r ba l l bush ings - T o f > c i r c u l a r j s l a f e ~ Locxd iVsg -rod - Loa -=1 ii'ig cab - Botl'ovn c i r c u l a r f>late - Spacer -i-eei. A IT b i sf on F i g . 3 - 5 _ S c h e w a f i ' c d i a g r a m o.f Hhe l o a d i n g e ^ a i b m e n - f 39 v e r t i c a l m o t i o n by two Thompson l i n e a r b a l l b u s h i n g s . I t was p r e v e n t e d f r o m r o t a t i n g a b o u t i t s v e r t i c a l a x i s by means o f an a n t i r o t a t i o n g u i d e ( f i g . 3.5). The p i s t o n g u i d e b u s h i n g s were m o u n t e d a t t h e c e n t r e o f a t h i c k c i r c u l a r p l a t e ( t o p p l a t e ) w h i c h c o u l d be l o c a t e d p a r a l l e l and c e n t r a l l y o v e r t h e c i r c u l a r :base p l a t e by means o f t h r e e u p r i g h t r o d s h a v i n g s h o u l d e r s a t t h e i r u p p e r e n d s . The b a s e p e d e s t a l was a t t a c h e d c e n t r a l l y o v e r t h e b a s e c i r c u l a r p l a t e . Thus t h e l o a d i n g p i s t o n c o u l d be g u i d e d i n i t s v e r t i c a l m o t i o n i n t h e same v e r t i c a l p l a n e as t h e b a s e p e d e s t a l . V e r t i c a l l o a d on t h e s amp l e d u r i n g c o n s o l i d a t i o n was a p p l i e d by means o f an a i r p i s t o n t h r o u g h t h e l o a d i n g y o k e . S h e a r i n g o f t h e s a m p l e c o u l d be done w i t h s t r a i n c o n t r o l l e d , s t r e s s c o n t r o l l e d o r s t r e s s - s t r a i n c o n t r o l l e d t y p e s o f l o a d i n g s . T h i s was a c h i e v e d by m o u n t i n g a s t r a i n d r i v e i n p a r a l l e l w i t h t h e a i r p i s t o n . T h i s a r r a n g e m e n t a l s o p e r m i t t e d a f l e x i b i l i t y o f l o a d i n g p a t h t o f a i l u r e ; f a i l u r e i n a x i a l c o m p r e s s i o n o r a x i a l e x t e n s i o n c o u l d be i n d u c e d u n d e r b o t h s t r e s s o r s t r a i n c o n t r o l l e d l o a d i n g . The v e r t i c a l l o a d was m e a s u r e d by a b e r y l l i u m c o p p e r d i a p h r a g m l o a d c e l l h a v i n g a f u l l r e s i s t a n c e b r i d g e . V e r t i c a l d e -f o r m a t i o n o f t h e s amp l e was m e a s u r e d on t h e p i s t o n r o d by means o f a 0 . 0 0 0 1 i n c h d i a l g a u g e , t h u s e l i m i n a t i n g any c o n t r i b u t i o n f r o m t h e d e f o r m a t i o n o f t h e l o a d c e l l . 40 CHAPTER 4 EXPERIMENTAL PROCEDURE P r e p a r a t i o n o f S amp l e s 1• U n d i s t u r b e d C l a y S amp l e s were t r i m m e d f r o m b l o c k s o f c l a y w h i c h h a d b e e n s e a l e d and s t o r e d i n a h u m i d r o o m , and c u t t o t h e s i z e 4 " x l " x 2 1/4" u s i n g a s p e c i a l l y c o n s t r u c t e d t r i m m i n g a p p a r a t u ( f i g . 4 . 1 ) . Wa te r c o n t e n t s we re d e t e r m i n e d f r o m t h e t r i m m i n g s f r o m l a t e r a l f a c e s o f t h e s a m p l e s . A p r o c e d u r e was d e v e l o p e d t o make r u b b e r membranes r e q u i r e d t o e n c l o s e t h e s amp l e and f o r use as l a t e r a l p r e s s u r e d i a p h r a g m s . The p r o c e d u r e t o make t h e r u b b e r membranes i s d e s c r i b e d i n d e t a i l i n A p p e n d i x 1. To p r o v i d e some s t r e t c h , t h e l i n e a r d i m e n s i o n s o f t h e samp le membrane were made a b o u t 4% s m a l l e r t h a n n e c e s s a r y t o e n c l o s e t h e s a m p l e , t o p and b o t t o m p o r o u s s t o n e s , a n d s t a i n l e s s s e a l i n g p l a t e s ( f i g . 3 . 2 ) . B e f o r e p r e p a r i n g t h e p l a n e s t r a i n s p e c i m e n , t h e v o l u m e c h a n g e a n d p r e s s u r e m e a s u r i n g d e v i c e s were c a r e f u l l y d e a i r e d . L a t e r a l p r e s s u r e d i a p h r a g m s were a s s e m b l e d u n d e r d e a i r e d w a t e r i n a t a n k so as n o t t o e n t r a p any a i r i n t h e 42 s y s t e m . T h e i r c o n n e c t i o n s t o t h e vo lume change and p r e s s u r e m e a s u r i n g d e v i c e was a l s o made u n d e r w a t e r . The l a t e r a l d i a p h r a g m s were t h e n c o a t e d w i t h a t h i n l a y e r o f s i l i c o n e g r e a s e , champed t o g e t h e r f a c e t o f a c e a n d p l a c e d u n d e r p r e s s u r e u n t i l l r e q u i r e d , i n o r d e r t o p r e v e n t any d i f f u s i o n o f a i r t h r o u g h t h e r u b b e r membranes . T h e r e was no t e n d e n c y f o r t h e d i a p h r a g m s t o b u r s t w i t h f r e q u e n t u s e . In f a c t t h e same d i a p h r a g m s were u s e d f o r a l l t h e t e s t s made so f a r . F o r p r e p a r i n g t h e p l a n e s t r a i n s p e c i m e n , t h e t o p and b o t t o m p o r o u s s t o n e s were b o i l e d i n w a t e r f o r a b o u t 10 m i n u t e s and l e t c o o l t o room t e m p e r a t u r e . One e n d o f t h e box s h a p e d s a m p l e membrane was s e a l e d t o t h e b a s e p e d e s t a l b y . m e a n s o f t h e l o w e r s t a i n l e s s s e a l i n g p l a t e . The b o t t o m d r a i n a g e l i n e was c o n n e c t e d t o a s m a l l p e r s p e x r e s e r v o i r f i t t e d w i t h a n e e d l e v a l v e a n d a vacuum l i n e , D e a i r e d w a t e r was r u n f r o m t h e r e s e r v o i r i n t o t h e s e a l e d membrane and b u i l t up t o a d e p t h o f a b o u t one i n c h . C a r e was t a k e n t o e l i m i n a t e any a i r b u b b l e s t r a p p e d b e t w e e n t h e membrane and t h e s e a l i n g p l a t e . The membrane was s t r e t c h e d open a t t h e t o p e n d , a n d t h e l o w e r p o r o u s s t o n e q u i c k l y t r a n s f e r r e d o n t o t h e s t a i n l e s s p l a t e , Any e x c e s s w a t e r was drawn b a c k i n t o t h e r e s e r v o i r l e a v i n g t h e p o r o u s s t o n e b a r e l y s u b -m e r g e d . A r e c t a n g u l a r s l e e v e a b o u t 1/4" h i g h e r t h a n t h e t o p o f t h e p o r o u s s t o n e was p l a c e d a r o u n d t h e b a s e p e d e s t a l and t h e s amp l e membrane s t r e t c h e d o p e n and t u r n e d b a c k on t h e s l e e v e ( f i g . 4 . 2 ) . W a t e r was a g a i n r u n f r o m t h e p e r s p e x 4 3 Fig. 4-2 - K u b J ? e r m e m b r a n e i n s t a l l i n g c | a y s f r e a c h e d o n s k e v e f o r s p e c i m e n 44 r e s e r v o i r t i l l i t s t a y e d a b o u t 1/4" above t h e t o p o f p o r o u s s t o n e . The c l a y s amp l e was t r i m m e d , w e i g h e d and c a r e f u l l y p o s i t i o n e d ( u n d e r t h e s m a l l d e p t h o f w a t e r ) o v e r t h e p o r o u s s t o n e . " The t o p p o r o u s s t o n e w h i c h was k e p t s c r e w e d t o t h e s e a l i n g p l a t e was p o s i t i o n e d on t h e t o p o f t he s a m p l e . The r e c t a n g u l a r s l e e v e was t h e n moved up s l o w l y and t h e membrane s i m u l t a n e o u s l y " s l i d o f f " c a r e f u l l y t i l l i t s u p p e r e n d r e a c h e d t h e t o p o f t h e u p p e r s e a l i n g p l a t e . Any e x c e s s w a t e r be tween t h e s amp l e and t h e membrane was q u i c k l y r emoved by r o l l i n g t h e w a t e r o f f i n t h e upward d i r e c t i o n u s i n g two c i r c u l a r r o d s w h i c h were w o r k e d up s i m u l t a n e o u s l y a l o n g t h e o p p o s i t e s i d e s o f t h e s a m p l e . By t h i s t e c h n i q u e t h e membrane c o u l d be p l a c e d w i t h o u t d e f o r m i n g t h e s a m p l e a n d no a i r was t r a p p e d be tween t h e s a m p l e and t h e membrane . ( F l o o d i n g w i t h w a t e r as d e s c r i b e d above may i n v o l v e some s u r f a c e s o f t e n i n g i n a medium t o s t i l l c l a y , b u t was n e c e s s a r y i n o r d e r t o o b t a i n a s a t u r a t e d s a m p l e . F u l l s a t u r a t i o n i s an e s s e n t i a l r e q u i r e m e n t f o r t h e c o n s o l i d a t e d -u n d r a i n e d t e s t s i f p o r e p r e s s u r e s a r e t o be r e l i a b l e ) . . The t o p c i r c u l a r p l a t e w i t h i t s l o a d i n g cap m o u n t i n g was s l i p p e d i n t o p o s i t i o n o v e r t h e u p r i g h t r o d s . The membrane was t h e n s e a l e d a t i t s u p p e r end be tween t h e s e a l i n g p l a t e and t h e l o a d i n g cap w h i c h h a d t h e t o p d r a i n a g e l e a d c o n n e c t e d t o a n o t h e r p e r s p e x r e s e r v o i r . A s m a l l vacuum ( abou t 3 i n c h e s o f m e r c u r y ) was a p p l i e d t o b o t h p e r s p e x r e s e r v o i r s a n d t h e i r n e e d l e v a l v e s o p e n e d t o remove any e x c e s s w a t e r t h r o u g h t h e 45 d r a i n a g e l i n e s . F i g . 4 . 3 shows a c l a y s a m p l e i n p l a c e . The samp le was a l l o w e d t o r e m a i n u n d e r t h i s vacuum w h i l e t h e r e s t o f t h e e q u i p m e n t was a s s e m b l e d . The membrane and l o a d i n g cap were c o a t e d l i b e r a l l y w i t h s i l i c o n e ' g r e a s e and t h e a s s e m b l y t a k e n t o t h e l o a d i n g p l a t f o r m . The end p l a t e s a n d t h e l a t e r a l p r e s s u r e d i a p h r a g m s were a s s e m b l e d a r o u n d t h e s a m p l e and t h e b o l t s t i g h t e n e d . The c l e a r a n c e be tween t h e cap o r b a s e and t h e r e c t a n g u l a r o p e n i n g f o r m e d by l a t e r a l p r e s s u r e d i a p h r a g m s and t h e e n d p l a t e s was a d j u s t e d t o be t h e same on a l l s i d e s by u s i n g a f e e l e r g a u g e . The box f o r m e d by t h e l a t e r a l d i a p h r a g m s and t h e e n d p l a t e s , r e s t e d on f o u r s h o r t s p a c e r b l o c k s p o s i t i o n e d on t h e b o t t o m c i r c u l a r p l a t e , a r o u n d t h e b a s e p e d e s t a l . ( I t i s p r o p o s e d t o r e p l a c e t h e s e s p a c e r b l o c k s by l o a d c e l l s , i n o r d e r t o measu re t h e amount o f l o a d t r a n s -f e r r e d i n f r i c t i o n be tween t h e s amp l e a s s e m b l y and t h e s u r -r o u n d i n g l a t e r a l d i a p h r a g m s a n d e n d p l a t e s b o x ) . The l o a d c e l l was s c r e w e d o n t o t h e t o p e n d o f t h e l o a d i n g r o d and d i a l gauge p o s i t i o n e d a g a i n s t a b r a c k e t c l a m p e d to t h e same 2 r o d . A p r e s s u r e o f 0 .5 k g / c m was t h e n s i m u l t a n e o u s l y a p p l i e d i n t h e v e r t i c a l and l a t e r a l d i r e c t i o n s t h r o u g h t h e a i r p i s t o n and t h e v o l u m e change a n d p r e s s u r e m e a s u r i n g d e v i c e r e s p e c t i v e l y . The d r a i n a g e l i n e s were r emoved f r o m t h e p e r s p e x r e s e r v o i r s and a i r f r e e c o n n e c t i o n s made t o t h e vo lume c h a n g e and p r e s s u r e m e a s u r i n g d e v i c e w i t h w a t e r d r i p p i n g f r o m b o t h e n d s . F i g . 4 . 4 shows t h e s a m p l e a s s e m b l y i n the l o a d i n g frame. 