Effect of Alternating Stress

8/2/2019 Effect of Alternating Stress

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Mechan ics of Materi als 4 (1985) 109-11 9 109North-Holland

E F F E C T O F A L T E R N A T I N G S T R E S S O N T H E C R E E P O F F R O Z E N S O I L SV . R . P A R A M E S W A R A NDivision of Building Research, Nationa l Research Council of Canada, Ottawa, Ontario, Canada KI A OR 6Received 16 July 1985

Cyclic creep behaviour of a frozen saturated s and and frozen clay was studied by super imposi ng alternating stresses over amean static compressive stress on the samples. Cyclic loading increased the creep rate of these materials considerably, whichcould be due to the increase in unfrozen water content generated by the transient thermal energy produced by mechanicalcycling. The str ain inc remen t per cycle was foun d to increase with increasing strain in the frozen sand,, wherea s it decreased inthe frozen clay, s howing a tendency for hardening. The difference could be due to the fact that the mean st ress on the samplewas larger than a threshold stress in the former and smaller in the latter material.

IntroductionC r e e p o r t i m e - d e p e n d e n t i n e l a s t i c d e f o r m a t i o n

o f f r o z e n s o i l m a t e r i a l s h a s b e e n s t u d i e d t o s o m ee x t e n t a s a f u n c t i o n o f t e m p e r a t u r e a n d s t re s s, a n da t t e m p t s h a v e b e e n m a d e b y s e v e r a l a u t h o r s t o f itt h e e x p e r i m e n t a l c r e e p d a t a t o c l a s s i c a l c r e e pe q u a t i o n s d e v e l o p e d f r o m t h e o b s e r v e d b e h a v i o u ro f m a n y v i s c o e l a s ti c m a t e r i a ls , i n p a r t i c u l a r m e t a l sa n d a l l o y s . F o r d e s i g n i n g f o u n d a t i o n s i n f r o z e ng r o u n d , t h e b e a r i n g c a p a c i t y o f t he f r o z e n s o il h a st o b e k n o w n , w h i c h i n t u r n d e p e n d s o n t h e c r e e pc h a r a c t e r i s t i c s o f t h e f r o z e n s o i l . I n g e n e r a l , t h el o n g - t e r m c r e e p s t r e n g t h o f t he s o i l u n d e r c o n s t a n ts t r e s s is u s e d f o r d e s i g n . I n p r a c t i c e , h o w e v e r ,f o u n d a t i o n s a r e i n v a r i a b l y s u b j e c t e d t o v a r i o u sk i n d s o f d y n a m i c s t r e ss e s f ro m i n t r i n si c a n d e x t r a -n e o u s s o u r c e s , in a d d i t i o n t o t h e s t a ti c s t re s s e s d u et o t h e s t r u c t u r a l l o a d s . R a p i d c h a n g e s i n m e c h a n i -c a l s t r e s s e s c o u l d a l s o c a u s e t h e r m a l c h a n g e s i n t h es o i l , a n d a l t e r t h e c r e e p b e h a v i o u r o f s o i l s .

I t h a s b e e n s h o w n t h a t s m a l l d y n a m i c s t r e s s e sd o i n d e e d i n c r e a s e t h e d i s p l a c e m e n t r a t e o f a p i l ef o u n d a t i o n i n f ro z e n s o il ( P a r a m e s w a r a n , 1 98 2 ,1 9 8 4 ), b u t t o d a t e , t h e e f f e c t s d u e t o d y n a m i cs t re s s e s ar e t a k e n c a r e o f b y u s i n g a n i g n o r a n c ef a c t o r ( a s a f e t y f a c t o r ) i n t h e d e s i g n . K n o w l e d g eo n t h e d y n a m i c m e c h a n i c a l p r o p e r t i e s o f f r o z e ns o i l s i s s p a r s e , b u t f o r s o m e i n f o r m a t i o n o n t h e

d y n a m i c m o d u l i ( K a p l a r , 1 9 6 9; S t e v e n s , 1 9 7 5 ;V i n s o n , 1 9 7 8 a ; V i n s o n e t al ., 1 9 7 8 b ; V i n s o n a n dC h a i c h a n a v o n g , 1 9 7 8 c ) . D u e t o t h e l a c k o f s u c hk n o w l e d g e a n d u n c e r t a i n t i e s i n t h i s a r e a , d e s i g n o ff o u n d a t i o n s h a s t o b e e x t r e m e l y c o n s e r v a ti v e . Ab e t t e r u n d e r s ta n d i n g o f th e d e f o r m a t i o n b e h a v i o u ro f f r o z e n s o i l m a t e r i a l s u n d e r d y n a m i c l o a d i n g o rc o m b i n e d l o a d in g , a n d t h e us e o f su c h i n f o r m a t i o ni n l i f e p r e d i c t i o n a n a l y s i s , w i l l r e s u l t n o t o n l y i nl e ss c o n s e r v a t i v e d e s i g n r u l e s , b u t a l s o i n e n h a n c e dr e l i a b i l i t y o f a s t r uc tu r e . Th i s w i l l l e a d to a r e duc -t i o n i n t h e i g n o r a n c e f a c t o r ( f a c t o r o f s a f e t y ) ,t h e r e b y r e d u c i n g t h e c o s t o f h a r d w a r e , a s p i l em a t e r i a l s c a n b e u s e d e f f e c t i v e l y . T h e c h a l l e n g e s ,t h e r e f o r e , a r e i n t h e d y n a m i c c r e e p a r e a w h e r et h e r e i s n e e d t o d e v e l o p c o n s t i t u t i v e e q u a t i o n s t od e p i c t t h e b e h a v i o u r o f f r o z e n s o i l s a n d a l s o t h en e e d t o g e n e r a t e m o r e e x p e r i m e n t a l d a t a o n v a r i -o u s f r o z e n s o i l s . T h i s p a p e r i s a s m a l l s t e p i n t h i sd i r e c t i o n a n d d i s c u s s e s s o m e r e c e n t r e s u l t s o b -t a i n e d f r o m c y c l i c c r e e p t e s t s o n s o m e f r o z e n s o il s .

