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Transmission of loads through grounded ice rubble
Sayed, M.
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National Research ConseY nationalCouncil Canada de rechwches Canada
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Institute for lnstitut de Research in recherche en Construction construction
Transmission of Loads Through Grounded
-Ice Rubble
by M. SayedAppeared in
IAHR Special Report 89-5, February 1989
Workina Grouo on Ice Forces: 4th State-of-the-Art Report
p. 259-275 '
(IRC Paper No. 1601)
Reprinted with permission NRCC 3047 5 ? NRC
-
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I R CL I B R A R Y
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4
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BIBLIOTH~QUE
I R C
1
CNFlC-
IC157Dans cette etude de synthbe, l'auteur ktudie le rale que jouent les champs de fragments
ancrds au sol dans le transfext des charges de glace flottante sur les structures se trouvant en
mer. Les etudes sur le terrain et en laboratoire fournissent de l'infonnation concernant la
geomdme et la composition des champs de fragments, ainsi que certaines rnesures des
contraintes. L'auteur examine les mdthodes employdes pour estimer la resistance
A
l'ancrage au sol, ainsi que d'autres analyses portant sur la stabilitk des champs de
fragments.
TRANSMISSION OF LOADS THROUGH GROUNDED I C E RUBBLE M. Sayed Research O f f i c e r I n s t i t u t e f o r Research i n C o n s t r u c t i o n N a t i o n a l Research C o u n c i l Canada Ottawa, O n t a r i o CANADA
ABSTRACT: T h i s review examines t h e r o l e o f grounded r u b b l e f i e l d s i n t r a n s f e r r i n g f l o a t i ng i c e l o a d s t o o f f s h o r e s t r u c t u r e s . F i e l d and 1 a b o r a t o r y s t u d i e s p r o v i d e i n f o r m a t i o n c o n c e r n i n g r u b b l e f i e l d s geometry, c o m p o s i t i o n , and some s t r e s s measurements. Methods o f e s t i m a t i n g g r o u n d i n g r e s i s t a n c e and o t h e r a n a l y s e s . t h a t d e a l w i t h s t a b i l i t y o f r u b b l e f i e l d s a r e discussed.
1.
INTRODUCTIONThe processes o f i c e r u b b l e f o r m a t i o n , grounding, f r e e z i n g , and response t o a p p l i e d f o r c e s r e m a i n p o o r l y understood. E a r l y o b s e r v a t i o n s o f r u b b l e f i e l d s i n t h e B e a u f o r t Sea i d e n t i f i e d t w o p o s s i b l e s c e n a r i o s :
( a ) Grounded r u b b l e c a n t r a n s f e r p a r t o f f l o a t i n g i c e f o r c e s t o t h e berm, and t h u s reduce 1 oads o n t h e s t r u c t u r e .
( b ) Because a r u b b l e f i e l d ' s w i d t h i s l a r g e r t h a n t h a t o f t h e s t r u c t u r e , f l o a t i n g i c e f o r c e s w o u l d a c t a g a i n s t a l a r g e r a r e a a n d t h u s e x e r t a l a r g e r t o t a l f o r c e o n t h e r u b b l e f i e l d . Therefore, a f r o z e n r u b b l e f i e l d w o u l d i n c r e a s e t h e f o r c e s o n t h e s t r u c t u r e t h a t i t s u r r o u n d s . I n c e r t a i n o f f s h o r e a r e a s , t h e assessment o f a s t r u c t u r e ' s s t a b i l i t y r e q u i r e s k n w l e d g e o f t h e l i k e l i h o o d o f a r u b b l e f i e l d t o f o r m a n d i t s geometry, t h e a b i l i t y o f grounded r u b b l e t o t r a n s f e r h o r i z o n t a l f o r c e s t h r o u g h i t s k e e l t o t h e berm, s p a t i a l s t r e s s d i s t r i b u t i o n s i n t h e r u b b l e , and i n t e g r i t y o f t h e f i e l d u n d e r t h e a c t i o n o f f l o a t i n g i c e . A v a i l a b l e 1 i t e r a t u r e , however, p r o v i d e s o n l y s p a r s e i nformat i o n c o n c e r n i n g t h e s e problems. A s u r v e y o f f i e l d o b s e r v a t i o n s o f grounded r u b b l e geometry, morphology and s t r e s s measurements; a d i s c u s s i o n o f r e l e v a n t l a b o r a t o r y s t u d i e s , r u b b l e mechanical p r o p e r t i e s , and a v a i l a b l e a n a l y t i c a l m e t h o d s w i l l be c o v e r e d i n t h i s r e v i e w .
