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Plane strain creep rupture of a saturated undisturbed clay Mallawaratchie, Dayalal Pandula 1970

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PLANE STRAIN CREEP RUPTURE OF A SATURATED UNDISTURBED CLAY by DAYALAL PANDULA MALLAWARATCHIE B.Sc. (ENG), U n i v e r s i t y o f C e y l o n , 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e D e p a r t m e n t o f C i v i l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA Jun e , 197 0 In presenting this thesis in part ia l fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for f inancial gain shall not be allowed without my written permission. Department of C i v i l Engineering The University of Br i t i sh Columbia Vancouver 8 , Canada ABSTRACT Undrained c o n s t a n t s t r e s s l e v e l creep r u p t u r e t e s t s have been performed on an u n d i s t u r b e d , n o r m a l l y c o n s o l i d a t e d under K c o n d i t i o n s , s e n s i t i v e c l a y i n a o r e c t a n g u l a r (1" x 4" x 2^ -" high) plane s t r a i n apparatus. The behaviour r e s u l t i n g from t o t a l s t r e s s paths o f i n c r e a s i n g (keeping constant) and d e c r e a s i n g (keeping constant) was compared. S e v e r a l undrained creep t e s t s have a l s o been performed i n which t r i a x i a l specimens were 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 under K q con-d i t i o n s and then loaded by i n c r e a s i n g a^, as w e l l as de-c r e a s i n g a2' The plane s t r a i n and t r i a x i a l creep r u p t u r e t e s t r e s u l t s were compared along w i t h those r e p o r t e d by Snead (1970) . Snead t e s t e d the same c l a y but 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 under i s o t r o p i c s t r e s s and a x i a l l y loaded i n the c o n v e n t i o n a l t r i a x i a l apparatus, The comparison o f creep r e s u l t s under plane s t r a i n c o n d i t i o n s shows t h a t although the l i n e o f minimum s t r a i n r a t e versus time and the a x i a l s t r a i n a t minimum s t r a i n r a t e are e s s e n t i a l l y the same f o r i n c r e a s i n g and d e c r e a s -i n g s t r e s s paths, the d e v i a t o r s t r e s s e s ^ a i ~ a ^ v e r s u s minimum s t r a i n r a t e s are d i f f e r e n t . The comparison of t e s t r e s u l t s shows t h a t the d i s -c r e p a n c i e s i n the creep r u p t u r e behaviour under plane s t r a i n and t r i a x i a l c o n d i t i o n are s l i g h t , so long as the c l a y i s i n i t i a l l y K q c o n s o l i d a t e d . However, l a r g e d i s c r e p a n c i e s are seen i f the t r i a x i a l samples are 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 . In a d d i t i o n , a l l of the t e s t data were compared along the l i n e s of a v a i l a b l e methods f o r the p r e d i c t i o n of s l o p e f a i l u r e . Of p a r t i c u l a r i n t e r e s t was the o b s e r v a t i o n t h a t both i n c r e a s i n g and d e c r e a s i n g plane s t r a i n g i v e the same p r e d i c t i o n of time to s l o p e f a i l u r e . However the plane s t r a i n t e s t s p r e d i c t much s h o r t e r times to f a i l u r e than do the i s o t r o p i c a l l y c o n s o l i d a t e d t r i a x i a l t e s t s . i v TABLE OF CONTENTS Chapter Page I INTRODUCTION . . . . . . . . . . . . . . . 1 I I LITERATURE REVIEW . . . . . . . . . . . . 5 F i e l d O b s e r v a t i o n of Creep and Creep Creep and Creep Rupture S t u d i e s . . . . . . 7 Summary . . . . . . . . . . . . . . . . . 28 I I I LABORATORY TESTING . . . . . . . . . . . . 30 Development of a T e s t i n g Programme . . . . 30 D e s c r i p t i o n of S o i l T e s t e d . . . . . . . . 32 D e s c r i p t i o n of the Apparatus Used i n T h i s Study . . . . . . . . . . . . . . . . 33 D i s c u s s i o n o f T e s t i n g Procedure (Plane S t r a i n T ests) . . . . . . . . . . . . . . 40 IV RESULTS OF PLANE STRAIN CREEP RUPTURE T e s t s i n Which Was Increa s e d . . . . . 47 Comparison of " a ^ I n c r e a s e d " and " c ^ Decreased" Types of creep t e s t s . . . . . . . . . 63 S \intITlcl o a s o o o o o a o o D o a o a a 33 V COMPARISON OF PLANE STRAIN AND TRIAXIAL S UHTlTll cl3T y o » e o » t > o o o o o o o o o o Q 95 VI PREDICTION OF SLOPE FAILURE . . . . . . . -97 Summary . . . . . . . . . . . . . . . . . . 106 V Chapter Page VI I SUMMARY AND CONCLUSIONS . . . . . . . . . . 108 APPENDIX I - EXPERIMENTAL PROCEDURE . . . . . . . 117 II - CALCULATION OF STRAIN RATES . . . . 119 I I I - WATER CONTENT, STRESSES AT THE END OF CONSOLIDATION AND DURING CREEP . . . . . . . . . . . . . . . 121 v i LIST OF TABLES Table Page 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 . . . . . . 34 II Some r e s u l t s o f undrained plane s t r a i n creep t e s t - i n c r e a s e d . . . . . . . . . . 55 I I I a D a t the same e and e from F i g u r e 4.4, f o r undrained plane s t r a i n t e s t s - i n c r e a s e d . . . . . . . . . . 62 IV Some r e s u l t s o f undrained plane s t r a i n creep t e s t s - decreased . . . . . . . . . 70 V a D a t the same e and e from F i g u r e 4.9, f o r undrained plane s t r a i n t e s t s v i i LIST OF FIGURES F i g u r e Page 2.1 A t y p i c a l creep r u p t u r e curve f o r metals c o n c r e t e and p l a s t i c s . ( A f t e r G a r o f a l o , 2.2 A t y p i c a l s t r a i n - t i m e curve f o r 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 under s u s t a i n e d d e v i a t o r s t r e s s ( A f t e r Snead, 1970) . . . . . 11 2.3 Logarithm of a x i a l s t r a i n r a t e v e r s u s e l a p s e d time f o r n o r m a l l y c o n s o l i d a t e d undrained creep t e s t s on Haney c l a y ( A f t e r Snead, 1970) . . . . . . . . . . . . . . 13 2.4 Log s t r a i n r a t e v e r s u s l o g time f o r s a t u r a t e d i l l i t e ( A f t e r Campanella, 1965) . . 15 2.5 R e l a t i o n s h i p between creep r u p t u r e l i f e and s t r a i n r a t e ( A f t e r S a i t o and Uezawa, 19 6 J_ ) o a o o o o o o o o o o o o o o o o o o 1 7 2.6 T o t a l r u p t u r e l i f e o f l a b o r a t o r y creep t e s t s ( A f t e r Snead, 1970) . . . . . . . . . . . 19 2.7 R e l a t i o n s h i p between time t o r u p t u r e and c u r r e n t s t r a i n r a t e ( A f t e r Snead, 1970) . . . 21 2.8 A x i a l s t r a i n r a t e v ersus a x i a l s t r a i n curves f o r n ormally c o n s o l i d a t e d Haney c l a y u s i n g c o n v e n t i o n a l t r i a x i a l apparatus ( A f t e r Snead, 1970) . . . . . . . . . . . . . . . . 23 2.9A A n a l y s i s of y i e l d v a l u e on the b a s i s o f e f f e c t i v e s t r e s s a p p l i c a t i o n of the y i e l d v a l u e ( A f t e r S h i b a t a and Karube, 1969) . . . 27 2.9B I n f l u e n c e of r a t e o f s t r e s s a p p l i c a t i o n of the y i e l d v a l u e ( A f t e r S h i b a t a and Karube, 3.1 Sample under plane deformations . . . . . . < , 36 3.2 Schematic diagram of the l o a d i n g equipment f o r the plane s t r a i n apparatus . . . . . 37 v i i i F i g u r e Page 3.3 S c h e m a t i c l a y o u t o f p l a n e s t r a i n a p p a r a t u s w i t h a p p a r a t u s t o measure volume c h a n g e s and p r e s s u r e s . . . . . . . . . . . . . . . . 39 4.1 T y p i c a l p l o t o f a x i a l s t r a i n v e r s u s t i m e f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s 4.4 L o g a x i a l s t r a i n r a t e v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s - i n c r e a s e d ( u n d i s t u r b e d Haney c l a y ) . 50 4.2 L o g a r i t h m o f a x i a l s t r a i n r a t e v e r s u s l o g a r i t h m o f t i m e f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s - i n c r e a s e d (Haney c l a y ) . . . . . . . . . 4.3A P o r e w a t e r p r e s s u r e v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s -4.3B Skempton "A" v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s - i n c r e a s e d . . . 57 4.3C E f f e c t i v e s t r e s s r a t i o v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s 60 4.5 C o m p a r i s o n o f a D v e r s u s e f o r u n d r a i n e d p l a n e s t r a i n i n c r e m e n t a l l o a d i n g t e s t s -u n d i s t u r b e d Haney c l a y . . . . . . . . . . . 64 4.6 C o m p a r i s o n o f d e f o r m a t i o n b e h a v i o u r o f u n d r a i n e d p l a n e s t r a i n c r e e p t e s t f o r t h e c a s e s o f " a ^ i n c r e a s e d " and "o^ d. 6 G JC G ci S GCil a o o s o o a i o o a a a a o a o o 66 4.7 L o g a r i t h m o f a x i a l s t r a i n r a t e v e r s u s l o g a r i t h m o f t i m e f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s 4.8 L i n e s o f minimum s t r a i n r a t e s - p l a n e s t r a i n . . 69 4.9 L o g a x i a l s t r a i n r a t e v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s 4.10A a D v e r s u s minimum s t r a i n r a t e f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s . . . . . . . . . . 74 4.10B T/O* 1 a t e v e r s u s e f o r u n d r a i n e d p l a n e , m. m , . m N A s t r a i n c r e e p t e s t s . . . . . . . . . . . . . 74 I X F i g u r e Page 4„11A T/O' v e r s u s a x i a l s t r a i n f o r u n d r a i n e d m p l a n e s t r a i n c r e e p t e s t s . . . . . . . . . . 76 4.11B P o r e p r e s s u r e v e r s u s a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s . . . . . 76 4.12 V a r i a t i o n s o f H e n k e l " a " and a x i a l s t r a i n f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s . . . 79 4.13 O c t a h e d r a l s t r e s s p a t h s f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s ( U n d i s t u r b e d Haney c l a y ) . . . . . . . . . . . . . . . . 81 5.1 C o m p a r i s o n o f l i n e s o f minimum s t r a i n r a t e s 89 5.2 x . / ( a * . ) a t minimum s t r a i n r a t e v e r s u s o c t o c t c ^ o c t ' m ^ o r u n c ^ r a i n e d c r e e p t e s t s on Haney C lcL^ • « o a o o » o * a » a » a o o a a o o 9 3> 5.3 T . / ( a ' , ) a t minimum s t r a i n r a t e o c t ' o c t c v e r s u s t f o r u n d r a i n e d c r e e p t e s t s on 5.4 x j / a ' ^ a t (Y ^) v e r s u s (y ,) f o r o c t 7 . o c t 1 o c t m o c t m _„t' .  ' o c t m g e t ... u n d r a i n e d c r e e p t e s t s - Haney c l a y . . . . . 94 6.1 R e l a t i o n b e t w e e n t o t a l t i m e t o r u p t u r e and minimum s t r a i n r a t e f o r u n d r a i n e d p l a n e s t r a i n c r e e p t e s t s . . . . . . . . . . . . 98 6.2 R e l a t i o n b e t w e e n t o t a l t i m e t o r u p t u r e and minimum s t r a i n r a t e . . . . . . . . . . . . 100 6.3 R e l a t i o n b e t w e e n c u r r e n t s t r a i n r a t e and t i m e t o r u p t u r e f o r u n d r a i n e d p l a n e s t r a i n C JT" 6 G 16 S t S • o e a » o t t t t O 0 o o * o o 0 1 0 4 6.4 R e l a t i o n b etween c u r r e n t s t r a i n r a t e and t i m e t o r u p t u r e . . . . . . . . . . . . . . 105 X LIST OF SYMBOLS a l , 2 , 3 P r i n c i p a l t o t a l s t r e s s e s a' 0 ' 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 K C o e f f i c i e n t of e a r t h p r e s s u r e a t r e s t o a Q D e v i a t o r s t r e s s (a^ - a^) t E l a p s e d time t Time to minimum s t r a i n r a t e m t T o t a l r u p t u r e l i f e t t Time to r u p t u r e e s Secondary creep s t r a i n r a t e e Minimum s t r a i n r a t e m x Shear s t r e s s a' E f f e c t i v e s t r e s s t ^ Time to f a i l u r e H H a l f the h e i g h t of specimen c C o e f f i c i e n t o f c o n s o l i d a t i o n v u Pore p r e s s u r e A & B Skempton 1s pore p r e s s u r e parameters a Henkel pore p r e s s u r e parameters a' Mean normal e f f e c t i v e s t r e s s m x . O c t a h e d r a l shear s t r e s s o c t 0' . O c t a h e d r a l e f f e c t i v e normal s t r e s s o c t X I Y , O c t a h e d r a l shear s t r a i n 'oct Y , O c t a h e d r a l shear s t r a i n r a t e .' o c t s, 0 P r i n c i p a l s t r a i n s (a 1 .) Mean normal e f f e c t i v e s t r e s s a t the end of o c t c c o n s o l i d a t i o n ( Y .) Minimum o c t a h e d r a l shear s t r a i n r a t e o c t m x i i ACKNOWLEDGEMENTS The w r i t e r wishes t o express h i s most g r a t e f u l thanks to h i s r e s e a r c h s u p e r v i s o r , Dr. R.G. Campanella f o r the continuous quidance d u r i n g the course o f t h i s r e s e a r c h . He f u r t h e r wishes t o express h i s a p p r e c i a t i o n to Dr. W.D.L. F i n n and Dr. P.M. Byrne f o r r e v i e w i n g the manuscript and making v a l u a b l e s u g g e s t i o n s . The w r i t e r a l s o wishes to express h i s thanks t o h i s c o l l e a g u e s i n S o i l Mechanics a t U.B.C. f o r t h e i r a s s i s t a n c e d u r i n g t h i s r e s e a r c h . In p a r t i c u l a r , the con-t i n u e d i n t e r e s t and a d v i c e g i v e n by Mr. Y.P. V a i d i s g r a t e f u l l y a p p r e c i a t e d . The author i s inde b t e d t o the governments o f Canada and Ceylon f o r a Commonwealth s c h o l a r s h i p which supported him d u r i n g t h i s r e s e a r c h . The t e c h n i c a l a s s i s t a n c e s u p p l i e d by the s t a f f o f the C i v i l E n g i n e e r i n g Department i s g r a t e f u l l y acknowledged. 1 CHAPTER I INTRODUCTION Creep or continuous time-dependent s h e a r i n g deform-a t i o n s o f e a r t h s t r u c t u r e s , s l o p e s and f o u n d a t i o n s , s u b j e c t e d t o s u s t a i n e d s t r e s s e s , have been observed by s e v e r a l r e p o r t e r s . H a e f e l i (1953), H a e f e l i and Shaerer (1953), Henkel (1957), S u k l j e (1957), S a i t o (1969). These time-dependent s h e a r i n g deformations have g i v e n the engineer many d i f f i c u l t i e s p a r t i c u l a r l y i n the d e s i g n o f s l o p e s , 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 o f c l a y s o i l s , as he i s unable t o p r e d i c t r e l i a b l y the long term b e h a v i o u r . T h e r e f o r e , t h e r e i s an immediate need f o r r e s e a r c h on creep and creep r u p t u r e o f c l a y s . Due to the nature o f t h e i r d e p o s i t i o n most sedimen-t a r y c l a y s t r a t a have undergone v e r t i c a l c o n s o l i d a t i o n w i t h no l a t e r a l y i e l d . T h i s i s termed K c o n s o l i d a t i o n . Thus, l a b o r a t o r y samples i n i t i a l l y c o n s o l i d a t e d under K q c o n d i t i o n s are more r e p r e s e n t a t i v e o f f i e l d c o n d i t i o n s than the u s u a l h y d r o s t a t i c a l l y c o n s o l i d a t e d samples. Furthermore, f a i l u r e s o f many types of f o u n d a t i o n s t r u c t u r e s such as r e t a i n i n g w a l l s , long f o o t i n g s , as w e l l as c u t s , f i l l s and s l o p e s , f r e q u e n t l y take p l a c e under c o n d i t i o n s o f plane s t r a i n . 2 Thus, the p a r t i c u l a r cases of s t r e s s - s t r a i n c o n d i t i o n o f s o i l (1) under the c e n t r e l i n e of a s t r i p f o u n d a t i o n , and (2) behind a long r e t a i n i n g w a l l under a c t i v e e a r t h p r e s s u r e , can b e s t be s i m u l a t e d i n the l a b o r a t o r y w i t h the use of K q c o n s o l i d a t e d samples sheared i n the plane s t r a i n apparatus. A t p r e s e n t no i n v e s t i g a t i o n s have been r e p o r t e d i n which creep r u p t u r e ( f a i l u r e under s u s t a i n e d s h e a r i n g s t r e s s e s ) has been performed under plane s t r a i n c o n d i t i o n s . I t i s f o r these reasons t h a t the p r e s e n t study on plane s t r a i n creep r u p t u r e was undertaken. In many long range s t a b i l i t y problems the l o a d i n g i n v o l v e s an i n c r e a s e i n the major p r i n c i p a l s t r e s s ( f i l l s and o t h e r s t r u c t u r e s p l a c e d on weaker s o i l s ) . However, i n the long-term s t a b i l i t y o f c u t s , s l o p e s and r e t a i n i n g w a l l s , the s t r e s s change which lea d s to f a i l u r e i s p r i m a r i l y a decrease i n l a t e r a l p r e s s u r e or a decrease i n the minor p r i n c i p a l s t r e s s . The l a b o r a t o r y t e s t which most c l o s e l y reproduces t h i s type o f f i e l d c o n d i t i o n i s a creep t e s t i n which the a x i a l s t r e s s i s kept c o n s t a n t and f a i l u r e i s brought about by d e c r e a s i n g the l a t e r a l s t r e s s . A t p r e s e n t no i n v e s t i g a t i o n s have been r e p o r t e d i n which creep r u p t u r e i s brought about by r e d u c i n g the l a t e r a l s t r e s s . T h e r e f o r e t h i s i s another a s p e c t of creep r u p t u r e which was c o n s i d e r e d i n t h i s study. Thus, the i n v e s t i g a t i o n h e r e i n c o n s i d e r s the e f f e c t of (1) K c o n s o l i d a t i o n (2) plane s t r a i n c o n d i t i o n 3 (3) t o t a l s t r e s s paths of l o a d i n g (comparison of i n c r e a s i n g major p r i n c i p a l s t r e s s a^, to d e c r e a s i n g the minor p r i n c i p a l s t r e s s a^) on the creep r u p t u r e behaviour of undrained specimens of a s e n s i t i v e c l a y . The most commonly used t e s t apparatus to study creep and creep r u p t u r e i s the " t r i a x i a l " apparatus, because o f i t s s i m p l i c i t y and a v a i l a b i l i t y . In a " t r i a x i a l " t e s t a c y l i n d r i c a l specimen of s o i l i s f i r s t i s o t r o p i c a l l y con-s o l i d a t e d and then a x i a l l y loaded. During creep the s t a t e of s t r e s s i s a x i a l l y symmetric (where the i n t e r m e d i a t e and minor p r i n c i p a l s t r e s s e s and are always e q u a l ) . U s u a l l y the r e s u l t s of t r i a x i a l t e s t are a p p l i e d t o f i e l d problems where the a c t u a l i n i t i a l c o n s o l i d a t i o n i s o f t e n a n i s o t r o p i c and creep o c c u r s when the t h r e e p r i n c i p a l s t r e s s e s are d i f f e r e n t . Is t h e r e any j u s t i f i c a t i o n t o apply the r e s u l t s of t r i a x i a l t e s t s t o f i e l d c o n d i t i o n ? A d e f i n i t e answer to t h i s q u e s t i o n i s unknown a t the p r e s e n t , but should be c o n s i d e r e d b e f o r e the r e s u l t s of l a b o r a t o r y t r i a x i a l t e s t s can be r e a l l y meaningful as a means of p r e d i c t i n g creep r u p t u r e i n the f i e l d . S t u d i e s on creep r u p t u r e of a s e n s i t i v e c l a y (the same c l a y used i n t h i s study) i n the c o n v e n t i o n a l t r i a x i a l apparatus have been r e p o r t e d by Snead (1970). In the i n v e s t i g a t i o n r e p o r t e d h e r e i n , the r e s u l t s of Snead 1s creep r u p t u r e t e s t s o b t a i n e d from t r i a x i a l samples have been 4 compared wi t h those o b t a i n e d from plane s t r a i n t e s t s . How-ever i n a l l of Snead's t e s t s the samples were 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 . Thus some creep r u p t u r e t e s t s were a l s o performed i n which the t r i a x i a l specimen was f i r s t c o n s o l i d a t e d under K c o n d i t i o n and then loaded by o J i n c r e a s i n g a^, as w e l l as d e c r e a s i n g w i t h = o"^ . F i e l d o b s e r v a t i o n of creep have shown t h a t f a i l u r e s of e a r t h s t r u c t u r e s , s l o p e s and f o u n d a t i o n s occur a f t e r a r e l a t i v e l y long p e r i o d of continuous movements. T h e r e f o r e i f the mechanisms of creep r u p t u r e i s understood, i t should be p o s s i b l e to p r e d i c t the time to f a i l u r e d u r i n g p r e - f a i l u r e movements and thus a l l o w r e m e d i a l and s a f e t y measures to be taken a c c o r d i n g l y . The p o s s i b i l i t y of p r e d i c t i n g the time of o c c u r r e n c e of s lope f a i l u r e i n the f i e l d u s i n g the a v a i l a b l e methods ( S a i t o , 1965; Snead, 1970), w i t h l a b o r a t o r y data, was c o n s i d -ered i n t h i s study. The p r e d i c t e d times o b t a i n e d from plane s t r a i n d a t a was compared w i t h those from t r i a x i a l d a t a . 