UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Comparative behaviour of an undisturbed clay under triaxial and plane strain conditions Vaid, Yoginder P. 1971

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1971_A1 V35_3.pdf [ 8.27MB ]
Metadata
JSON: 831-1.0050548.json
JSON-LD: 831-1.0050548-ld.json
RDF/XML (Pretty): 831-1.0050548-rdf.xml
RDF/JSON: 831-1.0050548-rdf.json
Turtle: 831-1.0050548-turtle.txt
N-Triples: 831-1.0050548-rdf-ntriples.txt
Original Record: 831-1.0050548-source.json
Full Text
831-1.0050548-fulltext.txt
Citation
831-1.0050548.ris

Full Text

COMPARATIVE BEHAVIOUR OF AN UNDISTURBED CLAY UNDER TRIAXIAL AND PLANE STRAIN CONDITIONS by Yoginder P. Vaid B.Sc. Engineering, Panjab U n i v e r s i t y , India, 1959 M.A.Sc., U n i v e r s i t y of B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of C i v i l Engineering We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1971 I n 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 t h e L i b r a r y s h a l l m a k e 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 a n d s t u d y . 1 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 m a y b e g r a n t e d b y t h e H e a d o f m y 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 b e a l l o w e d w i t h o u t m y 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 C i v i l E tog'ne-g-n n g 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 V a n c o u v e r 8 , C a n a d a D a t e May 2g , 1971 ABSTRACT Many f i e l d p r o b l e m s i n s o i l s a p p r o x i m a t e p l a n e s t r a i n c o n d i t i o n s . C o n v e n t i o n a l l a b o r a t o r y p r a c t i c e , h o w e v e r , c o n s i s t e n t l y u s e s t r i a x i a l c o m p r e s s i o n t e s t i n g f o r e v a l u a t i n g s t r e n g t h and d e f o r m a t i o n p r o p e r t i e s o f s o i l s . P o s s i b l e d i f f e r e n c e s b e t w e e n t r i a x i a l a n d p l a n e s t r a i n b e h a v i o u r o f n a t u r a l s o i l s h a v e so f a r r e c e i v e d l i t t l e a t t e n t i o n . New p l a n e s t r a i n and K Q - t r i a x i a l a p p a r a t u s e s h a v e b e e n d e s i g n e d i n w h i c h i t i s now p o s s i b l e t o s h e a r s a m p l e s u n d e r v a r i o u s s t r e s s p a t h s . A s e r i e s o f t r i -a x i a l and p l a n e s t r a i n t e s t s w e r e p e r f o r m e d on i d e n t i c a l l y K Q - c o n s o l i d a t e d s a m p l e s o f an u n d i s t u r b e d , s e n s i t i v e , m a r i n e c l a y . D r a i n e d and u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n t e s t s u n d e r b o t h i n c r e a s i n g a n d d e c r e a s i n g s t r e s s e s w e r e c a r r i e d o u t . S i m i l a r s e r i e s o f t e s t s w e r e a l s o made on h e a v i l y o v e r c o n s o l i d a t e d s p e c i m e n s . I t i s d e m o n s t r a t e d t h a t t h e u s e o f t r i a x i a l t e s t r e s u l t s w h e r e p l a n e s t r a i n c o n d i t i o n s p r e v a i l i n v a r i -a b l y l e a d s t o an o v e r e s t i m a t e o f d e f o r m a t i o n s and an i i u n d e r e s t i m a t e o f s t r e n g t h . M e t h o d s t o e s t i m a t e s t r a i n s i n u n d r a i n e d p l a n e s t r a i n s h e a r f r o m t h e r e s u l t s o f t r i a x i a l t e s t s u n d e r i d e n t i c a l s t r e s s p a t h s h a v e b e e n d e v e l o p e d . S i m i l a r l y , s t r a i n s d u r i n g d r a i n e d p l a n e s t r a i n s h e a r 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 c o u l d be p r e d i c t e d f r o m d r a i n e d and u n d r a i n e d t r i a x i a l r e s u l t s , u s i n g an e x t e n d e d . f o r m o f R e n d u l i c ' s h y p o t h e s i s . TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION 1 CHAPTER 2 L I T E R A T U R E REVIEW . . . . 7 2 . 1 S h e a r B e h a v i o u r o f K - c o n s o l i d a t e d C l a y s U n d e r S t r e s s C o n d i t i o n s o f t h e T r i a x i a l T e s t 8 2 . 2 S h e a r B e h a v i o u r o f K 0 - c o n s o l i d a t e d C l a y 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 14 CHAPTER 3 THE APPARATUSES 21 3 . 1 P l a n e S t r a i n A p p a r a t u s 21 G e n e r a l p r i n c i p l e 21 L a t e r a l p r e s s u r e d i a p h r a m s 22 ' F r i c t i o n l e s s ' end p l a t e s 24 M e a s u r e m e n t o f s i d e f r i c t i o n 24 3 . 2 K Q - T r i a x i a l A p p a r a t u s 25 3 . 3 L o a d i n g E q u i p m e n t 28 3 . 4 D a t a A q u i s i t i o n 31 3 . 5 I m p o r t a n t C h a r a c t e r i s t i c s Common t o B o t h A p p a r a t u s e s 31 K 0 - c o n s o l i d a t i o n 31 I n f l u e n c e o f l a t e r a l f l u i d p r e s s u r e s y s t e m c o m p l i a n c e on m e a s u r e d K0 35 3 . 6 M e a s u r e d K Q V a l u e s 40 CHAPTER 4 LABORATORY TEST ING 46 4 . 1 D e s c r i p t i o n o f C l a y T e s t e d 46 4 . 2 E x p e r i m e n t a l P r o c e d u r e s . 47 I n s t a l l i n g s p e c i m e n s i n a p p a r a t u s e s . . . 47 K 0 - c o n s o l i d a t i o n 47 S h e a r t e s t i n g 50 4 . 3 D e v e l o p m e n t o f T e s t i n g P r o g r a m 51 S t r e s s p a t h s i n v e s t i g a t e d 52 CHAPTER 5 PLANE STRAIN TEST RESULTS ON NORMALLY CONSOLIDATED HANEY CLAY 54 5 . 1 U n d r a i n e d T e s t R e s u l t s 55 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 55 P o r e p r e s s u r e s 61 E f f e c t i v e s t r e s s p a t h s 67 5 . 2 D r a i n e d T e s t R e s u l t s 70 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 71 V o l u m e c h a n g e s 75 F a i l u r e c o n d i t i o n s 75 5 . 3 C o m p a r i s o n and C o r r e l a t i o n o f D r a i n e d and U n d r a i n e d T e s t s 77 D r a i n e d and u n d r a i n e d s t r e s s - s t r a i n c h a r a c t e r i s t i c s 77 S t r e s s ay 93 5 . 4 D r a i n e d and U n d r a i n e d S t r e n g t h C h a r a c t e r i s t i c s . . . 95 CHAPTER 6 RESULTS OF T R I A X I A L TESTS ON NORMALLY CONSOLIDATED HANEY CLAY 99 6 . 1 U n d r a i n e d T e s t R e s u l t s 99 6 . 2 D r a i n e d T e s t R e s u l t s 107 6 . 3 C o m p a r i s o n a n d C o r r e l a t i o n o f D r a i n e d and U n d r a i n e d T e s t R e s u l t s I l l 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 l l F a i l u r e c o n d i t i o n s . 118 CHAPTER 7 COMPARISON OF PLANE STRAIN AND T R I A X I A L RESULTS - N . C . HANEY CLAY 123 7 . 1 C o n v e n t i o n a l C o m p a r i s o n 124 U n d r a i n e d t e s t s 124 D r a i n e d t e s t s 134 7 . 2 C o r r e l a t i o n o f T r i a x i a l and P l a n e S t r a i n B e h a v i o u r - S t r e s s - s t r a i n R e l a t i o n s 143 U n d r a i n e d e f f e c t i v e s t r e s s p a t h s . . . . 145 S t r e s s - s t r a i n c o m p a r i s o n s 147 7 . 3 P r e d i c t i o n o f D r a i n e d P l a n e S t r a i n B e h a v i o u r by t h e C a m b r i d g e S t r e s s -s t r a i n T h e o r y 164 7 . 4 C o r r e l a t i o n o f T r i a x i a l and P l a n e S t r a i n F a i l u r e C o n d i t i o n s 171 U n d r a i n e d s t r e n g t h 171 F a i l u r e c r i t e r i a 173 CHAPTER 8 TEST RESULTS ON H E A V I L Y OVER-CONSOLIDATED HANEY CLAY 178 8 . 1 The I n f l u e n c e o f S t r e s s P a t h on T r i a x i a l and P l a n e S t r a i n R e s u l t s . 178 U n d r a i n e d t e s t r e s u l t s 181 D r a i n e d t e s t r e s u l t s . . 187 C o m p a r i s o n o f d r a i n e d and u n d r a i n e d b e h a v i o u r 189 C y - s t r e s s i n p l a n e s t r a i n 193 8 . 2 C o m p a r i s o n o f T r i a x i a l and P l a n e S t r a i n R e s u l t s 196 S t r e s s - s t r a i n b e h a v i o u r 199 P o r e p r e s s u r e s and v o l u m e c h a n g e s . . . . 201 F a i 1 u r e c o n d i t i o n s 202 8 . 3 O c t a h e d r a l S t r e s s - S t r a i n R e l a t i o n s a n d F a i l u r e C o n d i t i o n s 203 E f f e c t i v e s t r e s s p a t h s 203 S t r e s s - s t r a i n c o m p a r i s o n s 205 F a i l u r e c o n d i t i o n s , 212 CHAPTER 9 SUMMARY AND CONCLUSIONS 215 B I B L I O G R A P H Y 227 A P P E N D I X A F r i c t i o n C o r r e c t i o n t o M e a s u r e d A x i a l S t r e s s i n P l a n e S t r a i n T e s t s 233 L I S T OF F IGURES F i g u r e P a g e 1 . 1 F i x e d p r i n c i p a l s t r e s s d i r e c t i o n s i n p l a n e s t r a i n and t r i a x i a l s a m p l e s 5 3 . 1 E x p l o d e d v i e w 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 23 3 . 2 K Q - t r i a x i a l a p p a r a t u s 26 3 . 3 S c h e m a t i c l a y o u t o f l o a d i n g , d i s p l a c e m e n t , v o l u m e c h a n g e and p r e s s u r e m e a s u r i n g s y s t e m 29 3 . 4 e - l o g a ' r e l a t i o n s h i p s - u n d i s t u r b e d Haney c l a y 41 3 . 5 R e l a t i o n s h i p s b e t w e e n 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 d u r i n g o n e - d i m e n s i o n a l c o n s o l i d a t i o n . 43 3 . 6 V a r i a t i o n o f K Q w i t h o v e r c o n s o l i d a t i o n r a t i o 45 N o r m a l l y c o n s o l i d a t e d Haney c l a y -P l a n e s t r a i n s h e a r : 5 . 1 U n d r a i n e d d e v i a t o r 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 56 5 . 2 U n d r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 58 5 . 3 U n d r a i n e d e f f e c t i v e 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 60 5 . 4 S t r e s s r a t i o a'I(a"+a ' ) - s t r a i n r e l a t i o n s h i p s . 62 y x z v i i 5 . 5 U n d r a i n e d p o r e p r e s s u r e c h a n g e - s t r a i n r e l a t i o n s h i p s . . . 63 5 . 6 V a r i a t i o n o f p o r e p r e s s u r e p a r a m e t e r ' a ' w i t h a x i a l s t r a i n 66 5 . 7 U n d r a i n e d e f f e c t i v e s t r e s s p a t h s 69 5 . 8 D r a i n e d d e v i a t o r 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 7 2 5 . 9 D r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 73 5 . 1 0 D r a i n e d v o l u m e t r i c s t r a i n - a x i a l s t r a i n r e l a t i o n s h i p s 76 5 . 1 1 S t a t e b o u n d a r y s u r f a c e f o r c o m p r e s s i o n t e s t s 81 5 . 1 2 C o m p a r i s o n o f p r e d i c t e d and o b s e r v e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n 84 5 . 1 2 a C o m p a r i s o n o f p r e d i c t e d and o b s e r v e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d a c t i v e c o m p r e s s i o n . . 85 5 . 1 3 T y p i c a l u n d r a i n e d s t r e s s p a t h and a s s u m e d c u r r e n t y i e l d l o c u s 88 5 . 1 4 C o m p a r i s o n o f o b s e r v e d and p r e d i c t e d s h e a r s t r a i n s d u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n 91 5 . 1 5 C o m p a r i s o n o f s h e a r s t r e s s - s t r a i n r e l a -t i o n s h i p d u r i n g d r a i n e d and u n d r a i n e d a c t i v e e x t e n s i o n . . 94 T r i a x i a l s h e a r : 6 . 1 U n d r a i n e d d e v i a t o r 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 101 6 . 2 U n d r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 102 6 . 3 U n d r a i n e d p o r e p r e s s u r e c h a n g e - s t r a i n r e l a t i o n s h i p s 103 6 . 4 V a r i a t i o n o f p o r e p r e s s u r e p a r a m e t e r ' a ' w i t h a x i a l s t r a i n 105 6 . 5 U n d r a i n e d e f f e c t i v e s t r e s s p a t h s 106 6 . 6 D r a i n e d d e v i a t o r 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 108 6 . 7 D r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 109 6 . 8 D r a i n e d v o l u m e t r i c s t r a i n - a x i a l s t r a i n r e l a t i o n s h i p s 110 6 . 9 C o m p r e s s i o n and e x t e n s i o n s t a t e b o u n d a r y s u r f a c e s .112 6 . 1 0 C o m p a r i s o n o f o b s e r v e d a n d p r e d i c t e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n 114 6 . 1 1 C o m p a r i s o n o f o b s e r v e d and p r e d i c t e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d a c t i v e c o m p r e s s i o n 115 6 . 1 2 C o m p a r i s o n o f o b s e r v e d and p r e d i c t e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d p a s s i v e e x t e n s i o n . 117 6 . 1 3 C o m p a r i s o n o f s h e a r s t r e s s - s t r a i n r e l a t i o n s h i p d u r i n g d r a i n e d and u n d r a i n e d a c t i v e e x t e n s i o n 119 C o m p a r i s o n o f 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 : 7 . 1 U n d r a i n e d d e v i a t o r 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 126 7 . 2 U n d r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 129 7 . 3 U n d r a i n e d e f f e c t i v e s t r e s s p a t h s 131 7 . 4 D r a i n e d d e v i a t o r 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 135 7 . 5 D r a i n e d 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 - s t r a i n r e l a t i o n s h i p s 137 7 . 6 D r a i n e d v o l u m e t r i c s t r a i n - a x i a l s t r a i n r e l a t i o n s h i p s 139 7 . 7 U n d r a i n e d o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s 146 7 . 8 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n i n u n d r a i n e d c o m p r e s s i o n 148 7 . 9 P o s t p e a k o c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n i n u n d r a i n e d c o m p r e s s i o n 150 7 . 1 0 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n i n u n d r a i n e d e x t e n s i o n 152 7 . 1 1 C o m p a r i s o n o f o b s e r v e d and p r e d i c t e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d p l a n e s t r a i n p a s s i v e c o m p r e s s i o n 155 7 . 1 2 Common s t a t e b o u n d a r y s u r f a c e c u r v e f o r d r a i n e d a c t i v e c o m p r e s s i o n 156 7 . 1 3 C o m p a r i s o n o f o b s e r v e d and p r e d i c t e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d p l a n e s t r a i n a c t i v e c o m p r e s s i o n 158 7 . 1 4 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n d u r i n g d r a i n e d a c t i v e e x t e n s i o n 159 7 . 1 5 O c t a h e d r a l s t r e s s r a t i o - s h e a r s t r a i n r e l a t i o n d u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n 162 7 . 1 6 O c t a h e d r a l s t r e s s r a t i o - s h e a r s t r a i n r e l a t i o n d u r i n g d r a i n e d a c t i v e c o m p r e s s i o n 163 7 . 1 7 C o m p a r i s o n o f o b s e r v e d s t a t e b o u n d a r y s u r f a c e c u r v e and t h e s t a t e b o u n d a r y s u r f a c e c u r v e p r e d i c t e d by t h e C a m b r i d g e t h e o r y f o r u n d r a i n e d p l a n e s t r a i n c o m p r e s s i o n 167 7 . 1 8 C o m p a r i s o n o f o b s e r v e d s t r e s s - s t r a i n r e l a t i o n s and t h o s e p r e d i c t e d by t h e C a m b r i d g e t h e o r y d u r i n g p l a n e s t r a i n d r a i n e d p a s s i v e c o m p r e s s i o n 169 O v e r c o n s o l i d a t e d Haney c l a y -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 : 8 . 1 U n d r a i n e d d e v i a t o r 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 182 8 . 2 V a r i a t i o n o f p o r e p r e s s u r e p a r a m e t e r ' a ' w i t h a x i a l s t r a i n 183 8 . 3 U n d r a i n e d e f f e c t i v e s t r e s s p a t h s 186 8 . 4 D r a i n e d d e v i a t o r 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 188 8 . 5 D r a i n e d a x i a l s t r a i n - v o l u m e t r i c s t r a i n r e l a t i o n s h i p s 190 8 . 6 C o m p a r i s o n o f s h e a r s t r e s s - s t r a i n b e h a v i o u r d u r i n g d r a i n e d and u n d r a i n e d p a s s i v e e x t e n s i o n 192 8 . 7 F a i l u r e e n v e l o p e s f o r N.C and 0 . C Haney c l a y 194 8 . 8 E f f e c t i v e 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 d u r i n g u n d r a i n e d p l a n e s t r a i n . 195 8 . 9 V a r i a t i o n o f s t r e s s r a t i o Oy/{o^+a^) w i t h a x i a l s t r a i n d u r i n g p l a n e s t r a i n s h e a r 197 8 . 1 0 F a i l u r e e n v e l o p e s - t r i a x i a l and p l a n e s t r a i n 204 8 . 1 1 O c t a h e d r a l e f f e c t i v e s t r e s s p a t h s d u r i n g u n d r a i n e d e x t e n s i o n 205 8 . 1 2 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n d u r i n g u n d r a i n e d e x t e n s i o n 207 8 . 1 3 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n d u r i n g u n d r a i n e d c o m p r e s s i o n 208 8 . 1 4 O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n d u r i n g d r a i n e d p a s s i v e e x t e n s i o n 210 8 . 1 5 O c t a h e d r a l s t r e s s r a t i o - s t r a i n r e l a t i o n d u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n 211 L I S T OF TABLES T a b l e . P a g e I P h y s i c a l p r o p e r t i e s o f Haney C l a y 48 I I Summary o f P l a n e S t r a i n T e s t R e s u l t s on N . C . H a n e y C l a y 96 I I I Summary o f T r i a x i a l T e s t R e s u l t s on N . C . H a n e y C l a y 120 IV C o m p a r i s o n o f F a i l u r e U n d e r U n d r a i n e d T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s 133 V C o m p a r i s o n o f F a i l u r e U n d e r D r a i n e d T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s 140 VI C o r r e l a t i o n o f U n d r a i n e d S t r e n g t h U n d e r T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s 172 V I I C o m p a r i s o n b e t w e e n O b s e r v e d P l a n e S t r a i n and cj)" P r e d i c t e d f r o m T r i a x i a l R e s u l t s by D i f f e r e n t F a i l u r e C r i t e r i a . . . 176 V I I I Summary o f D r a i n e d and U n d r a i n e d T r i a x i a l T e s t R e s u l t s on O . C . Haney C l a y 179 IX Summary o f D r a i n e d and U n d r a i n e d P l a n e S t r a i n T e s t R e s u l t s on O . C . Haney C l a y . . 180 X C o m p a r i s o n o f T r i a x i a l and P l a n e S t r a i n T e s t R e s u l t s on O . C . H a n e y C l a y 198 XI C o r r e l a t i o n o f U n d r a i n e d S t r e n g t h u n d e r T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s -O . C . Haney C l a y 213 x i i i L I S T OF SYMBOLS ° x y z P r i n c i p a l t o t a l s t r e s s e s i n x , y , z d i r e c t i o n s 0 ^ z 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 n x , y , z d i r e c t i o n s P r i n c i p a l c o n s o l i d a t i o n s t r e s s e s i n x , y , z x c , y c , z c d i r e c t i o n s . a," p 3 M a j o r , i n t e r m e d i a t e and 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 Q c t O c t a h e d r a l o r mean p r i n c i p a l t o t a l s t r e s s p , O " Q C £ Mean p r i n c i p a l e f f e c t i v e s t r e s s P c Mean p r i n c i p a l c o n s o l i d a t i o n s t r e s s p^ Mean 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 f a i l u r e p g E q u i v a l e n t p r e s s u r e q D e v i a t o r s t r e s s , ( 0 1 - 0 3 ) T . O c t a h e d r a l s h e a r s t r e s s o c t A T . C u m m u l a t i v e c h a n g e i n o c t a h e d r a l c o m p o n e n t 0 o f s h e a r s t r e s s a l c , 0 z c M a j o r p r i n c i p a l c o n s o l i d a t i o n s t r e s s Au C h a n g e i n p o r e p r e s s u r e A p ' I n c r e m e n t o f p r e s s u r e i n l a t e r a l f l u i d s y s t e m C,. U n d r a i n e d s t r e n g t h , ( 0 1 - 0 3 ) „„/2 u 3 max e P r i n c i p a l s t r a i n s i n x , y , z d i r e c t i o n s x , y , z p t J e-j 2 3 M a j o r , i n t e r m e d i a t e and m i n o r p r i n c i p a l s t r a i n s O c t a h e d r a l s h e a r V o l u m e o f s a m p l e Y . s h e a r s t r a i n ' o c t V o l u m e t r i c s t r a i n , AV/V 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 C o h e s i on C o m p l i a n c e o f l a t e r a l f l u i d p r e s s u r e s y s t e m S t r e s s r a t i o , q/p a t f a i l u r e S t r e s s r a t i o , /T~ T ^/p o c t S t r e s s r a t i o , ( a i - a 3 ) / ( a \ +a3) C o m p l i a n c e f a c t o r s S t r e s s r a t i o , ( o z - a 3 ) / ( o 1 - 0 3 ) R a t i o o f l a t e r a l t o v e r t i c a l e f f e c t i v e s t r e s s d u r i n g 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 C o m p r e s s i b i l i t y w i t h r e s p e c t t o mean p r i n c i p a l e f f e c t i v e s t r e s s V o i d r a t i o S l o p e o f v i r g i n K Q - c o n s o l i d a t i o n l i n e S l o p e o f i s o t r o p i c s w e l l i n g l i n e H e n k e l p o r e p r e s s u r e p a r a m e t e r S k e m p t o n p o r e p r e s s u r e p a r a m e t e r a t f a i l u r e ACKNOWLEDGEMENTS F i n a n c i a l s u p p o r t f o r t h e i n v e s t i g a t i o n s r e p o r t e d i n t h i s t h e s i s was p r o v i d e d by The N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a and 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 . G r a t e f u l a c k n o w l e d g e m e n t i s e x p r e s s e d f o r t h i s s u p p o r t . The a u t h o r w i s h e s t o t h a n k h i s r e s e a r c h s u p e r v i s o r , D r . R. G . C a m p a n e l l a , f o r h i s g u i d a n c e , e n c o u r a g e m e n t and a d v i c e . He w o u l d a l s o l i k e t o t h a n k D r . W. D. L i a m F i n n f o r h i s i n t e r e s t and e n c o u r a g e m e n t and D r . P . M. B y r n e f o r many h e l p f u l d i s c u s s i o n s . The t e c h n i c a l a s s i s t a n c e o f t h e s t a f f o f t h e c i v i l e n g i n e e r i n g w o r k s h o p i n f a b r i c a t i n g t h e t e s t i n g e q u i p m e n t s i s g r a t e f u l l y a c k n o w l e d g e d . CHAPTER I INTRODUCTION In t h e d e s i g n o f f o u n d a t i o n s and e a r t h s t r u c t u r e s t h e p r o b l e m s o f g r e a t e s t c o n c e r n a r e d e f o r m a t i o n a n d s t a -b i l i t y . S o i l p a r a m e t e r s n e e d e d t o t a c k l e t h e s e p r o b l e m s a r e g e n e r a l l y d e r i v e d 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 c o m -p r e s s i o n t e s t . The s t r e s s and s t r a i n c o n d i t i o n s o f t h i s t r i a x i a l t e s t , h o w e v e r , r a r e l y p r e v a i l i n p r a c t i c a l p r o b -l e m s . Even i n t h e c a s e o f l o a d i n g a c i r c u l a r f o o t i n g , t r i a x i a l c o n d i t i o n s a r i s e o n l y a t p o i n t s on t h e c e n t r a l a x i s b e n e a t h t h e f o o t i n g . In c o n t r a s t t o t h i s , t h e r e a r e many f i e l d p r o b l e m s i n w h i c h c o n d i t i o n s a p p r o x i m a t e t h o s e o f p l a n e s t r a i n . S o i l p r o b l e m s r e l a t i n g t o r e t a i n i n g w a l l s , s t r i p f o o t i n g s , s l o p e s , e m b a n k m e n t s , l o n g e x c a v a -t i o n s e t c . a r e f a m i l i a r e x a m p l e s o f t h e p l a n e s t r a i n c o n -d i t i o n . When c o n f r o n t e d w i t h t h e s e p r a c t i c a l p r o b l e m s , i t i s a l m o s t i n v a r i a b l y f o u n d t h a t t h e o n l y d a t a a v a i l a b l e on t h e p r o p e r t i e s o f s o i l h a v e b e e n o b t a i n e d f r o m t h e t r i a x i a l c o m p r e s s i o n t e s t . B e c a u s e o f t h e s c a r c i t y o f i n f o r m a t i o n c o n c e r n i n g 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 c o n -d i t i o n s , - t h e p o s s i b l e d i f f e r e n c e b e t w e e n t h e t r i a x i a l and t h e p l a n e s t r a i n s t r e s s c o n d i t i o n s i s u s u a l l y n e g l e c t e d . T h i s c a n h a r d l y be j u s t i f i e d s i n c e t h e r e i s i n s u f f i c i e n t e x p e r i m e n t a l e v i d e n c e , p a r t i c u l a r l y f o r c l a y s , w h i c h shows t h a t t h e r e a r e no i m p o r t a n t d i f f e r e n c e s i n 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 and t r i a x i a l s t r e s s s y s t e m s . V e r y l i t t l e has b e e n d o n e t o p r o p e r l y c o r r e l a t e d a t a f r o m d i f -f e r e n t t y p e s o f t e s t s i n t h e t r i a x i a l and t h e p l a n e s t r a i n a p p a r a t u s e s . I t i s c l e a r t h a t t h e r e i s a g r e a t n e e d f o r s u c h a c o r r e l a t i o n i f s o i l p a r a m e t e r s d e r i v e d f r o m t h e t r i a x i a l t e s t s a r e t o be u s e d t o s o l v e f i e l d p r o b l e m s a p p r o x i m a t i n g p l a n e s t r a i n c o n d i t i o n s . Many a p p a r e n t a n o m a l i e s and d i f f e r e n c e s may a r i s e when an a t t e m p t i s made t o d e t e r m i n e p r a c t i c a l s o i l p a r a m e t e r s f r o m t e s t s i n d i f f e r e n t t y p e s o f a p p a r a t u s e s , and e v e n f o r d i f f e r e n t t y p e s o f t e s t s i n t h e same a p p a r a t u s . F o r a g i v e n c o n s o l i d a t i o n h i s t o r y , t h e s t r e s s - s t r a i n and t h e s t r e n g t h b e h a v i o u r o f c l a y s i s known t o d e p e n d on t h e m a n n e r i n w h i c h s t r e s s e s a r e c h a n g e d t o i n d u c e f a i l u r e . The c o n d i t i o n o f no l a t e r a l s t r a i n d u r i n g c o n s o l i d a t i o n ( ^ - c o n s o l i d a t i o n ) i s o f t e n t h e s t a r t i n g p o i n t f o r most , d e f o r m a t i o n p r o b l e m s o f 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 m e c h a n i c a l b e h a v i o u r o f t h e s e c l a y s , i n p a r t i c u l a r , i s v e r y s e n s i t i v e t o t h e v a r i a t i o n o f t o t a l s t r e s s p a t h t o f a i l u r e ( H e n k e l & S o w a , 1 9 6 3 ; L a d d & B a i l e y , 1 9 6 4 ; L a d d , 1 9 6 5 ; H e n k e l , 1 9 7 0 ) . The n a t u r e o f t h i s v a r i a t i o n i s l i k e l y t o be a f u n c t i o n o f t h e o v e r c o n s o l i d a t i o n r a t i o w h i c h d i r e c t l y a f f e c t s t h e K Q v a l u e ( t h e r a t i o b e t w e e n h o r i z o n t a l and v e r t i c a l e f f e c t i v e s t r e s s e s d u r i n g o n e -d i m e n s i o n a l c o n s o l i d a t i o n ) i n t h e d e p o s i t . In v i e w o f t h e i m p o r t a n c e o f t h i s p r o b l e m i n t h e f i e l d , i t . i s e s s e n t i a l t h a t s h e a r b e h a v i q u r o f K Q - c o n s o l i d a t e d c l a y s be p r o p e r l y c o r r e l a t e d f r o m d i f f e r e n t t y p e s o f t e s t s i n t h e same a p p a r a t u s . No c o m p r e h e n s i v e s t u d y i n t h i s d i r e c t i o n h a s s o f a r b e e n r e p o r t e d e v e n u n d e r t r i a x i a l c o n d i t i o n s . C o m p a r i s o n b e t w e e n p l a n e s t r a i n and t r i a x i a l c o n d i t i o n s u n d e r s i m i l a r t o t a l s t r e s s p a t h s t o f a i l u r e h a s r a r e l y b e e n a t t e m p t e d . Lambe ( 1 9 6 4 , 1 9 6 7 ) , i n h i s s t r e s s p a t h m e t h o d , e m p h a s i s e s t h e g r e a t n e e d f o r o b t a i n i n g s o i l p a r a m e t e r s f r o m t e s t s i n w h i c h t h e c o n s o l i d a t i o n h i s t o r y and s u b s e q u e n t s t r e s s c h a n g e s d u p l i c a t e t h o s e a n t i c i p a t e d i n t h e f i e l d . . A t p r e s e n t , t h e i d e a l i s e d s t r e s s - s t r a i n t h e o r i e s f o r c l a y m a t e r i a l s ( e . g . t h e C a m b r i d g e t h e o r y : R o s c o e &, ; B u r l a n d , 1 9 6 8 ) a r e n o t s u f f i c i e n t l y a d v a n c e d t o e n a b l e p r e d i c t i o n o f s t r a i n s i n n a t u r a l c l a y s u n d e r a v a r i e t y o f s t r e s s p a t h s and s t r e s s s y s t e m s . N o n - l i n e a r and p a t h d e p e n d e n t s t r e s s r s t r a i n r e l a t i o n s h i p s , h o w e v e r , a r e f i n d i n g i n c r e a s e d u s e w i t h a d v a n c e d n u m e r i c a l t e c h n i q u e s , l i k e t h e f i n i t e e l e m e n t m e t h o d , f o r s o l v i n g d e f o r m a t i o n p r o b l e m s i n t h e f i e l d ( C l o u g h & W o o d w a r d , 1 9 6 7 ; M i t c h e l l , 1 9 6 9 ) . M o s t o f t h e l a b o r a t o r i e s u s u a l l y do n o t h a v e a c c e s s t o t h e more c o m p l i c a t e d p l a n e s t r a i n a p p a r a t u s . T h e r e f o r e , i f i t i s p o s s i b l e t o c o r r e l a t e d a t a f r o m t h e t r i a x i a l and t h e p l a n e s t r a i n t e s t s u n d e r s i m i l a r s t r e s s p a t h s , t h e e a s i l y e x e c u t a b l e t r i a x i a l t e s t c o u l d be u s e d t o e s t i m 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 . F o r p l a n e d e f o r m a t i o n a n a l y s i s by f i n i t e e l e m e n t s , 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 w o u l d be n e e d e d u n d e r s t r e s s p a t h s l i k e l y t o be a n t i c i p a t e d i n t h e g i v e n f i e l d p r o b l e m . In t h i s t h e s i s t h e d e v e l o p m e n t o f two p i e c e s o f a p p a r a t u s e s i s d e s c r i b e d : a p l a n e s t r a i n and a K Q - t r i a x i a l a p p a r a t u s . In t h e s e a p p a r a t u s e s s i m i l a r s e r i e s o f t e s t s w e r e p e r f o r m e d on a s a t u r a t e d u n d i s t u r b e d c l a y u s i n g " i d e n t i c a l end o f o n e - d i m e n s i o n a l c o n s o l i d a t i o n c o n d i t i o n s " a n d , f o l l o w i n g a v a r i e t y o f s t r e s s p a t h s t o f a i l u r e . In F i g . 1 . 1 , x , y , z a x e s d e n o t e t h e f i x e d d i r e c t i o n s o f p r i n c i p a l a x e s w i t h i n t h e t r i a x i a l and t h e p l a n e s t r a i n s p e c i m e n s . In b o t h t h e a p p a r a t u s e s i t was p o s s i b l e t o f o l l o w any d e s i r e d s t r e s s p a t h t o f a i l u r e i n t h e s t r e s s p l a n e a v s . a . The s t r e s s p a t h s a c t u a l l y s t u d i e d c o n s i s t e d o f b o t h c o m p r e s s i o n and e x t e n s i o n modes o f f a i l u r e , w i t h e i t h e r i n c r e a s i n g o r d e c r e a s i n g one o f t h e s e two s t r e s s e s o a n d A a z , w h i l e t h e o t h e r was h e l d c o n s t a n t . In t h i s m a n n e r , f o u r d i f f e r e n t s t r e s s p a t h s w e r e o b t a i n e d . I f z - d i r e c t i o n i s (a) P lane Strain Sample X (radial) <X,€ Y (tangential) <Jy = Ox €y = € x (b) Tri a x i a l S a m p l e Fig. I-I FIXED PRINCIPAL STRESS DIRECTIONS IN PLANE STRAIN AND TRIAXIAL SAMPLES. t a k e n t o c o i n c i d e w i t h t h e a x i s o f t h e s p e c i m e n , t h e s e s t r e s s p a t h s a r e : 1 . P a s s i v e c o m p r e s s i o n 2. A c t i v e c o m p r e s s i o n : 3 . P a s s i v e e x t e n s i o n : 4. A c t i v e e x t e n s i o n : a i n c r e a s e d , a h e l d c o n s t a n t Z X a d e c r e a s e d , o h e l d c o n s t a n t X z o i n c r e a s e d , a h e l d c o n s t a n t X z a d e c r e a s e d , a h e l d c o n s t a n t Z A F o r e a c h o f t h e s e s t r e s s p a t h s c o n s o l i d a t e d u n -d r a i n e d and d r a i n e d t e s t s w e r e p e r f o r m e d . E a c h t y p e o f t e s t was made b o t h u n d e r p l a n e s t r a i n and t r i a x i a l s t r e s s c o n d i t i o n s . The e f f e c t o f c o n s o l i d a t i o n h i s t o r y was s t u d i e d by c a r r y i n g o u t two s e r i e s o f t e s t s - i n t h e f i r s t s e r i e s n o r m a l c o n s o l i d a t i o n and i n t h e s e c o n d s e r i e s h e a v y o v e r -c o n s o l i d a t i o n was u s e d as t h e p r e s h e a r c o n d i t i o n . C o r r e l a t i o n o f s o i l p a r a m e t e r s has b e e n a t t e m p t e d f r o m d i f f e r e n t s t r e s s p a t h s i n t h e same t e s t a p p a r a t u s . A l s o a c o m p a r i s o n and c o r r e l a t i o n o f s t r e s s - s t r a i n - s t r e n g t h c h a r a c t e r i s t i c s has b e e n made f o r s i m i l a r s t r e s s p a t h s u n d e r p l a n e s t r a i n and t r i a x i a l c o n d i t i o n s . E s t i m a t i o n o f s o i l 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 r o m r e s u l t s i n t h e t r i a x i a l t e s t s i s t h e n i n d i c a t e d . CHAPTER I I L I T E R A T U R E REVIEW T h e r e i s a v e r y l i m i t e d amount o f t e s t d a t a r e -p o r t e d f o r c l a y m a t e r i a l s w h i c h w e r e c o n s o l i d a t e d u n d e r K Q - c o n d i t i o n a n d i n w h i c h s u b s e q u e n t s t r e s s c h a n g e s c o r -r e s p o n d e d t o p l a n e s t r a i n ( H e n k e l and W a d e , 1 9 6 6 ; D u n c a n and S e e d , 1 9 6 6 a ; H a m b l y and R o s c o e , 1 9 6 9 ; D i c k e y e_t. a l . , 1 9 6 8 ) . The i n f l u e n c e o f v a r y i n g 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 on s t r e s s - s t r a i n - s t r e n g t h b e h a v i o u r has g e n e r a l l y b e e n i g n o r e d n o t o n l y u n d e r p l a n e s t r a i n b u t a l s o f o r t h e t r i a x i a l s t r e s s c o n d i t i o n s . In p a r t i c u l a r , no i n f o r m a t i o n seems t o e x i s t on s t r e s s - s t r a i n - 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 h e a v i l y K o ~ o v e r c o n s o l i d a t e d c l a y s . The f o l l o w i n g l i t e r a t u r e r e v i e w w i l l be c o n s i d e r e d u n d e r two s e p a r a t e s e c t i o n s . U n d e r t h e f i r s t s e c t i o n a r e d e s c r i b e d s t u d i e s , u n d e r t h e t r i a x i a l c o n d i t i o n s , on t h e s t r e s s - s t r a i n - s t r e n g t h r e s p o n s e o f K Q - c o n s o l i d a t e d c l a y s , and t h e i n f l u e n c e o f v a r y i n g 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 on t h i s r e s p o n s e . The s e c o n d s e c t i o n d e a l s w i t h s i m i l a r s t u d i e 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 , a l o n g w i t h c o m p a r i s o n b e t w e e n p l a n e s t r a i n and t r i a x i a l r e s u l t s w h e r e v e r a t t e m p t e d . 2 . 1 S h e a r b e h a v i o u r o f K Q - c o n s o 1 i d a t e d c l a y s u n d e r s t r e s s  c o n d i t i o n s o f t h e t r i a x i a l t e s t . In a l l t r i a x i a l t e s t s , i n c l u d i n g t h e K Q - t r i a x i a l , t h e d i r e c t i o n s o f p r i n c i p a l a x e s a r e f i x e d . A l t h o u g h an i n f i n i t e v a r i e t y o f s t r e s s p a t h s i n a v s . a . p l a n e "Z. X ( s e e F i g . 1 . 1 ) c a n be f o l l o w e d d u r i n g s h e a r , t h e r e -s u l t i n g s t r a i n s g i v e r i s e t o e i t h e r an 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 f a i l u r e . The d i r e c t i o n o f m a j o r p r i n c i p a l s t r e s s a t f a i 1 u r e , r e l a t i v e t o i t s d i r e c t i o n a t t h e end o f K - n o r m a l c o n s o l i d a t i o n , r e m a i n s o ' u n a l t e r e d i n a x i a l c o m p r e s s i o n s h e a r , w h e r e a s i t i s r e o r i e n t e d t h r o u g h 90° i n a x i a l e x t e n s i o n s h e a r . The r e v e r s e s i t u a t i o n h o l d s f o r h e a v i l y K - o v e r c o n s o l i d a t e d J o s p e c i m e n s , b e c a u s e t h e r a d i a l s t r e s s , a , e x c e e d s t h e A v e r t i c a l s t r e s s , a z , a t t h e end o f r e b o u n d o r o v e r -c o n s o l i d a t i o n . T h e r e f o r e , t h e s t r e s s s y s t e m o f t h e K Q - t r i a x i a l t e s t p e r m i t s s t u d y o f s t r e n g t h m o b i l i z a t i o n u n d e r c o n d i t i o n s o f 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 w i t h no r e o r i e n t a t i o n o r w i t h 90° r e o r i e n t a t i o n o f p r i n c i p a l s t r e s s e s . H a n s e n and G i b s o n ( 1 9 4 9 ) s h o w e d t h a t t h e u n d r a i n e d s t r e n g t h o f K - c o n s o l i d a t e d c l a y s h a v i n g t h e same h i s t o r y o f c o n s o l i d a t i o n d e p e n d s on t h e d i r e c t i o n o f t h e m a j o r p r i n c i p a l s t r e s s a t f a i l u r e i n r e l a t i o n t o t h e d i r e c t i o n o f m a j o r p r i n c i p a l s t r e s s a t c o n s o l i d a t i o n . A s s u m i n g i s o -t r o p y o f e f f e c t i v e s t r e n g t h p a r a m e t e r s , z' and cf>', and S k e m p t o n - p o r e p r e s s u r e p a r a m e t e r , A ^ , t h e y showed t h a t t h e u n d r a i n e d s t r e n g t h w o u l d be l e a s t f o r p a s s i v e e x t e n -s i o n and maximum f o r a c t i v e c o m p r e s s i o n . T h i s v a r i a t i o n r e s u l t s f r o m t h e f a c t t h a t t h e c h a n g e s i n p o r e p r e s s u r e s , and t h u s t h e v a l u e s , o f t h e u n d r a i n e d s t r e n g t h , d e p e n d s on t h e d e g r e e 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 s t r e s s e s w h i c h , i n t u r n , d e p e n d s on t h e o r i e n t a t i o n o f t h e f a i l u r e p l a n e , c ' , and A ^ , h o w e v e r , a r e u n l i k e l y t o be i s o t r o p i c f o r m o s t c l a y s . Many i n v e s t i g a t o r s h a v e d e m o n s t r a t e d t h e v a r i a t i o n o f u n d r a i n e d s t r e n g t h w i t h o r i e n t a t i o n o f t h e f a i l u r e p l a n e , by p e r f o r m i n g u n c o n s o l i d a t e d - u n d r a i n e d , ( U U ) , t r i -a x i a l t e s t s on s p e c i m e n s t r i m m e d w i t h t h e i r a x e s a t d i f -f e r e n t a n g l e s t o t h e p l a n e on w h i c h m a j o r p r i n c i p a l s t r e s s a c t e d d u r i n g o n e - d i m e n s i o n a l c o n s o l i d a t i o n ( W a r d , 1 9 5 6 ; Ward e t . a j_ . , 1 959 ; H v o r s l e v , 1 9 6 0 ; L o , 1 9 6 5 ; B i s h o p , 1 9 6 6 ; D u n c a n & S e e d , 1 9 6 6 ; Lo & M i l l i g a n , 1 9 6 7 ; C o n l o n e t . a l . , 1 9 7 0 ) . S u c h s p e c i m e n s , h o w e v e r , d i f f e r e d f r o m . an e l e m e n t i n t h e f i e l d i n t h a t t h e a n i s o t r o p i c s t r e s s s y s t e m u n d e r w h i c h t h e s p e c i m e n s w e r e c o n s o l i d a t e d had b e e n r e l e a s e d d u r i n g s a m p l i n g and r e p l a c e d by an i s o t r o p i c s t r e s s s y s t e m s u f f i c i e n t t o m a i n t a i n c o n s t a n t v o l u m e . I t h a s , h o w e v e r , b e e n shown ( S k e m p t o n & S o w a , 1 9 6 3 ; L a d d & L a m b e , 1 9 6 3 ; N o o r a n y a n d S e e d , 1 9 6 5 ) t h a t t h e u n d r a i n e d s t r e n g t h o f a t r i a x i a l s p e c i m e n f r o m w h i c h t h e 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 has b e e n u n l o a d e d w i t h o u t c h a n g e i n w a t e r c o n t e n t i s a l m o s t e q u a l t o t h e u n d r a i n e d s t r e n g t h o f an i d e n t i c a l s p e c i m e n t e s t e d w i t h no r e l e a s e o f t h e 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 ( i . . e . i n - s i t u s p e c i m e n ) , p r o v i d e d t h e d i r e c t i o n o f c o m p r e s s i v e s t r a i n t o f a i l u r e i s t h e same i n b o t h c a s e s . The s t r a i n s r e s u l t i n g f r o m t h e u n l o a d i n g 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 r e g e n e r a l l y v e r y s m a l l and c a u s e l i t t l e a l t e r a t i o n i n m i c r o s t r u c t u r e , w h i c h seems t o be t h e r e a s o n f o r t h e two s p e c i m e n s g i v i n g t h e same u n d r a i n e d s t r e n g t h . In v i e w o f t h e f o r e g o i n g o b s e r -v a t i o n , i t seems l i k e l y t h a t t h e n a t u r e o f v a r i a t i o n o f u n d r a i n e d s t r e n g t h w i t h o r i e n t a t i o n o f f a i l u r e p l a n e , as d e t e r m i n e d f r o m UU t e s t s , w o u l d be s i m i l a r t o t h e i n - s i t u s t r e n g t h f o r a l l - o r i e n t a t i o n s o f t h e f a i l u r e p l a n e . F o r i n i t i a l l y n o r m a l l y K Q - c o n s o l i d a t e d c l a y s i n w h i c h 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 had a c t e d i n t h e v e r t i c a l d i r e c -t i o n , UU s t r e n g t h o f v e r t i c a l s p e c i m e n was f o u n d t o be t h e g r e a t e s t and t h e l o w e s t UU s t r e n g t h was a s s o c i a t e d w i t h f a i l u r e p l a n e o r i e n t e d h o r i z o n t a l l y . H e a v i l y o v e r c o n s o l i -d a t e d c l a y s (Ward e_t. a j_ . ) , on t h e o t h e r h a n d , had h o r i -z o n t a l s p e c i m e n s t h e s t r o n g e s t and v e r t i c a l s p e c i m e n s t h e w e a k e s t . L a d d a n d B a i l e y ( 1 9 6 4 ) and L a d d ( 1 9 6 4 , 6 5 , 67) p e r f o r m e d u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n t e s t s on n o r m a l l y K Q - c o n s o l i d a t e d s p e c i m e n s o f u n d i s t u r b e d K a w a s a k i and r e m o l d e d B o s t o n b l u e c l a y s . F o r i d e n t i c a l s p e c i m e n s , C u / a ^ c i n e x t e n s i o n was f o u n d t o be a p p r o x i m a t e l y h a l f o f t h e v a l u e i n c o m p r e s s i o n f o r b o t h t y p e s o f c l a y s . A t maximum o b i i q u i t y . K a w a s a k i c l a y had a C o u l o m b cf>" o f 40° and 52° i n 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 r e s p e c t i v e l y . The c o r r e s p o n d i n g v a l u e s f o r B o s t o n b l u e c l a y w e r e 26° and 3 8 ° . A x i a l s t r a i n a t f a i l u r e i n c o m p r e s s i o n was g e n e r a l l y l e s s t h a n 1/2% c o m p a r e d t o more t h a n 6% i n e x t e n s i o n . 