Experimental procedureMaterials and preparation of test specimens

C y l i n d r i c al t e s t s p e c im e n s w e r e m a d e f r o m t h r e ed i f f e r e n t m a t e r i a l s : O t t a w a s a n d ( A S T M S p e c i f i -

0167-6 636/85 /$3.30 1985, Elsevier Science Publishers B.V. (Nort h-Hol land)


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1 1 0 ~ [ R . P a r a m e u w a r a n / ( r e e p ~ ![ / ~ 'o z en v m l~

c a t i o n C - 1 0 9 p a s s i n g s i e v e N o . 3 0 a n d r e t a i n e d o ns i e v e N o . 1 00 , a n d h a v i n g a n a v e r a g e g r ai n d i a m e -t e r o f 0 . 2 - -0 . 6 r a m ) , a na tu r a l c l a y f r om I nuv ik ,N o r t h w e s t T e r r i t o r ie s , a n d a s il ty c la y f r o mT h o m p s o n , M a n i t o b a .

C y l i n d r i c a l s p e c i m e n s o f f r o z e n s a n d w e r e p r e -p a r e d i n s p l i t p l e x i g l a s m o u l d s . T h e s a n d w a sc o m p a c t e d a t a n o p t i m u m m o i s t u r e c o n t e n t o f14% , in l a ye r s i n t he m ou ld , w h ic h w a s t he n c on -n e c te d t o a v a c u u m p u m p t o re m o v e e n t r a p p e da i r . A f t e r e v a c u a t i o n t h e s a n d w a s s a t u r a t e d w i t hd e a e r a t e d d i s t i l l e d w a t e r . T h e s p e c i m e n s w e r e t h e nf r o z e n u n i a x i a l l y i n t h e m o u l d k e p t i n s i d e a ni n s u l a t e d b o x w i t h t h e t o p e n d e x p o s e d t o t h e a i ri n s id e a c o l d r o o m m a i n t a i n e d a t - 1 0 C . T h e w a t e re x p e l le d d u r i n g f r ee z i n g w a s r e m o v e d f r o m t h eb o t t o m t h r o u g h a c a p i l l a ry t u b e c o n t a i n i n g a h e a t e rw i r e . A f t e r f r e e z ing , t he e nds o f t he c y l ind r i c a ls p e c i m e n w e r e t r i m m e d a n d f a c e d o n a l a t h e i n -s i d e t h e c o l d r o o m . T h e f i n i s h e d t e s t s p e c i m e n sc o n t a i n e d a b o u t 2 0 % m o i s t u r e b y w e i g h t o f s o i lg r a i n s , a n d h a d a b u l k d e n s i t y o f a b o u t 2 0 4 0k g m

C y l i n d r i c a l s p e c i m e n s o f t h e n a t u r a l c l a yb r o u g h t f r o m p e r m a f r o s t a r e a s ( I n u v i k , N . W . T . ,a n d T h o m p s o n , M a n i t o b a ) w e r e p r e p a r e d b y m i x -i n g t h e d r i e d s o i l w i t h w a t e r ( 5 0% b y w e i g h t o f d r ys o i l ) a n d p a c k i n g t h e r e s u l t i n g s l u r r y i n t o c y l i n -d r i c a l c a v i t i e s c u t i n t o a s t y r o f o a m b l o c k , a n dl i n e d w i t h p o l y e t h y l e n e s h e e t s . T h e s p e c i m e n s w e r ea l l o w e d t o f r e e z e u n i d i r e c t i o n a l l y b y e x p o s i n g t h eo p e n e n d t o t h e a i r i n s i d e t h e c o l d r o o m . A f t e rc o m p l e t e f r e e z i n g t h e c y l i n d r i c a l s p e c i m e n s w e r er e m o v e d f r o m t h e s t y r o f o a m b l o c k a n d t h e i r e n d st r i m m e d a n d f a c e d o n a l a t h e . T h e i c e l e n s e s i n t h ef r o z e n s o i l t e s t s p e c i m e n s w e r e d i s t r i b u t e d u n i -f o r m l y , b u t r a n d o m l y o r i e n t e d . T h e a v e r a g e m o i s -t u r e c o n t e n t i n t h e s p e c i m e n s w a s a b o u t 4 5 % .

B y t h e s e m e t h o d s t e s t s p e c i m e n s h a v i n g d i a m e -t e r s o f 50 . 8 m m ( 2 in ) a s w e l l a s 76 . 2 m m ( 3 in ) ,b o t h h a v i n g L / D ( l e n g t h t o d i a m e t e r ) r a t i o s l i g h t lyg r e a t e r t h a n 2 , w e r e m a d e .E q u i p m e n t a n d t e s t m e t h o d

A s c h e m a t i c d i a g r a m o f t h e e x p e r i m e n t a l s e t -u pi n s i d e a c o l d r o o m t o s t u d y t h e c r e e p o f t h e f r o z e nso i l s a m p le s i s show n in F ig . 1 . F o r a c r e e p t e s t , a

J I ,

F i g. 1 . S c h e m a t i c d i a g r a m o f t h e e x p e r i m e n t a l s e t u p t o s t u d yc r e e p o f c y li n d r ic a l s a m p l e s o f f ro z e n s o il . A - - F r o z e n s o ils a m p l e , B - - S t e e l p e d e s t a l, C - - L o a d c el l, D - - L e v e r a r m ,E E l e c t ro d y n a m i c s h a k e r, J - - H y d r a u l i c ja c k , L L i n e arv a r i a b l e d i f f e re n t i a l t r a n s d u c e r ( L V D T ) , P L o a d i n g p l a t f o r m ,T T h e r m o c o u p l e .

c y l i n d r i c a l t e s t s p e c i m e n ( A ) w r a p p e d i n a c e l -l o p h a n e j a c k e t a n d w i t h a t h e r m o c o u p l e T a t -t a c h e d t o i t , w a s m o u n t e d o n t h e p e d e s t a l ( B ) , a n dt h e l e v e r a r m ( D ) w a s a d j u s t e d h o r i z o n t a l l y w i t h

F i g . 2. E x p e r i m e n t a l s e t - u p i n s i d e t h e c o l d r o o m , H i s t h ee l e c t r o h y d r a u l i c s h a k e r .