5 CHAPTER 2 LITERATURE REVIEW T h i s l i t e r a t u r e review w i l l p r e s e n t the p e r t i n e n t i n f o r m a t i o n on creep and creep r u p t u r e . I t has t o be emphasized t h a t no i n f o r m a t i o n i s a v a i l a b l e a t p r e s e n t on creep and creep r u p t u r e behaviour o f K q c o n s o l i d a t e d samples which deformed under plane s t r a i n c o n d i t i o n s w i t h the creep d e v i a t o r s t r e s s b e i n g a p p l i e d by e i t h e r i n c r e a s i n g or d e c r e a s i n g . As the need f o r b e t t e r u n d e r s t a n d i n g of creep i s demonstrated by f a i l u r e s o f f o u n d a t i o n s and s l o p e s , f i e l d o b s e r v a t i o n of creep a l s o has to be d i s c u s s e d . The l i t e r a t u r e review w i l l be pre s e n t e d i n s e c t i o n s as f o l l o w s s -1. F i e l d o b s e r v a t i o n o f creep and creep f a i l u r e s . 2. Creep and creep r u p t u r e s t u d i e s . F i e l d O b s e r v a t i o n o f Creep and Creep F a i l u r e s Many f i e l d o b s e r v a t i o n s of creep i n s o i l s , snow and i c e were r e p o r t e d by H a e f e l i (1953). H a e f e l i and Shaerer (1953) has d e s c r i b e d i n d e t a i l the e f f e c t o f creep on an abutment of a b r i d g e . S e v e r a l c r a c k s which appeared i n a r e i n f o r c e d c o n c r e t e b r i d g e , were caused by s o i l creep which r e s u l t e d i n movements of one of the abutments. A h o r i z o n t a l s t i f f e n i n g beam was b u i l t to r e s i s t t h i s move-ment. A measuring d e v i c e , which p e r m i t t e d the r e c o r d i n g o f creep p r e s s u r e was f i t t e d t o the s t i f f e n i n g beam. I t was observed t h a t the creep p r e s s u r e c o n t i n u o u s l y i n c r e a s e d w i t h time from 1944 to 1950, except f o r some se a s o n a l f l u c t u a t i o n s . Long term f a i l u r e s of a r e t a i n i n g w a l l and a c u t -t i n g i n London c l a y were d e s c r i b e d by Henkel (1957). A t the s i t e of the c u t t i n g he r e p o r t e d t h a t s u b s t a n t i a l movements as w e l l as t e n s i o n c r a c k s near the top of the sl o p e were observed s e v e r a l months b e f o r e f a i l u r e o c c u r r e d . A t the s i t e o f the r e t a i n i n g w a l l , 3 f t movement of the w a l l was observed a few months b e f o r e f a i l u r e o c c u r r e d . A l a n d s l i d e which o c c u r r e d a f t e r l o n g term creep movements along the Gradot Ridge i n Macedonia i n 1956 was d e s c r i b e d by S u k l j e (1956). Along the upper boundary o f the s l i d e a d i s c o n t i n u o u s s e r i e s o f deep c r a c k s were formed over a l e n g t h of about 270 metres. Cracks of over 30 f t i n depth had been measured 30 years b e f o r e f a i l u r e . One year b e f o r e f a i l u r e the lower boundary of the c r a c k s was observed t o have subsided 20 cm. F u r t h e r subsidence appeared some weeks b e f o r e f a i l u r e . 7 S a i t o and Uezawa (1961) r e p o r t e d the o c c u r r e n c e of many l a n d s l i d e s along c u t t i n g s on Japanese r a i l w a y t r a c k s . Measurements of time dependendent movements o f the c r a c k s a t the top of the s l o p e s were r e c o r d e d by S a i t o and Uezawa s e v e r a l days b e f o r e f a i l u r e o c c u r r e d . From these measurements they attempted to p r e d i c t the time to f a i l u r e . I t i s e v i d e n t from o b s e r v a t i o n s d e s c r i b e d above. t h a t f a i l u r e o f t e n o c c u r s a f t e r movements over a long p e r i o d of time. Most of these movements can be approximated by plane s t r a i n c o n d i t i o n s . The l a b o r a t o r y plane s t r a i n apparatus c o u l d be used to study these creep movements. There-f o r e , by u n derstanding the mechanisms of creep, the p r e d i c t i o n of time to f a i l u r e may be attempted and r e m e d i a l and s a f e t y measures taken a c c o r d i n g l y . Creep and Creep Rupture S t u d i e s I n v e s t i g a t i o n s by Casagrande and W ilson (1951) have shown t h a t some types of b r i t t l e u n d i s t u r b e d c l a y s and c l a y s h a l e s c o n t i n u o u s l y deform under s u s t a i n e d l o a d , and t h a t f a i l u r e u l t i m a t e l y occurs under a s u s t a i n e d l o a d a p p r e c i a b l y l e s s than the s t r e n g t h i n d i c a t e d by a normal undrained com-p r e s s i o n t e s t . For the s u s t a i n e d l o a d i n g case, Casagrande and W ilson a p p l i e d the d e v i a t o r l o a d i n f o u r t o e i g h t i n c r e -ments a t s h o r t i n t e r v a l s of time, 1 minute being the most common i n t e r v a l . A f t e r the d e v i a t o r i c l o a d was a p p l i e d to 8 the sample i t deformed w i t h time, i n c r e a s i n g i t s a r e a . T h i s means t h a t the s t r e s s on the sample decreased s l i g h t l y w i t h time. F a i l u r e was i n v a r i a b l y preceded by a p o i n t of i n f l e c -t i o n i n the S t r a i n - T i m e curve f o l l o w e d by continuous d e f o r m a t i o n a t an i n c r e a s i n g r a t e . Shear c r a c k s i n the samples were observed s h o r t l y a f t e r the p o i n t of i n f l e c t i o n i n the time-deformation curve took p l a c e . For these reasons, they d e f i n e d time to f a i l u r e as the e l a p s e d time between the a p p l i c a t i o n o f the f i n a l l o a d increment and t h i s p o i n t o f i n f l e c -t i o n i n the time-deformation curve. For Mexico C i t y c l a y , they found: (1) the time to f a i l u r e i n c r e a s e d w i t h decrease i n l o a d , and (2) the l o g o f the time to f a i l u r e was l i n e a r l y r e l a t e d t o the a p p l i e d s t r e s s . A t y p i c a l s t r a i n - t i m e curve f o r metals, c o n c r e t e and p l a s t i c s i s shown i n F i g u r e 2.1. I t has been s u b d i v i d e d i n t o f o u r separate stages by many r e s e a r c h e r s . These stages are as f o l l o w s : -1. Instantaneous d e f o r m a t i o n 0 t o e . o 2. Primary Creep stage from t Q t o t ^ . 3. Secondary creep stage from t ^ to t 2 . 4. T e r t i a r y creep stage from t 2 to t r . The i n s t a n t a n e o u s deformation c o n s i s t s o f both e l a s t i c and p l a s t i c deformations a l t h o u g h i t i s o f t e n r e f e r r e d t o as the i n i t i a l e l a s t i c d e f o r m a t i o n . Primary creep i s the 9 FIGURE 21 A TYPICAL CREEP RUPTURE CURVE FOR METALS, CONCRETE AND PLASTICS. CAFTER GAROBALO, 1965".) ""; 10 stage d u r i n g which the s t r a i n r a t e i s c o n t i n u o u s l y d e c r e a s i n g w h i l e the secondary creep i s t h a t d u r i n g which the s t r a i n r a t e i s n e a r l y c o n s t a n t . The t e r t i a r y c reep i s the f i n a l stage d u r i n g which the s t r a i n r a t e i n c r e a s e s g r a d u a l l y l e a d -i n g to creep r u p t u r e . S i m i l a r s t r a i n - t i m e curves f o r c l a y s have been observed by S a i t o and Uezawa (1961) f o r t r i a x i a l t e s t s . V i a l o v and S k i b i t s k y (1957) i n v e s t i g a t e d the e f f e c t of creep i n f r o z e n s o i l s based on shear along rods which had been f r o z e n i n the s o i l . They observed t h a t the r a t e o f d e f o r m a t i o n i n i t i a l l y decreased to a c o n s t a n t and then i n c r e a s e d g r a d u a l l y to f a i l u r e , as shown i n F i g u r e 2.1. V i a l o v and S k i b i t s k y showed the e x i s t e n c e o f a upper y i e l d s t r e n g t h d e f i n e d as the maximum s u s t a i n e d s h e a r i n g s t r e s s which would not cause f a i l u r e w i t h time. Snead (1970) performed creep t e s t s on a undrained 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 s e n s i t i v e c l a y , c a l l e d Haney c l a y , u s i n g the c o n v e n t i o n a l t r i a x i a l apparatus. A t y p i c a l s t r a i n - t i m e curve i s g i v e n i n F i g u r e 2.2. He observed t h a t the s t r a i n r a t e i n i t i a l l y d e creased, reached a minimum, and then, i n c r e a s e d g r a d u a l l y p r o c e e d i n g to r u p t u r e . He c o u l d not f i n d a stage when the s t r a i n r a t e remained c o n s t a n t . He concluded t h a t , once a minimum s t r a i n r a t e i s reached, the sample w i l l e v e n t u a l l y r u p t u r e and f a i l u r e can be c o n s i d e r e d to have o c c u r r e d . He confirmed the e x i s t e n c e of an upper O I " 1 1 1 — 1  O SOO IOOO ISOO 2 0 0 0 25*00 ELAPSED TIME FIGURE2-2 A TYPICAL S T R A I N - T I M E CURVE FOR 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 SUSTAINED .DEVMTOR ST R E S S . C A F T E R S NEAD, 1970.) 12 y i e l d s t r e n g t h f o r Haney c l a y which was about 82% of the s t r e n g t h o b t a i n e d from a s p e c i f i e d i n c r e m e n t a l l o a d i n g t e s t . T h i s i n d i c a t e s t h a t samples c o u l d f a i l under s u s t a i n e d shear-i n g s t r e s s e s a p p r e c i a b l y l e s s than the s t r e n g t h i n d i c a t e d by a standard l a b o r a t o r y t e s t . Snead (1970) o b t a i n e d the l o g - l o g p l o t o f s t r a i n r a t e and time, as shown i n F i g u r e 2.3 by pe r f o r m i n g a s e r i e s of creep r u p t u r e t e s t s w i t h v a r y i n g s u s t a i n e d s h e a r i n g s t r e s s e s u s i n g the c o n v e n t i o n a l t r i a x i a l a pparatus. A l l samples were c o n s o l i d a t e d to an e f f e c t i v e h y d r o s t a t i c p r e s s u r e of 75 PSI. For d e v i a t o r creep s t r e s s e s g r e a t e r than 43.4 PSI, i t was observed t h a t i n i t i a l l y the s t r a i n r a t e de-cre a s e d , reached a minimum then i n c r e a s e d r a p i d l y p r o c e e d i n g to r u p t u r e . Primary and secondary stages o f creep can not be d i s t i n g u i s h e d on t h i s p l o t . The time t o f a i l u r e and the time to reach minimum s t r a i n r a t e i n c r e a s e s w i t h the decrease i n d e v i a t o r s t r e s s . From the ex p e r i m e n t a l r e s u l t s o b t a i n e d i t was observed t h a t the l o c u s of a l l p o i n t s having a minimum s t r a i n r a t e f o r a g i v e n f a i l u r e s t r e s s l i e on a s t r a i g h t l i n e on t h i s l o g versus l o g t p l o t . The E q u a t i o n o f t h i s l i n e was found to be:-l o g 1 Q t = - .142 - 1.15 l o g 1 Q e m ± .116 . . . 2.1 where t = e l a p s e d time u n t i l the minimum s t r a i n r a t e i n minutes. 13 -f- D E N O T E S POINTS O F MINIMUM STRAIN RATES 'o° io' zoa i d /o* ELAPSED TIME (M/N) F I G U R E 2 3 LOGARITHM OF AXIAL S T R A I N R A T E V F R S U S t LOG Hl^PSED TIM£ FOft NORMALLY CONSOLIDATED ^DRAINED CREEP TESTS ON HANEY CLAY. (AFTER SNEAD, 117$ e - minimum s t r a i n r a t e i n p e r c e n t per minute and ± .116 was m t- f o b t a i n e d when 95% of the data p o i n t s are c o n s i d e r e d . A l l s t r a i n r a t e - t i m e curves s t a r t below the l i n e of minimum s t r a i n r a t e s and proceed towards t h i s l i n e i f f a i l u r e i s t o take p l a c e . For the sample w i t h a d e v i a t o r s t r e s s of 42.8 PSI the curve appears to be proc e e d i n g towards the l i n e o f minimum s t r a i n r a t e s but changes i t s course and contin u e s p a r a l l e l t o the l i n e o f minimum s t r a i n r a t e s . Thus i t was p r e d i c t e d t h a t the sample should never f a i l under the imposed s t r e s s e s . For s t r e s s e s below the upper y i e l d s t r e n g t h f o r c o n s o l i d a t e d i l l i t e , Campanella (1965) observed t h a t s t r a i n r a t e was c o n t i n u a l l y d e c r e a s i n g f o r the d u r a t i o n of the t e s t , and were r e p r e s e n t e d by p a r a l l e l s t r a i g h t l i n e s on a l o g - l o g p l o t o f s t r a i n r a t e and time as shown i n F i g u r e 2.4. P a r a l l e l s t r a i g h t l i n e s on t h i s p l o t were p r e d i c t e d by Singh and M i t c h e l l (1968) f o r s t r e s s e s below the upper y i e l d and t i l l minimum s t r a i n r a t e was reached f o r s t r e s s e s above upper y i e l d . Singh and M i t c h e l l (1969) used the s l o p e "m" of these s t r a i g h t l i n e s to p r e d i c t a f t e r long times, whether the s t r a i n r a t e s may almost cease, c o n t i n u e a t ever d e c r e a s i n g r a t e s (m > 1) or i n some cases s t a r t i n c r e a s i n g e v e n t u a l l y r e s u l t -i n g i n creep r u p t u r e (m <_ 1) . I t was observed by Snead (1970) and s e v e r a l o t h e r i n v e s t i g a t o r s t h a t once the minimum s t r a i n r a t e was reached, the s t r a i n r a t e began to i n c r e a s e and the sample was bound t o 15 . o o o o i l l I I I l I I I I I J •2 S I 2 «5 10 20 100 200 ' 0 0 ° ELAPSED TIME-fM/N.) FIGURE 24 LOG STRAIN RATE VERSUS LOG TIME FOR SATURATED I LL/TE (AFTER CAMPANELLA, f a i l . Snead used the e x i s t e n c e of a minimum s t r a i n r a t e as a f a i l u r e c r i t e r i o n . S a i t o and Uezawa (1961) proposed a l i n e a r r e l a t i o n -ship' between the l o g o f secondary s t r a i n r a t e and the l o g of the t o t a l time t o r u p t u r e . They performed t r i a x i a l compression t e s t s on f o u r Japanese s o i l s and t h e i r r e s u l t s t o g e t h e r w i t h those o f o t h e r i n v e s t i g a t o r s , are shown i n F i g u r e 2.5. T h i s F i g u r e shows the e r r o r band c a l l e d 95% c o n f i d e n c e l i m i t s e n c l o s i n g 95% o f a l l data p o i n t s . The eq u a t i o n of the s t r a i g h t l i n e i n F i g u r e 2.5 was o b t a i n e d by S a i t o and Uezawa to be l o g 1 Q t r = 2.33 - .916 lO9" 1 0 £ s . . . » 2.2 -4 e g secondary s t r a i n r a t e expressed i n 10 per minute t r t o t a l r u p t u r e l i f e . I t i s important t o note t h a t E q u a t i o n 2.2 has been o b t a i n e d from d i f f e r e n t types of s o i l s , s t r e s s l e v e l s , con-s o l i d a t i o n h i s t o r y and drainage c o n d i t i o n s . E q u a t i o n 2.2 was s i m p l i f i e d by S a i t o and Uezawa to e q u a t i o n 2.3 by approximating .916 log^g e g as e q u a l t o 9 log,,, e . Thus, ^ 10 s t • e = 216 . . . . 2.3 r s The E q u a t i o n 2.3 was a p p l i e d by S a i t o (1965') t o n a t u r a l s l o p e s and f u l l s c a l e experiments d u r i n g secondary 17 FIGURE 2S RELATIONSHIP 8 E - T W E E N C R E E P R U P T U R E L I F E AND STRAIN RATE (AFTER 3AITO <S.UEZAWA,\%l) 18 creep stage. He p r e d i c t e d w i t h reasonable accuracy the time of o ccurrence of s l o p e f a i l u r e by u s i n g E q u a t i o n 2.3. One wonders why S a i t o was a b l e to p r e d i c t a c c u r a t e l y the time of occurrence of slope f a i l u r e from the r e s u l t s o f c o n v e n t i o n a l t r i a x i a l creep t e s t s which do not s i m u l a t e the u s u a l f i e l d c o n d i t i o n s . Is i t because of the wide c o n f i d e n c e l i m i t s o f ± 500%; the way i n which e g was measured i n the f i e l d ; o r p o s s i b l e c a n c e l l i n g - o u t of opposing i n a c c u r a c i e s ? Perhaps the e m p i r i c a l r e l a t i o n s h i p s h o l d without t h e o r e t i c a l j u s t i f i -c a t i o n . In any event i t was hoped t h a t some of these q u e s t i o n s c o u l d be answered by the r e s u l t s of the i n v e s t i g a t i o n r e p o r t e d h e r e i n . Snead (1970) found t h a t a secondary creep stage d i d not e x i s t f o r Haney c l a y , and suggested t h a t the secondary s t r a i n r a t e measured by S a i t o and Uezawa was approximately e q u a l to the minimum s t r a i n r a t e c a l c u l a t e d by him. Snead (19 70) observed a l i n e a r r e l a t i o n s h i p between the l o g a r i t h m of minimum s t r a i n r a t e and the t o t a l r u p t u r e l i f e as shown i n F i g u r e 2.6. Uezawa's s t r a i g h t l i n e r e l a t i o n s h i p w i t h the 95% c o n f i d e n c e l i n e s are a l s o shown i n F i g u r e 2.6. Snead's e q u a t i o n of the s t r a i g h t l i n e i n F i g u r e 2.6 i s g i v e n by log,„ t = .751 - .92 l o g , n ± .272 . . . . 2.4 ^10 r ^10 m where t t o t a l r u p t u r e l i f e i n minutes. e minimum s t r a i n r a t e p e r c e n t per minute. 19 fo° 10' io3- /o3 /o* TOTAL RUPTURE LIFE (MIN-) FIGURE 2 . 6 T O T A L R U P T U R E L I F E O F L A B O R A T O R Y CREEP TESTS (AFTER SNEAD, 19 70.) 20 The 95% c o n f i d e n c e l i m i t s f o r Haney c l a y are s m a l l e r than those o b t a i n e d by S a i t o and Uezawa and t h e r e f o r e i t was suggested by Snead (1970) t h a t the r e l a t i o n between " t " and " e s " i s s i m i l a r f o r o t h e r s o i l s but not n e c e s s a r y unique f o r a l l s o i l s as suggested by S a i t o and Uezawa. S a i t o 1 s (1965) method of p r e d i c t i n g the o c c u r r e n c e o f time to s l o p e f a i l u r e has been a p p l i e d f o r creep stages b e f o r e t e r t i a r y c reep. Snead (1970) on the o t h e r hand proposed a method of p r e d i c t i n g the o c c u r r e n c e of time to s l o p e f a i l u r e f o r t e r t i a r y creep stage. Snead d e f i n e d the "time to r u p t u r e " as the e l a p s e d time from the i n s t a n t c o n s i d e r e d t i l l f a i l u r e and o b t a i n e d a l i n e a r r e l a t i o n s h i p between l o g o f time t o r u p t u r e " t t " and c u r r e n t s t r a i n r a t e , e, as shown i n F i g u r e 2.7. The e q u a t i o n o b t a i n e d i s g i v e n below l o g ^ 0 t t = .23 - a log-^Q £ . . . . 2.5 where t t time to r u p t u r e i n minutes e c u r r e n t s t r a i n r a t e i n p e r c e n t per minute a c o n s t a n t . a was found to be = 1 . 1 7 Thus, the e q u a t i o n reduced to t t = —^— . . . . 2.6 e S a i t o (1969) a l s o proposed a method f o r p r e d i c t i n g s l o p e f a i l u r e d u r i n g t e r t i a r y c r e e p . In t h i s method he assumed a r e l a t i o n s h i p between " t t " and "e" s i m i l a r t o E q u a t i o n 2.6, to o b t a i n an e x p r e s s i o n f o r s t r a i n by mathematical 21 IO | I 1 1 1 1 1 1 1 1 I 10° 10' 10* 'o3 io* so* TIME T O RUPTURE - MINAS FIGURE 2-1 RELATIONSHIP BETWEEN TIME To RUPTURE AND CURRENT STRAIN RATE (AFTER SNEAD, 1970.) 