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 M a n g l e r u d c l a y by B j e r r u m and Kenny ( 1 9 6 7 ) show s i m i l a r d i f f e r e n c e s i n u n d r a i n e d s t r e n g t h o f i d e n t i c a l s p e c i m e n s . No d a t a was g i v e n r e g a r d i n g i n c o m p r e s s i o n and e x t e n s i o n . A c o r r e l a t i o n o f d r a i n e d and u n d r a i n e d c o n v e n -t i o n a l a x i a l c o m p r e s s i o n t e s t s ( c e l l p r e s s u r e = c o n s t a n t ) on 5 u n d i s t u r b e d N o r w e g i a n c l a y s was done by S i m o n s ( 1 9 6 3 ) . The same C o u l o m b was f o u n d f o r b o t h t y p e s o f t e s t s on i n i t i a l l y K Q - c o n s o l i d a t e d s p e c i m e n s , p r o v i d e d ( a i / a 3 ) m a x was u s e d f o r t h e f a i l u r e c o n d i t i o n . B j e r r u m and L a n d v a ( 1 9 6 6 ) made s i m i l a r c o n c l u s i o n s f o r a n o t h e r N o r w e g i a n q u i c k c l a y . U n d r a i n e d was i n a l l c a s e s l e s s t h a n d r a i n e d cK i f maximum d e v i a t o r s t r e s s was u s e d as t h e f a i l u r e c o n d i t i o n . T h i s c h a r a c t e r i s t i c i s t y p i c a l o f a l l s e n s i t i v e c l a y s . L e w i n and B u r l a n d ( 1 9 7 0 ) p e r f o r m e d a s e r i e s o f d r a i n e d t r i a x i a l t e s t s on a n i s o t r o p i c a l l y 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 s l a t e d u s t , i n o r d e r t o d e m o n s t r a t e t h e d e p e n d e n c e o f s t r a i n s on t h e d i r e c t i o n o f s t r e s s i n c r e m e n t v e c t o r . The s t r e s s i n c r e m e n t d e f i n e d by (AaJ* 2 + 2Ao - g 2 ) ' 5 = c o n s t a n t , was i m p o s e d on i d e n t i c a l s a m p l e s w h i c h w e r e c o n s o l i d a t e d t o a p p r o x i m a t e l y K Q - c o n d i t i o n . B o t h s h e a r and v o l u m e t r i c s t r a i n s w e r e f o u n d t o be t h e l a r g e s t f o r t h e d i r e c t i o n o f s t r e s s i n c r e m e n t v e c t o r c o r r e s p o n d i n g t o t h e g r e a t e s t i n c r e a s e i n d e v i a t o r s t r e s s , o^- a'. F o r t h o s e d i r e c t i o n s o f t h e s t r e s s i n c r e m e n t v e c t o r w h i c h c o r r e s p o n d e d t o t h e u n l o a d i n g o f t h e 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 , b o t h s h e a r and v o l u m e t r i c s t r a i n s w e r e f o u n d t o be p r a c t i c a l l y i n s i g n i f i c a n t . The s i z e o f t h e i n c r e m e n t u s e d was 5% o f t h e l e n g t h o f t h e b a s i c s t r e s s s t a t e v e c t o r , ( o j + 20-3 )^ . T h e s e r e s u l t s , w h i c h w e r e f i r s t o f t h e i r k i n d , c l e a r l y d e m o n s t r a t e d t h e d e p e n d e n c e o f s t r a i n s on t h e a p p l i e d s t r e s s p a t h . The f e a t u r e o f p a r t i c u l a r i n t e r e s t was t h e e x t r e m e l y s m a l l s t r a i n s a s s o c i a t e d w i t h e x t e n s i o n s t r e s s p a t h s , w h e n c o m p a r e d t o t h o s e d u r i n g c o m p r e s s i o n s t r e s s p a t h s . No i n f o r m a t i o n was p r e s e n t e d on t h e f a i l u r e c o n d i t i o n s u n d e r t h e s t r e s s p a t h s s t u d i e d . On t h e b a s i s o f t h e f o r e g o i n g v e r y l i m i t e d d a t a t h e f o l l o w i n g o b s e r v a t i o n s c a n be made r e g a r d i n g t h e b e -h a v i o u r o f K - c o n s o l i d a t e d c l a y s : o J 1 . They a r e a n i s o t r o p i c w i t h r e s p e c t t o t h e i r u n d r a i n e d s t r e n g t h . T h i s v a r i a t i o n o f u n d r a i n e d s t r e n g t h may r e s u l t f r o m a n i s o t r o p y w i t h r e s p e c t t o t h e v a l u e s o f t h e e f f e c t i v e s t r e n g t h p a r a m e t e r s o r a n i s o t r o p y w i t h r e s p e c t t o d e v e l o p m e n t o f c h a n g e s i n p o r e p r e s s u r e , o r b o t h ; i t may a l s o r e s u l t f r o m 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 s t r e s s d i r e c t i o n s . ! 2 . In 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 h e same e f f e c t i v e s t r e n g t h p a r a m e t e r s a r e r e p o r t e d f o r b o t h u n -d r a i n e d and d r a i n e d s h e a r u s i n g ( V i V ^ ^ m a x a s t ' i e f a i l u r e c o n d i t i o n . 3 . (j)"* i n u n d r a i n e d e x t e n s i o n h a s b e e n r e p o r t e d t o be as much as 12° l a r g e r t h a n t h e v a l u e d u r i n g u n d r a i n e d c o m p r e s s i o n . 4 . S t r a i n s u n d e r d r a i n e d c o n d i t i o n s d e p e n d v e r y much on t h e m a g n i t u d e and t h e d i r e c t i o n o f t h e s t r e s s i n c r e m e n t i n t h e t r i a x i a l s t r e s s p l a n e . 5 . No i n f o r m a t i o n w h a t s o e v e r i s a v a i l a b l e on h e a v i l y o v e r c o n s o l i d a t e d c l a y s when t e s t e d u n d e r t h e t r i -a x i a l s t r e s s s y s t e m . UU t e s t s on t h e s e c l a y s ( w i t h 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 r e m o v e d ) , h o w e v e r , show t h a t t h e n a t u r e o f a n i s o t r o p y o f u n d r a i n e d s t r e n g t h ( h o r i z o n t a l s a m p l e s s t r o n g e s t ) i s d i f f e r e n t f r o m t h e t y p e o f a n i s o t r o p y e n c o u n t e r e d i n i n i t i a l l y 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 ( v e r t i c a l s a m p l e s s t r o n g e s t ) . 6 . D r a i n e d f a i l u r e c o n d i t i o n s i n a x i a l e x t e n s i o n and a c t i v e c o m p r e s s i o n h a v e n o t b e e n s t u d i e d . C o n s e q u e n t l y , no c o r r e l a t i o n o f . the d i f f e r e n t t y p e s o f t e s t s p o s s i b l e i n t h e t r i a x i a l a p p a r a t u s has b e e n m a d e . 2 . 2 S h e a r b e h a v i o u r o f K Q - c o n s o l i d a t e d c l a y s u n d e r p l a n e s t r a i n  c o n d i t i ons . M o s t p l a n e s t r a i n e q u i p m e n t s u t i l i z e r e c t a n g u l a r t e s t s p e c i m e n s . C o n s e q u e n t l y , d i r e c t i o n s o f t h e p r i n c i p a l s t r e s s e s r e m a i n f i x e d as i n t h e c a s e o f K - t r i a x i a l t e s t s . o H e n c e a g a i n , o n l y a x i a l c o m p r e s s i o n o r e x t e n s i o n t y p e s o f t e s t s a r e p o s s i b l e . H o w e v e r , an i n f i n i t e v a r i e t y o f s t r e s s p a t h s i n t h e p l a n e n o r m a l t o t h e d i r e c t i o n o f z e r o s t r a i n , i . e . , a , a s t r e s s p l a n e , c a n be f o l l o w e d t o i n d u c e c o m -2 X p r e s s i o n o r e x t e n s i o n f a i l u r e . H e n k e l and Wade ( 1 9 6 6 ) r e p o r t e d c o m p a r i s o n o f u n d r a i n e d t r i a x i a l and p l a n e s t r a i n p a s s i v e c o m p r e s s i o n t e s t s on n o r m a l l y K Q - c o n s o l i d a t e d r e m o l d e d W e a l d c l a y . I t was shown t h a t C u / o j c r a t i o i n p l a n e s t r a i n was a b o u t 8% h i g h e r when c o m p a r e d t o t h e K - t r i a x i a l v a l u e . A x i a l s t r a i n t o f a i l u r e i n p l a n e s t r a i n was 2% c o m p a r e d t o 6% u n d e r K Q - t r i a x i a l c o n d i t i o n s . H o w e v e r , a t maximum o b l i q u i t y , {o'/o' C o u l o m b cj)' was h i g h e r by o n l y 1 . 2 ° i n p l a n e 1 j max s t r a i n t h a n t h e t r i a x i a l v a l u e . E f f e c t i v e s t r e s s p a t h s i n t h e two t e s t s w e r e u n i q u e l y d e f i n e d i n t e r m s o f o c t a h e d r a l s t r e s s e s — 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 s t r e s s , O " Q C J . J ( T h i s i s a l s o known as t h e 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 n o t e d by s y m b o l p) and o c t a h e d r a l s h e a r s t r e s s , T In t e r m s o f p r i n c i p a l s t r e s s e s , a i , o 2 , c r 3 , o c t a h e d r a l s t r e s s e s a r e e x p r e s s e d as °oct = p = 1 / 3 ( a r + a * + a 3 ) a o c t = 1 / 3 ( a i + ° z + a s ) ( 2 ' 2 ) T o c t " ^ \ 2 2 2 ( a i - a 2 ) + ( a 2 - a 3 ) + ( a 3 - o i ) ( 2 . 3 ) The c h a n g e i n p o r e p r e s s u r e , A u , was shown t o be c o n t r o l l e d e s s e n t i a l l y by t h e c h a n g e s i n o c t a h e d r a l t o t a l n o r m a l s t r e s s , Aa and o c t a h e d r a l s h e a r s t r e s s , A T i . e . o c t ' o c t Au = A a o c t + a A x o c t ( 2 . 4 ) w h e r e ' a ' i s t h e H e n k e l p o r e p r e s s u r e p a r a m e t e r . The v a l u e o f t h e p r i n c i p a l s t r e s s a s s o c i a t e d w i t h z e r o s t r a i n d i r e c t i o n was f o u n d t o be i n t e r m e d i a t e b e t w e e n t h e o t h e r two 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 , and t h e r a t i o 0 2 / ( 0 1 + 0 - 3 ) s t a y e d e s s e n t i a l l y c o n s t a n t d u r i n g u n d r a i n e d s h e a r . L a d a n y i ( 1 9 6 7 ) i n d i s c u s s i o n t o H.enkel and W a d e ' s p a p e r a r g u e d t h a t p a r t o f t h e o b s e r v e d d i f f e r e n c e i n s t r e n g t h and s t r e s s - s t r a i n b e h a v i o u r i n t h e two t y p e s o f c o m p r e s s i o n t e s t s c o u l d be e x p l a i n e d by u s i n g a l t e r n a t e s t r e s s - s t r a i n p a r a m e t e r s . I t was s u g g e s t e d t h a t t h e r e m i g h t be a u n i q u e o c t a h e d r a l s h e a r s t r e s s - s t r a i n ( T Q C ^ . V S . Y o c ^ ) r e l a t i o n s h i p , s i m i l a r t o t h e one i n d u c t i l e m a t e r i a l s w h i c h y i e l d a c c o r d i n g t o t h e von M i s e s y i e l d c o n d i t i o n . O c t a h e d r a l s h e a r s t r a i n , ^ o c t ' 1 S d e f i n e d 1 n t e r m s o f p r i n c i p a l s t r a i n s e l 5 e 2 , E 3 as Y o c t 3 1_ M 2 2 2 ( e i - e 2 ) + ( E Z - E S ) + U s - E i ) (2.5) C o m p a r a t i v e t r i a x i a l and p l a n e s t r a i n u n d r a i n e d c o m p r e s s i o n t e s t s , s i m i 1 a r t o t h o s e o f H e n k e l and W a d e , w e r e r e p o r t e d by S h i b a t a and K a r u b e ( 1 9 6 7 ) on r e m o l d e d O s a k a c l a y . S h i b a t a and K a r u b e a l s o c o n c l u d e d t h a t t h e u n d r a i n e d e f f e c t i v e s t r e s s p a t h s w e r e e s s e n t i a l l y u n i q u e i n t e r m s o f o c t a h e d r a l s t r e s s e s . A t f a i l u r e (oWo* ) , max h o w e v e r , t h e v a l u e o f C o u l o m b <j>" i n p l a n e s t r a i n was 39° t o 47° when c o m p a r e d t o v a l u e o f 35° t o 38° u n d e r t r i a x i a l c o n d i t i o n s . U n d r a i n e d p l a n e s t r a i n 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 w e r e p e r f o r m e d by D u n c a n and S e e d ( 1 9 6 6 ) on u n d i s t u r b e d S a n - F r a n c i s c o Bay M u d . S i m i l a r t e s t s w e r e a l s o r e p o r t e d by D i c k e y e_t. a j_ . ( 1 9 6 8 ) on s a m p l e s o f B o s t o n B l u e C l a y . F o r i d e n t i c a l end o f K - c o n s o l i d a t i o n c o n d i t i o n o b o t h t h e s e c l a y s s h o w e d u n d r a i n e d s t r e n g t h ( ( a x - a 3 ) / 2 ) max i n e x t e n s i o n t o be o n l y 75% o f t h e c o m p r e s s i o n v a l u e . In B o s t o n B l u e C l a y , p e a k d e v i a t o r s t r e s s i n c o m p r e s s i o n was r e a c h e d a t 1 . 5 % a x i a l s t r a i n c o m p a r e d t o 1% a x i a l s t r a i n i n e x t e n s i o n . The c o r r e s p o n d i n g v a l u e s f o r Bay Mud w e r e 3 . 5 % and 10% r e s p e c t i v e l y . A t ( a " i - a 3 ) m = . f o r B o s t o n max B l u e C l a y was f o u n d t o be 30° and 42° r e s p e c t i v e l y i n 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 s h e a r . The c o r r e s p o n d i n g v a l u e s a t ( a i / a 3 ) m , v w e r e 34° and 4 2 ° . F o r Bay Mud v a l u e u s i n g max " ( a i - o 3 ) m , u o r ( a f / a 3 ) , v as t h e f a i l u r e c o n d i t i o n was e s s e n -max ma x t i a l l y t h e same and a m o u n t e d t o 38° i n c o m p r e s s i o n a g a i n s t 35° i n e x t e n s i o n . H a m b l y and R o s c o e ( 1 9 6 9 ) p e r f o r m e d a s e r i e s o f p l a n e s t r a i n t e s t s on ^ - c o n s o l i d a t e d s p e c i m e n s o f r e m o l d e d K a o l i n e . D r a i n e d and u n d r a i n e d t e s t s w e r e made u s i n g a v a r i e t y o f s t r e s s p a t h s t o i n d u c e c o m p r e s s i o n o r e x t e n s i o n f a i l u r e . They t o o , f o u n d t h a t e x t e n s i o n u n d r a i n e d s t r e n g t h was s l i g h t l y l e s s t h a n 2 / 3 o f t h e c o m p r e s s i o n v a l u e . H o w e v e r , <(>' was f o u n d t o be t h e s a m e , i r r e s p e c t i v e o f t h e s t r e s s p a t h t o f a i l u r e , and e q u a l l e d t h e v a l u e o b t a i n e d f r o m t r i a x i a l t e s t s on t h e same c l a y . T h i s seems t o be i n c o n t r a d i c t i o n w i t h a l l t h e p r e v i o u s l y q u o t e d r e s u l t s . One r a t h e r s u r p r i s i n g f e a t u r e o f t h e d r a i n e d e x t e n s i o n t e s t s i n v o l v i n g l a r g e u n l o a d i n g o f t h e mean n o r m a l s t r e s s w a s , t h a t t h e r e was no v o l u m e e x p a n s i o n a t any s t a g e o f t h e t e s t . A l s o i r r e s p e c t i v e o f t h e s t r e s s p a t h , a y ' / ( ° x ' + a z " ) w a s f ° u n c ' t o be e s s e n t i a l l y c o n s t a n t d u r i n g t h e t e s t . From t h e f o r e g o i n g v e r y l i m i t e d d a t a t h e f o l l o w i n g o b s e r v a t i o n s c a n be made r e g a r d i n g p l a n e s t r a i n b e h a v i o u r o f c l a y s : 1 . No i n f o r m a t i o n e x i s t s on h e a v i l y K Q - o v e r -c o n s o l i d a t e d s p e c i m e n s . F o r K o - n o r m a l l y c o n s o l i d a t e d s a m p l e s , 2 . U n d r a i n e d s t r e n g t h i n e x t e n s i o n was a b o u t 66% t o 75% o f t h e c o m p r e s s i o n v a l u e . E x t e n s i o n f a i l u r e s t r a i n was 3 t o 5 t i m e i l a r g e r t h a n t h e s t r a i n r e q u i r e d t o c o m p r e s s i o n f a i l u r e . 3 . C o n c l u s i o n s r e g a r d i n g t h e v a r i a t i o n s o f C o u l o m b a r e c o n t r a d i c t o r y . E x t e n s i o n cf>' was shown t o be e i t h e r l a r g e r by up t o 1 2 ° , o r s m a l l e r by 3 ° , o r e v e n e q u a l t o c o m p r e s s i o n <{>" a c c o r d i n g t o t h e r e s u l t s o f d i f f e r e n t i n v e s t i g a t o r s . 4 . The r a t i o o f t h e e f f e c t i v e p r i n c i p a l s t r e s s c o r r e s p o n d i n g t o t h e d i r e c t i o n o f z e r o s t r a i n t o t h e sum o f t h e o t h e r two 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 , s t a y e d e s s e n t i a l l y c o n s t a n t d u r i n g p l a n e s t r a i n s h e a r t e s t s . The r e l a t i o n s h i p was f o u n d t o h o l d i n d e p e n d e n t o f t h e a p p l i e d s t r e s s p a t h . The e x t r e m e l y l i m i t e d d a t a on c o m p a r i s o n o f t r i -a x i a l and p l a n e s t r a i n b e h a v i o u r o f n o r m a l l y K Q - c o n s o l i d a t e d c l a y s s h o w e d t h a t : 1 . In u n d r a i n e d c o m p r e s s i o n t e s t s common e f f e c -t i v e s t r e s s p a t h s w e r e f o l l o w e d i n t e r m s 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 . P o r e p r e s s u r e c h a n g e s w e r e e s s e n t i a l l y c o n t r o l l e d by c h a n g e s i n t o t a l 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 . 2 . C o n f l i c t i n g r e s u l t s e x i s t e d on t h e r e l a t i v e v a l u e s o f <J>' u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . P l a n e s t r a i n c o m p r e s s i o n cj>' was shown t o be l a r g e r by 1 . 2 ° t o 9° o r e v e n e q u a l t o t h e t r i a x i a l a c c o r d i n g t o t h e r e s u l t s o f d i f f e r e n t i n v e s t i g a t o r s . R e s u l t s o f o n l y one i n v e s t i g a t o r s h o w e d e x t e n s i o n cj)" t o be 4° l a r g e r i n p l a n e s t r a i n t h a n t h e t r i a x i a l v a l u e ( L a d d , 1 9 6 7 ) . In v i e w o f t h e a b o v e m e n t i o n e d l i m i t e d and o f t e n c o n t r a d i c t o r y d a t a , t h i s t h e s i s i s an a t t e m p t t o s t u d y a n d c o m p a r e t h e t r i a x i a l and p l a n e s t r a i n b e h a v i o u r o f c l a y s . The c o m p a r i s o n i s a t t e m p t e d u n d e r a number o f a p p l i e d s t r e s s p a t h s , on b o t h i n i t i a l l y n o r m a l l y c o n s o l i d a t e d and h e a v i l y o v e r c o n s o l i d a t e d s p e c i m e n s . An u n d e r s t a n d i n g o f t h e p l a n e s t r a i n s h e a r b e h a v i o u r o f c l a y s i s e x t r e m e l y i m p o r t a n t f r o m t h e v i e w p o i n t o f f i e l d a p p l i c a t i o n . In p a r t i c u l a r , c o r r e l a t i o n o f t h e t r i a x i a l b e h a v i o u r w i t h t h e one 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 w o u l d p e r m i t e s t i m a -t i o n o f l a t t e r f r o m t h e e a s i l y e x e c u t a b l e t r i a x i a l t e s t s . M o s t o f t h e r e s e a r c h s u m m a r i z e d e a r l i e r i n t h i s c h a p t e r was d o n e on r e m o l d e d c l a y s . In t h i s s t u d y a n a t u r a l , u n d i s t u r b e d , m o d e r a t e l y s e n s i t i v e c l a y was c h o s e n , i n s t e a d . In v i e w o f t h e i m p o r t a n t s t r u c t u r a l d i f f e r e n c e s b e t w e e n r e m o l d e d and n a t u r a l c l a y s , t h e c o n c l u s i o n d e r i v e d f r o m t e s t s on r e m o l d e d c l a y s may n o t s t r i c t l y h o l d f o r n a t u r a l c l a y s . T h i s a p p a r e n t l y was t h e r e a s o n f o r c h o o s i n g a n a t u r a l c l a y f o r t h e s t u d y r e p o r t e d h e r e i n . CHAPTER I I I THE APPARATUSES 3 . 1 . 0 P l a n e S t r a i n A p p a r a t u s M a r k - I v e r s i o n 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 h a s b e e n d e s c r i b e d by V a i d ( 1 9 6 8 ) . V a r i o u s m o d i f i c a t i o n s w e r e p r o p o s e d t h e r i n t o be i n c o r p o r a t e d i n t h e f u t u r e d e s i g n . In t h e f o l l o w i n g p a r a g r a p h s o n l y t h e g e n e r a l p r i n c i p l e o f t h e a p p a r a t u s and t h e i m p r o v e m e n t s made i n M a r k - I a r e d e s c r i b e d . 3 . 1 . 1 G e n e r a l P r i n c i p l e The a p p a r a t u s was d e s i g n e d t o e n a b l e c o n s o l i d a -t i o n u n d e r K Q - c o n d i t i o n and s u b s e q u e n t s h e a 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 . The 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 i s i n i t i a l l y 4 " l o n g , 1 " w i d e and 2 V h i g h . F i g . 1 . 1 d e f i n e d t h e o r i e n t a t i o n o f t h e p l a n e s t r a i n s p e c i m e n i n r e l a t i o n t o t h e r e f e r e n c e c a r t e s i a n c o - o r d i n a t e s y s t e m . T h r o u g h o u t t h i s t h e s i s t h e s u b s c r i p t s x , y , z w i l l d e n o t e t h e f i x e d d i r e c t i o n s o f t h e p r i n c i p a l a x e s w i t h i n t h e t e s t s p e c i m e n . When r e f e r r i n g t o p r i n c i p a l s t r e s s e s , o r s t r a i n s , t h e A r a b i c s u b s c r i p t s 1 , 2 , 3 w i l l be u s e d t o d e n o t e m a j o r , i n t e r m e d i a t e , and m i n o r v a l u e s o f t h e s e q u a n t i t i e s r e s p e c t i v e l y . V e r t i c a l s t r e s s , a , was t r a n s -m i t t e d t o t h e s p e c i m e n t h r o u g h a r i g i d l o a d i n g c a p , w h e r e a s 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 m s s e a l e d on s t i f f b a c k i n g p l a t e s w e r e 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 , a . The c o n d i t i o n o f z e r o X 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 , y , was s a t i s f i e d by c o n f i n i n g t h e s p e c i m e n l e n g t h b e t w e e n a p a i r o f r i g i d 1 f r i c t i o n 1 e s s 1 end p l a t e s . The l a t e r a l p r e s s u r e d i a -phrams and t h e r i g i d end p l a t e s w e r e p o s i t i o n e d a r o u n d t h e s p e c i m e n by c l a m p i n g them t o g e t h e r . An e x p l o d e d v i e w o f t h e a p p a r a t u s i s shown i n F i g . 3 . 1 . D u r i n g K Q - c o n s o l i d a t i o n t h e s a m p l e was p r e v e n t e d f r o m e x p e r i e n c i n g any s t r a i n i n t h e y - d i r e c t i o n by t h e p r e s e n c e o f r i g i d end p l a t e s a n d , i n t h e x - d i r e c 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 v o l u m e 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 m s . The 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 m s was s m a l l and d i d n o t s e r i o u s l y a f f e c t t h e K Q - v a l u e . The e f f e c t o f m a g n i t u d e o f c o m p l i a n c e on t h e m e a s u r e d K - v a l u e w i l l be d i s c u s s e d l a t e r i n t h i s o c h a p t e r . 3 . 1 . 2 L a t e r a l P r e s s u r e D i a p h r a m s T h e s e d i a p h r a m s c o n s i s t e d o f s h a l l o w , box s h a p e d , w a t e r f i l l e d , t h i n r u b b e r m e m b r a n e s s e a l e d by r u b b e r Sample membrane onload cel l Top drainage , . , , . „ — L o a d i n g cop L o c a t i n g pins. Fr ict ion less end plates Diophragm membranes-^ — . P o r o u s sta in less 0 - ring Locating pins Stainless plate L n VI u '#///////, f V//////// /////. I Base pedesta l Bottom load cell Diaphragm sealing p l a t e s 4 Stiffner Diaphragm support plate 4 0 1 4 I 1-020 | r — — • ! Bottom dra inage Fig.31 EXPLODED VIEW OF THE PLANE STRAIN APPARATUS ro O - r i n g s on t h e f a c e s o f b a c k i n g p l a t e s ( F i g . 3 . 1 ) . The b a c k i n g p l a t e s w e r e made o u t o f 3 / 4 " t h i c k s t a i n l e s s , i n s t e a d o f p e r s p e x u s e d i n t h e e a r l i e r M a r k - I , and w e r e s t i f f e n e d as b e f o r e t o k e e p t h e c o m p l i a n c e o f t h e l a t e r a l f l u i d p r e s s u r e s y s t e m t o a m i n i m u m . 3 . 1 . 3 ' F r i c t i o n 1 e s s ' End P l a t e s T h e s e p l a t e s w e r e made o u t o f a l u m i n u m i n s t e a d o f p e r s p e x u s e d i n t h e e a r l i e r M a r k - I . The 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 w e r e h i g h l y p o l i s h e d . When a s s e m b l i n g a r o u n d t h e s p e c i m e n , 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 a p p l i e d t o t h i s p o l i s h e d s u r f a c e t o k e e p t h e f r i c t i o n a l d r a g b e t w e e n t h e s a m p l e and t h e p l a t e t o a m i n i m u m . T h e s e p l a t e s w e r e i n s t r u m e n t e d w i t h c o l u m n t y p e s t r a i n g a g e d a l u m i n u m l o a d c e l l s i n o r d e r t o m e a s u r e t h e p r i n c i p a l s t r e s s , ( s e e F i g . 3 . 1 ) . The a r e a o v e r w h i c h was m e a s u r e d a m o u n t e d t o a t l e a s t 60% o f t h e a r e a o f t h e s p e c i m e n end a t any t i m e d u r i n g t h e t e s t . 3 . 1 . 4 M e a s u r e m e n t o f S i d e F r i c t i o n D u r i n g t h e d e f o r m a t i o n o f t h e s p e c i m e n i n t h e v e r t i c a l d i r e c t i o n , p a r t o f t h e v e r t i c a l l o a d i s t r a n s -f e r r e d t h r o u g h s i d e f r i c t i o n t o t h e r i g i d 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 . The m a g n i t u d e o f t h i s f r i c t i o n a l d r a g w o u l d d e p e n d on t h e e f f e c t i v e n e s s o f l u b r i c a t i o n b e t w e e n t h e m o v i n g and t h e s t a t i o n a r y b o u n d a r i e s , and a l s o on t h e i n t e n s i t y o f n o r m a l p r e s s u r e b e t w e e n t h e m . S i l i c o n e g r e a s e was u s e d as l u b r i c a n t t o k e e p t h e f r i c t i o n t o a m i n i m u m v a l u e . In o r d e r t o h a v e a d i r e c t m e a s u r e o f t h e s i d e f r i c t i o n , t h e b a s e p e d e s t a l o f t h e s p e c i m e n was i n s t r u m e n t e d w i t h an a l u m i n u m l o a d c e l l ( s i m i l a r t o t h o s e u s e d t o m e a s u r e a ) w h i c h r e g i s -t e r e d t h e v e r t i c a l l o a d t r a n s f e r r e d a t t h e b o t t o m o f t h e s p e c i m e n . W i t h t h e k n o w l e d g e o f t h e l o a d a p p l i e d a t t h e t o p and t h a t t r a n s f e r r e d t o t h e b o t t o m a p r o c e d u r e was d e v e l o p e d ( A p p e n d i x A) t o d e t e r m i n e an a v e r a g e v a l u e o f v e r t i c a l s t r e s s , a , w h i c h c o r r e c t e d f o r s i d e f r i c t i o n e f f e c t s . 3 . 2 . 0 K Q - T r i a x i a l A p p a r a t u s D e t a i l s o f t h e K Q - t r i a x i a l a p p a r a t u s h a v e b e e n d e s c r i b e d e l s e w h e r e ( C a m p a n e l l a & V a i d , 1 9 7 1 ) . O n l y a b r i e f d e s c r i p t i o n o f i t s i m p o r t a n t f e a t u r e s i s p r e s e n t e d h e r e i n . F i g . 3 . 2 shows t h e a p p a r a t u s w i t h a l l e s s e n t i a l d e t a i l s . The a p p a r a t u s i s e s s e n t i a l l y a c o n v e n t i o n a l t r i -a x i a l c e l l w i t h t h e d i f f e r e n c e t h a t t h e a r e a o f t h e l o a d i n g p l u n g e r i s e x a c t l y e q u a l t o t h a t o f t h e s o i l s p e c i m e n a n d , t h a t s t a i n l e s s s t e e l was u s e d t o b u i l d a l l Fig . 3-2 k 0 - TRIAXIAL APPARATUS. i t s c o m p o n e n t s . The l o a d i n g p l u n g e r i s 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 by a p a i r o f l i n e a r Thompson B a l l B u s h i n g s and i s s e a l e d t o t h e h e a d o f t h e t r i a x i a l c e l l by a f l e x i b l e r o l l i n g d i a p h r a m ( s e e F i g . 3 . 2 ) . In t h i s m a n n e r a f r i c t i o n l e s s s e a l i s o b t a i n e d and t h e a x i a l l o a d m e a s u r e d o u t s i d e t h i s c e l l i s p r e c i s e l y e q u a l t o t h a t t r a n s f e r r e d t o t h e s o i l s p e c i m e n . T h u s , a v e r y u n -d e s i r a b l e c h a r a c t e r i s t i c 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 c e l l s was e l i m i n a t e d . The t h i c k s t a i n l e s s c y l i n d e r was u s e d i n o r d e r t o k e e p t h e c o m p l i a n c e o f t h e c e l l t o a m i n i m u m v a l u e . Thus when s p e c i m e n s w e r e K - c o n s o l i d a t e d o by s h u t t i n g o f f t h e d r a i n a g e l e a d t o t h e c e l l , a c o n d i -t i o n o f z e r o l a t e r a l s t r a i n was o b t a i n e d due t o t h e f a c t t h a t t h e v o l u m e o f w a t e r e x p e l l e d f r o m t h e s p e c i m e n m a t c h e d e x a c t l y w i t h t h e v o l u m e o f p l u n g e r m o v i n g i n . The c e l l , i n f a c t , i s s u i t e d t o make b o t h 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 o r K Q - c o n s o l i d a t e d t r i a x i a l t e s t s . F o r i s o t r o p i c c o n s o l i d a t i o n t h e s p e c i m e n c a p i s n o t s c r e w e d t o t h e l o a d i n g p l u n g e r . A v e r y n o t a b l e f e a t u r e o f t h e c e l l i s t h e p o s s i b i l i t y i t o f f e r s t o make h i g h p r e s s u r e t e s t s . The maximum c e l l p r e s s u r e w h i c h c a n be u s e d a t p r e s e n t i s a b o u t 500 p s i , w h i c h h a p p e n s t o be t h e b u r s t p r e s s u r e f o r t h e t y p e o f r o l l i n g d i a p h r a m s e a l u s e d . 3 . 3 . 0 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 l a y o u t o f t h e l o a d i n g s y s t e m a l o n g w i t h p r e s s u r e a n d v o l u m e c h a n g e m e a s u r i n g d e v i c e s i s shown i n F i g . 3 . 3 . The v e r t i c a l l o a d was a p p l i e d by a r o l l i n g d i a p h r a m p i s t o n w h i c h was f u l l y s a t u r a t e d w i t h w a t e r on b o t h s i d e s . E a c h s i d e o f t h i s p i s t o n was c o n -n e c t e d by m e a n s ' o f 1 / 8 " O . D . c o p p e r t u b e s t o s m a l l w a t e r r e s e r v o i r s t h r o u g h w h i c h a i r p r e s s u r e c o u l d be a p p l i e d , and a l s o t o a d i s p l a c e m e n t p l u n g e r a c t u a t e d by a c o n s t a n t r a t e s t r a i n d r i v e . The l a t e r a l p r e s s u r e s y s t e m was s i m i l a r l y c o n n e c t e d t o an a i r p r e s s u r e s u p p l y and t o t h e same d i s p l a c e m e n t p l u n g e r . I t was p o s s i b l e t o p e r f o r m a l l s h e a r t e s t s e i t h e r u n d e r s t r e s s c o n t r o l l e d 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 . F o r s t r e s s c o n t r o l l e d l o a d i n g a p a r t i c u l a r s t r e s s was i n c r e a s e d o r d e c r e a s e d i n d i s c r e t e s t e p s u n t i l f a i l u r e u n d e r t h e c h o s e n s t r e s s p a t h o c c u r r e d . T h i s t y p e o f s h e a r l o a d i n g i s u n s u i t e d t o o b t a i n p o s t p e a k s t r e s s - s t r a i n b e h a v i o u r o f t h e s o i l . T h i s may be a s e r i o u s d i s a d v a n t a g e p a r t i c u l a r l y i n c a s e o f s e n s i t i v e s o i l s w h i c h show maximum o b l i q u i t y a f t e r t h e p e a k d e v i a t o r s t r e s s i s r e a c h e d 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 . S t r e n g t h p a r a m e t e r s w i t h r e s p e c t t o e f f e c t i v e s t r e s s e s i n s u c h s o i l s a r e f o u n d i d e n t i c a l i n C - U and C -D t e s t s , p r o v i d e d maximum o b l i q u i t y Air pressure Air pressure Differential pressure t ransducer ± 2 psid Displacement plunger Pressure t ransducer Force multiplier D i s p l a c e m e n t valve 'Pressure t ransducer L E G E N D <J> Whitey Ball Valve Fig.3-3 SGHEM ATIC LAYOUT OF LOADING .DISPLACEMENT, VOLUME CHANGE AND PRESSURE MEASURING SYSTEM . ro 10 i s u s e d as t h e f a i l u r e c r i t e r i o n . S t r e s s c o n t r o l l e d C - U t e s t s , t h e r e f o r e , c a n n o t be s u b s t i t u t e d f o r t i m e c o n s u m i n g C - D t e s t s t o o b t a i n d r a i n e d s t r e n g t h p a r a m e t e r s n e e d e d f o r l o n g - t e r m s t a b i l i t y a n a l y s e s . S t r a i n c o n t r o l l e d t e s t s c o u l d be made by d i s -p l a c i n g w a t e r a t a c o n s t a n t r a t e i n t o t h e l o a d i n g p i s t o n o r i n t o o r o u t 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 . D i s -p l a c e m e n t o f w a t e r a t a c o n s t a n t r a t e was a c h i e v e d w i t h t h e s t r a i n d r i v e m o v i n g t h e d i s p l a c e m e n t p l u n g e r a t a c o n s t a n t r a t e . F o r e x a m p l e , s t r a i n c o n t r o l l e d a x i a l c o m p r e s s i o n t e s t s w i t h i n c r e a s i n g a c o u l d be made by t h e c o n s t a n t r a t e o f w a t e r d i s p l a c e m e n t i n t o t h e t o p o f t h e l o a d i n g p i s t o n . S i m i l a r t e s t s w i t h d e c r e a s i n g a A c o u l d be made by r e m o v i n g w a t e r f r o m t h e l a t e r a l p r e s s u r e s y s t e m a t a c o n s t a n t r a t e . S i m i l a r l y , s t r a i n c o n t r o l l e d e x t e n s i o n t e s t w i t h d e c r e a s i n g az was p o s s i b l e by d i s -p l a c e m e n t p l u n g e r f o r c i n g w a t e r i n t o t h e b o t t o m o f t h e l o a d i n g p i s t o n w h e r e a s s i m i l a r t e s t w i t h i n c r e a s i n g a A c o u l d be made by f o r c i n g w a t e r a t a c o n s t a n t r a t e i n t o t h e l a t e r a l p r e s s u r e s y s t e m . A i r p r e s s u r e was a p p l i e d t h r o u g h 6 ' l o n g s a t u r a t e d 1 / 8 " O . D . s a r a n t u b i n g s , i n o r d e r t o p r e v e n t d i f f u s i o n o f a i r i n t o p o r e s p a c e o r l a t e r a l w a t e r p r e s s u r e s y s t e m ( P o u l o s , 1 9 6 4 ) . The l i n e a i r p r e s s u r e was l i m i t e d t o a b o u t 120 p s i . W h e n e v e r h i g h p r e s s u r e was n e e d e d i t was g e n e r a t e d t h r o u g h a p r e s s u r e a m p l i f i e r c o n s i s t i n g o f two d o u b l e r o l l i n g d i a p h r a m s w i t h an a r e a r a t i o o f 6 ( s e e F i g . 3 . 3 ) . 3 . 4 . 0 D a t a A q u i s i t i o n F o r t e s t s i n b o t h a p p a r a t u s e s , l o a d s w e r e m e a s u r e d by l o a d c e l l s , . f l u i d p r e s s u r e s by p r e s s u r e t r a n s d u c e r s , d i s p l a c e m e n t s by l i n e a r d i f f e r e n t i a l t r a n s f o r m e r s and v o l u m e c h a n g e s by d i f f e r e n t i a l p r e s s u r e t r a n s d u c e r s . S i g n a l s f r o m a l l t h e t r a n s d u c e r s , l o a d c e l l s o r t r a n s r -f o r m e r s w e r e f e d i n t o a V i d a r D i g i t a l D a t a A q u i s i t i o n S y s t e m . T e s t d a t a was a c q u i r e d s i m u l t a n e o u s l y on a m a g n e t i c t a p e and a p r i n t e r . M a g n e t i c t a p e was t h e n u s e d as i n p u t d a t a f i l e w h i l e r e d u c i n g t e s t d a t a w i t h t h e I . B . M . 3 6 0 / 6 7 c o m p u t e r . a t U . B . C . D a t a a c q u i r e d on t h e p r i n t e r h e l p e d t o k e e p t r a c k o f s a t i s f a c t o r y p r o g r e s s o f t h e e x p e r i m e n t s . 3 . 5 . 0 I m p o r t a n t C h a r a c t e r i s t i c s Common t o B o t h A p p a r a t u s e s 3 . 5 . 1 K - C o n s o l i d a t i o n —o Two d i f f e r e n t m e t h o d s c o u l d be u s e d f o r n o r m a l K - c o n s o l i d a t i o n o f t h e s o i l s p e c i m e n s . In t h e f i r s t o r m e t h o d a s t a t e o f h y d r o s t a t i c s t r e s s , e q u a l t o t h e d e s i r e d v e r t i c a l c o n s o l i d a t i o n s t r e s s , was b u i l t on t h e u n d r a i n e d s p e c i m e n . The d r a i n a g e v a l v e on t h e l a t e r a l f l u i d p r e s s u r e s y s t e m was t h e n c l o s e d b e f o r e c o m m e n c e -ment o f c o n s o l i d a t i o n . T h i s e n s u r e d a c o n s t a n t v o l u m e 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 s y s t e m , t h u s p r e v e n t i n g a n y s t r a i n i n t h e x - d i r e c t i o n . In t h e s e c o n d m e t h o d , a g a i n a s t a t e o f h y d r o s t a t i c s t r e s s was b u i l t , b u t n o w , e q u a l t o t h e d e s i r e d b a c k p r e s s u r e d u r i n g 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 s y s t e m was t h e n made u n d r a i n e d and s p e c i m e n c o n s o l i d a t e d u n d e r s t r a i n c o n t r o l l e d l o a d i n g w i t h d r a i n a g e p e r m i t t e d f r o m t o p a n d p o r e p r e s s u r e r e c o r d e d a t t h e b o t t o m o f t h e s p e c i m e n . In t h e f i r s t m e t h o d v e r y h i g h g r a d i e n t s o c c u r w i t h i n t h e s p e c i m e n i n t h e i n i t i a l s t a g e s o f 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 i s i s s o m e t i m e s c o n s i d e r e d o b j e c t i o n a b l e . H o w e v e r , s i m i l a r s i t u a t i o n s e x i s t i n 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 when i s o t r o p i c c o n s o l i d a t i o n i s done i n a s i n g l e i n c r e m e n t . In t h e s i n g l e i n c r e m e n t m e t h o d o f K - c o n s o l i d a t i o n t h e l a t e r a l s t r e s s , a , o ' x p r o g r e s s i v e l y d e c r e a s e d as c o n s o l i d a t i o n p r o g r e s s e d u n t i l e q u i l i b r i u m was r e a c h e d a t t h e end o f c o n s o l i d a -t i o n . F o r t y - e i g h t h o u r s w e r e a l l o w e d f o r n o r m a l c o n -s o l i d a t i o n . S i n c e a had d e c r e a s e d f r o m i t s i n i t i a l A v a l u e , t h e l a t e r a l f l u i d p r e s s u r e s y s t e m u n d e r t h e f i n a l a x , c o n t a i n e d an e x c e s s a m o u n t o f w a t e r e q u a l t o t h e c h a n g e i n a t i m e s t h e s m a l l 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 s y s t e m . T h i s , c o n s e q u e n t l y , c a u s e d t h e s p e c i m e n t o u n d e r g o a v e r y s m a l l c o m p r e s s i v e l a t e r a l s t r a i n , t h e r e b y r e s u l t i n g i n t h e f i n a l a v a l u e n o t t r u l y c o n s i s t e n t w i t h t h e a c t u a l K Q - v a l u e , b u t s l i g h t l y l a r g e r . C o m p l i a n c e e f f e c t s and o b s e r v e d K Q v a l u e s a r e d i s c u s s e d l a t e r i n t h i s c h a p t e r . In t h e K - c o n s o l i d a t i o n by s t r a i n c o n t r o l l e d o J l o a d i n g , t h e u s e o f s l o w r a t e s o f s t r a i n r e s u l t s i n much s m a l l e r g r a d i e n t s d u r i n g t h e e n t i r e c o n s o l i d a t i o n p r o c e s s , t h u s o v e r c o m i n g t h e o b j e c t i o n o f one i n c r e m e n t c o n s o l i d a t i o n . H o w e v e r , as t h e c o n s o l i d a t i o n p r o g r e s s e d , l a t e r a l s t r e s s a ' i n c r e a s e d , ' b u t due t o t h e s m a l1 . c o m p l i a n c e o f t h e s y s t e m , A f e l l s l i g h t l y s h o r t o f t h e v a l u e t r u l y c o n s i s t e n t w i t h t h e a c t u a l K - c o n d i t i o n . T h u s , a t t h e end o f c o n s o l i d a t i o n o u n d e r t h e d e s i r e d v e r t i c a l s t r e s s , t h e s p e c i m e n u n d e r w e n t a s m a l l e x t e n s i o n a l l a t e r a l s t r a i n , w h i c h was p r o p o r t i o n a l t o t h e p r o d u c t o f c h a n g e i n o f r o m i t s i n i t i a l t o t h e f i n a l X v a l u e and t h e 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 s y s t e m . D u r i n g o v e r c o n s o l i d a t i o n t h e m e a s u r e d e q u i l i b r i u m v a l u e o f a a t t h e c o m p l e t i o n o f s w e l l i n g w a s , i n b o t h A m e t h o d s o f c o n s o l i d a t i o n , t o o l a r g e c o m p a r e d t o t h a t c o r -r e s p o n d i n g t o t r u e K Q - c o n d i t i o n . T h i s was b e c a u s e a x a t t h e end o f o v e r c o n s o l i d a t i on was i n b o t h c a s e s s m a l l e r t h a n t h e end o f n o r m a l c o n s o l i d a t i o n v a l u e f r o m w h e r e t h e s p e c i -mens w e r e r e b o u n d e d . In a l l t h e t e s t s d e s c r i b e d i n t h i s t h e s i s i n c r e -m e n t a l c o n s o l i d a t i o n m e t h o d was e m p l o y e d . One o f t h e r e a s o n s f o r t h i s d e c i s i o n was t o a v o i d e x c e s s i v e l y l a r g e t i m e s r e -q u i r e d f o r s t r a i n c o n t r o l l e d c o n s o l i d a t i o n o f t h e r e l a t i v e l y l o n g t r i a x i a l s p e c i m e n s . Due t o t h e r a t h e r b r i t t l e n a t u r e o f t h e c l a y u s e d i n t h i s s t u d y , e x t r e m e l y s l o w r a t e s w o u l d be n e e d e d f o r s t r a i n c o n t r o l l e d c o n s o l i d a t i o n i n o r d e r t o p r e v e n t u n d r a i n e d f a i l u r e o f t h e s p e c i m e n . The 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 s y s t e m d i d p e r m i t a v e r y s m a l l l a t e r a l s t r a i n w h i c h w o u l d h a v e c a u s e d u n d r a i n e d f a i l u r e i f t h e s p e c i m e n c o u l d n o t d r a i n as f a s t a s i t was b e i n g l o a d e d . T h i s s i t u a t i o n d i d n o t a r i s e i n one i n c r e m e n t K o - c o n s o l i d a t i o n w h e r e a x d e c r e a s e d r a t h e r t h a n i n c r e a s e d 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 , and t h e l a t e r a l p r e s s u r e s y s t e m c o n t a i n e d a t a l l t i m e s s l i g h t e x c e s s w a t e r c o r r e s p o n d -i n g t o t h e i n s t a n t a n e o u s a . T h i s r e s u l t e d i n a s m a l l l a t e r a l 3 x c o m p r e s s i v e s t r a i n and t h e r e f o r e , t h e r e was no t e n d e n c y f o r u n d r a i n e d f a i l u r e d u r i n g c o n s o l i d a t i o n . The e f f e c t o f s i n g l e i n c r e m e n t and s t r a i n c o n -t r o l l e d c o n s o l i d a t i o n on t h e K Q - v a l u e and s u b s e q u e n t u n d r a i n e d a x i a l c o m p r e s s i o n s h e a r b e h a v i o u r was s t u d i e d f o r two Haney c l a y s p e c i m e n s . B o t h s p e c i m e n s w e r e n o r m a l l y c o n s o l i d a t e d t o t h e same v e r t i c a l e f f e c t i v e s t r e s s - one by a s i n g l e i n c r e m e n t and t h e o t h e r by s t r a i n c o n t r o l l e d c o n s o l i d a t i o n . The K Q-value f o r incremental consolidation was found to be s l i g h t l y l a r g e r (0.55 - 0.56) than the value under s t r a i n c o n t r o l l e d c o n s o l i d a t i o n (0.53 - 0.54). Thus the d i f f e r e n c e in the two K Q values was only about 5%. A d d i t i o n a l comparative t e s t s were performed and again the d i f f e r e n c e r a r e l y exceeded the above mentioned value. The t r i a x i a l - u n d r a i n e d s t r e n g t h of these two specimens was found to be almost i d e n t i c a l and so was the d e v i a t o r s t r e s s and pore pressure vs. a x i a l s t r a i n response. Since there was e s s e n t i a l l y no d i f f e r e n c e i n the shear behaviour of the specimens c o n s o l i d a t e d in two d i f f e r e n t ways, the method i n v o l v i n g one increment consolidation was used because of i t s s i m p l i c i t y and convenience. 