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V.R. Parameswaran / creep of roze n soils 111

t h e l o a d c e l l ( C ) a b o v e t h e s p e c i m e n . T h e h y d r a u -l ic j a c k ( J ) w a s u s e d t o r a i s e a n d l o w e r t h e l e v e ra r m ( D ) . T h e c o m b i n e d w e i g h t o f t h e b e a m ( D ) ,t h e s h a k e r ( E ) a n d t h e l o a d i n g p l a t f o r m ( P ) p r o -v i d e d t h e s t a t i c l o a d o n t h e s p e c i m e n . W e i g h t sw e r e p l a c e d o n t h e p l a t f o r m ( P ) t o i n c r e a s e t h es t a t i c l o a d i n s o m e t e s t s . D y n a m i c l o a d w a s a p -p l i e d o n t h e f r o z e n s o i l s p e c i m e n b y e i t h e r a ne l e c t r o d y n a m i c s h a k e r ( E ) s h o w n i n F i g . 1, o r f o rl a r g e r c y c l i c l o a d s , b y a n e l e c t r o h y d r a u l i c s h a k e r( H ) s h o w n i n F i g. 2. T h e f r e q u e n c y a n d a m p l i t u d eo f t h e d y n a m i c l o a d w a s c o n t r o l l e d b y f e e d i n g as u i t a b l e s i n u s o i d a l w a v e f o r m s i g n a l t o t h e s h a k e rf r o m a w a v e g e n e r a t o r a n d a m p l i f ie r . D y n a m i cl o a d s w i t h f r e q u e n c i e s o f 1 0 H z a n d 1 5 H z , a n dp e a k - t o - p e a k a m p l i t u d e s o f u p t o 1 0 % o f t he s t a ti cl o a d w e r e u s e d .

T h e s t at ic a n d d y n a m i c c o m p o n e n t s o f t h e lo a da p p l i e d o n t h e s p e c i m e n w e r e m o n i t o r e d c o n t i n u -o u s l y f r o m t h e o u t p u t o f t h e l o a d c e l l ( C ) o n ac h a r t r e c o r d e r . T h e d y n a m i c l o a d w a s a l s o m o n i -t o r e d a c c u r a t e l y u s i n g a n o s c i l l o s co p e h a v i n g ac a m e r a a t t a c h m e n t . T h e d e f o r m a t i o n o f t h e t e s ts p e c i m e n ( a x i a l c o m p r e s s i o n ) , m e a s u r e d b y a l i n -e a r v a r i a b l e d if f e re n t i a l t r a n s d u c e r ( L V D T ) L , w a sa l s o r e c o r d e d o n t h e c h a r t r e c o r d e r . A l l t h e d a t af r o m e a c h t e s t , s u c h a s t h e t e m p e r a t u r e o f t h e

F i g . 3. C l o s e u p v i e w o f t h e t e s t s p e c i m e n a n d L V D T ( l in e a rv a r i a b l e d i f f e r e n t i a l t r a n s d u c e r ) .

s p e c i m e n , r o o m a i r t e m p e r a t u r e n e a r t h e s p e c i -m e n , t h e s t a t i c l o a d o n t h e s a m p l e , a n d a x i a ld e f o r m a t i o n , w e r e a l s o l o g g e d a t r e g u l a r i n t e r v a l s( 1 t o 2 h o u r s ) t h r o u g h a n a u t o m a t i c d a t a a c q u i s i -t i o n s y s t e m u si n g a d e s k t o p c o m p u t e r , a n d t h es t r e s s , s t r a i n , a n d s t r a i n r a t e o f t h e s a m p l e w e r ec a l c u la t e d a t e v e r y i n s t a n t o f m e a s u r e m e n t . T e s t sw e r e c a rr ie d o u t a t - 2 . 5 C a n d at - 1 0 C , t het e m p e r a t u r e o f t h e s a m p l e b e i n g m o n i t o r e d b ys m a l l t h e r m o c o u p l e s ( T ) a t t a c h e d t o t h e s p e c i m e n .P r i o r t o s t a r t i n g a t e s t , t h e t e m p e r a t u r e o f t h es p e c i m e n w a s a l l o w e d t o c o m e t o e q u i l ib r i u m w i t ht h e r o o m t e m p e r a t u r e .

F i g . 2 s h o w s t h e e x p e r i m e n t a l s e t - u p i n s i d e t h ec o l d r o o m a n d F i g . 3 s h o w s a c lo s e - u p v i e w o f th es p e c im e n a n d L V D T .

R e s u l t s a n d d i s c u s s i o n s

F i g u r e s 4 ( a ) , 5 ( a ) a n d 6 ( a ) s h o w t y p i c a l c r e e pc u r v e s d e p i c t i n g t h e v a r i a t i o n o f a x i a l s tr a i n w i t ht i m e f o r f r o z e n s a m p l e s o f T h o m p s o n c l a y , l n u v i kc l a y a n d s a t u r a t e d s a n d , r e s p e c t iv e l y . T h e r e g i o n sw i t h a n d w i t h o u t t h e s u p e r i m p o s e d a l t e r n a t i n gl o a d a r e s h o w n b y t h e d a s h e d a n d f u l l l i n e s r e s p e c -t i v e l y . T h e e f f e c t o f a l t e r n a t i n g l o a d i n i n c r e a s i n gt h e c r e e p r a t e i s o b v i o u s i n t h e s e f i g u r e s , a s s h o w nb y t h e i n c r e a s e in s l o p e o f t h e c r e e p c u r v e s i n t h e s er e g i o n s . T h e i n c r e m e n t s i n c r e e p s t r a i n a n d s t r a i nr a t e a r e p a r t i c u l a r l y m a r k e d i n F i g . 6 ( a ) f o r t h ef r o z en s a n d s a m p l e s u b je c t e d t o a m u c h l a r g ers t r e s s t h a n t h e o t h e r t w o s a m p l e s . F i g u r e s 4 ( b ) ,a n d 5 ( b ) a n d 6 ( b ) s h o w t h e c o r r e s p o n d i n g c r e e pr a t e c u r v e s f o r t h e s e s a m p l e s . T h e v a l u e s o f t h ec r e e p r a t e s w i t h a n d w i t h o u t a l t e r n a t i n g s t r e s s , t h ei n c r e m e n t s i n c r e e p s t r a i n p e r c y c l e o f l o a d , s t r a i na t t h e b e g i n n i n g o f c y c l in g a n d t h e s t re s s o n t h e s es a m p l e s a r e g i v e n i n T a b l e 1 . T h e s t r a i n i n c r e m e n tp e r c y c l e (Ac/AN) d e c r e a s e s w i t h i n c r e a s i n g s t r a i nf o r t h e T h o m p s o n c l a y s a m p l e s , w h e r e a s i t i n -c r e a s e s w i t h i n c r e a s i n g s t r a i n f o r t h e f r o z e n s a n d .F o r I n u v i k c a l y , w h e r e t h e p a r t i c l e s i z e w a s m u c hf i n e r t h a n t h e o t h e r t w o m a t e r i a l s , t e s t s c a r r i e d o u ti n e i g h t s p e c i m e n s at - 2 . 5 C a t m e a n s t r es s e sb e t w e e n 0 . 6 a n d 0 . 9 M P a d i d n o t s h o w m u c hv a r i a t i o n i n t h e v a l u e o f (At/AN) w i t h s t r a i n ( c ) .F i g u r e 7 ( a ) s h o w s t h e v a r i a t i o n o f (At/AN) w i t h