22 i n t e g r a t i o n . He found r e a s o n a b l e agreement between the p r e -d i c t e d and observed time of occurrence o f s l o p e f a i l u r e . S t r e s s - S t r a i n Rate - S t r a i n R e l a t i o n s h i p - Upon i n v e s t i -g a t i o n o f a v a i l a b l e r e s e a r c h on metals, Lubahn and F e l g a r (1961) suggested t h a t a r e l a t i o n e x i s t s between s t r e s s , s t r a i n and s t r a i n r a t e f o r metals a t c o n s t a n t temperature which i s independent of the s t r a i n r a t e h i s t o r y . T h i s r e l a t i o n can be w r i t t e n i n the form of s = f ( e , e) a t c o n s t a n t temperature s c u r r e n t s t r e s s e c u r r e n t s t r a i n e c u r r e n t s t r a i n r a t e . Snead (1970) extended t h i s concept to s o i l s , but r e s t r i c t e d i t s use t o the f o l l o w i n g c o n d i t i o n s : -1. Sample having the same c o n s o l i d a t i o n h i s t o r y and not h e a v i l y over c o n s o l i d a t e d . 2. Undrained. 3. C o n t i n u a l l y i n c r e a s i n g compressive a x i a l s t r a i n s . 4. Constant temperature. Snead i n v e s t i g a t e d the v a l i d i t y of the a p p l i c a t i o n o f t h i s r e l a t i o n by p l o t t i n g the data of the i n c r e m e n t a l l o a d i n g and s t r a i n c o n t r o l l e d t e s t s on normally c o n s o l i d a t e d undrained Haney c l a y as shown i n F i g u r e 2.8. Along the curves of s t r a i n 23 2 2 13 I I I h Q? J X - 4 - 6 / 2 - 4 6 IO A X I A L STRAIN PERCENT 2 0 FIGURE 2 . 8 A X I A L S T R A I N R A T E VERSUS AXIAL STRAIN CURVES FOR N O R M A L L Y O D N A S O L I D A T E D H A M E Y C L A Y USING CONVENTIONAL T R I A X / A L A P P A R A T U S . C ^ T E R S N E ^ ^ T Q ) c o n t r o l l e d and i n c r e m e n t a l l o a d i n g t e s t s the v a l u e s of d e v i a t o r s t r e s s a D a t t h a t s t r a i n and s t r a i n r a t e are g i v e n , w h i l e f o r the creep t e s t s the c o n s t a n t d e v i a t o r s t r e s s a t any s t r a i n and s t r a i n r a t e should be independent of the t h r e e types o f t e s t s . A r e a s o n a b l e agreement was o b t a i n e d by him as shown i n F i g u r e 2 . 8 . T h i s concept was checked f o r o t h e r c o n s o l i d a t i o n h i s t o r i e s and found to be i n r e a s o n a b l e agreement. I t should be noted t h a t the c o n s o l i d a t i o n h i s t o r i e s of the t h r e e types of t e s t s namely creep t e s t s , i n c r e m e n t a l l o a d i n g t e s t , s t r a i n c o n t r o l l e d t e s t s were the same. Snead showed i t was p o s s i b l e to p r e d i c t w i t h r e a s o n a b l e accuracy the s t r e s s - s t r a i n curve f o r s t r a i n r a t e c o n t r o l l e d and i n c r e m e n t a l l o a d i n g t e s t s by u s i n g data from creep t e s t s . Snead ( 1 9 7 0 ) d i d not make an attempt t o e v a l u a t e a f u n c t i o n a l r e l a t i o n s h i p between, s t r e s s and s t r a i n r a t e , but p r e d i c t e d the behaviour of one type of t e s t based upon another. But i s t h i s h y p o t h e s i s o f 0 Q = f ( e , e) v a l i d ( 1 ) f o r any c o n s o l i d a t i o n s t r e s s path such as f o r K q c o n s o l i -dated samples ( 2 ) f o r plane s t r a i n c o n d i t i o n s as w e l l as t r i a x i a l and ( 3 ) when the shear t e s t s and creep t e s t s are performed by i n c r e a s i n g as w e l l as d e c r e a s i n g 0 ^ ? T h i s i s one of the reasons why t h i s i n v e s t i g a t i o n on creep r u p t u r e was undertaken. 25 A n a l y s i s of Creep i n Terms of E f f e c t i v e S t r e s s e s - Creep d a t a o b t a i n e d from undrained s t r e s s c o n t r o l l e d t e s t s have not g e n e r a l l y been analyzed i n terms of e f f e c t i v e s t r e s s e s , f o r the f o l l o w i n g reasons: 1. The d i f f i c u l t y i n o b t a i n i n g a c c u r a t e and r e l i a b l e pore p r e s s u r e s and hence e f f e c t i v e s t r e s s e s which are r e p r e -s e n t a t i v e of the e n t i r e sample. For example, end r e s t r a i n t s of the l o a d i n g p l a t e n s o f t e n cause non-uniform pore p r e s s u r e s throughout the sample. A l s o j u s t p r i o r t o creep r u p t u r e the r e c o r d e d pore p r e s s u r e s are a l s o q u e s t i o n a b l e , s i n c e the s t r a i n r a t e s are l a r g e and may cause c o r r e s p o n d i n g l y h i g h r a t e s of change i n pore p r e s s u r e s g i v i n g n o n - e q u a l i z a t i o n o f pore p r e s s u r e s . 2. I t has been found by s e v e r a l i n v e s t i g a t o r s t h a t the pore p r e s s u r e s i n a sample under s u s t a i n e d s h e a r i n g s t r e s s e s o f t e n i n c r e a s e , r e s u l t i n g i n a decrease i n e f f e c t i v e s t r e s s e s , which should cause a l o s s i n s t r e n g t h . Yet the s t r a i n r a t e of t h i s same sample has been found to decrease, i n d i c a t i n g s t r a i n hardening and a p o s s i b l e g a i n i n s t r e n g t h which can not be e x p l a i n e d by c o n s i d e r i n g e f f e c t i v e s t r e s s e s . When an undrained t r i a x i a l specimen of n o r m a l l y c o n s o l i d a t e d s e n s i t i v e c l a y was s u b j e c t e d to s u s t a i n e d shear-26 i n g s t r e s s e s , i t e x h i b i t e d a steady time-dependent i n c r e a s e i n pore p r e s s u r e . Snead (1970), Walker (1969). Walker (1969) analyzed t h i s behaviour i n terms of an 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 . He showed t h a t d u r i n g creep the e f f e c t i v e s t r e s s s t a t e i n the sample changed w i t h time towards the f a i l u r e envelope f o r the c l a y . S h i b a t a and Karube (1969) performed a s e r i e s o f s p e c i a l d r a i n e d creep t e s t s , d u r i n g which the water co n t e n t was p r a c t i c a l l y m aintained c o n s t a n t , on norm a l l y c o n s o l i d a t e d and o v e r c o n s o l i d a t e d c l a y samples having the same i n i t i a l water c o n t e n t . Undrained creep t e s t s on norm a l l y c o n s o l i d a t e d and o v e r c o n s o l i d a t e d c l a y samples were a l s o performed. The data on upper y i e l d s t r e n g t h were pre s e n t e d and an a l y z e d on the b a s i s o f an e f f e c t i v e s t r e s s concept. The " y i e l d v a l u e " envelopes o f norm a l l y c o n s o l i d a t e d c l a y p l o t t e d on x - a' c o - o r d i n a t e system was approximated by s t r a i g h t l i n e s w i t h i n t e r c e p t of c ' c o t y' on the a x i s and sl o p e Y ' as shown i n F i g u r e 2.9. The y i e l d v a l u e s l o p e parameter Y ' measured by the undrained creep s t r e n g t h t e s t was seen t o be a v a r i a b l e depending on the time o f l o a d i n g from the f i r s t increment t o the l a s t . The sl o p e Y^ 1 measured by the d r a i n e d creep s t r e n g t h t e s t was found to be c l o s e to the maximum angle o f sh e a r i n g r e s i s t a n c e o b t a i n e d from normal compression t e s t s . T h e r e f o r e Walker (1969), S h i b a t a and Karube (1969) have made an attempt t o study the r e s u l t s of creep t e s t s i n terms o f e f f e c t i v e s t r e s s e s . 27 oa O-f 0-6 0-8 »0 12. 1-4- 16 FIGURE 2 9A A/VMLYVS/S OF YiELD VALUE ON THE e^SlS OF EFFECTIVE STRESS CONCEPT. CAFTER SHIBATA AND KARUBE, iq&) J I I I 1 1 1 L O 0-2 04 0-6 0 8 ' 0 1-2 I-+ IC FIGURE 29 B INFLUENCE OF RATE OF STRESS APPLICATION OF THE YIELD VALUE. (AFTER SHl&AT/\ ANX> KARUBE, 28 Summary 1. A t p r e s e n t no i n v e s t i g a t i o n of creep r u p t u r e has been done t a k i n g i n t o account the e f f e c t of (a) K q c o n s o l i d a t i o n (b) plane s t r a i n c o n d i t i o n (c) t o t a l s t r e s s paths o f l o a d i n g (comparison of i n c r e a s i n g and d e c r e a s i n g type o f creep t e s t s ) . I t was d i s c u s s e d i n the l i t e r a t u r e review t h a t the above c o n d i t i o n s are o b t a i n e d i n the f i e l d and can be si m u l a t e d i n the l a b o r a t o r y by u s i n g a plane s t r a i n apparatus. I t i s because o f the reasons o u t l i n e d above t h a t the study on plane s t r a i n creep r u p t u r e was undertaken. 2. In a v a i l a b l e l i t e r a t u r e on t r i a x i a l t e s t s t h e r e i s agree-ment t h a t f o r samples under s u s t a i n e d s h e a r i n g s t r e s s e s , the time to f a i l u r e i n c r e a s e s w i t h the decrease i n sus-t a i n e d s h e a r i n g s t r e s s e s . 3. I t has been observed by s e v e r a l i n v e s t i g a t o r s t h a t samples of s e n s i t i v e o r remoulded c l a y s f a i l e d under s u s t a i n e d s h e a r i n g s t r e s s e s a p p r e c i a b l y l e s s than the s t r e n g t h i n d i c a t e d by a standard l a b o r a t o r y shear t e s t . These i n v e s t i g a t o r s have showed the e x i s t e n c e o f a upper y i e l d or maximum creep s t r e s s which w i l l not cause f a i l u r e with, time. 4. The e x i s t e n c e of a minimum s t r a i n r a t e was used by Snead (1970) as a f a i l u r e c r i t e r i o n . 5. Snead (1970) observed the e x i s t e n c e of a l i n e o f minimum s t r a i n r a t e s f o r normally c o n s o l i d a t e d samples t e s t e d undrained i n the t r i a x i a l apparatus. T h i s l i n e o f minimum s t r a i n r a t e s was used by Snead as a f a i l u r e c r i t e r i o n . 6. Snead (1970) h y p o t h e s i z e d t h a t = f ( e , e) f o r t r i a x i a l samples o f Haney c l a y w i t h the same i n i t i a l c o n d i t i o n s f o r d i f f e r e n t types of t e s t s ( i . e . , creep t e s t s , i n c r e -mental l o a d i n g t e s t s , s t r a i n r a t e c o n t r o l l e d shear t e s t s ) . A l l samples should be t e s t e d undrained a t con-s t a n t temperature f o r c o n t i n u a l l y i n c r e a s i n g compressive a x i a l s t r a i n s , and the samples not h e a v i l y overcon-s o l i d a t e d . 7. S a i t o ' s (1965) method f o r creep stage b e f o r e t e r t i a r y creep and Snead's (1970) and S a i t o ' s (1969) methods f o r t e r t i a r y creep stage were the o n l y methods a v a i l a b l e f o r the p r e d i c t i o n of the time to s l o p e f a i l u r e under s u s t a i n e d s h e a r i n g s t r e s s e s . 8. Although a few i n v e s t i g a t o r s have attempted to study the r e s u l t s o f creep i n terms of e f f e c t i v e s t r e s s e s , s t u d i e s of creep has been mainly i n v e s t i g a t e d i n terms of t o t a l s t r e s s e s . 30 CHAPTER 3 LABORATORY TESTING Development of a T e s t i n g Programme T h i s study was r e s t r i c t e d to nor 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 . The p r e c o n s o l i d a t i o n p r e s s u r e under K c o n d i t i o n was about 60 PSI as determined by a standard o •* l a b o r a t o r y c o n s o l i d a t i o n t e s t . T h e r e f o r e a l l samples were K c o n s o l i d a t e d to 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 75 PSI i n o the t e s t i n g programme i n o r d e r t o ensure t h a t the c l a y was no r m a l l y c o n s o l i d a t e d . The t e s t i n g programme was planned t o i n c l u d e the f o l l o w i n g s e r i e s of undrained creep r u p t u r e t e s t s ? 1. K q , n o r m a l l y c o n s o l i d a t e d samples, wherein the v e r t i c a l s t r e s s (major p r i n c i p a l s t r e s s a^) was i n c r e a s e d i n one increment, w h i l e the l a t e r a l p r e s s u r e was kept c o n s t a n t . T h i s type of t e s t w i l l be c a l l e d a creep t e s t i n which was i n c r e a s e d . 2. K q , norm a l l y c o n s o l i d a t e d samples, wherein the l a t e r a l s t r e s s (minor p r i n c i p a l s t r e s s a^) was reduced i n one increment w h i l e the v e r t i c a l s t r e s s was kept c o n s t a n t . This type of test w i l l be called a creep test in which a.j was decreased. The above l i s ted undrained creep tests in the laboratory can have pract ical significance in several f i e ld situations. If a thick layer of clay having low permeability and a long drainage path was subjected to sustained shear-ing stresses, the drainage would be very small even over a considerable period of time. This condition can be simulated in the laboratory by performing undrained creep tests. In most f i e ld conditions,however, there is par t ia l or f u l l drainage after a considerable period of time. These conditions can only be handled in the laboratory by considering both undrained and drained states. But this investigation on creep rupture was restricted to only the undrained drainage condition. Further, a comparison of increased and rj^ decreased types of creep test could be done only i f both types of tests are run under undrained conditions. Temperature - Temperature fluctuations during undrained tests on saturated samples has a marked effect on observed pore pressures (Campanella and Mitche l l , 1968) . These pore pressure variations may cause significant variation of the strength of the samples. Mitchel l and Campanella (1963) , Campanella and Mitchel l (1968), Mi tche l l , Singh and Campanella (1969) have also i l lus trated the influence of 32 temperature on s o i l creep. T h e r e f o r e a l l t e s t s were performed i n a c o n s t a n t temperature e n c l o s u r e , maintained a t 21°C ± .5°C by means of an a i r c o n d i t i o n e r . Reference T e s t s - I t was nec e s s a r y t o perform a standard undrained i n c r e m e n t a l l o a d i n g t e s t to es t i m a t e the d e v i a t o r i c s t r e s s which would cause creep r u p t u r e of K q c o n s o l i d a t e d samples. An i n c r e m e n t a l l o a d i n g t e s t i s d e f i n e d i n t h i s t h e s i s as a shear t e s t i n which the r a t e of a p p l i c a t i o n o f l o a d i s maintained a t 1 K G every 10 minutes so t h a t f a i l u r e takes p l a c e i n 4— to 5 hours. For the case when i s decreased the " i n c r e m e n t a l l o a d i n g t e s t " i s performed by d e c r e a s i n g by about 0.5 PSI every 10 minutes so t h a t f a i l u r e takes p l a c e i n 4^ - t o 5 hours. D e s c r i p t i o n o f S o i l T e sted The c l a y used i n t h i s t e s t i n g programme was o b t a i n e d from an open p i t i n Haney, B r i t i s h Columbia. Block samples of t h i s c l a y were c u t , by d i g g i n g a p i t around an u n d i s t u r b e d volume of c l a y of about 3 f e e t square by 2 f e e t depth. B l o c k s of c l a y of approximately -^ c u b i c f o o t i n s i z e were c u t w i t h a piano w i r e . These b l o c k were wrapped i n the f i e l d w i t h saran wrap, t r a n s p o r t e d to the l a b o r a t o r y where they were cut i n t o s m a l l e r b l o c k s of 1 f t . l e n g t h , 5 i n . width 4 i n . h e i g h t and g i v e n 5 or 6 c o a t i n g s of wax. The b l o c k s were s t o r e d i n a moist room u n t i l r e q u i r e d . 33 T h i s c l a y , which i s l o c a l l y known as Haney c l a y has been used f o r r e s e a r c h by o t h e r s a t TJ.B.C. Byrne (1966), H i r s t (1966), Gupta (1967), Lou (1967), V a i d (1968) and Snead (1970). I t i s b e l i e v e d to have been d e p o s i t e d i n a p o s t g l a c i a l environment and subsequently leached by r a i n water c a u s i n g a s e n s i t i v e s t r u c t u r e . The p r o p e r t i e s of the c l a y t e s t s have been d e s c r i b e d i n d e t a i l by Byrne (1966) and Snead (1970) . I t has 46% c l a y (% > 2y) and a n a t u r a l water content o f about 41%, l i q u i d l i m i t o f 44% and a P l a s t i c i t y Index = 18%. I t i s medium s t i f f i n the u n d i s t u r b e d s t a t e and has a s e n s i t i v i t y o f about 12. The p r e c o n s o l i d a t i o n p r e s s u r e o b t a i n e d from a one d i m i n e n s i o n a l c o n s o l i d o m e t e r was 60 PSI. The p h y s i c a l p r o p e r t i e s of Haney c l a y are summarized i n T a b l e I . D e s c r i p t i o n of the Apparatus Used i n T h i s Study The main p i e c e of apparatus used i n t h i s study was the plane s t r a i n apparatus d e s c r i b e d by V a i d (196 8). Only the important d e t a i l s w i l l be d i s c u s s e d here. In a d d i t i o n to the plane s t r a i n t e s t s , f o u r t e s t s were performed u s i n g a s p e c i a l l y designed K q t r i a x i a l apparatus (Campanella and V a i d , 19 70). The main f e a t u r e s o f the K q t r i a x i a l apparatus w i l l be a l s o e x p l a i n e d . 34 TABLE I PHYSICAL PROPERTIES OF HANEY CLAY S p e c i f i c G r a v i t y 2 . 8 0 L i q u i d L i m i t 4 4 % P l a s t i c L i m i t 2 6 % P l a s t i c i t y I n d e x 1 8 % N a t u r a l Water C o n t e n t 4 1 . 5 ± 1 % P e r c e n t F i n e r t h a n 2 M i c r o n s 4 6 % A c t i v i t y 0 . 4 % U n d i s t u r b e d 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 0 . 8 PSI Remolded 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 0 . 9 P S I S e n s i t i v i t y 1 2 Maximum P a s t P r e s s u r e 6 0 PSI 35 P l a n e S t r a i n A p p a r a t u s - The p l a n e s t r a i n 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 d e s i g n e d t o c o n s o l i d a t e a r e c t a n g u l a r s p e c i m e n o f s o i l ( F i g u r e 3.1) o f 4 i n . l e n g t h , 1 i n . w i d t h and 2 t o 2~ i n . h e i g h t u n d e r c o n d i t i o n s o f no l a t e r a l y i e l d and t o s u b j e c t i t t o a c o n d i t i o n o f p l a n e s t r a i n (no l a t e r a l y i e l d i n l o n g i t u d i n a l d i r e c t i o n ) d u r i n g s h e a r . The l a t e r a l p r i n c i p a l s t r e s s was a p p l i e d t o t h e sample by u s i n g f l e x i b l e w a t e r f i l l e d r u b b e r d i a p h r a g m s i n a s t e e l b a c k e d p e r s p e x chamber. The l o n g i t u d i n a l p r i n c i p a l s t r e s s was n o t m e a s u r e d i n t h i s a p p a r a t u s b u t was a u t o m a t i c a l l y a p p l i e d t h r o u g h r i g i d end p l a t e s o f t h i c k p e r s p e x . D u r i n g K q c o n s o l i d a t i o n b o t h l o n g -t u d i n a l and l a t e r a l d e f o r m a t i o n s were p r e v e n t e d by t h e end p l a t e s and by m a i n t a i n i n g a c o n s t a n t v o lume o f w a t e r i n t h e l a t e r a l p r e s s u r e d i a p h r a g m s . The v e r t i c a l and l a t e r a l s t r e s s e s on t h e s a m ple were c o n t r o l l e d i n d e p e n d e n t l y by means o f an a i r p i s t o n and 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 r e s p e c t i v e l y . The 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 e q u i p m e n t i s g i v e n as i n V a i d (1968) F i g u r e 3.2. The l o a d f r o m t h e a i r p i s t o n i s t r a n s m i t t e d t h r o u g h t h e l o a d i n g y o k e , l o a d c e l l , l o a d i n g r o d and t h e r e c t a n g u l a r l o a d i n g c a p . The l o a d i n g r o d was 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 two Thompson l i n e a r b a l l b u s h i n g s . The v e r t i c a l l o a d was m e a s u r e d by a b e r y l l i u m c o p p e r d i a p h r a g m l o a d c e l l h a v i n g a f u l l y a c t i v e s t r a i n gauge b r i d g e . 