2. Saturated Sand Samples The procedure f o r s e t t i n g up a sand sample was s i m i l a r to that f o r a c l a y specimen up to the stage o f p l a c -i n g the lower porous stone. A r e c t a n g u l a r forming jacket was employed f o r making the sample by d e p o s i t i n g sand under water. This jacket could be s p l i t i n two l o n g i t u d i n a l halves and was l i n e d i n s i d e with porous p l a s t i c which was connected to a vacuum lead. The membrane was p u l l e d against the sides of j a c k e t by appl y i n g vacuum to the porous p l a s t i c and keeping the top end o f membrane st r e t c h e d out by a t h i n r e c t a n g u l a r frame so that a s e a l was obtained around the top periphery o f the j a c k e t ( f i g . 4 . 5 ) . Sand was b o i l e d i n water i n a long necked f l a s k and l e t c o o l under vacuum overnight. The f l a s k was then f i l l e d w i t h water to the top and a s p e c i a l hollowed out stopper w i t h a glass tube stem was put on sec u r e l y . A d d i t i o n a l water was added to f i l l the stem to the top. F r e s h l y b o i l e d water cooled to room temperature was then poured i n t o the sample space i n s i d e the forming j a c k e t so as to f i l l i t to the top. The f l a s k was i n v e r t e d (the s o i l allowed to f i l l the neck and the stem), clamped on a r i n g stand and p o s i t i o n e d over the centre of the water f i l l e d j a c k e t . When the e x i t t i p o f the flask'was submerged under water i n the j a c k e t , sand flowed out of the f l a s k and was replaced by water,. For preparing loose Samples', the sand was allowed to f a l l f r e e l y i n t o the jac k e t without d i s t u r b i n g o r moving the f l a s k i n t h i s process. When vhe sand f i l l e d the jac k e t to the d e s i r e d depth and came i n contact w i t h the e x i t t i p , flow a u t o m a t i c a l l y stopped. At t h i s point the f l a s k was moved back and f o r t h on the bench top to l e v e l o f f the top of the sample. The r i n g stand w i t h the f l a s k was then removed and very c a r e f u l l y and-slowly the top s t a i n l e s s s e a l i n g p l a t e was pushed i n t o the jacket and against the sand. Only bottom drainage was used f o r sand samples and so the top porous stone was omitted from the assembly. While h o l d i n g the s e a l i n g p l a t e i n p o s i t i o n the membrane was brought very c a r e f u l l y over the s e a l i n g p l a t e . Extreme care was taken so as not to entrap any a i r between the p l a t e and the membrane. The membrane was then sealed at the top with the l o a d i n g cap, by b r i n g i n g the top p l a t e i n p o s i t i o n over the upright rods. A vacuum of about 8" of mercury was a p p l i e d through the bottom drainage l i n e and the forming j a c k e t was c a r e f u l l y removed. Dense samples were prepared i n e s s e n t i a l l y the same manner as loose samples, except that during formation the base p l a t e was v i b r a t e d continuously. This was accomplish-ed by p r e s s i n g a v i b r a t i n g t o o l against the base p l a t e . When the s e a l i n g p l a t e was seated on the top the base was v i b r a t e d again to den s i f y the top l a y e r s o f sand and take 50 out any s e a t i n g i r r e g u l a r i t y . A f t e r the forming j a c k e t was removed, the height of the sample was recorded to the nearest 0.0 01" using a reference d i a l i n d i c a t o r . Length and width were c a l c u l a t e d from the in n e r dimensions of the forming jacket making due c o r r e c t i o n f o r the th i c k n e s s o f rubber membrane. Further procedure i n s e t t i n g up of sample i n the l o a d i n g device was the same as f o r the c l a y specimens. 51 CHAPTER 5 CHARACTERISTICS OF THE APPARATUS Measurement of A x i a l Load The load c e l l used f o r the measurement of a x i a l force, on the sample had a r a t e d c a p a c i t y of 300 kg. I t was accompanied by an e l e c t r i c a l readout device and the system was c a l i b r a t e d against dead weights. The c a l i b r a t i o n was found to be l i n e a r with l o a d , and the a x i a l s t r e s s on the 2 sample could be estimated to the nearest 0.001 kg/cm . The l o a d c e l l had n e g l i g i b l e zero d r i f t over a long p e r i o d of usage. The p i s t o n f r i c t i o n i n the guide bushings f o r the l o a d i n g rod was i n s i g n i f i c a n t since no s e a l s were r e q u i r e d . However, during the v e r t i c a l deformation of the sample the f r i c t i o n a l drag between the sample and l a t e r a l diaphragms and end p l a t e s may r e q u i r e a small c o r r e c t i o n to the measured a x i a l f o r c e . The magnitude of t h i s c o r r e c t i o n w i l l depend on the e f f e c t i v e n e s s of the l u b r i c a t i o n between the moving and the s t a t i o n a r y v e r t i c a l boundaries, and also the i n t e n -s i t y of normal pressure between them. With s i l i c o n e grease 52 a s t h e l u b r i c a n t , i t was f e l t t h a t t h e f r i c t i o n b e t w e e n t h e r u b b e r d i a p h r a g m s and t h e s amp le membrane s h o u l d be s m a l l , s i n c e t h e c o e f f i c i e n t o f f r i c t i o n s h o u l d be l e s s t h a n 0 .02 w h i c h i s t h e m e a s u r e d v a l u e be tween p e r s p e x and s a m p l e membrane ( C o r n f o r t h 1 9 6 4 , B l i g h t 1 9 6 3 ) . I t i s h o w e v e r , p r o p o s e d t h a t i n t he f u t u r e d e s i g n t h e s i d e f r i c t i o n a l f o r c e w i l l be d i r e c t l y m e a s u r e d and t h e a x i a l l o a d c o r r e c t e d a c c o r d i n g l y . T h i s w i l l be done by s u p p o r t i n g t h e e n d p l a t e s and d i a p h r a g m s a s s e m b l y on l o a d c e l l s i n s t e a d o f s p a c e r b l o c k s u s e d i n t h e p r e s e n t i n v e s t i g a t i o n s . The a x i a l f o r c e w i l l t h e n be c o r r e c t e d a t a l l s t a g e s o f t h e t e s t t o a c c o u n t f o r t h e p o s s i b i l i t y o f a v a r y i n g f r i c t i o n a l f o r c e . M e a s u r e m e n t o f P r e s s u r e s The e l e c t r i c a l t r a n s d u c e r s u s e d f o r t h e m e a s u r e -ment o f p r e s s u r e s were o f t h e b o n d e d s t r a i n gauge t y p e made by D a t a S e n s o r s I n c . They were p l a c e d as c l o s e t o t h e a p p a -r a t u s as p o s s i b l e t o k e e p d r a i n a g e l e a d s s h o r t and m i n i m i s e t h e c o m p l i a n c e o f t h e s y s t e m s . The t r a n s d u c e r s h a d a r a n g e o f 0-150 p . s . i . 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 o f 0 . 0 0 0 2 7 c u b i c i n c h e s f o r 100 p s i c h a n g e i n p r e s s u r e . . T h e y were a l s o a c c o m p a n i e d 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 t h e s y s t e m was c a l i b r a t e d a g a i n s t a d e a d 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 f o u n d l i n e a r w i t h p r e s s u r e , and p r e s s u r e c h a n g e s o f 2 0 . 0 0 1 k g / c m c o u l d be d e t e c t e d . The t r a n s d u c e r m e a s u r e s p r e s s u r e on an a b s o l u t e s c a l e and a b a r o m e t e r was i n s t a l l e d 53 so t h a t t h e p r e s s u r e s c o u l d be r e f e r r e d t o a t m o s p h e r i c ( gauge ' p r e s s u r e s ) . . The u n d r a i n e d l a t e r a l d i a p h r a g m s d u r i n g t h e one d i m e n s i o n a l c o n s o l i d a t i o n o f t h e s p e c i m e n s f o r m e d a c l o s e d s y s t e m a n d , t h e r e f o r e , a f f e c t e d by t e m p e r a t u r e v a r i a t i o n s ( C a m p a n e l l a 196 8 ) . The e x p e r i m e n t a l s e t up was t h e r e f o r e made i n a c o n s t a n t t e m p e r a t u r e r oom. The maximum v a r i a t i o n i n t e m p e r a t u r e d u r i n g t h e t e s t was t h e r e b y l i m i t e d t o _ + 0 . 5 ° C . Any v a r i a t i o n s i n p o r e w a t e r p r e s s u r e s due t o t e m p e r a t u r e c h a n g e s were p r a c t i c a l l y e l i m i n a t e d by t h i s p r o c e d u r e . M e a s u r e m e n t o f A x i a l D e f o r m a t i o n ' A s t a n d a r d 0 . 0 0 0 1 " d i a l gauge was u s e d t o m e a s u r e a x i a l d e f o r m a t i o n o f the s a m p l e . The d e f o r m a t i o n was m e a s u r e d on t h e l o a d i n g p i s t o n a n d t h u s any c o n t r i b u t i o n f r o m t h e l o a d m e a s u r i n g c e l l was e l i m i n a t e d . K - C o n s o l i d a t i o n The l a t e r a l p r e s s u r e d i a p h r a g m s were d e s i g n e d t o p r e v e n t any l a t e r a l d e f o r m a t i o n o f t h e s a m p l e d u r i n g c o n s o -l i d a t i o n by m a i n t a i n i n g a c o n s t a n t vo lume o f w a t e r i n thera. H o w e v e r , when a v e r t i c a l s t r e s s was a p p l i e d t o t h e s a m p l e w i t h t h e l a t e r a l d i a p h r a g m s i n t h e u n d r a i n e d c o n d i t i o n , t h e p r e s s u r e r e s p o n s e i n t h e l a t e r a l d i a p h r a g m s amoun ted t o o n l y a b o u t 20% o f t h e a p p l i e d v e r t i c a l p r e s s u r e a t l o w p r e s s u r e 54 l e v e l s , and rose to about 40% at higher pressure l e v e l s . This was due to the volume compliance of the diaphragms under a change i n pressure. I f the l a t e r a l diaphragms had zero compliance and were kept undrained, they, i n conjunction w i t h the end p l a t e s , would form a system l i k e a one dimensional consolidometer. Thus under a v e r t i c a l pressure increment on an undrained saturated specimen the pressure response i n such undrained l a t e r a l diaphragms would be t h e o r e t i c a l l y equal to the v e r t i c a l increment. U n f o r t u n a t e l y , i t i s impossible to have a system p e r f e c t l y r i g i d and some com-p l i a n c e i n the l a t e r a l diaphragms had to be. t o l e r a t e d . The r e l a t i v e l y h i g h compliance o f the l a t e r a l pressure system was due to the use of perspex f o r the diaphragm support p l a t e m a t e r i a l . I t i s proposed to make the l a t e r a l pressure system more r i g i d i n the future design by r e p l a c i n g the perspex diaphragm support p l a t e s w i t h t h i c k s t a i n l e s s s t e e l p l a t e s , s t i f f e n e d more e f f e c t i v e l y . Nondisplacement valves and pressure transducers w i l l be mounted r i g h t on the diaphragm p l a t e s , thus d i s p e n s i n g w i t h any drainage leads c o n t r i b u t i n g to compliance., In the present i n v e s t i g a t i o n s i t was, t h e r e f o r e , decided to adopt the f o l l o w i n g procedure to achieve K Q c o n s o l i d a t i o n . Instead o f b u i l d i n g up the v e r t i c a l pressure under c o n d i t i o n s of undrained l a t e r a l diaphragms, equal increments of l a t e r a l and v e r t i c a l pressure were a p p l i e d to the undrained sample simultaneously. This step i s equi v a l e n t 55 to a p p l y i n g a v e r t i c a l pressure increment i n the presence o f i n f i n i t e l y s t i f f compliance l a t e r a l