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T a b l e 1l ) v n a n f i c c r e e p d a t a f r o m t h r e e r e p r e s e n t a t i v e s s a m p l e sT e s t M a t e r i a l M e a n P e a k - t o - p e a k C r e e p s t r a i n r a t e s ( s 1 )N o . s t a ti c a l t e r n a t i n g W i t h o u t W i t h

s t r es s s t r e ss s h a k e r s h a k e ro , ,, ( M P a ) % ( M P a )

S t r a i n i n c r - S t r a i n a tm e n t p e r s t a r t ofc y c l e ( A { / 1 N } c ~ c l in g{ ( 5 )

1 0 T h o m p s o n 0 . 5 3 4 0 . 0 3 2 3 . 2 1 1 0 s 5 . 3 1 1 0 ~; 2 . 1 0 1 0 "~ 1 .2 7c l a y ( 6 ;~ o f s t a t i c 3 . 3 1 5 . 1 9 " " 1 . 8 8 2 . 0 4

s t r e s s ) 3 . 2 6 4 . 9 4 ' " 1 . 6 8 " " 2 . 7 72 . 8 8 3 . 9 1 1 . 0 3 3 . 6 72 . 2 6 3 . 1 8 0 . 9 2 4 . 2 01 . 9 4 2 . 4 4 0 . 5 0 4 . 6 4

1 5 l n u v i k 0 . 8 3 3 0 . 0 1 3 8 . 1 0 1 0 I~ 2 . 2 0 1 0 ~ 9 . 2 3 1 0 in 0 . 7 3c l a y ( 2 % ) 1 3 . 9 1 . 9 5 5 . 6 2 0 . 7 9

0 2 . 3 2 2 . 3 2 0 . 8 23 0 O t t a w a 2 . 2 3 7 0 . 2 2 4 1 . 4 8 1 0 g 8 . 6 6 1 0 ~ 7 . 1 8 1 0 '~ 1 .9 0

s a n d ( 1 0 ~ } 1 . 3 9 1 0 . 7 0 9 . 2 7 2 . 4 82 . 8 4 " " 1 4 . 9 1 2 . 0 6 3 . 5 0

3 2 O t t a w a 2 . 6 0 9 0 . 3 3 0 6 . 1 9 1 0 s 1 0. 3 1 0 s 4 . 1 0 1 0 '~ 5 .9 1s a n d ( 1 2 ,~ ) 2 . 4 7 9 . 9 4 7 . 4 7 7 . 8 4

2 . 8 3 7 . 5 7 4 7 . 8 8 . 7 7

T h e s e f i g u r e s a l s o s h o w t h a t a t a p a r t i c u l a r s t r a i n ,s a m p l e s s u b j e c t e d t o h i g h e r s t r e s s e s ( l in e A A ) s h o wh i g h e r v a l u e s o f ( A { / A N ) , a s w o u l d n o r m a l l y b ee x p e c t e d . F i g u r e s 8 ( a ) a n d 8 ( b ) s h o w s i m i l a r p l o t s ,n a m e l y , I n ( A { / A N ) v s . s t r a i n ( { ) , a n d l n ( A { / A N )vs . l n ( ) , r e spe c t ive ly , f o r f r oz e n s a nd spe c im e ns .U n l i k e i n f r o z e n c l a y , t h e s e p l o t s s h o w t h a t A { / , A Ni n g e n e r a l i n c r e a s e w i t h i n c r e a s i n g s t r a i n , s h o w i n gt h e r e b y , a c c e l e r a t i o n o f cy c l i c c r e e p . D u e t o t h es c a t t e r i n t h e d a t a t h e r e i s n o d e f i n i t e t r e n d s h o w -ing the e f f e c t o f s t r e s s on ( A { / k N ) a s i n t he c a seo f f r o z e n c l a y s p e c i m e n s , w h e r e & / A N w a s l a r g e rf o r a s p e c i m e n u n d e r a l a r g e r s t r e s s . H o w e v e r , f o ra p a r t i c u l a r s p e c i m e n , A e / A N d o e s i n c r e a s e w i t hi n c r e a s i n g s t r a in .