2 . FIELD STUDIES
2.1 Geometry and morphology:
K r y (1977) gave a d e s c r i p t i o n o f t h e r u b b l e f i e l d t h a t formed o n t h e s h a l l o w s l o p e d beach around t h e a r t i f i c i a l i s l a n d a t t h e N e t s e r k l o c a t i o n
d u r i n g t h e w i n t e r o f 1975-76. The o b s e r v a t i o n s were concerned w i t h t h e
I
geometry o f t h e r u b b l e f i e l d , s a i l p r o f i l e s and r u b b l e s e t t l e m e n t s o v e r t h eseason. The measurements o f F r e d e r k i n g and \ / r i g h t (1982) c o n c e n t r a t e d o n a r a d i a l l i n e i n t h e r u b b l e f i e l d a t t h e Issungnak l o c a t i o n . They o b t a i n e d
p r o f i l e s o f s a i l and k e e l dimensions, t e m p e r a t u r e , p o r o s i t y , s a l i n i t y , and
I
i
The p r e c e d i n g t w o r e f e r e n c e s p r e s e n t t h e most complete p u b l i s h e d d e s c r i p t i o n o f r u b b l e f i e l d s t o d a t e . McGonigal (1983) a l s o r e p o r t e d o n a d e t a i l e d program o f r u b b l e f i e l d i n v e s t i g a t i o n s a t Issungnak. O t h e r s t u d i e s , a l t h o u g h p r i m a r i l y focussed o n s t a b i ' l i t y o f i s l a n d s , g i v e some i n f o r m a t i o n r e g a r d i n g r u b b l e f i e l d geometry ( f o r exampl e, S t r i l c h u k 1977, and Semeniuk 1977). Geometry d a t a a r e a v a i l a b l e , a s w e l l , f r o m t h e r u b b l e f i e l d s a t Amerk (Croasdale, 1985) and Kaubvik ( F r e d e r k ing, 1988). These a r e c a i s s o n s t r u c t u r e s s i t t i n g o n submarine berms 1 0 m o r more b e n e a t h w a t e r l e v e l . The t y p i c a l f e a t u r e s common t o most r u b b l e f i e l d s a r e summarized below.
F i g u r e 1: Rubble f i e 1 d a t Kaubvik, 1987.
R u b b l e ( a r o u n d a r t i f i c i a l i s l a n d s ) may become grounded o v e r submarine berms i n t h e l a n d f a s t i c e zone o f t h e B e a u f o r t Sea, where w a t e r d e p t h i s u s u a l l y l e s s t h a n 20 m. A p h o t o g r a p h o f t h e r u b b l e f i e l d a t K a u b v i k i s s h w n i n F i g u r e 1. The e x t e n t o f grounded r u b b l e f r o m t h e i s l a n d depends o n t h e b a t h y m e t r y o v e ? t h e berm and i c e c o v e r movements. As a n example, t h e boundary o f t h e r u b b l e f i e l d a t Kaubvik i s superimposed on t h e b a t h y m e t r y c o n t o u r s i n F i g u r e 2. The r u b b l e e x t e n d s t o t h e 18 m d e p t h c o n t o u r t c w a r d t h e e a s t and w e s t b u t ends a t s h a l l a w e r d e p t h s t w a r d s t h e n o r t h
aria-south
a p p a r e n t l y because i c e movements were s m a l l f r o m t h e s e d i r e c t i o n s .F i g u r e 2: Boundary o f t h e r u b b l e f i e l d and w a t e r d e p t h c o n t o u r s a t Kaubvik
,
A r u b b l e f i e l d b e g i n s t o f o r m i n t h e f a l l as a r e s u l t o f s e v e r a l I
I
s e p a r a t e p i l e u p events. The f i e l d g r a d u a l l y grcws t o r e a c h i t s maximum f
I e x t e n t , u s u a l l y by February. D u r i n g t h e f i e l d ' s growth, p a r t s o f t h e p i l e u p s c a n a p p a r e n t l y b e d i s l o d g e d a n d moved by f l o a t i n g i c e . Consequently, s t e e p s a i l s l o p e s (sometimes n e a r v e r t i c a l ) a r e o f t e n
i
observed. I n d i v i d u a l p i l e u p s j o i n t o f o r m o v a l r i n g s o f " h i l l s " and " v a l l e y s " a r o u n d t h e i s l a n d ( s e e F i g u r e 1). A t t h e o u t e r edge o f t h e f i e l d , a t i d a l crack s e p a r a t e s t h e grounded r u b b l e f r o m f l o a t i n g i c e .As a n example o f s a i l and k e e l geometry, t h e r a d i a l l i n e p r o f i l e a t Issungnak ( f r o m F r e d e r k i n g and W r i g h t , 1982) i s s h w n i n F i g u r e 3. W h i l e t h i s p r o f i l e i s t y p i c a l o f most r u b b l e f i e l d s , s a i l h e i g h t s can b e h i g h e r ,
r e a c h i n g 10 m where l a r g e i c e movements occur.