3.5.2 Influence of L a t e r a l F l u i d Pressure System Compliance on Measured K —o Both methods of K Q - c o n s o l i d a t i o n imposed a small amount of l a t e r a l s t r a i n on the specimens during the c o n s o l i d a t i o n process. As explained e a r l i e r , t h i s was due to the small compliance of the l a t e r a l pressure systems. For both apparatuses t h i s compliance was approx-2 imately 0.06 c.c/Kg/cm and was s e n s i b l y l i n e a r with 2 2 pressures l a r g e r than 1 Kg/cm and up to about 10 Kg/cm . It can be shown that t h i s small compliance d i d not r e s u l t i n m e a s u r e d K Q - v a l u e 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 t o be g r e a t l y i n e r r o r f r o m t h e t r u e K Q - v a l u e . The m a g n i t u d e o f d i f f e r e n c e i s a f u n c t i o n o f r a t i o o f t h i s c o m p l i a n c e and t h e c o m p r e s s i b i l i t y o f t h e s o i l s k e l e t o n . A s s u m e a t r u e K Q - 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 e c i -men i n e q u i l i b r i u m u n d e r a v e r t i c a l e f f e c t i v e s t r e s s , a ' , and l a t e r a l e f f e c t i v e s t r e s s o' = K o'. Z X 0 z L e t V = v o l u m e o f t h e s o i l s p e c i m e n i n c . c c = 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 s y s t e m i n c . c / K g / c m m y = c o m p r e s s i b i l i t y o f s o i l cm^/ Kg - a f u n c t i o n o f mean n o r m a l e f f e c t i v e s t r e s s , p , u n d e r K Q o r a p p r o x i m a t e K Q - c o n s o l i d a t i o n c o n d i t i o n s . Aa^ = i n c r e m e n t i n v e r t i c a l e f f e c t i v e s t r e s s u n d e r f u l l y d r a i n e d c o n d i -t i o n s , and w i t h l a t e r a l p r e s s u r e s y s t e m k e p t u n d r a i n e d . Then i f c = 0 ( i . e . f o r t h e c a s e o f i n f i n i t e l y s t i f f s y s t e m ) t h e i n c r e a s e i n l a t e r a l p r e s s u r e A a x = K o A o z (3 .1 ) S i n c e c ^ O , t h e c h a n g e i n p r e s s u r e i n l a t e r a l p r e s s u r e s y s t e m w i l l n o t e q u a l K Q A a z b u t A p ' w h e r e A p ' < K Q A O ^ . C h a n g e i n v o l u m e o f t h e s p e c i m e n t h e n i s A a ' + 2 A p ' A V l = m v V — ^ ( 3 . 2 ) In c o m p a r i s o n c h a n g e s i n v o l u m e o f t h e s p e c i m e n i n t h e p r e s e n c e o f i n f i n i t e l y s t i f f l a t e r a l p r e s s u r e s y s t e m i s A a ' + 2K A a ' A V 2 = m V — - ^ z ( 3 . 3 ) v 3 E x p a n s i o n o f t h e c^O l a t e r a l p r e s s u r e s y s t e m u n d e r i n -c r e a s e d p r e s s u r e A p ' i s A V 3 = c A p ' . Then i t i s o b v i o u s t h a t t h e d e f i c i e n c y i n v o l u m e c h a n g e , A V 2 - A V l 5 e q u a l s c A p ' , i . e . c A p ' = 2/3 m v V ( K Q A a z ' - A p ' ) , o r S u b s t i t u t i n g f o r V ( = 150 c . c and 80 c . c r e s p e c t i v e l y f o r p l a n e s t r a i n and t r i a x i a l s p e c i m e n s ) and c ( = 0 . 0 6 2 c . c / K g / c m f o r b o t h a p p a r a t u s e s ) , A " K K A o ^ = , , 0 . 0 0 0 6 = IT f 0 r P l a n e s t r a i n ( 3 ' 5 ) v K K A V = | 0 - 0 0 1 1 4 = TT f o r t r i a x i a l ( 3 . 6 ) w h e r e n = ! + 0 - 0 0 0 6 P m u n . 0 . 0 0 1 1 4 T m.. The r a t i o o f l a t e r a l t o v e r t i c a l e f f e c t i v e s t r e s s a f t e r t h e v e r t i c a l s t r e s s i n c r e m e n t , A a ^ , i s now K a : + Ap (K ) = o z 0 m a' + A a ^ (K ) v o ' m = K z + - Aa/ Aa ( 3 . 7 ) E q u a t i o n 3 . 7 shows t h a t t h e e r r o r i n t h e m e a s u r e d K v a l u e , o ( K o ) m , d e p e n d s on n w h i c h i s a f u n c t i o n o f t h e c o m p r e s s i -b i l i t y o f c l a y . F o r t h e c l a y t e s t e d , m y was o f t h e o r d e r 2 o f 0 . 0 5 cm / K g i n t h e n o r m a l l y c o n s o l i d a t e d r a n g e . C o n -s e q u e n t l y t h e m e a s u r e d (K ) w i l l n o t d i f f e r f r o m t h e t r u e o m K by more t h a n 2%. V a l u e s o f m d u r i n g r e b o u n d o f t h i s o v 3 2 2 c l a y f r o m o ^ = 6 Kg/cm t o = 0 . 3 Kg/cm w e r e i n t h e 2 r a n g e o f 0 . 0 0 4 t o 0 . 0 4 5 cm / K g . U s i n g t h i s r a n g e o f v a l u e s o f m y i n E q s . 3 . 5 t o 3 . 7 i t c a n be shown t h a t t h e m e a s u r e d (K ) c o u l d be a b o u t 10% l a r g e r t h a n t h e t r u e K when o m 3 o 2 t h e s a m p l e was r e b o u n d e d f r o m a' = 6 t o a' = 0 . 3 Kg/cm . r z z 3 In o r d e r t o o b t a i n o v e r c o n s o l i d a t e d s a m p l e s as n e a r t o t h e K Q - c o n d i t i o n as p o s s i b l e , 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 s y s t e m was a r t i f i c i a l l y r e d u c e d by e x p a n d i n g t h e t o t a l v o l u m e o f l a t e r a l p r e s s u r e s y s t e m . T h i s was a c h i e v e d by means o f a d i s p l a c e m e n t v a l v e i n w h i c h t h e p l u n g e r c o u l d move o u t t o i n c r e a s e t h e t o t a l v o l u m e 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 ( s e e F i g . 3 . 3 ) . 3 . 6 . 0 M e a s u r e d K - V a l u e s o B o t h t h e p l a n e s t r a i n and t h e K Q t r i a x i a l e q u i p -m e n t s h a v e t h e i m p o r t a n t c a p a b i l i t y o f b e i n g u s e d as o n e - d i m e n s i o n a l o e d o m e t e r s w i t h m e a s u r e m e n t s o f t h e l a t e r a l e f f e c t i v e s t r e s s e s . Thus t h e m a g n i t u d e o f K = a ' / a " , t h e c o e f f i c i e n t o f l a t e r a l e a r t h p r e s s u r e a t r e s t , c a n be d e t e r m i n e d as a f u n c t i o n o f t h e c o n -s o l i d a t i o n h i s t o r y . T h i s i s p a r t i c u l a r l y i n t e r e s t i n g when ^ - c o n s o l i d a t i o n i s d o n e u n d e r s t r a i n c o n t r o l l e d c o n d i t i o n s and a c o n t i n u o u s v a r i a t i o n o f K v a l u e s o w i t h o v e r c o n s o l i d a t i o n r a t i o i s o b t a i n e d . A c y c l i c K Q - c o n s o l i d a t i o n t e s t was p e r f o r m e d on u n d i s t u r b e d Haney c l a y - t h e s o i l u s e d i n t h i s s t u d y . The t e s t was p e r f o r m e d i n t h e K Q t r i a x i a l a p p a r a t u s b u t p l a n e s t r a i n a p p a r a t u s c o u l d be u s e d l i k e w i s e . The v e r t i c a l e f f e c t i v e s t r e s s , a ' , was b u i l t z on t h e s p e c i m e n t o a b o u t 6 Kg/cm d u r i n g t h e f i r s t l o a d i n g c y c l e , w h i c h was f o l l o w e d by a r e b o u n d t o 2 o"z ~ 0 . 6 Kg/cm . D u r i n g t h e s e c o n d l o a d i n g c y c l e 2 was b u i l t up t o a b o u t 1 6 . 5 Kg/cm ( 2 3 5 p s i ) w h i c h 2 was f o l l o w e d by s e c o n d r e b o u n d t o ~ 0 . 5 Kg/cm . F i g . 3 . 4 shows e - l o g a ' r e l a t i o n s h i p s f o r t h e e n t i r e h i s t o r y o f c o n s o l i d a t i o n . The s t r e s s e s r e p r e -s e n t e d a r e b o t h , and p. e - l o g and e - l o g p a r e p a r a l l e l i n t h e n o r m a l l y c o n s o l i d a t e d r a n g e <TZ'= vertical effective stress p = mean normal effective stress 0 . 7 2 | 1 1 L _ — CT1- kg/cm2 F i g . 3 - 4 e - logO"' RELATIONSHIPS-UNDISTURBED HANEY CLAY. {o" > 4 Kg/cm ) and a r e t y p i c a l o f a s e n s i t i v e c l a y . The n o r m a l l y c o n s o l i d a t e d b r a n c h o f t h e e - l o g a " c u r v e f o r s e c o n d l o a d i n g c y c l e was p r e c i s e l y a l o n g t h e e x t e n s i o n o f t h e n o r m a l l y c o n s o l i d a t e d b r a n c h o f t h e c u r v e f o r t h e f i r s t l o a d i n g c y c l e . 1 • A l s o shown i n F i g . 3 . 4 i s t h e e v s . l o g p r e l a -t i o n s h i p f o r a s t r a i n c o n t r o l l e d i s o t r o p i c c o n s o l i d a t i o n t e s t on t h e same c l a y and i n t h e same a p p a r a t u s . The s p e c i m e n u s e d f o r t h e i s o t r o p i c c o n s o l i d a t i o n t e s t had a s l i g h t l y l o w e r i n i t i a l v o i d r a t i o c o m p a r e d t o t h e s p e c i m e n u s e d i n K Q c o n s o l i d a t i o n t e s t . T h i s r e s u l t s i n i n i t i a l p a r t o f e v s . l o g p r e l a t i o n s h i p f o r i s o t r o p i c c o n s o l i d a -t i o n t o l i e b e l o w t h e s i m i l a r r e l a t i o n s h i p f o r K c o n s o l i -r o 2 d a t i o n . H o w e v e r , f o r p > 5 Kg/cm , i . e . , i n t h e n o r m a l l y c o n s o l i d a t e d r a n g e , t h e e - l o g p r e l a t i o n s h i p s f o r t h e two t y p e s o f c o n s o l i d a t i o n a r e p a r a l l e l . F o r a g i v e n p , K Q c o n s o l i d a t i o n r e s u l t s i n l o w e r v o i d r a t i o when c o m p a r e d t o t h a t u n d e r i s o t r o p i c c o n s o l i d a t i o n . T h e s e r e s u l t s a r e s i m i l a r t o t h o s e r e p o r t e d by K h e r a and K r i z e k ( 1 9 6 6 ) and L e w i n and B u r l a n d ( 1 9 7 0 ) . H o w e v e r , f o r a g i v e n p , t h e d i f f e r e n c e i n v o i d r a t i o f o r t h e two t y p e s o f c o n s o l i d a t i o n i s v e r y p r o n o u n c e d i n t h e c l a y t e s t e d , a p p a r e n t l y b e c a u s e o f t h e s e n s i t i v e n a t u r e . F i g . 3 . 5 shows t h e r e l a t i o n s h i p b e t w e e n l a t e r a l e f f e c t i v e s t r e s s , a ' , and v e r t i c a l e f f e c t i v e s t r e s s , a' CTZ = Vertical stress 0~x = Lateral stress 8 ^ 6 I 4 2 (T) — (2) First rebound cycle (D-(D Reloading cycle ( ^ ) ~ S e c o n d rebound cycle o ( ^ ^ - R e l < jading 0 2 4 6 8 10 12 14 16 18 fj z-kg/cm 2 F i g . 3 - 5 RELATIONSHIP BETWEEN VERTICAL AND L A T E R A L EFFECTIVE S T R E S S E S DURING ONE DIMENSIONAL CONSOLIDATION-UNDISTURBED HANEY C L A Y . I t i s s e e n t h a t t h e r e l a t i o n s h i p i s l i n e a r f o r t h e n o r m a l l y c o n s o l i d a t e d c l a y and i s n o t a l t e r e d by an i n t e r r u p t e d u n l o a d i n g and r e l o a d i n g s e q u e n c e . The s l o p e o f t h i s s t r a i g h t l i n e i s 0 . 5 4 , w h i c h i s t h u s t h e a v e r a g e v a l u e o f K u n d e r t h e c o n d i t i o n o f n o r m a l c o n s o l i d a t i o n , o V a r i a t i o n o f K Q w i t h o v e r c o n s o l i d a t i o n r a t i o , ( O . C . R . ) = a' /o'l i s shown i n F i g . 3 . 6 . K i n c r e a s e s max as t h e c l a y i s r e b o u n d e d f r o m i t s n o r m a l l y c o n s o l i d a t e d s t a t e . I t a c h i e v e s a v a l u e o f a b o u t 2 . 0 f o r o v e r c o n s o l i -d a t i o n r a t i o o f 2 0 . F o r t h e same o v e r c o n s o l i d a t i o n r a t i o , K Q seems t o be i n d e p e n d e n t o f t h e m a g n i t u d e o f f r o m w h i c h t h e r e b o u n d c y c l e i s i n i t i a t e d . The r e l a t i o n s h i p , K Q v s . o v e r c o n s o l i d a t i o n r a t i o d u r i n g r e l o a d i n g c y c l e , i s d i f f e r e n t when c o m p a r e d t o t h e s i m i l a r r e l a t i o n s h i p d u r i n g r e b o u n d . F o r a g i v e n O . C . R . , K Q d u r i n g r e l o a d i n g i s s m a l l e r t h a n d u r i n g r e b o u n d . 1-7 1 4-O Re bou Re bou id fro nd froi T. (<J 2 )n 10X = 6 nax : 16" •Ikg/c 4kg/c m 2 2 m Reboi t-jnd • h - R e l o 3ding 2 4 6 8 10 12 14 16 18 O C R . = (C7r)max/trz Fig.3-6 VARIATION OF K0 WITH OVER CONSOLIDATION RATIO - UNDISTURBED HANEY C L A Y . -p. CHAPTER IV LABORATORY TESTING 4 . 1 . 0 D e s c r i p t i o n o f C l a y T e s t e d The c l a y u s e d i n t h i s s t u d y was t a k e n f r o m an o p e n p i t b e l o n g i n g t o t h e Haney B r i c k and T i l e C o . , H a n e y , B . C . T h i s p i t i s l o c a t e d a b o u t 30 m i l e s e a s t o f U . B . C . on t h e n o r t h b a n k o f t h e F r a s e r R i v e r . B l o c k s a m p l e s o f t h i s c l a y , w h i c h w i l l be r e f e r r e d t o as Haney c l a y , w e r e o b t a i n e d i n J u n e , 1 9 6 7 . A t h r e e - f o o t d e e p t r e n c h was dug a r o u n d an a r e a a b o u t t h r e e f e e t s q u a r e , t h u s i s o l a t i n g a l a r g e b l o c k o f s o i l . The t o p one f o o t o r so o f d i s t u r b e d c l a y was r e m o v e d , and a p p r o x -i m a t e l y n i n e i n c h e s c u b e b l o c k s w e r e t r i m m e d u s i n g a f i n e p i a n o w i r e . The b l o c k s w e r e c a r e f u l l y w r a p p e d i n t h e f i e l d w i t h S a r a n w r a p . A f t e r t r a n s p o r t a t i o n t o t h e l a b o r a t o r y , t h e y w e r e s e a l e d w i t h s e v e r a l c o a t i n g s o f w a x . The b l o c k s w e r e s t o r e d i n a m o i s t room u n t i l r e q u i r e d . No n o t i c e a b l e c h a n g e i n w a t e r c o n t e n t o f t h e s e b l o c k s was o b s e r v e d , e v e n f o r s t o r a g e p e r i o d o f up t o t h r e e y e a r s . Haney c l a y i s t h o u g h t t o h a v e b e e n d e p o s i t e d i n a m a r i n e e n v i r o n m e n t ( A r m s t r o n g , 1 9 5 7 ) . S u b s e q u e n t u p l i f t o f t h e l a n d r e l a t i v e t o t h e s e a c a u s e d t h e d e p o s i t t o be e x p o s e d , and o v e r t h e e n s u i n g y e a r s p e r c o l a t i n g r a i n w a t e r has l e a c h e d o u t m o s t o f t h e s a l t . Haney c l a y t h u s p o s s e s s e s a s e n s i t i v e s t r u c t u r e . T a b l e 1 shows i t s t y p i c a l p h y s i c a l p r o p e r t i e s . 4 . 2 . 0 E x p e r i m e n t a l P r o c e d u r e s 4 . 2 . 1 I n s t a l l i n g S p e c i m e n s i n A p p a r a t u s e s D e t a i l e d p r o c e d u r e s t o i n s t a l l c l a y s p e c i m e n s has b e e n d e s c r i b e d by V a i d ( 1 9 6 8 ) f o r t h e p l a n e s t r a i n t e s t s and by C a m p a n e l l a and V a i d ( 1 9 7 1 ) f o r t h e K -t r i a x i a l t e s t s . 4 . 2 . 2 K - c o n s o l i d a t i o n —o A l l s p e c i m e n s w e r e f i r s t n o r m a l l y c o n s o l i d a t e d t o t h e same v e r t i c a l e f f e c t i v e s t r e s s o f a p p r o x i m a t e l y 2 6 Kg/cm . C o n s o l i d a t i o n was d o n e a g a i n s t a b a c k p r e s -s u r e o f 1 Kg/cm , s t a r t i n g f r o m a h y d r o s t a t i c t o t a l 2 s t r e s s s t a t e o f a p p r o x i m a t e l y 7 . 5 Kg/cm f o r p l a n e 2 s t r a i n and 7 Kg/cm f o r K o - t r i a x i a l t e s t s . L a r g e r i n i t i a l s t r e s s was u s e d f o r p l a n e s t r a i n t e s t s i n o r d e r t o c o m p e n s a t e f o r some o f t h e v e r t i c a l l o a d b e i n g t r a n s f e r r e d t h r o u g h s i d e f r i c t i o n ; t h u s r e s u l t i n g i n P H Y S I C A L P R O P E R T I E S OF UNDISTURBED HANEY CLAY L i q u i d L i m i t 46 % P l a s t i c L i m i t 26 % P l a s t i c i t y I n d e x 20 % N a t u r a l w a t e r c o n t e n t 4 1 - 4 4 % D e g r e e o f s a t u r a t i o n 100 % S p e c i f i c g r a v i t y o f s o l i d s 2 . 8 0 P e r c e n t f i n e r t h a n 2 m i c r o n s 46 % U n c o n f i n e d c o m p r e s s i v e s t r e n g t h ~ 1 Kg/cm c S e n s i t i v i t y - 6 - 1 0 A c t i v i t y - P . I / % < 2 u 0 . 4 4 Maximum p a s t p r e s s u r e - ^ a / c m 2 ( f r o m K - c o n s o l i d a t i o n t e s t s ) " 9 o P r e d o m i n a n t c l a y m i n e r a l C h l o r i t e l o w e r v e r t i c a l s t r e s s a t t h e s a m p l e b o t t o m , b u t g i v i n g t h e d e s i r e d v e r t i c a l e f f e c t i v e s t r e s s o f 6 K g / c m 2 as t h e a v e r a g e v a l u e . The l a t e r a l f l u i d p r e s s u r e s y s t e m s w e r e k e p t u n d r a i n e d 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 and no a l l o w a n c e was made f o r t h e i r s m a l l f l e x i b i l i t y . A p e r i o d o f 48 h o u r s was a l l o w e d f o r c o n s o l i d a t i o n f o r t e s t s i n v o l v i n g n o r m a l l y c o n s o l i d a t e d s a m p l e s . O v e r c o n s o l i d a t e d s p e c i m e n s w e r e o b t a i n e d by u n l o a d i n g t h e v e r t i c a l s t r e s s t o g e t t h e d e s i r e d o v e r -c o n s o l i d a t i o n r a t i o , w h i c h i s d e f i n e d h e r e i n as t h e r a t i o o f t h e maximum p a s t t o t h e f i n a l v e r t i c a l e f f e c -t i v e s t r e s s u n d e r w h i c h t h e s p e c i m e n was a l l o w e d t o s w e l l . As b e f o r e , v e r t i c a l s t r e s s was t a k e n o f f w h i i l e k e e p i n g t h e l a t e r a l f l u i d p r e s s u r e s y s t e m s u n d r a i n e d . As p o i n t e d o u t i n C h a p t e r I I I , l a r g e c h a n g e s i n s t r e s s e s a r e a s s o c i a t e d w i t h v e r y s m a l l s t r a i n s d u r i n g r e b o u n d o f c l a y s , b e c a u s e o f t h e i r g r e a t l y r e d u c e d c o m p r e s s i b i l i t y . To a c h i e v e o v e r c o n s o l i d a t i o n as c l o s e t o t h e K Q - c o n d i t i o n as f e a s i b l e , a d j u s t m e n t s w e r e made f o r t h e 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 s y s t e m by means o f t h e d i s p l a c e m e n t v a l v e ( s e e F i g . 3 . 3 ) . The amount o f a d j u s t m e n t w o u l d d e p e n d on t h e d e c r e a s e i n l a t e r a l p r e s s u r e w h i l e u n l o a d i n g t h e v e r t i c a l s t r e s s d u r i n g o v e r c o n s o l i d a t i o n . T w e n t y - f o u r h o u r s w e r e a l l o w e d f o r s w e l l i n g u n d e r t h e r e d u c e d v e r t i c a l s t r e s s b e f o r e t h e s a m p l e s w e r e s u b j e c t e d t o s h e a r t e s t i n g . 4 . 2 . 3 S h e a r T e s t i n g A l l t e s t s w e r e made u s i n g s t r a i n c o n t r o l l e d l o a d i n g o r p r e s . s u r e c h a n g e , w i t h t h e e x c e p t i o n o f a few d r a i n e d t e s t s on o v e r c o n s o 1 i d a t e d s p e c i m e n s , w h i c h w e r e l o a d c o n t r o l l e d . T h e s e t e s t s r e q u i r e d v e r y s m a l l s t r a i n s t o f a i l u r e w h i c h , i n t u r n , n e c e s s i t a t e d e x t r e m e l y s l o w t e s t i n g r a t e s . S u c h s l o w r a t e s c o u l d n o t be s e l e c t e d on t h e s t r a i n d r i v e . T i m e t o f a i l u r e f o r 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 was e s t i m a t e d u s i n g r e c o m -m e n d a t i o n s o f B i s h o p and H e n k e l ( 1 9 6 2 ) and B l i g h t ( 1 9 6 3 ) . S u f f i c i e n t l y s l o w t e s t i n g r a t e s w e r e u s e d , so as t o r e s u l t i n t i m e t o f a i l u r e f a r i n e x c e s s o f t h e c a l c u l a t e d v a l u e . D r a i n e d t e s t s w e r e made by p e r m i t t i n g d r a i n a g e f r o m t h e t o p o n l y w h i l e p o r e p r e s s u r e was m e a s u r e d a t t h e b o t t o m o f t h e s p e c i m e n . T e s t i n g r a t e s u s e d w e r e s u c h , t h a t a t no t i m e t h e d i f f e r e n c e b e t w e e n t h e p o r e p r e s s u r e s a t t h e t o p and t h e b o t t o m o f t h e s p e c i m e n a m o u n t e d t o more t h a n 4% o f t h e c u r r e n t v e r t i c a l e f f e c t i v e s t r e s s . The d i s t r i b u t i o n o f t h i s e x c e s s p o r e p r e s s u r e o v e r t h e h e i g h t o f t h e s p e c i m e n was a s s u m e d t o be p a r a b o l i c when c a l c u l a t i n g t h e e f f e c t i v e s t r e s s e s ( B y r n e , 1 9 6 6 ; S m i t h & W a h l s , 1 9 6 9 ) . T h i s t e s t i n g t e c h n i q u e e n a b l e d e v a l u a t i o n o f e f f e c t i v e s t r e s s e s i n t h e s a m p l e a t a l l s t a g e s o f t h e t e s t w i t h c o n f i d e n c e . The r a n g e o f a x i a l s t r a i n r a t e s u s e d f o r m o s t o f t h e t e s t s w e r e b e t w e e n 0 . 1 t o 0 . 1 5 % p e r h o u r . S i m i l a r t e s t i n g r a t e s w e r e u s e d f o r p l a n e s t r a i n and K Q - t r i a x i a l t e s t s , i n o r d e r t o e l i m i n a t e any r a t e e f f e c t s on t h e s h e a r b e h a v i o u r o f c l a y s . A t t h e end o f t h e s h e a r t e s t , s p e c i m e n s w e r e a l l o w e d t o s w e l l u n d e r a s m a l l e f f e c t i v e s t r e s s o f a b o u t 2 0 . 1 Kg/cm b e f o r e r e m o v a l f o r f i n a l w a t e r c o n t e n t d e t e r -m i n a t i o n ( H e n k e l and S o w a , 1 9 6 3 ) . 4 . 3 . 0 D e v e l o p m e n t o f t h e T e s t i n g P r o g r a m The m a i n a i m o f t h i s t h e s i s was t o c o m p a r e , f o r t h e i d e n t i c a l end o f K - c o n s o l i d a t i o n s t a t e , t h e p l a n e o s t r a i n and t r i a x i a l b e h a v i o u r o f Haney c l a y u n d e r s i m i l a r t o t a l s t r e s s p a t h s t o f a i l u r e . The c o m p a r i s o n was t o be made f o r b o t h n o r m a l l y and h e a v i l y o v e r c o n s o l i d a t e d i n i t i a l s t a t e s . 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 w e r e o b t a i n e d by ^ - c o n s o l i d a t i o n t o a v e r t i c a l e f f e c t i v e s t r e s s o f 2 a p p r o x i m a t e l y 6 Kg/cm (maximum p a s t p r e s s u r e f o r t h e 2 c l a y was a p p r o x i m a t e l y 4 Kg/cm ) . H e a v i l y o v e r c o n s o l i -d a t e d s p e c i m e n s w e r e o b t a i n e d by a l l o w i n g t h 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 s w e l l u n d e r a r e d u c e d v e r t i c a l e f f e c t i v e s t r e s s o f 0 . 3 Kg/cm , t h u s g i v i n g an o v e r -c o n s o l i d a t i o n r a t i o o f a b o u t 2 0 . The o v e r c o n s o l i d a t i o n r a t i o s a c t u a l l y o b t a i n e d w e r e i n t h e r a n g e o f 15 t o 1 9 . T h i s was b e c a u s e o f t h e i n a b i l i t y t o e s t i m a t e t h e f i n a l a v e r a g e v e r t i c a l s t r e s s , w h i c h d e p e n d s on s i d e f r i c t i o n i n t h e p l a n e s t r a i n a p p a r a t u s . V a r i a t i o n s i n o v e r -c o n s o l i d a t i o n r a t i o , f r o m t h e d e s i r e d v a l u e o f 2 0 , o c c u r r e d i n t h e K - t r i a x i a l t e s t s , b e c a u s e o f t h e o d i f f i c u l t y i n a d j u s t i n g t h e p r e c i s i o n p r e s s u r e r e g u l a t o r s t o h o l d c o n s t a n t p r e s s u r e i n t h e l o a d i n g p i s t o n w h i l e o p e r a t i n g i n t h e v e r y low p r e s s u r e r a n g e . 4 . 3 . 1 S t r e s s P a t h s I n v e s t i g a t e d The a x e s o f p r i n c i p a l s t r e s s ( a n d s t r a i n ) a r e f i x e d by b o t h a p p a r a t u s e s , b u t i t was p o s s i b l e t o i n t e r -c h a n g e t h e r e l a t i v e m a g n i t u d e o f t h e p r i n c i p a l s t r e s s e s , o and a , a t any s t a g e o f t h e t e s t . In t h i s way i t was Z X p o s s i b l e t o make e i t h e r a x i a l c o m p r e s s i o n o r e x t e n s i o n t e s t s w i t h a n y d e s i r e d s t r e s s p a t h i n a z v s . a x s t r e s s p l a n e . H o w e v e r , t h e i n v e s t i g a t i o n was r e s t r i c t e d t o t h e s t u d y o f t h e f o l l o w i n g s t r e s s p a t h s : A x i a l C o m p r e s s i o n P a s s i ve - The v e r t i c a l s t r e s s , c , was i n c r e a s e d w h i l e h o l d i n g t h e l a t e r a l s t r e s s , a , c o n s t a n t a t end o f c o n s o l i d a t i o n v a l u e . A c t i v e - The l a t e r a l s t r e s s , a , was d e c r e a s e d X w h i l e h o l d i n g t h e v e r t i c a l s t r e s s , a , c o n s t a n t a t t h e end o f c o n s o l i d a t i o n v a l u e . A x i a l E x t e n s i o n A c t i v e - The v e r t i c a l s t r e s s , a , was d e c r e a s e d w h i l e h o l d i n g t h e l a t e r a l s t r e s s , a , a t t h e end o f X c o n s o l i d a t i o n v a l u e . P a s s i ve - The l a t e r a l s t r e s s , o , was i n c r e a s e d X w h i l e h o l d i n g t h e v e r t i c a l s t r e s s , a , a t t h e end o f : c o n s o l i d a t i o n v a l u e . F o r e a c h o f t h e s e s t r e s s p a t h s , c o n s o l i d a t e d u n d r a i n e d and d r a i n e d t e s t s w e r e m a d e . One s e r i e s o f t e s t s w e r e made on 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 and t h e s e c o n d s e r i e s c o n s i s t e d o f h e a v i l y o v e r c o n s o l i d a t e d s p e c i m e n s . E a c h t y p e o f t e s t was made b o t h u n d e r p l a n e s t r a i n and t r i a x i a l s t r e s s c o n d i t i o n s . CHAPTER V PLANE STRAIN TEST RESULTS ON NORMALLY CONSOLIDATED HANEY CLAY In t h i s c h a p t e r r e s u l t s o f t e s t s on n o r m a l l y c o n s o l i d a t e d Haney c l a y 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 a r e d e s c r i b e d . The r e s u l t s a r e p r e s e n t e d i n a m a n n e r w h i c h w o u l d d e m o n s t r a t e t h e i n f l u e n c e o f a p p l i e d s t r e s s p a t h on t h e p l a n e s t r a i n r e s p o n s e o f ' i d e n t i c a l l y ' K Q - c o n s o l i -d a t e d s p e c i m e n s . U n d r a i n e d b e h a v i o u r u n d e r d i f f e r e n t c o n s o l i d a t i o n s t r e s s e s c a n u s u a l l y be d e r i v e d by u s i n g n o r m a l i s e d s t r e s s p a r a m e t e r s . The e x i s t e n c e o f a n o r m a l i s e d s t r e s s s t r e s s - s t r a i n b e h a v i o u r f o r a n o r m a l l y c o n s o l i d a t e d c l a y i s w e l l known ( H v o r s l e v , 1 9 6 0 ; H e n k e l , 1 9 6 0 ; R o s c o e and P o o r o o s h a s b , 1 9 6 3 ) . T h i s was f o u n d t o be t r u e f o r Haney c l a y a l s o . T h r e e p a s s i v e c o m p r e s s i o n u n d r a i n e d t e s t s , e a c h c o n s o l i d a t e d t o d i f f e r e n t v e r t i c a l c o n s o l i d a -t i o n s t r e s s a^, y i e l d e d e s s e n t i a l l y i d e n t i c a l n o r m a l i s e d d e v i a t o r s t r e s s , ( a z - c r x ) / a Z c > v s - a x i a l s t r a i n , e , r e l a -t i o n s h i p . S i m i l a r l y , o t h e r n o r m a l i s e d p l o t s , e . g . , c h a n g e i n p o r e p r e s s u r e , A u / a ^ v s . e z w e r e f o u n d t o be i d e n t i c a l f o r t e s t s w i t h d i f f e r e n t v a l u e s o f a ' . When c o m p a r i n g t h e p l a n e s t r a i n b e h a v i o u r 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 , v a r i a t i o n s o f s p e c i f i c s t r e s s o r s t r a i n p a r a m e t e r s a r e p l o t t e d a g a i n s t a x i a l s t r a i n , e . C o m p r e s s i v e s t r a i n s and v o l u m e d e c r e a s e s a r e c o n -s i d e r e d p o s i t i v e . 5 . 1 . 0 U n d r a i n e d T e s t R e s u l t s 5 . 1 . 1 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 . 5 . 1 shows n o r m a l i s e d d e v i a t o r s t r e s s , l a - a I/a " v s . a x i a l s t r a i n , e , f o r i d e n t i c a l l y 1 z x 1 z c ' z J c o n s o l i d a t e d s a m p l e s , u n d e r t h e f o u r u n d r a i n e d s t r e s s p a t h s - a c t i v e and p a s s i v e c o m p r e s s i o n s and e x t e n s i o n s . The r e l a t i o n s h i p i s i d e n t i c a l f o r t h e two c o m p r e s s i o n s t r e s s p a t h s . T h i s r e s u l t was as e x p e c t e d , b e c a u s e i n u n d r a i n e d t e s t s t h e e f f e c t i v e s t r e s s p a t h i s p r e -d e t e r m i n e d by t h e p o r e w a t e r p r e s s u r e c h a r a c t e r i s t i c s o f t h e s a m p l e . In s p i t e o f t h e v a r i a t i o n s i n t h e a p p l i e d t o t a l s t r e s s , f o r a s p e c i m e n w i t h a g i v e n c o n s o l i d a t i o n h i s t o r y , o n l y one e f f e c t i v e s t r e s s p a t h c a n be o b t a i n e d d u r i n g c o m p r e s s i o n s h e a r . The d e v i a t o r s t r e s s - s t r a i n r e s p o n s e d e p e n d s on t h e v a r i a t i o n s o f t h e e f f e c t i v e s t r e s s e s w i t h i n t h e s p e c i m e n a n d , t h e r e f o r e , s h o u l d be t h e same i f d i f f e r e n t s y s t e m s o f t o t a l s t r e s s e s g i v e r i s e t o t h e same e f f e c t i v e s t r e s s p a t h . S i m i l a r l y , . •0-8 2 0 2 Axial Strain - € z % F i g . 5 1 D E V I A T O R 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 D U R I N G U N D R A I N E D P L A N E S T R A I N S H E A R - N . C . H A N E Y C L A Y . |a - a x l / ° " Z c v s - e z r e l a t i o n s h i p i s i d e n t i c a l f o r t h e two e x t e n s i o n t e s t s f o r t h e same r e a s o n i n g t h a t a n y s y s t e m o f t o t a l s t r e s s e s l e a d i n g t o e x t e n s i o n s h e a r r e s u l t s i n t h e same e f f e c t i v e s t r e s s p a t h . Haney c l a y was v e r y b r i t t l e i n c o m p r e s s i o n f a i l u r e ( l a , - a u I , „ ) ; t h e a x i a l s t r a i n a t f a i l u r e z x m a x was o n l y 0 . 4 % . - On t h e o t h e r hand t h e e x t e n s i o n f a i l u r e was o f a p l a s t i c t y p e w i t h f a i l u r e s t r a i n a r o u n d 7%. The u n d r a i n e d s t r e n g t h , (|a - a I „ w / 2 ) , 3 1 z x 1 max i n e x t e n s i o n was o n l y 70% o f t h e c o m p r e s s i o n v a l u e . I t was i n t e r e s t i n g t o n o t e t h a t a t l a r g e s t r a i n s t h e d e v i a t o r s t r e s s i n c o m p r e s s i o n d r o p p e d b e l o w t h e v a l u e t h e s p e c i m e n s c a r r i e d a t t h e end o f c o n s o l i d a t i o n , and t h e peak d e v i a t o r s t r e s s i n e x t e n s i o n was e v e n s m a l l e r t h a n t h e end o f c o n s o l i d a t i o n v a l u e . C o m p r e s -s i o n t e s t s w e r e c a r r i e d t o a b o u t 18% a x i a l s t r a i n . The d e v i a t o r s t r e s s t h e n had d r o p p e d t o 40% o f t h e p e a k v a l u e and was s t i l l d e c r e a s i n g . T h u s , no a p p r o a c h t o a r e s i d u a l s t r e n g t h was a p p a r e n t . In a x i a l c o m p r e s s i o n s h e a r , t h e c o n d i t i o n o f maximum o b l i q u i t y , {oi'/o3') v was r e a c h e d a t a much max l a r g e r s t r a i n t h a n t h e maximum d e v i a t o r s t r e s s ( F i g . 5 . 2 ) . T h i s i s a w e l l known c h a r a c t e r i s t i c o f s e n s i t i v e c l a y s and i s due t o a p r o g r e s s i v e r i s e o f p o r e p r e s s u r e 8 - 6 -4 -2 0 2 4 6 8 Axial Strain-£ z% Fig.5-2 PRINCIPAL EFFECTIVE STRESS RATIO- STRAIN RELATIONSHIP DURING UNDRAINED SHEAR IN PLANE STRAIN-N.C. HANEY CLAY. a f t e r t h e maximum d e v i a t o r s t r e s s i s r e a c h e d ( C r a w f o r d , 1 9 5 9 ; B j e r r u m & S i m o n s , 1 9 6 0 ) . In e x t e n s i o n s h e a r , how -e v e r , p o i n t s o f \ o z - o x | m a x and ( a i 7 t J 3 ' ) m a x c o i n c i d e d . M o b i l i z a t i o n o f C o u l o m b f r i c t i o n , as c h a r a c t e r i s e d by t h e e f f e c t i v e s t r e s s r a t i o , o ' / o ' o r a ' / a " , was p r a c t i c a l l y £. A A L. i d e n t i c a l f o r t h e two c o m p r e s s i o n s t r e s s p a t h s and a l s o f o r t h e two e x t e n s i o n p a t h s . F i g . 5 . 3 shows t h e v a r i a t i o n o f e f f e c t i v e s t r e s s e s cC > CT", CT" d u r i n g s h e a r . The s t r e s s e s h a v e b e e n n o r m a l i s e d x y z J by d i v i d i n g them by a ^ c , t h e v e r t i c a l c o n s o l i d a t i o n s t r e s s . The v a r i a t i o n o f e a c h s t r e s s was e s s e n t i a l l y t h e same f o r b o t h c o m p r e s s i o n t e s t s and a l s o f o r t h e two e x t e n s i o n t e s t s . T h e r e f o r e , r e s u l t s f r o m o n l y one c o m p r e s s i o n and one e x t e n s i o n t e s t s a r e s h o w n . In c o m p r e s s i o n s h e a r , Oy, t h e s t r e s s a s s o c i a t e d w i t h z e r o s t r a i n d i r e c t i o n was a l w a y s i n t e r m e d i a t e b e t w e e n t h e o t h e r two s t r e s s e s a' and A a". In c o n t r a s t , d u r i n g e x t e n s i o n s h e a r , a" was t h e m i n o r z 3 y p r i n c i p a l e f f e c t i v e s t r e s s u n t i l a b o u t 2% a x i a l e x t e n s i o n a l s t r a i n . T h i s seems c o n t r a r y t o t h e f a m i l i a r c o n c e p t t h a t s t r e s s i n t h e d i r e c t i o n o f z e r o s t r a i n has a l w a y s an i n t e r -m e d i a t e v a l u e r e l a t i v e t o t h e o t h e r two s t r e s s e s . H o w e v e r , a s s u m i n g l i n e a r e l a s t i c b e h a v i o u r a t s m a l l s t r a i n s i t c a n be shown t h a t m u s t 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 i n t h e i n i t i a l s t a g e s o f t h e e x t e n s i o n s h e a r . A Fig . 5-3 E F F E C T I V E 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 D U R I N G U N D R A I N E D P L A N E STRAIN S H E A R - N . C H A N E Y C L A Y . s i m i l a r s i t u a t i o n c a n be shown t o e x i s t i n t h e r e s u l t s o f H a m b l y a n d R o s c o e ( 1 9 6 9 ) . A t f a i l u r e , w a s , as u s u a l , 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 r r e s p e c t i v e o f t h e r e l a t i v e m a g n i t u d e o f a " , t h e r a t i o a " / ( o * + a * ) 3 y y v x z' s t a y e d e s s e n t i a l l y c o n s t a n t ( F i g . 5 . 4 ) a t 0 . 3 7 ± 0 . 0 2 d u r i n g u n d r a i n e d s h e a r . T h i s i s s i m i l a r t o t h e r e s u l t s o f H a m b l y & R o s c o e ( 1 9 6 9 ) and H e n k e l and Wade ( 1 9 6 6 ) . 5 . 1 . 2 P o r e P r e s s u r e s F i g . 5 . 5 shows t h e c h a n g e i n p o r e p r e s s u r e , A u , f o r t h e f o u r i d e n t i c a l s p e c i m e n s u n d e r t h e i m p o s e d s t r e s s p a t h s . F o r t h e p a s s i v e c o m p r e s s i o n and e x t e n s i o n p a t h s t h e p o r e p r e s s u r e r i s e s c o n t i n u o u s l y d u r i n g t e s t s , due p a r t l y t o i n c r e a s e i n mean n o r m a l s t r e s s and p a r t l y t o c h a n g e s i n s h e a r s t r e s s e s . 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 t h e r e was a s u b s t a n t i a l r i s e o f p o r e p r e s s u r e a f t e r a s m a l l i n i t i a l d r o p i n a c t i v e c o m p r e s s i o n , d e s p i t e t h e t e s t i n v o l v e d d e c r e a s i n g mean n o r m a l s t r e s s . T h i s b e h a v i o u r i s a s s o c i a t e d w i t h s t r u c t u r a l c o l l a p s e o f s e n s i t i v e s o i l s k e l e t o n . O n l y a c t i v e e x t e n s i o n s h e a r r e s u l t e d i n n e t n e g a t i v e c h a n g e i n p o r e . p r e s s u r e s . N o t e t h e w i d e v a r i a t i o n s i n Au d u r i n g a c t i v e and p a s s i v e e x t e n s i o n . S i n c e u n d r a i n e d e f f e c t i v e s t r e s s p a t h s a r e known t o be i d e n t i c a l u n d e r s i m i l a r s t r a i n p a t h s , i t s h o u l d -4% Undrained active 0-2-A Undrained passive . Drained active *3 X + e Compress ion X Undrained active _ O Undrained passive + Drained active © Drained passive -8 - 4 0 4 8 Axial S t r a i n - € z % 12 16 Fig.5-4 S T R E S S R A T I O * - S T R A I N R E L A T I O N S H I P DURING P L A N E S T R A I N S H E A R -N.C. H A N E Y C L A Y . - I -8 -6 -4 -2 0 2 4 6 8 Axial Strain - € z % F i g .5-5 P O R E P R E S S U R E C H A N G E - S T R A I N R E L A T I O N S H I P S D U R I N G U N D R A I N E D P L A N E S T R A I N S H E A R - N . C . H A N E Y C L A Y . 2 be p o s s i b l e t o c h a r a c t e r i s e u n i q u e l y t h e c h a n g e s i n p o r e p r e s s u r e i n t e r m s o f s t r e s s c h a n g e s d u r i n g e i t h e r c o m p r e s -s i o n o r e x t e n s i o n s h e a r . T h i s i s a c c o m p l i s h e d by t h e u s e o f p o r e p r e s s u r e p a r a m e t e r s . F o r s t a t e s o f s t r e s s w h i c h a r e n o t a x i a l l y s y m m e t r i c , c h a n g e s i n p o r e p r e s s u r e s a r e b e t t e r e x p r e s s e d by H e n k e l ' s E q u a t i o n 2 . 4 , t h a n i n Skempton's ( 1 9 5 4 ) : . Au = A a Q C t + a A TQCT ( 2 . 4 ) E a r l i e r , H e n k e l ( 1 9 6 0 ) p r o p o s e d a v a r i a t i o n o f E q . 2 . 4 w h i c h was e x p r e s s e d as A u = A a o c t + 2 2 2 ( A a i - A a 2 ) + ( A a 2 - A a 3 ) + ( A a 3 - A a i ) ( 5 . 1 ) B o t h E q s . 2 . 4 and 5 . 1 r e l a t e t h e s h e a r i n d u c e d p o r e p r e s s u r e l i n e a r l y t o some m e a s u r e o f c h a n g e i n s h e a r s t r e s s e s ; how-e v e r , E q . 2 . 4 r e l a t e s t h e s h e a r i n d u c e d p o r e p r e s s u r e t o c h a n g e i n o c t a h e d r a l s h e a r s t r e s s , w h e r e a s E q . 5 . 1 r e l a t e s t h e s h e a r i n d u c e d p o r e p r e s s u r e t o o c t a h e d r a l c o m p o n e n t o f c h a n g e i n s h e a r s t r e s s . E q . 5 . 1 seems t o be o f a more g e n e r a l n a t u r e , b e c a u s e i t p r e d i c t s a d e f i n i t e c h a n g e i n p o r e p r e s s u r e e v e n i f s t r e s s c h a n g e s a r e s u c h t h a t T . and a o c t s t a y c o n s t a n t . E q . 2 . 4 d u r i n g s u c h a s t r e s s c h a n g e w i l l i n c o r r e c t l y p r e d i c t a z e r o c h a n g e i n p o r e p r e s s u r e . Even s o , E q . 5 . 1 p r o v e s i n s e n s i t i v e t o t h e p r o n o u n c e d e f f e c t o f r o t a t i o n o r r e o r i e n t a t i o n o f p r i n c i p a l s t r e s s e s on t h e i n d u c e d p o r e p r e s s u r e s , as d e m o n s t r a t e d by D u n c a n and S e e d ( 1 9 6 6 ) and D i c k e y e_t. a l _ . ( 1 9 6 8 ) . An e x p r e s s i o n s i m i l a r t o E q . 5 . 1 b u t w i t h s t r e s s e s r e f e r r e d t o f i x e d a x e s , x , y , z w i l l t a k e a c c o u n t , i n a s i m p l e w a y , o f p o r e p r e s s u r e i n d u c e d by c h a n g e s i n mean n o r m a l s t r e s s and t h o s e i n d u c e d i n a c u m u l a t i v e way by c h a n g e s i n s h e a r s t r e s s e s , i n c l u d i n g r o t a t i o n o r r e o r i e n t a t i o n o f p r i n c i p a l a x e s . The d e s i r e d e x p r e s s i o n i s Au = A a x + A a y + La z ( 5 . 2 ) 3 \| ( A a x - A c y )2 + ( A a y - A a 2 ) 2 + ( A a z ~ A a x ) 2 A s i m i l a r e q u a t i o n was s u g g e s t e d by B a k e r and K r i z e k ( 1 9 6 9 ) . In F i g . 5 . 6 i s shown t h e v a r i a t i o n o f p o r e p r e s -s u r e p a r a m e t e r ' a ' (as d e f i n e d i n e q u a t i o n 5 . 2 ) w i t h a x i a l s t r a i n , f o r t h e d i f f e r e n t s t r e s s p a t h s . B o t h c o m p r e s s i o n t e s t s l i e on a s i n g l e c u r v e and so do t h e two e x t e n s i o n t e s t s , Extension • Active O Passive a , 1-6-w E o h_ o D. <o 12 i -3 CO ( 0 <0 l _ ' a. a> a-0-8-0 4o- i-0-+ L J Compression • Active •+• Passive -8 -6 -4 -2 0 Axial Strain % Fig.5-6 V A R I A T I O N OF PORE P R E S S U R E P A R A M E T E R ' a ' WITH A X I A L S T R A I N DURING U N D R A I N E D P L A N E S T R A I N S H E A R -N.C. H A N E Y C L A Y . b u t t h e n a t u r e o f v a r i a t i o n o f ' a ' w i t h s t r a i n b e a r s no r e s e m b l a n c e i n t h e two g r o u p s o f t e s t s . A v e r a g e v a l u e o f ' a ' a t f a i l u r e ( l c r z - c r x l r n a x ) i n c o m p r e s s i o n was 1 . 2 c o m p a r e d t o 0 . 9 i n e x t e n s i o n . The v a l u e o f p o r e p r e s s u r e p a r a m e t e r ' a ' i s a f u n c t i o n o f t h e c o m p r e s -s i b i l i t y o f c l a y due t o c h a n g e s i n s h e a r s t r e s s e s . B e c a u s e o f t h e . i r r e v e r s i b 1 e n a t u r e o f c l a y b e h a v i o u r , t h i s c o m p r e s s i b i l i t y i s b o u n d t o be l a r g e r u n d e r i n -c r e a s i n g s h e a r s t r e s s e s when c o m p a r e d t o t h a t u n d e r d e c r e a s i n g s h e a r s t r e s s e s . T h i s d i f f e r e n c e i s l i k e l y t o be more p r o n o u n c e d i n Haney c l a y w h i c h has a s e n s i -t i v e s t r u c t u r e t o f u r t h e r c o m p r e s s i o n f o l l o w i n g o n e -d i m e n s i o n a l c o n s o l i d a t i o n . 5 . 1 . 3 E f f e c t i v e S t r e s s P a t h s F u l l i m p l i c a t i o n s o f t h e d i f f e r e n c e s b e t w e e n c o m p r e s s i o n and e x t e n s i o n modes o f d e f o r m a t i o n become e v i d e n t when t h e e f f e c t i v e s t r e s s p a t h s f o l l o w e d i n two t y p e s o f t e s t s a r e c o n s i d e r e d . S t r e s s p a t h s h a v e b e e n u s e d i n t h e s t u d y o f u n d r a i n e d t e s t s by many r e s e a r c h e r s ( R e n d u l i c , 1 936 ; R o s c o e e_t. a j_ . , 1 958 ; H e n k e l , 1 960 ; L a m b e , 1 9 6 4 , 1 9 6 7 ) , and a w i d e v a r i e t y o f s t r e s s s p a c e s h a v e b e e n u s e d . A s i m p l e s t r e s s s p a c e i n w h i c h t h e c o -o r d i n a t e s a r e o' and a " i s u s e d h e r e i n t o r e p r e s e n t 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 . F i g . 5 . 7 shows t h e s t r e s s p a t h s f o l l o w e d i n t h e f o u r p l a n e s t r a i n t e s t s . S i n c e t h e two c o m p r e s s i o n and t h e two e x t e n s i o n p a t h s a r e i d e n t i c a l , o n l y p a s s i v e c o m p r e s s i o n and a c t i v e e x t e n s i o n r e s u l t s a r e p r e s e n t e d i n t h i s f i g u r e . B o t h and a^, as b e f o r e , h a v e b e e n d i v i d e d by o^c' ^ e ^ w o s t r e s s p a t h s s t a r t f r o m t h e same p o i n t P i n s t r e s s s p a c e , w h i c h r e p r e s e n t s i d e n t i c a l end o f c o n s o l i d a t i o n s t a t e . D u r i n g c o m p r e s s i o n t e s t t h e s t r e s s p a t h f o l l o w s t h e c u r v e l a b e l l e d P Q , w h i l e i n t h e e x t e n s i o n t e s t t h e s t r e s s p a t h f o l l o w e d i s P R . A x i a l s t r a i n s i n p e r c e n t h a v e b e e n i n d i c a t e d i n t h e s t r e s s s p a c e and t h e e f f e c -t i v e s t r e s s f a i l u r e e n v e l o p e s (01/03 ) f o r b o t h r max c o m p r e s s i o n and e x t e n s i o n s t a t e s h a v e a l s o b e e n s h o w n . As was shown i n F i g . 5 . 1 t h e maximum v a l u e o f d e v i a t o r s t r e s s , \o -o | , i n c o m p r e s s i o n o c c u r r e d a t 0 . 4 % Z X a x i a l s t r a i n b u t , i t w i l l be s e e n i n F i g . 5 . 