diaphragms which would r e g i s t e r ah equal pressure i n c r e a s e . Just before the con-s o l i d a t i o n of the sample was commenced the diaphragms were made undrained by s h u t t i n g o f f the n->ndisplacement valve on the volume change and pressure measuring device. The opposite diaphragms were kept interconnected so that both had equal pressure i n them at any stage of the t e s t . As the sample c o n s o l i d a t e d under a constant t o t a l v e r t i c a l s t r e s s , the pressure i n the diaphragms g r a d u a l l y decayed. Because of t h e i r f i n i t e compliance, they contained s l i g h t l y excess amounts o f water corresponding to the pressure, change i n them at any i n s t a n t a f t e r the s t a r t o f c o n s o l i d a t i o n . Consequently, at the end of c o n s o l i d a t i o n , the sample would experience a very small compressive l a t e r a l s t r a i n which i s p r o p o r t i o n a l to the volume compliance of the diaphragms between the i n i t i a l and the f i n a l pressures i n them. To prevent any l a t e r a l s t r a i n i n g o f the sample i n order to achieve t r u l y one dimensional c o n s o l i d a t i o n , the p i p e t t e o f the volume change and pressure measuring device was used to e x t r a c t from the l a t e r a l diaphragms the predetermined amount o f water at any instantaneous pressure. The adjustments were made i n such a way that at no time during c o n s o l i d a t i o n di d the l a t e r a l diaphragms contain an excess volume o f water of more than 0.01 c c . By t h i s technique the specimen could be c o n s o l i d a t e d to p r a c t i c a l l y a true one dimensional con-56 d i t i o n ; t h e maximum l a t e r a l s t r a i n was t h e n l e s s t h a n 0 .0 00 07 f o r an i n i t i a l l y 2 1/4 i n c h h i g h s p e c i m e n . F i g . 5.1 shows t h e vo lume c o m p l i a n c e o f t h e l a t e r a l p r e s s u r e d i a p h r a g m s a g a i n s t p r e s s u r e when m e a s u r e d w i t h d i a p h r a g m s c l a m p e d f a c e t o f a c e . T h e s e m e a s u r e m e n t s i n c l u d e d t h e c o n t r i b u t i o n f r o m t h e s h o r t s a r a n d r a i n a g e l i n e s as w e l l as t h e vo lume change and p r e s s u r e m e a s u r i n g d e v i c e . In t h e t e s t s on a n o r m a l l y c o n s o l i d a t e d u n d i s t u r b e d c l a y t o be d e s c r i b e d l a t e r , t h e p r e s s u r e i n u n d r a i n e d l a t e r a l 2 2 d i a p h r a g m s d r o p p e d f r o m 6 .5 k g / c m t o a b o u t 4 . 0 leg/cm d u r i n g c o n s o l i d a t i o n o f t h e s a m p l e . F rom f i g . 5.1 t h i s c o r r e s p o n d s t o a p p r o x i m a t e l y 0 .3 c c . o f vo lume c o m p l i a n c e . I f d u r i n g c o n s o l i d a t i o n , a d j u s t m e n t s a r e n o t made f o r vo lume c o m p l i a n c e o f t h e l a t e r a l d i a p h r a g m s , t h e i n i t i a l l y 2 1/4 i n c h h i g h s a m p l e w o u l d e x p e r i e n c e a l a t e r a l c o m p r e s s i v e s t r a i n o f a p p r o x i m a t e l y 0 . 0 0 2 . H o w e v e r , w i t h t h e p r o p o s e d i m p r o v e -ment i n t h e d e s i g n o f t h e l a t e r a l - p r e s s u r e s y s t e m i t i s e x -p e c t e d t h a t i t s much s m a l l e r vo lume c o m p l i a n c e u n d e r a s i m i l a r p r e s s u r e d r o p w i l l y i e l d p r a c t i c a l l y a z e r o l a t e r a l s t r a i n c o n d i t i o n . Any a d j u s t m e n t s f o r vo lume c o m p l i a n c e d u r i n g c o n s o l i d a t i o n o f t h e s p e c i m e n s w i l l t h e n be u n n e c e s s a r y . A s t a n d a r d one d i m e n s i o n a l c o n s o l i d a t i o n t e s t w i t h l o a d i n c r e m e n t r a t i o o f one was p e r f o r m e d on an u n d i s t u r b e d c l a y i n t h e new a p p a r a t u s . D u r i n g t h e c o n s o l i d a t i o n p r o c e s s , t h e l a t e r a l d i a p h r a g m s were k e p t u n d r a i n e d and no a l l o w a n c e was made f o r t h e i r c o m p l i a n c e by p e r i o d i c a l l y d r a w i n g o u t w a t e r . F i g . 5.2 shows a t y p i c a l p l o t o f v o i d r a t i o , e , v s . 5 7 fe 1-5 op I : 1 _ J 1 1 — i — I I I I 1 u _ — ' 1 — i — L 0-1 0-2 0-3 0-4 0-5 0-6 0-7 08 0? H> 2 3 4 . iP 6 T log 0 f c Fig . 5-2 - C o « \ | > a - r i w r \ of pressure void . T < X T I ' O ' xela+fonsVu\> f-rom C o n s o l rdovwc^T-59 log of v e r t i c a l c o n s o l i d a t i o n pressure, o"^c, obtained from the t e s t along w i t h the corresponding curve obtained i n a standard r i n g consolidometer. I t may be noted that the r e s u l t s from the new apparatus agree c l o s e l y with tho.3e from a standard consolidometer. S l i g h t d i f f e r e n c e i n the p o s i t i o n of the two curves was due p a r t l y to s l i g h t l y d i f f e r e n t i n i t i a l void r a t i o s o f the specimens, and p a r t l y to squeez-i n g out of c l a y under higher pressures, past the clearance between the porous d i s c and r i n g i n the r i n g c o n s o l i d a t i o n 2 t e s t . At the end of c o n s o l i d a t i o n under cx =7.2 kg/cm , l c the sample had undergone a l a t e r a l compressive s t r a i n of only 0.006 which amounted to 3% of the v e r t i c a l s t r a i n . Height change of the sample at any time during c o n s o l i d a t i o n was found p r o p o r t i o n a l to the volume of water drained at that time. This i n d i c a t e s the u n i f o r m i t y of the small l a t e r a l s t r a i n the sample underwent at any stages of the c o n s o l i d a -t i o n process. C o e f f i c i e n t of c o n s o l i d a t i o n , c v , determined e i t h e r from height change w i t h time, or volume drained with time during any c o n s o l i d a t i o n increment, gave the same r e s u l t . For the same v e r t i c a l c o n s o l i d a t i o n pressure a > l c the value o f c y found from the t e s t i n the new apparatus agreed c l o s e l y w i t h that found from the standard r i n g con-s o l i d a t i o n t e s t . 60 S a t u r a t i o n o f t he S p e c i m e n s D u r i n g t h e p r o c e s s o f b u i l d i n g up v e r t i c a l and l a t e r a l s t r e s s e s on t h e u n d r a i n e d samp le b e f o r e t h e c o m -mencement o f c o n s o l i d a t i o n , a t e s t was made t o c h e c k s a t u -r a t i o n o f t h e s a m p l e s . F o r an u n d r a i n e d s o i l s p e c i m e n t h e c h a n g e i n p o r e p r e s s u r e u n d e r p l a n e s t r a i n c o n d i t i o n s can be e x p r e s s e d b y an e q u a t i o n s i m i l a r t o S k e m p t o n ' s f o r t h e t r i a x i a l c o n d i t i o n s ( B i s h o p a n d H e n k e l 1 9 6 2 ) : Au = B [Aa g + A ( A o 1 - A a 3 ) ] ( 5 . 1 ) where Au i s t h e i n c r e m e n t i n p o r e p r e s s u r e due t o i n c r e m e n t s Ao"2 and* Aa^ i n 03 and r e s p e c t i v e l y . A a n d B a r e e m p i r i c a l p o r e p r e s s u r e p a r a m e t e r s u n d e r p l a n e s t r a i n c o n d i t i o n s . F o r a f u l l y s a t u r a t e d s o i l B = 1, as u n d e r t r i a x i a l c o n d i t i o n s . E q u a l i n c r e m e n t s o f Aa^ and Ao"g were a p p l i e d t o t h e samp le by i n c r e a s i n g t h e l a t e r a l and v e r t i c a l p r e s s u r e s and t h e i n c r e a s e Au i n p o r e p r e s s u r e was r e c o r d e d . U n d e r t h i s l o a d i n g c o n d i t i o n , B = A u / A a 3 ( 5 . 2 ) I n t h e t e s t s o n c l a y s a m p l e s a B v a l u e o f o v e r 96% was. m e a s u r e d . To f u r t h e r i n c r e a s e t h e d e g r e e o f s a t u r a t i o n s a m p l e s were l e f t u n d r a i n e d u n d e r f u l l c o n s o l i d a t i o n 61 s t r e s s e s f o r about 12 hours before the s t a r t of c o n s o l i d a -t i o n process. Since the t o t a l s t r e s s e s a p p l i e d to the sample before c o n s o l i d a t i o n were of larg e magnitude, high pore pressures were generated which helped any a i r present to go i n t o s o l u t i o n . A t a b l e showing the measurements o f B value f o r a t y p i c a l t e s t on c l a y i s in c l u d e d i n Appendix 2. Uni f o r m i t y of Deformations As the samples could be con s o l i d a t e d one dimensional-l y , the deformations were e s s e n t i a l l y uniform throughout p r i o r to shear. In the t e s t s to be described l a t e r , normally con-s o l i d a t e d undisturbed c l a y specimens f a i l e d E (a-^ -o" ^  ) m a x 3 ^ n undrained shear under a x i a l compression at a s t r a i n o f about 0.75%. Drained dense sand specimens f a i l e d at about 2% a x i a l s t r a i n . At such small f a i l u r e s t r a i n s l i t t l e non-uni f o r m i t y of deformation should a r i s e , A x i a l extension f a i l u r e s occurred at higher a x i a l s t r a i n s . S t r a i n c o n t r o l l e d shear t e s t s i n a x i a l compression were continued a f t e r the peak was d e f i n e d , u n t i l l about 6% a x i a l s t r a i n o r u n t i l l maximum o c c u r r e < 3 . An examination o f the specimens at the end of the t e s t showed that they had bulged o r contracted symmetrically at the. c e n t r e , i . e . , b u l g i n g o r c o n t r a c t i o n was the same at a l l v e r t i c a l s e c tions along the e n t i r e l e n g t h of the specimens ( f i g . 5.3). This suggests that the f r i c t i o n on the end p l a t e s i s n e g l i g i b l e f o r both sand and c l a y t e s t e d , and that h a r d l y any nonuniformity of deformation would r e s u l t i n the l o n g i t u d i n a l d i r e c t i o n o f the specimens F i g . 5-3 _ U«ifoTW v c r K c a l secfi ' o n o.le-nf "Ike U n g t k of- «, «lcfarmed: J>lan«. s^xaiv\ s^ >eci'««eir» . i n c»>i*«l e x t e n s i o n ^ <J>J i n a x i a l cor*J>resj ion. . 63 due to the presence of the end p l a t e s . In the present i n v e s t i g a t i o n s no p r o v i s i o n was made to introduce f r i c t i o n l e s s ei.d platens on top and bottom of the specimen i n order to increase the homogenity of the s t r e s s and s t r a i n f i e l d s during shear. However, the design could e a s i l y be adapted to incorporate t h i s improve-ment. This may be p a r t i c u l a r l y important i n case o f sands, whose drained strength i s i n f l u e n c e d to a great extent by the rate o f volume change t a k i n g place at f a i l u r e . In drained t r i a x i a l t e s t s on sands the rat e of volume change at f a i l u r e has been found to be dependent on the degree of end r e s t r a i n t (Barden 6 Khayatt 1966). However, there i s some d i f f e r e n c e o f opi n i o n on t h i s conclusion (Bishop £ Green 1965). Shear Stage The v e r t i c a l l o a d i n g Bellofram a i r p i s t o n gave a s u f f i c i e n t l y r a p i d response under s t r a i n r ates experienced during the t e s t s . The house supply pressure was passed v i a a d j u s t a b l e p r e c i s i o n r e g u l a t o r s , and b u i l t to the de s i r e d value at various i n l e t s as re q u i r e d . The r e g u l a t o r s held the pressures w i t h i n +0.5% of the i n i t i a l l y set values. The constant s t r a i n rate d r i v e which was mounted above and i n p a r a l l e l w i t h the a i r p i s t o n ( f i g . 