36 FIGURE 3-1 SAMPLE UNDER PLANE DEFORMATIONS. 37 Ant iroiadioh. guide 4 11 Loading P k t f o r i n IT Loai cell Bracket f o r d i a l Thompson linear ball busKinds -Top circulA.Tr ja/ate L o a d i n g TOL LoaAi'ng C&.f> Up r/^kt rods Bottom 0 ' r C u / a . r p/ate . Space r f e e t A I T i^"sto«x - Y o k e -Cross ka.rs FIGURE 32 SCHEMATIC OF THE LOADiMG EQUIPMENT FOR THE PLANE STRAIN APPARATUS. 38 V e r t i c a l d e f o r m a t i o n of the sample was measured on the p i s t o n rod by means of .0001 i n c h d i a l gauge. In a few t e s t s the v e r t i c a l deformations were measured by u s i n g a LVDT ( d i s p l a c e -ment transformer) and a c h a r t r e c o r d e r . A schematic l a y o u t of the volume change and p r e s s u r e measuring d e v i c e i s g i v e n i n F i g u r e 3.3. Drainage l i n e s from the top and bottom of the sample were connected to t h i s d e v i c e which has a c a l i b r a t e d p i p e t t e f o r measuring volume changes and a s t r a i n gauge t r a n s d u c e r f o r measuring pore water p r e s s u r e . The drainage l e a d s from the l a t e r a l p r e s s u r e diaphragms were a l s o connected to t h i s d e v i c e and the diaphragm p r e s s u r e was measured w i t h the same t r a n s d u c e r . The back p r e s s u r e was a p p l i e d through the graduated p i p e t t e connected to a 6 f t . long c o i l o f O.D. saran t u b i n g which was used to prevent the d i f f u s i o n of a i r i n t o the p r e s s u r e measuring d e v i c e . A s i m i l a r arrangement was used t o apply the diaphragm p r e s s u r e when r e q u i r e d . A t the end of K c o n s o l i d a t i o n , the sample was under o ' ^ a d e v i a t o r s t r e s s under which creep r u p t u r e does not o c c u r . For the o c c u r r e n c e of creep r u p t u r e t h i s d e v i a t o r s t r e s s had to be i n c r e a s e d by i n c r e a s i n g or d e c r e a s i n g . T h i s was done by u s i n g a t h r e e way v a l v e and r a p i d l y changing or as the case may be by s w i t c h i n g the v a l v e to a p r e -determined a i r p r e s s u r e . The c o n d i t i o n of c o n s t a n t y e r t i c a l s u s t a i n e d s t r e s s was maintained by s l i g h t l y i n c r e a s i n g the ® Wondi'splacehieKt valve Plane Strain-Ap-pajredus Laieral cLtykrag* Soil Sao»f>le LoaamoJ T L RtsSefUoirv Wafer-TJ T6f> drainage LateraJ d cfrajnage leads I IL D Ll U GTAaaat&d -wVJatai-9 ^ft Saraji tubfn<3 FIG 3.3 SCHEMATIC LAYOUT OF PLANE STRAIN APPARATUS W/7~H APPARATUS To MEASURE VOLUME CHANGES AND PRESSURES. air pressure in the a ir piston as the sample compressed and i t s area increased s l ight ly . The experimental procedure of the increasing and decreasing type of undrained creep tests in the plane strain apparatus is given in Appendix I. K q Tr iax ia l Apparatus - The important features of the K Q t r i a x i a l apparatus w i l l be discussed here. This apparatus is essentially a t r i a x i a l apparatus with a special arrangement to consolidate cy l indr ica l specimens of s o i l under K q condition or ver t i ca l deformation only. During creep the state of stress is axia l ly symmetric - o^). The measurement of stresses, sample pore pressures, ver t i ca l deformation and the application of the creep deviator stress was done in the same way as the undrained plane strain creep rupture tests. Discussion of Testing Procedure (Plane Strain Tests) The following items w i l l be discussed in this section: (1) K q consolidation, (2) f r i c t i o n between la tera l diaphragm and sample, (3) measurement of (intermediate effective principal stress) , and (4) errors in the measure-ment of pore water pressure. 1. K Consolidation - During K consolidation the la tera l —o ^ o deformation of the sample was prevented by maintaining a constant volume of water in the la tera l pressure diaphragms. Before c o n s o l i d a t i o n the v e r t i c a l and l a t e r a l p r e s s u r e s on the sample were s e t a t 90 PSI. A f t e r c o n s o l i d a t i o n the p r e s s u r e i n the l a t e r a l p r e s s u r e diaphragms reduced to an average v a l u e o f 55.2 PSI. Because of t h e i r compliance the diaphragms undergo volume decrease o f 0.3 c c , when the p r e s s u r e reduced from 90 PSI to 55.0 PSI. The " i n c o m p r e s s i b l e " water i n the diaphragm would have squeezed i n t o the sample g i v i n g a compressive l a t e r a l s t r a i n o f about .002. However, p r e v i o u s r e s e a r c h by V a i d (1968) i n d i c a t e d t h a t t h i s s m a l l s t r a i n caused an e r r o r i n the l a t e r a l p r e s s u r e of about o n l y 4% from the t r u e K q c o n d i t i o n . Thus, i n t h i s study compliance c o r r e c t i o n was n e g l e c t e d . F r i c t i o n - In e s t i m a t i n g the a x i a l s t r e s s e s on the sample the f r i c t i o n a l drag on the l o a d i n g r o d and the f r i c t i o n between sample and l a t e r a l diaphragm membranes, should be c o n s i d e r e d . Since s e a l s on the l o a d i n g s h a f t are not r e q u i r e d , the f r i c t i o n on the l o a d i n g r od was n e g l i g i b l e . The f r i c t i o n a l drag between the sample, and l a t e r a l diaphragms and end p l a t e s was measured by V a i d a t U.B.C. and was found to be q u i t e a p p r e c i a b l e . The f r i c t i o n c o r r e c t i o n f o r the v e r t i c a l s t r e s s was found t o be h i g h as 6% of the v e r t i c a l s t r e s s a t f a i l u r e . Formulae t o c o r r e c t f o r f r i c t i o n were d e r i v e d from data o b t a i n e d by V a i d (1970) and are as f o l l o w s : -For the type of creep t e s t i n which was i n c r e a s e d = 0.100 x I n i t i a l l a t e r a l p r e s s u r e For the type o f creep t e s t i n which was decreased C 2 = 0.096 x I n i t i a l l a t e r a l p r e s s u r e Where and = c o r r e c t i o n f o r v e r t i c a l s t r e s s i n PSI. and C 2 were taken as c o n s t a n t s from the b e g i n -n i n g t o the end of creep t e s t s s i n c e t o t a l time o f creep l o a d i n g was r e l a t i v e l y s h o r t term ( l e s s than 7 days) In very long term t e s t s (more than two weeks) V a i d (1970) observed i n c r e a s e i n f r i c t i o n w i t h time. Measurement of al, - In t h i s study was not measured. As a2 i s r e q u i r e d f o r the c a l c u l a t i o n of c e r t a i n parameter i t was d e c i d e d to estimate i t by a formula d e r i v e d from V a i d ' s (1970) d a t a . o 2 = K(a' + ol) Where K = 0.34. Pore P r e s s u r e s - During a l l undrained t e s t s , the pore water p r e s s u r e s were measured at the base o f the samples u s i n g an e l e c t r i c a l p r e s s u r e t r a n s d u c e r . There are two main sources of i n a c c u r a c y i n the measurement of pore water p r e s s u r e i n the sample. There have to be taken 43 i n t o c o n s i d e r a t i o n b e f o r e the pore p r e s s u r e s w i t h i n the sample, as i n d i c a t e d by the measuring system, are taken to be r e p r e s e n t a t i v e of the sample. These i n a c c u r a c i e s are due t o : (a) The t i m e - l a g i n the response o f the measuring system due to i t s compliance. (b) The non-uniform pore water p r e s s u r e w i t h i n the sample due to non-uniform s t r e s s c o n d i t i o n s . The response time of the measuring system i s a f u n c t i o n o f compliance o f the measuring system, the per-m e a b i l i t y o f the sample and the area of the sample over which the pore water p r e s s u r e i s measured. For the measuring system used the time r e q u i r e d t o r e c o r d 9 5% of the a p p l i e d pore water p r e s s u r e change would be about one minute. T h i s computation was based on a r e l a t i o n s h i p f cr piezometers (Penman, 1960). T h e r e f o r e except f o r i n i t i a l minutes of the creep t e s t s when the pore water p r e s s u r e r i s e s r a p i d l y t h i s e r r o r s hould not be s i g n i f i c a n t . Side f r i c t i o n on the sample may r e s u l t i n a non-uniform d i s t r i b u t i o n of s t r e s s e s i n the sample. However, the s i d e f r i c t i o n on the sample was assumed to be c o n s t a n t d u r i n g creep and a f u n c t i o n o f the i n i t i a l l a t e r a l p r e s s u r e . In r e a l i t y the d i s t r i b u t i o n of s i d e f r i c t i o n might change when the sample i s loaded thus g i v i n g r i s e t o non uniform pore p r e s s u r e s . F r i c t i o n a l r e s t r a i n t s a t the l o a d i n g p l a t e n s r e s u l t i n non-uniform a x i a l s t r e s s e s due to b u l g i n g of the t e s t specimen thus g i v i n g r i s e to non-uniform pore p r e s s u r e s i n undrained t e s t s . Furthermore, i n s e n s i t i v e c l a y s non-uniform a x i a l s t r a i n s a l s o g i v e r i s e to non-uniform pore p r e s s u r e s due to s t r a i n dependent s t r u c t u r a l breakdown. Because of t h i s the pore p r e s s u r e i n the end zones (where the pore p r e s s u r e s were measured) i n the specimen may be q u i t e d i f f e r e n t from t h a t a t mid-height. The s i m p l e s t way to measure r e p r e s e n t a t i v e pore p r e s s u r e s i s to a l l o w the pore p r e s s u r e s to e q u a l i z e throughout the sample by t r a n s f e r o f m o i s t u r e . B l i g h t (1963) proposed the f o l l o w i n g e q u a t i o n f o r the time r e q u i r e d f o r 95% e q u a l i z a t i o n of pore p r e s s u r e w i t h i n a specimen of s o i l s u b j e c t e d to a c o n s t a n t r a t e t o l o a d i n g . H 2 tj- = 1.6 — . . . . 3.1 v Where t ^ time to f a i l u r e o r time a t which pore p r e s s u r e measurements are r e p r e s e n t a t i v e of the sample H h a l f the h e i g h t o f the specimen c v c o e f f i c i e n t of c o n s o l i d a t i o n T h i s e q u a t i o n g i v e s a time of 150 minutes f o r 95% e q u a l i z a t i o n of pore p r e s s u r e . T h i s time of 150 minutes may be extremely c o n s e r v a t i v e , i . e . , f a r too l a r g e , f o r two reasons. F i r s t l y , the v a l u e of "c " d u r i n g undrained 45 l o a d i n g i s d i f f i c u l t to e v a l u a t e s i n c e one uses the v a l u e o b t a i n e d d u r i n g drainage to o b t a i n n o r m a l l y c o n s o l i d a t e d samples. Thus the a c t u a l v a l u e of " c v " f o r the undrained t e s t ( i n which e f f e c t i v e s t r e s s e s are decreasing) may be many times l a r g e r than t h a t measured d u r i n g c o n s o l i d a t i o n . Secondly, the time f o r e q u a l i z a t i o n should be l e s s i n creep t e s t s than i n l o a d c o n t r o l t e s t s because the l o a d i s a p p l i e d i n a s h o r t p e r i o d o f time r a t h e r than a t a c o n s t a n t r a t e . S t r a i n c o n t r o l l e d t e s t s performed by V a i d (1970) on the same c l a y and u s i n g the same apparatus i n d i c a t e t h a t pore p r e s s u r e s are e s s e n t i a l l y u n i f o r m w i t h i n the sample a f t e r an e l a p s e d time o f 60 minutes. Hence f o r s t r a i n con-t r o l l e d t e s t s pore p r e s s u r e s measured a t the base of the sample are r e l i a b l e a f t e r an e l a p s e d time of 60 minutes. A g a i n i n the creep t e s t where the l o a d i s a p p l i e d almost i n s t a n t a n e o u s l y , the e l a p s e d time r e q u i r e d t o o b t a i n 95% e q u a l i z a t i o n of pore p r e s s u r e s should be c o n s i d e r a b l y l e s s than 60 minutes. There i s no known method of e s t i m a t i n g the time f o r 95% e q u a l i z a t i o n o f pore p r e s s u r e s f o r undrained creep t e s t s of a s e n s i t i v e c l a y . T h e r e f o r e on the b a s i s o f the r e s u l t s of V a i d (1970) i t may be reas o n a b l e to assume t h a t any pore p r e s s u r e s measured b e f o r e 60 minutes may be i n a c c u r a t e . 46 For the type of creep tests in which was decreased the time to 9 5 % equalization of pore pressures should be very small because the coefficient of consolidation is very much greater during rebound or decreasing effective stresses than during i n i t i a l consolidation. Pore pressures recorded at the end of a creep test are also questionable since at fa i lure the strain rate and the rate of change of pore pressures are high giving non-equalization of pore pressures. 4 7 CHAPTER 4 RESULTS OF PLANE STRAIN CREEP RUPTURE TESTS During K c o n s o l i d a t i o n a l l samples were d r a i n e d o f o r 3 6 hours. A f t e r c o n s o l i d a t i o n the water content of a l l samples was found to be 3 4 . 4 ± 0 . 4 % , w h i l e the K Q v a l u e was measured to be 0 . 5 7 ± . 0 1 , a f t e r c o r r e c t i n g f o r sample s i d e f r i c t i o n . T h i s d e v i a t i o n i n K q v a l u e may be due t o s l i g h t v a r i a t i o n i n sample s i z e , temperature and volume compliance. A f t e r c o n s o l i d a t i o n was completed the samples were kept undrained f o r 1 2 hours f o r e q u a l i z a t i o n of pore water p r e s s u r e s . A t the end of t h i s p e r i o d a p o r e - p r e s s u r e b u i l d - u p was observed which had an average v a l u e of 3 . 2 PSI, or 4 % of c o n s o l i d a t i o n s t r e s s . T h i s r i s e i n pore p r e s s u r e was e x p l a i n e d by Byrne ( 1 9 6 6 ) , Lou ( 1 9 6 7 ) and Snead ( 1 9 7 0 ) i n the t r i a x i a l samples as due to the p r e v e n t i o n of c o n t i n u e d secondary compression a f t e r the d r a i n a g e l i n e s were c l o s e d . T e s t s i n Which Was Increased In t h i s s e c t i o n the r e s u l t s of a l l undrained creep t e s t s on K q 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 n the plane s t r a i n apparatus when a, was i n c r e a s e d , w i l l be d i s c u s s e d . A l l s t r e s s e s were c o r r e c t e d f o r sample s i d e f r i c t i o n which was taken as c o n s t a n t w i t h time. The i n c r e m e n t a l l o a d i n g t e s t gave a maximum d e v i a t o r s t r e s s , ( a , - a O of 43.2 PSI a t an a x i a l s t r a i n of 1.05 p e r c e n t . U s i n g t h i s d e v i a t o r s t r e s s as the r e f e r e n c e s t r e n g t h , t e s t s were performed a t creep d e v i a t o r s t r e s s e s o f 44.5, 41.8, 40.7, 39.5, 39.0 and 38.2 PSI. The s t r e s s e s on the samples a f t e r c o n s o l i d a t i o n and d u r i n g creep, and the sample water con-t e n t s are g i v e n i n Appendix I I I . A t y p i c a l s t r a i n - t i m e curve f o r plane s t r a i n creep r u p t u r e f o r the undrained t e s t s i n which was i n c r e a s e d i s shown i n F i g u r e 4.1. The s t r a i n r a t e i n i t i a l l y d e creased, then reached a minimum and g r a d u a l l y i n c r e a s e d to r u p t u r e . T h i s curve c o u l d be d i v i d e d i n t o primary, secondary, and t e r t i a r y c reep, although d u r i n g secondary creep stage the s t r a i n r a t e i s seen to decrease s l i g h t l y t i l l the minimum s t r a i n r a t e i s o b t a i n e d . F i g u r e 4.2 shows the p l o t of l o g s t r a i n r a t e , e a g a i n s t l o g e l a p s e d time, t . For the samples which f a i l e d , the s t r a i n r a t e i n i t i a l l y d ecreased, then reached a minimum and f i n a l l y the s t r a i n r a t e i n c r e a s e d r a p i d l y l e a d i n g to r u p t u r e . At no stage o f the creep t e s t s was the s t r a i n r a t e c o n s t a n t . T h e r e f o r e a secondary stage f o r creep does not e x i s t f o r Haney c l a y t e s t e d under plane s t r a i n c o n d i t i o n . ? m co $ 2 o CO 2 8 0) R fc? C X) m H -< "0 2 r "D O H O 71 r (0 H $ 2 AXIAL STRAIN - PERCENT < m 2 m •n o to c g 2 2 tn O 1 m 2 (6 A o \ 2 ^ 1 o •n S S TEST JM 6TR/<U/\ NO. PS 1 i 8 8 2 O i-n -0 Q <^  — n a? H o a <TE<"fO-7RSZ 94-5%<5KM W/c s3*2 50 /0 'OO I OOO 19 ooo FIGURE 4 . 2 LOGARITHM OR AXIAL STRAIN RATE VERSUS LOGARITHM OF TIME FOR UNDRAINED PLANE: STRAIN CREEP TESTS - 0 7 INCREASED (HANEY CLAY) I t i s p o s s i b l e , however, to i d e n t i f y a creep stage of approximately c o n s t a n t s t r a i n r a t e by drawing a s t r a i g h t l i n e between p o i n t s B and C f o r the s t r a i n - t i m e p l o t i n F i g u r e 4.1. The slope of l i n e BC i s approximately equal to the minimum s t r a i n r a t e . F i g u r e 4.2 shows t h a t the lower the d e v i a t o r s t r e s s the s m a l l e r the minimum s t r a i n r a t e . The e x p e r i m e ntal data of F i g u r e 4.2 suggests t h a t the p o i n t s of minimum s t r a i n r a t e f a l l on a s t r a i g h t l i n e on the l o g - l o g p l o t o f s t r a i n r a t e and e l a p s e d time. T h i s was a l s o the case f o r the r e s u l t s r e p o r t e d by Snead (1970) , f o r c o n v e n t i o n a l t r i a x i a l creep r u p t u r e t e s t s on Haney c l a y . The e q u a t i o n of the s t r a i g h t l i n e o b t a i n e d from F i g u r e 4.2 i s g i v e n by l o g , _ t = - . 7 4 - 1 . 1 6 l o g , n e . . . . 