7 , t h i s p o i n t i s r e a c h e d b e f o r e t h e s t r e s s p a t h b e c o m e s t a n - ; g e n t i a l t o t h e e f f e c t i v e s t r e s s f a i l u r e e n v e l o p e . The p o i n t o f t a n g e n c y c o r r e s p o n d s t o an a x i a l s t r a i n o f a b o u t 3 % . In t h e e x t e n s i o n t e s t a v e r y l a r g e r e d u c t i o n o f t h e v a l u e o f t o o k p l a c e d u r i n g s h e a r , and b o t h t h e p o i n t o f t a n g e n c y t o t h e e f f e c t i v e s t r e s s f a i l u r e e n v e l o p e and t h e peak d e v i a t o r s t r e s s w e r e r e a c h e d a t a F i g . 5 - 7 UNDRAINED EFFECT IVE S T R E S S P A T H S DURING P L A N E S T R A I N S H E A R - N.C. H A N E Y C L A Y . s t r a i n , | e z | > o f a b o u t 7%. In b o t h c o m p r e s s i o n and e x t e n s i o n p a t h s , t h e s t r a i n s i n c r e a s e r a p i d l y as t h e f a i l u r e e n v e l o p e s a r e a p p r o a c h e d a n d , i f d e f o r m a t i o n s i n t h e f i e l d a r e t o be l i m i t e d , t h e i m p o s e d s t r e s s e s m u s t be c o n t r o l l e d so t h a t t h e s t r e s s p a t h s w i l l n o t g e t t o o c l o s e t o t h e f a i l u r e e n v e l o p e s . The a v e r a g e v a l u e o f cf>" w a s - 3 0 . 4 ° i n c o m p r e s s i o n and 2 6 . 1 ° i n e x t e n s i o n . T h e s e r e l a t i v e v a l u e s a r e s i m i l a r t o t h o s e r e p o r t e d by D u n c a n and S e e d ( 1 9 6 6 ) f o r t h e Bay m u d , w h i c h i m p l i e s t h a t Haney c l a y i s a n i s o t r o p i c w i t h r e s p e c t t o i t s e f f e c t i v e s t r e n g t h p a r a m e t e r s . The l a r g e i n c r e a s e i n e x t e n s i o n cf>" o v e r t h e c o m p r e s -s i o n v a l u e r e p o r t e d by D i c k e y e_t. a j_ . ( 1 9 6 8 ) i s l i k e l y t o be t h e r e s u l t o f n e g l e c t i n g f r i c t i o n on t h e v e r t i c a l b o u n d a r i e s o f t h e s p e c i m e n . T h i s n e g l e c t r e s u l t s i n an u n d e r e s t i m a t e o f t h e m i n o r p r i n c i p a l s t r e s s and c o n s e q u e n t l y a s u b s t a n t i a l e r r o r i n t h e r a t i o ( 0 1 / 0 3 ) ^ f o r a s m a l l e r r o r i n a j . D u r i n g c o m p r e s s i o n t e s t t h e n e g l e c t o f f r i c t i o n c a u s e s t h e m a j o r p r i n c i p a l s t r e s s , O i , t o be o v e r e s t i m a t e d a n d , t h e r e f o r e , t h e r a t i o (ai'/oHf i s i n f l u e n c e d o n l y t o a s m a l l d e g r e e . 5 . 2 . 0 D r a i n e d T e s t R e s u l t s O n l y t h r e e s t r e s s p a t h s , a c t i v e and p a s s i v e c o m -p r e s s i o n and a c t i v e e x t e n s i o n , w e r e s t u d i e d f o r d r a i n e d p l a n e s t r a i n c o n d i t i o n s . P a s s i v e e x t e n s i o n t e s t c o u l d n o t be p e r f o r m e d due t o l i m i t a t i o n s 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 ; i . e . t h e c a p a c i t y o f t h e l a t e r a l p r e s s u r e 2 d i a p h r a g m s was a r o u n d 12 Kg/cm . The v a l u e o f o r e -A q u i r e d t o c a u s e p a s s i v e e x t e n s i o n f a i l u r e w o u l d h a v e 2 b e e n a r o u n d 18 Kg/cm . 5 . 2 . 1 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 . 5 . 8 shows t h e v a r i a t i o n o f d e v i a t o r s t r e s s , | o z - CJ x | , and F i g . 5 . 9 r e p r e s e n t s t h e v a r i a t i o n o f a ' l a ' o r a ^ / 0 , w i t h a x i a l s t r a i n , e , i n t h e t h r e e Z X X Z Z t y p e s o f t e s t s . Among t h e c o m p r e s s i o n p a t h s , t h e s p e c i m e n s u b j e c t e d t o p a s s i v e c o m p r e s s i o n had h i g h e r I A T , _ c r v I m = v b e c a u s e o f h i g h e r e f f e c t i v e s t r e s s e s a t z x ma x f a i l u r e when c o m p a r e d t o s p e c i m e n s u b j e c t e d t o a c t i v e c o m p r e s s i o n . As shown i n F i g . 5 . 9 b o t h t h e s e s p e c i m e n s a t t a i n e d a l m o s t t h e same peak e f f e c t i v e s t r e s s r a t i o , 01/03 a n d , t h e r e f o r e , had t h e same l i m i t i n g a n g l e o f f r i c t i o n cj)". B u t t h e a x i a l s t r a i n r e q u i r e d t o d e v e l o p t h i s <}>" was a b o u t 12% i n p a s s i v e c o m p r e s s i o n c o m p a r e d t o o n l y a b o u t 4% i n a c t i v e c o m p r e s s i o n . W h i l e a n a l y s i n g s t a b i l i t y i n s o i l s w h e r e t h e u l t i m a t e o r r e s i d u a l s t r e n g t h i s l o w e r t h a n t h e p e a k s t r e n g t h ( s u c h as t h e c l a y c o n s i d e r e d h e r e i n ) , t h e a s s u m p t i o n o f a c o n s t a n t F i g . 5 - 8 D E V I A T O R 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 DURING D R A I N E D P L A N E S T R A I N S H E A R - N . C . H A N E Y C L A Y . F i g . 5 - 9 E F F E C T I V E S T R E S S R A T I O - S T R A I N R E L A T I O N S H I P S DURING DRAINED P L A N E S T R A I N S H E A R -N.C. H A N E Y C L A Y . c o m p r e s s i o n cf>" w i l l , t h e r e f o r e , l e a d t o an e s t i m a t e on t h e u n s a f e s i d e . F a i l u r e d u r i n g a c t i v e e x t e n s i o n o c c u r r e d w i t h a l o w p e a k d e v i a t o r s t r e s s ( a b o u t 55% o f t h e a c t i v e c o m p r e s s i o n v a l u e ) . T h i s was due t o s m a l l e r e f f e c t i v e s t r e s s e s on t h e s a m p l e a t f a i l u r e . A l s o t h e a s s o -c i a t e d cj)" f o r e x t e n s i o n was l o w e r t h a n f o r c o m p r e s s i o n f a i l u r e by an a m o u n t o f a b o u t 3 ° . The a x i a l s t r a i n a t f a i l u r e was a r o u n d 7%. P r e v i o u s l y , F i g . 5 . 3 s h o w e d t h a t d u r i n g u n d r a i n e d e x t e n s i o n a " was t h e m i n o r and n o t t h e i n t e r m e d i a t e y p r i n c i p a l s t r e s s d u r i n g e a r l y s t a g e s o f t h e s h e a r . A s i m i l a r s i t u a t i o n was f o u n d t o e x i s t f o r d r a i n e d a c t i v e e x t e n s i o n s h e a r , w h e r e a y r e m a i n e d t h e m i n o r p r i n c i p a l s t r e s s u n t i l a b o u t 2% a x i a l s t r a i n . T h e r e -a f t e r , a " , a s s u m e d a v a l u e i n t e r m e d i a t e b e t w e e n o ' and y x o ^ . H o w e v e r , t h e s t r e s s r a t i o , a y / ( o^+a^ ) , w a s f ° u n d t o s t a y e s s e n t i a l l y c o n s t a n t d u r i n g d r a i n e d s h e a r a l s o a n d , t h e m a g n i t u d e o f t h i s r a t i o ( 0 . 3 7 ± 0 . 0 2 ) was f o u n d t o be i n d e p e n d e n t o f t h e a p p l i e d s t r e s s p a t h ( s e e F i g . 5 . 4 ) . T h i s r a t i o had t h e same c o n s t a n t m a g n i t u d e d u r i n g u n d r a i n e d s h e a r . 5 . 2 . 2 V o l u m e C h a n g e s F i g . 5 . 1 0 shows v o l u m e t r i c s t r a i n s , v , d u r i n g d r a i n e d s h e a r as a f u n c t i o n o f a x i a l s t r a i n , e z, f o r t h e t h r e e t e s t s . A c o m p a r i s o n o f F i g . 5 . 1 0 w i t h F i g . 5 . 5 w i l l show t h e s i m i l a r i t y o f t h e v o l u m e t r i c s t r a i n s w i t h p o r e p r e s s u r e c h a n g e s f o r t h e c o r r e s p o n d i n g s t r e s s p a t h s . P a s s i v e . c o m p r e s s i o n s h e a r was a s s o c i a t e d w i t h v e r y l a r g e v o l u m e d e c r e a s e s and t h e r a t e o f v o l u m e c h a n g e i s s e e n t o be c o n s i d e r a b l e a t peak d e v i a t o r s t r e s s . T h i s i m p l i e s t h a t n o t a l l t h e i n p u t e n e r g y was b e i n g d i s s i p a t e d i n o v e r c o m i n g s h e a r s t r e s s e s , b u t a p a r t o f i t was u t i l i z e d i n d o i n g w o r k a g a i n s t t h e c o n f i n i n g p r e s s u r e . A s i m i l a r s i t u a t i o n e x i s t e d f o r a c t i v e c o m -p r e s s i o n , b u t t o a l e s s e r d e g r e e . T h i s v o l u m e d e c r e a s e b e h a v i o u r i s due i n p a r t t o . b r e a k d o w n o f s t r u c t u r a l f r a m e w o r k o f p a r t i c l e s i n t h e s e n s i t i v e m a r i n e c l a y , w h i c h i s b r o u g h t a b o u t by a p p l i e d s h e a r s t r e s s e s . The c l a y s t r u c t u r e as a r e s u l t i s r e n d e r e d more c o m p r e s s i b l e . D u r i n g a c t i v e e x t e n s i o n s h e a r , a v e r y s m a l l v o l u m e i n c r e a s e o c c u r r e d . T h i s w o u l d i m p l y t h a t t h e a c t i v e e x t e n s i o n r e s p o n s e d u r i n g d r a i n e d s h e a r w i l l be v e r y c l o s e t o t h a t d u r i n g u n d r a i n e d s h e a r . 5 . 2 .-3 F a i l u r e C o n d i t i o n s As shown i n F i g . 5 . 9 t h e peak e f f e c t i v e s t r e s s r a t i o , 01/03, i n b o t h t y p e s o f a x i a l c o m p r e s s i o n was • 1 4 J 1 ' 1 1 1 - 8 - 4 0 4 8 12 16 Axial strain - € z % F i g . 5 1 0 V O L U M E T R I C S T R A I N - A X I A L S T R A I N R E L A T I O N S H I P S DURING D R A I N E D P L A N E STRAIN S H E A R -N.C . H A N E Y C L A Y . a p p r o x i m a t e l y t h e same and c o r r e s p o n d s t o an a v e r a g e (J>" = 2 8 . 8 ° . On t h e o t h e r h a n d i n e x t e n s i o n was 2 6 . 5 ° . T h i s r e s u l t i s d i f f e r e n t f r o m t h a t r e p o r t e d by H a m b l y and R o s c o e (1 9 6 9 ) , who f o u n d t h e same <f>" f o r d r a i n e d p l a n e s t r a i n c o m p r e s s i o n and e x t e n s i o n ; h o w e v e r , t h e i r r e s u l t was f o r a r e m o l d e d c l a y as o p p o s e d t o u n d i s t u r b e d n a t u r a l s e n s i t i v e c l a y r e p o r t e d h e r e i n . 5 . 3 . 0 C o m p a r i s o n and C o r r e l a t i o n o f D r a i n e d and U n d r a i n e d  T e s t R e s u l t s T h e r e seems t o be no s i m i l a r i t y b e t w e e n t h e c o m -p r e s s i o n and e x t e n s i o n p l a n e s t r a i n b e h a v i o u r o f Haney c l a y . T h u s , a c o m p a r i s o n b e t w e e n d r a i n e d and u n d r a i n e d t e s t s w i l l be c o n s i d e r e d s e p a r a t e l y f o r 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 modes o f s h e a r . 5 . 3 . 1 D r a i n e d and U n d r a i n e d S t r e s s - S t r a i n C h a r a c t e r i s t i c s The h y p o t h e s i s t h a t a u n i q u e r e l a t i o n s h i p e x i s t s b e t w e e n v o i d r a t i o and e f f e c t i v e s t r e s s e s f o r a s a t u r -a t e d 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 c l a y was f i r s t p r o p o s e d by R e n d u l i c ( 1 9 3 7 ) , who a r g u e d t h a t t h e new v o i d r a t i o a f t e r a c h a n g e i n e f f e c t i v e s t r e s s e s i s n o t d e p e n d e n t on t h e s t r e s s p a t h b u t i s e x c l u s i v e l y d e t e r m i n e d by t h e new 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 . H i s t e s t s c o n s i s t e d o f c o n v e n t i o n a l l o a d i n c r e a s i n g d r a i n e d and u n d r a i n e d t r i a x i a l t e s t s on s a m p l e s w h i c h w e r e i n i t i a l l y 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 . R e n d u l i c a l s o s u g g e s t e d t h e 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 s w o u l d f a l l i n t o t h e same p a t t e r n . L a t e r , H e n k e l ( 1 9 6 0 ) v e r i f i e d and a m p l i f i e d R e n d u l i c ' s h y p o t h e s i s u s i n g t e s t s w i t h more e l a b o r a t e s t r e s s p a t h s . I n v e s t i g a t i o n s by W h i t m a n e_t. a_l_. ( 1 960 ) , S k e m p t o n and Sowa (1 9 6 3 ) a n d f u r t h e r r e s u l t s o f H e n k e l and Sowa ( 1 9 6 3 ) , h o w e v e r , d e m o n s t r a t e d t h a 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 s p e c i m e n s do n o t f i t i n t h e p a t t e r n o f u n i q u e v o i d r a t i o e f f e c t i v e s t r e s s r e l a t i o n s h i p f o r 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 . The r e a s o n a d v a n c e d f o r t h i s d i s a g r e e m e n t was t h e p r e s u m a b l y d i f f e r e n t m i c r o s t r u c t u r e b u i l t up d u r i n g d i s s i m i l a r c o n s o l i d a t i o n h i s t o r i e s o f t h e s p e c i m e n s , r e s u l t i n g i n d i f f e r e n t p r o p e r t i e s , e v e n i f t h e e f f e c t i v e s t r e s s e s w e r e t h e s a m e . R o s c o e e_t. a l ' s ( 1 9 5 8 ) c o n c e p t o f a u n i q u e s t a t e b o u n d a r y s u r f a c e i s an a l t e r n a t e s t a t e m e n t o f R e n d u l i c ' s c o n c e p t o f u n i q u e n e s s o f v o i d r a t i o and e f f e c t i v e s t r e s s e s f o r t h e t r i a x i a l t e s t s . R o s c o e and P o o r o o s h a s b ( 1 9 6 3 ) p r o p o s e d a t w o - d i m e n s i o n a l p l o t o f t h e e n t i r e s t a t e b o u n d a r y s u r f a c e by u s i n g p/p and q/p as a x e s . Where p = 1/3 ( o f + 0 - 2 + a g ) q = ( o f - 3 ) P e = e q u i v a l e n t p r e s s u r e - w h i c h i s t h e p r e s s u r e on t h e v i r g i n c o n s o l i d a t i o n l i n e c o r r e s p o n d i n g t o t h e c u r r e n t v o i d r a t i o o f t h e s p e c i m e n . The s t r e s s p a r a m e t e r p and q s p e c i f y c o m p l e t e l y t h e c u r r e n t s t r e s s s t a t e i n t h e t r i a x i a l t e s t s . R e n d u l i c ' s u n i q u e n e s s c o n c e p t t h e n i m p l i e s t h a t i s o t r o p i c a l 1 y 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 c l a y when t e s t e d i n l o a d i n c r e a s i n g d r a i n e d o r u n d r a i n e d c o m p r e s s i o n p o s s e s s e s a u n i q u e s u r f a c e i n ( p , q , e ) s p a c e . No a t t e m p t a p p e a r s t o h a v e b e e n made t o i n v e s t i g a t e t h e p o s s i b i l i t y t h a t R e n d u l i c ' s h y p o t h e s i s may a l s o h o l d f o r a n o r m a l l y c o n s o l i d a t e d c l a y w i t h a g i v e n t y p e o f a n i s o t r o p i c c o n s o l i d a t i o n h i s t o r y , e . g . , ^ - c o n s o l i d a t i o n h i s t o r y . S i n c e K Q - c o n s o l i d a t i o n i s b e l i e v e d t o i m p a r t t o t h e c l a y a m i c r o s t r u c t u r e d i f f e r e n t f r o m t h a t o b t a i n e d u n d e r i s o t r o p i c c o n s o l i d a t i o n , t h e u n i q u e s u r f a c e i n ( p , q , e ) s p a c e f o r K Q - c o n s o l i d a t e d c l a y , ( c a l l e d t h e a n i s o -t r o p i c y i e l d o r s t a t e b o u n d a r y s u r f a c e h e r e i n a f t e r ) i n c a s e s u c h a s u r f a c e e x i s t s , w i l l be d i f f e r e n t f r o m t h e i s o t r o p i c y i e l d s u r f a c e i n t h e same s p a c e . The p o s s i b i l i t y t h a t a u n i q u e a n i s o t r o p i c y i e l d s u r f a c e may e x i s t f o r n o r m a l l y K Q - c o n s o l i d a t e d Haney c l a y w i l l now be e x a m i n e d . I f s u c h a s u r f a c e d o e s e x i s t , t h e i m p l i c a t i o n s t h e r e o f c a n t h e n be u s e d t o c o r r e l a t e d r a i n e d and u n d r a i n e d t e s t s . A u n i q u e y i e l d s u r f a c e i n ( p , q , e ) s p a c e s u g g e s t s t h a t v o i d r a t i o i s a f u n c t i o n o f mean n o r m a l s t r e s s , p , and o f an a p p r o p r i a t e m e a s u r e o f s h e a r s t r e s s , w h i c h i s q i n t h e t r i a x i a l t e s t s . D u r i n g p l a n e s t r a i n d e f o r m a t i o n 02 t ° i o r ° 3 a n d , t h e r e f o r e , T ^ w i l l be t h e more a p p r o -p r i a t e m e a s u r e o f s h e a r s t r e s s i n p r e f e r e n c e t o q . I t i s , t h e r e f o r e , p o s t u l a t e d t h a t a u n i q u e y i e l d s u r f a c e i n ( p , T o c t ' e ^ s P a c e m i g h t e x i s t f o r l o a d i n c r e a s i n g c o m p r e s s i o n t e s t s on ^ - c o n s o l i d a t e d Haney c l a y . The c o r r e s p o n d i n g t w o - d i m e n s i o n a l p l o t o f t h i s s u r f a c e w o u l d t h e n be w i t h p / p „ and T „ + / p as a x e s . S i n c e o n l y K - c o n s o l i d a t i o n r r e o c t r e o c o n d i t i o n s a r e c o n s i d e r e d , p g w i l l be r e f e r r e d t o t h e v i r g i n K Q - c o n s o l i d a t i o n l i n e ( F i g . 3 . 4 ) as o p p o s e d t o v i r g i n i s o t r o p i c c o n s o l i d a t i o n l i n e c o n s i d e r e d by R o s c o e and P o o r o o s h a s b ( 1 9 6 3 ) f o r t r e a t i n g 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 . F i g . 5 . 1 1 shows a l l d r a i n e d and u n d r a i n e d c o m p r e s -s i o n t e s t s p l o t t e d w i t h P / P e and T o c ^ / P e a s a x e s . I t c a n be s e e n t h a t e x c e p t f o r t h e s m a l l i n i t i a l d e v i a t i o n s t h e l o a d i n c r e a s i n g d r a i n e d p a s s i v e c o m p r e s s i o n t e s t r e s u l t s l i e on t h e s t a t e b o u n d a r y s u r f a c e c u r v e d e t e r m i n e d by t h e ' A O 4 A ^undrained Undrained + Passive 0 Active Drained Passive A Active i 0-4 0-3 0-2 0-0-5 0-6 0-7 0-8 0-9 10 JL Pe F i g.5ll S T A T E B O U N D A R Y S U R F A C E C U R V E FOR 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 -N.C. H A N E Y C L A Y . u n d r a i n e d t e s t s . The i n i t i a l d e p a r t u r e f r o m t h e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e i s b e l i e v e d t o be due t o an i n c o m p l e t e d i s s i p a t i o n o f e x c e s s p o r e p r e s s u r e s a t s m a l l s t r a i n s o f t h e o r d e r o f 1/2% e . T h i s d i s c r e p a n c y , w h i c h a r i s e s as a r e s u l t o f s t r a i n c o n t r o l l e d l o a d i n g , c o u l d p o s s i b l y be e l i m i n a t e d i n a s t r e s s c o n t r o l l e d t y p e o f t e s t . R e s u l t s o f - u n l o a d i n g d r a i n e d a c t i v e c o m p r e s s i o n t e s t , h o w e v e r , f a l l s l i g h t l y b e l o w t h e s t a t e b o u n d a r y s u r f a c e c u r v e f o r t h e u n d r a i n e d t e s t s . T h i s i s i n a c c o r d a n c e w i t h R e n d u l i c ' s r e s t r i c t i o n on t h e u n i q u e n e s s c o n c e p t , w h i c h was c o n s i d e r e d v a l i d f o r o n l y t h o s e s t r e s s p a t h s w h i c h r e s u l t e d i n c o n s o l i d a t i o n o r v o l u m e d e c r e a s e o f t h e s p e c i m e n . P l a n e s t r a i n s p e c i m e n s , when s h e a r e d u n d e r d r a i n e d a c t i v e c o m p r e s s i o n , u n d e r w e n t a s m a l l i n i t i a l i n c r e a s e i n v o i d r a t i o . I f as a f i r s t a p p r o x i m a t i o n t h e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e c a n be c o n s i d e r e d t o be a p p l i c a b l e f o r l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n s t r e s s p a t h s , t h e n i t i s p o s s i b l e t o p r e d i c t c h a n g e i n v o i d r a t i o due t o t h e a d d i t i o n o f a s t r e s s i n c r e m e n t i n d r a i n e d p l a n e s t r a i n t e s t s by r e v e r s i n g t h e p r o c e d u r e u s e d t o c o n s t r u c t F i g . 5 . 1 1 . F o r e x a m p l e , f o r t h e c u r r e n t s t a t e o f s t r e s s ( p , T o c t)-]> t n e r a t i o T o c - ( - / P c a n D e d e t e r m i n e d , and t h e n f r o m F i g . 5 . 1 1 t h e p o i n t w h e r e t h i s T o c ^ - / P r a t i o c u t s t h e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e i s f o u n d and t h e v a l u e o f p / p g i s r e a d . S i n c e p i s k n o w n , t h i s g i v e s p g w h i c h i s t h e p o i n t on t h e v i r g i n ^ - c o n s o l i d a t i o n l i n e h a v i n g t h e same v o i d r a t i o as t h e s t r e s s s t a t e ( p , x o c t ) - | . A f t e r t h e s t r e s s i n c r e m e n t i s a p p l i e d t h e new v a l u e o f p e i s f o u n d i n t h e same m a n n e r f o r t h e new s t a t e o f s t r e s s ( p , T o c t ) 2 " K n o w i n g t h e c o m p r e s s i o n i n d e x , A, (A = e - j - 6 2 / 1 n p 2 ~ l np.j = . 252 f r o m F i g . 3 . 4 ) t h e d i f f e r e n c e i n v o i d r a t i o f o r t h e two s t a t e s o f s t r e s s c a n be d e t e r -m i n e d , w h i c h c a n be e x p r e s s e d as a v o l u m e t r i c s t r a i n . T Q c t / p v s . v o l u m e t r i c s t r a i n r e l a t i o n s h i p p r e -d i c t e d by t h e a b o v e m e n t i o n e d t e c h n i q u e f o r t h e d r a i n e d p a s s i v e c o m p r e s s i o n t e s t i s shown i n F i g . 5 . 1 2 by t h e s o i l d c u r v e . The o b s e r v e d T Q c t / p v s . v o l u m e t r i c s t r a i n r e l a t i o n i s a l s o s h o w n . E x c e p t f o r t h e s m a l l o v e r p r e d i c t i o n i n t h e i n i t i a l s t a g e s , t h e r e i s an e x c e l l e n t a g r e e m e n t b e t w e e n t h e p r e d i c t e d and o b s e r v e d v o l u m e t r i c s t r a i n s . As a l r e a d y p o i n t e d o u t , t h e d i s c r e p a n c y i n t h e i n i t i a l s t a g e s o f t h e t e s t c o u l d be t h e r e s u l t o f o n l y i n c o m p l e t e d i s s i -p a t i o n o f e x c e s s p o r e p r e s s u r e s d u r i n g t h e s t r a i n c o n t r o l l e d t y p e o f d r a i n e d s h e a r . P r e d i c t e d and o b s e r v e d v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d a c t i v e c o m p r e s s i o n a r e shown i n F i g . 5 . 1 2 a . F o r v a l u e s o f T o c t / P < 0 - 4 1 t h e p r e d i c t e d s t r a i n s a r e z e r o . T h e r e a f t e r , t h e o b s e r v e d s t r a i n s t e n d t o be l a r g e r t h a n p r e d i c t e d . 0-42 0-34 1 + Observed passive compression Predicted from undrained compression tests 1 + / 0 2 4 6 8 Volumetric strain - v % F i g . 5 1 2 C O M P A R I S O N OF P R E D I C T E D AND O B S E R V E D V O L U M E T R I C S T R A I N S DURING D R A I N E D P L A N E S T R A I N P A S S I V E C 0 M P R E 5 S I 0 N -N.C. H A N E Y C L A Y . 0.46 P 0 .34 0 .30 + 0 C BSERVED ACT OMPRESSION "IVE {+ \ + \ X PR CO EDICTED FRO MPRESSION M UNDRAINED TESTS 0 1 2 3 4 VOLUMETRIC STRAIN v % FIG. 5.12a C O M P A R I S O N O F O B S E R V E D A N D P R E D I C T E D V O L U M E T R I C S T R A I N S D U R I N G D R A I N E D P L A N E S T R A I N A C T I V E C O M P R E S S I O N - N .C . H A N E Y C L A Y . I t i s t h e r e f o r e s u g g e s t e d , t h a t t h e R e n d u l i c a p p r o a c h c a n be e x t e n d e d t o p r e d i c t v o l u m e t r i c s t r a i n s i n l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n t e s t s f r o m t h e r e s u l t s o f u n d r a i n e d c o m p r e s s i o n t e s t s , p r o v i d e d t h e s p e c i m e n s c o n s i d e r e d h a v e t h e same c o n s o l i d a t i o n h i s t o r y . A l t e r n a t i v e l y , p o r e p r e s s u r e s c o u l d be p r e d i c t e d d u r i n g u n d r a i n e d t e s t s f r o m t h e r e s u l t s o f d r a i n e d t e s t s . R e n d u l i c ' s h y p o t h e s i s was l i m i t e d t o c a s e s w h e r e d e v i a t o r s t r e s s was b e i n g i n c r e a s e d and t h e c l a y u n d e r w e n t c o n s o l i d a t i o n . R o s c o e and S c h o f i e l d ( 1 9 6 3 ) c o n s i d e r e d t h e s i t u a t i o n w h i c h i n v o l v e d u n l o a d i n g o f s h e a r s t r e s s e s . A c c o r d i n g t o t h e i r s u g g e s t i o n , t h e v o l u m e t r i c s t r a i n s d u r i n g d r a i n e d a c t i v e e x t e n s i o n t r i a x i a l s h e a r ( w h i c h i n v o l v e s u n l o a d i n g o f b o t h q and p) w o u l d be d e t e r m i n e d s o l e l y by t h e c h a n g e s i n p . The i n c r e a s e i n v o i d r a t i o , A e , due t o a r e d u c t i o n i n p f r o m p^ t o P2 was p r o p o s e d t o be g o v e r n e d by Ae = K I n p^/p2 w h e r e K i s t h e s l o p e o f i s o t r o p i c s w e l l i n g c u r v e . I f t h e same c r i t e r i o n i s u s e d t o e s t i m a t e v o l u m e t r i c s t r a i n s i n p l a n e s t r a i n d r a i n e d a c t i v e e x t e n s i o n s h e a r , , t h e o b s e r v e d s t r a i n s w e r e f o u n d t o be i n c l o s e a g r e e m e n t w i t h p r e d i c t i o n . V o l u m e t r i c s t r a i n s i n t h i s a c t i v e e x t e n -s i o n t e s t w e r e v e r y s m a l l (< 0 . 7 5 % a t f a i l u r e ) a n d , t h e r e -f o r e , t h e i r p r e d i c t i o n seems t o be o f h a r d l y a n y i m p o r t a n c e . In t h e d r a i n e d t e s t s v o l u m e t r i c s t r a i n s a l o n e , h o w e v e r , a r e i n s u f f i c i e n t t o d e s c r i b e t h e c o m p l e t e s t a t e o f s t r a i n . C o n s i d e r a t i o n has been g i v e n t o t h e p r e d i c t i o n o f s h e a r s t r a i n s i n d r a i n e d t e s t on t h e a s s u m p t i o n t h a t n o r m a l l y c o n s o l i d a t e d s a t u r a t e d c l a y s c a n be a s s u m e d t o y i e l d a c c o r d i n g t o t h e w o r k h a r d e n i n g t h e o r y o f p l a s t i c i t y (as d o n e i n C a m b r i d g e s t r e s s - s t r a i n t h e o r y ) . A p r e d i c -t i o n o f s h e a r s t r a i n s i n t h e d r a i n e d p a s s i v e c o m p r e s s i o n t e s t , f r o m t h e r e s u l t s o f u n d r a i n e d . c o m p r e s s i o n t e s t s , c a n be a t t e m p t e d u s i n g n o r m a l i t y c o n d i t i o n o f t h e p l a s -t i c i t y t h e o r y , i f t h e f o l l o w i n g a s s u m p t i o n s a r e m a d e : 1 . The e m p i r i c a l s t r e s s - v o i d r a t i o s u r f a c e o f t h e R e n d u l i c t y p e c a n be r e g a r d e d as t h e y i e l d s u r f a c e w h i c h i s a s s u m e d t o be s y m m e t r i c a b o u t p a x i s i n ( p , T o c t ) s p a c e . I r r e c o v e r a b l e o r p l a s t i c s t r a i n s o c c u r o n l y f o r s t a t e s o f t h e s a m p l e on t h i s y i e l d s u r f a c e . 2 . The c u r r e n t y i e l d l o c u s c a n be c o n s i d e r e d t o be i d e n t i c a l w i t h t h e u n d r a i n e d s t r e s s p a t h c o r r e s p o n d i n g t o t h e c u r r e n t v o i d r a t i o s t a t e o f t h i s s p e c i m e n . In t h e C a m b r i d g e t h e o r y t h i s i s e q u i v a l e n t t o t h e a s s u m p t i o n , K = 0. 3 . A l l s t r a i n s a r e c o n s i d e r e d i r r e c o v e r a b l e . In F i g . 5 . 1 3 a t y p i c a l c u r r e n t y i e l d l o c u s i s shown i n ( p , T j.) a x e s . T h i s l o c u s i s t h e u n d r a i n e d s t r e s s p a t h c o r r e s p o n d i n g t o t h e c u r r e n t v o i d r a t i o o f t h e s a m p l e . I f a s t r e s s i n c r e m e n t i s now a p p l i e d on t h e s t r e s s s t a t e a t P , t h e n o r m a l i t y c o n d i t i o n r e q u i r e s FIG. 5.13 T Y P I C A L UNDRAINED S T R E S S P A T H AND A S S U M E D C U R R E N T Y IELD L O C U S FOR N.C. H A N E Y C L A Y . 6 y o c t 6v dx o c t dp (5.3) w h e r e 6 Y o c t 1 3 \ 2 2 2 ( 6 e i - 6 e 2 ) + {&£2-&£a) + ( c S e 3 - 6 e i ) (5.4) 6v = 6 e i + 6 e 2 + 6e (5.5) C o n s i d e r a s o i l e l e m e n t i n e q u i l i b r i u m u n d e r a s t a t e ( p , T o c t > e ) - ] a n c ' l e t a s t r e s s i n c r e m e n t be a p p l i e d r e s u l t i n g i n t h e new e q u i l i b r i u m s t a t e , ( p , T Q c t e ^ . R e s t r i c t i n g t h e s t r e s s c h a n g e s t o t h e s t r e s s p a t h c o r r e -s p o n d i n g t o d r a i n e d p a s s i v e c o m p r e s s i o n , i n c r e m e n t i n 6v due t o t h e a p p l i e d s t r e s s i n c r e m e n t c a n be d e t e r m i n e d f r o m t h e e x t e n d e d R e n d u l i c a n i s o t r o p i c y i e l d s u r f a c e , u s i n g t h e p r o c e d u r e d e s c r i b e d e a r l i e r i n t h i s s e c t i o n . The c u r r e n t y i e l d l o c u s c o r r e s p o n d i n g t o t h e s t a t e ( p , T t , e). j w i l l be the u n d r a i n e d s t r e s s p a t h w i t h e = e-j . A g r a p h i c a l e v a l u a t i o n o f t h e s l o p e o f t h i s y i e l d l o c u s a t t h e b a s i c s t r e s s s t a t e ( p , T g i v e s t h e m a g n i t u d e o f t h e s t r a i n i n c r e m e n t r a t i o , &Y0Ct/&y> a n d h e n c e < S Y o c t c a n be d e t e r m i n e d a s Sv i s a l r e a d y k n o w n . R e p e t i t i o n o f t h i s i n c r e m e n t a l p r o c e d u r e i n s m a l l s t e p s o f i n c r e m e n t s i n s t r e s s r a t i o , Toc^/P> d e t e r m i n e s t h e d e s i r e d p r e d i c t e d s h e a r s t r e s s - s t r a i n r e l a t i o n s h i p . I t may be m e n t i o n e d h e r e , t h a t f o r a n y s t r e s s s t a t e ( p , T o c ^ - ) » t h e s l o p e o f c u r r e n t y i e l d l o c i i s a f u n c t i o n o f s t r e s s r a t i o T o c - ( - / P o n l y and c a n be d e t e r m i n e d f r o m t h e s i n g l e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e o f F i g . 5 . 1 1 . The p r e d i c t e d T t / p v s . f&YQCt r e l a t i o n s h i p f o r t h e d r a i n e d p a s s i v e c o m p r e s s i o n t e s t i s shown i n F i g . 5 . 1 4 , a l o n g w i t h t h e o b s e r v e d r e l a t i o n s h i p . The p r e d i c t i o n o f s h e a r s t r a i n s c a n n o t be made f o r T o c t / P v a l u e s > 0 . 3 8 w h i c h i s t h e c r i t i c a l s t r e s s r a t i o , ( T 0 Ct/P)cT' a t w n i c n t n e t a n g e n t t o t h e u n d r a i n e d s t r e s s p a t h s ( o r y i e l d l o c i ) b e c o m e s h o r i z o n t a l ( s e e F i g . 5 . 1 3 ) . F rom t h e n o r m a l i t y c o n d i t i o n t h i s i m p l i e s u n l i m i t e d s h e a r d i s t o r t i o n , <5Y 0 C t> w i t h o u t any v o l u m e c h a n g e , i . e . ( S Y o c t / 5 v ->- °°. H o w e v e r , t h e p r e d i c t e d s t r e s s - s t r a i n r e l a t i o n s h i p f o r v a l u e s o f T o c t / ' P < ^ o c t ^ ^ C T 1 S i n s a t i s f a c t o r y a g r e e m e n t w i t h t h e o b s e r v e d r e l a t i o n s h i p up t o f&Y0Ct ~ 1 - 5 % , w h i c h c o r r e s p o n d s t o an a x i a l s t r a i n e z ~ 2 . 5 % . The a x i a l s t r a i n a t f a i l u r e i n d r a i n e d p a s s i v e c o m p r e s s i o n was a r o u n d 12% a n d , t h e r e f o r e , n o r m a l i t y c o n d i t i o n o f p l a s t i c i t y t h e o r y c a n , a t b e s t , 0.46 0.42 + OBSERVED + + + A- \ PREDICTE COMPRES D FROM UNDR S10N TESTS AINED 0 2 4 6 8 J 'oct FIG.5.14 COMPARISON OF OBSERVED AND PREDICTED SHEAR STRAINS DURING DRAINED PLANE STRAIN PASSIVE COMPRESSION - N.C. HANEY ' CLAY. p r o v i d e r e a s o n a b l e p r e d i c t i o n o f s h e a r s t r a i n s u n t i l a b o u t 20% o f t h e f a i l u r e s t r a i n s . F o r c l a y s i n w h i c h t h e c o n d i t i o n o f T Q C t = max i s i d e n t i c a l w i t h t h e c o n d i -t i o n o f T o c t / P = max ( s u c h as i n r e m o l d e d c l a y s ) , s h e a r s t r a i n p r e d i c t i o n s c o u l d be a t t e m p t e d f o r t h e e n t i r e d r a i n e d s t r e s s p a t h . D u r i n g d r a i n e d a c t i v e c o m p r e s s i o n s h e a r , t h e a p p l i e d s t r e s s i n c r e m e n t s a r e s u c h t h a t t h e s t r e s s i n c r e m e n t v e c t o r a t t h e s t r e s s p o i n t P i s d i r e c t e d t o t h e l e f t o f t h e t a n g e n t t o t h e y i e l d l o c u s ( s e e F i g . 5 . 1 3 ) . S u c h s t r e s s c h a n g e s i m p l y u n l o a d i n g , i . e . t h e y do n o t c a u s e p l a s t i c d i s t o r t i o n . B e c a u s e a l l s t r a i n s w e r e a s s u m e d i r r e c o v e r a b l e , t h e c l a y w o u l d r e m a i n r i g i d w i t h r e s p e c t t o s h e a r s t r a i n s d u r i n g t h e i m p o s e d a c t i v e c o m p r e s s i o n d r a i n e d s h e a r . S t r e s s c h a n g e s d u r i n g d r a i n e d a c t i v e e x t e n s i o n s h e a r a l s o c o r r e s p o n d t o u n l o a d i n g and t h i s w o u l d a g a i n i m p l y r i g i d b e h a v i o u r i n s h e a r . R o s c o e and B u r l a n d ( 1 9 6 8 ) u s e d t h e c o n c e p t o f a d o u b l e y i e l d l o c u s t o d e t e r m i n e i r r e c o v e r a b l e s h e a r d i s t o r -t i o n f o r s t a t e p a t h s b e l o w t h e y i e l d s u r f a c e . F o r K = 0 c l a y s , t h e i r c o n c e p t i m p l i e s t h a t t h e ^0C^/P v s . Y O C T r e l a t i o n s h i p f o r t h o s e d r a i n e d t e s t s w h o s e s t a t e p a t h s l i e e n t i r e l y b e l o w t h e y i e l d s u r f a c e i s i d e n t i c a l t o t h e T o c t ^ v s ' Y o c t r e ^ a t i o n s h i p f o r t h e c o r r e s p o n d i n g u n d r a i n e d t e s t . In t h e a c t i v e c o m p r e s s i o n u n d r a i n e d t e s t , ( T Q C t / p ) C T = 0 . 3 8 was r e a c h e d a t Y O C T = 0 . 1 % a n d , t h e r e -f o r e , t h e i d e n t i t y o f T o c ^ - / P v s . s h e a r s t r a i n s r e l a t i o n i n u n d r a i n e d and d r a i n e d t e s t s c a n n o t e v e n be a t t e m p t e d by R p s c o e and B u r l a n d ' s m e t h o d f o r Y O C T > 0 . 1 % . F o r d r a i n e d a c t i v e e x t e n s i o n t e s t , h o w e v e r , t h e i r m e t h o d c o r r e c t l y p r e d i c t s an a l m o s t i d e n t i c a l T Q c t / p v s . Y O C T r e l a t i o n s h i p t o t h a t o f t h e c o r r e s p o n d i n g u n d r a i n e d t e s t ( F i g . 5 . 1 5 ) . 5 . 3 . 2 S t r e s s a " y One common f e a t u r e o f a l l t h e u n d r a i n e d and d r a i n e d p l a n e s t r a i n t e s t was t h e n a t u r e o f v a r i a t i o n o f p r i n c i p a l s t r e s s , a s s o c i a t e d w i t h t h e d i r e c t i o n o f z e r o s t r a i n . S i m i l a r t o t h e o b s e r v a t i o n o f H a m b l y and R o s c o e ( 1 9 6 9 ) f o r a r e m o l d e d K a o l i n , t h e r a t i o o ' / ( o ' + a ' ) y x z s t a y e d e s s e n t i a l l y c o n s t a n t d u r i n g p l a n e s t r a i n s h e a r o f Haney c l a y ( F i g . 5 . 4 ) . 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 t h e m a g n i t u d e o f t h i s r a t i o , w h i c h r e s e m b l e s P o i s s o n ' s r a t i o f o r an e l a s t i c m a t e r i a l , was v e r y n e a r l y e q u a l t o K Q / ( 1 + K Q ) . The l a t t e r e x p r e s s i o n a l s o e q u a l s P o i s s o n ' s r a t i o i f l i n e a r e l a s t i c b e h a v i o u r i s a s s u m e d d u r i n g o n e - d i m e n s i o n a l ( K Q ) c o n s o l i d a t i o n . S i m i l a r r e l a t i o n s h i p s i . e . C7y/ ( c ^ + C T ' z ) ~ K 0 / 0 + K 0 ) c a n °e shown t o e x i s t i n t h e r e s u l t s o f H e n k e l and Wade ( 1 9 6 6 ) and H a m b l y and R o s c o e 0.42 0.18 0.1 + y + / 1 / UNDRA + DRAIN INED ACTIVE ED ACTIVE E EXTENSION XTENSION + 0 2 4 6 8 X o c t % FIG.5.15 COMPARISON OF SHEAR STRESS - STRAIN RELATIONSHIP DURING PLANE STRAIN DRAINED AND UNDRAINED ACTIVE EXTENSION _ N.C. HANEY CLAY. ( 1 9 6 9 ) . S u c h a r e l a t i o n s h i p c a n p r o v e v e r y u s e f u l f o r e s t i m a t i n g o y i n p l a n e s t r a i n , i f K Q v a l u e o f t h e n o r m a l l y c o n s o l i d a t e d c l a y i s k n o w n . 5 . 4 . 0 D r a i n e d and U n d r a i n e d S t r e n g t h C h a r a c t e r i s t i c s The r e s u l t s o f a l l t h e p l a n e s t r a i n t e s t s a r e s u m -m a r i z e d i n T a b l e I I . F o r t h e same t y p e o f d r a i n e d and u n d r a i n e d t e s t s t h e r e l a t i v e s t r e n g t h , as c h a r a c t e r i s e d by |a -a | / 2 , d e p e n d s on t h e n a t u r e and t h e amount o f L. A IN Cl A v o l u m e c h a n g e i n t h e d r a i n e d t e s t . P a s s i v e c o m p r e s -s i o n t e s t s a r e t h e c o n v e n t i o n a l t y p e s o f c o m p r e s s i o n t e s t , i n w h i c h d r a i n e d s t r e n g t h i s much l a r g e r t h a n t h e u n d r a i n e d s t r e n g t h . Haney c l a y , b e c a u s e o f i t s s e n s i -t i v e n a t u r e , u n d e r w e n t a v o l u m e d e c r e a s e i n a c t i v e d r a i n e d c o m p r e s s i o n d e s p i t e d e c r e a s i n g mean n o r m a l s t r e s s e s ; t h i s r e s u l t e d i n d r a i n e d s t r e n g t h b e i n g h i g h e r t h a n t h e u n d r a i n e d s t r e n g t h o f an i d e n t i c a l s p e c i m e n . T h i s i s c o n t r a r y t o t h e u s u a l c o n c e p t t h a t a c t i v e d r a i n e d s t r e n g t h i s a l w a y s s m a l l e r t h a n t h e u n d r a i n e d v a l u e ( B i s h o p and H e n k e l , 1 9 6 2 ) . D u r i n g a c t i v e a x i a l e x t e n -s i o n t h e s p e c i m e n u n d e r w e n t a s m a l l s w e l l i n g , a n d t h e r e -f o r e d r a i n e d s t r e n g t h m o b i l i z e d was s m a l l e r t h a n t h e c o r r e s p o n d i n g u n d r a i n e d v a l u e . I t i s s u r p r i s i n g t h a t t h e r e m o l d e d c l a y u s e d by H a m b l y a n d R o s c o e ( 1 9 6 9 ) showed a End o f C o n s o l i d a t i o n F a i l u r e C o n d i t i o n (o 1 _ a 3 ) m a x (af -O-3 ; m a x *z'c K o A x i a l S t r a i n % O i - a 3  a z c a v% 0 A x i a l S t r a i n % ai/O-3 * m . m Y c U n d r a i n e d T e s t s P a s s i v e c o m p r e s s i o n A c t i v e c o m p r e s s i o n A c t i v e e x t e n s i o n P a s s i v e e x t e n s i o n 6 . 0 1 5 . 9 3 5 . 9 0 5 . 8 7 . 5 5 . 5 5 . 5 6 . 5 7 . 4 . 5 - 7 . 1 - 5 . 2 . 5 8 2 . 5 9 . 3 9 2 . 3 9 4 1 . 2 1 . 1 5 . 9 1 . 9 0 0 0 0 0 2 2 2 2 . 4 9 . 5 2 . 5 9 . 5 6 2 5 . 3 ° 2 5 . 6 ° 2 6 . 3 ° 2 6 . 0 ° 2 . 9 2 . 6 - 7 . 1 - 5 . 2 3 . 1 0 3 . 0 0 2 . 5 9 2 . 5 6 3 0 . 8 ° 3 0 . 0 ° 2 6 . 3 ° 2 6 . 0 ° 3 0 . 8 ° 30 . 0 ° 2 6 . 3 ° 2 6 . 0 ° D r a i n e d T e s t s P a s s i v e c o m p r e s s i o n A c t i v e c o m p r e s s i o n A c t i v e e x t e n s i o n 5 . 9 6 ' 5 . 9 8 5 . 8 7 . 5 4 . 5 6 . 5 5 1 2 . 0 4 . 5 - 7 . 0 . 9 5 . 6 0 5 . 3 4 1 — 6 . 0 0 . 9 - 0 . 8 2 2 2 . 8 8 . 8 5 . 6 1 2 9 . 0 ° 2 8 . 7 ° 2 6 . 5 ° 1 2 . 0 4 . 5 - 7 . 0 2 . 8 8 2 . 8 5 2 . 6 1 2 9 . 0 ° 2 8 . 7 ° 2 6 . 5 ° 32° 31 0 2 6 . 5 ° S t r e s s e s i n K g / c m 2 4" = i>" m e a s u r e d T m T cj) = <j)' c o r r e c t e d f o r v o l u m e c h a n g e CTl v o l u m e d e c r e a s e i n t h e d r a i n e d a c t i v e e x t e n s i o n s h e a r , and a h i g h l y f l o c c u l a t e d m a r i n e c l a y u s e d i n t h i s s t u d y u n d e r -w e n t s w e l l i n g . C o n s i d e r a t i o n s o f t h e d i f f e r e n c e s i n s o i l s t r u c t u r e o f a r e m o l d e d and an u n d i s t u r b e d m a r i n e c l a y w o u l d p r e d i c t l a r g e r s w e l l i n g d u r i n g u n l o a d i n g t y p e s h e a r o f a r e m o l d e d c l a y ( S c o t t , 1 9 6 3 ) . A c o m p a r i s o n o f t h e m e a s u r e d e f f e c t i v e s t r e n g t h p a r a m e t e r , <j>", d u r i n g d r a i n e d and u n d r a i n e d s h e a r i s a l s o p r e s e n t e d i n T a b l e I I f o r b o t h f a i l u r e c o n d i t i o n s -Ia-,-av I v a n d ( ° i / a 3 ) m , v . D u r i n g d r a i n e d s h e a r t h e two z x m a x max f a i l u r e c o n d i t i o n s c o i n c i d e . A t |o -o I , i>" was e s s e n -1 z x 1 max r t i a l l y t h e same ( 2 5 . 9 ° ± 0 . 6 ° ) f o r a l l s t r e s s p a t h s e x c e p t i n g d r a i n e d c o m p r e s s i o n . A t {al/al) t h e m e a s u r e d <j)" i n d r a i n e d c o m p r e s s i o n was a b o u t 1 . 5 ° s m a l l e r t h a n t h e c o r r e s p o n d i n g u n d r a i n e d c o m p r e s s i o n v a l u e , w h e r e a s t h e d r a i n e d and u n d r a i n e d e x t e n s i o n <$>" w e r e e s s e n t i a l l y t h e s a m e . H o w e v e r , a f u n d a m e n t a l c o m p a r i s o n b e t w e e n d r a i n e d and u n d r a i n e d a t (oi/o$)m^v c a n o n l y be made i f d r a i n e d max t e s t s a r e c o r r e c t e d f o r e n e r g y e x p e n d e d i n v o l u m e c h a n g e a t f a i l u r e . T h i s i s p a r t i c u l a r l y e s s e n t i a l f o r t e s t s on Haney c l a y i n w h i c h s i g n i f i c a n t v o l u m e c h a n g e s w e r e t a k i n g p l a c e n e a r d r a i n e d c o m p r e s s i o n f a i l u r e . The c o r r e c t i o n t o m e a s u r e d p e a k d e v i a t o r s t r e s s was a p p l i e d as r e c o m m e n d e d by B i s h o p ( 1 9 5 3 , 1 9 6 4 ) . Thus f o r t h e d r a i n e d t e s t s ( a z _ c V c o r r e c t e d l a z - c V m e a s u r e d + a x ' d e z (5.6) w h e r e d v / d e z i s t h e s l o p e o f v o l u m e t r i c s t r a i n v s . a x i a l s t r a i n p l o t a t |a - a v l . The c o r r e c t e d 4>" i s t h e n c a l -Z A ITlU X c u l a t e d by . r _ ^ 0 z " a x ^ c o r r e c t e d  * c o r r e c t e d " ( ° z . ° x ) c o r r e c t e d + 2 ° x (5.7) In T a b l e I I b o t h m e a s u r e d <(>" and <J>" c o r r e c t e d f o r v o l u m e c h a n g e c o m p o n e n t i n d r a i n e d t e s t a r e s h o w n . I t c a n be s e e n t h a t was p r a c t i c a l l y t h e same f o r a l l c o m p r e s s i o n t e s t s - d r a i n e d o r u n d r a i n e d . T h i s r e s u l t f o r p l a n e s t r a i n t e s t s i s s i m i l a r t o t h e r e s i t on c l a y s f r o m t h e c o n v e n t i o n a 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 t e s t s . S i m i l a r l y i n u n d r a i n e d and d r a i n e d e x t e n s i o n was t h e same ( t h e r e i s no e n e r g y c o m p o n e n t i n d r a i n e d a c t i v e e x t e n s i o n t e s t , s i n c e d v / d e z = 0). B u t a s s o c i a t e d w i t h c o m p r e s s i o n f a i l u r e was on t h e a v e r a g e 5° l a r g e r t h a n (j)' a s s o c i a t e d w i t h e x t e n s i o n f a i l u r e . CHAPTER VI RESULTS OF T R I A X I A L TESTS ON NORMALLY CONSOLIDATED HANEY CLAY In t h i s c h a p t e r t h e r e s u l t s o f t r i a x i a l t e s t s on n o r m a l l y c o n s o l i d a t e d H a n e y c l a y a r e d e s c r i b e d . F o r t h e same t o t a l s t r e s s p a t h t h e t r i a x i a l b e h a v i o u r was f o u n d t o be q u a l i t a t i v e l y v e r y s i m i l a r t o t h e 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 . The r e a s o n s a d v a n c e d f o r a p a r t i c u l a r k i n d o f o b s e r v e d p l a n e s t r a i n b e h a v i o u r , u n d e r a g i v e n t o t a l s t r e s s p a t h , t h e r e f o r e , a p p l y t o t r i a x i a l c o n d i t i o n s a l s o . The t r i a x i a l r e s u l t s a r e d i s c u s s e d o n l y b r i e f l y . D e t a i l s a r e p r e s e n t e d f o r t h o s e t r i a x i a l t e s t s o n l y w h i c h d e v i a t e i n a m a r k e d way f r o m t h e i r p l a n e s t r a i n c o u n t e r p a r t s . 