3.5) made i t p o s s i b l e to f o l l o w a v a r i e t y of s t r e s s paths to f a i l u r e * 64 A s t r e s s c o n t r o l l e d a x i a l compression t e s t could be made by usin g the a i r p i s t o n to apply p e r i o d i c l o a d i n g increments while m a i n t a i n i n g constant pressure i n l a t e r a l diaphragms, whereas an a x i a l extension t e s t could be made by i n c r e a s i n g the l a t e r a l diaphragm pressure under constant a x i a l s t r e s s . A s t r a i n c o n t r o l l e d a x i a l compression or extension t e s t c o u l d be performed by making the s t r a i n d r i v e push or p u l l on the middle yoke crossbar ( f i g . 3.5) thereby i n c r e a s i n g or decreasing the a x i a l l o a d . A combined s t r e s s - s t r a i n c o n t r o l l e d t e s t could also be made by using a i r p i s t o n f o r s t r e s s c o n t r o l i n the i n i t i a l stages o f the t e s t , and then s w i t c h i n g over to s t r a i n c o n t r o l l a t e r on. This k i n d o f t e s t e l i m i n a t e s the disadvantage of r a p i d l o a d i n g on the sample i n the conventional constant s t r a i n rate t e s t , and al s o provides post peak i n f o r m a t i o n which cannot be obtained i n a conventional s t r e s s c o n t r o l l e d t e s t . In the s t r a i n c o n t r o l l e d t e s t s so f a r made, a • constant rate o f s t r a i n was not completely obtained. At the s t a r t of sh e a r i n g , the s t r a i n r a t e was l e s s than the c a l i b r a t -.ed value and approached the c a l i b r a t e d value around the peak d e v i a t o r s t r e s s . This behaviour was due to the f i n i t e deformations o f the yoke rods above the d r i v i n g point ( f i g . 3.5) under v a r y i n g v e r t i c a l f o r c e . Consequently, the de-formation t r a n s f e r r e d to the sample amounted to the a l g e b r a i c d i f f e r e n c e between the movement of the s t r a i n d r i v e and the deformation of the yoke rods. This drawback w i l l be removed 65 i n the future design by mounting the s t r a i n r a t e d r i v e so as to push or p u l l d i r e c t l y on the top crossbar o f the yoke. Measurement o f In the i n v e s t i g a t i o n s reported h e r e i n , no attempt was made to measure cr^' ^ n "*-^ e f u - t u : r e however, the design of the end p l a t e s w i l l be modified to in c l u d e load c e l l s . 66 CHAPTER 6 SOKE EXPERIMENTAL RESULTS The Test Program The tests to be described were performed to es t a b l i s h the f e a s i b i l i t y of v a l i d testing with the new apparatus. Tests were performed on a l o c a l undisturbed' clay and on uniform Ottawa sand (A.S.T.M. standard C-190, 20-30 sieve s i z e ) . the properties of clay tested have been described in d e t a i l by Byrne (1966). It i s known l o c a l l y as Haney clay, and i s thought to have been deposited i n a marine environment and subsequently leached by rain water causing i n s e n s i t i v e clay structure. Haney clay has a natural water content of about 41%, l i q u i d l i m i t of 44% and p l a s t i c l i m i t of 26%. I t i s medium s t i f f when sampled and has a s e n s i t i v i t y of about 12. Preconsolidation pressure 2 i s about 2.2 kg/cm . The following types of tests were performed: 1. Consolidation Tests One dimensional consolidation tests were performed on specimens of Haney clay to determine the value of K . 6 7 To achieve one dimensional c o n s o l i d a t i o n , l a t e r a l s t r a i n i n g of the samples was completely prevented by a d j u s t i n g the volume of water i n the l a t e r a l diaphragms f o r zero compliance. Some t e s t s were also performed to determine the i n f l u e n c e of small l a t e r a l s t r a i n s on the measured value of s t r e s s r a t i o , aq /a., , at the end of c o n s o l i d a t i o n . A small ' 3c l c ' ex t e n s i o n a l l a t e r a l s t r a i n was imposed on the sample by withdrawing an amount of water from the l a t e r a l diaphragms i n excess o f tha t which corresponded to zero compliance. Whereas a small compressive l a t e r a l s t r a i n was imposed on the sample when no adjustments were made f o r compliance of l a t e r a l diaphragms during the c o n s o l i d a t i o n process. The l o n g i t u d i n a l s t r a i n was zero i n a l l cases because of the presence of r i g i d end p l a t e s . 2. Shear Tests The f o l l o w i n g three types of shear t e s t s were per-formed on c l a y specimens c o n s o l i d a t e d to e s s e n t i a l l y i d e n t i c -a l s t r e s s e s . a. AC-1 K , normally c o n s o l i d a t e d specimen, sheared under o plane s t r a i n c o n d i t i o n , using s t r a i n c o n t r o l l e d a x i a l com-p r e s s i o n , while m a i n t a i n i n g constant l a t e r a l diaphragm pressure. T h i s t o t a l s t r e s s path i s r e p r e s e n t a t i v e o f the s t r e s s c o n d i t i o n s under the centre l i n e of a s t r i p loaded area (A6' R i s of no consequence as long as Aa-, > Aa_). 68 b. AC-2 K q , normally c o n s o l i d a t e d specimen, sheared under plane s t r a i n c o n d i t i o n , u s i n g s t r e s s c o n t r o l l e d a x i a l com-pres s i o n by decreasing l a t e r a l diaphragm pressure, while m a i n t a i n i n g constant a x i a l l o a d . This t o t a l s t r e s s path i s r e p r e s e n t a t i v e of s t r e s s c o n d i t i o n s behind a long r e -t a i n i n g w a l l under a c t i v e e a r t h pressure c o n d i t i o n s . c. AE K q , normally c o n s o l i d a t e d specimens, sheared under plane s t r a i n c o n d i t i o n , using s t r a i n c o n t r o l l e d a x i a l e x t e n s i o n , while m a i n t a i n i n g constant l a t e r a l diaphragm pressure. This t o t a l s t r e s s path i s r e p r e s e n t a t i v e of s t r e s s c o n d i t i o n s under the centre l i n e of a long rectangu-l a r excavation. Under t h i s s t r e s s path the p r i n c i p a l axes are r o t a t e d through 9 0°. The same three types o f t e s t s were performed on dense sand, w i t h the d i f f e r e n c e that the c o n s o l i d a t i o n was done under equal v e r t i c a l and l a t e r a l diaphragm pressures. In other words c o n d i t i o n o f zero s t r a i n during c o n s o l i d a -tions-was f u l f i l l e d i n l o n g i t u d i n a l d i r e c t i o n o n l y . Pre-vention of l a t e r a l s t r a i n of the sample was not attempted, as the s t r e s s change during c o n s o l i d a t i o n i n undrained l a t e r a l diaphragms occurred immediately upon opening the drainage valve on the specimen, g i v i n g no time f o r volume of water to be adjusted f o r zero compliance. However, 69 w i t h the proposed improvement i n the design o f l a t e r a l pressure diaphragms, i t w i l l be p o s s i b l e to c o n s o l i d a t e sand specimens also under c o n d i t i o n s of one dimensional s t r a i n . A l l c l a y samples were c o n s o l i d a t e d to the same v e r t i c a l e f f e c t i v e c o n s o l i d a t i o n pressure, c r ^ c , of a p p r o x i -mately 6 kg/cm', which would e f f e c t i v e l y take them i n t o the normally loaded zone. C o n s o l i d a t i o n l a s t e d f o r a p e r i o d of approximately 36 hours and specimens were l e f t undrained f o r another 12 hours (to l e t secondary compression generate major part of i t s pore pressures and cause e q u a l i z a t i o n throughout the specimen) before commencement of shear. In sand samples only high i n i t i a l d e n s i t y was used. This was done f o r convenience o f reproducing the same i n i t i a l v o id r a t i o i n the three types o f t e s t s . Only drained t e s t s were made on saturated samples w i t h volume change measurements. Test types AC-2 and AE were made by c o n s o l i d a t i n g the samples to higher v e r t i c a l and l a t e r a l e f f e c t i v e s t r e s s e s than were used f o r t e s t type AC-1. This was done to get approximately same value of (c^+c^)/2 at f a i l u r e i n a l l types of t e s t s , and thus e l i m i n a t e any i n f l u e n c e o f mean normal e f f e c t i v e s t r e s s on the measured value of (Beer De 1965 , Barden'and Khayatt 1966 ). Clay samples were sheared undrained with pore pressure measurements. Rate o f s t r a i n or r a t e of l o a d i n g was slow enough i n order to achieve f u l l e q u a l i s a t i o n of 70 pore pressures. Time to f a i l u r e was evaluated (using the measured values of c o e f f i c i e n t of c o n s o l i d a t i o n o f the samples during c o n s o l i d a t i o n stage) as suggested by Bishop and Henkel (1962) and B l i g h t (1963). Sand samples were sheared at a constant r a t e of s t r a i n or constant rate of l o a d i n g so as to cause f a i l u r e i n about one hour. This time to f a i l u r e was chosen f o r convenience of r e c o r d i n g data at s u i t a b l e time i n t e r v a l s and o b t a i n enough readings f o r p l o t t i n g t e s t data. Test Results - Clay Stress Ratio o"gc/a-]_c a f t e r C o n s o l i d a t i o n The r e s u l t s from c o n s o l i d a t i o n of f i v e specimens are summarised i n t a b l e I. Specimens PS-C2 to PS-C4 were c o n s o l i d a t e d s t r i c t l y under one dimensional c o n d i t i o n . The r e s u l t i n g s t r e s s r a t i o , a3./ai., = K , was 0.55 and was es-OC J-'— o s e n t i a l l y the same f o r a l l three t e s t s . In specimen PS-C1, inducing a small amount of l a t e r a l e x t e n s i o n a l s t r a i n caused a s l i g h t drop i n the value of s t r e s s r a t i o to 0.53. Inducing a small l a t e r a l compressive s t r a i n i n sample PS-C5 als o r e s u l t e d i n a s l i g h t drop i n the s t r e s s r a t i o to 0.54. The observed small drop i n s t r e s s r a t i o f o r compressive l a t e r a l s t r a i n when compared to K Q value, was probably due to the d i f f e r e n c e i n procedure f o r c o n s o l i d a t i o n of specimen PS-C5 and r e s t o f the specimens. During one dimensional 70, ! * 1 3 « 0 <Q > o o o . . o 1 3 t | T -t- c wi (5 0 c •> ^ 0 V) q \ to to K> ro Ki X u «; K 0 c o C 1 • < o CM' to K> CD _£ -+-V •s 1 I 5 o > 00 to Kl VD o C o -X o -3 ~o s: o 11 «« rO «\ h- «o in in o 0\ to 10 ** lO N to t\ l« o c cy | Q O <?\ in o o\ IP 0 o c .o « C o u «-», o •* T — 0 •? « c .o « .5 5 r x VI UI ~6 « >• t-c "o 1-w> "6 L. "tf t-T-6 « U K o <A o <v on %> (J o Z •5 o =: O 0 w i r-l •r -•- -*-rt tf c c 2 ° z o 1-w - 1 62 CM O v% Kl O <A CL • ft U i 71 ( K Q ) c o n s o l i d a t i o n p r o c e s s , p e r i o d i c w i t h d r a w i n g o f e x c e s s w a t e r f r o m t h e l a t e r a l d i a p h r a g m s c a u s e d d r o p i n t h e i n s t a n t a n e o u s l a t e r a l p r e s s u r e a t e v e r y a d j u s t m e n t . T h i s a p p a r e n t l y r e s u l t e d i n a l a r g e r v e r t i c a l d e f o r m a t i o n o f t h e s e s p e c i m e n s c o m p a r e d t o t h a t o f s p e c i m e n P S - C 5 , w h i c h was c o n s o l i d a t e d w i t h no a d j u s t m e n t s i n v o l u m e c o m p l i a n c e o f d i a p h r a g m s . I t may be n o t e d i n t a b l e I t h a t s a m p l e PS-C5 u n d e r w e n t s m a l l e r v o l u m e t r i c and a x i a l s t r a i n s due . t o c o n s o l i d a t i o n c o m p a r e d t o r e s t o f t h e s p e c i m e n s . F rom t h e s e few t e s t s i t w o u l d a p p e a r t h a t v e r y s m a l l amounts o f l a t e r a l e x t e n s i o n a l o r c o m p r e s s i v e s t r a i n s o f 0 . 