4.1 ^10 m ^10 m Where t e l a p s e d time u n t i l minimum s t r a i n r a t e m * i n minutes minimum s t r a i n r a t e i n p e r c e n t per minute Once the s t r a i n r a t e o f a sample passes through a minimum i t has been c o n s i s t a n t l y observed t h a t the sample w i l l e v e n t u a l l y f a i l . T h i s was a l s o observed by Snead (1970) f o r t r i a x i a l samples. He s a i d t h a t the e x i s t e n c e o f a minimum s t r a i n r a t e c o u l d be used as a f a i l u r e c r i t e r i o n . F or example f o r the p o i n t A i n F i g u r e 4.2, the sample under these c o n d i t i o n s has r e a c h e d a minimum s t r a i n r a t e , and t h e sample was bound t o f a i l i f t h e a p p l i e d s t r e s s e s on t h e sample were k e p t c o n s t a n t . On t h e o t h e r hand i f a sample n e v e r r e a c h e s a minimum s t r a i n r a t e , l i k e t h e i n s t a n t a n e o u s s t r a i n r a t e i n d i c a t e d by p o i n t B i n F i g u r e 4.2, i t s h o u l d n o t f a i l . T h u s , c u r v e s o f a l l t h e s a m p l e s w h i c h f a i l e d s t a r t e d f r o m t h e l e f t o f t h e l i n e o f minimum s t r a i n r a t e s , and moved t o w a r d s and i n t e r s e c t e d i t . The sample w h i c h d i d n o t f a i l i n i t i a l l y moved t o w a r d s t h e l i n e o f minimum s t r a i n r a t e s , b u t g r a d u a l l y c h a n g e d i t s c o u r s e and p r o c e e d e d p a r a l l e l t o t h e l i n e o f minimum s t r a i n r a t e s . P r e s u m a b l y i t w i l l n e v e r i n t e r s e c t t h e l i n e o f minimum s t r a i n r a t e and n e v e r f a i l . The s i d e f r i c t i o n a l o n g t h e sample b o u n d a r i e s c o u l d a c c o u n t f o r s u c h b e h a v i o u r . I f t h e s i d e f r i c t i o n i n c r e a s e s w i t h t i m e , due t o s q u e e z i n g o u t o f s i l i c o n e g r e a s e between t h e sample membrane and 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 membranes, t h e n t h e " s u s t a i n e d " s t r e s s i s no l o n g e r c o n s t a n t b u t w o u l d d e c r e a s e w i t h t i m e . T h i s w o u l d c a u s e a r e d u c t i o n i n s t r a i n r a t e a t any p a r t i c u l a r t i m e , e x p l a i n i n g t h e b e h a v i o u r o f l o g s t r a i n r a t e - l o g e l a p s e d t i m e c u r v e f o r t h e s a m p l e s w h i c h d i d n o t f a i l . U n f o r t u n a t e l y , i t was n o t p o s s i b l e t o measure s i d e f r i c t i o n i n t h e s e e x p e r i m e n t s . However, i t i s b e l i e v e d t h a t t h e e x i s t e n c e o f a v a r y i n g s i d e f r i c t i o n w i t h t i m e o f any l a r g e c o n s e q u e n c e , i s s m a l l . F i r s t o f a l l , s i m i l a r 53 behaviour f o r the curves of samples which d i d not f a i l was observed by Snead (1970), who t e s t e d t r i a x i a l samples f o r which t h e r e was no s i d e f r i c t i o n . Secondly, s i d e f r i c t i o n t e s t s by V a i d (1970) on the same type of plane s t r a i n apparatus showed t h a t the s i d e f r i c t i o n was e s s e n t i a l l y c o n s t a n t f o r the t e s t d u r a t i o n s o f a few days. T h e r e f o r e an i n c r e a s e o f s i d e f r i c t i o n w i t h time f o r creep r u p t u r e of samples under plane s t r a i n c o n d i t i o n should be s m a l l and should not a f f e c t the s t r a i n - t i m e curves upto a p e r i o d of 4-7 days d u r a t i o n . An upper y i e l d s t r e n g t h f o r the r e s u l t s shown i n F i g u r e 4.2 would be between 38.2 and 39.0 PSI. That i s , f a i l u r e w i l l occur a t s t r e s s e s g r e a t e r than 39.0 PSI but w i l l not occur a t a s t r e s s below 38.2 PSI. The observance of an upper y i e l d s t r e s s i s i n agreement wi t h the hypotheses o f Murayama and S h i b a t a (1961), V i a l o v and S k i b i t s k y (1957) and Snead (1970) which s t a t e t h a t a upper y i e l d s t r e n g t h e x i s t s f o r s o i l s , below which creep r u p t u r e w i l l not o c c u r . The upper y i e l d s t r e n g t h f o r r e s u l t s i n F i g u r e 4.2 corresponds to between 88.7 and 90.6 p e r c e n t of the s t r e n g t h o b t a i n e d from the i n c r e m e n t a l l o a d i n g t e s t . The curve c o r r e s p o n d i n g to the upper y i e l d s t r e n g t h c u t s the p l o t of l o g e v e r s u s l o g t i n t o two p a r t s ( F i g u r e 4.2). The s t r a i n r a t e - t i m e c o n d i t i o n of a l l the samples 54 which f a i l e d are p l o t t e d i n the upper p a r t whereas the s t r a i n r a t e - t i m e c o n d i t i o n s o f the samples which d i d not f a i l are p l o t t e d i n the lower p a r t o f l o g e versus l o g t p l o t . T h e r e f o r e the s t r a i n r a t e - t i m e c o n d i t i o n of any sample p l o t t e d on the l o g e ver s u s l o g t would enable us to p r e d i c t whether i t would f a i l o r not, under c o n s t a n t a p p l i e d s t r e s s e s . I f t h i s p a r t i c u l a r c o n d i t i o n i s p l o t t e d i n the upper p a r t a t "C" i n F i g u r e 4.2 then the sample would f a i l and i f p l o t t e d i n the lower p a r t a t "B" the sample would not f a i l . T h e r e f o r e f o r c o n s t a n t a p p l i e d s t r e s s e s , l o g e versus l o g t p l o t f o r the d e v i a t o r s t r e s s r e p r e s e n t i n g the upper y i e l d s t r e n g t h c o u l d be used as a f a i l u r e c r i t e r i o n . T able I I g i v e s some of the r e s u l t s o f the creep r u p t u r e t e s t s . From t h i s t a b l e i t c o u l d be seen t h a t the time to minimum s t r a i n r a t e and the t o t a l time t o r u p t u r e i n c r e a s e d w i t h the decrease i n d e v i a t o r s t r e s s . With the i n c r e a s e i n time t o f a i l u r e , the s t r a i n t o minimum s t r a i n r a t e was observed to i n c r e a s e s l i g h t l y . From Tab l e I I i t c o u l d be seen t h a t the t o t a l time t o r u p t u r e i s about 2.4 to 3.0 times the time to minimum s t r a i n r a t e . In o t h e r words, more than t w o - t h i r d s the e l a p s e d time t o r u p t u r e was spent d u r i n g t e r t i a r y creep stage. Pore P r e s s u r e s - I t was d i s c u s s e d i n Chapter 3, t h a t pore p r e s s u r e o f samples measured b e f o r e a time of 60 minutes 55 TABLE H SOME RESULTS O F UNDRAINED PLANE STRAIN CREEP TEST - cr, INCREASED. Test No. < Dev/a.for PferCeKt 0/ Mm/niuni Straj'h. rSe •PerCetdlmi* Axial Strain SfrajA ra+<? -fti-cmt T V f v ^ e to mini M C / I V » v S ^ r a j ^ raie - fni'v - frrxt'n. P S I - C I / Q 3 2 •o9o •54 3 8 F S 1 - C 2 4 1 - 8 9 7 - 3 • Q 2 3 •>56 2 6 84 PSI -C3 4 0 7 94-S 0070 £ 7 SO 154 Psi -Gf 3 9 - 5 9 / 7 •OOS4 •60 90 2J4 Psi -Cs v 3 9 - 0 9 0 6 •0O22 • 6 2 P 2 v 5 69,5 "RSI-C6 3 3 - 2 000035 • 4 4 — -4300 * PARAMETERS MEASURED AT THE TIME W H E N THE EXPERIMENT WAS STOPPED. <H>M - MAXIMUM DEVIATOR STRESS OBTAINED FROM AN INCREMENTAL L.QADING TEST. 56 and a t the end of the creep t e s t may be c o n s i d e r e d i n a c c u r a t e . F i g u r e 4.3A shows the pore water p r e s s u r e versus a x i a l s t r a i n f o r s e v e r a l o f the creep t e s t s r e p o r t e d i n F i g u r e 4.2. From F i g u r e 4.3A i t c o u l d be seen t h a t : (1) the pore p r e s s u r e i n c r e a s e d w i t h i n c r e a s e i n a x i a l s t r a i n , as observed by Snead (1970) and (2) the t e s t w i t h lowest s t r e s s l e v e l , and t h e r e f o r e l o n g e s t d u r a t i o n , i s observed to develop the l a r g e s t pore p r e s s u r e f o r the same s t r a i n . T h i s may be due to the a d d i t i o n a l time a v a i l a b l e f o r s t r u c t u r a l breakdown of the s e n s i t i v e s o i l s t r u c t u r e . For undrained s o i l specimens the change i n pore p r e s s u r e under plane s t r a i n c o n d i t i o n can be expressed by an e q u a t i o n s i m i l a r to:Skempton 1s (1954) f o r t r i a x i a l c o n d i t i o n s . (Bishop and Henkel, 1962) Au = B [ A o 3 + A (La1 ~ A a 3 ) ] Where "Au" i s the increment i n pore p r e s s u r e due t o increments i n " A a ^ " a n d - " A a ^ " . "A" i s an e m p i r i c a l pore p r e s s u r e p a r a -meter known as the Skempton's "A" v a l u e . For a f u l l y s a t u r -ated s o i l "B" = 1, which was the case i n the creep t e s t s performed. F i g u r e 4.3B shows the Skempton "A" parameter v e r s u s a x i a l s t r a i n . From F i g u r e 4.3B i t can be seen t h a t f o r any 57 44-5 PSI /03-? % 0 S M VJ/C 6~3 A X I A L S T R A I N OS AFTER CONSOLIDAT 0 3 - PSi H7t % C73M Kjfc T) - T I M E AFTER C.ONSQL IDA"lON= SS-1 PSt ^^4-7 Tf--8S<*)in = 34 2 T} = \S4 M IN = 34-2 T = 4300 MIN X O i M W/c TO FAILURE Tl 2^4" P E R C E N T ION = £<?-6 PSI F I G U R E 43A PORE W A T E R P R E S S U R E ; V E R S U S AXIAL STRAIN FOR UNDRAINED PLANE STRAIN CREEP TESTS -<T/ INCREASING AXIAL STRAIN 6 ? 4 PERCENT 3-z FIGURE 4 3 8 SKEMPTON A VERSUS AXIAL STRAIN FOR UNDRAINED PLANE STRAIN CREEP TESTS-C: INCREASED. FIGURE 43C A X I A L STRAIN - PERCENT EFFECT/V£ S T R E S S RATIO VERSUS AXIAL STRAIN FOR. UNDRAINED P L A M E STRAIN CREEP T E S T S -<7T INCREASED. 58 particular axial strain the lower the deviator stress, the higher was the value of Skempton "A". This is similar to the conclusions of Crawford (1959), that "A" value at fa i lure is dependent on time to fa i lure . Figure 4.3C shows the variation of effective stress ratio "o^/o^" versus axial strain for several of the creep tests. The effective stress rat io increases with axial s tra in , mainly due to increase in pore pressure with axial s train . For the samples which fa i l ed , "a^/a^" increases even after the minimum strain rate is reached. Therefore, based on a al/ol fa i lure cr i t er ion , a sample, whose 1' 3 max ' * ' strain rate is beginning to increase, would not be considered on the verge of fa i lure , but on the basis of minimum strain rate i t is on the verge of fa i lure . This particular disagree-ment concerning fai lure cr i ter ion need c l a r i f i c a t i o n through additional research. For the sample which did not f a i l the increase in " a | / a ^ " with axial strain is smaller than that for the other tests (Figure 4.3C). This test was stopped at a strain of 0.45 percent when the "a^/o^" rat io was s t i l l increasing -5 and strain rate of 3.5 x 10 percent/min.was s t i l l decreasing. The decision to stop the test was taken because of the probable undetected increase in side f r i c t i on after about a week or more of sustained load (Vaid, 1970). 59 S t r e s s - S t r a i n - S t r a i n Rate R e l a t i o n s h i p - F i g u r e 4.4 shows the p l o t of l o g s t r a i n r a t e v e r s u s a x i a l s t r a i n f o r both creep and i n c r e m e n t a l l o a d i n g t e s t s . The d e v i a t o r s t r e s s i s marked along the a p p r o p r i a t e creep curve, w h i l e the d e v i a t o r s t r e s s e s a t the end of the s t r e s s increment f o r i n c r e m e n t a l l o a d i n g t e s t are a l s o i n d i c a t e d . For the samples which f a i l e d i n creep the s t r a i n r a t e d e c r e a s e s , reaches a minimum and i n c r e a s e s w i t h the i n c r e a s e o f a x i a l s t r a i n . However, i t 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 t h a t a t the minimum s t r a i n r a t e a l l of the samples had undergone an a x i a l compressive s t r a i n of about 0.6%. For the sample which d i d not f a i l the s t r a i n r a t e decreased a t an ever d e c r e a s i n g r a t e w i t h a x i a l s t r a i n , but the s t r a i n never reached 0.6%. For the i n c r e m e n t a l t e s t , loads were added a t i n t e r -v a l s o f 10 minutes. I t was observed t h a t the s t r a i n r a t e i n c r e a s e d s l i g h t l y j u s t a f t e r the l o a d was added and decreased s l i g h t l y t h e r e a f t e r . The s t r a i n r a t e s p l o t t e d i n F i g u r e 4.4 were those e v a l u a t e d from a smooth curve drawn through p o i n t s o f s t r a i n - t i m e o b t a i n e d j u s t b e f o r e the next increment of l o a d was added. I t should be r e c a l l e d t h a t a t the end of K c o n s o l i -o d a t i o n , the samples were under a d e v i a t o r i c s t r e s s ( i . e . , - a^) of about 29.6 PSI, (a l s o i n d i c a t e d i n F i g u r e 4 . 4 ) . When t h i s d e v i a t o r i c s t r e s s was i n c r e a s e d beyond 34.0 PSI the samples f a i l e d i n creep r u p t u r e . T h e r e f o r e t h e r e are two <7*'4 ISPs I go 03 AFTER CONSOL IDATION -29G PSI 0£ AFTER CONSOLIDATION*55-1 <=$r_ CREEP TESTS <Tj> =44 5 RSI Oo = 418 0SI OB *40-7flSI C i » 39 O RSX 05 > 38 2 BSr INCREMENTAL SS-7% <£„ w / c =347. w/c =34-a W/^34-2 LOADING1 T&Sr " T 2 FS ^ZT STRAIN ~ PERCE NT " 3 * 0-4 AXIAL FIGURE 4 4 LOG AXIAL STRAIN RATE VERSUS AXIAL STRAIN FOR UNDRAINED PLANE STRAIN CREEP TESTS-cr, INCREASED CUNDISTURSED HANEY CLAY.) increments of d e v i a t o r s t r e s s which could be considered. The f i r s t one being the " a d d i t i o n a l " d e v i a t o r s t r e s s added at the end of c o n s o l i d a t i o n . The other i s the " t o t a l " d e v i a t o r s t r e s s on the sample during creep, as given i n Figur e 4.4. The " a d d i t i o n a l " d e v i a t o r s t r e s s may be of value s i n c e i t i n d i c a t e s the a d d i t i o n a l load t h a t can be a p p l i e d i n the f i e l d to s t r a t a i n i t i a l l y under K q c o n s o l i d a -t i o n . The " t o t a l " d e v i a t o r s t r e s s on the other hand i s a more fundamental parameter and hence has been used i n t h i s study. Snead's (1970) hypothesis namely a Q = f ( e , e) or t h a t at the same s t r a i n and s t r a i n r a t e the d e v i a t o r s t r e s s e s should be the same f o r both creep and incremental l o a d i n g t e s t s , could be evaluated from the r e s u l t s of Figu r e 4.4. I n v e s t i g a t i o n of r e s u l t s i n d i c a t e reasonably good agreement between the creep and incremental l o a d i n g t e s t s i n terms of " t o t a l " d e v i a t o r s t r e s s on the sample as given i n Table I I I . But i n terms of the " a d d i t i o n a l " d e v i a t o r s t r e s s e s added a f t e r c o n s o l i d a t i o n , e r r o r s of the order of 20% and hi g h e r , e x i s t as given i n Table I I I . Note i n Fi g u r e 4.4 t h a t when comparing incremental w i t h creep t e s t s at the same e and e the a Q i n the incremental l o a d i n g t e s t was always higher than from creep t e s t s . In a l a t e r s e c t i o n t e s t data f o r decreasing s t r e s s paths w i l l be evaluated f o r both incremental and creep, l o a d i n g w i t h respect to s t r a i n r a t e , s t r a i n , s t r e s s behaviour. 62 T A B L E 7H OS AT THE SAME C AMD £ FROM F/GUftE 4 . 4 , F O P UNDRAINED P U N £ STRAIM T E S T S - 07 /NORE^SE-D. " T O T A L " 07 PSI A D D I T I O N A L " Oi - PSI INCREMENT/*] LOADING TEST C R E E P T E S T INCREMENT/U loABlMG T£ST CREEP T E S T 361 v38 2 6-A* 8£ 3 9 T 39 O 9 a 9-6 42-0 v39S 12 -4 [Ql 42-3 4 0 7 J2 7 11 1 43 Q, 4 ' 8 13-4 '2 -4 COMPARISON OF "g INCREASED" AND "a., DECREASED" TYPES OF CREEP TESTS I n t h i s s e c t i o n , t h e r e s u l t s o f t h e c r e e p t e s t s i n w h i c h "g^ was d e c r e a s e d " w i l l be d i s c u s s e d i n c o m p a r i s o n w i t h t h e r e s u l t s o f t h e c r e e p t e s t s i n w h i c h "g^ was i n c r e a s e d " . The s a m p l e s f o r t h e s e two t y p e s o f t e s t s were c o n s o l i d a t e d t o t h e same i n i t i a l c o n d i t i o n s . The s l i g h t v a r i a t i o n s i n w a t e r c o n t e n t and i n i t i a l s t r e s s e s on t h e s a m p l e s a r e due t o s l i g h t v a r i a t i o n s i n s o i l , sample s i z e , t e m p e r a t u r e and volume c o m p l i a n c e . B i s h o p and H e n k e l (1962) have r e p o r t e d t h a t f o r f u l l y s a t u r a t e d c l a y s , u n d r a i n e d t r i a x i a l s h e a r t e s t w i t h g^ c o n s t a n t and g^ d e c r e a s i n g g i v e t h e same r e s u l t s a s t h e u n d r a i n e d t e s t s where g^ i s k e p t c o n s t a n t and g^ i s i n c r e a s e d . F o r 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 t e s t s ( w i t h 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 ^ o^) s i m i l a r r e s u l t s were o b t a i n e d b y V a i d ( 1 9 6 8 ) . C o m p a r i s o n o f t h e t e s t r e s u l t s o f g^ v e r s u s s t r a i n e ( F i g u r e 4.5) f o r t h e i n c r e m e n t a l l o a d i n g t e s t s , show t h a t t h e t e s t w i t h g^ c o n s t a n t and g^ d e c r e a s i n g g i v e a p p r o x i m a t e l y t h e same r e s u l t s as t e s t s where g^ i s k e p t c o n s t a n t and g^ i s i n c r e a s e d . T h e r e f o r e t h e "g^ i n c r e a s e d " and "g^ d e c r e a s e d " t y p e o f s h e a r t e s t s may be c o n s i d e r e d t o be a n a l o g o u s . T h u s , i f s h e a r t e s t s a r e c o m p a r a b l e w i t h c r e e p t e s t s , i t may be c o n c l u d e d t h a t i n p l a n e s t r a i n t h e g^ i n c r e a s e d t y p e o f u n d r a i n e d c r e e p t e s t s h o u l d g i v e t h e same 64 9 46 a 42 4 0 38 36 h 64 a TO 32 < > So UJ Q 28 0 0 cr, INCREASING » y. CTj J)ECR£AS/NG L "ft — / O 6-2. 0-4 0-4 0-8 I O |2. 1-4 1-6 1-8 Ax'AL, v S T R A / N - 6 PERCENT FIGURE 4S COMPARISON O F OD. VERSUS € POR UNDRAINED PLANE STRAIN INCREMENTAL LOADING TESTS. -UNDISTURBED HANEY CLAY. behaviour as the decreased type of creep t e s t . The i n c r e m e n t a l l o a d i n g t e s t i n which was decreased gave a maximum d e v i a t o r s t r e s s o f 44.1 PSI a t an a x i a l s t r a i n o f 1.45 p e r c e n t . Using t h i s d e v i a t o r s t r e s s as the r e f e r e n c e s t r e n g t h , creep t e s t s were performed a t 46.1, 44.8, 42.6, 42.5 and 41.3 PSI. A l l s t r e s s e s were c o r r e c t e d f o r the a n t i c i p a t e d sample s i d e f r i c t i o n . Sample water c o n t e n t s and the s t r e s s e s of samples a t the end of c o n s o l i d a t i o n and d u r i n g creep t e s t s are g i v e n i n Appendix I I I . F i g u r e 4.6 shows a t y p i c a l s t r a i n - t i m e curve f o r creep t e s t i n which was decreased along w i t h a t y p i c a l curve f o r creep t e s t i n which was i n c r e a s e d . I t c o u l d be seen from these two curves t h a t the s t r a i n - t i m e c h a r a c t e r -i s t i c s f o r the two types of curves are s i m i l a r . F i g u r e 4.7 shows the l o g s t r a i n r a t e v e r s u s l o g time curves f o r d e c r e a s i n g creep t e s t s . These curves are s i m i l a r t o those o b t a i n e d f o r creep t e s t s i n which was i n c r e a s e d , and a l i n e of minimum s t r a i n r a t e s e x i s t s f o r the d e c r e a s i n g case. The upper y i e l d s t r e n g t h f o r creep t e s t s i n which was decreased was a (c^ - a^) v a l u e between 42.5 and 41.3 PSI which are 96.2 and 93.5 p e r c e n t of the r e f e r e n c e s t r e n g t h . In the " i n c r e a s i n g a^" t e s t s the upper y i e l d was about 89% of the r e f e r e n c e s t r e n g t h . Thus, t h e r e was a marked d i f f e r e n c e between the upper y i e l d s t r e n g t h determined from a, i n c r e a s i n g and a-, d e c r e a s i n g type o f POINT OF MINIMUM STRAIN RATE CT/ INCREASED TEST Na flSJ-GS s 3 2 0 - MINUTES COMPARISON OF DEFORMATION BEHAVIOR PLANE STRAIN CREEP TEST FOR THE INCREASED " AND DECREASED." v560 UNDRAINED 640 CASES OF CTv cn Oi-- BSE %-2 % W/C»34-4 io JOO T / M £ - MINUTES 10,000 FIGURE4.7 LOGARITHM OF AXIAL STRAIN RATE VERSUS LOGARITHM OF TIME FOR UNDRAINED PLANE STRAIN CREEP TESTS - 0 3 DECREASED. 68 c r e e p r u p t u r e t e s t s . T h i s d i f f e r e n c e i n u p p e r y i e l d s t r e n g t h w i l l be d i s c u s s e d i n t h e l a t t e r p a r t o f t h i s c h a p t e r . F i g u r e 4.8 shows t h e c o m p a r i s o n o f t h e l i n e s o f '. minimum s t r a i n r a t e s f o r t h e two t y p e s o f c r e e p t e s t s . As c a n be s e e n t h e s e two s t r a i g h t l i n e s f a l l v e r y c l o s e t o e a c h o t h e r . F o r p r a c t i c a l p u r p o s e s t h e y c o u l d be t a k e n as one s t r a i g h t l i n e . F i g u r e 4.8 s u g g e s t t h a t i t d o e s n o t m a t t e r how t h e s u s t a i n e d s h e a r i n g s t r e s s i s a p p l i e d s o l o n g as t h e i n i t i a l s t a t e i s t h e same and t h a t i s f o r c o m p r e s s i v e s t r a i n s . T a b l e IV g i v e s some o f t h e r e s u l t s o f t h e d e c r e a s i n g p l a n e s t r a i n c r e e p r u p t u r e t e s t s . From t h i s t a b l e i t c o u l d be s e e n t h a t t h e t i m e t o minimum s t r a i n r a t e and t h e t o t a l t i m e t o r u p t u r e i n c r e a s e d w i t h t h e d e c r e a s e i n d e v i a t o r s t r e s s . W i t h t h e i n c r e a s e i n t i m e t o f a i l u r e , t h e s t r a i n a t minimum s t r a i n r a t e was o b s e r v e d t o be a p p r o x i m a t e l y c o n s t a n t a t 0.56 p e r c e n t f o r a l l s a m p l e s w h i c h was t h e same b e h a v i o u r o b s e r v e d f o r t h e " a ^ i n c r e a s e d " t e s t s . However, t h e sample w h i c h d i d n o t f a i l h ad a p e r c e n t a x i a l s t r a i n o f 1.77 b e f o r e t h e t e s t was s t o p p e d . From T a b l e IV i t c o u l d a l s o be s e e n t h a t t h e t o t a l t i m e t o r u p t u r e i s a b o u t 2.6 t o 3.2 t i m e s t h e t i m e t o minimum s t r a i n r a t e S i m i l a r v a l u e s were o b t a i n e d f o r i n c r e a s i n g a , t y p e o f c r e e p t e s t s . 