F i g u r e s 7 ( a ) a n d ( b ) s h o w r e s p e c t i v e l y , t h a t f o rt h e T h o m p s o n c l a y s a m p l e s t h e c r e e p s t r a i n i n c r e -m e n t p e r c y c l e o f a l t e r n a t i n g l o a d c a n b e r e l a t e dt o t h e s t r a i n a t t h e t i m e o f c y c l in g , b y t h e f o l l o w -i n g e q u a t i o n s :I n ( A { / A N ) oc { (1 )a n dI n ( & { / A N ) oc In c . (2)

T h e s e e q u a t i o n s c a n i n t u r n b e e x p r e s s e d a s :A { / A N = A e x p ( k { ) ( 3 )a n dA { / k N = B e" (4 )w h e r e k a nd n a r e s lope s o f t he l i ne s i n F ig s . 7 ( a )a n d ( b ) r e s p e c t iv e l y , a n d A a n d B a r e c o n s t a n t s .V a l u e s o f k a n d n o b t a i n e d f r o m F i g s. 7 ( a ) a n d( b ) a r e - 0 . 7 2 a n d - 0 . 9 0 , r e s p ec t iv e l y ; t h e d i m e n -s ions f o r k b e ing ( s t r a in% ) 1, a nd n , a nu m be r .F i g u r e s 8 ( a ) a n d ( b ) s h o w t h a t f o r f r o z e n s a n d a l s othe r e i s a ge ne r a l i nc r e a se i n ( A { / A N ) w i t h i n -c r e a s i n g s t r a i n , b u t w i t h m o r e s c a t t e r i n t h e d a t at h a n t h o s e f o r c l a y . A r e p r e s e n t a t i v e v a l u e o f n i n( 4 ) c a l c u l a t e d f r o m t h e s l o p e o f th e d a s h e d l i n es i nF igu r e 8 ( b ) i s 2 . 5 . F r om the se va lue s o f n a ndu s i n g ( 4 ) a s t r e s s d e p e n d e n c e o f ( A t / A N ) c a n b ec a l c u l a t e d . F o r c r e e p o f m a t e r i a l s a t h i g h h o m o l o -g o u s t e m p e r a t u r e s ( T / T , n , w h e r e T i s t he t e s t i ngt e m p e r a t u r e , a n d T ,,,, t h e m e l t i n g t e m p e r a t u r e , b o t hi n d e g r e e K ) t h e s t re s s d e p e n d e n c e o f c r e e p s t r a i nc a n b e g i v e n b y a g e n e r a l p o w e r l a w , f i r s t p r o -p o s e d b y N o r t o n ( 1 9 2 9 ) a n d u s e d b y B a i l ey ( 1 93 5 ) ,D o r n ( 1 9 62 ) , a n d s e v e r a l o t h e r s :{ = . f ( t ) o " ( 5 )


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IL R. Parameswaran / creep of froze n soils 115

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1 16 I ,( R. Par am esw aran / Creep of froze n soils

w he r e o i s t he s t r e s s , f ( t ) i s a f unc t ion o f t im e ,a n d a a n d b a re c o n s t a n t s . B a s e d o n t h i s p o w e rl a w c r e e p , a n d f r o m t e s t s p e r f o r m e d i n v a r i o u sf r oz e n so i l s suc h a s s a nds , s i l t s a nd c l a ys , V ya lov( 1 9 6 2 ) p r o p o s e d a g e n e r a l c r e e p l a w f o r f r o z e ns o i l s :( ~ - c , , ) = C o ' " " ( 6 )w h e r e % i s t h e i n s t a n t a n e o u s s t r a in , C = f ( T , t )a n d m i s a c o n s t a n t , c h a r a c t e r i s t i c o f t h e m a t e r i a l .T h i s i n d i c a t e s t h a t t h e s t r a i n i n c r e m e n t a f t e r t h ei n s t a n t a n e o u s s t r ai n % ( w h i c h h a s b e e n f o u n d t ob e n e g l i g i b l y s m a l l i n m o s t i n s t a n c e s i n t h e c r e e po f f r o z e n s o i l s ) i s p r o p o r t i o n a l t o t h e a p p l i e d s t r e s sr a i s e d t o a p o w e r , w h i c h i s c o n s t a n t f o r t h em a t e r i a l. T y p i c a l v a lu e s o f m f o r O t t a w a s a n d a n dc la ys a r e 0 . 77 a nd 0 . 4 , r e spe c t ive ly ( S a y le s , 1968 ).C o m b i n i n g ( 4 ) a n d ( 6 ) :A t / A N o c ~ " or. o ' ' / ' ' ' (7 )a n d u s i n g v a l u e s o f n f r o m t h e p r e s e n t e x p e r i -m e n t s a n d t h e v al u e s o f m q u o t e d a b o v e :A ( / A N c ~ 0 " 4 0 ( 3 C ( o 1 /0 " 4 ) 0 " 9 0 - ~ - 1 / O ' 2 2 5 ( 8 )f o r t h e f r o z e n T h o m p s o n c l a y , a n dA e / A N OC~ : 5 ( O 1 / 0 . 7 7 ) 2 " 5 3 . 2 5- - o (9)f o r f r o z e n s a n d . ( I n t h e p r e s e n t e x p e r i m e n t s o i se q u a l t o t h e m e a n s t a t ic s t r e s s o r e .) T h e n e g a t i v ee x p o n e n t o n o i n ( 8 ) s u g g e s t s h a r d e n i n g o f t h ef r o z e n c l a y m a t e r i a l w i t h i n c r e a s i n g s t r a i n d u e t oc y c l i c s t r e s s i n g , w h e r e a s t h e p o s i t i v e e x p o n e n t i n( 9 ) s u g g e s t s s o f t e n i n g o f t h e f r o z e n s a n d .

A l l t h e t e s ts r e p o r t e d h e r e w e r e c a r r i e d o u t i n ac o l d r o o m a t a t e m p e r a t u r e o f - 2 . 5 C _+ 0 . 5 C . Af e w te s ts w e r e a ls o d o n e a t - 1 0 C , b u t a t t h isl o w e r t e m p e r a t u r e t h e r e w a s h a r d l y a n y e f f e c t d u et o t h e c y c l i c l o a d i n g i n i n c r e a s i n g t h e c r e e p r a t e . I ft h e p e a k - t o - p e a k a m p l i t u d e o f t h e a l t e r n a t i n g l o a dc o u l d b e i n c r e a s e d , t h e r e i s a p o s s i b i l i t y t h a t o n ec o u l d o b s e r v e t h e i n f l u e n c e o f c y c li c l o a d i n g a t t h el o w e r t e m p e r a t u r e t o o . T o s t u d y t h e e f f e c t o fc h a n g i n g t h e f r e q u e n c y o f l o a d in g , s o m e t e s t s w e r ea l s o d o n e a t 1 5 H z , a n d i n s o m e t e s t s , a l t e r n a t i n gs t re s s es o f b o t h 1 0 H z a n d 1 5 H z w e r e s u p e r i m -p o s e d i n t e r m i t t e n t l y . T h e e f f e c t o f th e a l t e r n a t i n g

s t r e s s w a s m u c h l e s s p r o n o u n c e d a t t h e h i g h e rf r e q u e n c i e s t h a n t h a t a t 1 0 H z . T h i s c o u l d b e d u et o t h e l i m i t a t i o n o f t h e m a c h i n e a n d p r e s e n t s e tu p , w h e r e t h e s t r e s s a m p l i t u d e d e c r e a s e s a sf r e q u e n c y o f l o a d i n g i s i n c r e a s e d .