0 0 1 t o 0 .003 d u r i n g c o n s o l i d a t i o n , o n l y s l i g h t l y a f f e c t t h e m e a s u r e d K v a l u e . H o w e v e r , t h i s s m a l l v a r i a t i o n i n K ' o o v a l u e s may n o t h a v e any e f f e c t on t he s u b s e q u e n t s h e a r b e h a v i o u r o f s p e c i m e n s . S t r i c t a d h e r e n c e t o one d i m e n s i o n a l s t r a i n may be r e q u i r e d o n l y t o d e f i n e a t r u e K q v a l u e . In s p e c i m e n s PS-C1 t o PS-C4 t h e v o l u m e t r i c s t r a i n e q u a l l e d e x a c t l y t h e a x i a l s t r a i n a t t h e e n d o f c o n s o l i d a t i o n . T h i s i n d i c a t e s t h e t r u l y one d i m e n s i o n a l n a t u r e o f c o n s o l i -d a t i o n o f t h e s e s p e c i m e n s . I n s p e c i m e n PS-C5 v o l u m e t r i c s t r a i n e x c e e d e d t h e a x i a l a p p a r e n t l y b e c a u s e o f i n d u c e d l a t e r a l c o m p r e s s i o n and t h e d i f f e r e n c e i n p r o c e d u r e o f c o n s o l i d a t i o n . 72 S t r e s s - S t r a i n R e l a t i o n s h i p s . F i g . 6 .1 shows t h e d e v i a t o r s t r e s s , (a-^-a^), v s . a x i a l s t r a i n f o r t h r e e e s s e n t i a l l y i d e n t i c a l s a m p l e s s h e a r e d u n d e r d i f f e r e n t t o t a l s t r e s s p a t h s . The r e s u l t s a r e a l s o s u m m a r i s e d i n T a b l e I I . The c h a r a c t e r i s t i c f e a t u r e t o be n o t e d i s t h e s m a l l a x i a l s t r a i n , a b o u t 1% o r l e s s , a t w h i c h t h e maximum d e v i a t o r s t r e s s was r e a c h e d i n t h e p l a n e s t r a i n c o m p r e s s i o n t e s t s . T h i s b e h a v i o u r a g r e e s w i t h t h e o b s e r v a -t i o n s o f H e n k e l and Wade (1966 ) i n t h e i r p l a n e s t r a i n t e s t s on r e m o l d e d W e a l d c l a y . P l a n e s t r a i n f a i l u r e i n a x i a l e x t e n s i o n i n v o l v e d t h e r o t a t i o n o f p r i n c i p a l axes t h r o u g h 9 0 ° , and f a i l u r e o c c u r r e d a t a l a r g e a x i a l e x t e n s i o n a l s t r a i n . S i m i l a r l a r g e d i f f e r e n c e s i n f a i l u r e s t r a i n s be tween a x i a l c o m p r e s s i o n and a x i a l e x t e n s i o n o f K Q c o n s o l i d a t e d t r i a x i a l s p e c i m e n s o f c l a y s , h a s been r e p o r t e d by L a d d ( 1 9 6 4 ) . In s t r a i n c o n t r o l l e d c o m p r e s s i o n t e s t s u n d e r p l a n e s t r a i n ( A C - 1 ) , ( a - T / c f q ) ' o c c u r r e d a t s t r a i n s much l a r g e r t h a n a t w h i c h ( a T - a 3 ) m a x o c c u r r e d ( f i g . 6 .2 and t a b l e I I ) . T h i s k i n d o f b e h a v i o u r i s w e l l known f o r c l a y s w i t h a s e n s i t i v e s t r u c t u r e , and i s due t o t h e i n c r e a s e i n p o r e p r e s s u r e s by p r o g r e s s i v e b r eakdown o f s t r u c t u r e e v e n a f t e r t h e o c c u r r e n c e o f ( a i - a 3 ) m a x ( C r a w f o r d 1 9 5 9 , B j e r r u m and S imons 1 9 6 0 ) . In t h e a x i a l e x t e n s i o n t e s t (AE) p o r e p r e s s u r e s were h a r d l y c h a n g i n g a r o u n d t h e peak d e v i a t o r . s t r e s s ; AC-l c» -A~ AC-2 a. -a- AE <x M a i co*w|9"r« ion '"CT< )n cr *4ec 4_ ps-cz • ct ^ st\ou>» ° P r—--—--—__>; PS-C3 E 3 0 bn q .. •? 1 1 •• 1 A '/ S-e 12. -10 - 8 - 6 -<f - 2 O 2. 4- €> A x t a l S + T a m - jp>«rccnr Fi$ 6-1 _ Pcvicvtor stress VS. a.*tal 5.rTa.in for cortsoWdatea und-ra«necA f>lane sfrain Teste on Haney day • 7? a-r « * 5 i f « c4 o o » t o ? Jo is o cO fe l J4 1 "E 3 S tfl to ti> ro •p' KJ to c < N «• to i rJ-|0 1 • K> C CH 1 w 00 i VO O i 1 1 0 b* 1 & •4-«< N 0\ <* 10 oo CO VN b"1 vi fO vo tr> *N V *t 00 10 to VO V9 In r>4 vo civ i vo U l l- to m VO m + 10 b*. Os 10 |0 •O to lt> b* 0 VO 0 OA vt\ o vo o vi) tf C * C P  u 0 K o A . .4-<5 0 i 0 •3 »-« d A . 0 «i f >\ -C -t-1 < N 0 < U J < T < CM «J 1 <o CL to VJ 1 <A D-IO u 1 Q. >« 0 I-u (A C C «t a h u Cy T5 C 6 ^ u o C o 41 .c Q \J V v. M C J C J J -t- \ 0 \ / 0 u V V e c t "5 i -H i «o «( X K 8 6 C _0 u ii XV-• d < < in < s 3 15 6 -15 O I-3 -T3 ff c o 74 i 75 c o n s e q u e n t l y b o t h (a . .-a . ) and ( c K ' / a ' ) _^ o c c u r r e d a t t h e I d max J- 3 max same s t r a i n . I t may be n o t e d t h a t t h e r e was h a r d l y any d i f f e r e n c e • i n s t r e s s - s t r a i n b e h a v i o u r o f s p e c i m e n s u n d e r s t r e s s p a t h s AC-1 and A C - 2 . In none o f t h e s t r a i n c o n t r o l l e d s h e a r t e s t s was an a p p a r e n t f a i l u r e p l a n e o b s e r v e d and f a i l u r e o c c u r r e d by a g e n e r a l p l a s t i c f l o w . In s t r e s s c o n t r o l l e d p l a n e s t r a i n c o m p r e s s i o n t e s t , A C - 2 , h o w e v e r , s u d d e n f a i l u r e on a s i n g l e r u p t u r e p l a n e was i n e v i t a b l e . S t r e n g t h C h a r a c t e r i s t i c s S p e c i m e n s P S - C 1 , PS-C2 a n d PS-C5 h a d p r a c t i c a l l y t h e same ( a 1 - a „ ) ( t a b l e I I ) . T h e s e s p e c i m e n s were c o n -s o l i d a t e d u n d e r e s s e n t i a l l y i d e n t i c a l ° " ^ c » b u t i n s p e c i m e n s PS-C1 and P S - C 5 , t h e s t r e s s r a t i o ° " 3 c / t f l c a t t h e end o f c o n s o l i d a t i o n was s l i g h t l y d i f f e r e n t c o m p a r e d t o t h e s t r e s s r a t i o K Q o f s p e c i m e n PS-C2 . T h i s s u g g e s t s t h a t f o r t h e same 0"^c> t h e u n d r a i n e d s t r e n g t h o f c l a y i n a x i a l c o m p r e s s i o n was n o t a f f e c t e d by s l i g h t d i f f e r e n c e i n t h e i r a 3 C / a i c « F u r t h e r m o r e , t h e u n d r a i n e d s t r e n g t h was t h e same b o t h u n d e r i n c r e a s i n g and d e c r e a s i n g a x i a l c o m p r e s s i o n . The a v e r a g e v a l u e o f t h e r a t i o o f h a l f t h e p e a k d e v i a t o r s t r e s s t o t h e m a j o r c o n s o l i d a t i o n s t r e s s , su/-o*^ , f o r a x i a l c o m p r e s s i o n f a i l u r e was 0 . 3 0 . In c o n t r a s t f a i l u r e o f an e s s e n t i a l l y i d e n t i c a l s p e c i m e n P S - C 3 , u n d e r a x i a l e x t e n s i o n r e s u l t e d i n a much l o w e r ( 0 . 2 1 ) v a l u e o f t h i s 76 r a t i o . T h i s k i n d o f s t r e n g t h l o s s i s r e g a r d e d a s t h e r e s u l t o f r e o r i e n t a t i o n o f t h e p r i n c i p a l axes ( L a d d 1 9 6 5 , Broms and C a s b a r i a n 1 9 6 5 , Duncan and S e e d 1 9 6 6 ) . I t i s i n t e r e s t i n g t o n o t e t h a t ( a ^ / a 3 ) m a x w a s same i r r e s -p e c t i v e o f t h e t o t a l s t r e s s p a t h t o f a i l u r e . P o r e P r e s s u r e s F o r s p e c i m e n s c o n s o l i d a t e d t o e s s e n t i a l l y i d e n t i c a l s t r e s s e s , t h e p o r e p r e s s u r e s g e n e r a t e d d u r i n g s h e a r d e p e n d t o a g r e a t e x t e n t on t h e t o t a l s t r e s s p a t h t o f a i l u r e ( f i g . 6 . 3 ) . U n d e r i n c r e a s i n g a x i a l c o m p r e s s i o n , A C - 1 , t h e p o r e p r e s s u r e i n c r e a s e d t h r o u g h o u t t h e s h e a r i n g p r o c e s s , b u t a p p r o a c h e d an a l m o s t c o n s t a n t v a l u e a t ^ l ^ ^ m a x ' U P t o ^ a i " a 3 ^ m a x ^ e P o r e P r e s s u r e b u i l d up i n t h i s t e s t was due t o i n c r e a s e i n b o t h mean n o r m a l and s h e a r i n g s t r e s s e s , and a l s o t o a b r e a k d o w n o f s e n s i t i v e s o i l s t r u c t u r e u n d e r i n c r e a s i n g s h e a r i n g s t r a i n s ( C r a w f o r d 1 9 5 9 , H i r s c h f e l d 1 9 6 0 ) . C o n t i n u e d i n c r e a s e i n p o r e p r e s s u r e a f t e r ( a , - a q ) was s o l e l y due t o s t r u c t u r a l c o l l a p s e o f J- ° max s o i l . U n d e r d e c r e a s i n g a x i a l c o m p r e s s i o n , A C - 2 , t h e p o r e p r e s s u r e i n i t i a l l y d e c r e a s e d , b u t s t a r t e d t o i n c r e a s e a f t e r a b o u t 0 . 1 % a x i a l c o m p r e s s i o n , w i t h t h e r e s u l t t h a t t h e n e t c h a n g e a t f a i l u r e was p o s i t i v e . T h i s t e s t was s i m i l a r t o AC-1 i n t h a t i t i n v o l v e d i n c r e a s e i n s h e a r tl 78 s t r e s s e s on t h e s p e c i m e n ; h o w e v e r , t h e mean n o r m a l s t r e s s c o n t i n u o u s l y d e c r e a s e d . . I n i t i a l d e c r e a s e i n p o r e p r e s s u r e w a s , t h e r e f o r e , a s s o c i a t e d w i t h d o m i n a t i n g i n f l u e n c e o f d e c r e a s e i n mean n o r m a l s t r e s s e s c o m p a r e d t o t h a t o f i n -c r e a s e i n s h e a r i n g s t r e s s e s . P r o g r e s s i v e s t r a i n i n g u n d e r l o a d i n g i n c r e m e n t s r e s u l t e d i n s t r a i n d e p e n d e n t p o r e p r e s s u r e s ( s t r u c t u r a l b r e a k d o w n , c a u s i n g r i s e i n p o r e p r e s s u r e s ) . F o r an i n s e n s i t i v e o r a r e m o l d e d c l a y t h e p o r e p r e s s u r e i n t h i s t y p e o f t e s t g e n e r a l l y d e c r e a s e s t h r o u g h o u t t h e t e s t and n e t c h a n g e a t f a i l u r e i s n e g a t i v e ( B i s h o p and H e n k e l 1 9 6 2 ) . U n d e r a x i a l e x t e n s i o n , A E , t h e i n i t i a l p o r e p r e s s u r e r e s p o n s e was s i m i l a r t o t h a t u n d e r a x i a l c o m p r e s s i o n , A C - 2 , b u t a t a g i v e n a x i a l s t r a i n t h e d e c r e a s e i n p o r e p r e s s u r e was much l a r g e r f o r A E . F u r t h e r s t r a i n i n g c a u s e d t h e p o r e p r e s s u r e t o r i s e , b u t a t a much s l o w e r r a t e t h a n u n d e r p a t h A C - 2 , and was h a r d l y c h a n g i n g a r o u n d f a i l u r e ( i . e . ( a i - a 3 ) m a x ^ • As s o o n as f a i l u r e was p a s s e d p o r e p r e s s u r e s t a r t e d b u i l d i n g up o n c e more a t a f a s t e r r a t e . T h i s s t r e s s p a t h l i k e A C - 2 , i n v o l v e s a c o n t i n u o u s d e c r e a s e i n mean n o r m a l s t r e s s b u t u n l i k e A C - 2 , c a u s e d a r e l e a s e o f c o n s o l i d a t i o n s h e a r s t r e s s i n t h e i n i t i a l s t a g e s . T h i s r e l e a s e o f s h e a r s t r e s s m i g h t be t h e r e a s o n f o r a g r e a t e r i n i t i a l d r o p o f p o r e p r e s s u r e when c o m p a r e d t o t h a t u n d e r AC-2 i n w h i c h s h e a r i n g s t r e s s e s c o n t i n u o u s l y i n c r e a s e d . 