69 INC LEASED DECREASE! 01 IO 100 MINS / O O O 10,000 TIME FIGURE 4.8 LINES OF MINIMUM STRAIN RATES -PLANE STRAIN 70 TABLE.SOME RESULTS OF UNDRAINED PLANE STRAIN CREEP TESTS - G£ DECREASED. Test No. Creep-PSI Percent of Mini tnmtvt Strain rate Ru-Cfcrit/Mi'h at Hinirnutri Stw'n raie - Percent Thne to rnir\i fv»u*n vStraiK rat* - m iV\ T o t a l W *o /ai'/uve - rniVx RS3- Cl 461 /o4a •034 SS /o 2? PS3-C2 44>8 /OJ-7 •o/a 56 30 8 2 PS3-C3 42-6 96 3 •0O37 56 IOO 32/ PS3-C4 425 962 •0029 •55 125 35/ *PS3-G5 41-3 R35 •oooo? 117 — 7200 * P A R A M E T E R S MEASURED AT THE TIME W H E N T H E EKPERIMENT WAS STOPPED. 3DM - M A X I M U M D E V / A T O R S T R E S S OBTAINED F R O M AN INCREMENTAL LOADING T E S T - (<r - a-,) 71 S t r e s s - S t r a i n - S t r a i n Rate R e l a t i o n s h i p - F i g u r e 4.9 shows the p l o t of l o g of s t r a i n r a t e v e r s u s a x i a l s t r a i n f o r the creep t e s t i n which was decreased. The behaviour i s s i m i l a r to t h a t o b t a i n e d f o r creep t e s t s i n which was i n c r e a s e d . The d e v i a t o r s t r e s s e s (c^ - a^) are i n d i c a t e d i n F i g u r e 4.9 f o r both creep t e s t s and i n c r e m e n t a l l o a d i n g t e s t . The h y p o t h e s i s t h a t a Q = f ( e , e) can be e v a l u a t e d w i t h the r e s u l t s of F i g u r e 4 . 9 . I n v e s t i g a t i o n of the r e s u l t s i n d i c a t e r e a s o n a b l y good agreement between the creep and i n c r e m e n t a l l o a d i n g t e s t s i n terms of the " t o t a l " d e v i a t o r s t r e s s on the sample as g i v e n i n Table V. But i n terms of the " a d d i t i o n a l " d e v i a t o r s t r e s s added a f t e r c o n s o l i d a t i o n , e r r o r s o f the order of 2 0 % was ob t a i n e d as g i v e n i n Table V. Note t h a t i n F i g u r e 4 . 9 , comparing i n c r e m e n t a l l o a d i n g w i t h creep t e s t s a t the same e and e the i n i n c r e m e n t a l l o a d i n g t e s t i s always lower than from creep t e s t s . T h i s i s o p p o s i t e to the r e s u l t s o b t a i n e d f o r i n c r e a s i n g type o f creep t e s t s as shown i n F i g u r e 4 . 4 . F i g u r e 4 . 1 0 A shows the observed behaviour of d e v i a t o r s t r e s s e s versus l o g minimum s t r a i n r a t e f o r i n c r e a s i n g and d e c r e a s i n g type of creep t e s t s . An approximate upper y i e l d v a l u e i s a l s o i n d i c a t e d i n t h i s p l o t . The curves on the p l o t of a n versus minimum e can not cut the s t r a i g h t 72 0 5 s 42 s PSI 426 est CT2 AFTER CONSOLIDATION - 3 0 J FBI C77 = S 4 - 6 ASI v „ CTj, = 4<Sl PSX I04-2%G3M Vt/c =340 A <a 03 * 44 8 Psx ro/-7 % Oh* w/e = S4-6 • • 0 i=42 -6Rsx ?6-3%CTSM W/c=J4€ Oi = 42-5 BSI 96-2% C J > M W/C ^V£*4 cn, - 4 i - 3 PSI 03-5% cri>M IA//C =v?4-5» © © *SH£AR TEST O 3 J>EC/?S4S/MC_ W/c--34£ C77 = 8 4 - 6 ftsx CXi COMSOL = 301 PSI g5> = 41-3 PS£ J)iD NOT FAIL. C-4 0-8 I A X I A L STRAIN •2 1-6 - PERCENT 2 0 FIGURE 4-9 LOG A X / A L S T R A I N R A T E V E R S U S A X I A L . S T R A I N F O R UNDRAINED PLANE STRAIN CREEP T E S T S -O3 DECREASING. 73 T A B L E 2 OF A T "THE SAME £ AND £ F R O M FIGURE 4 - . 9 , FOR UNDRAINED PLANE STRAIN TESTS ~ O3 DECREASED. ' T O T A L " <5 - PSI ADDITIONAL 0 3 - PSI 'INCREMENTAL CREEP INCREMENTAl CREEP LOADING T£Sr TEST LOADING TEST TEST 39- 0 4/3 8 9 W-4 42 5 IO-2 126 411 426 H-2 1 2 7 A 3 0 44-8 f 3 1 14-9 2 to JO ° 10 " I O " 10" MINIMUM STRAIN RATE - PERCENT/MINUTE FIGURE 4.10A as VERSUS MINIMUM STRAIN RATE FOR UNDRAINED PLANE STRAIN! CREEP TESTS. •50 •-4S o <T7 \NCRE\S2D. + 03 J)£CRi:A6£D. ar3 D E C R E A S E D V 07 '*'CREAS£I> IO" I O ' * RATE ~ 6^ FIGURE 4 1 0 8 Vcr^ ' AT VERSUS FOR UNDRAINED PLANE STRAIN CREEP TESTS. l i n e s r e p r e s e n t i n g the upper y i e l d v a l u e , as t h e o r e t i c a l l y a minimum s t r a i n r a t e does not e x i s t f o r samples which do not f a i l . T h e r e f o r e the two curves must a s y m p t o t i c a l l y approach the upper y i e l d v a l u e as shown i n F i g u r e 4.10A. For any p a r t i c u l a r v a l u e o f minimum s t r a i n r a t e , o " D f o r the d e c r e a s i n g type of creep t e s t i s g r e a t e r than a Q f o r the i n c r e a s i n g type of creep t e s t . These r e s u l t s show t h a t although t h e r e seems to be a unique curve r e p r e s e n t i n g the minimum i or a p l o t of l o g e versus l o g time or e = A t m f o r d i f f e r e n t t o t a l s t r e s s paths o f a x i a l compressive l o a d i n g ( i n c r e a s i n g c r ^ when compared to d e c r e a s i n g a^) a D 7* f (e) a t e^. The s t r a i n a t e m was found t o be approx-i m a t e l y equal to 0.6 pe r c e n t f o r i n c r e a s i n g and d e c r e a s i n g creep t e s t s . T h e r e f o r e the h y p o t h e s i s t h a t OJ-J = f ( e , e) can not apply f o r d i f f e r e n t t o t a l s t r e s s paths o f l o a d i n g . The comparison of the e f f e c t i v e s t r e s s r a t i o T / a ^ (where T = ^ and a' i s the mean normal e f f e c t i v e 2 m s t r e s s = 4(0"-! + ol + a I)) a t e f o r the i n c r e a s i n g a, and 3 1 2 3 ' m r 1 d e c r e a s i n g creep t e s t s as shown i n F i g u r e 4.10B. Again t h e r e i s a marked d i f f e r e n c e i n the s t r e s s r a t i o a t e . f o r m these two types o f creep t e s t s , showing t h a t samples o f d e c r e a s i n g t e s t s are s t r o n g e r than i n c r e a s i n g t e s t s i n terms o f e f f e c t i v e s t r e s s e s . , The comparison o f the e f f e c t i v e s t r e s s r a t i o T / O ' w i t h a x i a l s t r a i n i s g i v e n i n F i g u r e 4.11A. For any 76 1 DECREASING CQ T y P £ J OP C R E E P T E S T S CPEC P TESTS - <T3 DECREASED CT, = <84 6 RSI O i COMSOL *30 • I RSI ^ . A T/- » 86 M / M <5, 44 8 R S I lOll°/aGj>M W/C*&4-C „ 0 TV , 321M /NJ 4 2 6 Psi <?C v3 % O w \*ljc-34< + 4 T/.1300MIM 0 i « 4 / - 3 PSX 'tesT^CGiwj Uj/c ,34-8 CREEP TEST -CT, INCREASED Tf . TT»vi e fo /<a,i" /u>*c. 6^4 OU Ta r e To £ 4 3,2 A X / A L S T R A I N I - PERCENT FIGURE 4MA V/c^f VERSUS AXIAL STRAIN UNDRAINED PLANE STRAIN CREEP TESTS. FOR TYPICAL TEST FOR INCREASING TYPE OF CREEP TESTS DECREASING crj T Y P E OF CREEP TESTS _ _ AVERAGE. _POPE PRESSURE AT THE BEGINNING OF CR£EP T E S T * 18-2 PSL O 0-4 O S 12 1-6 2 0 2-4 *8 S-2 AXIAL. STRAIN PERCENT FIGURE 4-118 PORE PRESSURE: VERSUS AXIAL STRAIN FOR. UNDRAINED PLANE STRAIN CREEP TESTS p a r t i c u l a r s t r a i n , T / ° ^ x i s h i g h e r f o r the d e c r e a s i n g when compared to the i n c r e a s i n g type of creep t e s t s . From the p r o c e e d i n g d i s c u s s i o n i t can be seen t h a t d e c r e a s i n g t e s t s have a h i g h e r s t r e s s r a t i o T / a ^ f ° r a n Y s t r a i n and s t r a i n r a t e . A p o s s i b l e e x p l a n a t i o n of t h i s behaviour may l i e i n the comparison of pore p r e s s u r e s and o c t a h e d r a l s t r e s s paths, and hence these w i l l be d i s c u s s e d . Pore P r e s s u r e s - The F i g u r e 4.11B shows the comparison of pore p r e s s u r e f o r the i n c r e a s i n g and d e c r e a s i n g types of creep t e s t s . Although a D was i n c r e a s e d a t the b e g i n n i n g of these two types of creep t e s t s the mean normal s t r e s s was decreased i n the d e c r e a s i n g type of creep t e s t s , w h i l e the mean normal s t r e s s was i n c r e a s e d i n the i n c r e a s i n g a2_ type of creep t e s t s . For the d e c r e a s i n g type o f creep t e s t s the i n i t i a l decrease i n pore water was a s s o c i a t e d w i t h the dominant i n f l u e n c e o f decrease i n t o t a l normal s t r e s s compared to t h a t of i n c r e a s e i n s h e a r i n g s t r e s s e s . However w i t h the i n c r e a s e i n s t r a i n under s u s t a i n e d s t r e s s the pore p r e s s u r e r i s e was due to breakdown of s e n s i t i v e s o i l s t r u c t u r e under i n c r e a s i n g s h e a r i n g s t r a i n s . (Crawford 1959; H i r s c h f i e l d 1960; Gupta 1968). The shape of the curves f o r the sample which d i d not f a i l i s s i m i l a r t o those of the samples which f a i l e d . T h e r e f o r e i t i s d i f f i c u l t t o determine whether a sample would f a i l or not from the p l o t s o f pore p r e s s u r e versus a x i a l s t r a i n as shown i n F i g u r e 4.11B. 78 Pore p r e s s u r e parameter "A" has been found to be s e n s i t i v e t o change i n t o t a l s t r e s s path. T h i s s e n s i t i v i t y i s even more pronounced i f shear occurs when 7* (Henkel 1960; V a i d 1968). However, f o r undrained shear under non-symmetrical s t a t e s of s t r e s s e s ( i . e . , 7* o^) the changes i n pore p r e s s u r e s have been shown to be b e t t e r expressed i n terms of changes i n o c t a h e d r a l normal and s h e a r i n g s t r e s s e s as g i v e n i n E q u a t i o n 4.2 (Henkel and Wade 1966) . Aa,-fAa^ + Aa., , -A u = —-—y - + | ^ ( A a 1 - A a 2 ) 2 + ( A a 2 - A a 3 ) 2 + ( A a 3 - A a 1 ) 2 . . 4.2 Where Au i s the increment of pore p r e s s u r e due to increments of Aa^, Aa 2 and A a 3 a i s the Henkel pore p r e s s u r e parameter. a2 was e s t i m a t e d as p r e v i o u s l y d i s c u s s e d i n Chapter 3. There-f o r e the comparison of Henkel "a" parameter f o r i n c r e a s i n g and d e c r e a s i n g type o f creep t e s t s w i l l be done. Henkel "a" parameter versus a x i a l s t r a i n i s g i v e n i n F i g u r e 4.12. The curves f o r the two types of creep t e s t s are s i m i l a r . The upper two curves r e p r e s e n t samples which d i d not f a i l . "a" parameter a t any p a r t i c u l a r s t r a i n i n c r e -ased w i t h the decrease i n oQ and i n c r e a s e i n time to reach t h i s s t r a i n . For each t e s t the parameter "a" i n c r e a s e d 79 Ar denotes poi^S Nor F4U. — CTi, 40-7 7/.3.21 MIN 9<Jh s 44S P&I qj = 44-8 tex Tf * 86 M I N ^2x461 Rsr TS ' 29 M I N S C i * A4S(>st 0 Q PLANE STRA N- err I N C R E A S E D ^ + P L A N E s r ^ i N - 0 5 J)ircR£/4S£D O d~S F6~ 2-4 A X I A L STRAIN PERCENT 32 FIGURE 4.12 VARIATION OF HENKEL "a" AND AXIAL STRAIN FOR UNDRAINED PLANE STRAIN CREEP TESTS. 80 w i t h i n c r e a s e i n a x i a l s t r a i n . T h e r e f o r e the "a" v a l u e i s dependent on a x i a l s t r a i n and e l a p s e d time. The "a" v a l u e s a t minimum e i n c r e a s e d w i t h the decrease i n a Q f o r both i n c r e a s i n g and d e c r e a s i n g t e s t s ( F igure 4.12). As the 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 s not equal to the minor p r i n c i p a l s t r e s s f o r plane s t r a i n t e s t s , the e f f e c t i v e s t r e s s paths may be b e t t e r expressed i n terms o f o c t a h e d r a l s t r e s s e s . The o c t a h e d r a l shear s t r e s s "x " and o c t o c t " a r e 9 i v e n by T o c t = I ( a 1 - a 2 ) 2 + ( a 2 - a 3 ) 2 + ( a 3 - a 1 ) 2 a ' = a 1 = o c t m Where a|, , o'^ are e f f e c t i v e major, i n t e r m e d i a t e and minor p r i n c i p a l s t r e s s e s . F i g u r e 4.13 shows the o c t a h e d r a l s t r e s s paths i n d i m e n s i o n l e s s form f o r the undrained plane s t r a i n creep t e s t s . A l l s t r e s s paths s t a r t a t h i g h normal e f f e c t i v e s t r e s s which decrease w i t h creep due to i n c r e a s i n g pore p r e s s u r e s . The s l i g h t v a r i a t i o n s i n T . i s due to the e s t i m a t e d ^ o c t v a r i a t i o n i n a^ as and are kept c o n s t a n t d u r i n g creep. I t should be noted t h a t a ' o c t a t ^ f ° r the d e c r e a s i n g o"3 t e s t s are lower than t h a t o f i n c r e a s i n g type o f creep t e s t s . The s t r e s s paths i n F i g u r e 4.13 f o r the i n c r e a s i n g t y P e of creep t e s t have been r e l a t i v e l y d i s p l a c e d more •44 y DENOTES POINTS OF MINIMUM STRAIN RATES •2c Go FIGURE 413 •68 AFTER CONSOLIDATION Q 0 CREEP TESTS -07 INCREASED +. + CREEP TESTS - <rs DECREASED ^ X INCREMENTAL LOADING TEST - 0 7 INCREASING A A INCREMENTAL LOADING TEST -<§ DECREASING •72 •76 80 84 •88 •95 9 T /•Oo OCTAHEDRAL STRESS PATHS FOR UNDRAlN'ED PLANE STRAIN CREEP TESTS. (UNDISTUR8ED HANEY CLAY) CO towards the a o c t a x i s when compared to the o t h e r type of creep t e s t s . T o c t a t f a i l u r e or a t minimum e f o r samples which f a i l e d when was decreased was g r e a t e r than t h a t f o r samples which f a i l e d when o^ was i n c r e a s e d . Upper Y i e l d S t r e n g t h - P o s s i b l e e x p l a n a t i o n s o f the d i f f e r ence i n the upper y i e l d s t r e n g t h f o r the i n c r e a s i n g and d e c r e a s i n g plane s t r a i n creep t e s t s may be due to the f o l l o w i n g : 1. Higher i n c r e a s e i n f r i c t i o n w i t h time f o r the d e c r e a s i n g a3 type o f creep t e s t s , when compared to the i n c r e a s e i n f r i c t i o n f o r the other type of creep t e s t s . I t i s d i f f i c u l t to understand why a h i g h e r f r i c t i o n c o u l d be o b t a i n e d f o r the d e c r e a s i n g type o f creep t e s t s , as the f r i c t i o n should decrease w i t h the decrease i n . 2. Instantaneous l o a d i n g o f the samples g i v i n g an "impulse" would be s m a l l e r i n the case o f "unloading" f o r "a^ decreased" t e s t s . F u r t h e r the t r a n s i e n t pore p r e s s u r e s would decrease the s t r e n g t h o f the i n c r e a s i n g type of creep t e s t , because both mean normal s t r e s s and shear s t r e s s e s are i n c r e a s e d a t the same time, w h i l e i n the d e c r e a s i n g type of creep t e s t s , mean normal s t r e s s i s decreased but the shear s t r e s s e s are i n c r e a s e d . 3. Higher s t r e n g t h f o r the d e c r e a s i n g type o f creep t e s t s because of p r e s t r e s s i n g due to lower a 1 .. o c t 83 Summary 1. For both the i n c r e a s i n g and d e c r e a s i n g types o f plane s t r a i n creep r u p t u r e t e s t s , the s t r a i n r a t e i n i t i a l l y decreased reached a minimum and then i n c r e a s e d g r a d u a l l y u n t i l f a i l u r e . Secondary creep s t r a i n r a t e does not e x i s t f o r plane s t r a i n creep r u p t u r e t e s t s . 2. When the minimum s t r a i n r a t e i s reached, the sample under c o n s t a n t a p p l i e d s t r e s s e s w i l l i n e v i t a b l y r u p t u r e and f a i l u r e can be c o n s i d e r e d t o o c c u r . 3. E x p e r i m e n t a l data suggest t h a t the p o i n t s of minimum s t r a i n r a t e f a l l on a s t r a i g h t l i n e on the l o g - l o g p l o t of s t r a i n r a t e and e l a p s e d time, f o r i n c r e a s i n g type of creep t e s t s . T h i s s t r a i g h t l i n e was found t o be almost the same f o r the d e c r e a s i n g type of creep t e s t s . 4. The curve o f a sample having a d e v i a t o r s t r e s s o f approximately equal t o the upper y i e l d s t r e n g t h i n the lo g e versus l o g t p l o t would g i v e an i n d i c a t i o n whether any o t h e r sample would f a i l o r not. A s t r a i n -r a t e - t i m e c o n d i t i o n o f a sample p l o t t e d above t h i s curve would i n d i c a t e t h a t the sample would f a i l i n creep, and below t h i s curve t h a t i t would not f a i l . Snead's ( 1 9 7 0 ) h y p o t h e s i s namely a Q = f ( e , e) was i n good agreement i n terms of " t o t a l " d e v i a t o r s t r e s s e s f o r i n c r e m e n t a l l o a d i n g t e s t s and creep t e s t s . In terms o f " a d d i t i o n a l " a Q e r r o r s of the order of 2 0 % were observed. Snead's h y p o t h e s i s was found t o be not v a l i d f o r d i f f e r e n t t o t a l s t r e s s paths o f l o a d i n g . The s t r a i n - t i m e and s t r a i n r a t e - t i m e behaviour of i n c r e a s -i n g and d e c r e a s i n g types of creep t e s t s were • found to be s i m i l a r . But the upper y i e l d s t r e n g t h and -minimum s t r a i n r a t e behaviour were found t o be q u i t e d i f f e r e n t . 85 CHAPTER 5 COMPARISON OF PLANE STRAIN AND TRIAXIAL RESULTS T h i s chapter d i s c u s s e s the comparison o f s t r e s s , s t r a i n and s t r a i n r a t e behaviour o f samples t e s t e d under undrained c o n d i t i o n 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 f o r plane s t r a i n , c o n v e n t i o n a l t r i a x i a l and K q t r i a x i a l a pparatus. The r e s u l t s from the c o n v e n t i o n a l t r i a x i a l were o b t a i n e d from Snead (1970) and c o n s i d e r s o n 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 samples loaded i n a x i a l compression w i t h a2 = °3 • T N E K q t r i a x i a l apparatus i n i t i a l l y c o n s o l i -dates the samples under (no l a t e r a l y i e l d ) and one d i m e n s i o n a l c o n d i t i o n s . Four K t r i a x i a l creep t e s t s were o performed, t h r e e i n which was i n c r e a s e d and one i n which a^ was decreased. The. f o l l o w i n g types of creep t e s t s w i l l be compared. 1. Creep t e s t s performed i n the c o n v e n t i o n a l t r i a x i a l apparatus w i t h i n c r e a s i n g . 2. Creep t e s t s performed i n the plane s t r a i n apparatus by i n c r e a s i n g and by d e c r e a s i n g . 3. Creep t e s t s performed i n the K Q t r i a x i a l apparatus by i n c r e a s i n g a. and by d e c r e a s i n g a _ . A f t e r c o n s o l i d a t i o n the plane s t r a i n and K o t r i a x i a l samples (K c o n s o l i d a t i o n ) were under a d e v i a t o r o s t r e s s w h i l e the c o n v e n t i o n a l t r i a x i a l samples (hydro-s t a t i c c o n s o l i d a t i o n ) were not under any d e v i a t o r s t r e s s . Thus the e f f e c t i v e s t r e s s paths d u r i n g c o n s o l i d a t i o n are d i f f e r e n t f o r K q and h y d r o s t a t i c c o n s o l i d a t e d samples. During creep the c o n v e n t i o n a l t r i a x i a l and K Q t r i a x i a l samples would deform l a t e r a l l y w i t h ~ a 3 w h i l e the plane s t r a i n samples would deform l a t e r a l l y w i t h no s t r a i n i n the l o n g i t u d i n a l a x i s of the sample and was not equal to o^. T h e r e f o r e d u r i n g creep the modes o f a p p l i c a t i o n and v a r i a t i o n , cc the s t r e s s e s and s t r a i n s are d i f f e r e n t f o r the d i f f e r e n t types of t e s t s . However, a com-p a r i s o n of the behaviour of the samples i n creep w i l l be attempted by u s i n g o c t a h e d r a l normal e f f e c t i v e s t r e s s a' .; o c t a h e d r a l shear s t r e s s , T .; o c t a h e d r a l shear o c t o c t s t r a i n , y ,; and o c t a h e d r a l shear s t r a i n r a t e , y 'oct ' 'oct Y o c t = | ^(e1-e2)2+(e2-e3)2+(e3-e1)2 . . . . 