I n o r d e r t o u n d e r s t a n d t h e b e h a v i o u r o f f r o z e ns o i l s u n d e r c y c l i c l o a d i n g , i t i s w o r t h w h i l e c o n s i d -e r i n g s i m i l a r b e h a v i o u r o f o t h e r m a t e r i a l s s u c h a sm e t a l s , t h a t h a v e b e e n s t u d i e d t o s o m e e x t e n t . I nm e t a l s , c y c l i c s t r e s s i n g h a s b e e n f o u n d t o c a u s eha r de n ing a s w e l l a s so f t e n ing . C Y c l i c c r e e p a c c e l -e r a t i o n a n d s o f t e n i n g h a v e b e e n o b s e r v e d i n c o p p e r( M e l e k a a n d E v e r s h e d , 1 9 5 9 / 6 0 ) l e a d ( K e n n e d y ,1 9 6 2 ), h i g h t e m p e r a t u r e a l l o y s ( L a z a n , 1 9 4 9 ), a n di n s e v e r a l o t h e r m e t a l s , a s w e l l a s i n p l a s t i c s a n dp l o y m e r s ( B e n h a m a n d H u t c h i n s o n , 1 9 70 ). C y c li cc r e e p r e t a rd a t i o n a n d h a r d e n i n g o f th e m a t e r i a lh a v e b e e n o b s e r v e d i n z i n c ( P r i c e , 1 9 6 7 ) , c o p p e ra l l o y s ( D a v i e s a n d W i l s h i re , 1 9 6 7 ) a n d n i c k e l a l -l o y s ( W e b s t e r a n d P i e a r c e y , 19 6 6 ). I n g e n e r a l ,c r e e p a t h i g h t e m p e r a t u r e is c a u s e d b y g e n e r a t i o na n d a c c u m u l a t i o n o f p o i n t d e f e c t s ( v a c a n c i e s ) i nm e t a l s a n d v o i d s i n c er a m i c s . D u r i n g c y c l in g m o r ep o i n t d e f e c t s a r e f o r m e d t h a n u n d e r s t a t i c s t r e s sa n d t h e s e c a u s e a c c e l e r a t i o n o f c re e p r a t e ( S h i n e t .a l . , 1 9 8 3 ) . T h e s e v a c a n c i e s / v o i d s a r e n u c l e a t e d a tg r a i n b o u n d a r i e s o r g r a i n - p a r t ic l e i n t e rf a c e s d u e t os t r e s s c o n c e n t r a t i o n s a n d e l a s t i c a c c o m m o d a t i o n .T h e f a i l u r e p a t t e r n u n d e r h i g h t e m p e r a t u r e c y c l i cl o a d i n g w a s a l s o f o u n d t o b e d i f f e r e n t f r o m c l a s s i -c a l c r e e p o r f a t i gue f a i l u r e s i n t ha t , c r a c ks f r e -q u e n t l y f o l l o w g ra i n b o u n d a r i e s a n d p a r t i c l e -g r a i ni n t er f ac e s . B e n h a m a n d H u t c h i n s o n ( 19 7 0 ) s u g -g e s t e d t h a t i n p o l y m e r s c y c li c s o f t e n i n g c o u l d b ed u e t o t e m p e r a t u r e r i s e a n d d i s s i p a ti o n o f e n e rg yd u r i n g c y c l i n g . H e n c e c y c l i c c r e e p i n g e n e r a l c a nb e c o n s i d e r e d t o b e a t r a n s i e n t t h e r m a l c r e e pa c t i v a t e d b y m e c h a n i c a l w o r k . I n s o m e m a t e r i a l sb o t h a c c e l e r a t i o n s a n d r e t a r d a t i o n o f t h e c r e e pr a t e h a v e b e e n o b s e r v e d , a s f o r e x a m p l e , i na l u m i n i u m ( S h e t t y a n d M e s h i i, 1 9 7 5) , a l u m i n i u ma l l o y s ( M a n j o i n e , 1 9 49 ), c o p p e r ( L o r e n z o a n dLa i r d , 1984 ) , a nd in a s t a in l e s s s t e e l ( M or r i s a ndH a r r i s , 1 9 7 8 ). I n t h e s e m e t a l s a c c e l e r a t i o n o f cy c l i cc r e e p h a s b e e n e x p l a i n e d a s d u e t o e n h a n c e d d i s lo -c a t i o n g l i d e b y c l i m b p r o c e s s e s , e t c . , a n d r e t a r d a -t i o n , d u e t o e x h a u s t i o n o f a v a i l a b l e g l i d e d i s l o c a -t i o n ( L o r e n z o a n d L a i r d , 1 9 8 4 ) . I n u n f r o z e n s o i l