6 . 1 . 0 U n d r a i n e d T e s t R e s u l t s F o r i d e n t i c a l K - c o n s o l i d a t e d s p e c i m e n s t h e o r r e s u l t s o f t e s t s u n d e r t h e f o u r t o t a l s t r e s s p a t h s a r e shown i n F i g . 6 . 1 t h r o u g h F i g . 6 . 6 . The f o l l o w i n g c h a r a c t e r i s t i c s o f t h e r e s u l t s c a n be n o t e d f r o m t h e s e f i g u r e s . 1 . The two c o m p r e s s i o n s t r e s s p a t h s r e s u l t e d i n i d e n t i c a l \az~ax^°zc v s ' E z r e l a t l o n s n i P a n - d s o d i d t h e two e x t e n s i o n s t r e s s p a t h s ( F i g . 6 . 1 ) . H o w e v e r , t h e r e l a t i o n s h i p was d i f f e r e n t f o r c o m p r e s s i o n and e x t e n s i o n s t r e s s p a t h s . C o m p r e s s i o n f a i l u r e ( l a - a I ) o c c u r r e d r . 1 z x 1 m a x ' a t o n l y 0 . 4 % a x i a l s t r a i n c o m p a r e d t o a b o u t 1% a x i a l s t r a i n r e q u i r e d t o i n d u c e . e x t e n s i o n f a i l u r e . 2 . The e x t e n s i o n u n d r a i n e d s t r e n g t h , l a - a L . , . , / 2 , 3 1 z x 1 max was s l i g h t l y l e s s t h a n h a l f o f t h e c o m p r e s s i o n v a l u e ( F i g . 6 . 1 ) . T h i s r e s u l t i s s i m i l a r t o t h o s e r e p o r t e d by L a d d ( 1 9 6 5 , 6 7 ) and B j e r r u m a n d Kenny ( 1 9 6 7 ) . The p e a k d e v i a -t o r s t r e s s i n e x t e n s i o n was e v e n s m a l l e r t h a n t h e v a l u e o f d e v i a t o r s t r e s s t h e s p e c i m e n c o u l d s u s t a i n a t t h e end o f K Q - c o n s o l i d a t i o n . T h e r e was a v e r y l a r g e p o s t p e a k d r o p i n d e v i a t o r s t r e s s d u r i n g c o m p r e s s i o n s h e a r . 3 . The c o n d i t i o n o f ( a i / a 3 ) m a x w a s r e a c h e d a t a b o u t 6% a x i a l s t r a i n d u r i n g a x i a l c o m p r e s s i o n s h e a r ( F i g . 6 . 2 ) . D u r i n g a x i a l e x t e n s i o n s h e a r t h e maximum d e v i a t o r s t r e s s and t h e maximum s t r e s s r a t i o , ( a f / a i " ) „ , o c c u r r e d max a t t h e same s t r a i n . 4 . D u r i n g a c t i v e e x t e n s i o n s t r e s s p a t h , d e s p i t e a v e r y l a r g e u n l o a d i n g o f mean n o r m a l s t r e s s e s , t h e n e t c h a n g e i n p o r e p r e s s u r e a t f a i l u r e was p o s i t i v e ( F i g . 6 . 3 ) . T h i s i s i n d i c a t i v e o f t h e p r o n o u n c e d i n c r e a s e i n c o m p r e s s i b i l i t y 0.6 -8 -6 -4 -2 0 2 4 6 8 AXIAL STRAIN - ez % FIG. 6.1 DEVIATOR S T R E S S - S T R A I N RELATIONSHIP DURING UNDRAINED T R I A X I A L S H E A R - N.C. H A N E Y C L A Y . -8 -6 -4 -2 0 2 4 6 8 AXIAL STRAIN-ez % FIG. 6.2 PRINCIPAL EFFECTIVE STRESS RATIO-STRAIN RELATIONSHIPS DURING UNDRAINED TRIAXIAL SHEAR - N.C. HANEY CLAY. FIG.613 P O R E P R E S S U R E C H A N G E - STRAIN R E L A T I O N S H I P S DURING UNDRAINED TR IAX IAL S H E A R - N.C. H A N E Y C L A Y . o f t h e s e n s i t i v e c l a y s k e l e t o n due t o i m p o s e d s h e a r i n g s t r e s s e s . 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 ' e 1 r e l a t i o n s h i p i s p r a c t i c a l l y i d e n t i c a l f o r s i m i l a r s t r a i n p a t h s ( F i g . 6 . 4 ) . H o w e v e r , t h e r e l a t i o n s h i p s f o r 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 s t r e s s p a t h s h a v e no s i m i l a r i t y w i t h e a c h o t h e r . 5 . E f f e c t i v e s t r e s s p a t h s f o l l o w e d i n a'/a" v s . r z z c a"/a" s t r e s s s p a c e w e r e p r a c t i c a l l y i d e n t i c a l f o r s i m i l a r s t r a i n p a t h s ( F i g . 6 . 5 ) . The a v e r a g e v a l u e o f cj>" a t ( o " j 7 a 3 ) m = v f o r a x i a l c o m p r e s s i o n s h e a r was f o u n d t o be max 2 6 . 6 ° c o m p a r e d t o 21° d u r i n g a x i a l e x t e n s i o n s h e a r . T h i s r e s u l t i s o p p o s i t e t o t h o s e r e p o r t e d by L a d d and B a i l e y ( 1 9 6 4 ) and L a d d ( 1 9 6 7 ) , who r e p o r t e d cj>" v + a n c . n = m n v > o l ? c < n n r r e x t e n s i o n r c o m p r e s s i o n + 8 t o 10° f o r one n a t u r a l and one r e m o l d e d c l a y . In t h e c o n v e n t i o n a l t y p e o f t r i a x i a l a p p a r a t u s , d i s c o u n t i n g o f e v e n a v e r y s m a l l ram f r i c t i o n c a n r e s u l t i n g r o s s o v e r e s t i m a t e s o f t h e r a t i o {a{/az)^ i n e x t e n s i o n t e s t s . F o r t h e a c t i v e e x t e n s i o n t e s t t h e a x i a l s t r e s s i s t h e m i n o r p r i n c i p a l s t r e s s a t f a i l u r e and i t s m a g n i t u d e i s g e n e r a l l y s m a l l , c o n s i d e r i n g t h e u s u a l r a n g e o f p r e s s u r e s f o r l a b o r a t o r y t e s t i n g o f c l a y s . F o r a g i v e n a m o u n t o f e r r o r i n 0 - 3 , t h e r a t i o {oi/az)^ i s a f f e c t e d more s e v e r e l y , p a r t i c u l a r l y when 03 i s r e l a t i v e l y s m a l l . The K 0 - t r i a x i a l a p p a r a t u s u s e d i n t h i s s t u d y was e q u i p p e d w i t h a f r i c t i o n l e s s ram a n d , COMPRESSION A ACTIVE + PASSIVE - 8 - 6 -4 - 2 0 2 4 AXIAL STRAIN - ez % F I G . 6.4 P O R E P R E S S U R E P A R A M E T E R ' a ' - S T R A I N R E L A T I O N S H I P S D U R I N G U N D R A I N E D T R I A X I A L S H E A R - N.C. H A N E Y C L A Y . FIG. 6.5 EFFECTIVE STRESS PATHS DURING UNDRAINED TRIAXIAL SHEAR - N.C. HANEY CLAY. t h e r e f o r e , no e r r o r s s h o u l d a r i s e i n e s t i m a t i n g a x i a l s t r e s s a c t i n g on t h e s p e c i m e n . 6 . 2 . 0 D r a i n e d T e s t R e s u l t s F i g . 6 . 6 and 6 . 7 s h o w , r e s p e c t i v e l y , t h e d e v i a t o r s t r e s s and 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 r e -l a t i o n s h i p s f o r t h e f o u r d r a i n e d t r i a x i a l t e s t s on i n i t i a l l y i d e n t i c a l s p e c i m e n s . In a x i a l c o m p r e s s i o n t h e maximum s t r e n g t h , (a -cr )m, v / 2 , m o b i l i s e d was u n d e r z x m a x t h e p a s s i v e c o m p r e s s i o n s t r e s s p a t h , b e c a u s e t h e s p e c i -men had h i g h e r 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 . B o t h c o m p r e s s i o n s p e c i m e n s , h o w e v e r , a t t a i n e d a p p r o x i m a t e l y t h e same p e a k e f f e c t i v e s t r e s s r a t i o ( ° i / 0 3 ) m a ) ( - S i m -i l a r l y , d r a i n e d p a s s i v e e x t e n s i o n s t r e s s p a t h r e s u l t e d i n l a r g e r p e a k d e v i a t o r s t r e s s due t o l a r g e e f f e c t i v e s t r e s s e s on t h e s p e c i m e n a t f a i l u r e when c o m p a r e d t o s p e c i m e n s u b j e c t e d t o a c t i v e e x t e n s i o n s t r e s s p a t h . The peak e f f e c t i v e s t r e s s r a t i o and h e n c e t h e v a l u e o f c t " a s s o c i a t e d w i t h p a s s i v e e x t e n s i o n , h o w e v e r , was much s m a l l e r t h a n t h e v a l u e o f e f f e c t i v e s t r e s s r a t i o a s s o -c i a t e d w i t h a c t i v e e x t e n s i o n s h e a r , a l t h o u g h p r a c t i c a l l y t h e same s t r a i n was n e e d e d t o m o b i l i s e i t . The r e a s o n f o r t h i s d i s c r e p a n c y i s o b v i o u s f r o m F i g . 6 . 8 , w h i c h shows t h e e x t r e m e l y l a r g e v o l u m e t r i c s t r a i n r a t e s i n t h e s p e c i m e n s u b j e c t e d t o p a s s i v e e x t e n s i o n when c o m p a r e d -16 -12 -8 -4 0 4 8 12 16 20 AXIAL STRAIN - ez % FIG. 6.7 P R I N C I P A L E F F E C T I V E S T R E S S RATIO - STRAIN R E L A T I O N S H I P S DURING D R A I N E D TRIAXIAL S H E A R - N.C. H A N E Y C L A Y . 9 e -s $8 12 & l < Q: f— \ CO „ cor dPRESSION A ACTIVE + PASSIVE EXTEr o © JSION ACTIVE PASSIVE 0 o| -2 -16 -12 -8 -4 0 4 8 • J2 16 20 AXIAL STRAIN - <=z % FIG. 6 .8 AXIAL STRAIN - VOLUMETRIC STRAIN RELATIONSHIPS DURING DRAINED TRIAXIAL SHEAR - N.C. HANEY CLAY. t o t h e s p e c i m e n u n d e r a c t i v e e x t e n s i o n . I t w i l l be shown l a t e r i n t h i s c h a p t e r t h a t ( 0 1 / 0 3 ) 3 „ when c o r -m a x r e c t e d f o r e n e r g y due t o v o l u m e c h a n g e was a l m o s t t h e same i n t h e two e x t e n s i o n t e s t s . A l l s p e c i m e n s u n d e r w e n t v o l u m e d e c r e a s e a t f a i l u r e i r r e s p e c t i v e o f t h e t y p e o f s t r e s s p a t h f o l l o w e d ( F i g . 6 . 8 ) . T h i s i s i n t e r e s t i n g , e s p e c i a l 1 y f o r t h e s p e c i m e n s u b j e c t e d t o a c t i v e e x t e n s i o n s t r e s s p a t h , w h e r e e v e n t h e v e r y l a r g e u n l o a d i n g o f mean n o r m a l s t r e s s r e s u l t e d i n n e t v o l u m e c o m p r e s s i o n u n t i l f a i l u r e . The p e a k e f f e c t i v e s t r e s s r a t i o , ( a I 7 a 3 ) m = v , max d u r i n g a x i a l c o m p r e s s i o n s h e a r c o r r e s p o n d s t o an a v e r a g e m e a s u r e d t t " = 2 5 . 8 ° . D u r i n g a x i a l e x t e n s i o n s h e a r t h e m e a s u r e d = 2 1 . 8 ° and 1 4 . 5 ° r e s p e c t i v e l y f o r t h e a c t i v e and p a s s i v e c o n d i t i o n s . 6 . 3 . 0 C o m p a r i s o n and C o r r e l a t i o n o f D r a i n e d and U n d r a i n e d  T e s t R e s u l t s 6 . 3 . 1 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 R e n d u l i c ' s h y p o t h e s i s o f u n i q u e n e s s o f v o i d r a t i o and e f f e c t i v e s t r e s s was s e e n t o h o l d r e a s o n a b l y w e l l f o r l o a d 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 s h e a r o f ^ - 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 i s shown i n t h e p l o t o f T Q c t / p e v s . p / P e i n F i g . 6 . 9 w h e r e t h e r e s u l t s f r o m a l l FIG. 6.9 COMPRESSION AND E X T E N S I O N S T A T E B O U N D A R Y S U R F A C E S FOR T R I A X I A L T E S T S - N.C. H A N E Y C L A Y . s u c h t e s t s f a l l e s s e n t i a l l y on t h e same c u r v e - t h e R e n d u l i c t r i a x i a l y i e l d s u r f a c e c u r v e . I t , t h e r e f o r e , i m p l i e s t h a t v o l u m e c h a n g e s i n d r a i n e d p a s s i v e c o m p r e s -s i o n K Q - t r i a x i a l t e s t c o u l d be p r e d i c t e d f r o m R e n d u l i c y i e l d s u r f a c e c u r v e d e t e r m i n e d f r o m t h e u n d r a i n e d t e s t on s i m i l a r l y c o n s o l i d a t e d s p e c i m e n s . S u c h a p r e d i c t e d c u r v e o f T o c t / P ' v s - v o l u m e t r i c s t r a i n , v , i s shown i n F i g . 6 . 1 0 a l o n g w i t h t h e o b s e r v e d r e l a t i o n s h i p . A v e r y good a g r e e m e n t i s o b t a i n e d b e t w e e n p r e d i c t i o n s and o b s e r v a t i o n s . F o r t h e t r i a x i a l t e s t r e s u l t s , h o w -e v e r , t h e s h e a r s t r e s s p a r a m e t e r q = ( a r a 3 ) c o u l d be u s e d i n s t e a d o f , T t , as done by R o s c o e ej t . a j_ . ( 1 9 5 8 ) f o r r e p r e s e n t i n g R e n d u l i c ' s u n i q u e n e s s r e l a t i o n s h i p . B u t f o r t h e s a k e o f c o n s i s t e n c y w i t h p r e s e n t a t i o n o f p l a n e s t r a i n r e s u l t s , x ^ has b e e n u s e d h e r e i n . F o r t r i a x i a l s t r e s s c o n d i t i o n , T q c ^ . i s a c o n s t a n t m u l t i p l e o f q . V o l u m e t r i c s t r a i n s p r e d i c t e d f o r d r a i n e d a c t i v e c o m p r e s s i o n s h e a r f r o m u n d r a i n e d y i e l d s u r f a c e a r e shown i n F i g . 6 . 1 1 w h e r e t h e o b s e r v e d T o c t / P v s . v r e l a t i o n -s h i p i s a l s o s h o w n . The p r e d i c t e d s t r a i n s a r e , i n g e n e r a l , s m a l l e r t h a n t h e o b s e r v e d , e x c e p t i n t h e e a r l i e r s t a g e s o f t h e t e s t . .48 .44 .32 0.28 /+ PREDICTE D FROM UND SION TESTS SERVED RAINED COMPRES + OBJ • 0 2 4 6 8 10 VOLUMETRIC STRAIN - v % FIG.6.10 COMPARISON OF O B S E R V E D AND PREDICTED VOLUMETRIC STRAINS DURING TR IAX IAL DRAINED PASSIVE COMPRESSION - N.C. H A N E Y CLAY. FIG. 6.11 COMPARISON OF O B S E R V E D AND PREDICTED VOLUMETRIC STRAINS DURING T R I A X I A L DRAINED ACT IVE COMPRESSION - N.C. H A N E Y C L A Y . The e x i s t e n c e o f a u n i q u e y i e l d s u r f a c e f o r u n d r a i n e d and l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n t e s t s s u g g e s t s , t h a t t h e u n d r a i n e d a n d l o a d i n c r e a s i n g d r a i n e d e x t e n s i o n t e s t may a l s o l i e on a common y i e l d s u r f a c e , w h i c h may be c a l l e d t h e e x t e n s i o n y i e l d s u r f a c e . I f t h i s was t r u e , t h e n v o l u m e c h a n g e s i n d r a i n e d p a s s i v e e x t e n s i o n t e s t c o u l d be p r e d i c t e d f r o m t h e r e s u l t s o f u n -d r a i n e d e x t e n s i o n t e s t s by t h e same t e c h n i q u e as e m p l o y e d f o r c o m p r e s s i o n t e s t s . F i g . 6 . 1 2 shows t h e c o m p a r i s o n b e t w e e n t h e p r e d i c t e d and t h e o b s e r v e d v o l u m e t r i c s t r a i n s . F o r t h e p a r t o f t h e s t r e s s p a t h w h i c h i n v o l v e s d e c r e a s i n g s t r e s s r a t i o , T o c t / P ' P r e d i c t e d s t r a i n s a r e t o o l a r g e . H o w e v e r , f o r t h e p a r t o f t h e s t r e s s p a t h w h i c h i n v o l v e s i n c r e a s i n g s t r e s s r a t i o , i n c r e m e n t s o f p r e d i c t e d v o l u m e t r i c s t r a i n s a r e c l o s e t o t h e o b s e r v e d i n c r e m e n t s . The l i m i t a t i o n s r e g a r d i n g p r e d i c t i o n s o f s h e a r s t r a i n s i n d r a i n e d c o m p r e s s i o n t e s t s f r o m r e s u l t s o f u n -d r a i n e d c o m p r e s s i o n t e s t s a r e t h e same as e x p l a i n e d f o r p l a n e s t r a i n t e s t s . M e t h o d s b a s e d on t h e o r y o f p l a s t i c i t y c a n , a t b e s t , be a p p l i e d u n t i l s t r e s s r a t i o T 0 c ^ / P r e a c h e s a v a l u e c o r r e s p o n d i n g t o t h e c o n d i t i o n o f tQC^ = maximum i n t h e u n d r a i n e d t e s t s . T h i s c o r r e s p o n d s t o s h e a r s t r a i n s i n d r a i n e d t e s t w h i c h , f o r H a n e y c l a y , a r e l e s s t h a n 20% o f t h e f a i l u r e s t r a i n s . C o m p a r i s o n b e t w e e n o b s e r v e d and FIG. 6.12 COMPARISON OF O B S E R V E D AND PREDICTED • VOLUMETRIC S T R A I N S DURING T R I A X I A L DRAINED PASSIVE E X T E N S I O N - N.C. H A N E Y C L A Y . p r e d i c t e d s t r a i n s f o r T o c ^ / P v a l u e s b e l o w t h e l i m i t i n g v a l u e was f o u n d t o be o f t h e same t y p e as d e m o n s t r a t e d f o r p l a n e s t r a i n t e s t s ( s e e F i g . 5 . 1 4 ) . The s t r e s s r a t i o , T o c ^ / P » v s . s h e a r s t r a i n , Y o c t » r e l a t i o n s h i p f o r d r a i n e d a c t i v e e x t e n s i o n t e s t was a l m o s t i d e n t i c a l t o t h e r e l a t i o n s h i p f o r t h e c o r r e s p o n d i n g u n d r a i n e d t e s t ( F i g . 6 . 1 3 ) . T h i s was t o be e x p e c t e d , s i n c e v o l u m e c h a n g e s a s s o c i a t e d w i t h d r a i n e d a c t i v e e x t e n s i o n w e r e v e r y s m a l l , and t h e r e f o r e , t h e s i t u a t i o n was c l o s e t o t h a t o f t h e u n d r a i n e d e x t e n s i o n . A s i m i l a r r e s u l t was p o i n t e d o u t f o r t h e p l a n e s t r a i n c o n d i t i o n s i n F i g . 5 . 1 5 . P r e d i c t i o n o f s h e a r s t r a i n s d u r i n g d r a i n e d p a s s i v e e x t e n s i o n c o u l d n o t be a t t e m p t e d . T h i s was so b e c a u s e , d u r i n g e x t e n s i o n s h e a r no u n i q u e s t r e s s - v o i d r a t i o r e l a t i o n s h i p common t o u n d r a i n e d and l o a d i n c r e a s i n g d r a i n e d t e s t s c o u l d be e s t a b l i s h e d . 6 . 3 . 2 F a i l u r e C o n d i t i o n s The r e s u l t s o f a l l t r i a x i a l t e s t s a r e s u m m a r i z e d i n T a b l e I I I . The p e a k d e v i a t o r s t r e s s i n e a c h d r a i n e d t e s t was f o u n d t o be l a r g e r t h a n t h e peak d e v i a t o r s t r e s s i n t h e c o r r e s p o n d i n g u n d r a i n e d t e s t . The r e a s o n f o r . t h i s was t h e n e t v o l u m e c o m p r e s s i o n e x p e r i e n c e d by a l l t h e s p e c i m e n s u n t i l f a i l u r e . T h i s seems t o be an u n u s u a l 0.4 P j . + - U N D R A I N E D i -A C T I V E E X T E : N S I O N 1 / H h D R A I N E D A 3 T 1 V E E X T E N S I O N I +/ +\ / —iiZ 0 2 4 6 8 10 >^ct % FIG. 6.13 COMPARISON OF S H E A R S T R E S S - STRAIN RELAT IONSHIP DURING T R I A X I A L DRAINED AND UNDRAINED E X T E N S I O N - N . C . H A N E Y C L A Y . End o f C o n s o l i d a t i o n F a i l u r e C o n d i t i o n (a i - a 3 ^max ( a 1 / 0 - 3 ) U n d r a i n e d T e s t s °z'c K 0 A x i a l S t r a i n % a 1 -a 3 0 -z c a v% 0 1 / 0 - 3 < r A x i a l S t r a i n % o r / 0 3 Y m Y c P a s s i v e c o m p r e s s i o n 5 . 8 4 . 5 6 . 4 . 5 2 8 1 . 3 9 0 2 . 1 1 2 0 . 9 ° 8 . 0 2 . 6 0 2 6 . 4 ° 2 6 . 4 ° A c t i v e c o m p r e s s i o n 5 . 9 1 . 5 5 . 4 5 . 5 3 4 1 . 50 0 2 . 1 4 21 . 2 ° 6 . 0 2 . 6 5 2 6 . 8 ° 2 6 . 8 ° A c t i v e e x t e n s i o n 5 . 9 1 . 5 6 - 7 . 7 . 2 7 2 . 8 9 0 2 . 2 3 2 2 . 4 ° - 7 . 7 2 . 2 3 2 2 . 4 ° 2 2 . 4 ° P a s s i v e e x t e n s i o n 5 . 9 2 . 5 5 - 5 . 8 . 2 5 . 8 5 0 1 . 9 9 1 9 . 4 ° - 5 . 8 1 . 9 9 1 9 . 4 ° 1 9 . 4 ° D r a i n e d T e s t s P a s s i v e c o m p r e s s i o n 5 . 9 6 . 5 6 1 6 . 0 . 8 3 4 — 6 . 8 2 . 5 4 2 5 . 8 ° 1 6 . 0 2 . 5 4 2 5 . 8 ° 2 7 . 2 ° A c t i v e c o m p r e s s i o n 5 . 9 7 . 5 5 7 . 0 . 5 5 5 — 1 . 8 2 . 5 4 2 5 . 8 ° 7 . 0 2 . 5 4 2 5 . 8 ° 2 7 . 8 ° A c t i v e e x t e n s i o n 5 . 9 4 . 5 6 - 9 . 0 . 3 0 6 — 0 . 7 2 . 1 8 21 . 8 ° - 9 . 0 2 . 2 5 21 . 8 ° 21 . 8 ° P a s s i v e e x t e n s i o n 5 . 9 1 . 5 5 - 9 . 2 . 8 0 8 — 9 . 8 1 . 6 9 1 4 . 5 ° - 9 . 2 1 . 6 9 1 4 . 5 ° 2 0 . 0 ° S t r e s s i n K g / c m 2 ^m = ^ ' m e a s u r e d cf)" c o r r e c t e d f o r v o l u m e c h a n g e ro o r e s u l t when l o o k e d i n t h e l i g h t o f e x i s t i n g d a t a on r e m o l d e d c l a y s ( B i s h o p & H e n k e l , 1 9 6 2 ) . B u t c o n s i d e r i n g t h e s e n s i t i v e n a t u r e o f t h e c l a y u s e d i n t h i s s t u d y , t h i s b e h a v i o u r c a n be r e g a r d e d as t h e r e s u l t o f i n c r e a s e d c o m p r e s s i b i l i t y due t o i m p o s e d s h e a r s t r e s s e s . T h i s i n d u c e s t e n d e n c y t o v o l u m e d e c r e a s e more t h a n t h e t e n -d e n c y t o v o l u m e i n c r e a s e d u r i n g s t r e s s p a t h s a s s o c i a t e d w i t h u n l o a d i n g o f mean n o r m a l s t r e s s e s . E f f e c t i v e s t r e n g t h p a r a m e t e r tt" i s shown t a b u l a t e d f o r a l l t h e t r i a x i a l t e s t s i n T a b l e I I I . F o r d r a i n e d t e s t s , b o t h t h e m e a s u r e d tt" v a l u e and t h e cf>" v a l u e c o r r e c t e d f o r v o l u m e t r i c s t r a i n r a t e s a t f a i l u r e ( a s e x p l a i n e d i n C h a p t e r V) a r e s h o w n . A t maximum d e v i a t o r s t r e s s f a i l u r e c o n d i t i o n , tj>" was e s s e n t i a l l y same ( 2 1 ° ± 1 . 5 ° ) f o r a l l s t r e s s p a t h s e x c e p t d r a i n e d c o m p r e s s i o n and d r a i n e d p a s s i v e e x t e n s i o n . A t { o { / a z ) m . t h e m e a s u r e d ct" i n max d r a i n e d c o m p r e s s i o n was a b o u t 0 . 6 ° s m a l l e r t h a n t h e c o r r e s p o n d i n g u n d r a i n e d c o m p r e s s i o n v a l u e ; w h e r e a s p a s s i v e e x t e n s i o n d r a i n e d <j>" was as much as 5° t o 6° s m a l l e r t h a n t h e c o r r e s p o n d i n g u n d r a i n e d and d r a i n e d a c t i v e e x t e n s i o n v a l u e s . H o w e v e r , when d r a i n e d <)>" was c o r r e c t e d f o r v o l u -m e t r i c s t r a i n r a t e s , e s s e n t i a l l y t h e same tt" was f o u n d f o r d r a i n e d and u n d r a i n e d c o m p r e s s i o n f a i l u r e . S i m i l a r l y , c o r r e c t e d d r a i n e d tt" and u n d r a i n e d tt" d u r i n g e x t e n s i o n f a i l u r e was f o u n d t o be e s s e n t i a l l y t h e s a m e . B u t d u r i n g c o m p r e s s i o n f a i l u r e was on t h e a v e r a g e 5° l a r g e r t h a n (j)"* d u r i n g e x t e n s i o n f a i l u r e . CHAPTER V I I COMPARISON OF PLANE STRAIN AND T R I A X I A L RESULTS N. C . HANEY CLAY In t h i s c h a p t e r t h e s t r e s s - s t r a i n and t h e s t r e n g t h b e h a v i o u r o f n o r m a l l y c o n s o l i d a t e d Haney c l a y i s c o m p a r e d a n d c o r r e l a t e d f o r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . The e n d o f ^ - c o n s o l i d a t i o n was i d e n t i c a l f o r a l l s a m p l e s . C o n v e n t i o n a l c o m p a r i s o n o f t h e s t r e s s - s t r a i n b e h a v i o u r and o f e f f e c t i v e s t r e n g t h p a r a m e t e r , <j>", i s c o n s i d e r e d f i r s t . T h i s i s done t o p o i n t o u t t h e e s s e n t i a l d i f f e r e n c e s b e t w e e n t h e t r i a x i a l and p l a n e s t r a i n r e s p o n s e , and t h e p o s s i b l e e r r o r s i n v o l v e d w h i l e s o l v i n g a p l a n e s t r a i n p r o b l e m u s i n g t r i a x i a l t e s t r e s u l t s . In l a t e r s e c t i o n s a t t e m p t s a r e made t o c o r r e l a t e t r i a x i a l and p l a n e s t r a i n b e h a v i o u r , i . e . , t o p r e d i c t p l a n e s t r a i n b e h a v i o u r f r o m t r i -a x i a l t e s t r e s u l t s . Two a p p r o a c h e s a r e e x a m i n e d f o r c o r -r e l a t i n g s t r e s s s t r a i n b e h a v i o u r . The f i r s t i s an e m p i r i c a l a p p r o a c h , w h i c h f o l l o w s a l o n g t h e l i n e s o f s u g g e s t i o n s made by Newmark ( 1 9 6 0 ) and R e n d u l i c ( 1 9 3 7 ) . The s e c o n d i s r e l a t e d t o c o n c e p t s p r o p o s e d by R o s c o e and B u r l a n d ( 1 9 6 8 ) , whose ' r e v i s e d ' and ' m o d i f i e d ' C a m b r i d g e s t r e s s - s t r a i n t h e o r i e s e n a b l e p r e d i c t i o n o f d r a i n e d p l a n e s t r a i n b e h a v i o u r f r o m s o i l p a r a m e t e r s d e t e r m i n e d f r o m 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 t e s t s . L a s t l y , t h e v a r i o u s f a i l u r e t h e o r i e s 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 a r e e x a m i n e d t o c o r r e l a t e t r i a x i a l and p l a n e s t r a i n s t r e n g t h b e h a v i o u r . 7 . 1 . 0 C o n v e n t i o n a l C o m p a r i s o n T h i s c o n s i s t s o f c o m p a r i n g t h e t r i a x i a l a n d p l a n e s t r a i n b e h a v i o u r i n t e r m s o f s t r e s s p a r a m e t e r s w h i c h a r e f u n c t i o n s o f t h e m a j o r and 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 o n l y . C o m p a r i s o n s i n c l u d i n g 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 w i l l be c o n s i d e r e d i n l a t e r s e c t i o n s . The s t r a i n p a r a m e t e r s u s e d i n c o n v e n t i o n a l c o m p a r i s o n a r e t h e a x i a l s t r a i n , e z , a s s o c i a t e d w i t h a x i a l s t r e s s , a , and v o l u m e t r i c s t r a i n , v . 7 . 1 . 1 U n d r a i n e d T e s t s I t has p r e v i o u s l y b e e n shown ( C h a p t e r s V and V I ) t h a t t h e u n d r a i n e d b e h a v i o u r o f H a n e y c l a y was 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 , p r o v i d e d c o m p r e s s i o n and e x t e n s i o n modes o f s h e a r w e r e c o n s i d e r e d s e p a r a t e l y . F o r e x a m p l e , t h e b e h a v i o u r o f d e c r e a s i n g l a t e r a l s t r e s s t e s t s ( a c t i v e c o m p r e s s i o n ) was t h e same as i n c r e a s i n g a x i a l s t r e s s t e s t s ( p a s s i v e c o m p r e s s i o n ) . T h u s , i n c o m p a r i s o n o f t r i a x i a l and p l a n e s t r a i n r e s u l t s no d i s t i n c t i o n w i l l be made b e t w e e n a c t i v e and p a s s i v e c o m p r e s s i o n , o r a c t i v e and p a s s i v e e x t e n -s i o n , and t h e y w i l l be s i m p l y t e r m e d u n d r a i n e d c o m p r e s s i o n and u n d r a i n e d e x t e n s i o n r e s p e c t i v e l y . F i g u r e 7 . 1 shows t h e n o r m a l i s e d d e v i a t o r s t r e s s , jcr -aA/o'l , v s . a x i a l s t r a i n , e , r e l a t i o n s h i p s d u r i n g Z X Z C Z u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . The s i m i l a r i t y o f t h e t r i a x i a l and p l a n e s t r a i n r e s u l t s f o r b o t h c o m p r e s s i o n and e x t e n -s i o n may be n o t e d . I t i s i n t e r e s t i n g t h a t u n d r a i n e d c o m -p r e s s i o n f a i l u r e , ( l a -a l m ) , t o o k p l a c e a t a r e l a t i v e l y Z X vii a X s m a l l v a l u e o f a x i a l s t r a i n , o r a b o u t 1 / 2 % , and was t h e same f o r b o t h p l a n e s t r a i n and t r i a x i a l c o n d i t i o n s . T h i s s m a l l s t r a i n a t f a i l u r e i s d i f f e r e n t f r o m t h a t r e p o r t e d by H e n k e l and Wade ( 1 9 6 6 ) f o r a r e m o l d e d c l a y , i n i t i a l l y K o - c o n s o l i d a t e d . They r e p o r t e d 2% a x i a l s t r a i n 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 c o m p r e s s i o n and 6% a x i a l s t r a i n t o f a i l u r e u n d e r t r i a x i a l c o m p r e s s i o n . In c o n t r a s t t o t h e c o m p r e s s i o n b e h a v i o u r , t h e e x t e n s i o n d e v i a t o r s t r e s s - s t r a i n r e l a t i o n s h i p was p l a s t i c i n c h a r a c t e r f o r b o t h t r i a x i a l a n d p l a n e s t r a i n c o n d i t i o n s . A g a i n 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 t h e l a r g e a x i a l s t r a i n f o r e x t e n s i o n f a i l u r e , a b o u t 7 % , was t h e same f o r b o t h t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . I t i s , t h e r e f o r e , c o n c l u d e d t h a t f o r u n d i s t u r b e d Haney c l a y , p l a n e FIG.7.1 COMPARISON OF DEVIATOR 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 UNDER UNDRAINED TRIAXIAL AND P L A N E STRAIN S H E A R - N.C. H A N E Y C L A Y . s t r a i n c o n d i t i o n s do n o t r e s u l t i n f a i l u r e s t r a i n s w h i c h a r e d i f f e r e n t f r o m t h o s e 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 u / a ^ c , t h e r a t i o o f u n d r a i n e d s t r e n g t h , |c - a I „ „ / 2 , t o t h e m a j o r p r i n c i p a l c o n s o l i d a t i o n s t r e s s , 1 z x ' m a x r r a z c ' d u r i n g u n d r a i n e d c o m p r e s s i o n was 0 . 2 9 3 f o r p l a n e s t r a i n and 0 . 2 6 5 f o r t r i a x i a l c o n d i t i o n s . T h u s , t h e p l a n e s t r a i n u n d r a i n e d s t r e n g t h was a b o u t 11% h i g h e r t h a n t h e t r i a x i a l v a l u e . S i m i l a r d i f f e r e n c e s b e t w e e n p l a n e s t r a i n and t r i a x i a l c o m p r e s s i o n s t r e n g t h w e r e r e p o r t e d by H e n k e l and Wade ( 1 9 6 6 ) f o r a r e m o l d e d c l a y , and by L a d d ( 1 9 6 7 ) f o r B o s t o n B l u e c l a y . T h e r e was a s i g n i f i c a n t l o s s i n s t r e n g t h o n c e t h e peak was p a s s e d f o r b o t h t r i a x i a l and p l a n e s t r a i n c o m p r e s s i o n s h e a r . A t an a x i a l s t r a i n o f 5% t h e d e v i a t o r s t r e s s had f a l l e n b e l o w t h e v a l u e a t t h e end o f c o n s o l i d a t i o n f o r b o t h t y p e s o f t e s t a n d , t h e d e v i a t o r s t r e s s - s t r a i n c u r v e s m e r g e d t o g e t h e r t h e r e a f t e r . I t t h e r e f o r e a p p e a r s t h a t p o s t peak s t r e n g t h b e h a v i o u r o f t h e c l a y t e s t e d a t r e l a t i v e l y l a r g e s t r a i n s i s t h e same u n d e r b o t h t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . C o m p r e s s i o n t e s t s , w h i c h w e r e c a r r i e d t o s t r a i n s up t o 1 5 % , p o s s e s s e d i d e n t i c a l d e v i a t o r 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 t r i a x i a l and p l a n e s t r a i n o n c e t h e a x i a l s t r a i n e x c e e d e d 5 % . C / a , " r a t i o d u r i n g p l a n e s t r a i n e x t e n s i o n was u 1 c » f f o u n d t o be 0.197 c o m p a r e d t o t h e t r i a x i a l v a l u e o f 0 .13 . T h u s , u n d r a i n e d s t r e n g t h i n p l a n e s t r a i n e x t e n s i o n was as much as 50% h i g h e r t h a n t h e t r i a x i a l v a l u e . S i m i l a r r e s u l t s w e r e q u o t e d by L a d d (1967) f o r B o s t o n B l u e c l a y , w h i c h had 67% h i g h e r u n d r a i n e d e x t e n s i o n s t r e n g t h i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . The r a t e a t w h i c h f r i c t i o n was m o b i l i z e d , as i r e p r e s e n t e d by t h e r a t i o o f t h e m a j o r t o 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 , was h i g h e r i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s , f o r b o t h c o m p r e s s i o n and e x t e n s i o n modes o f s h e a r ( F i g . 7 . 2 ) . D u r i n g b o t h t r i a x i a l and p l a n e s t r a i n c o m p r e s s i o n , p o r e p r e s s u r e s w e r e s t i l l i n c r e a s i n g when t h e maximum d e v i a t o r s t r e s s c o n d i t i o n o c c u r r e d a n d , i n c o n s e q u e n c e , t h e peak v a l u e s o f t h e e f f e c t i v e s t r e s s r a t i o , ( a r / o 3 ) m = v > was r e a c h e d a t l a r g e r s t r a i n s . How-ma x e v e r , i n p l a n e s t r a i n t h e p e a k s t r e s s r a t i o o c c u r r e d a t 3% a x i a l s t r a i n and s h o w e d a m a r k e d d r o p t h e r e a f t e r , w h e r e a s u n d e r t r i a x i a l c o n d i t o n 6% a x i a l s t r a i n was r e q u i r e d u n t i l (a r/o 3 ) m = 1 v , w h i c h s t a y e d e s s e n t i a l l y c o n s t a n t w i t h m a X f u r t h e r s t r a i n . D u r i n g e x t e n s i o n s h e a r t h e p e a k d e v i a t o r s t r e s s and p e a k e f f e c t i v e s t r e s s r a t i o w e r e r e a c h e d a t . t h e same s t r a i n o f a b o u t 7% f o r b o t h t r i a x i a l a n d p l a n e s t r a i n c o n d i t i o n s . FIG. 7.2 COMPARISON OF E F F E C T I V E S T R E S S R A T I O - S T R A I N R E L A T I O N S H I P S DURING UNDRAINED T R I A X I A L AND P L A N E STRAIN S H E A R - N.C. H A N E Y C L A Y . The u n d r a i n e d p l a n e s t r a i n and 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 e f f e c t i v e s t r e s s p a t h s i n a ' / a " , X z c a " z / a z c s t r e s s s p a c e a r e shown i n F i g . 7 . 3 . The r e m a r k a b l e s i m i l a r i t y o f t h e t r i a x i a l and p l a n e s t r a i n c o m p r e s s i o n and a l s o t h e e x t e n s i o n p a t h s may be n o t e d . As was shown i n F i g . 7 . 1 t h e maximum v a l u e o f d e v i a t o r s t r e s s i n c o m -p r e s s i o n o c c u r r e d a t a b o u t 0 . 5 % a x i a l s t r a i n f o r b o t h t r i -a x i a l and p l a n e s t r a i n c o n d i t i o n b u t , i t c a n be s e e n i n F i g . 7 . 3 , t h i s p o i n t was r e a c h e d b e f o r e t h e s t r e s s p a t h s become t a n g e n t i a l t o t h e f a i l u r e e n v e l o p e s . The p o i n t o f t a n g e n c y c o r r e s p o n d s t o a b o u t 3% a x i a l s t r a i n f o r p l a n e s t r a i n and 6% a x i a l s t r a i n f o r t r i a x i a l c o n d i t i o n s . The v a l u e o f ( J ) ' c o r r e s p o n d i n g t o t h e e f f e c t i v e s t r e s s f a i l u r e e n v e l o p e s ( a f / a i * = v ) a r e 3 0 . 4 ° i n p l a n e s t r a i n and 2 6 . 6 ° max u n d e r t r i a x i a l c o n d i t i o n s . T h i s i s c o n s i s t e n t w i t h r e s u l t s on r e m o l d e d c l a y r e p o r t e d by H e n k e l and Wade ( 1 9 6 6 ) and a l s o by S h i b a t a and K a r u b e (1 9 6 7 ) , who s h o w e d c o m p r e s s i o n <{>' i n p l a n e s t r a i n t o be 1 . 2 ° and 5° l a r g e r r e s p e c t i v e l y . I t i s i n t e Y e s t i n g t o n o t e h e r e t h a t t h e v a l u e s o f <J>" a t maximum d e v i a t o r s t r e s s w e r e a b o u t 5° l o w e r t h a n t h o s e a t p e a k e f f e c t i v e s t r e s s r a t i o f o r b o t h p l a n e s t r a i n a n d t r i -a x i a l t e s t s . The e x t e n s i o n s t r e s s p a t h s become t a n g e n t t o t h e e f f e c t i v e s t r e s s f a i l u r e e n v e l o p e s a t t h e same s t r a i n 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 . The F I G . 73 C O M P A R I S O N O F E F F E C T I V E 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 A N D P L A N E S T R A I N S H E A R - N . C . H A N E Y C L A Y . v a l u e s o f <j>' d u r i n g e x t e n s i o n f a i l u r e a r e 2 6 . 1 ° f o r p l a n e s t r a i n a n d 21° f o r t r i a x i a l c o n d i t i o n s . F o r B o s t o n B l u e c l a y , L a d d ( 1 9 6 7 ) r e p o r t e d p l a n e s t r a i n e x t e n s i o n cf>' t o be 42° c o m p a r e d t o 38° u n d e r t r i a x i a l c o n d i t i o n s . I t i s , t h e r e f o r e , c o n c l u d e d t h a t a t ( 0 1 / 0 3 ) i s l a r g e r i n max 3 p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s by a b o u t 4° t o 5° i n u n d i s t u r b e d H a n e y c l a y ; t h e c o n c l u s i o n a p p l i e s t o b o t h c o m p r e s s i o n and e x t e n s i o n modes o f s h e a r . A summary o f u n d r a i n e d f a i l u r e c h a r a c t e r i s t i c s u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s i s p r e s e n t e d i n T a b l e I V . B o t h , maximum d e v i a t o r s t r e s s and maximum s t r e s s r a t i o f a i l u r e c o n d i t i o n s a r e c o n s i d e r e d f o r c o m -p a r i s o n o f t r i a x i a l and p l a n e s t r a i n b e h a v i o u r . The s h e a r s t r e n g t h , C u , o f any p a r t i c u l a r u n d r a i n e d s p e c i m e n d e p e n d s on t h e e f f e c t i v e s t r e s s e s a c t i n g a t t h e t i m e o f f a i l u r e and on t h e s h e a r s t r e n g t h p a r a m e t e r s . S i n c e t h e e f f e c t i v e s t r e s s e s u s e d d u r i n g c o n s o l i d a t i o n p r o c e s s w e r e i d e n t i c a l , t h e s t r e n g t h d i f f e r e n c e b e t w e e n t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s m u s t be e x p l a i n e d i n t h e p o r e p r e s s u r e c h a n g e s a f t e r c o n s o l i d a t i o n , and i n t h e s h e a r s t r e n g t h p a r a m e t e r s , <j>'. D u r i n g c o m p r e s s i o n s h e a r u n d e r i d e n t i c a l s t r e s s p a t h s , t h e c h a n g e i n p o r e p r e s s u r e a t f a i l u r e was a l m o s t t h e same u n d e r b o t h t r i a x i a l a n d p l a n e s t r a i n c o n d i t i o n s a n d , t h e r e f o r e , h i g h e r s t r e n g t h C o m p a r i s o n o f F a i l u r e u n d e r U n d r a i n e d T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s Fa i 1 u r e C o n d i t i o n ( a i - a a ) v 1 3 ' m a x (o ^ ^ m a x A x i a l S t r a i n % V ° l c o-r/0-3 A x i a l S t r a i n % o r / a s U n d r a i n e d C o m p r e s s i o n P l a n e s t r a i n 0 . 5 0 . 2 9 3 2 . 5 0 2 5 . 4 ° 3 3 . 0 5 3 0 . 4 ° T r i a x i a l 0 . 4 5 0 . 2 6 5 2 . 1 2 21 . 0 ° 6 2 . 6 2 2 6 . 6 ° U n d r a i n e d E x t e n s i o n P l a n e s t r a i n - 7 . 1 0 . 1 9 7 2 . 5 7 2 6 . 1 ° - 7 . 1 2 . 5 7 2 6 . 1 ° T r i a x i a l - 7 . 5 0 . 1 3 2 . 1 21 . 0 ° - 7 . 5 2 . 1 2 1 . 0 ° C u = ^ - ^ ) m a x / 2 a," = m a j o r c o n s o l i d a t i o n s t r e s s 0 0 C O i n p l a n e s t r a i n was a s s o c i a t e d w i t h l a r g e r i n p l a n e s t r a i n . D u r i n g e x t e n s i o n s h e a r u n d e r i d e n t i c a l s t r e s s p a t h s , t h e c h a n g e i n p o r e p r e s s u r e a t f a i l u r e was s m a l l e r i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n a n d , t h e r e -f o r e , h i g h e r s t r e n g t h i n p l a n e s t r a i n was a s s o c i a t e d w i t h n o t o n l y l a r g e r <)>' b u t a l s o s m a l l e r p o r e p r e s s u r e s i n p l a n e s t r a i n . • 7 . 1 . 2 D r a i n e d T e s t s D u r i n g d r a i n e d s h e a r t h e t o t a l s t r e s s p a t h i s t h e same as t h e e f f e c t i v e s t r e s s p a t h . A c t i v e a n d p a s s i v e s h e a r modes g i v e r i s e t o d i f f e r e n t e f f e c t i v e s t r e s s p a t h s , and s i n c e s o i l r e p o n s e i s a f u n c t i o n o f e f f e c t i v e s t r e s s e s , d r a i n e d a c t i v e and p a s s i v e b e h a v i o u r i s n o t i d e n t i c a l . C o m p a r i s o n b e t w e e n t r i a x i a l and p l a n e s t r a i n b e h a v i o u r i s p r e s e n t e d f o r i d e n t i c a l s t r e s s p a t h s t o f a i l u r e . A p a s s i v e 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 o u l d n o t be p e r f o r m e d a n d , t h e r e f o r e , no c o m p a r i -s o n w i t h t r i a x i a l r e s u l t s c a n be m a d e . F i g . 7 . 4 shows d e v i a t o r 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 d u r i n g d r a i n e d p l a n e s t r a i n and 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 . P l a n e s t r a i n c u r v e s , f o r a l l t h e . t e s t s , l i e a b o v e t h e c o r r e s p o n d i n g c u r v e s f o r t r i a x i a l c o n d i t i o n s . T h u s , t h e p l a n e s t r a i n t e s t a l w a y s g i v e s TRIAXI PLANE 6 AL STRAIN 5 / / / / / / CM • E o \ C P 1 / / /-x—x——y 1 X . * K * \ ^ - ^ b ° 1 • PASS x-*-x ACTI — 2 \ N A i \\ , j c OMPRESSION VE VE E IXTENSION v 11 \ -10 - 8 - 4 0 4 8 12 16 AXIAL STRAIN - ez % FIG. 7.4 C O M P A R I S O N O F D E V I A T O R 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 D U R I N G D R A I N E D T R I A X I A L A N D P L A N E S T R A I N S H E A R -N.C. H A N E Y C L A Y . a h i g h e r s t r e n g t h t h a n t h e c o r r e s p o n d i n g t r i a x i a l t e s t . D r a i n e d f a i l u r e i n p a s s i v e c o m p r e s s i o n was r e a c h e d a t 12% a x i a l s t r a i n i n p l a n e s t r a i n c o m p a r e d t o 16% a x i a l s t r a i n u n d e r t r i a x i a l c o n d i t i o n s . P l a n e s t r a i n r e l a t i o n s h i p s h o w e d a c h a r a c t e r i s t i c p e a k , w h e r e a s t h e t r i a x i a l r e l a -t i o n s h i p d i d n o t . D r a i n e d f a i l u r e i n a c t i v e c o m p r e s s i o n o c c u r r e d a t s m a l l e r a x i a l s t r a i n s - 4 . 5 % i n p l a n e s t r a i n and a b o u t 7% u n d e r t r i a x i a l c o n d i t i o n s . A g a i n , t h e p o s t peak l o s s i n s t r e n g t h was more m a r k e d f o r p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . D u r i n g d r a i n e d a c t i v e e x t e n s i o n , f a i l u r e was r e a c h e d a t 7% a x i a l s t r a i n f o r p l a n e s t r a i n and a b o u t 9% a x i a l s t r a i n f o r t r i a x i a l c o n d i t i o n s . I t i s , t h e r e f o r e , c o n c l u d e d t h a t f o r a g i v e n s t r e s s p a t h t h e a x i a l s t r a i n s t o d r a i n e d f a i l u r e i n p l a n e s t r a i n was a l w a y s s o m e w h a t l e s s t h a n t h o s e f o r t r i a x i a l , b u t t h e g e n e r a l b e h a v i o u r was n o t v e r y d i f f e r e n t . The c h a n g e i n p o r e p r e s s u r e d u r i n g d r a i n e d s h e a r i s z e r o . T h e r e f o r e , t h e d e v i a t o r s t r e s s m o b i l i z e d a t any s t r a i n u n d e r a g i v e n s t r e s s p a t h d e p e n d s o n l y on t h e m o b i l i z e d f r i c t i o n ( a s r e f l e c t e d 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 r a t i o ) . The s t r e s s r a t i o - s t r a i n r e l a t i o n s h i p s a r e shown i n F i g . 7 . 