79 I t i s l i k e l y that w i t h i d e n t i c a l i n i t i a l s t r e s s c o n d i t i o n s and under no change i n o"m, an a n i s o t r o p i c a l l y normally con-s o l i d a t e d c l a y develops l a r g e r p o s i t i v e pore pressures under i n c r e a s i n g than decreasing sh?;ar s t r e s s e s . Furthermore, under AE the r a t e o f decrease of a i n the i n i t i a l stages m ° o f the t e s t s was 3 to 4 times g r e a t e r than that under AC-2, which may be another cause o f r a p i d and l a r g e r drop i n pore pressure under AE when compared to t h a t under AC-2. A slower b u i l d up i n pore pressure a f t e r the i n i t i a l drop may be due to the compensating i n f l u e n c e of decreasing mean normal s t r e s s e s (causing pore pressure drop), i n c r e a s i n g shearing s t r e s s e s and s t r u c t u r a l breakdown of s o i l (causing pore pressure i n c r e a s e ) . An a c c e l e r a t e d r i s e i n pore pressure a f t e r the peak d e v i a t o r s t r e s s was apparently due to an i n -crease i n the mean normal s t r e s s combined w i t h s t r u c t u r a l breakdown of s o i l . F i g . 6.4 shows the v a r i a t i o n o f pore pressure parameter A (Eq. 5.1) with a x i a l s t r a i n f o r the three s t r e s s paths. For a saturated specimen, B = 1 and, t h e r e f o r e , equation 5.1 becomes Au = Aa„ + A(Aa 1-Aa q) (6.1) Under a x i a l extension decreased to zero and path, AE, the shearing s t r e s s e s then increased i n the opposite f i r s t 80 81 d i r e c v i o n u n t i l l f a i l u r e was r e a c h e d . The change i n p o r e p r e s s u r e due t o s h e a r i n g s t r e s s e s w i l l , h o w e v e r , d e p e n d on t h e t o t a l change i n s h e a r i n g s t r e s s e s , i . e . , ( A c ^ - A a ^ ) , where Aa a n d Aa s t a n d f o r c h a n g e s i n a x i a l and l a t e r a l a a t o t a l p r i n c i p a l s t r e s s e s r e s p e c t i v e l y . To t a k e a c c o u n t o f t h i s f a c t , e q u a t i o n ( 6 . 1 ) was w r i t t e n i n t h e f o l l o w i n g f o r m : Au = Aa^ + A ( A a a - A a j l ) ( 6 . 2 ) I t may be s e e n i n f i g . 6 .4 t h a t l i k e p o r e p r e s s u r e s , p o r e p r e s s u r e p a r a m e t e r A a l s o depends on t h e t o t a l s t r e s s p a t h t o f a i l u r e . I n p a r t i c u l a r t h e v a r i a t i o n o f A w i t h a x i a l s t r a i n , u n d e r a x i a l e x t e n s i o n , A E , b e a r s no r e s e m b l a n c e t o i t s c o r r e s p o n d i n g v a r i a t i o n u n d e r a x i a l c o m p r e s s i o n a n d i t s v a l u e a t f a i l u r e was f o u n d d i f f e r e n t u n d e r t h e t h r e e t o t a l s t r e s s p a t h s i n v e s t i g a t e d ( t a b l e ''.I). T h i s i m p l i e s t h a t A v a l u e f r o m t h e a^ i n c r e a s i n g a x i a l c o m p r e s s i o n p l a n e s t r a i n t e s t c a n n o t be u s e d t o e s t i m a t e p o r e p r e s s u r e s i n s i t u a t i o n s where t o t a l s t r e s s p a t h t o f a i l u r e u n d e r p l a n e s t r a i n i s d i f f e r e n t . I t , t h e r e f o r e , a p p e a r s t h a t p o r e p r e s s u r e p a r a -m e t e r A i s v e r y s e n s i t i v e t o c h a n g e i n t o t a l s t r e s s p a t h to f a i l u r e ( H e n k e l 1 9 6 0 ) . T h i s s e n s i t i v i t y seems v e r y p r o n o u n c e d p a r t i c u l a r l y when s h e a r o c c u r s u n d e r n o n s y m m e t r i c a l s t a t e s o f s t r e s s and i n w h i c h r o t a t i o n o f p r i n c i p a l a x e s may 82 a l s o .be i n v o l v e d . However, f o r undrained shear under non-symmetrical st a t e s of s t r e s s , the changes i n pore pressures have been shown to be b e t t e r expressed i n terms of changes i n o c tahedral normal and shearing s t r e s s e s (Equation 2.7). The pore pressure parameter "a" i n equation (2.7) has then been found to be r e l a t i v e l y unaffected by the v a r i a t i o n i n t o t a l s t r e s s path to f a i l u r e i n the undrained t r i a x i a l t e s t s (Henkel 1960). In the present i n v e s t i g a t i o n s no measurements were made o f o^j but i t i s i n t e r e s t i n g to note that the use o f equation ( 2 . 7 ) , assuming at f a i l u r e equal to.(a£+ag)/2 gives approximately the same value o f pore pressure parameter "a" (=0.9 8) at ( a i ~ a 3 ) m a x i r r e s p e c t i v e of the t o t a l s t r e s s path to f a i l u r e i n plane s t r a i n . E f f e c t i v e S t r e s s Paths F i g . 6 . 5 shows e f f e c t i v e s t r e s s paths followed i n \\a^-o^)/2 vs. (a£+ap/2 s t r e s s plane by e s s e n t i a l l y i d e n t i c a l samples i n the three types of t e s t s . E f f e c t i v e s t r e s s paths under a x i a l compression AC-1 and AC-2 are s i m i l a r and almost i d e n t i c a l up to (a,-a-)^ .^ Under a x i a l e x t e n s i o n , the s t r e s s path followed i s very d i f f e r e n t when compared to those under a x i a l compression. This i s apparently due to the r e l e a s e o f c o n s o l i d a t i o n d e v i a t o r s t r e s s , ( a i c ~ a 3 C ) » from the sample i n the i n i t i a l stages of the t e s t . F i g . 6 . 5 a l s o shows the e f f e c t i v e s t r e s s path f o r an i s o t r o p i c a l l y 83 84 c o n s o l i d a t e d s p e c i m e n o f t h e same c l a y , u n d e r a x i a l c o m -p r e s s i o n s h e a r . I t i s i n t e r e s t i n g t h a t t he s t a r t i n g p o i n t s o f p l a n e s t r a i n s t r e s s p a t h s l i e : o n t h e p a t h o f t h e i s o -t r o p i c a l l y c o n s o l i d a t e d t r i a x i a l s p e c i m e n . I t i s s e e n t h a t t h e p l a n e s t r a i n c o m p r e s s i o n s t r e s s p a t h s a l w a y s l i e above t h a t f o r t h e i s o t r o p i c t r i a x i a l s p e c i m e n . T h i s f a c t i m p l i e s t h a t i t i s n o t p o s s i b l e t o p r e d i c t p l a n e s t r a i n s t r e s s p a t h s o f a n i s o t r o p i c a l l y c o n s o l i d a t e d s p e c i m e n f r o m t e s t s o n l . i s o t r o p i c a l l y c o n s o l i d a t e d t r i a x i a l s p e c i m e n s . T h i s phenomenon i s i n a g r e e m e n t w i t h t h e o b s e r v a t i o n s o f o t h e r i n v e s t i g a t o r s ( H e n k e l and Sowa 1 9 6 3 , L a d d 1 9 6 5 ) , who r e -p o r t e d t h a t s t r e s s p a t h s o f a n i s o t r o p i c a l l y c o n s o l i d a t e d t r i a x i a l s p e c i m e n s c o u l d n o t be p r e d i c t e d f r o m t h o s e o f i s o t r o p i c a l l y c o n s o l i d a t e d s p e c i m e n s . S i n c e (a.T/cr£) _ v was t h e same u n d e r a x i a l com-X 6 max p r e s s i o n AC-1 a n d a x i a l e x t e n s i o n A E , t h e f a i l u r e e n v e l o p c o r r e s p o n d i n g t o maximum o b l i q u i t y i s . i n d e p e n d e n t o f t h e t o t a l s t r e s s p a t h t o f a i l u r e . A s s u m i n g c ' = 0 f o r t h e s e n o r m a l l y c o n s o l i d a t e d s p e c i m e n s , t h e c a l c u l a t e d v a l u e o f <}>' a t ( a . - o . ) v was 2 8 . 3 ° and a t (On '/a^) v <j>' was 3 3 . 5 ° . 1 3 max ± 6 max The c o r r e s p o n d i n g v a l u e s f r o m c o n v e n t i o n a l t r i a x i a l t e s t s on i s o t r o p i c a l l y c o n s o l i d a t e d s p e c i m e n s o f t h e same c l a y , was 2 6 . 6 ° and 3 1 . 8 ° r e s p e c t i v e l y ( S n e a d 1 9 6 8 ) . T h i s i n -c r e a s e i n v a l u e u n d e r p l a n e s t r a i n c o n d i t i o n s o v e r $ ' v a l u e s u n d e r t r i a x i a l c o n d i t i o n s o f 1 . 7 ° i s o f t h e same o r d e r o f m a g n i t u d e as r e p o r t e d by H e n k e l and Wade (1966 ) 85 f o r r e m o l d e d Wea ld c l a y . T e s t R e s u l t s - Sand Sand s a m p l e s were c o n s o l i d a t e d u n d e r e q u a l a x i a l (a^) and l a t e r a l Cc^') e f f e c t i v e s t r e s s e s w i t h z e r o s t r a i n i n t h e l o n g i t u d i n a l d i r e c t i o n . C o n s e q u e n t l y t h e l o n g i t u d i -n a l s t r e s s w o u l d be t h e m i n o r p r i n c i p a l e f f e c t i v e s t r e s s a t t h e end o f c o n s o l i d a t i o n . H o w e v e r , a t f a i l u r e ( ( a .-a 0 ) _ ) t h e l o n g i t u d i n a l s t r e s s i n a l l t y p e s o f s h e a r t e s t s w o u l d c o r r e s p o n d t o t h e i n t e r m e d i a t e p r i n c i p a l e f f e c t i v e s t r e s s , and 0."/, a . ' w o u l d c o n s t i t u t e t h e m a j o r and m i n o r p r i n c i p a l a JO e f f e c t i v e s t r e s s s y s t e m . In t h e s e i n v e s t i g a t i o n s , s i n c e no m e a s u r e m e n t s were made o f t h e l o n g i t u d i n a l s t r e s s , t h e s t r e s s v a r i a b l e s d u r i n g s h e a r t e s t s on s a n d were e x p r e s s e d i n t e r m s o f , and o ^ " . S t r e s s - S t r a i n R e l a t i o n s h i p s I n f i g . 6 .6 a r e p l o t t e d t h e a b s o l u t e v a l u e o f d e v i a t o r s t r e s s , |o* - a 0 | , and i n f i g . 6 . 7 a'/a^ {a"f a" f o r e x t e n s i o n t e s t ) v s . a x i a l s t r a i n , f o r e s s e n t i a l l y i d e n t i c a l s p e c i m e n s s h e a r e d u n d e r d i f f e r e n t s t r e s s p a t h s . S p e c i m e n s PS-S2 and PS-S3 h a d s t i f f e r s t r e s s - s t r a i n c u r v e s , a p p a r e n t -l y due t o t h e i r b e i n g c o n s o l i d a t e d t o h i g h e r i n i t i a l s t r e s s e s when c o m p a r e d t o s p e c i m e n PS-S I . F a i l u r e o f s p e c i m e n s i n a x i a l c o m p r e s s i o n was w i t h a c h a r a c t e r i s t i c 87 88 p e a k a n d a t l ow a x i a l s t r a i n s . T h i s b e h a v i o u r i s i n a g r e e -ment w i t h t h e r e s u l t s o f C o r n f o r t h ( 1 9 6 4 ) . F a i l u r e i n a x i a l e x t e n s i o n o c c u r r e d a t a r e l a t i v e l y l a r g e r a x i a l s t r a i n and a s h a r p p e a k d i d n o t e x i s t . No a p p a r e n t f a i l u r e p l a n e c o u l d be s e e n i n any o f t h e s p e c i m e n s . A l s o no n e c k i n g o c c u r r e d i n t h e e x t e n s i o n t e s t . Vo lume C h a n g e s d u r i n g S h e a r A l l s a m p l e showed a n e t e x p a n s i o n o r d i l a t i o n a t f a i l u r e . T h i s was mos t l i k e l y due t o t h e f a c t t h a t t h e y we re i n i t i a l l y a t maximum d e n s i t y and t e s t s were p e r f o r m e d a t r e l a t i v e l y l o w p r e s s u r e s . U n d e r i n c r e a s i n g a a x i a l a ' c o m p r e s s i o n , A C - 1 , t h e s a m p l e d e c r e a s e d i n vo lume i n i t i a l l y b u t e x p a n d e d c o n t i n u o u s l y t h e r e a f t e r ( f i g . 6 . 