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V.R. Param eswaran / creep of rozen soils 117

m a t e r i a l s c y c l i c c r e e p e f f e c t is m o r e c o m p l i c a t e dd u e t o t h e i n f l u e n c e o f w a t e r, b u t t h e e f f e c t o fc y c l i c c r e e p h a s b e e n f o u n d t o d e c r e a s e w i t h i n -c r e a s i n g l o a d c y c l e a n d m o i s t u r e c o n t e n t d u e t oc o n s o l i d a t i o n ( H o l u b e c , 1 9 6 9 ; H o l u b e c a n d W i l -son , 1970) .A t h re sho l d s t r e s s (Ot h ) , ha s be e n de f i ne d , a bovew h i c h c y c l ic c r e e p a c c e l e r a t e s a n d b e l o w w h i c hr e t a r d a t i o n o c c u r s . L o r e n z o a n d L a i r d ( 1 98 4 )a n a l y z e d t h e e x p e r i m e n t a l d a t a o n v a r i o u s m e t a l sp u b l i s h e d b y d i f f e r e n t a u t h o r s a n d f o u n d t h a t a ta ny t e mpe ra t u re T , Ot h i s g i ve n by :Oth = (2 .9 X 10 -4 ) X G " ( T m / T ) ( 1 0 )w h e r e Tm i s t h e m e l t i n g t e m p e r a t u r e ( i n t h e p r e -s e n t c a s e f o r f r o z e n s o i l s Tm = 0 C = 2 7 3 K ) a n dG , t h e s h e a r m o d u l u s . F o r c o p p e r , o t h w a s f o u n dt o b e 6 5 M P a .

U s i n g r e p r e s e n t a t i v e v a lu e s f o r G a s 2 G P a a n d4 G P a , r e s p e c t i v e l y , f o r t h e f r o z e n c l a y a n d f r o z e nsa nd (Vi nson , 1978a ) i n (10 ) , t he t h re sho l d s t r e s se sf o r c h a n g e o v e r in c y c l i c c r e e p b e h a v i o u r f r o m t h er e t a r d i n g t y p e t o t h e a c c e l e r a t i n g t y p e a r e 0 . 5 8 7M P a f o r th e c la y a n d 1 . 1 73 M P a f o r t h e s a n d .T a b l e 1 s h o w s t h a t i n t h e p r e s e n t e x p e r i m e n t s t h em e a n s t a ti c s t re s s u s e d f o r t h e c l a y w a s o n l y 0 . 5 3 4M P a , w h i c h i s l o w e r t h a n t h e c a l c u l a t e d v a l u e o ft h e t h r e s h o l d s t r e s s, a n d h e n c e w e o b s e r v e r e t a r d a -t i o n . O n t h e o t h e r h a n d t h e m e a n s t r e s s a p p l i e d o nt h e s a n d s p e c i m e n s w a s o f t h e o r d e r o f 2 . 3 5 M P a ,w h i c h w a s t w o t i m e s t h e t h r e s h o l d s t r e s s c a l c u -l a t e d a b o v e , a n d h e n c e t h e c y c l i c c r e e p a c c e l e r a t e sm o r e a n d m o r e , a s s h o w n b y t h e i n c r e a s e i n( A t / A N ) w i t h i n c r e a s i n g s t r a i n .

P l a s t i c d e f o r m a t i o n o f f r o z e n s o i l s i s m a i n l yd u e t o t h e v i s c o u s f l o w o c c u r r i n g i n t h e i c e p h a s e .A t a n y t e m p e r a t u r e , u n f r o z e n w a t e r i s a lw a y s p r e -s e n t i n t h e s o il a t t h e i n t e r p a r t i c l e j u n c t i o n , t h ea m o u n t b e i n g h i g h e r , t h e c l o s e r i s t h e t e m p e r a t u r et o 0 C , a nd t he f i ne r t he g ra i n s i z e o f t he so i l . Th i su n f r o z e n w a t e r d e c r e a s e s t h e i n t e r p a r t i c l e f r i c t i o ns t re s s, de c re a se s t he v i s c os i t y o f t he so i l, a nd p ro -v i d e s p a t h s f o r d i f f u s i v e f l o w i n t h e s o i l . T h eu n f r o z e n w a t e r c a n a l s o m i g r a t e a l o n g t h e p a r t i c l ei n t e r f a c e s f r o m r e g i o n s o f h i g h s t r e s s t o t h o s e o fl o w s t r e s s a n d d e c r e a s e t h e s t r e n g t h o f t h e s o i l .I n p u t o f m e c h a n i c a l e n e r g y , a s i n c y c l ic l o a d i n g ,

c o u l d i n c r e a s e t h e t h e r m a l e n e r g y i n t h e s o il b yh y s t e r e t i c e f f e c t a n d c a u s e a n i n c r e a s e i n t h ea m o u n t o f u n f r o z e n w a t e r c o n t e n t . I n f r o z e n s o i l si t i s p r o b a b l y t h i s m e c h a n i s m t h a t i n c r e a s e s t h ec r e e p r a t e d u r i n g c y c l i c l o a d i n g . I n t h e p r e s e n te x p e r i m e n t s a l s o t h e r e w a s p o s i t i v e e v i d e n c e s h o w -i n g a n i n c r e a s e i n t e m p e r a t u r e o f t h e s a m p l e d u r -i ng c yc l i ng , a s shown i n F i g . 9 fo r a s a nd s a mpl e .T h e d a s h e d p o r t i o n s o f t h e l o w e r c u r v e d e n o t e t h ep e r i o d s o f c y c li c s t re s s in g , a n d t h e c o r r e s p o n d i n gt e m p e r a t u r e s a s i n d i c a t e d b y a f i n e t h e r m o c o u p l ee m b e d d e d i n t h e m i d d l e o f t h e t e s t s p e c i m e n , a r es h o w n i n t h e u p p e r c u r v e . I n t h i s t e s t t h e c y c l i cs t r es s w a s a p p l i e d b y a h e a v y e l e c t r o h y d r a u l i cs h a k e r w i t h a p e a k l o a d c a p a c i t y o f 1 3 6 0 k g , a n dh e n c e t h e t e m p e r a t u r e o f t h e t e s t s p e c i m e n w a sf o u n d t o i n c r e a s e a l m o s t b y a d e g r e e d u r i n g c y -c l i ng !