5 . F o r a l l t h e s t r e s s p a t h s s t u d i e d , t h e p l a n e s t r a i n t e s t a l w a y s had h i g h e r s t r e s s r a t i o s a t a g i v e n s t r a i n t h a n t h e c o r r e s p o n d i n g t r i a x i a l t e s t . The FIG. 7.5 C O M P A R I S O N OF E F F E C T I V E S T R E S S R A T I O - STRAIN R E L A T I O N S H I P S DURING DRAINED T R I A X I A L AND P L A N E STRAIN S H E A R - N.C. H A N E Y C L A Y . p r e c e d i n g c o n c l u s i o n s r e g a r d i n g r e l a t i v e s t r a i n s t o p e a k d e v i a t o r s t r e s s d u r i n g d r a i n e d p l a n e s t r a i n a n d t r i a x i a l s h e a r , u n d e r a n y g i v e n s t r e s s p a t h , a p p l y t o t h e o c c u r r e n c e o f p e a k s t r e s s r a t i o s as w e l l . C o m p a r i s o n o f v o l u m e t r i c s t r a i n s , v , u n d e r t r i -a x i a l and 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 l l t h e s t r e s s p a t h s s t u d i e d , i s p r e s e n t e d i n F i g . 7 . 6 . D u r i n g a c t i v e and p a s s i v e c o m p r e s s i o n , v o l u m e t r i c s t r a i n - a x i a l s t r a i n r e l a t i o n s h i p s a r e e s s e n t i a l l y i d e n t i c a l u n t i l f a i l u r e . T h i s i m p l i e s i d e n t i c a l r a t e s o f v o l u m e t r i c s t r a i n d u r i n g 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 u n d e r t h e same a p p l i e d s t r e s s p a t h . H o w e v e r , d u r i n g d r a i n e d a c t i v e e x t e n -s i o n s h e a r , t h e p l a n e s t r a i n s p e c i m e n s h o w e d s w e l l i n g u n t i l f a i l u r e , w h e r e a s t h e t r i a x i a l s p e c i m e n s h o w e d a n e t c o m p r e s s i o n a t f a i l u r e a f t e r s l i g h t s w e l l i n g i n t h e i n i t i a l s t a g e s . F o r a g i v e n t y p e o f t e s t t h e r e i s no d i f f e r e n c e b e t w e e n v a l u e s o f f o r t h e a c t i v e o r t h e p a s s i v e c a s e . T h i s was t h e b e h a v i o u r o b s e r v e d i n u n d r a i n e d t e s t s . A l s o t h e <j)'* v a l u e s i n d r a i n e d t e s t s a r e n o t t o o d i f f e r e n t t o t h o s e i n u n d r a i n e d t e s t s f o r (crf/ai*) c o n d i t i o n o f f a i l u r e max u n d e r s i m i l a r s t r a i n p a t h s . A summary o f d r a i n e d f a i l u r e c h a r a c t e r i s t i c s u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s i s g i v e n i n T a b l e V . f o r d r a i n e d c o m p r e s s i o n i n p l a n e •10 - 8 - 4 0 16 AXIAL STRAIN - e z % FIG.7.6 V O L U M E T R I C S T R A I N - A X I A L STRAIN R E L A T I O N S H I P S DURING DRAINED 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 - N.C. H A N E Y C L A Y . End o f C o n s o l i d a t i o n F a i l u r e C o n d i t i o n ( a i " a 3 ) m a x o r ( a r / a ^ m a x °zc K 0 A x i a l S t r a i n % v % a'z o i - a 3 P a s s i v e C o m p r e s s i o n P l a n e s t r a i n T r i a x i a l 5 . 9 6 5 . 9 6 3 . 2 3 3 . 3 3 0 . 5 4 0 . 5 6 12 16 6 . 0 6 . 8 8 . 6 7 8 . 2 1 3 . 0 1 3 . 2 4 5 . 6 6 4 . 9 7 2 . 8 8 2 . 5 4 29° 25 . 8 ° A c t i v e C o m p r e s s i o n P l a n e s t r a i n T r i a x i a l 5 . 9 8 5 . 9 7 3 . 3 6 3 . 2 8 0 . 5 6 0 . 5 5 4 . 5 7 0 . 9 1 . 8 5 . 5 5 5 . 4 6 1 . 9 5 2 . 1 5 3 . 6 0 3 . 3 1 2 . 8 5 2 . 5 4 2 8 . 7 ° 2 5 . 8 ° A c t i v e E x t e n s i o n P l a n e s t r a i n T r i a x i a l 5 . 8 7 5 . 9 4 3 . 2 4 3 . 3 0 0 . 5 5 0 . 5 6 - 7 - 9 - 0 . 8 0 . 7 1 . 2 5 1 . 4 9 3 . 2 5 3 . 2 5 2 . 0 0 1 . 7 6 2 . 6 1 2 . 1 8 2 6 . 5 ° 21 . 8 ° S t r e s s e s i n K g / c m 2 s t r a i n was 3° h i g h e r t h a n t h a t u n d e r t r i a x i a l c o n d i t i o n s . T h i s r e s u l t i s d i f f e r e n t f r o m t h a t o f H a m b l y and R o s c o e ( 1 9 6 9 ) , who r e p o r t e d t h e same <j>" f o r t r i a x i a l a n d p l a n e s t r a i n d r a i n e d c o m p r e s s i o n o f a r e m o l d e d c l a y . i n d r a i n e d e x t e n s i o n was 5° h i g h e r i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . T h u s , f o r c o m p r e s s i o n i n p l a n e s t r a i n was 3 t o 4° - h i g h e r t h a n t h a t f o r t r i a x i a l , and f o r e x t e n s i o n was 5° h i g h e r i n p l a n e s t r a i n , r e g a r d l e s s o f d r a i n e d o r u n d r a i n e d , p e a k d e v i a t o r s t r e s s o r p e a k C\fa1 f a i l u r e c o n d i t i o n s . The d r a i n e d s t r e n g t h o f any p a r t i c u l a r s p e c i m e n d e p e n d s on t h e e f f e c t i v e s t r e s s e s a c t i n g a t t h e t i m e o f f a i l u r e and on t h e a n g l e o f s h e a r r e s i s t a n c e I f t h e e f f e c t i v e s t r e s s e s u s e d 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 a r e t h e same and one o f t h e p r i n c i p a l s t r e s s e s , a* o r a " , c. X i s h e l d c o n s t a n t d u r i n g s h e a r , t h e s t r e n g t h d i f f e r e n c e s c a n a r i s e o n l y due t o d i f f e r e n c e s i n <j>". F o r a l l t h e d r a i n e d s t r e s s p a t h s s t u d i e d , e i t h e r a ' o r a " was h e l d X z. c o n s t a n t . H e n c e u n d e r a g i v e n s t r e s s p a t h , t h e t r i a x i a l o r p l a n e s t r a i n s t r e n g t h s h o u l d be a p r e d e t e r m i n e d q u a n t i t y i f t h e m a g n i t u d e o f <j>" i s k n o w n . F o r e x a m p l e , f o r t h e p a s s i v e c o m p r e s s i o n s t r e s s p a t h i n w h i c h a ' i s h e l d c o n s t a n t a t o " t h e d r a i n e d s t r e n g t h w i l l be g i v e n by v z x ' m a x xc 1 - s i n (j)' - 1 ( 7 . 1 ) F o r a c t i v e c o m p r e s s i o n , o^ i s h e l d c o n s t a n t a t a" a n d , t h e r e f o r e , v z c x ' m a x z c 1 -1 - s i n cj) 1 + s i ncf>" ( 7 . 1 a ) S i m i l a r l y , f o r a c t i v e e x t e n s i o n w i t h a* h e l d c o n s t a n t a t A (0- - v ) = a-x x c z ' m a x x c 1 _ 1 - s i net 1 + s i ntt ( 7 . 1 b ) U s i n g E q s . 7 . 1 t o 7 . 1 b and t h e m e a s u r e d v a l u e s o f cj>" i n T a b l e V , t h e p l a n e s t r a i n s t r e n g t h w o u l d be h i g h e r t h a n t h e t r i a x i a l v a l u e by 2 2 % , 7% and 12% r e s p e c t i v e l y f o r p a s s i v e c o m p r e s s i o n , a c t i v e c o m p r e s s i o n and a c t i v e e x t e n -s i o n s t r e s s p a t h s . The m e a s u r e d i n c r e a s e i n p l a n e s t r a i n s t r e n g t h o f o n l y 14% i n p a s s i v e c o m p r e s s i o n was due t o s m a l l e r v a l u e o f o" a t f a i l u r e i n p l a n e s t r a i n c o m p a r e d t o t h a t u n d e r t r i a x i a l c o n d i t i o n . S m a l l d i f f e r e n c e s i n o " o r f r o m t h e i r end o f c o n s o l i d a t i o n v a l u e s o c c u r r e d , A Z p a r t l y f r o m s m a l l e x c e s s p o r e p r e s s u r e s a t f a i l u r e and p a r t l y due t o c h a n g e i n x - s e c t i o n a l a r e a o f t h e s p e c i m e n w i t h s t r a i n . In a d d i t i o n , s p e c i m e n s s u b j e c t e d t o t h e same s t r e s s p a t h u n d e r t r i a x i a l and p l a n e s t r a i n c o n -d i t i o n had s l i g h t v a r i a t i o n s i n t h e end o f c o n s o l i d a t i o n s t r e s s e s , w h i c h d i r e c t l y i n f l u e n c e d t h e i r d r a i n e d s t r e n g t h . 7 . 2 . 0 C o r r e l a t i o n o f T r i a x i a l and P l a n e S t r a i n B e h a v i o u r : S t r e s s - S t r a i n R e l a t i o n s F o r l i n e a r e l a s t i c m a t e r i a l s w h i c h a r e i s o -t r o p i c t h e g e n e r a l 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 v o l v e o n l y two i n d e p e n d e n t c o n s t a n t s - Y o u n g ' s m o d u l u s , E , and P o i s s o n ' s r a t i o , v. F o r n o n l i n e a r m a t e r i a l s t h e s e r e l a t i o n s h i p s become more c o m p l e x . S i m p l e a p p r o x i m a -t i o n s w h i c h a r e a d e q u a t e i n many c a s e s , i n c l u d i n g t h e p l a s t i c r a n g e , i n v o l v e t h e c o n c e p t o f f u n c t i o n a l r e l a -t i o n s h i p b e t w e e n o c t a h e d r a l n o r m a l s t r e s s , a ^, and o c t a h e d r a l n o r m a l s t r a i n , v / 3 , and b e t w e e n o c t a h e d r a l s h e a r s t r e s s , ^ Q C ^ > and o c t a h e d r a l s h e a r s t r a i n , Y O C T -E a c h o f t h e s e r e l a t i o n s i s , i n many c a s e s , i n d e p e n d e n t o f t h e o t h e r . In s o i l s , h o w e v e r , s h e a r s t r e s s e s may c a u s e v o l u m e i n c r e a s e o r d e c r e a s e a t c o n s t a n t mean n o r m a l s t r e s s . C o n s e q u e n t l y , 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 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 n o t o f o c t a h e d r a l s h e a r s t r e s s , a r e n o t a p p l i c a b l e t o s o i l s . In o t h e r w o r d s , t h e r e w i l l be a c o u p l i n g i n t h e r e l a t i o n -s h i p s c o n n e c t i n g t h e f o u r q u a n t i t i e s , c T o c^-> v> ^0ct' Newmark (I960) s u g g e s t e d t h e f o l l o w i n g t h r e e d i m e n s i o n a l 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 o r c o h e s i v e s o i l . v = f i ( p , T o c t ) ( 7 . 2 ) W * f 2 <P. T o c t > ( 7 ' 3 > w h e r e fi and f 2 a r e a r b i t r a r y f u n c t i o n s . A l l o t h e r q u a n t i t i e s h a v e b e e n d e f i n e d p r e v i o u s l y . T h e s e r e l a t i o n -s h i p s d i s r e g a r d any i n f l u e n c e o f t h e t h i r d s t r e s s i n v a r i a n t , o^o^ot, on s t r e s s - s t r a i n b e h a v i o u r , w h i c h may n o t be t h e c a s e . F o r t h e c a s e o f u n d r a i n e d t e s t s , v i s z e r o and E q . 7 . 2 r e d u c e s t o f i ( p , T . ) = 0 o r T o c t = f s ( P ) ( 7 . 4 ) E q . 7 . 4 i m p l i e s t h a t u n d r a i n e d s t r e s s p a t h s on t h e o c t a -h e d r a l s t r e s s p l a n e w i l l be u n i q u e f o r t e s t s u n d e r d i f -f e r e n t s t r e s s s y s t e m s . The c o m b i n a t i o n o f E q s . 7 . 3 a n d 7 . 4 y i e l d s ^oct • f < K c t > < 7 - 5 > E q u a t i o n 7 . 5 i n d i c a t e s t h a t a u n i q u e r e l a t i o n s h i p s e x i s t s b e t w e e n o c t a h e d r a l s h e a r 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 . L a d a n y i ( 1 9 6 7 ) a l s o s u g g e s t e d t h e p o s -s i b i l i t y o f s u c h a r e l a t i o n s h i p . 7 . 2 . 1 U n d r a i n e d E f f e c t i v e S t r e s s P a t h s F i g . 7 . 7 shows e f f e c t i v e s t r e s s p a t h s f o l l o w e d on t h e o c t a h e d r a l s t r e s s p l a n e f o r a l l t r i a x i a l and p l a n e s t r a i n t e s t s . The s t r e s s e s h a v e b e e n n o r m a l i z e d by d i v i d i n g them w i t h p c , t h e o c t a h e d r a l e f f e c t i v e n o r m a l 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 . I t c a n be s e e n t h a t t h e r e s u l t s f r o m a l l t h e c o m p r e s s i o n t e s t s f a l l e s s e n t i a l l y on t h e same c u r v e , t h u s v e r i f y i n g t h e u n i q u e n e s s e x p r e s s e d by E q . 7 . 4 . S i m i l a r c o n c l u s i o n s w e r e r e a c h e d by H e n k e l and Wade ( 1 9 6 6 ) and S h i b a t a and K a r u b e ( 1 9 6 7 ) b u t , o n l y f o r p a s s i v e c o m p r e s s i o n t e s t s on C0MPRESSI0N-TRIAXIAL A ACTIVE + PASSIVE PLANE STRAIN • ACTIVE 0 PASSIVE 0.4 0.3 • 0.2 0.4 EXTENSION TRIAXIAL xACTIVE © PASSIVE PLANE STRAIN o ACTIVE A PASSIVE 0.1 © © 0.5 0.6 0.7 0.8 0.9 1.0 FIG.7.7 OCTAHEDRAL E F F E C T I V E S T R E S S PATHS DURING UNDRAINED TRIAXIAL AND P L A N E STRAIN S H E A R - N.C. H A N E Y C L A Y . r e m o l d e d c l a y s . F o r H a n e y c l a y t h e t r i a x i a l a n d p l a n e s t r a i n s t r e s s p a t h s w e r e f o u n d t o be u n i q u e e v e n a f t e r t h e p e a k d e v i a t o r s t r e s s was r e a c h e d . No a p p r e c i a b l e d i v e r g e n c e u n d e r t h e two s t r e s s s y s t e m s was n o t i c e a b l e u n t i l t h e c o n d i t i o n o f maximum s t r e s s r a t i o , T o c t / P ' was a p p r o a c h i n g . D u r i n g u n d r a i n e d e x t e n s i o n , h o w e v e r , t h e s t r e s s p a t h s ' f o l l o w e d w e r e n o t f o u n d t o be common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . In t h e s e t e s t s a d e c r e a s e o c c u r s i n b o t h x + and s t r e s s r a t i o , o c t x Q c t / p . F o r t r i a x i a l s t r e s s c o n d i t i o n s , s i n c e x Q C t |a -a 1 , t h i s u n l o a d i n g p r o c e s s i n v o l v e s a r e d u c t i o n o f T o c t t o z e r o when t h e s t r e s s s t a t e c o r r e s p o n d s t o a z = a . H o w e v e 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 T Q c t c a n n o t r e d u c e t o z e r o , as t h e n e c e s s a r y c o n d i t i o n f o r t h i s t o h a p p e n , i . e . a = a = a , i s n e v e r r e a l i z e d . T h u s , i n e x t e n s i o n x y z s h e a r no a g r e e m e n t c a n be e x p e c t e d b e t w e e n t h e o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s f o r t r i a x i a l and p l a n e s t r a i n c o n -d i t i o n s . 7.2.2 S t r e s s - S t r a i n C o m p a r i s o n s U n d r a i n e d c o m p r e s s i o n t e s t s F i g u r e 7.8 shows t h e o c t a h e d r a l s h e a r s t r e s s v s . o c t a h e d r a l s h e a r s t r a i n r e l a t i o n s h i p s . Due t o a s m a l l s c a t t e r i n t h e K - v a l u e s o f t h e s p e c i m e n s , x . a t t h e 1.24 1.0 + + + + • © ^ © A A 3 O Q A > • © C A ) u A A+® • Af © A © • + A © TRIAXIAI I ^ ACTIVF f 9 + PASSIVE PLANE STRAIN © ACTIVE • PASSIVE 0 0.1 0.2 0.3 0.4 0.5 X o c t % FIG. 7.8 O C T A H E D R A L S H E A R S T R E S S - S T R A I N R E L A T I O N DURING U N D R A I N E D T R I A X I A L AND P L A N E STRAIN C O M P R E S S I O N - N.C. H A N E Y C L A Y . 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 i n e a c h t e s t . In o r d e r t o h a v e t h e same s t a r t i n g p o i n t f o r a l l s t r e s s -s t r a i n c u r v e s , t h e n o r m a l i z e d o c t a h e d r a l s h e a r s t r e s s , x o c t / p c , has b e e n d i v i d e d by t h e v a l u e o f t h i s v a r i a b l e a t t h e end o f c o n s o l i d a t i o n . T h u s , a l l s t r e s s - s t r a i n c u r v e s s t a r t w i t h an o r d i n a t e o f u n i t y a t z e r o s h e a r s t r a i n . I t c a n be s e e n f r o m t h e f i g u r e t h a t a l l t h e c o m p r e s s i o n t e s t s do o b e y e x t r e m e l y w e l l t h e p o s t u l a t e d u n i q u e o c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n o f E q . 7 . 5 . C o m p r e s s i o n f a i l u r e (I a z~ a xIm a x) i n D ° t h p l a n e s t r a i n and t r i a x i a l t e s t s o c c u r r e d a t s t r a i n s b e l o w Y 0 C £ = 0 . 3 % . The o c t a h e d r a l s t r e s s - s t r a i n r e l a t i o n s h i p , t h e r e f o r e , i s s e e n t o h o l d a l m o s t u n t i l f a i l u r e c o n d i t i o n i s r e a c h e d . A l s o , i t was shown i n F i g . 7 . 7 t h a t o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s w e r e f o u n d t o be i d e n t i c a l 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 - a ) T h i s w o u l d s u g g e s t t h a t t h e o c t a h e d r a l s t r e s s -z x m a x s t r a i n r e l a t i o n s h i p common t o t r i a x i a l and p l a n e s t r a i n s h o u l d h o l d e v e n b e y o n d t h e c o n d i t i o n o f maximum d e v i a t o r s t r e s s . F i g . 7 . 9 shows t h a t s u c h a p o s t p e a k s t r e s s -s t r a i n r e l a t i o n d o e s h o l d r e m a r k a b l y w e l l u n t i l Y O C T ~ 3 % . U n d r a i n e d e x t e n s i o n t e s t s As a l r e a d y m e n t i o n e d , d u r i n g u n d r a i n e d e x t e n s i o n s h e a r , T Q C t d e c r e a s e s t o a m i n i m u m v a l u e b e f o r e i n c r e a s i n g t o 1.4 1.2 0 . 4 T R I A X I A L A A C + P A S T R A I N © AC • Pfi T I V E f ^ r |\/r A © • . , A + © © i+ 1 • + © + P L A N E O O I V L ; T I V E » S S I V E a + © + © 4 • © • i i © 8 > 0 2 4 6 8 10 X o c t % FIG. 7.9 POST P E A K O C T A H E D R A L S H E A R S T R E S S - S T R A I N R E L A T I O N DURING UNDRAINED T R I A X I A L A N D P L A N E STRAIN C O M P R E S S I O N - N.C. HANEY C L A Y . c a u s e f a i l u r e . F o r t r i a x i a l t e s t s > T o c t a t t a i n s t h e m i n i m u m v a l u e o f z e r o i n c o n t r a s t t o t h e p l a n e s t r a i n t e s t s w h e r e i t r e d u c e s t o a b o u t 50% o f i t s v a l u e a t t h e end o f c o n s o l i -d a t i o n ( F i g . 7 . 7 ) . A r e l a t i o n s h i p b e t w e e n T o c ^ - / P c a n < ^ Y Q C t s i m i l a r t o t h a t i n c o m p r e s s i o n t e s t s c a n n o t , t h e r e f o r e , e x i s t f o r e x t e n s i o n t e s t s . H o w e v e r , i f an a l t e r n a t i v e s h e a r s t r e s s p a r a m e t e r , w h i c h c a n be c o n s i d e r e d as o c t a -h e d r a l c h a n g e o f s h e a r s t r e s s , i s u s e d i n s t e a d o f ^ o c ^ > t h e n b o t h t h e p l a n e s t r a i n a n d t r i a x i a l t e s t s r e s u l t i n i d e n t i c a l e f f e c t i v e s t r e s s p a t h s a n d , t h e r e f o r e , a u n q i u e o c t a h e d r a l s t r e s s s t r a i n r e l a t i o n s h i p common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s may e x i s t . T h i s s h e a r s t r e s s p a r a m e t e r i s e x p r e s s e d as AT. - 1 ( A C T - A C T ) 2 + (ACT -ACT ) 2 + (ACT -ACT ) 2 ( 7.6) o c t 3 \ X y ' y z ' ^ z x and i s s i m i l a r t o t h a t u s e d i n p o r e p r e s s u r e E q u a t i o n 5 . 2 . A T Q C t t h u s i s a m e a s u r e o f c u m u l a t i v e c h a n g e i n o c t a h e d r a l c o m p o n e n t o f s h e a r s t r e s s . The r e l a t i o n s h i p b e t w e e n A T 0 C t / P c and o c t a h e d r a l s h e a r s t r a i n i s shown i n F i g . 7 . 1 0 f o r a l l t h e t r i a x i a l and p l a n e s t r a i n u n d r a i n e d t e s t s . The r e m a r k -a b l e u n i q u e n e s s o f t h e o c t a h e d r a l s t r e s s - s t r a i n r e l a t i o n -s h i p i s c l e a r l y d e m o n s t r a t e d i n t h i s f i g u r e . The v e r y 0.5 0.4 0 A > + © +© © * + % A® ? A • f PLANE TRIAXIAL + A I STRAIN © • ACTIVE PASSIVE ACTIVE PASSIVE 0 2 4 6 8 10 X o c t % FIG.7.10 O C T A H E D R A L S H E A R S T R E S S - S T R A I N RELATION DURING UNDRAINED T R I A X I A L AND P L A N E STRAIN EXTENSION - N.C. H A N E Y C L A Y . s i g n i f i c a n t f e a t u r e t o be n o t e d i s t h e v a l i d i t y o f t h i s r e l a t i o n f o r a l l s t r a i n s u n t i l f a i l u r e . D r a i n e d 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 : V o l u m e t r i c S t r a i n s : C o m p r e s s i o n T e s t s I t was shown i n C h a p t e r V and VI t h a t an e x t e n d e d f o r m o f R e n d u l i c 1 s h y p o t h e s i s o f u n i q u e n e s s o f v o i d r a t i o and e f f e c t i v e s t r e s s e s c o u l d be s u c c e s s f u l l y u s e d t o p r e d i c t v o l u m e t r i c s t r a i n s i n l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n t e s t s f r o m t h e r e s u l t s o f u n d r a i n e d c o m p r e s s i o n t e s t s . The h y p o t h e s i s was shown t o be v a l i d f o r b o t h t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s s e p a r a t e l y . The u n i q u e n e s s o f e f f e c t i v e s t r e s s p a t h s on t h e T Q c t v s . p p l a n e , f o r b o t h p l a n e s t r a i n and t r i a x i a l u n d r a i n e d c o m p r e s s i o n t e s t s ( F i g . 7 . 7 ) , now i m p l i e s t h e e x i s t e n c e o f an u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e i n T o c ^ / P e » P / P e a x e s » w h i c h i s common t o t r i a x i a l and p l a n e s t r a i n s t r e s s s y s t e m s . I t was a l s o shown i n C h a p t e r V t h a t e x c e l l e n t a g r e e m e n t was o b t a i n e d b e t w e e n v o l u m e t r i c s t r a i n s a c t u a l l y m e a s u r e d and t h o s e p r e d i c t e d f r o m t h e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e c u r v e f o r t h e c a s e o f d r a i n e d p l a n e s t r a i n p a s s i v e c o m p r e s -s i o n t e s t . S i n c e t h e u n d r a i n e d s t a t e b o u n d a r y s u r f a c e i s t h e same f o r p l a n e s t r a i n and t r i a x i a l u n d r a i n e d t e s t s , p r e c i s e l y t h e same p r e d i c t i o n s o f v o l u m e c h a n g e i n p l a n e s t r a i n t e s t w o u l d be made f r o m t h e r e s u l t s o f u n d r a i n e d t r i a x i a l c o m p r e s s i o n t e s t s ( s e e F i g . 7 . 1 1 ) . I t i s , t h e r e f o r e , s u g g e s t e d t h a t v o l u m e t r i c s t r a i n s i n l o a d i n -c r e a s i n g d r a i n 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 s c a n be p r e d i c t e d f r o m t h e r e s u l t s o f u n d r a i n e d t r i a x i a l t e s t on an i d e n t i c a l s p e c i m e n , by a p p l y i n g e x t e n d e d R e n d u l i c h y p o t h e s i s i n ( p , - T O C J . » e ) s p a c e . I t was n o t f o u n d p o s s i b l e ( C h a p t e r s V and V I ) t o make s a t i s f a c t o r y p r e d i c t i o n s o f v o l u m e t r i c s t r a i n s i n l o a d d e c r e a s i n g d r a i n e d a c t i v e c o m p r e s s i o n t e s t s , by t h e a p p l i c a t i o n o f R e n d u l i c ' s h y p o t h e s i s . T h i s was due t o t h e f a c t t h a t T o c ^ / P e v s • P^Pe c u r v e ^ o r s u c h t e s t s f e l l s l i g h t l y b e l o w t h e s i m i l a r c u r v e f o r u n d r a i n e d o r l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n t e s t s . T h i s s i t u a t i o n was common t o b o t h t r i a x i a l and p l a n e s t r a i n s t r e s s s y s t e m s . H o w e v e r , 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 common T Q C ^ . p / p e c u r v e i s o b t a i n e d f o r b o t h p l a n e s t r a i n and t r i a x i a l d r a i n e d a c t i v e c o m p r e s s i o n t e s t s . T h i s i s shown i n F i g . 7 . 1 2 . T h i s a m o u n t s t o s a y i n g t h a t t h e r e c a n be a s s u m e d t o e x i s t a s t a t e b o u n d a r y s u r f a c e c u r v e f o r d r a i n e d u n l o a d i n g a c t i v e c o m p r e s s i o n t e s t s , w h i c h i s d i f f e r e n t f r o m t h a t f o r t h e u n d r a i n e d c o m p r e s s i o n t e s t s , b u t i s common t o t r i a x i a l a n d p l a n e s t r a i n c o n d i t i o n s . I t , t h e r e f o r e , f o l l o w s t h a t t h e x 4 . / p „ v s . p / p „ r e l a t i o n s h i p o f t h e t r i a x i a l t e s t 0.44 + / PRE TRI DICTED FROM AXIAL COMPR UNDRAINED ESSION TEST! + / + 0 BSERVED 0 2 4 6 8 10 VOLUMETRIC STRAIN - v % FIG-7.11 COMPARISON OF OBSERVED AND PREDICTED V O L U M E T R I C S T R A I N S DURING P L A N E STRAIN DRAINED PASSIVE COMPRESSION - N.C. HANEY C L A Y . FIG. 7.12 COMMON STATE B O U N D A R Y S U R F A C E C U R V E FOR DRAINED TRIAXIAL AND P L A N E STRAIN A C T I V E C O M P R E S S I O N - N.C. H A N E Y C L A Y . c o u l d be u s e d t o p r e d i c t v o l u m e c h a n g e s i n t h e p l a n e s t r a i n t e s t . V o l u m e t r i c s t r a i n s t h u s p r e d i c t e d f o r d r a i n e d p l a n e s t r a i n a c t i v e c o m p r e s s i o n t e s t a r e shown i n F i g . 7 . 1 3 , a l o n g w i t h t h e o b s e r v e d v a l u e s . K e e p i n g i n v i e w t h e s m a l l m a g n i t u d e o f v o l u m e t r i c s t r a i n s , a g r e e m e n t b e t w e e n p r e d i c t i o n s and o b s e r v a t i o n s i s g o o d . V o l u m e t r i c S t r a i n s - E x t e n s i o n T e s t s I t was shown i n C h a p t e r V and VI t h a t u n d r a i n e d and d r a i n e d b e h a v i o u r d u r i n g a c t i v e e x t e n s i o n was v i r t u a l l y i d e n t i c a l f o r b o t h p l a n e s t r a i n and t r i a x i a l s t r e s s s y s t e m s . T h i s i s due t o t h e v e r y s m a l l v o l u m e c h a n g e s a s s o c i a t e d w i t h t h e d r a i n e d t e s t s , w h i c h r e n d e r s t h e s i t u a t i o n c l o s e t o t h e u n d r a i n e d o n e . I t was a l s o shown e a r l i e r i n t h i s c h a p t e r t h a t t h e u n d r a i n e d e x t e n s i o n s t r e s s - s t r a i n r e l a t i o n s h i p was u n i q u e i n t e r m s o f AT ^ v s . Y O C ^ ( F i g . 7 . 1 0 ) . I t , t h e r e f o r e , f o l l o w s t h a t d r a i n e d a c t i v e e x t e n s i o n t e s t s , b e c a u s e o f b e i n g a l m o s t i d e n t i c a l t o t h e i r u n d r a i n e d c o u n t e r p a r t s , w i l l a l s o p o s s e s s a u n i q u e A T Q C T v s . Y O C T r e l a t i o n s h i p . T h a t t h i s i s v e r y n e a r l y t r u e i s shown i n F i g . 7 . 1 4 . From t h i s r e l a t i o n s h i p one c a n p r e d i c t c h a n g e s i n mean n o r m a l e f f e c t i v e s t r e s s , p , i n p l a n e s t r a i n f r o m t h e r e s u l t s o f t r i a x i a l t e s t s . The v o l u m e t r i c s t r a i n s i n p l a n e s t r a i n d r a i n e d a c t i v e e x t e n s i o n t e s t c a n t h e n be e v a l u a t e d f r o m c h a n g e s i n mean n o r m a l s t r e s s , p , a n d t h e s w e l l i n g i n d e x , x, as was d i s c u s s e d i n C h a p t e r V . C h a n g e s i n p u n d e r p l a n e s t r a i n a r e f o u n d as f o l l o w s : f o r a g i v e n Y O C T > 0.46 0.34 0.3 PF + / AC JEDICTED FRO TIVE COMPRE M DRAINED T ISSION TEST Rl AXIAL +OBSERVED 0 1 2 3 4 VOLUMETRIC STRAIN —v % FfG. 7.13 COMPARISON OF OBSERVED AND PREDICTED V O L U M E T R I C STRAINS DURING P L A N E STRAIN DRAINED A C T I V E C O M P R E S S I O N - N.C. H A N E Y C L A Y . 0.5 0.4 0 + + + +* + A + A -+A ' A + A + + A + + T R I ; A P L A \ X I A L N E S T R A I N 0 2 4 6 8 Xoct % FIG.7.14 O C T A H E D R A L S H E A R S T R E S S - STRAIN R E L A T I O N DURING T R I A X I A L A N D P L A N E S T R A I N D R A I N E D ACT IVE E X T E N S I O N -N.C. H A N E Y C L A Y . ( A x o c j . ) p s = ( A T 0 C t ^ T * * " w n e r e s u b s c r i p t s r e f e r t o p l a n e s t r a i n a n d t r i a x i a l c o n d i t i o n s r e s p e c t i v e l y . D u r i n g d r a i n e d a c t i v e e x t e n s i o n s t r e s s p a t h , a ' i s h e l d c o n s t a n t a t a " a n d , t h e r e f o r e , A a " = 0 . I t was shown i n C h a p t e r V A \* A t h a t i n p l a n e s t r a i n ~ 0 . 3 7(0-^ + a p , . " . (AOy) s = 0 . 3 7 ( A a z + A d x ) and t h e n ( A T 0 C t ) = ( ^ ^ o c t ) T r e d u c e s t o 0 . 8 7 7 ( A a z ) p s = ( A t r ^ ) T and ( A p ) P • s A a . p . s + 0 . 3 7 p. s ( 7 . 7 ) V o l u m e t r i c s t r a i n s d u r i n g d r a i n e d e x t e n s i o n t e s t s , h o w e v e r , w e r e v e r y s m a l l ( l e s s t h a n 0 . 7 5 % i n a b s o l u t e m a g n i t u d e ) a n d , t h e r e f o r e , t h e i r p r e d i c t i o n may n o t be v e r y i m p o r t a n t . S i n c e l o a d i n c r e a s i n g d r a i n e d p a s s i v e e x t e n s i o n t e s t c o u l d n o t be p e r f o r m e d i n t h e p l a n e s t r a i n a p p a r a t u s , no a t t e m p t c a n be made t o c o r r e l a t e p l a n e s t r a i n and t r i -a x i a l v o l u m e c h a n g e s f o r t h i s t o t a l s t r e s s p a t h . S h e a r S t r a i n s : I t was p o i n t e d o u t i n b o t h C h a p t e r s V and VI t h a t n o r m a l i t y c o n d i t i o n o f t h e o r y o f p l a s t i c i t y c o u l d n o t be u s e d f o r p r e d i c t i o n o f p l a s t i c s t r a i n i n c r e m e n t r a t i o , 5 Y 0 C t / 5 v , f o r Haney c l a y when s t r e s s r a t i o T Q c t / p was > 0 . 3 8 . T h i s c o r r e s p o n d s t o t h e p o i n t on t h e s t a t e b o u n d a r y s u r f a c e c u r v e w h e r e t a n g e n t t o t h i s c u r v e b e c o m e s h o r i z o n t a l a n d , t h e r e f o r e , i m p l i e s u n l i m i t e d s h e a r s t r a i n , 5 Y o c t w i t h o u t v o l u m e c h a n g e . In l o a d i n c r e a s i n g d r a i n e d c o m p r e s s i o n t e s t s on H a n e y c l a y , h o w e v e r , t h i s s t r e s s r a t i o c o r r e s p o n d e d t o a Y o c t v a l u e o f a b o u t 20% o f t h a t a t f a i l u r e . T h e r e f o r e , t h e n o r m a l i t y c o n d i t i o n c o u p l e d w i t h e m p i r i c a l e x t e n d e d R e n d u l i c s t r e s s - v o l u m e s t r a i n r e l a t i o n s h i p i s o f l i m i t e d u s e f o r p r e d i c t i o n o f s h e a r s t r a i n s i n d r a i n 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 s f o r m t h e r e s u l t s o f d r a i n e d o r u n d r a i n e d t r i a x i a l c o m -p r e s s i on t e s t s . E q u a t i o n 7 . 3 s u g g e s t s t h a t t h e r e may be a common Toct^ v s * Y o c t r e ^ a t i o n s h i p f o r d r a i n e d c o m p r e s s i o n t e s t s common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . S u c h r e l a -t i o n s h i p s a r e shown p l o t t e d i n F i g u r e s 7 . 1 5 and 7 . 1 6 f o r d r a i n e d p a s s i v e and a c t i v e c o m p r e s s i o n t e s t s . B e c a u s e . o f s m a l l d i f f e r e n c e s i n t h e i n t i a l v a l u e s o f T o c ^ - / P > t h e r a t i o , ( T 0 C - t V p ) / ( T 0 C t / P ) c ' w a s u s e d a s t n e o r d i n a t e , w h e r e ( x o c t / p ) c i s t h e v a l u e o f ( T o c t / P ) a t t n e end o f c o n s o l i d a t i 1.6 1.5 1.4 1.0 + + + I + A A A + A + A A A" + A+ + + 1 A F 1 rRIAXIAL 'LANE STRAIN 0 2 4 6 8 10 ^oct % FIG. 715 O C T A H E D R A L S T R E S S R A T I O - S H E A R STRAIN R E L A T I O N DURING DRAINED T R I A X I A L AND P L A N E STRAIN P A S S I V E C O M P R E S S I O N - N X . H A N E Y C L A Y . 1.6 1.5 ID + + + A A+ t A A A + i A A + + f + TRIAXI/ A PLANE \L STRAIN 0 2 4 6 8 Xoct % FIG. 7.16 O C T A H E D R A L S T R E S S R A T I O - S H E A R S T R A I N R E L A T I O N DURING D R A I N E D T R I A X I A L A N D P L A N E S T R A I N A C T I V E C O M P R E S S I O N - N .C . H A N E Y C L A Y . I t c a n be s e e n t h a t t h e r e l a t i o n s h i p p o s t u l a t e d d o e s h o l d q u i t e w e l l f o r s h e a r s t r a i n s w h i c h a r e a b o u t 60% o f t h e f a i l u r e v a l u e i n p l a n e s t r a i n p a s s i v e c o m p r e s -s i o n . The a g r e e m e n t f o r a c t i v e c o m p r e s s i o n i s s e e n t o h o l d a l m o s t u n t i l f a i l u r e i n p l a n e s t r a i n . I t was shown i n F i g . 7 . 1 4 t h a t d u r i n g d r a i n e d a c t i v e e x t e n s i o n &x0Ct/Pc v s . Y o c t r e l a t i o n s h i p was common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . T h i s r e l a t i o n s h i p , t h e r e f o r e , c a n be u s e d t o p r e d i c t s h e a r s t r a i n s i n p l a n e s t r a i n d r a i n e d a c t i v e e x t e n s i o n t e s t f r o m t h e r e s u l t s o f s i m i l a r t e s t u n d e r t r i a x i a l c o n d i -t i o n s . 7 . 3 . 0 P r e d i c t i o n o f D r a i n e d P l a n e S t r a i n B e h a v i o u r F rom S o i l  P a r a m e t e r s D e t e r m i n e d i n T r i a x i a l C o m p r e s s i o n by t h e  C a m b r i d g e S t r e s s - S t r a i n T h e o r y R o s c o e and B u r l a n d ( 1 9 6 8 ) d e s c r i b e t h e e x t e n s i o n o f C a m b r i d g e s t r e s s - s t r a i n t h e o r y f o r p r e d i c t i n g p l a n e s t r a i n b e h a v i o u r o f a n o r m a l l y c o n s o l i d a t e d s a t u r a t e d r e m o l d e d c l a y by u s i n g s o i l p a r a m e t e r s d e t e r m i n e d f r o m 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 c o m p r e s s i o n t e s t s . In t h i s t h e o r y i t i s a s s u m e d t h a t b o t h t h e s t a t e b o u n d a r y s u r f a c e and t h e y i e l d l o c u s f o r s u c h a c l a y a r e s y m m e t r i c a l a b o u t t h e s p a c e d i a g o n a l , o{=oz=o3, i n t h e t h r e e - d i m e n s i o n 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 s p a c e . The e q u a t i o n o f t h e s t a t e b o u n d a r y s u r f a c e i n ( p , * / 3 T o c t ) t h r e e - d i m e n s i o n a l s t r e s s s p a c e i s JL_ = P0 M (7.8) M + n w h e r e p g , K, A r e f e r t o i s o t r o p i c c o m p r e s s i o n o r s w e l l i n g c o n d i t i o n s and c a n be o b t a i n e d f r o m i s o t r o p i c c o n s o l i d a -t i o n t e s t , n* = ^T0Ct^]P> M * = ^ 2 / 3 M. M i s t h e r a t i o b e t w e e n d e v i a t o r s t r e s s , q , and p i n t r i a x i a l c o m p r e s s i o n t e s t a t t h e c r i t i c a l s t a t e . (An e l e m e n t o f s o i l i s a s s u m e d t o h a v e r e a c h e d c r i t i c a l s t a t e i f i t c o n t i n u e s t o d e f o r m w i t h o u t c h a n g e i n e , p o r q . ) In t r i a x i a l c o m p r e s s i o n t e s t s on r e m o l d e d c l a y s , c r i t i c a l s t a t e i s r e a c h e d when q r e a c h e s a m a x i m u m , w h i c h o c c u r s a t t h e same t i m e when q/p r e a c h e s a m a x i m u m . R o s c o e and B u r l a n d a s s u m e t h e c l a y t o be an i s o t r o p i c r i g i d w o r k - h a r d e n i n g m a t e r i a l . F o r t h i s a s s u m e d c o n d i t i o n K = 0 and e q u a t i o n o f s t a t e b o u n d a r y s u r f a c e c u r v e b e c o m e s * Pe M ( 7 . 9 ) 2 2 * + * M n An a v e r a g e v a l u e o f <}>' d u r i n g t r i a x i a l c o m p r e s s i o n o f Haney c l a y was 27° ( C h a p t e r V I ) , w h i c h g i v e s M = 6s in< j )V 3 -s in t j> ' ' = 1 . 0 7 . F i g . 7 . 1 7 shows t h e p r e d i c t e d s t a t e b o u n d a r y s u r f a c e f o r H a n e y c l a y . A l s o shown i n t h i s f i g u r e a r e t h e r e s u l t s f r o m u n d r a i n e d c o m p r e s s i o n t e s t i n p l a n e s t r a i n . I t c a n be s e e n t h a t t h e o b s e r v e d u n d r a i n e d s t r e s s p a t h n e i t h e r l i e s on n o r b e a r s any r e s e m b l a n c e t o t h e s t a t e b o u n d a r y s u r f a c e c u r v e d e r i v e d f r o m t r i a x i a l t e s t s o i l p a r a m e t e r s . I t , t h e r e f o r e , w o u l d a p p e a r t h a t t h e s t r a i n s p r e d i c t e d f o r d r a i n e d p l a n e s t r a i n p a s s i v e c o m p r e s -s i o n t e s t f r o m t h e a s s u m e d s t a t e b o u n d a r y s u r f a c e ( E q . 7 . 9 ) a r e n o t l i k e l y t o b e a r a n y r e l a t i o n s h i p t o t h e o b s e r v e d s t r a i n s . F o r K = 0 c l a y s t h e u n d r a i n e d s t r e s s p a t h i s a l s o t h e c u r r e n t y i e l d l o c u s . The s h a p e o f t h e p r e d i c t e d and t h e o b s e r v e d u n d r a i n e d s t r e s s p a t h s t h e n s u g g e s t s ( F i g . 7 . 1 7 ) t h a t t h e s h e a r s t r a i n i n c r e m e n t s f o r a g i v e n c h a n g e Siy i n n , c a l c u l a t e d f r o m t h e p r e d i c t e d y i e l d l o c u s w i l l be t o o l a r g e when c o m p a r e d t o t h o s e c a l c u l a t e d f r o m t h e o b s e r v e d y i e l d l o c u s . T h i s i s b e c a u s e , f o r a g i v e n v a l u e o f n t h e s l o p e o f p r e d i c t e d y i e l d l o c u s i s much f l a t t e r O B S E R V E D U N D R A I N E C - S U R F A C E P R E D I C T E E ) S T A T E B 0 U I \ D A R Y \ 0 0 2 0 4 0 . 6 0 . 3 1 0 . 6 0 . 4 Pe .7.17 COMPARISON OF OBSERVED STATE BOUNDARY SURFACE CURVE AND THE STATE BOUNDARY SURFACE CURVE PREDICTED BY THE CAMBRIDGE THEORY FOR UNDRAINED PLANE STRAIN COMPRESSION - N.C. HANEY CLAY. t h a n t h a t o f t h e o b s e r v e d y i e l d l o c u s . C o n s e q u e n t l y , t h e r a t i o ( S Y o c t / ( S v i s t o o l a r g e i n t h e f o r m e r c a s e . T h a t t h e C a m b r i d g e t h e o r y d o e s o v e r p r e d i c t s t r a i n s w i l l be d e m o n s t r a t e d f o r t h e p a s s i v e d r a i n e d p l a n e s t r a i n t e s t . H a m b l y a n d R o s c o e ( 1 9 6 9 ) g a v e t h e f o l l o w i n g e q u a t i o n s f o r p r e d i c t i o n o f s t r a i n s d u r i n g p l a n e s t r a i n y i e l d , u s i n g t r i a x i a l p a r a m e t e r s M and X. T h e s e e q u a t i o n s c o r r e s p o n d t o w h a t i s known as t h e ' m o d i f i e d ' t h e o r y . 1+e /3 2 r T + 6s_ ( 7 . 1 0 ) 6e. 6e. 1+e 'JL /3 S s _ s 2n /3 ( 7 . 1 0 a ) w h e r e n/ = ( o ' - a ' ) / (ol+o') and s = ( a : + a ' ) / 2 . Z A Z ' X F i g u r e 7 . 1 8 shows t h e p r e d i c t e d 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 o r t h e d r a i n e d p l a n e s t r a i n p a s s i v e c o m p r e s -s i o n t e s t a c c o r d i n g t o E q s . 7 . 1 0 . A l s o shown i n t h e f i g u r e 0.33 OBSEFtf ^ P R E D I CTED h • 0 4 8 12 16 20 SHEAR STRAIN-( e 2 - e x ) % 0.41 0.33 0.25 OBSERVE D — ^ . ^ ^ ^ -PREDICTED 0 2 4 6 8 10 VOLUMETRIC STRAIN - v % FIG. 7.18 COMPARISON OF OBSERVED STRESS-STRAIN RELATIONS AND THOSE PREDICTED BY CAMBRIDGE THEORY DURING DRAINED PLANE STRAIN PASSIVE COMPRESSION - N.C. HANEY CLAY. a r e s t r a i n s a c t u a l l y o b s e r v e d i n t h i s t e s t . B o t h v o l u m e t r i and s h e a r s t r a i n s p r e d i c t e d by t h e t h e o r y a r e t o o l a r g e . In p a r t i c u l a r , as w o u l d be e x p e c t e d f r o m t h e s h a p e o f t h e p r e d i c t e d and t h e o b s e r v e d y i e l d l o c i ( F i g . 7 . 1 7 ) , t h e p r e d i c t e d s h e a r s t r a i n s a r e e x c e s s i v e l y l a r g e r t h a n t h e o b s e r v e d v a l u e s . F o r u n d i s t u r b e d Haney c l a y , t h e r e f o r e , t h e C a m b r i d g e t h e o r y d o e s n o t p r o v i d e s a t i s f a c t o r y p r e -d i c t i o n o f s t r a i n s i n l o a d i n g p l a n e s t r a i n t e s t s f r o m t h e s o i l p a r a m e t e r s d e t e r m i n e d i n t h e t r i a x i a l t e s t s . A s i m i l a r s t a t e m e n t w o u l d a p p l y f o r t h e a c t i v e d r a i n e d p l a n e s t r a i n t e s t s . F o r t h e d r a i n e d a c t i v e e x t e n s i o n t e s t , t h e a p p l i e d s t r e s s p a t h a l w a y s l i e s b e l o w t h e c u r r e n t y i e l d l o c u s . F o r s u c h s t r e s s c h a n g e s t h e ' m o d i -f i e d ' C a m b r i d g e t h e o r y p r e d i c t s z e r o s h e a r and v o l u m e t r i c s t r a i n s . R o s c o e and B u r l a n d ( 1 9 6 8 ) a l s o p r e s e n t e d a ' r e v i s e d ' v e r s i o n o f t h e ' m o d i f i e d ' C a m b r i d g e t h e o r y . The ' r e v i s e d ' t h e o r y d o e s p r e d i c t s h e a r s t r a i n s i n t h e d r a i n e d a c t i v e e x t e n s i o n p l a n e s t r a i n t e s t . The m a g n i t u d e o f t h e s h e a r s t r a i n a t any v a l u e o f n" w o u l d be e q u a l t o t h e s h e a r s t r a i n f o r t h e same v a l u e o f r\" i n t h e c o r r e -s p o n d i n g u n d r a i n e d t e s t . In o t h e r w o r d s , t h e s h e a r s t r e s s s t r a i n r e l a t i o n s h i p f o r t h e d r a i n e d a n d u n d r a i n e d a c t i v e e x t e n s i o n p l a n e s t r a i n t e s t s w o u l d be i d e n t i c a l . T h i s was shown t o be v e r y n e a r l y t r u e i n F i g . 5 . 1 5 w h e r e d r a i n e d and u n d r a i n e d p l a n e s t r a i n a c t i v e e x t e n s i o n t e s t s g i v e e s s e n t i a l l y i d e n t i c a l T o c t / P v s . Y o c t r e l a -t i o n s h i p s . The C a m b r i d g e s t r e s s - s t r a i n t h e o r y , a t p r e s e n t , i s u n a b l e t o p r e d i c t s t r a i n s i n 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 u s i n g t h e r e s u l t s o b t a i n e d i n t h e t r i a x i a l t e s t s 7 . 4 . 0 C o r r e l a t i o n o f T r i a x i a l a n d P l a n e S t r a i n  F a i l u r e C o n d i t i o n s 7 . 4 . 1 U n d r a i n e d S t r e n g t h The c o n v e n t i o n a l m e a s u r e f o r u n d r a i n e d s t r e n g t h o f s o i l i s o n e - h a l f t h e peak d e v i a t o r s t r e s s ( a i - o 3 ) /2 r max I t h a s p r e v i o u s l y b e e n shown t h a t f o r i d e n t i c a l s t r e s s p a t h s , ( a i - a 3 ) m , v / 2 a 1 " ^ was l a r g e r i n p l a n e s t r a i n t h a n max i c u n d e r t r i a x i a l c o n d i t i o n s . T h e s e a p p a r e n t d i f f e r e n c e s i n u n d r a i n e d s t r e n g t h c a n , h o w e v e r , be e x p l a i n e d i f t h e u n d r a i n e d s t r e n g t h i s c h a r a c t e r i s e d by maximum o c t a h e d r a l s h e a r s t r e s s , ( x „ . ) m , . T h i s f o l l o w s f r o m o c x max t h e o b s e r v e d u n i q u e n e s s o f o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s and t h e o c t a h e d r a l 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 . T a b l e VI shows t h e v a l u e s o f T o c t /p c a t (T O C T) M A X. ( The c o n d i t i o n o f (T . ) i s r e a c h e d a t t h e same t i m e OCt IH3X as (a 1 - 0 - 3 ) . ) I t c a n be s e e n t h a t t h e t r i a x i a l and max p l a n e s t r a i n c o m p r e s s i o n f a i l u r e o c c u r s a t e s s e n t i a l l y i d e n t i c a l v a l u e s o f T o c t / P c - I n a x i a l e x t e n s i o n , C o - r e l a t i o n o f U n d r a i n e d S t r e n g t h u n d e r T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s F a i l u r e C o n d i t i o n ( a i " a 3 ) m a x o r ^ o c t ^ a x ( a i - 0 - 3 )/2a: 1 c T o c t / p c U n d r a i n e d C o m p r e s s i o n P l a n e s t r a i n T r i a x i a l 0 . 2 9 3 0 . 2 6 5 . 3 6 3 . 3 5 6 U n d r a i n e d E x t e n s i o n P l a n e s t r a i n T r i a x i a l T o c t / p c ^ o c t / P c 0 . 1 9 3 0 . 1 3 0 0 . 2 4 2 0 . 1 7 5 0 . 4 7 9 0 . 