5.1 ^ o c t = d t ( y o c t ) . . . . 5.2 Where e^, , £3 are the p r i n c i p a l s t r a i n s . The e x i s t e n c e of a minimum s t r a i n r a t e can be used as a f a i l u r e c r i t e r i o n . Hence i t may be d e s i r a b l e to take a l l the parameters of s t r e s s e s , s t r a i n s and s t r a i n r a t e s f o r comparison purposes a t the minimum s t r a i n r a t e . Since the mean normal e f f e c t i v e s t r e s s a t the end o c o n s o l i d a t i o n (Y , ) i s not the same f o r d i f f e r e n t types of ' o c t c J * creep t e s t s , the d i m e n s i o n l e s s r a t i o s x . / ( a 1 .) and o c t O C t Q a ' 4 - / ( 0 ' , ) w i l l be used f o r comparison purposes. The o c t OCt Q e f f e c t i v e s t r e s s r a t i o , x ,/o1 . a t the minimum s t r a i n ' o c t ' o c t r a t e w i l l a l s o be c o n s i d e r e d f o r comparison purposes. Comparison of Creep T e s t s - The s t r a i n r a t e - t i m e behaviour of the samples i n the t h r e e types o f creep t e s t s were found to be s i m i l a r i n t h a t the s t r a i n r a t e i n i t i a l l y d ecreased reached a minimum and i n c r e a s e d g r a d u a l l y t o f a i l u r e . I t i s i n t e r e s t i n g to note t h a t the r a t i o of the t o t a l creep r u p t u r e l i f e , t o the time to minimum s t r a i n r a t e i s about 2.5 to 3 f o r plane s t r a i n , 3 to 4 f o r c o n v e n t i o n a l t r i a x i a l and 4 to 5 f o r K t r i a x i a l t e s t s . T h i s means t h a t most o f o the creep r u p t u r e l i f e i s spent d u r i n g t e r t i a r y creep stage, i . e . , a t p r o g r e s s i v e l y i n c r e a s i n g r a t e s . From the creep t e s t s i t was found t h a t the octahe-d r a l shear s t r a i n s a t minimum s t r a i n r a t e s v a r y from 3.4 to 7.65 p e r c e n t f o r samples 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 compared t o 0.9 p e r c e n t f o r plane s t r a i n and 0.45 p e r c e n t f o r K q t r i a x i a l . The c o r r e s p o n d i n g a x i a l s t r a i n s are 2.4 to 5.4% f o r c o n v e n t i o n a l t r i a x i a l , 0.6% f o r plane s t r a i n and 0.3% f o r K t r i a x i a l . I t i s i n t e r e s t i n g to note o ^ t h a t V a i d (1970) o b t a i n e d s i m i l a r v a l u e s f o r s t r a i n s a t 88 f a i l u r e (maximum f a i l u r e c r i t e r i o n ) f o r c o n v e n t i o n a l t r i a x i a l , plane s t r a i n and K t r i a x i a l shear t e s t s (run ^ o at c o n s t a n t s t r a i n r a t e s i m i l a r to the v a l u e s o f minimum s t r a i n r a t e o b t a i n e d from creep t e s t s ) . T h e r e f o r e the s t r a i n s a t minimum s t r a i n r a t e are q u i t e d i f f e r e n t f o r the thr e e types o f creep t e s t s . For the same minimum s t r a i n r a t e the s t r a i n i n c r e a s e s from the K t r i a x i a l , t o plane s t r a i n t o c o n v e n t i o n a l t r i a x i a l o ' ^ t e s t s ( i n c r e a s i n g a ^ ) . T h e r e f o r e i t might be expected t h a t the time t o any p a r t i c u l a r v a l u e of minimum s t r a i n r a t e would i n c r e a s e from K t r i a x i a l to plane s t r a i n to c o n v e n t i o n a l o ^ t r i a x i a l t e s t s ( i n c r e a s i n g a ^ ) . T h i s i s c l e a r l y seen from the l i n e s of minimum s t r a i n r a t e s as shown i n F i g u r e 5.1. F i g u r e 5.1 shows t h a t the l i n e o f minimum s t r a i n r a t e s f o r i n c r e a s i n g c o n v e n t i o n a l t r i a x i a l and plane s t r a i n t e s t s are almost p a r a l l e l . The i n c r e a s i n g , K Q t r i a x i a l t e s t s i n d i c a t e t h a t t h i s l i n e o f minimum s t r a i n r a t e s i s a l s o p r o b a b l y p a r a l l e l to the o t h e r l i n e s o f minimum s t r a i n r a t e s . The time t o reach any p a r t i c u l a r minimum s t r a i n r a t e f o r i n c r e a s i n g 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 i s about 3.5 times t h a t f o r i n c r e a s i n g and d e c r e a s i n g plane s t r a i n t e s t s , and about 8 times t h a t f o r i n c r e a s i n g a,, K t r i a x i a l t e s t s . r 1 o T h e r e f o r e the s t r a i n r a t e - t i m e behaviour of the i n c r e a s i n g a, c o n v e n t i o n a l t r i a x i a l , plane s t r a i n and K t r i a x i a l t e s t s 1 ^ o are q u i t e d i f f e r e n t . As the e x i s t e n c e o f a minimum s t r a i n r- 1 — — ' 1 1 1 1 1 1 1 | < Oi IO IO /OO /Ooo 10,000 TIME IN MINUTE FIGURE S.L COMPARISON OF LINES OF MINIMUM STRAIN RATES CO r a t e c o u l d be u s e d as a f a i l u r e c r i t e r i o n , F i g u r e 5.1 may be u s e d t o c o r r e l a t e t h e r e s u l t s o f t h e i n c r e a s i n g 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 t o f i e l d c o n d i t i o n s . C o m p a r i s o n o f S t r e s s R a t i o s - . To compare t h e r e s u l t s o f t h e d i f f e r e n t c r e e p t e s t s , t h e s t r e s s r a t i o , T . / ( a 1 ,) O C L O C t l c may be compared a t any p a r t i c u l a r minimum o c t a h e d r a l s h e a r s t r a i n r a t e (Y o c^.) as shown i n F i g u r e 5.2. N o t e t h a t (a' .) r e f e r s t o mean n o r m a l e f f e c t i v e s t r e s s a t w h i c h o c t c t h e sample was c o n s o l i d a t e d . The p o s s i b l e r e a s o n s f o r t h e d i f f e r e n c e s i n t h e s t r e s s r a t i o f o r t h e i n c r e a s i n g and d e c r e a s i n g p l a n e s t r a i n c r e e p t e s t s were s u g g e s t e d i n C h a p t e r 4. I t s h o u l d be n o t e d t h a t d i f f e r e n c e s i n t h e s t r e s s r a t i o f o r t h e i n c r e a s i n g and d e c r e a s i n g a ^ , K Q t r i a x i a l c r e e p t e s t seems t o be q u i t e s m a l l when compared t o t h e d i f f e r e n c e s i n t h e s t r e s s r a t i o f o r p l a n e s t r a i n i n c r e a s i n g and d e c r e a s i n g c r e e p t e s t s . F o r a l l c u r v e s i n F i g u r e 5.2 t h e r e i s a d e c r e a s e i n T ./(cr 1 . ) 3 o c t o c t c w i t h t h e d e c r e a s e i n minimum s t r a i n r a t e , b u t a t a d e c r e a s -i n g r a t e f o r 10 f o l d d e c r e a s e i n minimum s t r a i n r a t e . An u p p e r y i e l d s t r e n g t h i n t e r m s o f T . / ( a ' .) may be OC "C O C t Q d e f i n e d f o r d i f f e r e n t t y p e s o f c r e e p t e s t s . When c o m p a r i n g i n c r e a s i n g p l a n e s t r a i n and c o n v e n t i o n a l t r i a x i a l c r e e p t e s t s , t h e c u r v e ( F i g u r e 5.2) f o r p l a n e s t r a i n t e s t s a r e c o n s i d e r a b l y h i g h e r t h a 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 , •45r T k 0 0 a © CONVENTIONAL TR PLANE STRAIN -IAXIAL INCREASING INCREASING CT, sn. •2o 4- + X X P I A DECREASING NE STRAIN TRIAXIAL TRIAXIAL - $ECREA\S f\NCREASING C7 IN6 03 S\l63 lO-i MINIMUM 10 -a OCTAHEDRAL SHEAR STRAIN RATE -(Xoct)^ PERCENT/MINUTE FIGURE S.2. Foci/jfcr^ct}c AT MINIMUM STRAIN RATE VERSUS (abet)*, FOR UNDRAINED CREEP TESTS ON HANEY CLAY. i n d i c a t i n g t h a t plane s t r a i n specimens are s t r o n g e r and c o n s i d e r a b l y s t i f f e r than c o n v e n t i o n a l t r i a x i a l specimens. From F i g u r e 5.3 i t can be seen t h a t l o s s i n T 4-/(0' , ) becomes g r a d u a l l y s m a l l e r w i t h i n c r e a s e d e l a p s e d times, f o r a l l the types of creep t e s t s . T h e r e f o r e a simple r e l a t i o n s h i p l i k e a c o n s t a n t decrease i n s t r e n g t h per 10 f o l d i n c r e a s e i n time t o f a i l u r e as p o s t u l a t e d by H v o r s l e v (1960) and used by Bishop and Lovenbury (1969) may not be v a l i d f o r creep r u p t u r e o f Haney c l a y . F i g u r e 5.4 shows the comparison of the e f f e c t i v e s t r e s s r a t i o x ./a' , a t (Y . ) v e r s u s (Y , ) f o r oct' o c t 'oct m 'oct m the d i f f e r e n t types of creep t e s t s . Note t h a t both T ^ and a' . are e v a l u a t e d a t the minimum s t r a i n r a t e . For o c t the i n c r e a s i n g a. 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 x ./a' . ^ 1 o c t ' o c t decreases s l i g h t l y , i n c r e a s e s r a p i d l y and l e v e l s o f f as the l o g s t r a i n r a t e d e c r e a s e s . S i m i l a r curves o f (Figure 5.4) are o b t a i n e d f o r i n c r e a s i n g and d e c r e a s i n g plane s t r a i n creep t e s t s but the behaviour of these curves a t low (Y O_) i s not known as data was not o b t a i n e d i n t h i s r e g i o n 'oct m The v a l u e of x . / a 1 , a t (y . ) v a r i e s c o n s i d e r a b l y o c t o c t O C t w i t h the type o f t e s t . T h e r e f o r e a f a i l u r e c r i t e r i a i n the form of an e f f e c t i v e s t r e s s parameter based on a c r i t i c a l c o n d i t i o n can not i n i t s p r e s e n t form be used f o r creep r u p t u r e . C o n s i d e r a b l y more r e s e a r c h i s needed b e f o r e a r a t i o n a l e x p l a n a t i o n can be g i v e n f o r the da t a i n F i g u r e 5.4 TIME TO MINIMUM STRAIN 'OOO RATE - t K MINUTES i q o o o FIGURE S.3 Toot //tr'ocOc / 4 T ~ M I N I M U M STRAIN RATE VERSUS UNDRAINED CREEP TESTS O M HANEY CLAY U , FOR /cr 10 -2 IO FT MINIMUM OCTAHEDRAL SHEAR STRAIN RATE - (Xoct )^ / » - c W / W W e FIGURE £.4 Tact/(Tod AT (Zoct)^ VERSUS C^ocOm FOR UNDRAINED CREEP TESTS -HANEY CLAY. S t r e s s - S t r a i n - S t r a i n Rate R e l a t i o n s h i p - R e s u l t s from t h i s i n v e s t i g a t i o n compared wi t h Snead's (1970) r e s u l t s , show t h a t Snead's h y p o t h e s i s of a Q = f ( e , e) i s not v a l i d f o r i n c r e a s i n g a^, K q t r i a x i a l , c o n v e n t i o n a l t r i a x i a l and plane s t r a i n creep t e s t s taken t o g e t h e r . T h e r e f o r e i t should be noted t h a t the hy p o t h e s i s o f a Q = f ( e , e) i s not v a l i d , 1. When the i n i t i a l c o n d i t i o n s are d i f f e r e n t ( i . e . , c o n s o l i d a t i o n ) . 2. When t r i a x i a l and plane s t r a i n d eformation are compared even though the i n i t i a l c o n d i t i o n s are the same, ( i . e . , K t r i a x i a l and plane s t r a i n t e s t s ) , o * Summary From the comparison o f i n c r e a s i n g c o n v e n t i o n a l t e s t s w i t h those o f plane s t r a i n and K q t r i a x i a l creep t e s t s i t can be seen t h a t the creep behaviour o f K q c o n s o l i d a t e d c l a y i s q u i t e d i f f e r e n t from t h a t o f i s o t r o p i c a l l y con-s o l i d a t e d c l a y . I f the r e s u l t s o f i n c r e a s i n g plane s t r a i n and K q t r i a x i a l creep t e s t s can be used to p r e d i c t behaviour i n the f i e l d because o f t h e i r r e p r o d u c t i o n o f K Q f i e l d c o n d i t i o n s , i t can be concluded t h a t i n c r e a s i n g c o n v e n t i o n a l t r i a x i a l creep t e s t s do not g i v e a good i n d i c a t i o n o f creep behaviour under f i e l d c o n d i t i o n s namely because of the i n i t i a l 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 r e f o r e the r e s u l t s of the c o n v e n t i o n a l t r i a x i a l apparatus may not be r e p r e s e n t a t i v e of creep r u p t u r e i n the f i e l d , u n l e s s a c o r r e l a t i o n of the data from the d i f f e r e n t types of creep t e s t s i s made. 97 CHAPTER 6 PREDICTION OF SLOPE FAILURE In t h i s chapter the p r e d i c t i o n of creep r u p t u r e i n the f i e l d u s i n g S a i t o ' s method (1965) f o r secondary creep stage and by u s i n g Snead's method (1970) f o r t e r t i a r y creep w i l l be d i s c u s s e d and e v a l u a t e d w i t h the data o b t a i n e d from plane s t r a i n apparatus. The data r e p o r t e d by S a i t o and Uezawa (1961) and by Snead (1970) from the t r i a x i a l apparatus w i l l be compared w i t h the data o b t a i n e d from t h i s study. I t should be p o i n t e d out t h a t the l a b o r a t o r y plane s t r a i n apparatus should g i v e the b e t t e r s i m u l a t i o n of f i e l d con-d i t i o n s when compared to t r i a x i a l . Hence the p r e d i c t i o n o f s l o p e f a i l u r e u s i n g the r e s u l t s from plane s t r a i n t e s t s may be c o n s i d e r e d to be more a c c u r a t e than t h a t o b t a i n e d from the t r i a x i a l t e s t s . S a i t o ' s (1965) Method - The p l o t o f t o t a l r u p t u r e l i f e , t , versus minimum s t r a i n r a t e e i s g i v e n i n F i g u r e 6.1. r m 3 - o r f o r both i n c r e a s i n g and d e c r e a s i n g types of plane s t r a i n creep t e s t s . I t was observed t h a t a s t r a i g h t l i n e r e l a t i o n s h i p e x i s t s between l o g t and l o g as g i v e n by Eq u a t i o n 6.1 TOTAL TIME TO RUPTURE -MINUTES l o g 1 Q t = 2.00 - 1.20 l o g 1 Q ^ m . . . . 6.1 Where t t o t a l time to r u p t u r e i n minutes r . . . . -4 minimum s t r a i n r a t e i n l o per minute, m c T h i s s t r a i g h t l i n e i s compared w i t h the r e s u l t s of Snead (1968) , S a i t o and Uezawa (1961) along w i t h S a i t o and Uezawa's 95% c o n f i d e n c e l i n e s , as shown i n F i g u r e 6.2. The r e s u l t s of the f o u r undrained K t r i a x i a l creep t e s t s o ^ are a l s o g i v e n i n t h i s f i g u r e . Although Snead (1970) c r i t i c i z e d S a i t o ' s (1965) method, t h i s method i s the o n l y known method a t p r e s e n t to p r e d i c t time t o s l o p e f a i l u r e b e f o r e t e r t i a r y creep stage i s reached. I t was d i s c u s s e d , i n Chapter 4 w i t h the h e l p of F i g u r e 4.1 t h a t i f a "secondary s t r a i n r a t e " i s r e q u i r e d f o r Haney c l a y t h a t i t c o u l d be taken to be approximately equal to the minimum s t r a i n r a t e . In the p r e d i c t i o n of time t o s l o p e f a i l u r e , the e r r o r o f u s i n g t h i s assumption may be n e g l i g i b l e when e r r o r s of the order of 100% may be t o l e r a t e d . T h e r e f o r e i n t h i s d i s c u s s i o n S a i t o and Uezawa's secondary s t r a i n r a t e was assumed t o be equal to the minimum s t r a i n r a t e and g i v e n i n the same F i g u r e 6.2. From t h i s f i g u r e i t can be seen t h a t a l l the data l i e w i t h i n S a i t o and Uezawa's 95% c o n f i d e n c e l i n e s . I t should be p o i n t e d out t h a t these 95% c o n f i d e n c e l i m i t s r e p r e s e n t gross d e v i a t i o n s i n excess of 1100%. The equations of S a i t o and Uezawa's (1961) and Snead's (1970) are g i v e n by Equation 6.2 and Eq u a t i o n 6.3. SHEAD Olio) FOR TRIAXIAL CREEP TESTS. \ 10 FROM THIS STUDY FOfi PLANE STRAIN CREEP O N H A N E Y CL>4Y ^°Sk> "^ * 2 0 0 -/-20 /o°(0^ >»» 6^ _ m i n i fv»oLtv\ 5ii-a.r"*v >d.fe - /6" 4 /* T 1 ' n To"2 /O" 'Oc MINIMUM STRAIN RATE IO~4/MIN 100 to F-IGURE6.Z RELATION BETWEEN TOTAL TIME TO RUPTURE AND MINIMUM STRAIN RATE. 101 l o g t = 2.33 - 0.916 l o g i n e . . . . 6.2 ^ r ^10 s l o g t = 2.59 - 0.92 log... e . . . . 6.3 ^ r ^10 m Where t t o t a l time to r u p t u r e i n minutes r ^ -4 e g secondary s t r a i n r a t e i n 10 per minute -4 e minimum s t r a i n r a t e i n 10 per minute m c The s t r a i g h t l i n e s o b t a i n e d by S a i t o and Uezawa, and Snead f o r c o n v e n t i o n a l t r i a x i a l creep t e s t s on Haney c l a y and from t h i s study on K Q t r i a x i a l f a l l on p a r a l l e l s t r a i g h t l i n e s i n t h i s p l o t . For any p a r t i c u l a r v a l u e of s t r a i n r a t e s the estimated time to f a i l u r e f o r Snead's d a t a would be 6 times t h a t f o r K t r i a x i a l r e s u l t s and 3 times t h a t f o r S a i t o o and Uezawa's d a t a . The data f o r Haney c l a y f o r c o n v e n t i o n a l t r i a x i a l creep t e s t s and from plane s t r a i n creep t e s t s g i v e s t r a i g h t l i n e s w i t h d i f f e r e n t s l o p e s which are f a r a p a r t a t low e l a p s e d times but converge.at h i g h e r p r e d i c t e d t o t a l e l a p s e d times. T h e r e f o r e , f o r p r e d i c t e d times of s l o p e f a i l u r e o f l e s s than 10 days, the d a t a from the t r i a x i a l apparatus may be u n c o n s e r v a t i v e as p r e d i c t e d times to f a i l u r e o f 3 t o 6 times t h a t o b t a i n e d from plane s t r a i n c o n d i t i o n are i n d i c a t e d . S a i t o (1965) approximated the e q u a t i o n 6.2 to a simple r e l a t i o n between t o t a l time to f a i l u r e and secondary 102 s t r a i n r a t e g i v e n by t • e = 216 . . . . 6 . 4 r s He found t h a t h i s p r e d i c t i o n of time to s l o p e f a i l u r e was f a i r l y a c c u r a t e , f o r times of the order of few days. T h i s may be because the s t r a i g h t l i n e s r e l a t i o n s h i p o b t a i n e d from t h i s study and S a i t o and Uezawa converges f o r times o f the o r d e r of few days as shown i n F i g u r e 6.2. F u r t h e r the .error i n S a i t o ' s assumption o f t a k i n g the time to f a i l u r e from the time secondary s t r a i n r a t e was measured t o the time of a c t u a l f a i l u r e t o be the t o t a l r u p t u r e l i f e has t o be a s c e r t a i n e d . In Chapter 4 i t was found t h a t the t o t a l r u p t u r e l i f e was between 2.4 t o 3.2 times the time to minimum s t r a i n r a t e f o r plane s t r a i n creep r u p t u r e t e s t . T h i s means t h a t S a i t o ' s assumption g i v e s an e r r o r o f the o r d e r o f 30%. T h i s may c o n s i d e r e d s m a l l as the p r e d i c t i o n of time t o f a i l u r e w i t h the a v a i l a b l e methods can not be c o n s i d e r e d to g i v e even p r e d i c t i o n w i t h e r r o r s o f l e s s than 100%. T h e r e f o r e S a i t o ' s method by u s i n g d a t a from the plane s t r a i n creep t e s t s c o u l d be used w i t h r e a s o n a b l e a c c u r a c y f o r p r e d i c t i o n of slope f a i l u r e b e f o r e t e r t i a r y creep stage i s reached as b e t t e r methods are not a v a i l a b l e f o r t h i s stage of creep. i Snead's (1970) Method - For t e r t i a r y creep stage, Snead 1s (1970) methods w i l l be d i s c u s s e d . F i g u r e 6.3 shows the proposed l i n e a r r e l a t i o n s h i p between c u r r e n t s t r a i n r a t e and time to r u p t u r e f o r r e s u l t s from undrained plane s t r a i n creep t e s t s , f o r t e r t i a r y creep stage. Time t o r u p t u r e " t t " was d e f i n e d by Snead (1970) as the time e l a p s e d from the time the s t r a i n r a t e was measured t o the time of f a i l u r e , d u r i n g t e r t i a r y creep s t a g e . The e q u a t i o n o f the s t r a i g h t l i n e i n F i g u r e 6.3 i s g i v e n by log^Q t t r = - .37 - 1.05 log^Q e . . . . 