T h e i n p u t o f t h e r m a l e n e r g y c a u s e d b y a m e c h -a n i c al c y c li n g a n d t h e a m o u n t o f u n f r o z e n w a t e rp r o d u c e d c a n b e r o u g h l y c a l c u l a t e d . T h e e l e c -t r o d y n a m i c s h a k e r h a s a f o r c e r a t i n g o f 1 3 3 Nw i t h a m a x i m u m s t r o k e c a p a b i l i t y o f 6 . 2 5 i n ( 1 5 9m m ) p e a k - t o -p e a k . I f w e u s e t he r m s v a l u e o f p e a kf o r c e a n d 5 0 % o f s t r o k e a s o p e r a t i n g l e v e l , t h em e c h a n i c a l e n e r g y i n p u t p e r c y c l e is : 0 .7 0 7 x 1 3 3x ( 1 5 . 9 / 2 ) x 1 05 d y n e c m w h i c h i s a p p r o x i m a t e l ye qu a l t o 7 .5 Jou l e s pe r c y c l e o r 1 .786 c a l o r i e s . Th i sc o u l d c a u s e m e l t i n g o f 1 . 7 8 6 / 8 0 = 2 . 23 X 1 0 - 2g m s o f i c e p r o d u c i n g a b o u t 0 . 02 4 c m 3 o f w a t e r . I ft h i s w a t e r i s a s s u m e d t o b e d i s t r i b u t e d u n f o r m l ya round t he so i l g ra i n s i n a t e s t spe c i me n , i t c a n be

- 2 . 0 ~-2 .5- 3 . 0

~- -3. 5 I1 0 i I I I ~ r

z t

~ 54 I I I

50 100 150T I M E , h

F i g . 9 . E f f e c t o f c y cl ic s t r e s s i n i n c r e a s i n g t h e t e m p e r a t u r e o f af r o z e n s a n d s p e c i m e n .


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118 v.R. Parameswaran / Creep ofJ)'ozen soil~calculated, using the specific gravity of sand andmoisture content, that a layer of water of thicknessequal to 100 A (10 nm) will be formed. Not all themechanical energy will be converted to thermalenergy, and even if only a fraction is converted toheat that will cause melting of ice, sufficient un-frozen water will be formed in several hundredcycles to cause accelerated viscous creep of thefrozen soil samples.

Thus, the increase in creep strain rate duringcyclic loading as indicated by the increase in theslope between the static and cyclic loading regimeson the creep curve (strain vs. time) can be ex-plained by the increase in the amount of theunfrozen water content due to thermal energycaused by the mechanical energy input due tocyclic loading. But the rate of change of the strainincrement per cycle with strain, increases or de-creases depending on whether the applied meanstatic stress is above or below a threshold stress,which is a function of the shear modulus of thematerial and the homologous temperature (ratio ofthe testing temperature to the melting point). Inthe present tests, for frozen sand, the mean staticstress was much higher than the threshold stressand hence cyclic creep acceleration was observedin these samples as shown by the increase in strainincrement per cycle with increasing strain. On theother hand, for the frozen clay specimens, wherethe mean static stress was lower than the thresholdstress, the strain increment per cycle decreasedwith increasing strain showing a retardation ofcyclic creep.

In order to conclusively prove that a thresholdstress does exist for each frozen soil (such as sandand clay) further experiments are underway withfrozen sand specimens being tested at stresses lowerthan the threshold stress and frozen clay speci-mens being tested at stresses higher than thethreshold stress reported earlier.

ConclusionCreep rate of frozen saturated sand and clays

under compressive loading was increased consider-ably by superimposed alternating stresses of am-plitude up to 10% of the mean static stress. This

could be attributed to the increase in the amountof unfrozen water content caused by transientthermal energy produced by mechanical cycling ofthe material. The acceleration of cyclic creep infrozen sand and retardation in frozen clays (asshown by the increase and decrease respectively,of the strain increment per cycle with increasingstrain) could be explained by the fact that themean static stress was higher than a certainthreshold stress for the former and lower for thelatter. Using the analogy of high temperature creepof metallic materials, the threshold stress abovewhich the increment in strain per cycle increasedwith increasing strain, was calculated to be equalto 0.587 MPa for the frozen clays, and 1.173 MPafor the frozen sand.

Such increases in creep rates caused by cyclicloading could reduce the bearing capacity offoundations in frozen soils, and could necessitatean increase in the value of risk factor to be used inthe design of foundations in permafrost areas.

AcknowledgementSincere thanks are due to Colin Hubbs and

Harold Dahl for making the test specimens andcarrying out the tests, and to Douglas Bright forhis help in accessing the data through a datalogger and a desktop computer.

ReferencesBailey, R.W. (1935), "The utilization of creep test data inengineering design", Proc. Inst, Mech. Engng. 131, 131.Benham, P.P. and S.J. Hutchinson (1970), "Cyclic creep andfracture of polyvinyl chloride", Plastics and Polymers 38,259.Davies, P.W. and B. Wilshire (1967), "The effect of stresscycling on creep and fracture of a copper-7% aluminumalloy", Metallurgia 76, 93.Dorn, J.E. (1962), "Progress in understanding high temperaturecreep", H.W. Gillett Memorial Lecture, ASTM, Phila-delphia, 22.Holubec, I. (1969), "Cyclic creep of granular materials", De-partment of HighwaysOntario Report No. RR 147, 46.Holubec, I. and K.H. Wilson (1970), "A cyclic creep study ofpavement materials", Department of HighwaysOntario Re-port No. RR 163, 26.


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Kennedy , A.J. (1962), Processes of Creep and Fatigue in Metals,Oliver and Boyd, Edinburgh, 480.

Lazan, B.J. (1949), "Dynamic creep and rupture properties oftemperature-resistant materials under tensile stress", Proc .A m e r . S o c . T e s t i n g a n d M a t e r i a l s 49 , 757.

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Manjoine, M.J. (1949), "' Effects of pulsating loads on the creepcharacteristics of aluminum alloy 14S-T", P r o c . A m e r . S o c .T e s t i n g a n d M a t e r i a l s 4 9 , 788.

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Vinson, T.S., T. Chaichanavong and R.L. Czajkowski (1978b),"Behaviour of frozen clay under cyclic axial loading", J.G e ot ec h . E n g n g . D i v . A S C E 1 0 4 (No. GTF) 779.

Vinson, T.S.T. Chaichanavong (1978c), "Dynamic behaviourof ice under cyclic axial loading", J. Geotech. Eng. Div.A S C E 1 04 (No. GTF) 801.

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Effect of Alternating Stress