4 7 6 °]c ~ m a J ° r c o n s o l i d a t i o n s t r e s s p - mean c o n s o l i d a t i o n s t r e s s h o w e v e r , u n i q u e e f f e c t i v e s t r e s s p a t h s and 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 w e r e f o u n d o n l y i f A T Q C T was u s e d as t h e s h e a r s t r e s s p a r a m e t e r . T h e r e f o r e , a t f a i l u r e c o n d i -t i o n A T 0 C £ / P c i n p l a c e o f T O C ^ - / P C w a s f o u n d t o be t h e same u n d e r b o t h t r i a x i a l and p l a n e s t r a i n s t r e s s s y s t e m s 7 . 4 . 2 F a i l u r e C r i t e r i a A f a i l u r e c r i t e r i o n e x p r e s s e s a f u n c t i o n a l r e l a t i o n s h i p b e t w e e n 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 . T h e r e a r e t h r e e f a i l u r e c r i t e r i a u s u a l l y 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 1 s ( B i s h o p , 1 9 6 6 ) . F o r 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 ( c = 0 ) t h e s e c r i t e r i a c a n be w r i t t e n as M o h r - C o u 1 o m b a i - a 3 = sine})-* ( 7 . 1 1 ) a {+03 E x t e n d e d T r e s c a : 0 ^ - 0 3 = ap ( 7 . 1 2 ) E x t e n d von M i s e s : T o c t = 3~ a ^ ( 7 . 1 3 ) w h e r e a i s a s o i l c o n s t a n t . Of t h e s e t h r e e c r i t e r i a t h e M o h r - C o u l o m b d o e s n o t r e c o g n i z e a n y i n f l u e n c e o f 02 on 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 , I t has b e e n p r e v i o u s l y s h o w n , h o w e v e r , t h a t M o h r - C o u 1 o m b w a s , f o r a l l s t r e s s p a t h s , l a r g e r i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . The M o h r - C o u l o m b c r i t e r i o n , t h e r e -f o r e , u n d e r e s t i m a t e s t h e p l a n e s t r a i n s t r e n g t h o f Haney c l a y . The o t h e r two c r i t e r i a , t h e E x 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 , do a c c o u n t f o r t h e i n f l u e n c e o f 0 2 on f a i l u r e c o n d i t i o n s . C o n s i d e r i n g t r i a x i a l f a i l u r e c o n d i t i o n s as t h e r e f e r e n c e a t w h i c h a l l t h e t h r e e c r i t e r i a a r e made t o c o i n c i d e , t h e <j>' i m p l i e d 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 a c c o r d i n g t o e x t e n d e d T r e s c a and v o n M i s e s c r i t e r i a c a n be e v a l u a t e d . Then a c o m p a r i s o n o f o b s e r v e d a n d p r e d i c t e d a)' w o u l d show i f e i t h e r o f t h o s e f a i l u r e c r i t e r i a c o u l d be c o n s i d e r e d a p p l i c a b l e t o u n d i s t u r b e d Haney c l a y . I f t h e v a l u e o f Oz r e l a t i v e t o aT and o$ i s e x p r e s s e d by b = ( t h e n t h e T r e s c a and von M i s e s c r i t e r i a c a n be e x p r e s s e d as f o l l o w s ( B i s h o p , 1 9 6 6 ) : a i - a 3 a i+o 3 ( 7 . 1 5 ) E x t e n d e d von M i s e s : O 1-0" 3 _ a r+a 3 i + - 1 -b+b o a \ j ( 7 . 1 6 ) F o r a g i v e n t r i a x i a l ' a ' and t h e v a l u e o f ' b ' i n p l a n e s t r a i n , t h e l e f t h a n d s i d e s o f E q s . 7 . 1 5 and 7 . 1 6 e x p r e s s t h e v a l u e s o f s ino>" i m p l i e d by t h e E x t e n d e d T r e s c a a n d E x t e n d e d von M i s e s c r i t e r i a . T a b l e V I I shows t h e v a l u e s o f p l a n e s t r a i n <j>' p r e d i c t e d by E q s . 7 . 1 5 and 7 . 1 6 a l o n g w i t h o b s e r v e d v a l u e s o f cf)'. B o t h ( a i - a 3 ) m _ v and ( o i / a t ) f a i l u r e c o n d i t i o n s a r e c o n s i d e r e d f o r max max u n d r a i n e d c o m p r e s s i o n f a i l u r e . The o b s e r v e d 4>" i s c l o s e s t t o t h a t p r e d i c t e d by t h e E x t e n d e d von M i s e s c r i t e r i o n a t t h e (a r-0-3) u n d r a i n e d f a i l u r e c o n d i t i o n s . H o w e v e r , t h e c o m p a r i s o n b e t w e e n u n d r a i n e d and d r a i n e d f a i l u r e seems t o f a v o u r t h e E x t e n d e d T r e s c a c r i t e r i o n . D u r i n g t r i a x i a l e x t e n s i o n f a i l u r e b = l , and f r o m E q s . 7 . 1 5 and 7 . 1 6 t h i s i m p l i e s l a r g e s t f o r t h e t h e o b s e r v e d and p r e d i c t e d v a l u e s a t [01/03) max f o r b o t h C o m p a r i s o n B e t w e e n O b s e r v e d P l a n e S t r a i n a n d <j>'* P r e d i c t e d f r o m T r i a x i a l R e s u l t s by D i f f e r e n t F a i l u r e C r i t e r i a T r i a x i a l F a i 1 u r e P l a n e S t r a i n F a i l u r e a b O b s e r v e d P r e d i c t e d <j>" T r e s c a Von M i s e s U n d r a i n e d C o m p r e s s i o n a t ( a i " a 3 ) m a x 21 . 0 ° 0 . 8 1 4 0 . 2 2 " 2 5 . 4 ° 2 2 . 2 ° 2 4 . 4 ° 2 6 . 6 ° 1 . 0 5 3 0 . 2 8 5 3 0 . 4 ° 2 9 . 4 ° 3 3 . 1 ° D r a i n e d C o m p r e s s i o n A c t i v e & p a s s i v e 2 5 . 8 ° 1 . 0 1 7 0 . 2 8 5 2 8 . 8 ° 2 8 . 2 ° 3 2 . 0 ° t r i a x i a l s t a t e o f s t r e s s , when c o m p a r e d t o o t h e r s t a t e s w i t h b < l . D u r i n g p l a n e s t r a i n e x t e n s i o n f a i l u r e \ b ' was t y p i c a l l y a r o u n d 0 . 1 5 . B o t h T r e s c a and von M i s e s c r i t e r i a t h e n i m p l y l a r g e r t t ' f o r t r i a x i a l e x t e n s i o n t h a n f o r p l a n e s t r a i n c o n d i t i o n s . T h i s i s o p p o s i t e t o t h e o b s e r v e d p l a n e s t r a i n tj>' w h i c h was l a r g e r t h a n t r i a x i a l 4>" by a b o u t 5 ° . T h u s , i t m u s t be c o n c l u d e d t h a t none o f t h e c l a s s i c a l f a i l u r e c r i t e r i a , a t l e a s t i n t h e p r e s e n t f o r m , s a t i s -f a c t o r i l y p r e d i c t s f a i l u r e f o r a l l t y p e s o f s t r e s s p a t h s a n d s t r e s s s y s t e m s . CHAPTER V I I I TEST RESULTS ON H E A V I L Y OVERCONSOLI DATED HANEY CLAY 8 . 1 . 0 The I n f l u e n c e o f S t r e s s P a t h on T r i a x i a l and  P l a n e S t r a i n R e s u l t s The e f f e c t o f v a r i a t i o n i n a p p l i e d s t r e s s p a t h on t h e b e h a v i o u r o f H a n e y c l a y was e s s e n t i a l l y t h e same f o r b o t h t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . T h u s , t h e f o l l o w i n g d i s c u s s i o n o f r e s u l t s a p p l i e s t o b o t h g r o u p s ( t r i a x i a l and p l a n e s t r a i n ) o f t e s t s . The end o f c o n s o l i d a t i o n s t r e s s e s w e r e s l i g h t l y d i f f e r e n t f r o m s a m p l e t o s a m p l e i n e a c h g r o u p o f t e s t s ( T a b l e s V I I I & I X ) , w h i c h may a c c o u n t f o r some o f t h e o b s e r v e d d i f f e r e n c e i n b e h a v i o u r u n d e r t h e v a r i o u s a p -p l i e d s t r e s s p a t h s . I t may be m e n t i o n e d h e r e t h a t i n o v e r c o n s o l i d a t e d s a m p l e s t h e end o f c o n s o l i d a t i o n c o n d i t i o n was = > o ^ , and t h e r e f o r e , c o m p r e s s i o n s t r e s s p a t h s w e r e a s s o c i a t e d w i t h an i n i t i a l u n l o a d i n g o f d e v i a t o r s t r e s s and s u b s e q u e n t r e o r i e n t a t i o n o f p r i n c i p a l s t r e s s e s a t f a i l u r e . T a b l e s V I I I and IX w i l l be d i s -c u s s e d t h r o u g h o u t s e c t i o n 8 . 1 . TABLE V I I I Summary o f D r a i n e d and U n d r a i n e d T r i a x i a l T e s t R e s u l t s on O . C . Haney C l a y End o f C o n s o l i d a t i o n F a i l u r e C o n d i t i o n O.C R. (oi-o 3 ) 3 ' m a x ( 0 - 1 / 0 - 3 ) v w 3 ' m a x ' a ' z c K 0 p c ^°z^max (P ) v t c ' m a x O 1-0 3 v% a e z % 0 - 1 - 0 - 3 1 / 0 - 3 y% a a -z c p c U n d r a i n e d C o m p r e s s i o n 0 . 3 2 2 . 1 1 0 . 5 6 1 8 . 6 7 . 4 7 . 8 1 . 3 0 3 . 0 5 0 - . 6 2 3 . 5 1 . 0 6 3 . 4 5 0 - 0 . 3 6 E x t e n s i o n 0 . 3 1 2 . 2 0 . 5 5 1 9 . 2 7 . 6 - 7 . 8 1 . 0 5 3 . 1 0 0 - 1 . 9 - 3 . 0 0 . 8 8 3 . 4 5 0 - 1 . 6 8 D r a i ned C o m p r e s s i o n P a s s i v e 0 . 3 3 1 . 7 4 0 . 5 0 1 8 . 1 8 . 3 6 . 0 1 . 4 8 3 . 3 5 0 . 7 — 6 . 0 1 . 4 8 3 . 3 5 0 . 7 — A c t i ve 0 . 3 1 2 . 1 4 0 . 5 5 1 9 . 2 7 . 6 2 . 0 0 . 3 0 8 . 1 - 4 . 6 — 2 . 0 0 . 3 0 8 . 1 - 4 . 6 — D r a i ned E x t e n s i on A c t i ve 0 . 3 1 2 . 1 5 0 . 5 4 1 9 . 1 7 . 7 - 4 . 6 0 . 6 0 6 . 7 - 2 . 1 — - 4 . 6 0 . 6 0 6 . 7 - 2 . 1 — P a s s i v e 0 . 3 1 1 . 9 8 0 . 5 2 1 9 . 1 8 . 0 - 8 . 0 1 . 0 6 3 . 2 0 . 4 — - 8 . 0 1 . 0 6 3 . 2 0 . 4 — End o f C o n s o l i d a t i o n F a i 1 u r e C o n d i t i o n O . C . R . (a 1 - 0 " 3 ) 1 3 / m a x ( 0 - 1 / 0 - 3 ) v 1 1 3 'max a z c . K 0 P C ^° z^max a " z c ^ c ^ m a x Pc a i - a 3 a i / o - 3 a 01-a 3 o - f / 0 - 3 v% a U n d r a i ned C o m p r e s s i o n 0 . 3 5 1 . 6 4 0 . 5 0 1 7 . 3 8 . 1 3 . 8 1 . 4 2 4 . 5 0 - 0 . 4 8 2 . 5 1 . 1 6 4 . 8 0 - 0 . 3 E x t e n s i on 0 . 3 8 1 . 6 8 0 . 5 6 1 5 . 6 7 . 6 - 4 . 0 1 . 1 4 3 . 1 0 - 1 . 2 6 - 2 . 1 1 . 0 1 3 . 3 0 - 1 . 0 5 D r a i ned P a s s i v e c o m p r e s s i o n 0 . 3 5 1 . 5 9 0 . 5 6 1 6 . 6 8 . 5 4 . 8 1 . 6 6 4 . 2 2 . 2 — 4 . 8 1 . 6 6 4 . 2 2 . 2 — A c t i ve e x t e n s i o n 0 . 3 9 1 . 5 0 0 . 5 4 1 5 . 4 8 . 1 - 4 . 0 0 . 9 9 5 . 0 - 1 . 2 — - 4 . C 0 . 9 9 5 . 0 - 1 . 2 — P a s s i v e e x t e n s i o n 0 . 3 8 1 . 5 8 0 . 5 3 1 5 . 4 7 . 7 - 4 . 0 1 . 1 8 3 . 4 0 . 2 . — - 4 . C 1 . 1 8 3 . 4 0 . 2 — S t r e s s e s i n K g / c m 2 8 . 1 . 1 U n d r a i n e d T e s t R e s u l t s The d e v i a t o r s t r e s s - s t r a i n b e h a v i o u r d u r i n g u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n was v e r y s i m i l a r ( F i g . 8 . 1 ) and t h e a x i a l s t r a i n a t f a i l u r e was e s s e n t i a l l y t h e s a m e . The u n d r a i n e d s t r e n g t h , ( a i - a 3 ) / 2 , i n max e x t e n s i o n was a b o u t 8 1 % o f t h a t i n c o m p r e s s i o n ( T a b l e s V I I I , I X ) . S h e a r i n d u c e d p o r e p r e s s u r e s , as r e f l e c t e d i n t h e p o r e p r e s s u r e p a r a m e t e r , ' a ' ( E q . 5 . 2 ) w e r e e n t i r e l y n e g a t i v e d u r i n g e x t e n s i o n s h e a r , t h u s i n d i c a t i n g a d i l a t a n t s t r u c t u r e ( F i g . 8 ^ 2 ) . C o m p r e s s i o n s t r e s s p a t h , on t h e o t h e r h a n d , g a v e r i s e t o s h e a r i n d u c e d p o r e p r e s -s u r e s w h i c h w e r e i n i t i a l l y p o s i t i v e and p o r e p r e s s u r e s d i d n o t become n e g a t i v e u n t i l a b o u t 1% a x i a l s t r a i n . T h i s b e h a v i o u r i s i n a p p a r e n t c o n t r a s t t o t h a t o f f a m i l i a r i s o t r o p i c a l l y h e a v i l y o v e r c o n s o l i d a t e d s o i l s , i n w h i c h s h e a r i n d u c e d p o r e p r e s s u r e s a r e o f t e n f o u n d n e g a t i v e f r o m t h e b e g i n n i n g o f c o m p r e s s i o n s h e a r . One o f t h e r e a s o n s f o r t h i s d i f f e r e n c e i n p o r e p r e s s u r e b e h a v i o u r may l i e i n t h e m a n n e r i n w h i c h o v e r -c o n s o l i d a t i o n r a t i o ( O . C . R . ) i s d e f i n e d f o r i s o t r o p i c a l l y and K Q - c o n s o l i d a t e d s a m p l e s . F o r i s o t r o p i c a l l y c o n s o l i -d a t e d s a m p l e s , i t makes no d i f f e r e n c e w h e t h e r O . C . R . i s d e f i n e d as t h e r a t i o o f maximum t o r e b o u n d v e r t i c a l Fig.8.1 - D E V I A T O R 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 D U R I N G U N D R A I N E D T R I A X I A L A N D P L A N E S T R A I N S H E A R - 0. C . H A N E Y C L A Y . (a ) TRIA XIAL Extension — 1 0.8 -0.8 r-i.6 -2.4 \ ~ Compressio 'ma x^"*"*"*"""*" + n • (a,- OVrnox 0 (b) PLAN! i STRAIN Extension — 12 0.8 -1.6 Compression r 8 4 0 4 Axial Strain - € 2 % 8 .8 .2 - VARIATION OF PORE PRESSURE PARAMETER 'a' WITH AXIAL STRAIN DURING UNDRAINED TRIAXIAL AND PLANE STRAIN SHEAR- O.C.HANEY CLAY. e f f e c t i v e s t r e s s e s o r maximum t o r e b o u n d mean n o r m a l e f f e c t i v e s t r e s s e s . In c o n t r a s t , O . C . R . d e f i n e d by t h e two c r i t e r i a a r e v e r y d i f f e r e n t f o r K Q - c o n s o l i d a t e d c l a y s . In t h e t e s t s e r i e s p r e s e n t e d h e r e i n , O . C . R . by t h e u s u a l d e f i n i t i o n , ( a " ) m a v / a ' , was b e t w e e n z c max z c 1 5 . 4 t o 1 9 . 2 , w h i l e t h e v a l u e o f O . C . R . = ( P c ) m a x / P c > w i t h r e s p e c t t o . mean e f f e c t i v e s t r e s s e s was o n l y b e t w e e n 7 . 4 and 8 . 3 ( s e e T a b l e s V I I I , I X ) . C o n s e -q u e n t l y , t h e s h e a r i n d u c e d p o r e p r e s s u r e s i n c o m p r e s s i o n , a f t e r K Q - o v e r c o n s o l i d a t i o n , may n o t be r e g a r d e d as r e p r e s e n t a t i v e o f ' h e a v y ' o v e r c o n s o l i d a t i o n i f O . C . R . s h o u l d be d e f i n e d as ( p „ ) m , v / p „ . I t i s , t h e r e f o r e , c m a x c i m p o r t a n t t o be c l e a r a b o u t t h e p r o p e r d e f i n i t i o n o f O . C . R . w h i l e d e a l i n g w i t h K Q - o v e r c o n s o l i d a t e d c l a y s , p a r t i c u l a r l y when t h e i r b e h a v i o u r i s t o be c o m p a r e d w i t h i s o t r o p i c a l l y o v e r c o n s o l i d a t e d c l a y s . A n o t h e r f a c t o r w h i c h may be r e s p o n s i b l e f o r l a c k o f d i l a t a n c y d u r i n g c o m p r e s s i o n i s t h e i n i t i a l u n l o a d i n g o f s h e a r s t r e s s e s . The c l a y s t r u c t u r e i s known t o be l e s s d i l a t a n t t o d e c r e a s i n g t h a n t o i n c r e a s -i n g s h e a r i n g s t r e s s e s . In a d d i t i o n , t h e s e n s i t i v e c l a y u s e d i n t h i s s t u d y n e e d n o t be v e r y d i l a t a n t i n t h e o v e r c o n s o l i d a t e d s t a t e , p a r t i c u l a r l y when t h e maximum 2 p a s t v e r t i c a l e f f e c t i v e s t r e s s was o n l y 6 kg/cm ; i . e . , t h e o v e r c o n s o l i d a t e d s t r u c t u r e may r e f l e c t t o some e x t e n t t h e p r o n o u n c e d s e n s i t i v i t y o f t h e 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 t r u c t u r e by g e n e r a t i n g p o s i t i v e p o r e p r e s s u r e s due t o s h e a r . F o r b o t h c o m p r e s s i o n and e x t e n s i o n modes o f s h e a r , s t r a i n s w e r e f o u n d t o i n c r e a s e r a p i d l y a s e f f e c -t i v e s t r e s s f a i l u r e e n v e l o p e s ( t a n g e n t s t o t h e s t r e s s p a t h s t h r o u g h t h e o r i g i n ) w e r e a p p r o a c h e d ( F i g . 8 . 3 ) a n d , i f d e f o r m a t i o n s i n t h e f i e l d a r e t o be l i m i t e d , t h e i m p o s e d s t r e s s e s m u s t be c o n t r o l l e d so t h a t t h e s t r e s s p a t h s do n o t g e t t o o c l o s e t o t h e f a i l u r e e n v e l o p e s . E x t e n s i o n t e s t s , i n p a r t i c u l a r , r e q u i r e d v e r y s m a l l l o a d i n g b e f o r e t h e e f f e c t i v e s t r e s s p a t h s g o t v e r y c l o s e t o t h e f a i l u r e e n v e l o p e s . Maximum d e v i a t o r s t r e s s was r e a c h 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 ( ° " i 7 a 3 ) m a x o c c u r r e d f o r b o t h c o m p r e s s i o n and e x t e n s i o n s t r e s s p a t h s . I t i s i n t e r e s t i n g t o o b s e r v e t h a t t h e c o m p r e s s i o n e f f e c t i v e s t r e s s p a t h s s t a y e d t o t h e l e f t o f t h e s t a r t i n g p o i n t , P , e v e n u n t i l maximum d e v i a t o r s t r e s s was r e a c h e d . T h i s i m p l i e s t h a t i n t h e c o n v e n t i o n a l p a s s i v e c o m p r e s s i o n t e s t , i n w h i c h a A i s h e l d c o n s t a n t , p o s i t i v e p o r e p r e s s u r e s a r e g e n e r a t e d u n t i l f a i l u r e , and h e n c e a v o l u m e c o n t r a c t i o n w i l l o c c u r d u r i n g d r a i n e d s h e a r o f an i d e n t i c a l s a m p l e . SL 4 CTz'c 8 CT: r 4 zc Q / / B / 1 ( a ) TRIAXIAL Q \ T 6 — I€,l% \ A i r k / \\ 1 \ 4 1 ( b ) PLANE STRAIN ok y+-5 / 3 / \c - I P / \ / • >- 6 • zl /o y y • 4-2 s u 3 ^ - " — 8 C ^ ' / C T z c Fig.8-3 - EFFECTIVE STRESS PATHS DURING UNDRAINED TRIAXIAL AND PLANE STRAIN SHEAR O.C.HANEY CLAY. 8 . 1 . 2 D r a i n e d T e s t R e s u l t s A l t h o u g h t h e d e v i a t o r s t r e s s - s t r a i n b e h a v i o u r was s t i f f e r i n p a s s i v e c o m p r e s s i o n when c o m p a r e d t o p a s s i v e e x t e n s i o n ( F i g . 8 . 4 ) t h e a x i a l s t r a i n s t o f a i l u r e w e r e e s s e n t i a l l y t h e same ( T a b l e V I I I , I X ) . 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 t h e s a m p l e s u b j e c t e d t o a c t i v e c o m p r e s s i o n d i d n o t f a i l e v e n when t h e l a t e r a l e f f e c -t i v e s t r e s s was r e d u c e d t o a l m o s t z e r o ( p l a n e s t r a i n t e s t u n d e r t h e same s t r e s s p a t h was n o t p e r f o r m e d f o r t h i s r e a s o n ) . S i n c e t h e c l a y was o v e r c o n s o l i d a t e d , i t i s n o t s u r p r i s i n g t h a t i t s s t r e n g t h f o r t h e e f f e c t i v e s t r e s s s t a t e , = o ^ c ; ~ 0 , e x c e e d e d t h e maximum a p p l i e d s h e a r s t r e s s , a " 12. The s a m p l e w a s , t h e r e f o r e , c a u s e d t o f a i l by i n c r e a s i n g t h e v e r t i c a l s t r e s s , w h i l e l a t e r a l s t r e s s was m a i n t a i n e d a t t h e r e d u c e d v a l u e o f a p p r o x i m a t e l y z e r o . The d i s c o n t i n u i t y i n t h e d e v i a t o r s t r e s s - s t r a i n c u r v e i s a r e s u l t o f t h i s c h a n g e i n t h e mode o f l o a d i n g . A s i m i l a r d i s c o n t i n u i t y i n t h e p l a n e s t r a i n a c t i v e e x t e n s i o n s t r e s s - s t r a i n c u r v e ( F i g . 8 . 4 b ) i s a l s o due t o t h e c h a n g e o v e r t o t h e p a s s i v e t y p e e x t e n s i o n l o a d i n g a f t e r t h e v e r t i c a l e f f e c t i v e s t r e s s was r e d u c e d t o a l m o s t z e r o w i t h t h e s a m p l e u n d e r g o i n g no f a i l u r e . (b) PLANE STRAIN -12 -8 -4 0 4 8 Axial strain - € z % Fig.8.4 - DEVIATOR STRESS-STRAIN RELATIONSHIPS DURING DRAINED TRIAXIAL AND PLANE STRAIN SHEAR - O.C. HANEY CLAY . P a s s i v e c o m p r e s s i o n g a v e r i s e t o a v o l u m e c o n -t r a c t i o n u n t i l f a i l u r e ( F i g . 8 . 5 ) , w h i c h i s n o t t y p i c a l f o r t h e c o m p r e s s i o n o f h e a v i l y o v e r c o n s o l i d a t e d c l a y s . P o s s i b l e r e a s o n s f o r s u c h b e h a v i o u r h a v e a l r e a d y been c o n s i d e r e d i n t h e p r e v i o u s s e c t i o n on u n d r a i n e d t e s t s . T h e r e was a l s o a v o l u m e d e c r e a s e up t o f a i l u r e d u r i n g p a s s i v e e x t e n s i o n . H o w e v e r , t h i s v o l u m e d e c r e a s e was v e r y s m a l l and h e n c e t h e s h e a r b e h a v i o u r was v e r y c l o s e t o t h a t o f c o r r e s p o n d i n g u n d r a i n e d t e s t s . Due t o r e d u c t i o n o f e f f e c t i v e s t r e s s e s t o v e r y s m a l l v a l u e s i n a c t i v e c o m p r e s s i o n and e x t e n s i o n , v o l u m e e x p a n s i o n was q u i t e l a r g e . The d i s c o n t i n u i t y i n t h e v o l u m e t r i c s t r a i n c u r v e i n F i g . 8 . 5 b i s due t o t h e c h a n g e o v e r f r o m a c t i v e t o p a s s i v e e x t e n s i o n s h e a r , r e q u i r e d t o c a u s e f a i l u r e . 8 . 1 . 3 C o m p a r i s o n o f D r a i n e d and U n d r a i n e d B e h a v i o u r The c o n c e p t s o f u n i q u e n e s s o f v o i d r a t i o and e f f e c t i v e s t r e s s e s d u r i n g d r a i n e d and u n d r a i n e d s h e a r h a v e n o t g e n e r a l l y b e e n e x t e n d e d t o h e a v i l y o v e r c o n -s o l i d a t e d c l a y s , and i n p a r t i c u l a r f o r c l a y s w i t h o n e -d i m e n s i o n a l c o n s o l i d a t i o n h i s t o r y . T h e r e f o r e , no a t -t e m p t was made t o c o r r e l a t e v o l u m e c h a n g e s i n d r a i n e d (a ) TRIAXIAL Extension o Passive . Active r \ Compression •+• Passive A. Active -8 1 (b)PLANE STRAIN Q _ -o—o—o_ Extension .—.—y ° Passive Active I .-4 — + .+ v ^Passive Compression -12 -8 -4 0 4 Axial strain - € z % 8 F i g . 8 - 5 - VOLUMETRIC STRAIN - AXIAL STRAIN RELATIONSHIPS DURING DRAINED TRIAXIAL AND PLANE STRAIN SHEAR -O.C. HANEY CLAY. tests with pore pressures generated in the corresponding undrained tests. For the same applied stress path, the undrained deviator stress-strain response was s t i f f e r than the corresponding drained response. The strain to peak deviator stress was essentially equal for active and passive undrained and drained passive stress paths (see Tables VIII, IX). Fig. 8.6 shows that the deviator stress-strain response was essentially identical for drained and undrained passive extension stress paths. As pointed out earlier, this was due to negligible volumetric strains during drained shear, thus rendering the drained test virtually undrained. Due to volume contraction during passive compres-sion, drained strength, ( a i - a 3 ) /2, was higher than the undrained (Tables VIII, IX). Due to negligible volume changes during drained passive extension, drained and undrained strengths were essentially the same. Drained active stress paths, due to volume expansion at failure, resulted in lower drained strength compared to the undrained. There is no immediate significance in the effective stress ratios, a{/os> at failure. This would be expected, since the use of an effective stress ratio is associated with linear failure envelopes passing (a ) TRIA XI AL ) ^ Undrained " X ft \ ( u Drained 1-5 10 0-5 0 (b)PLAN »—— E STRAIN -©"I + 1 T -drained \ 1 - Drained j 15 10 0-5 - 8 - 6 - 4 -2 0 Axial strain - € z % Fig.8.6- COMPARISON OF SHEAR STRESS STRAIN BEHAVIOUR DURING DRAINED AND UNDRAINED PASSIVE EXTENSION IN TRIAXIAL AND PLANE STRAIN -O.C.HANEY CLAY. t h r o u g h t h e o r i g i n , w h i c h i s c e r t a i n l y n o t t h e c a s e f o r a h e a v i l y o v e r c o n s o l i d a t e d c l a y . H o w e v e r , i f {01/03) i s p l o t t e d as a f u n c t i o n o f (p ') t h e n t h e r e s u l t s C ITla X T o f d r a i n e d and u n d r a i n e d , n o r m a l l y and o v e r c o n s o l i d a t e d t e s t s l i e on a common e n v e l o p e ( F i g . 8 . 7 ) . H e r e (p ) c max i s t h e maximum mean n o r m a l c o n s o l i d a t i o n s t r e s s and p^ i s t h e mean n o r m a l e f f e c t i v e s t r e s s a t (ar/cO . The max r e s u l t s g i v e n i n F i g . 8 . 7 a r e s i m p l y a more g e n e r a l e x p r e s s i o n o f t h e f a c t t h a t t h e e f f e c t i v e s t r e s s Mohr e n v e l o p e s f o r d r a i n e d and u n d r a i n e d t e s t s a r e i d e n t i c a l . H o w e v e r , d i f f e r e n t f a i l u r e e n v e l o p e s a r e o b t a i n e d f o r c o m p r e s s i o n and e x t e n s i o n s h e a r . S i m i l a r e n v e l o p e s w e r e u s e d by H e n k e l ( 1 9 6 0 ) and S i m o n s ( 1 9 6 0 ) t o e x p r e s s t r i a x i a l f a i l u r 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 c l a y s . 8 . 1 . 4 g ^ - S t r e s s i n P l a n e S t r a i n The v a r i a t i o n o f e f f e c t i v e s t r e s s e s d u r i n g u n d r a i n e d s h e a r i s shown i n F i g . 8 . 8 . D u r i n g e x t e n s i o n s h e a r , a , t h e p r i n c i p a l s t r e s s a s s o c i a t e d w i t h t h e d i r e c -t i o n o f z e r o s t r a i n , had a v a l u e i n t e r m e d i a t e b e t w e e n t h e o t h e r two p r i n c i p a l s t r e s s e s . H o w e v e r , c o m p r e s s i o n s h e a r i n v o l v e d i n i t i a l u n l o a d i n g o f s h e a r s t r e s s e s and (7^ was t h e m a j o r and n o 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 s t r e s s d u r i n g e a r l y s t a g e s o f c o m p r e s s i o n . I t i s a common (b) PLANE STRAIN Compression —, e 7 ©—< -Exte nsio n 0.4 0.6 0.8 I 2 4 6 8 10 20 30 (Pc)mox/Pf Fig.8.7 - TRIAXIAL AND PLANE STRAIN FAILURE ENVELOPES-N.C. AND O.C. HANEY CLAY. EFFECTIVE STRESS-STRAIN RELATIONSHIPS DURING UNDRAINED PLANE STRAIN SHEAR-O.C.HANEY CLAY. p r a c t i c e t o r e g a r d i n p l a n e s t r a i n as 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 . T h a t t h i s a s s u m p t i o n i s n o t a l w a y s " t r u e i s c l e a r l y i n d i c a t e d i n F i g . 8 . 8 ( a n d a l s o i n F i g . 5 . 3 f o r n o r m a l l y c o n s o l i d a t e d e x t e n s i o n s h e a r ) . The e x p l a n a t i o n o f f e r e d f o r . a n o t a s s u m i n g an i n t e r -m e d i a t e v a l u e i n n o r m a l l y c o n s o l i d a t e d e x t e n s i o n s h e a r a p p l i e s t o o v e r c o n s o l i d a t e d c o m p r e s s i o n s h e a r a l s o . The v a r i a t i o n o f s t r e s s r a t i o , ay/(0x+az)-> w i t h a x i a l s t r a i n was g e n e r a l l y s i m i l a r u n d e r d r a i n e d o r u n d r a i n e d , c o m p r e s s i o n o r e x t e n s i o n t y p e s o f s h e a r ( F i g . 8 . 9 ) . E x c e p t f o r some s c a t t e r d u r i n g d r a i n e d p a s s i v e e x t e n s i o n , t h e a v e r a g e v a l u e o f t h i s r a t i o a t f a i l u r e ( ( a i - a 3 ) m = „ ) was a r o u n d 0 . 4 3 a n d was p r a c t i c a l l y max i n d e p e n d e n t o f t h e s t r e s s p a t h . The c o r r e s p o n d i n g v a l u e f o r n o r m a l l y c o n s o l i d a t e d c l a y was 0 . 3 7 ± 0 . 0 2 . 8 . 2 . 0 C o m p a r i s o n o f T r i a x i a l and P l a n e S t r a i n R e s u l t s An e v a l u a t i o n o f t h e c o m p a r a t i v e t r i a x i a l and p l a n e s t r a i n b e h a v i o u r , u n d e r t h e same s t r e s s p a t h , w i l l be made w i t h r e f e r e n c e t o F i g s . 8 . 1 t o 8 . 7 , i n w h i c h t r i a x i a l and p l a n e s t r a i n r e s u l t s w e r e p r e s e n t e d s i d e by s i d e . A summary o f t h e c o m p a r i s o n i s c o n t a i n e d i n T a b l e X . D r a i n e d a c t i v e c o m p r e s s i o n and e x t e n s i o n s t r e s s p a t h s d i d n o t c a u s e f a i l u r e o f e i t h e r t h e t r i a x i a l 0.8 -6 - O . 6 0 V + . o • O X o ! o Extension 0.4 b O Undroined • Drained act ive Q £ x D ra ined passive -4 -2 (CT-<J,) >| 3 max * + Compression + Undrained ® Drained p a s s i v e Axial strain - £ ,°/o Fig.8.9- VARIATION OF STRESS RATIO.CXy/ (C^ +O^ ') WITH AXIAL STRAIN DURING PLANE STRAIN SHEAR O.C. HANEY CLAY . End o f C o n s o l i d a t i o n F a i l u r e C o n d i t i o n O . C . R . v 1 3 / m a x (a r / 0 3 ) m a x a z ' c K 0 Pc ^max ^ p c ^max Pc o" i - o 3 0 - 1 / 0 - 3 v% a a i - a 3 or/03 a U n d r a i n e d C o m p r e s s i o n T r i a x i a l P l a n e S t r a i n 0 . 3 2 0 . 3 5 2 . 1 1 1 . 6 4 0 . 5 6 0 . 50 1 8 . 6 1 7 . 3 7 . 4 8 . 1 7 . 8 3 . 8 1 . 3 0 1 . 4 2 3 . 0 5 4 . 5 0 0 - 0 . 6 2 - 0 . 4 8 3 . 5 0 2 . 5 0 1 . 0 6 1 . 1 6 3 . 4 5 4 . 8 0 0 - 0 . 3 6 - 0 . 3 0 U n d r a i ned E x t e n s i o n T r i a x i a l P l a n e S t r a i n 0 . 3 1 0 . 3 8 2 . 2 0 1 . 6 8 0 . 5 5 0 . 5 6 1 9 . 2 1 5 . 6 7 . 6 7 . 6 - 7 . 8 - 4 . 0 1 . 0 5 1 . 1 4 3 . 1 0 3 . 1 0 0 0 - 1 . 9 - 1 . 2 6 - 3 . 0 - 2 . 1 0 . 8 8 1 . 0 1 3 . 4 5 3 . 3 0 0 - 1 . 6 8 - 1 . 0 5 D r a i ned P a s s i v e C o m p r e s s i o n T r i a x i a l P l a n e S t r a i n 0 . 3 3 0 . 3 5 1 . 7 4 1 . 5 9 0 . 5 0 0 . 5 6 1 8 . 1 1 6 . 6 8 . 3 8 . 5 6 . 0 4 . 8 1 . 4 8 1 . 6 6 3 . 3 5 4 . 2 0 . 7 2 . 2 — 6 . 0 4 . 8 1 . 4 8 1 . 6 6 3 . 3 5 4 . 2 0 . 7 2 . 2 — D r a i ned P a s s i v e E x t e n s i on T r i a x i a l P l a n e S t r a i n 0 . 3 1 0 . 38 1 . 9 8 1 . 5 8 0 . 5 2 0 . 5 3 1 9 . 1 1 5 . 4 8 . 0 7 . 7 - 8 . 0 - 4 . 0 1 . 0 6 1 . 1 8 3 . 2 3 . 4 0 . 4 0 . 2 — - 8 . 0 - 4 . 0 1 . 0 6 1 . 1 8 3 . 2 3 . 4 0 . 4 0 . 2 — S t r e s s e s i n K g / c m 2 CO o r p l a n e s t r a i n s a m p l e s , and h e n c e a r e n o t c o n s i d e r e d f o r c o m p a r i s o n i n T a b l e X . U n f o r t u n a t e l y , t h e end o f c o n s o l i d a t i o n s t r e s s e s i n t r i a x i a l and p l a n e s t r a i n s a m p l e s , t e s t e d u n d e r t h e same a p p l i e d s t r e s s p a t h , w e r e n o t s t r i c t l y i d e n t i c a l . A p r e c i s e c o n t r o l o f t h e r e b o u n d v e r t i c a l s t r e s s i n p l a n e s t r a i n s a m p l e s c o u l d n o t be e x e r c i s e d due t o v a r y i n g a m o u n t s o f s i d e f r i c t i o n f r o m s a m p l e t o s a m p l e . As a r e s u l t , t h e s e s a m p l e s , a t t h e c o m p l e t i o n o f r e b o u n d , e n d e d u p , i n g e n e r a l , w i t h s l i g h t l y h i g h e r v e r t i c a l e f f e c t i v e s t r e s s e s and l o w e r K v a l u e s t h a n o t h e c o r r e s p o n d i n g t r i a x i a l s a m p l e s . H o w e v e r , i t i s f e l t t h a t t h e s m a l l d i f f e r e n c e s i n end o f c o n s o l i d a t i o n c o n d i t i o n s a r e n o t l i k e l y t o i n f l u e n c e t h e c o m p a r a t i v e t r i a x i a l and p l a n e s t r a i n s t r e s s - s t r a i n b e h a v i o u r t o a n y s i g n i f i c a n t e x t e n t . In p a r t i c u l a r , t h e f a i l u r e c o n d i t i o n s s h o u l d be t h e l e a s t a f f e c t e d . C o n v e n t i o n a l c o m p a r i s o n o f t h e t r i a x i a l and p l a n e s t r a i n b e h a v i o u r i s c o n s i d e r e d i n t h i s s e c t i o n . O c t a h e d r a l s t r e s s - s t r a i n and f a i l u r e r e l a t i o n s h i p s w i l l be d e a l t w i t h i n a l a t e r s e c t i o n . 8 . 2 . 1 S t r e s s - S t r a i n B e h a v i o u r F o r a l l t h e s t r e s s p a t h s s t u d i e d , p l a n e s t r a i n d e v i a t o r s t r e s s - s t r a i n b e h a v i o u r was s t i f f e r t h a n t h e c o r r e s p o n d i n g t r i a x i a l b e h a v i o u r . T h i s c a n be e a s i l y s e e n i n F i g s . 8.1 and 8.4 w h e r e , f o r a n y g i v e n a p p l i e d s t r e s s p a t h , t h e p l a n e s t r a i n c u r v e s o c c u p y a h i g h e r l o c a -t i o n t h a n 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 u r v e s . In g e n e r a l , t h e a x i a l s t r a i n t o peak d e v i a t o r s t r e s s i n p l a n e s t r a i n was a b o u t o n e - h a l f t h e v a l u e f o r t h e t r i a x i a l c o n d i t i o n s . T h i s was t r u e f o r u n d r a i n e d c o m p r e s s i o n and e x t e n s i o n a n d d r a i n e d p a s s i v e e x t e n s i o n s t r e s s p a t h s ( T a b l e X ) . D u r i n g d r a i n e d p a s s i v e c o m p r e s s i o n s t r e s s p a t h t h e a x i a l s t r a i n t o f a i l u r e i n p l a n e s t r a i n was a b o u t 75% o f t h e t r i a x i a l v a l u e . A l s o , p l a n e s t r a i n c o m p r e s s i o n f a i l u r e ( ( t J i - a 3 ) m , J max o c c u r r e d w i t h a c h a r a c t e r i s t i c s h a r p p e a k w h i c h was n o t p r e s e n t i n t h e c a s e o f t r i a x i a l f a i l u r e ( F i g s . 8 . 1 , 8.4). U n d r a i n e d c o m p r e s s i o n s t r e n g t h , ( o " i - 0 3 ) / 2 , i n p l a n e s t r a i n was h i g h e r t h a n t h e t r i a x i a l v a l u e by a b o u t 9%, c o r r e s p o n d i n g t o b o t h , ( o r 0 3 ) m , v and ( o ( / a J ) m a v max max f a i l u r e c o n d i t i o n s ( T a b l e X ) . S i m i l a r l y , p l a n e s t r a i n e x t e n s i o n u n d r a i n e d s t r e n g t h was h i g h e r t h a n t h e t r i a x i a l by r e s p e c t i v e l y 9% and 13% w i t h r e s p e c t t o t h e same two f a i l u r e c o n d i t i o n s . I t i s c o n c l u d e d t h a t d u r i n g u n d r a i n e d s h e a r o f u n d i s t u r b e d h e a v i l y o v e r c o n s o l i d a t e d Haney c l a y , p l a n e s t r a i n c o n d i t i o n s g i v e r i s e t o h i g h e r s t r e n g t h and l o w e r s t r a i n t o f a i l u r e t h a n t r i a x i a l c o n d i t i o n s . B o t h c o m p r e s s i o n and e x t e n s i o n u n d r a i n e d e f f e c -t i v e s t r e s s p a t h s on (a',a') p l a n e w e r e v e r y s i m i l a r A Z f o r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s ( F i g . 8 . 3 ) . F o r b o t h t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s , d u r i n g c o m p r e s s i o n o r e x t e n s i o n s h e a r , (oi/ot) max o c c u r r e d a t a s m a l l e r s t r a i n t h a n ( a i - a 3 ) m a x ' A x i a l s t r a i n s i n t r i a x i a l c o r r e s p o n d i n g t o [01/0$) max w e r e a b o u t 1 - 1 / 2 t i m e s t h o s 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 . A l s o , s t r a i n s w e r e f o u n d t o i n c r e a s e v e r y r a p i d l y a s t h e e f f e c t i v e s t r e s s f a i l u r e e n v e l o p e s w e r e a p p r o a c h e d . T h i s a p p l i e d t o b o t h c o m p r e s s i o n o r e x t e n s i o n s h e a r i n p l a n e s t r a i n and t r i a x i a l . 8 . 2 . 2 P o r e P r e s s u r e s and V o l u m e C h a n g e s The d i l a t i n g t e n d e n c y d u r i n g u n d r a i n e d t r i a x i a l e x t e n s i o n was l a r g e r t h a n t h a t 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 . T h i s i s s e e n i n F i g . 8 . 2 w h e r e ' a ' v a l u e s i n t r i a x i a l a r e more n e g a t i v e t h a n t h e c o r r e s p o n d i n g p l a n e s t r a i n v a l u e s . T h u s , p l a n e s t r a i n b o u n d a r y c o n d i t i o n s i n o v e r c o n s o l i d a t e d c l a y l e a d t o s u p r e s s e d d i l a t a n c y i n c o m p a r i s o n t o a x i s y m m e t r i c s t r e s s c o n d i t i o n s , a s has b e e n shown t o be t h e c a s e i n s a n d s ( C o r n f o r t h , 1 9 6 4 ; F i n n e j t . aj_. , 1 9 6 7 ) . S i m i l a r l y , d u r i n g u n d r a i n e d c o m p r e s s i o n ' a ' v a l u e s a t f a i l u r e i n t r i a x i a l w e r e more n e g a t i v e t h a n t h e c o r r e s p o n d i n g f a i l u r e v a l u e s i n p l a n e s t r a i n ( T a b l e X ) . V o l u m e c h a n g e s d u r i n g d r a i n e d s h e a r a r e t h e c o m b i n e d e f f e c t o f c h a n g e s i n mean n o r m a l s t r e s s e s and t h e a p p l i e d s h e a r s t r e s s e s . P a s s i v e c o m p r e s s i o n i n p l a n e s t r a i n g a v e r i s e t o l a r g e r v o l u m e c o m p r e s s i o n t h a n t r i a x i a l ( F i g . 8 . 5 ) , b e c a u s e o f l a r g e r i n c r e a s e s i n mean n o r m a l s t r e s s e s ( d u e t o h i g h e r [01/03) a t f a i l u r e ) and s m a l l e r d i l a t a n c y e f f e c t s . B o t h t r i a x i a l and p l a n e s t r a i n s a m p l e s c o n t r a c t e d u n t i l f a i l u r e ( T a b l e X ) . As d i s c u s s e d e a r l i e r , t h i s i s n o t a f a m i l i a r b e h a v i o u r f o r h e a v i l y o v e r c o n s o l i d a t e d c l a y s . P a s s i v e e x t e n s i o n d r a i n e d s h e a r r e s u l t e d i n v i r t u a l l y l i t t l e v o l u m e c h a n g e s . T h i s was a p p a r e n t l y due t o s m a l l c h a n g e s i n mean n o r m a l s t r e s s e s t o f a i l u r e and t h e c o u n t e r a c t i n g i n f l u e n c e o f s h e a r d i l a t a n c y . 8 . 2 . 3 F a i l u r e C o n d i t i o n s The t r i a x i a l and p l a n e s t r a i n g e n e r a l i s e d f a i l u r e e n v e l o p e s a r e shown i n F i g . 8 . 7 . C o n s i d e r i n g t h e p a r t s o f t h e e n v e l o p e s r e l e v a n t t o t h e o v e r c o n s o l i -d a t e d s o i l o n l y , 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 f a i l u r e e n v e l o p e l i e s a b o v e t h e t r i a x i a l c o m p r e s s i o n e n v e l o p e . T h u s , t r i a x i a l t e s t r e s u l t s w o u l d u n d e r p r e d i c t t h e p l a n e s t r a i n s t r e n g t h . H o w e v e r , t h e o v e r c o n s o l i d a t e d t r i a x i a l and p l a n e s t r a i n e x t e n s i o n f a i l u r e e n v e l o p e s a r e v i r t u a l l y i d e n t i c a l . The f a i l u r e ((a{/ot)m^v) s t a t e o f t h e o v e r c o n -m a x s o l i d a t e d s a m p l e s on t h e f a m i l i a r ( o i - c 3 ) / 2 v s . (or+03*)/2 p l o t i s shown i n F i g . 8 . 1 0 . I t c a n a g a i n be 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 e n v e l o p e l i e s d i s t i n c t l y a b o v e t h e t r i a x i a l c o m p r e s s i o n e n v e l o p e . E x t e n s i o n f a i l u r e e n v e l o p e s f o r t h e two t y p e s o f t e s t s a r e c o m p a r a t i v e l y much c l o s e r t o e a c h o t h e r . 8 . 3 . 0 O c t a h e d r a l 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 8 . 3 . 1 E f f e c t i v e S t r e s s P a t h s . In C h a p t e r V I I i t was shown t h a t d u r i n g n o r m a l l y c o n s o l i d a t e d u n d r a i n e d c o m p r e s s i o n t e s t s , w h i c h d i d n o t i n v o l v e u n l o a d i n g 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 e s , common o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s w e r e f o l l o w e d u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s . In o v e r c o n s o l i d a t e d c l a y s a m p l e s , e x t e n s i o n and n o t c o m p r e s s i o n t e s t i n g c o r r e s p o n d s t o no i n i t i a l u n l o a d i n g o f s h e a r s t r e s s e s a n d , t h e r e f o r e , e x t e n s i o n e f f e c t i v e s t r e s s p a t h s a r e e x p e c t e d t o be common t o t r i a x i a l and p l a n e s t r a i n c o n -d i t i o n . F i g . 8 . 1 1 shows t h e s e e f f e c t i v e s t r e s s p a t h s . 2.0 1.0 E u o» 1 CM b" 0.5 Extension P l a n e s t r a i n - T r i a x i a l 0.5 1.0 1.5 2.0 — r — kg/cm Fig.8.10- TRIAXIAL AND PLANE STRAIN FAILURE ENVELOPES - O.C. HANEY CLAY. o + 4-0 + +-+ o + o • +• Tri axia 1 o Plane Strain i 1.2 1.4 1.6 1.6 P_ Pc 2.0 Fig.8.11- OCTAHEDRAL EFFECTIVE STRESS PATHS DURING UNDRAINED TRIAXIAL AND PLANE STRAIN EXTENSION-O.C. HANEY CLAY. E x c e p t f o r some s c a t t e r n e a r f a i l u r e t h e s t r e s s p a t h s may be c o n s i d e r e d u n i q u e . 8 . 3 . 2 S t r e s s - S t r a i n C o m p a r i s o n s  U n d r a i n e d E x t e n s i o n The u n i q u e n e s s o f e f f e c t i v e s t r e s s p a t h s i n t h e o c t a h e d r a l p l a n e d u r i n g u n d r a i n e d e x t e n s i o n s u g g e s t s t h e e x i s t e n c e o f a common o c t a h e d r a l s h e a r 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 m i l a r t o t h a t f o u n d e a r l i e r ( C h a p t e r V I I ) f o r n o r m a l l y c o n s o l i d a t e d u n d r a i n e d c o m -p r e s s i o n t e s t s . F i g . 8 . 1 2 shows t h e o c t a h e d r a l s t r e s s -s t r a i n r e l a t i o n s h i p f o r o v e r c o n s o l i d a t e d c l a y i n e x t e n -s i o n . T h e r e i s a good a g r e e m e n t b e t w e e n t r i a x i a l a n d p l a n e s t r a i n r e l a t i o n s h i p s , e x c e p t n e a r f a i l u r e . U n d r a i n e d C o m p r e s s i o n C o m p r e s s i o n s t r e s s p a t h s i n v o l v e d i n i t i a l u n -l o a d i n g o f T o c t - T h e r e f o r e , t h e o c t a h e d r a l s t r e s s - s t r a i n r e l a t i o n b e t w e e n AT q c £ ( d e f i n e d i n E q . 7 . 6 ) and Y O C T > s i m i l a r t o t h a t o b s e r v e d f o r n o r m a l l y c o n s o l i d a t e d e x t e n s i o n t e s t s , may be e x p e c t e d t o be t h e same f o r p l a n e s t r a i n and t r i a x i a l . The e x p e r i m e n t a l r e l a t i o n -s h i p s a r e shown i n F i g . 8 . 1 3 . Due t o s i g n i f i c a n t d i f -f e r e n c e b e t w e e n c o n s o l i d a t i o n mean n o r m a l s t r e s s , p , 0.4 0 ( o o ) + 3 O O o l 4 O + •+ o + 0 + + Triaxial o Plane Strain i 0 I 2 3 4 5 *)©et % Fig.8.12 - OCTAHEDRAL SHEAR STRESS- STRAIN RELATIONSHIP DURING UNDRAINED TRIAXIAL AND PLANE STRAIN EXTENSION - 0. C . HANEY CLAY. 1.6 Pc oct 0 . 8 0-4 0 6-O 4-G 4 0 4-4-> G o + 4-0 • i 4- Triaxial o Plane Strain 1 *)'oct% Fig. 8.13 - OCTAHEDRAL SHEAR STRESS - STRAIN RELATIONSHIP DURING UNDRAINED TRIAXIAL AND PLANE STRAIN COMPRESSION - O.C.HANEY CLAY . on t r i a x i a l and p l a n e s t r a i n s a m p l e s ( T a b l e X ) , t h e o r d i n a t e i n F i g . 8 . 1 3 has b e e n d i v i d e d by p c > The a g r e e m e n t b e t w e e n t h e t r i a x i a l and p l a n e s t r a i n r e s u l t s i s s e e n t o be f a i r l y g o o d . D r a i n e d T e s t s I t was shown e a r l i e r t h a t v o l u m e c h a n g e s d u r i n g p a s s i v e e x t e n s i o n d r a i n e d t e s t s w e r e s o s m a l l t h a t t h e s e t e s t s c o u l d v i r t u a l l y be r e g a r d e d as u n d r a i n e d . T h i s t h e n i m p l i e s t h a t t h e o c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n s h i p w h i c h was f o u n d common t o u n d r a i n e d t r i -a x i a l and p l a n e s t r a i n e x t e n s i o n w o u l d a l s o h o l d f o r d r a i n e d p a s s i v e e x t e n s i o n . T o c i v s • Y o c t r e l a t i o n s h i p s o b s e r v e d d u r i n g d r a i n e d p a s s i v e e x t e n s i o n a r e shown i n F i g . 8 . 1 4 . The a g r e e m e n t b e t w e e n t r i a x i a l a n d p l a n e s t r a i n r e l a t i o n s h i p s seems good a t s m a l l s t r a i n (< 1%) . O c t a h e d r a l s t r e s s r a t i o - s t r a i n r e l a t i o n s d u r i n g d r a i n e d t r i a x i a l and p l a n e s t r a i n p a s s i v e c o m -p r e s s i o n a r e shown i n F i g . 8 . 