6 Where t t time to r u p t u r e i n minutes r ^ e c u r r e n t t e r t i a r y s t r a i n r a t e i n p e r c e n t / min. E q u a t i o n 6.5 c o u l d be used t o p r e d i c t s l o p e f a i l u r e i n the f i e l d , i f the c u r r e n t s t r a i n r a t e i s known. I t should be noted t h a t creep t e s t s i n which was i n c r e a s e d and creep t e s t s i n which was decreased g i v e s the same p r e d i c t e d times t o f a i l u r e . The s t r a i g h t l i n e r e l a t i o n s h i p s between l o g time to r u p t u r e and l o g c u r r e n t s t r a i n r a t e f o r data o b t a i n e d from plane s t r a i n creep t e s t s K q t r i a x i a l creep t e s t s and c o n v e n t i o n a l t r i a x i a l creep t e s t are g i v e n i n F i g u r e 6.4. -3 For c u r r e n t s t r a i n r a t e s of 10 p e r c e n t per minute the pre - f i 2 h iu u or UJ xy UJ s h X z m a a :> u U AXIAL DATA FROM ALL TESTS ARE PLOTTED. * x k-0 TRMXWL - V, INCREASED A 4 ^-O TRMXML - CTi .DECREASED. tty - time fo ru.f>tufe - mr»% £ - Current StfcAlA Tdite. ^Ce^t/m,'^ FROM THIS STUDY FOR PLANE STRAIN CREEP & TESTS ON HANEY CLAY " loo tb = ->37 - /OS lo0£ J10 J ' ° SNEAD (/970) FOR TR/AX/AL CRE£ P TESTS OM HANEY CLAY l o 9 ( o t t,.. 23 - l o Q / / /o' io 3 7 TIME: T O RUPTURE it*' MINS JO FIGURE 6.1 RELATION BETWEEN CURRENT STRAIN RATE AND TIME TO RUPTURE. 106 d i e t e d time to slope f a i l u r e i s approximately the same f o r both plane s t r a i n and K q t r i a x i a l creep t e s t s , but a time of 2.3 times i s p r e d i c t e d by c o n v e n t i o n a l t r i a x i a l creep t e s t s . For g r e a t e r times t o r u p t u r e t h i s e r r o r decreases but a t a slow r a t e . T h e r e f o r e the c o n v e n t i o n a l t r i a x i a l c reep t e s t s g i v e p r e d i c t i o n of times t o r u p t u r e which are u n c o n s e r v a t i v e when compared to t h a t o b t a i n e d from plane s t r a i n creep r u p t u r e t e s t s . Plane s t r a i n creep t e s t s g i v e the lowest p r e d i c t e d time t o f a i l u r e . Most slope f a i l u r e s take p l a c e under plane s t r a i n c o n d i t i o n . T h e r e f o r e E q u a t i o n 6.5 o b t a i n e d by performing l a b o r a t o r y creep t e s t s under c o n d i t i o n s of plane s t r a i n should be used to p r e d i c t s l o p e f a i l u r e s . T h i s must be confirmed by t e s t i n g programmes conducted on v a r i o u s s o i l s under v a r i o u s c o n d i t i o n s throughout the world, and by a p p l i c a t i o n o f r e s u l t s to f i e l d c o n d i t i o n s . Summary S a i t o ' s (1965) method f o r creep b e f o r e the t e r t i a r y stage and Snead's (1970) method f o r the t e r t i a r y c reep stage were d i s c u s s e d and found to be s a t i s f a c t o r y f o r the range of a p p l i c a t i o n a c c o r d i n g t o the creep stage. However, i t i s suggested t h a t to p r e d i c t s l o p e f a i l u r e the r e s u l t s o b t a i n e d from plane s t r a i n creep t e s t s should be used because most . s l o p e f a i l u r e s take p l a c e under c o n d i t i o n s of plane s t r a i n and because p r e d i c t e d times of f a i l u r e from r e s u l t s of con-v e n t i o n a l t r i a x i a l t e s t s were found t o be u n c o n s e r v a t i v e when compared to t h a t o b t a i n e d from plane s t r a i n creep t e s t s . The time of occurrence of s l o p e f a i l u r e c o u l d be r o u g h l y e s t i m a t e d d u r i n g creep stage b e f o r e t e r t i a r y creep by S a i t o ' s method and estimated f a i r l y a c c u r a t e l y as the creep stage reaches t e r t i a r y creep stage by Snead's method. The p r e d i c t i o n of time t o f a i l u r e f o r the two cases of i n c r e a s -i n g a, and d e c r e a s i n g a w e r e found to be the same. 108 CHAPTER 7 SUMMARY AND CONCLUSIONS The f o l l o w i n g i s a l i s t of c o n c l u s i o n s d e r i v e d from the a n a l y s i s o f d a t a : 1. For v a r i o u s types o f creep r u p t u r e t e s t s s t u d i e d the s t r a i n r a t e , i n i t i a l l y d ecreased, reached a minimum and then i n c r e a s e d g r a d u a l l y u n t i l f a i l u r e . Secondary creep s t r a i n r a t e d i d not e x i s t f o r these t e s t s . T h i s study confirmed the h y p o t h e s i s t h a t when the minimum s t r a i n r a t e i s reached, the sample under s u s t a i n e d s h e a r i n g s t r e s s e s w i l l i n e v i t a b l y r u p t u r e and f a i l u r e can be c o n s i d e r e d to occu r . The time to minimum s t r a i n r a t e i n c r e a s e d w i t h d e c r e a s i n g s u s t a i n e d s h e a r i n g s t r e s s e s . 2. A l i n e a r r e l a t i o n s h i p was observed between minimum s t r a i n r a t e and e l a p s e d time f o r creep r u p t u r e of n o r m a l l y c o n s o l i d a t e d samples under undrained plane s t r a i n con-d i t i o n when a.^  was i n c r e a s e d . T h i s r e l a t i o n s h i p was found to be almost the same f o r the type o f t e s t s i n which was decreased. 3. The curve of a sample having a d e v i a t o r s t r e s s j u s t below the upper y i e l d s t r e n g t h i n the s t r a i n r a t e e l a p s e d time 109 p l o t would g i v e an i n d i c a t i o n whether any oth e r sample under the same c o n s o l i d a t i o n h i s t o r y w i t h d i f f e r e n t s u s t a i n e d s h e a r i n g s t r e s s e s would f a i l or not. A p a r t i c u l a r s t r a i n r a t e - t i m e c o n d i t i o n o f a sample p l o t t e d above t h i s curve would i n d i c a t e t h a t the sample would f a i l i n creep and below t h i s curve t h a t i t would not f a i l . 4. Snead's (1970) h y p o t h e s i s namely a = f ( e , e) was i n good agreement i n terms of " t o t a l " d e v i a t o r s t r e s s e s f o r in c r e m e n t a l t e s t s and creep t e s t s . In terms of " a d d i t i o n a l " a D e r r o r s of the order of 20% was observed. The h y p o t h e s i s of Up = f (e, e) was found to be not v a l i d -(a) When the i n i t i a l c o n d i t i o n s of sample are d i f f e r e n t . (b) For the i n c r e a s i n g and d e c r e a s i n g types o f creep t e s t s when taken t o g e t h e r . (c) When t r i a x i a l and plane s t r a i n deformations are compared even though the i n i t i a l c o n d i t i o n s were the same. 5. The s t r a i n - t i m e and s t r a i n r a t e - t i m e behaviour of the types of plane s t r a i n creep t e s t s performed by i n c r e a s i n g and d e c r e a s i n g were almost the same. But the s t r e s s - s t r a i n r a t e - s t r a i n behaviour was found t o be q u i t e d i f f e r e n t . 6 . The creep r u p t u r e behaviour of K q c o n s o l i d a t e d c l a y was found to be q u i t e d i f f e r e n t from t h a t of 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 . 7 . S a i t o ' s ( 1 9 6 5 ) method f o r creep stage b e f o r e t e r t i a r y creep and Snead's ( 1 9 7 0 ) method f o r t e r t i a r y creep stage were d i s c u s s e d and found to be s a t i s f a c t o r y f o r the range o f a p p l i c a t i o n a c c o r d i n g to the creep s t a g e . The time of occurrence of s l o p e f a i l u r e c o u l d be r o u g h l y e s t i m a t e d d u r i n g creep stage b e f o r e t e r t i a r y creep by S a i t o ' s method and e s t i m a t e d f a i r l y a c c u r a t e l y by Snead's method as the creep stage reaches t e r t i a r y creep stage. The p r e d i c t i o n of time to f a i l u r e from data o b t a i n e d from plane s t r a i n samples w i t h i n c r e -ased was found to be the same f o r t h a t p r e d i c t e d from data o b t a i n e d from plane s t r a i n samples, w i t h decreased. The p r e d i c t e d time of f a i l u r e u s i n g r e s u l t s from t r i a x i a l specimens gave s e v e r a l times the p r e d i c t e d time u s i n g r e s u l t s from plane s t r a i n apparatus. F o l l o w i n g i s a l i s t of suggested t o p i c s f o r f u t u r e r e s e a r c h : 1 . The study of creep r u p t u r e under plane s t r a i n c o n d i t i o n w i t h measurement of and the sample s i d e f r i c t i o n , so t h a t the s u s t a i n e d s h e a r i n g s t r e s s i s kept c o n s t a n t I l l w i t h the i n c r e a s e of time. The study o f e x t e n s i o n creep r u p t u r e t e s t s i n which i s decreased and i n which i s i n c r e a s e d . The study on plane s t r a i n creep r u p t u r e c o u l d be repeated f o r d i f f e r e n t over-c o n s o l i d a t i o n r a t i o s , and drainage c o n d i t i o n s . The study o f comparison of r e s u l t s from d i f f e r e n t types of t e s t s . 2. S i m i l a r s t u d i e s of creep r u p t u r e i n the K t r i a x i a l o apparatus. The upper y i e l d s t r e n g t h s o f i n c r e a s i n g and d e c r e a s i n g types of undrained creep t e s t s to be compared, and these compared w i t h the plane s t r a i n r e s u l t s . 3. The e f f e c t of time of l o a d i n g of the creep d e v i a t o r s t r e s s on the l i n e of minimum s t r a i n r a t e s , upper y i e l d s t r e n g t h and t o t a l time to f a i l u r e . 4. Study of creep r u p t u r e i n terms of e f f e c t i v e s t r e s s e s , i n an attempt to o b t a i n f a i l u r e c r i t e r i a f o r creep to be used i n the f i e l d . 5. The data on upper y i e l d s t r e n g t h to be analyzed on the b a s i s of e f f e c t i v e s t r e s s e s concept, s i m i l a r to the i n v e s t i g a t i o n s done by S h i b a t a and Karube (1969) f o r o t h e r s o i l s under d i f f e r e n t c o n d i t i o n s . 6. An attempt to f i n d a b e t t e r method f o r p r e d i c t i n g time to f a i l u r e d u r i n g the creep stage b e f o r e t e r t i a r y creep stage. Snead's(1970) method and S a i t o 1 s (1969) method of p r e d i c t i n g time to s l o p e f a i l u r e d u r i n g t e r t i a r y creep stage to be compared and s t u d i e d f o r d i f f e r e n t types of s o i l under d i f f e r e n t c o n d i t i o n s . The p r e d i c t i o n of slope f a i l u r e t o be checked f o r f i e l d c o n d i t i o n s by u s i n g S a i t o ' s (1969) and Snead's (1970) methods. 113 REFERENCES 1. Bishop, A.W., Henkel, D.J. (1962), "The measurement of s o i l p r o p e r t i e s i n the t r i a x i a l t e s t , " Edward A r n o l d , Second E d i t i o n . 2. Bishop, A.W., and Lovenbury, H.T. (1969), "Creep c h a r a c t e r i s t i c s of two u n d i s t u r b e d c l a y s " , P r o c , 7th I n t . Conf. on S.M.F.E., Mexico, V o l . 1, pp. 29-38. 3. 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C o n f . on S.M. and F o und E n g . , V o l . I I , p. 315, 1957. 17. H e n k e l , D . J . (1960), "The 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 , pp. 533-554. 18. H e n k e l , D . J . and Wade, N.H. (1966), " P l a n e s t r a i n t e s t s on a s a t u r a t e d r e m o l d e d c l a y " , J o u r , o f S.M. and F o u n d . D i v . , ASCE, V o l . 92, S.M. 6, pp. 67-80. 19. H i r s c h f i e l d , R.C. (1960), " D i s c u s s i o n , S e s s i o n 4", 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 , pp. 1073-1079. 20. H i r s t , T . J . (1966), " 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 an u n d i s t u r b e d s e n s i t i v e c l a y " . M.A. S c . T h e s i s , U.B.C. 21. H v o r s e l e v , M.J. (1960), " P h y s i c a l components 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 . " P r o c . ASCE, Res. C o n f . 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 , pp. 437-501. 22. L o u , J.K. (1967), "The e f f e c t o f s e c o n d a r y c o m p r e s s i o n on s h e a r s t r e n g t h . " M.A.Sc. T h e s i s , U.B.C. 23. L u b a h n , J.D., and F e l g a r , R.P. (1961), " P l a s t i c i t y and c r e e p o f m e t a l s " , J o h n W i l e y and Sons I n c . , New Y o r k , p. 600. 115 24. M i t c h e l l , J.K. and C a m p a n e l l a , R.G. ( 1 9 6 3 ) , " C r e e p s t u d i e s on s a t u r a t e d c l a y s , " Symposium on L a b o r a t o r y s h e a r t e s t i n g s o i l s , ASTM-NRC, O t t a w a , C a n a d a , ASTM s p e c i a l T e c h n i c a l P u b l i c a t i o n s , No. 361. 25. M i t c h e l l , J.K., C a m p a n e l l a , R.G., and S i n g h , A. (1968) " S o i l c r e e p as a r a t e p r o c e s s . " J o u r , o f S.M. and F o und D i v . ASCE, V o l . 94, S.M. 1, pp. 231-254. 26. M i t c h e l l , J.K., S i n g h , A., C a m p a n e l l a , R.G., (1969) " B o n d i n g , E f f e c t i v e s t r e s s e s , and s t r e n g t h o f s o i l s , " J o u r , o f S.M. and F o u n d D i v . ASCE, V o l . 95, S.M. 5, pp. 1219-1246. 27. Murayama, S. and S h i b a t a , T. ( 1 9 6 1 ) , " R h e o l o g i c a l p r o p e r t i e s o f c l a y s " , P r o c . 5 t h I n t . c o n f . s o i l Mech. and Found E n g . , pp. 269-273, 1961. 28. Pao, Y.H. and M a r i n , J . ( 1 9 5 2 ) , " P r e d i c t i o n o f c r e e p c u r v e s f r o m s t r e s s s t r a i n d a t a , " P r o c . ASTM, 1952, V o l . 52, pp. 951-957. 29. Penman, A.D.M. ( 1 9 6 0 ) , "A s t u d y o f t h e r e s p o n s e t i m e o f v a r i o u s t y p e s o f P i e z o m e t e r , " C o n f . on p o r e p r e s s u r e and s u c t i o n i n s o i l s , L o n d o n , B u t t e r -w o r t h s , 1961. 30. S a i t o , M. and Uezawa, H. ( 1 9 6 1 ) , " F a i l u r e o f s o i l due t o c r e e p , P r o c e e d i n g o f t h e 5 t h I n t . C o n f . on S.M. & F . E . , P a r i s , V o l . I , pp. 315-318. 31. S a i t o , M. ( 1 9 6 5 ) , " F o r e c a s t i n g t h e t i m e o f o c c u r r e n c e o f a s l o p e f a i l u r e , " P r o c . 6 t h I n t . C o n f . on S.M. & F . E . , M o n t r e a l , V o l . I I , pp. 537-541. 32. S a i t o , M. ( 1 9 6 9 ) , " F o r e c a s t i n g t i m e o f s l o p e f a i l u r e by t e r t i a r y c r e e p , " P r o c . 7 t h I n t . C o n f . on S.M. & F . E . , M e x i c o , V o l . I I , pp. 677-683. 33. S i n g h , A and M i t c h e l l , J.K. ( 1 9 6 8 ) , " G e n e r a l s t r e s s -s t r a i n t i m e f u n c t i o n f o r s o i l s " . J o u r , o f S.M. & F ound D i v . ASCE, J a n u a r y 1968. 34. S i n g h , A . and M i t c h e l l , J.K. ( 1 9 6 9 ) , " C r e e p p o t e n t i a l and c r e e p r u p t u r e o f s o i l s , " P r o c . 7 t h I n t . C o n f . on S.M. and F . E . , M e x i c o , pp. 379-384. 35. S h i b a t a , T. and K a r u b e , D. ( 1 9 6 9 ) , " C r e e p r a t e and c r e e p s t r e n g t h or, c l a y s , " P r o c . 7 t h I n t . C o n f . o f S.M. & F . E . , M e x i c o , pp. 379-384. 116 36. S h e r i f , M.A. (1965), "Flow and F r a c t u r e P r o p e r t i e s of S e a t t l e C l a y s " , Research s e r i e s No. 1, U n i v e r s i t y of Washington S o i l E n g i n e e r i n g , January 1965. 37. Snead, D. (1970), "Creep s t u d i e s on an u n d i s t u r b e d s e n s i t i v e c l a y , " Forthcoming Ph.D. T h e s i s , U.B.C. 38. S u k l j e (1961), "A l a n d s l i d e due to long term creep," Proceedings 5th I n t . Conf. on S.M. & Found. Eng. V o l . I I , p. 727, 1961. 39. V a i d , Y.P. (196 8), " A plane s t r a i n apparatus f o r s o i l s , " M.A. Sc. T h e s i s , U.B.C. 40. V a i d , Y.P. (1970), Forthcoming Ph.D. T h e s i s , U.B.C. 41. V i a l o v , S. and S k i b i t s k y , A. (1957), " R h e o l o g i c a l p r o c e s s e s i n f r o z e n s o i l s and dense c l a y , " P r o c . 4th I n t . Conf. on S.M. & F.E., V o l . I , p. 121, 1957. 42. Walker, L.K. (1969), "Undrained creep of a s e n s i t i v e c l a y , " Geotechnique, December 1969. 117 APPENDIX I EXPERIMENTAL PROCEDURE The preparation and setting up of the sample in the plane strain apparatus was done in the same way as in Vaid (1970). Once the apparatus with the sample was set up in the loading frame, the ver t i ca l and la tera l stresses on the samples were gradually increased with the same increments to 90 PSI. The "B" value was estimated and found to be varying between 94% and 100%. To further increase the degree of saturation the samples were le f t undrained under the applied ver t i ca l and la tera l stress of 90 PSI for about 12 hours before the start of the consolidation process. The samples were K q consolidated for 3 6 hours, followed by a period of 12 hours during which the samples were l e f t undrained. The deviator stress required for creep rupture was obtained by using a three-way valve as described in Chapter 3 . Once this creep deviator stress was applied to the sample the ver t i ca l deformations and pore pressures were measured t i l l fa i lure of the sample, at different intervals of time (in order to plot a smooth strain log time curve t o c a l c u l a t e s t r a i n r a t e s Appendix I I ) . The c o n d i t i o n of c o n s t a n t v e r t i c a l s u s t a i n e d s t r e s s was maintained by s l i g h t l y i n c r e a s i n g the a i r p r e s s u r e i n the a i r p i s t o n as the sample compressed and i t s area i n c r e a s e d s l i g h t l y . (Chapter 3 ) . The water c o n t e n t of the samples were determined a t the end of creep r u p t u r e t e s t s . 119 A P P E N D I X I I C A L C U L A T I O N O F S T R A I N R A T E S The s t r a i n rates were computed by using the s t r a i n -log time p l o t as shown i n Figure A l . A smooth curve was drawn through the s t r a i n - l o g time points plotted from the "raw" data. The technique to calc u l a t e s t r a i n rates assumes a l i n e a r change i n s t r a i n for f i n i t e time i n t e r v a l s . The s t r a i n rate at a given time " t " was determined by substract-ing the value of the s t r a i n at (t - At) from the value at t + At and divided by time i n t e r v a l At (Figure A l ) . That i s the s t r a i n at B (Figure Al) was taken to bes Strain ordinate at C - s t r a i n ordinate at A time AC (natural s c a l e ) . lat'At! EQUAL T / M E INTERVALS (SMALL) i t  LOG T/ME F/GURE/d CALCULATION O F STRAIN RATES. 121 APPENDIX 111 WATER CONTENT, STRESSES AT THE END OF CONSOLIDATION AND DURING CREEP. A. UNTRAINED PLANE STRAIN CREEP TESTS-01 INCREASED Test No. Devlaiar Stress duriij Creep - fiSl PetCeri q qB After - PSI OS After ConSol'ckli'a - PSI , Creep - PSI <Jj cLun'Kg C*eef> . Psi Waiter Content - Percent PSl-Cl 445 103a 2.9-4 34-8 993 54 8 34-7 PSI -C2 4/8 Q7-3 290 550 Q7$ 342 RSJ.-C3 4 0 7 94-5 29-8 5S3 $5-2 34-2 RS1-C4 39-5 9/7 29-8 54$ 94 3 54-9 342 PS1-C5 39 0 906 29-8 55-8 94-8 v5v5-8 340 PS1-C& 38-2 £8 7 29-6 54i 93-J <54-S 342 8- UNDRAINED PLANE STRAIN CREEP TESTS- D E C R E A S E D . I Test No. Dc.via.tor SirfiBBdurig G-eeP-fel Percent of CJjJM 05, After ConSoli<Uii<ii\ - PSL eg A-fter CansoliAadui -Rsl CJ7d.Uri"np , Creep -PSI Creep -PSI Water Content -Percent. P S 3 - C 1 4 6 - 1 1 0 4 2 3 0 2 S4-4 84 Q 38S 3 4 0 P S 3 - C 1 4 4 •§ / 0 I - 7 S 0 4 542 8 4 - 6 39 g 34 £ P S 3 - C 3 4 2 - 6 9 6 - 3 3 0 - 1 542 84q 421 34 6 PS3-C4 4 2 5 9<S2 v 3 0 0 542 S4-2 41-G 34 4-PS3-C5 4 / - 3 9 3 - 5 3 0 0 548 84 B 43-6 34-8 

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