8 ) . T h i s k i n d o f vo lume c h a n g e b e h a v i o u r i s i n a g r e e m e n t w i t h t h e o b s e r v a -t i o n s o f o t h e r i n v e s t i g a t o r s ( C o r n f o r t h 1 9 6 4 ; F i n n , Wade and Lee 1 9 6 7 ) . U n d e r d e c r e a s i n g a a x i a l c o m p r e s s i o n a n d u n d e r a x i a l e x t e n s i o n , a n e t c o m p r e s s i o n o f t h e s a m p e l was n e v e r r e a l i s e d p r o b a b l y due t o c o n t i n u o u s l y d e c r e a s i n g mean n o r m a l e f f e c t i v e s t r e s s e s i n b o t h t h e s e t e s t s . The i n t e r -e s t i n g a s p e c t t o n o t e i s t he w i d e l y d i f f e r e n t r a t e s o f v o l u m e c h a n g e a t f a i l u r e ( ( c i-a „ )- ) i n t e s t t y p e AE when to 1 3 max c o m p a r e d t o t y p e s AC-1 and A C - 2 . I n a l l t y p e s o f t e s t s maximum r a t e s o f v o l u m e change o c c u r r e d n e a r f a i l u r e ; t h i s a g r e e s w i t h r e s u l t s o f C o r n f o r t h ( 1 9 6 4 ) . 90 E f f e c t i v e S t r e s s P a t h s D r a i n e d s t r e s s p a t h s on ( a - a )/2 v s . (.c'+o') / 2 1 3 1 3 s t r e s s p l a n e f o r t e s t s where one o f t h e p r i n c i p a l e f f e c t i v e s t r e s s e s i s h e l d c o n s t a n t a r e s t r a i g h t l i n e s a t ^ 4 5 ° t o t h e (c'+0/2 a x i s ( f i g . 6 . 9 ) . F o r t h e t h r e e e s s e n t i a l l y i d e n t i c a l . s p e c i m e n s t a k e n t o f a i l u r e u n d e r A C - 1 , AC-2 and A E , t h e s t r e s s p a t h s do n o t t e r m i n a t e on a common f a i l u r e e n v e l o p e . T a b l e I I I shows t h a t s h e a r i n g r e s i s t a n c e o f t h e s e e s s e n t i a l l y i d e n t i c a l s a m p l e s o f s a n d d i f f e r e d by a b o u t 4 ° i n <p* d e p e n d i n g on t h e t y p e o f t e s t ( c ' = 0 f o r a s a t u r a t e d s a n d ) . I t may be n o t e d i n t a b l e I I I t h a t t h e s p e c i m e n h a v i n g g r e a t e s t r a t e o f vo lume change a t f a i l u r e (PS-S2) h a d t h e maximum <f)'; and t h e one w i t h t h e l e a s t r a t e o f vo lume c h a n g e a t f a i l u r e (PS-S3) h a d t h e minimum cb'. The m e a s u r e d cb' v a l u e s o f a s a n d d e p e n d t o a m a r k e d e x t e n t on t h e r a t e o f vo lume change a t f a i l u r e ( B i s h o p and E l d i n 1 9 5 3 ) . T h u s t h e v a l u e o f <j>' was f o u n d a b o u t 3 ° s m a l l e r i n p l a n e s t r a i n e x t e n s i o n c o m p a r e d t o p l a n e s t r a i n c o m -p r e s s i o n . T h i s a p p a r e n t l y d e f i e s t h e c o n c l u s i o n s drawn f r o m t r i a x i a l 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 , where t h e same <f>* h a s b e e n f o u n d by a number o f i n v e s t i g a t o r s ( B i s h o p and E l d i n 1 9 5 3 , K i r k p a t r i c k 1 9 5 7 , C o r n f o r t h 1 9 6 4 , Wu e t a l 1 9 6 3 ) . In t h e d a t a p u b l i s h e d by R o s c o e e t a l ( 1963 ) i t was shown t h a t f o r d e n s e s a n d s p e c i m e n s w i t h t h e same i n i t i a l v o i d r a t i o s , t h e r a t e o f vo lume change a t f a i l u r e i n t r i -91 5>l. tin 00 < tn 6 __ .0 i 1 i Oo in rfl co in vo1 '•0 * S3 > <5 _ Z O Oo 1 in t~ Co 1 «-1 0 e a 0 b > — 00 wo + 0 S +• co cs + •'- - V x •— K ti eo 00 10 4 1 « 00 M- s-in 4 w 0 £ V tn 10 K. 4 eo •«* 4 r f 5 o" .£ > to VP vn ON VO vp in ve m •» 0< v» 1*? VI -t-• • <: CM V> < 10 < * i 0 3 vn • A. «s \A 1 J? m vO 1 •> vV E _2 o > > _ < 5 I c tn vv M 0 c c vi 6 V-u cv S 0 w t-u Cv TJ c c4 c • J 0 O c VI 0 .s «r» «bi >- V c C 6 Si-XL. f Q H - V -4-* it V C Of * —* I Cf .£ V. Ckl . A "0 < ~<$ 3 •/> cv K ci I VJ Ui "TJ z d ri E O a c5 -rr "5 t-3 : VI V -Q 0-92 a x i a l compression was about 4 0 to 5 0% g r e a t e r than i n t r i -a x i a l extension. Yet under c o n d i t i o n s o f plane s t r a i n , the r a t e o f volume change at f a i l u r e under a x i a l compression was about 2 1/2 times g r e a t e r than under a x i a l extension ( t a b l e I I I and f i g . 6.8). The much lower rate of volume change at f a i l u r e i n extension than compression under plane s t r a i n c o n d i t i o n s when compared to the conventional t r i -a x i a l c o n d i t i o n , may e x p l a i n the observed d i f f e r e n c e i n cb' between plane s t r a i n compression and extension t e s t s . * To the w r i t e r ' s knowledge no extension t e s t s under c o n d i t i o n s of plane s t r a i n have been reported i n the l i t e r a t u r e . I t i s , t h e r e f o r e , not p o s s i b l e to compare the observed behaviour. A standard t r i a x i a l compression t e s t was per-formed on the same sand at c l o s e l y the same i n i t i a l v o i d r a t i o as i n the plane s t r a i n t e s t s . The rat e of volume * I t i s i n t e r e s t i n g to note t h a t , a p p l i c a t i o n of Rowe's energy equation (Rowe, Barden and Lee 1964) f o r c o r r e c t i n g the s t r e s s r a t i o , a^Va^, at f a i l u r e , gives approximately the same value o f <b ( = 30.5°), i r r e s p e c t i v e of the s t r e s s path to f a i l u r e . In a s i m i l a r manner i f approximately the same value o f <j>' i s measured i n t r i a x i a l compression and extension by many i n v e s t i g a t o r s , the reason may be the compensating rates of volume change at f a i l u r e i n the two types of t e s t s . I f Roscoe's energy equation (Roscoe and S c h o f i e l d 1963) i s a p p l i e d to the plane s t r a i n t e s t data (using s t r e s s para-meters t = (0-^-03)72, s = (a£+ag)/2 and s t r a i n parameters 6v = £-^+£2, <5e = £,-£3 a n < 3 n e g l e c t i n g e l a s t i c s tored energy), i t i s also i n t e r e s t i n g to f i n d that approximately the same value of parameter M (=0.42) i s found i n compression and extension t e s t s on sand. 93 c h a n g e a t f a i l u r e was f o u n d t o be a l m o s t t h e same as i n t h e p l a n e s t r a i n i n c r e a s i n g cr_ a x i a l c o m p r e s s i o n t e s t , C l A C - 1 . The v a l u e o f . <*>" f o r t h e t r i a x i a l t e s t was 3 8 . 5 ° , c o m p a r e d t o a p p r o x i m a t e l y 4 4 ° f o r a x i a l c o m p r e s s i o n t e s t s u n d e r p l a n e s t r a i n c o n d i t i o n s . The i n c r e a s e i n tf)" v a l u e u n d e r p l a n e s t r a i n c o m p r e s s i o n o v e r t h e t r i a x i a l c o m p r e s s i o n v a l u e was 5 . 5 ° and o f t h e same o r d e r o f m a g n i t u d e as r e -p o r t e d by C o r n f o r t h ( 1 9 6 4 ) . The c o m p a r a b l e r a t e s o f vo lume c h a n g e i n t h e two t e s t s a r e a l s o i n a g r e e m e n t w i t h t h e o b -s e r v a t i o n s o f C o r n f o r t h ( 1 9 6 4 ) . 94 CHAPTER 7 SUMMARY AND CONCLUSIONS A new apparatus f o r shear t e s t i n g o f s o i l s under plane s t r a i n has been described. The main advantages claimed f o r t h i s apparatus over those used by other i n v e s t i g a t o r s , are: ( i ) Convenient and r e l a t i v e l y r a p i d c o n s o l i d a t i o n of samples under c o n d i t i o n s o f no l a t e r a l y i e l d p r i o r to shear; ( i i ) Permits a v a r i e t y of t o t a l s t r e s s path to f a i l u r e ; ( i i i ) No pressure chamber with f l u i d i s used around the specimen, thereby e l i m i n a t i n g any leakage i n t o the specimen e s p e c i a l l y f o r long term t e s t s . Further improvements to be inco r p o r a t e d i n the future design have been i n d i c a t e d . These include the measurements of intermediate p r i n c i p a l s t r e s s , f r i c t i o n on end p l a t e s , and use of f r i c t i o n l e s s end p l a t t e n s . Test technique has been described. From the plane s t r a i n t e s t s performed, both on a normally c o n s o l i d a t e d undisturbed c l a y and a sand, a general confirmation o f the form of previous r e s u l t s has been obtained. The value 95 of (j)'* was found l a r g e r under c o n d i t i o n s of plane s t r a i n when compared to the conventional t r i a x i a l c o n d i t i o n s . A reasonably c o n s i s t e n t p i c t u r e of the m a t e r i a l behaviour was observed from the t e s t r e s u l t s i n the apparatus. I t was, t h e r e f o r e , concluded that the apparatus was capable of y i e l d i n g the i n f o r m a t i o n d e s i r e d . 96 REFERENCES Ar t h u r , J.R.F. and Menzies, B.K., (1968) "Correspondence", Geotechnique, V o l . X V I I I , No. 2, p. 271-272. Barden, L. and Khayatt, A.J., (1966) "Increment S t r a i n Rate Ratios and Strength of Sand i n the T r i a x i a l Test", Geotechnique, V o l . XVI, No. 4, p. 338-357. 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( 1963 ) " S h e a r s t r e n g t h o f a n i s o t r o p i c a l l y c o n s o l i d a t e d c l a y s " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 8 9 , S . M . 6 , p . 1-26. B y r n e , P .M . ( 1966 ) " E f f e c t i v e s t r e s s p a t h s i n a s e n s i t i v e c l a y " , M .A . S c . T h e s i s , U . B . C . Campane J . l a , R .G . a n d M i t c h e l l , J . K . ( 1968 ) " I n f l u e n c e o f t e m p e r a t u r e v a r i a t i o n s on s o i l b e h a v i o u r " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 9 4 , No . SM3, p. 7 0 9 - 7 3 4 . C a s a g r a n d e , A . and P o u l o s , S . J . ( 1964 ) " I n v e s t i g a t i o n s o f s t r e s s d e f o r m a t i o n and s t r e n g t h c h a r a c t e r i s t i c s o f . c o m p a c t e d c l a y " , H a r v a r d s o i l m e c h . s e r i e s No . 7 4 , H a r v a r d U n i v . , C a m b r i d g e , M a s s . C h r i s t e n s e n , N . H . ( 1961 ) " M o d e l t e s t s on p l a n e a c t i v e e a r t h p r e s s u r e s i n s a n d s " , D a n i s h G e o t e c h n i c a l I n s t i t u t e B u l l e t i n N o . 1 0 . C o r n f o r t h , D . H . ( 1964 ) "Some e x p e r i m e n t s on t h e i n f l u e n c e o f s t r a i n c o n d i t i o n s on t h e s t r e n g t h o f s a n d " , G e o t e c h n i q u e , V o l . X I V , No . 2 , p . 1 4 3 - 1 6 6 . C r a w f o r d , C B . ( 1959 ) " T h e i n f l u e n c e o f r a t e o f s t r a i n on e f f e c t i v e s t r e s s e s i n a s e n s i t i v e c l a y " , P a p e r s on s o i l s , A S T M , S . T . P . N o . 2 5 4 . D u n c a n , J . M . and S e e d , H .B , ( 1966 ) " S t r e n g t h v a r i a t i o n a l o n g f a i l u r e s u r f a c e s i n c l a y " , J o u r n a l o f s o i l m e c h a n i c s and f o u n d a t i o n d i v . A S C E , V o l . 9 2 , S . M . 6 , p . 8 1 - 1 0 4 . 98 F i n n , W . D . L . , Wade, N . H . and L e e , K . L . (1967 ) " V o l u m e c h a n g e s i n t r i a x i a l and p i a n e s t r a i n t e s t s " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . , A S C E , V o l . 9 3 , S .M . 6J p . 2 9 7 - 3 0 8 . F u n g , Y . C . ( 1 9 6 5 ) " F o u n d a t i o n s o f s o l i d m e c h a n i c s " , P r e n t i c e H a l l I n c . , New J e r s e y . G r e e n , G . E . , ( 1967 ) " C o r r e s p o n d e n c e " , G e o t e c h n i q u e , V o l . X V I I , N o . 3, p . 2 9 5 . H a b i b , M.P . (195 3) " I n f l u e n c e o f t h e v a r i a t i o n o f t h e a v e r a g e p r i n c i p a l s t r e s s upon t h e s h e a r i n g s t r e n g t h o f s o i l s " , P r o c e e d . 3 r d I n t . C o n f . on S . M . F . E . , Z u r i c h , p . 1 3 1 - 1 3 6 . H a y t h o r n t h w a i t e , R .M. ( 1960 ) " S t r e s s a n d s t r a i n i n s o i l s " , P r o c e e d . 2nd s ympos ium on n a v a l s t r u c t u r a l m e c h a n i c s , Pe rgamon p r e s s , p . 