1 5 . S i m i l a r t o t h e c a s e 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 , r e a s o n a b l e a g r e e m e n t b e t w e e n t r i a x i a l and p l a n e s t r a i n r e s u l t was o b t a i n e d a t s m a l l s h e a r s t r a i n s f o r ( g e n e r a l l y 1% o r l e s s ) o v e r -c o n s o l i d a t e d c l a y . A t l a r g e r v a l u e s o f s h e a r s t r a i n s t r i a x i a l r e s u l t s c o r r e s p o n d e d t o h i g h e r T 0 C|-/P r a t i o f o r a g i v e n v a l u e o f s t r a i n . 0.5 0.4 0.2 0.1 0 A ( 0 0 0 > + \~J + + 0 + 4-0+ + 1 o + Triaxial o Plane Strain L . 0 I 2 3 4 5 Fig. 8.14- OCTAHEDRAL SHEAR STRESS" STRAIN RELATIONSHIP DURING DRAINED TRIAXIAL AND PLANE STRAIN PASSIVE EXTENSION-O.C.HANEY CLAY . 0.8 0.6 Toct 0.4 P + + + + c o -o c + 0 + o ^ J + 0 + o t-L________ +• Triaxial o Plane Strain 0 1 2 3 4 5 Fig. 8.15 - OCTAHEDRAL STRESS RATIO- SHEAR STRAIN RELATION DURING DRAINED TRIAXIAL AND PLANE STRAIN PASSIVE COMPRESSION -0. C. HANEY CLAY. 8.3.3 F a i l u r e C onditions  Undrained Strength The conventional measure of the undrained s t r e n g t h , ( o i - a 3 ) / 2 , was shown to be s m a l l e r under t r i a x i a l than under plane s t r a i n c o n d i t i o n s . The con-c l u s i o n was v a l i d f o r both compression and extension s t r e s s paths and at both ( a r a 3 ) m 3 v or (a {/a 3 ) M 3 V ma x max f a i l u r e c o n d i t i o n s . These apparent d i f f e r e n c e s were ex p l a i n e d f o r normally c o n s o l i d a t e d c l a y s when undrained streng t h was c h a r a c t e r i s e d by (T^  . ) m o . S i m i l a r com-0 c T. max parisons f o r o v e r c o n s o l i d a t e d samples are presented i n Table XI. It can be seen that the t r i a x i a l and plane s t r a i n undrained extension f a i l u r e occurs at e s s e n t i a l l y the same values of T 0 C f I n a x i a l compression, however, the r a t i o ^ T o c i / P c w a s found to be the c r i t i c a l param-e t e r , which was e s s e n t i a l l y equal under t r i a x i a l and plane s t r a i n c o n d i t i o n s . The reason f o r t h i s was e x p l a i n e d e a r l i e r while d i s c u s s i n g normally c o n s o l i -dated undrained extension f a i l u r e (Chapter V I I ) . F a i l u r e C r i t e r i a During conventional comparison of o v e r c o n s o l i d a t e d t r i a x i a l and plane s t r a i n r e s u l t s , i t was shown that o v e r c o n s o l i d a t e d Mohr envelopes were higher f o r plane C o - r e l a t i o n o f U n d r a i n e d S t r e n g t h U n d e r T r i a x i a l and P l a n e S t r a i n C o n d i t i o n s — O . C . H a n e y C l a y F a i l u r e Cond i t i on ( a i - a 3 ) m a x o r ^ o c t ^ a x ( a r / a 3 ) m a x o r ^ o c t ^ m a x U n d r a i n e d E x t e n s i o n ( 0 - 1 - 0 - 3 ) T o c t ( a i - 0 - 3 ) T o c t T r i a x i a l 1 . 0 5 0 . 4 8 0 . 8 8 0 . 4 4 P l a n e s t r a i n 1 . 1 4 0 . 4 7 1 . 0 1 0 . 4 3 U n d r a i n e d C o m p r e s s i o n ( 0 1 - 0 - 3 ) ^ o c t / P c ( 0 1 - 0 - 3 ) A T o c t / p c T r i a x i a l 1 . 3 0 1 . 3 9 1 . 0 6 1 . 2 1 P l a n e s t r a i n 1 . 4 2 1 . 4 1 1 . 1 6 1 . 2 5 S t r e s s e s i n k g / c m 2 ro s t r a i n t h a n f o r t h e t r i a x i a l c o n d i t i o n s , t h o u g h t h e e x t e n s i o n e n v e l o p e s d i f f e r e d o n l y t o a s m a l l e x t e n t ( F i g . 8 . 1 0 ) . T h i s i m p l i e s t h a t p l a n e s t r a i n s t r e n g t h w i l l be u n d e r e s t i m a t e d by 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 . Enough o v e r c o n s o l i d a t e d t e s t s w e r e n o t p e r f o r m e d i n e i t h e r t r i a x i a l o r p l a n e s t r a i n g r o u p s t o e n a b l e t h e o v e r c o n s o l i d a t e d Mohr f a i l u r e e n v e l o p e s t o be a c c u r a t e l y d e f i n e d . In t h e a b s e n c e o f a p p r o p r i a t e v a l u e s o f z' and cf>" f o r o v e r c o n s o l i d a t e d Haney c l a y , e x a m i n a t i o n o f t h e v a l i d i t y o f o t h e r f a i l u r e c r i t e r i a ( i . e . T r e s c a and von M i s e s ) was n o t a t t e m p t e d . CHAPTER IX SUMMARY AND CONCLUSIONS The r e s u l t s o f t r i a x i a l and p l a n e s t r a i n t e s t s h a v e b e e n d e s c r i b e d i n w h i c h u n d i s t u r b e d H a n e y c l a y was i n i t i a l l y c o n s o l i d a t e d t o ' i d e n t i c a l ' K - s t r e s s e s . N o t o o n l y t h e c o n v e n t i o n a l p a s s i v e c o m p r e s s i o n b u t a l s o a number o f o t h e r s t r e s s p a t h s w e r e i m p o s e d t o i n d u c e c o m p r e s s i o n o r e x t e n s i o n , d r a i n e d o r u n d r a i n e d f a i l u r e . T e s t r e s u l t s w e r e a n a l y s e d i n o r d e r t o : 1 . Compare a n d c o r r e l a t e r e s u l t s 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 f o r t h e same s t r e s s s y s t e m ( t r i a x i a l o r p l a n e s t r a i n ) , and 2 . Compare and c o r r e l a t e t r i a x i a l a n d p l a n e s t r a i n b e h a v i o u r u n d e r i d e n t i c a l s t r e s s p a t h s t o f a i 1 u r e . The s t u d y r e p o r t e d h e r e i n i s b e l i e v e d t o be t h e f i r s t o f i t s k i n d , i n w h i c h t h e b e h a v i o u r o f a n a t u r a l c l a y has b e e n c o m p a r e d and c o r r e l a t e d u n d e r t r i a x i a l a n d p l a n e s t r a i n c o n d i t i o n s , u s i n g a v a r i e t y o f s t r e s s p a t h s d u r i n g s h e a r . In a d d i t i o n , b o t h n o r m a l l y and h e a v i l y o v e r c o n s o l i -d a t e d p r e s h e a r c o n d i t i o n s h a v e b e e n c o n s i d e r e d . The r e s p o n s e o f Haney c l a y t o a v a r i a t i o n i n a p p l i e d s t r e s s p a t h t o f a i l u r e was s i m i l a r f o r b o t h g r o u p s ( t r i a x i a l and p l a n e s t r a i n ) o f t e s t s . On t h e b a s i s o f t h e r e s u l t s on n o r m a l l y c o n s o l i d a t e d Haney c l a y , t h e f o l l o w i n g c o n c l u s i o n s w e r e d e r i v e d w i t h r e g a r d t o 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 : 1 . T h e r e was no s i m i l a r i t y b e t w e e n u n d r a i n e d s t r e s s -s t r a i n b e h a v i o u r i n c o m p r e s s i o n and e x t e n s i o n ; e . g . , f o r t h e c l a y t e s t e d , t h e a x i a l s t r a i n t o p e a k d e v i a t o r s t r e s s i n e x t e n s i o n was 15 t i m e s l a r g e r t h a n i n c o m p r e s s i o n . F u r t h e r m o r e , t h e a x i a l s t r a i n t o peak d e v i a t o r s t r e s s i n d r a i n e d s h e a r was a f u n c t i o n o f t h e a p p l i e d c o m p r e s s i o n o r e x t e n s i o n s t r e s s p a t h ; e . g . , u n l o a d i n g s t r e s s p a t h s w e r e a s s o c i a t e d w i t h s m a l l e r f a i l u r e s t r a i n t h a n s i m i l a r l o a d i n g s t r e s s p a t h s . 2 . U n d r a i n e d s t r e n g t h i n e x t e n s i o n was c o n s i d e r a b l y s m a l l e r t h a n t h a t i n c o m p r e s s i o n . F o r t h e c l a y t e s t e d , t h i s was a s s o c i a t e d w i t h l a r g e r s h e a r i n d u c e d p o r e p r e s s u r e s and s m a l l e r cf>' i n e x t e n s i o n when c o m p a r e d t o t h a t u n d e r , c o m p r e s s i o n . 3 . F o r a g i v e n t y p e o f s h e a r ( c o m p r e s s i o n o r e x t e n -s i o n ) , t h e a n g l e o f s h e a r r e s i s t a n c e , <j>", was i n d e p e n d e n t o f t h e s t r e s s p a t h and d r a i n a g e c o n d i t i o n s when lal-ot) 3 ma x was u s e d as t h e f a i l u r e c o n d i t i o n a n d d r a i n e d t e s t r e s u l t s w e r e c o r r e c t e d f o r v o l u m e c h a n g e r a t e s . H o w e v e r , f o r t h e s e n s i t i v e H a n e y c l a y , <j>' i n u n d r a i n e d c o m p r e s s i o n c o r r e s -p o n d i n g t o ( c T i - a 3 ) . v f a i l u r e c o n d i t i o n was 5° s m a l l e r t h a n max <K a t (a{/a$) m^v f a i l u r e c o n d i t i o n . In a d d i t i o n , i n max e x t e n s i o n was s m a l l e r t h a n <(>' i n c o m p r e s s i o n a t ( a i / o 3 ) m a x -T h i s r e s u l t f o r H a n e y c l a y , i n w h i c h cf>" i n e x t e n s i o n was 5° s m a l l e r t h a n i n c o m p r e s s i o n , i s c o n t r a r y t o t h e r e s u l t s p u b l i s h e d e a r l i e r on r e m o l d e d c l a y s ( L a d d 1 9 6 7 ; H a m b l y and R o s c o e , 1 969 ) , w h e r e c o m p r e s s i o n and e x t e n s i o n cf>"s w e r e r e p o r t e d as b e i n g e i t h e r e q u a l o r e x t e n s i o n cj)" s e v e r a l d e g r e e s l a r g e r t h a n c o m p r e s s i o n . The m e a s u r e d <(>' (no v o l u m e c h a n g e r a t e c o r r e c -t i o n s ) i n d r a i n e d p a s s i v e e x t e n s i o n c a n be s e v e r a l d e g r e e s s m a l l e r t h a n c o r r e c t e d f o r v o l u m e c h a n g e r a t e s . T h i s w a s , f o r t h e c l a y t e s t e d , due t o s i g n i f i c a n t p a r t o f i n p u t e n e r g y b e i n g e x p e n d e d i n d o i n g w o r k a g a i n s t t h e r e l a t i v e l y h i g h c o n f i n i n g p r e s s u r e i n s u c h a t e s t . 4 . The s t r e s s r a t i o o*/(°^+0^ i n P l a n e s t r a i n was f o u n d e s s e n t i a l l y c o n s t a n t and i n d e p e n d e n t o f t h e s t r e s s p a t h o r d r a i n a g e c o n d i t i o n s . T h i s i s s i m i l a r t o e a r l i e r r e s u l t s o f H a m b l y and R o s c o e ( 1 9 6 9 ) on a r e m o l d e d c l a y . 5 . I t was shown t h a t R e n d u l i c ' s h y p o t h e s i s c a n be u s e d t o e s t i m a t e v o l u m e c h a n g e s i n c o n v e n t i o n a l d r a i n e d p a s s i v e c o m p r e s s i o n t e s t s f r o m t h e r e s u l t s o f s i m i l a r u n d r a i n e d t e s t s , p r o v i d e d s a m p l e s c o n s i d e r e d h a v e t h e same i n i t i a l c o n s o l i d a t i o n h i s t o r y . The s t r e s s p a r a m e t e r s u s e d t o e x p r e s s R e n d u l i c ' s u n i q u e n e s s o f v o i d r a t i o - e f f e c t i v e s t r e s s h y p o t h e s i s w e r e t h e o c t a h e d r a l mean n o r m a l e f f e c -t i v e s t r e s s , p , and o c t a h e d r a l s h e a r s t r e s s T j . . A l s o , i n c r e m e n t s o f v o l u m e c h a n g e d u r i n g d r a i n e d p a s s i v e e x t e n -s i o n w e r e s u c c e s s f u l l y e s t i m a t e d f r o m t h e c o r r e s p o n d i n g u n d r a i n e d t e s t s , f o r t h a t p a r t o f t h e s t r e s s p a t h w h e r e t h e s t r e s s r a t i o , T o c t / P » was i n c r e a s i n g . I t w o u l d be o f i n t e r e s t t o v e r i f y R e n d u l i c ' s h y p o t h e s i s f o r o t h e r l o a d i n c r e a s i n g d r a i n e d s t r e s s p a t h s . C o m p a r i s o n o f t r i a x i a l and p l a n e s t r a i n r e s u l t s on n o r m a l l y c o n s o l i d a t e d H a n e y c l a y , u n d e r i d e n t i c a l s t r e s s p a t h s , l e d t o t h e f o l l o w i n g c o n c l u s i o n s : 1 . The a x i a l s t r a i n t o f a i l u r e i n u n d r a i n e d s h e a r was t h e same u n d e r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s w h i c h i n c l u d e d b o t h c o m p r e s s i o n and e x t e n s i o n s t r e s s p a t h s . T h i s r e s u l t f o r Haney c l a y i s s o m e w h a t c o n t r a r y t o t h o s e p u b l i s h e d e a r l i e r f o r r e m o l d e d c l a y s ( H e n k e l and W a d e , 1 9 6 6 ) , w h e r e a x i a l s t r a i n t o u n d r a i n e d c o m p r e s s i o n f a i l u r e i n p l a n e s t r a i n was c o n s i d e r a b l y s m a l l e r t h a n t h a t u n d e r t r i a x i a l c o n d i t i o n s . H o w e v e r , d u r i n g d r a i n e d s h e a r o f Haney c l a y , i r r e s p e c t i v e o f t h e s t r e s s p a t h , a x i a l s t r a i n t o f a i l u r e i n p l a n e s t r a i n was a b o u t 75% o f t h a t u n d e r t r i a x i a l c o n d i t i o n s . A l s o , c o m p r e s s i o n f a i l u r e i n p l a n e s t r a i n was a l w a y s a c c o m p a n i e d by a s h a r p p o s t p e a k d r o p i n s h e a r r e s i s t a n c e , w h i c h was n o t p r e s e n t i n t h e t r i a x i a l t e s t s . T h i s s u g g e s t s t h a t p r o g r e s s i v e a c t i o n i n p l a n e s t r a i n c a n be more s e v e r e t h a n u n d e r t r i a x i a l c o n d i t i o n s . 2 . U n d r a i n e d s t r e n g t h was l a r g e r u n d e r p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . F o r t h e c l a y t e s t e d , C u / a ^ c i n p l a n e s t r a i n c o m p r e s s i o n was 0 . 2 9 3 c o m p a r e d t o t h e t r i a x i a l v a l u e o f 0 . 2 6 3 . The c o r r e s p o n d i n g v a l u e s i n e x t e n s i o n w e r e 0 . 1 9 3 and 0 . 1 3 0 . In c o m p r e s s i o n , h i g h e r ^ u ^ a l c ^ n P ^ a n e s t r a i n was a s s o c i a t e d w i t h h i g h e r tt'' i n p l a n e s t r a i n , as 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 i n t h e two t y p e s o f t e s t s w e r e e s s e n t i a l l y s a m e . In e x t e n s i o n e x c e s s i v e l y l a r g e r ^ / a ^ i n p l a n e s t r a i n was a s s o c i a t e d w i t h b o t h , h i g h e r <j>' and l o w e r p o r e p r e s s u r e s i n p l a n e s t r a i n c o m p a r e d t o t h o s e u n d e r t r i a x i a l c o n d i t i o n s . 3. A t b o t h f a i l u r e c o n d i t i o n s , ( a i - a 3 ) a n d v max ( o i / 0 3 ) m a x » p l a n e s t r a i n a)* was h i g h e r t h a n t r i a x i a l o)* by 4° t o 5° f o r a l l t h e s t r e s s p a t h s i n v e s t i g a t e d . T h u s , a c o n f i r m a t i o n o f t h e g e n e r a l p i c t u r e , t h a t t h e a n g l e s o f 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 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 a r e h i g h e r , has b e e n d e m o n s t r a t e d f o r a n a t u r a l c l a y . 4. O c t a h e d r a l e f f e c t i v e s t r e s s p a t h s i n t e r m s o f p and Tqc^ . w e r e f o u n d t o be t h e same f o r t r i a x i a l and p l a n e s t r a i n u n d r a i n e d c o m p r e s s i o n . H o w e v e r , i n u n d r a i n e d e x t e n s i o n , w h i c h i n v o l v e s a d e c r e a s e i n t h e s t r e s s r a t i o x o c j . / p and c o n s e q u e n t i a l r e o r i e n t a t i o n o f p r i n c i p a l s t r e s s e s d u r i n g s h e a r , common o c t a h e d r a l e f f e c t i v e s t r e s s p a t h s w e r e f o u n d i n t e r m s o f p and AT t ( E q . 7.6), w h e r e A x Q C t r e p r e s e n t s c u m u l a t i v e c h a n g e i n o c t a h e d r a l c o m p o n e n t o f s h e a r s t r e s s . T h i s c o r r e s p o n d e n c e o f o c t a h e d r a l s t r e s s p a t h s i s o f g r e a t i m p o r t a n c e i n t h e d e v e l o p m e n t o f 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 o r c o m p l e x s t r e s s f i e l d s . 5. A u n i q u e o c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n common t o u n d r a i n e d 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 was f o u n d t o e x i s t . The c o m p r e s s i o n r e l a t i o n s h i p was b e t w e e n T and v w h e r e a s , t h e e x t e n s i o n r e l a t i o n s h i p was o c t o c t b e t w e e n ATQCT and Y 0 C f F o r t h e c l a y t e s t e d , t h e c o m p r e s s i o n s t r e s s - s t r a i n r e l a t i o n s h i p was v a l i d e v e n u n t i l s t r a i n l e v e l s w h i c h w e r e s e v e r a l t i m e s l a r g e r t h a n a t w h i c h u n d r a i n e d f a i l u r e ( ( x r t o c c u r r e d . In o t h e r w o r d s , o c t max t h e u n i q u e n e s s o f t h e r e l a t i o n s h i p s e x i s t e d e v e n i n t h e u n s t a b l e p o s t f a i l u r e r a n g e . ( I n t h i s r a n g e T Q C T d e c r e a s e d b u t T o c t / P was i n c r e a s i n g . ) The e x t e n s i o n s t r e s s - s t r a i n r e l a t i o n s h i p was u n i q u e f o r t h e e n t i r e s t r e s s p a t h u n t i l f a i l u r e . ( T o c t a n c ' T o c t ^ P r e a c h e d p e a k v a l u e s a t t h e same s t r a i n i n e x t e n s i o n . ) 6. The u n i q u e n e s s o f o c t a h e d r a l e f f e c t i v e 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 and p l a n e s t r a i n c o m p r e s s i o n p e r m i t s R e n d u l i c ' s h y p o t h e s i s t o be u s e d t o e s t i m a t e v o l u m e c h a n g e s i n d r a i n e d p l a n e s t r a i n p a s s i v e c o m p r e s s i o n f r o m t h e r e s u l t s o f u n d r a i n e d t r i a x i a l c o m p r e s s i o n t e s t s . I t has b e e n f u r t h e r shown t h a t t h e v o l u m e c h a n g e s i n u n l o a d i n g t y p e p l a n e s t r a i n a c t i v e c o m p r e s s i o n c a n be e s t i m a t e d f r o m a s i m i l a r t r i a x i a l t e s t . F o r t h i s t y p e o f t e s t , a s u r f a c e i n ( p , T e ) s p a c e common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s c o u l d be a s s u m e d t o e x i s t . F u r t h e r l o a d i n g and u n l o a d i n g c o m p r e s s i o n t e s t s a r e r e -q u i r e d t o s u b s t a n t i a t e t h e s e c o n c l u s i o n s , w h i c h w e r e d e r i v e d f r o m o n l y a f e w t e s t s on a s p e c i f i c c l a y . 7. O c t a h e d r a l s h e a r s t r e s s - s t r a i n r e l a t i o n s d u r i n g d r a i n e d c o m p r e s s i o n w e r e f o u n d common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s i n t e r m s o f T Q C t/p v s . Y O C T -F o r t h e c l a y t e s t e d , t h e u n i q u e s t r e s s s t r a i n r e l a t i o n s h i p i n a c t i v e c o m p r e s s i o n was v a l i d f o r a l l s t r a i n s u n t i l f a i l u r e i n p l a n e s t r a i n . In p a s s i v e c o m p r e s s i o n t h e u n i q u e n e s s was r e s t r i c t e d t o s t r a i n s w h i c h w e r e l e s s t h a n 60% o f t h e f a i l u r e v a l u e i n p l a n e s t r a i n . 8 . F o r u n d i s t u r b e d Haney c l a y , i t has b e e n shown t h a t t h e C a m b r i d g e s t r e s s - s t r a i n t h e o r y r e s u l t s i n l a r g e o v e r p r e d i c t i o n o f s t r a i n s d u r i n g d r a i n e d p l a n e s t r a i n s h e a r u n d e r c o n v e n t i o n a l p a s s i v e c o m p r e s s i o n . 9 . A l t h o u g h t h e u n d r a i n e d s t r e n g t h , as c h a r a c t e r i s e d by C u = ( a 1 - a 3 ) / 2 , was l a r g e r i n p l a n e s t r a i n , t h e o c t a -h e d r a l s t r e n g t h was t h e same f o r t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s , when (T v was u s e d f o r c o m p r e s s i o n and 0 c x m a X ( A T „ , L v u s e d f o r e x t e n s i o n f a i l u r e . 0C L itiaX 1 0 . F o r u n d i s t u r b e d Haney c l a y , 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 t ' was u n d e r e s t i m a t e d by t h e 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 w i t h r e s p e c t t o b o t h ( o i - a 3 ) , and r max ( c i 7 a 3 ) m a x f a i l u r e c o n d i t i o n s . The o b s e r v e d p l a n e s t r a i n c o m p r e s s i o n <j>' a t ( a i - a 3 ) m a x w a s c l o s e s t t o t h a t p r e d i c t e d by e x t e n d e d von M i s e s f a i l u r e c r i t e r i o n , w h e r e a s a t { o i / o z ) , t h e o b s e r v e d <j>' was c l o s e s t t b t h a t i m p l i e d ill d A by e x t e n d e d T r e s c a f a i l u r e c r i t e r i o n . In e x t e n s i o n s h e a r , p l a n e s t r a i n was u n d e r e s t i m a t e d by a l l t h r e e f a i l u r e c r i t e r i a . I t was c o n c l u d e d t h a t none o f t h e f a i l u r e c r i t e r i a , i n t h e p r e s e n t f o r m , c a n a c c o u n t f o r f a i l u r e u n d e r a l l s t r e s s p a t h s and s t r e s s s y s t e m s . T e s t r e s u l t s on ' h e a v i l y ' o v e r c o n s o l i d a t e d Haney c l a y l e d t o t h e f o l l o w i n g c o n c l u s i o n s w i t h r e g a r d t o t h e r e s p o n s e u n d e r d i f f e r e n t a p p l i e d s t r e s s p a t h s : 1 . U n d r a i n e d c o m p r e s s i o n and e x t e n s i o n b e h a v i o u r was v e r y s i m i l a r and t h e a x i a l s t r a i n t o p e a k d e v i a t o r s t r e s s i n e i t h e r mode o f s h e a r was e s s e n t i a l l y t h e s a m e . H o w e v e r , t h e a x i a l s t r a i n t o f a i l u r e i n d r a i n e d s h e a r d e p e n d e d on t h e a p p l i e d s t r e s s p a t h , as was t h e c a s e f o r t h e n o r m a l l y c o n s o l i d a t e d c l a y . 2 . U n d r a i n e d s t r e n g t h i n c o m p r e s s i o n was s t i l l l a r g e r t h a n i n e x t e n s i o n , b u t t h e d i f f e r e n c e was much s m a l l e r t h a n i n t h e n o r m a l l y c o n s o l i d a t e d c l a y . An a p p r o a c h t o w a r d s e q u a l u n d r a i n e d s t r e n g t h i n c o m p r e s s i o n and e x t e n s i o n seems t o be i n d i c a t e d as t h e o v e r c o n s o l i d a -t i o n r a t i o ( O . C . R . ) i n c r e a s e s . 3 . A v e r y m i s l e a d i n g p i c t u r e o f o v e r c o n s o l i d a t e d b e h a v i o u r i s o b t a i n e d i f O . C . R . i n K Q - c o n s a l i d a t e d c l a y s i s d e f i n e d as t h e r a t i o o f maximum t o r e b o u n d e d v e r t i c a l c o n s o l i d a t i o n s t r e s s e s . F o r t h e c l a y t e s t e d , e v e n t h o u g h t h e O . C . R . was b e t w e e n 16 t o 1 9 , no d i l a t i o n o c c u r r e d d u r i n g t h e c o n v e n t i o n a l p a s s i v e c o m p r e s s i o n d r a i n e d s h e a r . I t i s p r o p o s e d t h a . t a more r a t i o n a l d e f i n i t i o n o f O . C . R . f o r a n i s o t r o p i c c o n s o l i d a t i o n c o n d i t i o n s i s t h e r a t i o o f maximum t o r e b o u n d e d mean 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 . In t e r m s o f mean s t r e s s e s t h e O . C . R . was b e t w e e n 7 t o 8, w h i c h s u g g e s t s t h a t t h e c l a y was n o t v e r y h e a v i l y o v e r -c o n s o l i d a t e d . 4 . M o h r ' s e f f e c t i v e s t r e s s e n v e l o p e s f o r o v e r c o n -s o l i d a t e d H a n e y c l a y c o r r e s p o n d i n g t o c o m p r e s s i o n f a i l u r e w e r e h i g h e r t h a n t h e e x t e n s i o n e n v e l o p e s . T h i s , a l o n g w i t h s i m i l a r r e s u l t s on 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 u g g e s t s t h a t n a t u r a l c l a y s may be i n h e r e n t l y a n i s o t r o p i c i n t h e i r e f f e c t i v e s t r e n g t h p a r a m e t e r s . F rom t h e c o m p a r i s o n o f t r i a x i a l and p l a n e s t r a i n b e h a v i o u r o f o v e r c o n s o l i d a t e d H a n e y c l a y , u n d e r i d e n t i c a l s t r e s s p a t h s , t h e f o l l o w i n g c o n c l u s i o n s w e r e d e r i v e d : 1 . I r r e s p e c t i v e o f t h e s t r e s s p a t h , t h e a x i a l s t r a i n t o peak d e v i a t o r s t r e s s was s m a l l e r i n p l a n e s t r a i n t h a n u n d e r t r i a x i a l c o n d i t i o n s . A s h a r p p e a k was a l w a y s a s s o c i a t e d w i t h p l a n e s t r a i n c o m p r e s s i o n f a i l u r e w h i l e a s i m i l a r p e a k was n o t p r e s e n t u n d e r t r i a x i a l c o n d i t i o n s . T h i s was a l s o s e e n i n n o r m a l l y c o n s o l i d a t e d b e h a v i o u r . 2 . U n d r a i n e d s t r e n g t h was l a r g e r i n p l a n e s t r a i n t h a n t r i a x i a l u n d e r b o t h c o m p r e s s i o n and e x t e n s i o n s t r e s s p a t h s . The h i g h e r v a l u e s i n p l a n e s t r a i n , f o r t h e c l a y t e s t e d , w e r e a g a i n a s s o c i a t e d w i t h h i g h e r 01/0$ and l o w e r p o r e p r e s s u r e s i n p l a n e s t r a i n . 3 . M o h r ' s e f f e c t i v e s t r e s s e n v e l o p e s f o r p l a n e s t r a i n f a i l u r e w e r e h i g h e r t h a n t h e c o r r e s p o n d i n g e n v e l o p e s f o r t r i a x i a l f a i l u r e . T h i s d i f f e r e n c e was l a r g e r i n c o m p r e s s i o n t h a n i n e x t e n s i o n . T h u s , i t c a n be s t a t e d t h a t a g e n e r a l c o n f i r m a t i o n has b e e n o b t a i n e d o f t h e f a c t t h a t p l a n e s t r a i n e f f e c t i v e s t r e n g t h p a r a m e t e r s a r e l a r g e r t h a n t r i a x i a l f o r o v e r c o n s o l i d a t e d as w e l l as 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 Haney c l a y . 4 . O c t a h e d r a l s t r e s s - s t r a i n r e l a t i o n s and u n d r a i n e d e f f e c t i v e s t r e s s p a t h s w e r e f o u n d common t o t r i a x i a l and p l a n e s t r a i n c o n d i t i o n s f o r t h e o v e r c o n s o l i d a t e d s o i l a l s o . H o w e v e r , t h e r e l a t i o n s h i p s w h i c h w e r e f o u n d common t o c o m p r e s s i o n 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 w e r e a p p l i c a b l e t o e x t e n s i o n s h e a r o f ' h e a v i l y ' o v e r c o n s o l i d a t e d c l a y . T h i s i s b e c a u s e , c o m p r e s s i o n and n o t e x t e n s i o n s t r e s s p a t h s i n o v e r c o n s o l i d a t e d c l a y a r e a s s o c i a t e d w i t h . d e c r e a s i n g T Q c t / p and c o n s e q u e n t r e o r i e n t a t i o n o f p r i n c i p a l s t r e s s e s a t f a i l u r e . S i m i l a r l y , c o n c l u s i o n s r e g a r d i n g e x t e n s i o n s h e a r 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 w e r e v a l i d f o r c o m -p r e s s i o n s h e a r o f o v e r c o n s o l i d a t e d c l a y . O c t a h e d r a l u n d r a i n e d s t r e n g t h was t h e same f o r 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 w i t h r e s p e c t t o b o t h f a i l u r e c o n d i t i o n s , ( o i - a 3 ) a v and (a 1/0$) a v » when t h e max max s t r e n g t h was c h a r a c t e r i s e d by T Q c t i n e x t e n s i o n and Ax . i n c o m p r e s s i o n . B I B L I O G R A P H Y A r m s t r o n g , J . E . ( 1 9 5 7 ) " S u r f i c i a l G e o l o g y o f N e w - W e s t m i n s t e r Map - a r e a , B r i t i s h C o l u m b i a , " G e o l o g i c a l S u r v e y o f C a n a d a , p p . 5 7 - 5 . B a k e r , W . H . and K r i z e k , R . J . ( 1 9 6 9 ) " P o r e P r e s s u r e E q u a t i o n s f o r A r i s o t r o p i c C l a y s , " J o u r n a l o f t h e 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 i s i o n , A S C E , V o l . 9 5 , N o . S M 2 , p p . 7 1 9 - 7 2 3 . B i s h o p , A . W . ( 1 9 6 4 ) " 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 . 1 4 . B i s h o p , A . W . ( 1 9 6 6 ) " T h e S t r e n g t h o f S o i l s as E n g i n e e r i n g M a t e r i a l s , " 6 t h R a k i n e L e c t u r e , G e o t e c h n i q u e , V o l . 1 6 , p p , 9 1 - 1 2 8 . B i s h o p , A . W . and E l d i n , A . K . ( 1 9 5 3 ) " T h e E f f e c t o f S t r e s s H i s t o r y on R e l a t i o n B e t w e e n cj) and P o r o s i t y i n S a n d , " P r o c e e d i n g s , 3 r d I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , Z u r i c h , V o l . 1 , p p . 1 0 0 - 1 0 5 . B i s h o p , A . W . and H e n k e l , D . J . ( 1 9 6 2 ) "The M e a s u r e m e n t o f S o i l P r o p e r t i e s i n t h e T r i a x i a l T e s t , " E d w i n A r n o l d L t d . , L o n d o n . B j e r r u m , L . and K e n n y , T . C . ( 1 9 6 7 ) " E f f e c t o f S t r u c t u r e on S h e a r B e h a v i o u r o f N o r m a l l y C o n s o l i d a t e d Q u i c k C l a y s , " P r o c e e d i n g s o f t h e G e o t e c h n i c a l C o n f e r e n c e , O s l o , V o l . 2 , p p . 1 9 - 2 7 . B j e r r u m , L . and L a n d v a , A . ( 1 9 6 6 ) " D i r e c t S i m p l e S h e a r T e s t s on a N o r w e g i a n Q u i c k C l a y , " G e o t e c h n i q u e , V o l . 1 6 , p p . 1 - 2 0 . B j e r r u m , L . and S i m o n s , N . E . ( I 9 6 0 ) " C o m p a r i s o n o f S h e a r 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 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 , " ASCE 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 p . 7 1 1 - 7 2 6 . B l i g h t , G . E . ( 1 9 6 3 ) "The E f f e c t o f N o n u n i f o r m P o r e P r e s s u r e s on L a b o r a t o r y M e a s u r e m e n t o f S h e a r S t r e n g t h o f S o i l s , " A S T M , S T P . N o . 3 6 1 , p p . 1 7 3 - 1 8 4 . B y r n e , P . M . ( 1 9 6 6 ) " 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 . , V a n c o u v e r . C a m p a n e l l a , R . G . and V a i d , Y . P . ( 1 9 7 1 ) " K - T r i a x i a l A p p a r a t u s , " U . B . C . S o i l M e c h a n i c s S e r i e s N o . 1 5 . C l o u g h , R .W. and W o o d w a r d , R . J . ( 1 9 6 7 ) " A n a l y s i s o f Embankment S t r e s s e s and D e f o r m a t i o n s , " J o u r n a l o f t h e 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 i s i o n , A S C E , V o l . 9 3 , N o . S M 4 , p p . 5 2 9 - 5 4 9 . C o n l o n , R . J . , T a n n e r , R . G . and C o l d w e l l , K . L . ( 1 9 7 0 ) "The G e o t e c h n i c a l D e s i g n o f t h e T o w n l i n e R o a d / R a i l T u n n e l , W e l l a n d , O n t a r i o , " P r o c e e d i n g s , 2 3 r d C a n a d i a n G e o t e c h n i c a l C o n f e r e n c e , B a n f f , A l b e r t a . C o r n f o r t h , D . H . ( 1 9 6 4 ) "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 . 1 4 , p p . 1 4 3 - 1 6 6 . C r a w f o r d , C . B . ( 1 9 5 9 ) "The 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 , p p . 3 6 - 6 1 . D i c k e y , J . W . , L a d d , C . C . and R i x n e r , J . J . ( 1 9 6 8 ) "A P l a n e S t r a i n S h e a r D e v i c e f o r T e s t i n g C l a y s , " Q u o t e d by H e n k e l , D . J . i n ASCE S p e c i a l i t y C o n f e r e n c e on L a t e r a l S t r e s s e s i n t h e G r o u n d , C o r n e l U n i v e r s i t y , 1 9 7 0 . D u n c a n , J . M . and S e e d , H . B . ( 1 9 6 6 ) " A n i s o t r o p y and S t r e s s R e o r i e n t a t i o n i n C l a y , " J o u r n a l o f t h e 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 i s o n , A S C E , V o l . 9 2 , N o . S M 5 , p p . 2 1 - 5 0 . D u n c a n , J . M . and S e e d , H . B . ( 1 9 6 6 a ) " 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 t h e 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 i s i o n , A S C E , V o l . 9 2 , N o . S M 6 , p p . 8 1 - 1 0 4 . F i n n , W . D . L . , W a d e , N . H . and L e e , K . L . ( 1 9 6 7 ) " V o l u m e C h a n g e i n T r i a x i a l and P l 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 a n i c s and F o u n d a t i o n D i v i s i o n , A S C E , V o l . 9 3 , N o . S M 6 , p p . 2 9 7 - 3 0 8 . H a m b l y , E . C . and R o s c o e , K . H . ( 1 9 6 9 ) " O b s e r v a t i o n s and P r e -d i c t i o n s o f S t r e s s e s and S t r a i n s D u r i n g P l a n e S t r a i n o f ' W e t ' C l a y s , " P r o c e e d i n g s , 7 t h I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g M e x i c o C i t y , V o l . 1 , p p . 1 7 3 - 1 8 1 . H a n s o n , J . B . and G i b s o n , R . E . ( 1 9 4 9 ) " U n d r a i n e d 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 , " G e o t e c h n i q u e , V o l . 1 , p p . 1 8 9 - 2 0 4 . H e n k e l , D . J . ( 1 9 6 0 ) " 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 , " ASCE 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 p . 5 3 3 - 5 5 4 . H e n k e l , D . J . ( 1 9 7 0 ) " G e o t e c h n i c a l C o n s i d e r a t i o n s o f L a t e r a l S t r e s s e s , " ASCE S p e c i a l i t y C o n f e r e n c e on L a t e r a l S t r e s s e s i n t h e G r o u n d , C o r n e l l U n i v e r s i t y , p p . 1 - 5 0 . H e n k e l , D . J . and S o w a , V . A . ( 1 9 6 3 ) "The 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 i n C l a y , " 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 , S T P . N o . 3 6 1 , p p . 2 8 0 - 2 9 1 . H e n k e l , D . J . and W a d e , N . H . ( 1 9 6 6 ) " 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 M e c h a n i c s and F o u n d a t i o n D i v i s i o n , A S C E , V o l . 9 2 , N o . S M 6 , p p . 6 7 - 8 0 . H v o r s l e v , M . J . ( 1 9 6 0 ) " P h y s i c a l C o m p o n e n t s o f 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 C l a y s , " ASCE 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 l d e r , C o l o r a d o , p p . 1 6 9 - 2 7 3 . K h e r a , R . P . and K r i z e k , R . J . ( 1 9 6 7 ) " S t r e n g t h 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 R e m o l d e d C l a y , " H . R . B . H i g h w a y R e s e a r c h R e c o r d , N o . 1 9 0 , p p . 8 - 1 8 . L a d a n y i , B . ( 1 967 ) " 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 a n i c s and F o u n d a t i o n D i v i s i o n , A S C E , V o l . 9 3 , N o . S M 5 , p p . 3 2 2 - 3 2 5 . L a d d , C . C . ( 1 9 6 4 ) " 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 , " ASCE C o n f e r e n c e on D e s i g n o f F o u n d a t i o n s f o r C o n t r o l o f S e t t l e m e n t , E v a n s t o n , 1 1 1 . , p p . 1 2 7 - 1 5 4 . 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 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 i n g s , 6 t h I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , M o n t r e a l , V o l . 1 , p p . 2 8 2 - 2 8 6 . L a d d , C . C , L a d d , C . C , ( 1 9 6 7 ) " D i s c u s s i o n on S e s s i o n 1 , " G e o t e c h n i c a l C o n f e r e n c e , O s l o , V o l . 2 , p p . 1 1 2 - 1 1 4 . and B a i l e y ( 1 9 6 4 ) V o l . 1 4 . " 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 L a d d , C . C . and L a m b e , T . W . ( 1 9 6 3 ) "The S t r e n g t h o f ' U n d i s t u r b e d ' C l a y D e t e r m i n e d f r o m U n d r a i n e d T e s t s , " 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 N o . 3 6 1 , p p . 3 4 2 - 3 7 1 . L a m b e , T . W . ( 1 9 6 4 ) " M e t h o d s o f E s t i m a t i n g S e t t l e m e n t s , " ASCE C o n f e r e n c e on D e s i g n o f F o u n d a t i o n s f o r C o n t r o l o f S e t t l e m e n t , E v a n s t o n , 1 1 1 . , p p . 4 7 -7 0 . L a m b e , T . W . ( 1 9 6 7 ) " S t r e s s P a t h M e t h o d , " 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 i s i o n , A S C E , V o l . 9 3 , N o . S M 6 , p p . 3 0 9 - 3 3 2 . L e w i n , P . I . and B u r l a n d , J . B . ( 1 9 7 0 ) " S t r e s s - P r o b e E x p e r i -m e n t s on S a t u r a t 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 , " G e o t e c h n i q u e , V o l . 2 0 , p p . 3 8 - 5 6 . L o , K . Y . ( 1 9 6 5 ) " S t a b i l i t y o f S l o p e s i n A n i s o t r o p i c S o i l s , " 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 i s i o n , A S C E , V o l . 9 1 , N o . S M 4 , p p . 8 5 - 1 0 6 . L o , K . Y . and M i l l i g a n , V . ( 1 9 6 7 ) " S h e a r S t r e n g t h P r o p e r t i e s o f two S t r a t i f i e d C l a y s , " 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 i s i o n , A S C E , V o l . 9 3 , N o . S M I , p p . 1 - 1 6 . , M i t c h e l l , J . K . ( 1 9 6 9 ) " D i s c u s s i o n on S e s s i o n 1 , " P r o c e e d i n g s , 7 t h I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , M e x i c o C i t y , V o l . 3 , p p . 1 5 9 - 1 6 8 . N e w m a r k , N . M . ( 1 9 6 0 ) " 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 , " ASCE 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 p . 1 7 - 3 2 . N o o r a n y , I. and S e e d , H . B . ( 1 9 6 5 ) " I n - S i t u 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 S o f t C l a y s , " 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 i s i o n , A S C E , V o l . 9 1 , N o . S M 2 , p p . 4 9 - 8 0 . P o u l o s , S . J . ( 1 9 6 4 ) " C o n t r o l o f L e a k a g e i n t h e T r i a x i a l T e s t , " H a r v a r d S o i l M e c h a n i c s S e r i e s N o . 7 1 . R e n d u l i c , L . ( 1 9 3 6 ) " R e l a t i o n b e t w e e n v o i d r a t i o and E f f e c -t i v e P r i n c i p a l S t r e s s e s f o r a R e m o l d e d S i l t y C l a y , " P r o c e e d i n g s o f 1 s t I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , C a m b r i d g e , M a s s . , V o l . 3 , p p . 4 8 - 5 1 . R e n d u l i c , L . ( 1 9 3 7 ) " E i n G r u n d g e s e t z d e r T o n m e c h a n i k und s i n e x p e r i m e n t e l 1 e r B e w e i s s , " Der B a u i n g e n i e u r , V o l . 1 8 , p p . 4 5 9 - 4 6 7 . R o s c o e , K. H. and B u r l a n d , J . B . ( 1 9 6 8 ) "On t h e G e n e r a l i s e d B e h a v i o u r o f ' W e t ' C l a y s , " E n g i n e e r i n g P l a s t i c i t y , J . Heyman and F . A . L e c k i e , e d . , C a m b r i d g e , p p . 5 3 5 - 6 0 9 . R o s c o e R o s c o e R o s c o e K . H . and P o o r o o s h a s b , H . B . ( 1 9 6 3 ) "A T h e o r e t i c a l and E x p e r i m e n t a l S t u d y o f S t r a i n s i n T r i a x i a l T e s t s on 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 , " G e o t e c h n i q u e V o l . 1 3 , p p . 1 2 . K . H . and S c h o f i e l d , A . N . ( 1 9 6 3 ) " 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 , ' " E u r o p e a n C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , V o l . 1 , p p . 4 7 - 5 4 . K . H . , S c h o f i e l d , A . N . and W r o t h , P . W . ( 1 9 5 8 ) "On t h e Y i e l d i n g o f S o i l s , " G e o t e c h n i q u e , V o l . 8 , p p . 2 2 - 5 3 . S c o t t , R . F . ( 1 9 6 3 ) " P r i n c i p l e s o f S o i l M e c h a n i c s W e s l e y P u b ! i s h i n g C o . A d d i s o n S h i b a t a , T . and K a r u b e , D. ( 1 9 6 7 ) " 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 a n i c s and F o u n d a t i o n D i v i s i o n , A S C E , V o l . 9 3 , N o . S M 5 , p p . 3 2 5 - 3 2 7 . S i m o n s , N . E . ( 1 9 6 0 ) "The E f f e c t o f O v e r c o n s o l i d a t i o n on t h e S h e a r 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 an U n d i s t u r b e d O s l o C l a y , " ASCE 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 p . 7 4 7 - 7 6 3 . S i m o n s , N . E . ( 1 9 6 3 ) " T h e I n f l u e n c e o f S t r e s s P a t h on T r i -a x i a l T e s t R e s u l t s , " 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 , S T P . N o . 3 6 1 , p p . 2 7 0 - 2 7 8 . S m i t h , R. E . and W a h l s , H . E . ( 1 9 6 9 ) " C o n s o l i d a t i o n U n d e r C o n s t a n t R a t e s o f S t r a i n , " J o u r n a l o f S o i l M e c h a n i and F o u n d a t i o n D i v i s i o n , A S C E , V o l . 9 5 . N o . S M 2 , p p . 5 1 9 - 5 4 0 . S k e m p t o n , A . W . ( 1 9 5 4 ) " T h e P o r e P r e s s u r e C o e f f i c i e n t s A and B , " G e o t e c h n i q u e , V o l . 4 , p p . 1 4 3 - 1 4 7 . S k e m p t o n , A . W . and S o w a , V . A . ( 1 9 6 3 ) " T h e B e h a v i o u r o f S a t u r a t e d C l a y s D u r i n g S a m p l i n g and T e s t i n g , " G e o t e c h n i q u e , V o l . 1 3 , p p . 2 6 9 - 2 9 0 . V a i d , Y . P . ( 1 9 6 8 ) "A P l a n e S t r a i n A p p a r a t u s f o r S o i l s , " M . A . S c . T h e s i s , U . B . C , V a n c o u v e r . W a r d , W . H . ( 1 9 5 6 ) " D i s c u s s i o n , " P r o c e e d i n g s o f t h e 4 t h I n t e r n a t i o n a l C o n f e r e n c e on S o i l M e c h a n i c s and F o u n d a t i o n E n g i n e e r i n g , L o n d o n , V o l . 3 , p p . 1 2 3 -1 2 4 . W a r d , W . H . , S a m u e l s , S . G . , and B u t l e r , M . E . ( 1 9 5 9 ) " F u r t h e r S t u d i e s o f t h e P r o p e r t i e s o f L o n d o n C l a y , " G e o -t e c h n i q u e , V o l . 9 , p p . 3 3 - 5 8 . W h i t m a n , R . V . , L a d d , C . C . and C r u z , P . da ( 1 9 6 0 ) " D i s c u s s i o n on S e s s i o n 3 , " ASCE 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 p . 1 0 4 9 - 1 0 5 6 . A P P E N D I X A F R I C T I O N CORRECTION TO MEASURED A X I A L STRESS IN PLANE STRAIN TESTS R e f e r r i n g t o F i g . A-1 , l e t a t a n y s t a g e o f t h e t e s t Fj. = The m e a s u r e d a x i a l f o r c e on t h e l o a d i n g c a p . F^ = The m e a s u r e d a x i a l f o r c e t r a n s m i t t e d t o t h e s a m p l e b o t t o m . L , B , H = R e s p e c t i v e l y t h e l e n g t h , w i d t h and h e i g h t o f t h e s a m p l e . h = H e i g h t o f t h e l o a d i n g c a p s u r f a c e ( s h o w n s h a d e d i n F i g . A-1) i n c o n t a c t w i t h l a t e r a l p r e s s u r e . d i a p h r a m s . o = S t r e s s i n l a t e r a l p r e s s u r e d i a p h r a m s . A 0^ = S t r e s s on r i g i d end p l a t e s , Then t h e t o t a l n o r m a l f o r c e , N , c o n t r i b u t i n g t o f r i c t i o n N = 2 { L ( H + h ) o v + B . H . a } T o t a l f r i c t i o n f o r c e F f v F t - F b Fig. A-I - NORMAL STRESSES BETWEEN VERTICAL SURFACES ON WHICH FRICTION ACTS . H e n c e , an a v e r a g e c o e f f i c i e n t o f f r i c t i o n Now t h e f r i c t i o n a l f o r c e , F , a c t i n g on t h e v e r t i c a l s u r f a c e o f t h e l o a d i n g c a p F = u , . 2 . L - H . a c p a x T h e r e f o r e , t h e a x i a l f o r c e , F ^ c , a c t u a l l y t r a n s m i t t e d t o t h e s a m p l e t o p F t c = F t " F c The a v e r a g e v e r t i c a l f o r c e , F . on t h e s a m p l e was t h e n a t a k e n as t h e mean o f F t c and F ^ , i . e . , F a . 1/2 F b + F t c I f t h e a r e a o f t h e s a m p l e was A t h e n t h e v e r t i c a l s t r e s s , a z , c o r r e c t e d f o r s i d e f r i c t i o n e f f e c t was 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050548/manifest

Comment

Related Items