1 8 5 - 1 9 3 . H a y t h o r n t h w a i t e , R .M. ( 1963 ) " D i s c u s s i o n " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . , A S C E , V o l . 8 9 , No . SM4. H e n k e l , D . J . ( 1960 ) " T h e s h e a r s t r e n g t h o f s a t u r a t e d r e m o l d e d c l a y s " , A S C E , r e s e a r c h c o n f e r e n c e on s h e a r s t r e n g t h o f c o h e s i v e s o i l s , B o u l d e r , C o l o r a d o , p . 5 3 3 - 5 5 4 . H e n k e l , D . J . a n d Sowa, V . A . , ( 1963 ) " T h e i n f l u e n c e o f s t r e s s h i s t o r y on s t r e s s p a t h s i n u n d r a i n e d t r i a x i a l t e s t s on c l a y " , S ympos ium on l a b o r a t o r y s h e a r t e s t i n g o f s o i l s , A . S . T . M . , STP 3 6 1 . H e n k e l , D . J . a n d Wade, N . H . ( 1966 ) " P l a n e s t r a i n t e s t s on a s a t u r a t e d r e m o l d e d c l a y " , J o u r n a l o f s o i l mech . and f o u n d , d i v . A S C E , V o l . 9 2 , S . M . 6 , p . 6 7 - 8 0 . H i r s c h f e l d , R . C . , ( 1960 ) " D i s c u - s i o n , S e s s i o n 4 " , A S C E , r e s e a r c h c o n f e r e n c e on s h e a r s t r e n g t h o f c o h e s i v e s o i l s , B o u l d e r , C o l o r a d o , p . 1 0 7 3 - 1 0 7 9 . J a c o b s o n , B. ( 1 9 5 7 ) , "Some f u n d a m e n t a l p r o p e r t i e s o f s a n d " , P r o c e e d . 4 t h I n t . C o n f . on S . M . F . E . , L o n d o n , V o l . 1. K i r k p a t r i c k , W . M . , (195 7) " C o n d i t i o n s f o r f a i l u r e o f s a n d s " , P r o c e e d . 4 t h I n t . C o n f . on S . M . F . E . , L o n d o n , V o l . 1 , p . 1 7 2 - 1 7 8 . K j e l l m a n , W . , ( 1 9 3 6 ) " R e p o r t on an a p p a r a t u s f o r consumate i n v e s t i g a t i o n s o f t h e m e c h a n i c a l p r o p e r t i e s o f s o i l s " , P r o c e e d . 1 s t I n t . C o n f . on S . M . F . E . , C a m b r i d g e , M a s s . , V o l . 2 , p . 1 6 - 2 0 . 99 K o , H . Y . a n d S c o t t , R . F . , ( 1967a ) " A new s o i l t e s t i n g a p p a r a t u s " , G e o t e c h n i q u e , V o l . X V I I , N o . 1, p . 4 0 - 5 7 . K o , H . Y . a n d S c o t t , R . F . ( 1967b ) " D e f o r m a t i o n o f s a n d i n s h e a r " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . , A S C E , V o l . 9 3 , S . M . 5 , p . 2 8 3 - 3 1 0 . K o , H . Y . a n d S c o t t , R . F . ( 1968 ) " D e f o r m a t i o n o f s a n d a t f a i l u r e " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 9 4 , S . M . 4 , p . 8 8 3 - 8 9 8 . L a d d , C . C , ( 1964 ) " S t r e s s s t r a i n m o d u l u s o f c l a y i n u n d r a i n e d s h e a r " , J o u r n a l o f s o i l mech . and f o u n d , d i v . A S C E , V o l . 9 0 , S . M . 5 , p . 1 0 3 - 1 3 2 . L a d d , C . C , ( 1 9 6 5 ) " S t r e s s - s t r a i n b e h a v i o u r o f a n i s o t r o -p i c a l l y c o n s o l i d a t e d c l a y s d u r i n g u n d r a i n e d s h e a r " , P r o c e e d . 5 t h I n t . c o n f . on S . M . F . E . , M o n t r e a l , V o l . 1 , p . 2 8 2 - 2 8 6 , L e e , K . L . and S e e d , H . B . ( 1964 ) " D i s c u s s i o n " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 9 0 , S . M . 6 , p . 1 7 3 - 1 7 5 . L e u s s i n k , H. and W i t t k e , W. (1963 ) " D i f f e r e n c e i n t r i a x i a l and p l a n e s t r a i n s h e a r s t r e n g t h " , S y m p o s i u m , L a b o r a t o r y s h e a r t e s t i n g o f s o i l s , O t t a w a , A S T M , STP l o . 3 6 1 , p . 7 7 - 8 9 . L e u s s i n k , H. (1965 ) " C o n t r i b u t i o n t o p a n e l d i s c u s s i o n , D i v . 2 " , P r o c e e d . 6 t h I n t . C o n f . on S . M . F . E . , M o n t r e a l , V o l . 3, p . . L o m i z e , G.M . and K r y z h a n o v s k y , A . L . (1967 ) " O n t h e s t r e n g t h o f s a n d " , P r o c e e d , o f t he G e o t e c h n i c a l C o n f . O s l o , V o l . 1, p . 2 1 5 - 2 1 9 . L o r e n z , H . , N e u m e u e r , H. a n d G u d e h u s , G . , (1965 ) " T e s t s c o n c e r n i n g c o m p a c t i o n and d i s p l a c e m e n t s p e r f o r m e d on s a m p l e s o f s a n d i n t he s t a t e o f p l a n e d e f o r m a t i o n " , P r o c e e d . 6 t h I n t . C o n f . on S . M . F . E . , M o n t r e a l , V o l . 1 , p . 2 9 3 - 2 9 6 . M a r s a l , R . J . , ( 1 9 6 5 ) " D i s c u s s i o n s D i v . 2 " , P r o c e e d . 6 t h I n t . C o n f . on S . M . F . E . , M o n t r e a l , ' V o l . 3. M o r e t t o , 0 . , ( 1965 ) " G e n e r a l r e p o r t , D i v . 2 " , P r o c e e d . 6 t h I n t . C o n f . on S . M . F . E . , M o n t r e a l , V o l . 3. 100 Newmark, N .M . ( 1960 ) " F a i l u r e h y p o t h e s e s f o r s o i l s " , A S C E , R e s e a r c h c o n f e r e n c e on s h e a r s t r e n g t h o f c o h e s i v e s o i l s , B o u l d e r , C o l o r a d o , p . 1 7 - 3 2 . O l s o n , R . E . a n d C a m p b e l l , L . M . ( 1 9 6 4 ) , " D i s c u s s i o n " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 9 0 , S . M . 6 , p . 1 6 7 - 1 7 3 . P e l t i e r , M.R. ( 1 9 5 7 ) , " E x p e r i m e n t a l i n v e s t i g a t i o n s on t h e i n t r i n s i c r u p t u r e c u r v e o f c o h e s i o n l e s s s o i l s " , P r o c e e d . 4 t h I n t . C o n f . on S . M . F . E . , L o n d o n , V o l . 1, p . 1 7 9 - 1 8 2 . R o s c o e , K . H . ( 1 9 5 3 ) , " A n a p p a r a t u s f o r a p p l i c a t i o n f o s i m p l e s h e a r t o s o i l s a m p l e s " , P r o c e e d . 3 r d I n t . C o n f . on S . M . F . E . , Z u r i c h , V o l . 1, p . 1 8 6 - 1 9 1 . R o s c o e , K . H . , S c h o f i e l d , A . N . and T h u r a i r a j a h , A . ( 1 9 6 3 ) , " A n e v a l u a t i o n o f t e s t d a t a f o r s e l e c t i n g a y i e l d c r i t e r i o n f o r s o i l s " , S ympos ium on L a b o r a t o r y s h e a r t e s t i n g o f s o i l s , O t t a w a , ASTM. STP No . 3 6 1 , p . 1 1 1 - 1 2 8 . R o s c o e , K . H . and S c h o f i e l d , A . N . ( 1963 ) " M e c h a n i c a l b e h a v i o u r o f an i d e a l i s e d wet c l a y " , P r o c e e d . E u r o p e a n C o n f . on s o i l m e c h . , V o l . 1 , p. 4 7 - 5 4 . Rowe, P.W. a n d B a r d e n , L. ( 1964 ) " I m p o r t a n c e o f f r e e e n d s in* t r i a x i a l t e s t i n g " , J o u r n a l s o i l mech . and f o u n d , d i v . A S C E , V o l . 9 0 , S . M . I , p . 1-27 . Rowe, P .W. , B a r d e n , L. and L e e , I .K . ( 1964 ) " E n e r g y c o m p o n e n t s t r i a x i a l c e l l and d i r e c t s h e a r t e s t s " , G e o t e c h n i q u e , V o l . X I V , N o . 3 , p . 2 4 7 - 2 6 1 . S h i b a t a , T . a n d K a r u b e , D. ( 1965 ) " I n f l u e n c e o f t h e v a r i a t i o n o f t h e i n t e r m e d i a t e p r i n c i p a l s t r e s s on t h e m e c h a n i c a l p r o p e r t i e s o f n o r m a l l y c o n s o l i d a t e d c l a y s " , P r o c e e d . 6 t h I n t . C o n f . on S . M . F . E . , M o n t r e a l , V o l . 1 , p . 3 5 9 - 3 6 3 . S n e a d , D . E . ( 1968 ) " C r e e p s t u d i e s on an u n d i s t u r b e d s e n s i t i v e c l a y " , F o r t h c o m i n g P h . D . t h e s i s , U . B . C . W h i t m a n , R .V . and L u s c h e r , U. ( 1962 ) " B a s i c e x p e r i m e n t s i n t o s o i l s t r u c t u r e i n t e r a c t i o n " , J o u r n a l o f s o i l m e c h . and f o u n d , d i v . A S C E , V o l . 8 8 , S . M . 6 , p . 1 3 5 - 1 6 7 . 101 •Wood, C . C . ( 1958 ) " S h e a r s t r e n g t h and vo lume c h a n g e c h a r a c t e r i s t i c s o f c o m p a c t e d s o i l s u n d e r c o n d i t i o n s o f p l a n e s t r a i n " , P h . D . t h e s i s , U n i v . o f L o n d o n . Wu, T . H . , L o h , A . K . and M a l v e r n , L . E . ( 1 9 6 3 ) " S t u d y o f f a i l u r e e n v e l o p e o f s o i l s " , J o u r n a l o f s o i l mech . and f o u n d , d i v . A S C E , V o l . 8 9 , N o . S . M . I , p . 14 5-181 . 102 APPENDIX 1 "PROCEDURE FOR MAKING RUBBER MEMBRANES" The r u b b e r membranes u s e d f o r t h e d i a p h r a g m s and t h e s a m p l e were made i n t h e l a b o r a t o r y by a s i n g l e d i p p r o c e s s . Compounded n a t u r a l r u b b e r l a t e x ( V u l t e x , l - F - 5 5 0 1 N a t u r a l ) made by t h e G e n e r a l L a t e x C o . o f C a n a d a , B r a m p t o n , O n t a r i o , was u s e d . D i p p i n g m o l d s were made o f a l u m i n u m and t h e s u r f a c e s o f m o l d s were f i n i s h e d t o a smoo th p o l i s h . B e f o r e d i p p i n g t h e m o l d i n t o l a t e x , i t was c l e a n e d t h o r o u g h l y w i t h a d e t e r g e n t , d r i e d a n d t h e n g i v e n a d i p i n a c o a g u l a n t . The c o a g u l a n t u s e d was a s o l u t i o n o f c a l c i u m n i t r a t e t e t r a h y d r a t e i n e t h y l a l c o h o l . The c o n c e n t r a t i o n o f t h e s a l t i n a l c o h o l g o v e r n s t h e t h i c k n e s s o f t h e l a t e x f i l m d e p o s i t on t h e m o l d . By t r i a l i t was f o u n d t h a t a 15% (by w e i g h t ) c o n c e n t r a t i o n o f t h e s a l t i n a l c o h o l w o u l d g i v e a f i l m t h i c k n e s s o f 0 . 0 1 0 " t o 0 . 0 1 2 " i n a s i n g l e d i p . The m o l d c o a t e d w i t h wet c o a g u l a n t was d i p p e d s l o w l y i n t o t h e l a t e x . C a r e was t a k e n n o t t o c r e a t e o r e n t r a p any a i r b u b b l e s i n t h i s . p r o c e s s . A f t e r a b o u t 2 t o 3 m i n u t e s o f d w e l l t i m e i n t h e l a t e x , t h e m o l d was w i t h d r a w n a t s u c h a r a t e t h a t t h e e x c e s s l a t e x w o u l d f l o w b a c k i n t o t h e t a n k 103 o f l a t e x and n o t c a u s e any r u n n i n g o n t h e s u r f a c e o f d e -p o s i t e d f i l m . T h e f i l m on t h e m o l d was a l l o w e d t o d r y a t room t e m p e r a t u r e ( a b o u t 7 0 ° ) f o r a b o u t 16 h o u r s . I t was t h e n c u r e d i n t h e o v e n f o r a b o u t 1 h o u r a t 1 0 0 - 1 1 0 ° C . When t h e m o l d c o o l e d down, t h e o u t s i d e o f t h e membrane was d u s t e d w i t h t a l c . I t was t h e n s t r i p p e d o f f t h e m o l d as more t a l c was a p p l i e d t o i t s i n n e r s u r f a c e . Membranes made i n t h i s m a n n e r s e e m e d ' t o g i v e no s i g n s o f d e t e r i o r a t i n g o v e r l o n g p e r i o d s o f u s a g e . In f a c t one s a m p l e membrane c o u l d be u s e d f o r 4 t o 5 t e s t s . The same d i a p h r a g m membranes s e r v e d f o r t h e e n t i r e t e s t i n g p r o g r a m . 104 APPENDIX 1 M E A S U R E M E N T OF B- VALUES S a m p l e numbeT P S - C 2 I n i t i a l . s t r e s s e s , °Z = 0-5 Kg/cm* U = 0-422 ,.• Verfi'c.a.1 Pressure Lcteral Dia.bWfa.grrt Pressure kg/a? AOJ POT2 p r e ssu re B -Value . ASi. ALL , 1475 • 7 1 • 4 S 5 -91 1730 2136 lozo o-5 0-5 • 4 9 4 •922 2o5>5 2704 0-5 0-5 - 4 9 4 • 988 2460 32 72. 3122 \o i-O / o /•o 3 ( 9 0 4 4 0 8 4255 Tabic A2 - I M«*saTemen\$ of B- Values =Jor a n und isfurbed s'j»<ci«en of Haney c(ay 

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