Temperature d i s t r i b u t i o n i n t h e r u b b l e u s u a l l y causes w a t e r t o f r e e z e i n t h e v o i d s between i c e b l o c k s n e a r w a t e r l e v e l . Thus, a s o - c a l l e d " c o n s o l i d a t e d l a y e r " forms. Such a l a y e r c o n t a i n s s o l i d i c e , w i t h o u t v o i d s , and appears t o have l a r g e r s t i f f n e s s and s t r e n g t h t h a n b u l k r u b b l e .
10 R I G 5 - 15 0 20 40 6 0 8 0 1 0 0 120 140 ( N O R T H ) H O R I Z O N T A L P O S I T I O N , rn ( S O U T H ) F i g u r e 3: L o n g i t u d i n a l r u b b l e p r o f i l e a t I s s u n g n a k , 1980 ( f r o m F r e d e r k i n g and W r i g h t , 1982). RUBBLE FIELD
-
SOLID ICE = V O I D-A- SEA BOTTOM
U N G R O U N D E D
---9-- ICE S U R F A C E C O N S O L I D A T I O
A v e r t i c a l t e m p e r a t u r e and s a l i n i t y p r o f i l e , a l s o f r o m Issungnak, i s shown i n F i g u r e 4. E s t i m a t e s o f c o n s o l i d a t e d ( o r f r o z e n ) l a y e r t h i c k n e s s o b t a i n e d by d r i l l i n g b o r e h o l e s u s u a l l y a g r e e w i t h t h a t o f t h e r e l a t i v e l y c o l d e r l a y e r o f r u b b l e n e a r w a t e r l e v e l .
The average c o n s o l i d a t e d l a y e r t h i c k n e s s , by January o r F e b r u a r y , v a r i e s between 2.5 m and 3 m ( F r e d e r k i n g and W r i g h t , 1982; and Croasdale,
!
I 1985). Below s u c h a l a y e r , t e m p e r a t u r e i s r e l a t i v e l y warm (above -5' C )
l
a n d i c e o f f e r s weak r e s i s t a n c e t o d r i l l i n g . The v e r t i c a l t e m p e r a t u r ep r o f i l e and c o n s o l i d a t e d l a y e r t h i c k n e s s v a r y w i t h i n a r u b b l e f i e l d a c c o r d i n g t o s a i l h e i g h t , s n m depth, and d a t e o f r u b b l e p i l e u p . G e n e r a l l y , t e m p e r a t u r e s n e a r w a t e r l e v e l a r e h i g h ( a n d t h e c o n s o l i d a t e d l a y e r i s t h i n ) u n d e r h i g h s a i l s and deep s n w c o v e r s . E x c e p t i o n s t o t h i s g e n e r a l t r e n d may o c c u r due t o t h e complex t h r e e - d i m e n s i o n a l geometry o f snow and s a i l a s w e l l as w i n d a c t i o n .
R u b b l e s e t t l e m e n t s o v e r w i n t e r were measured a t N e t s e r k by Kry (1977). Comparison o f s t e r e o - p a i r photographs showed t h a t s e t t l e m e n t s o f u p t o 1 m
o c c u r r e d between November and F e b r u a r y . Repeated s u r v e y s o f t h e r u b b l e a t K a u b v i k ( F r e d e r k i n g , 1988) s h w e d s e t t l e m e n t s , between January and A p r i l ,
T E M P E R A T U R E . O C S A L I N I T Y , o l o o
F i g u r e 4: V e r t i c a l t e m p e r a t u r e and s a l i n i t y p r o f i l e ( a t c o r e 5, F i g .
3 ) ,
I s sungnak 1980 ( f r o m FrederJc i n g and W r i g h t , 1982).
v a r y i n g f r o m 0.15 m i n s h a l l o w w a t e r a r e a s t o a rnaximm o f 0.45 m i n deep w a t e r a r e a s n e a r t h e o u t e r edge o f t h e f i e l d . H o r i z o n t a l d i s p l a c e m e n t s w e r e r e l a t i v e l y s m a l l , w i t h a maximm o f a p p r o x i m a t e l y 0.35 m o v e r t h e same d u r a t i o n .
2.2 S t resses:
C r o a s d a l e (1985) measured normal s t r e s s e s i n t h e r u b b l e f i e l d a t Amerk ( a l s o see Sayed e t a l . , 1986). S t r a i n gauged p a n e l s were i n s t a l l e d a t a number o f l o c a t i o n s i n t h e r u b b l e f i e l d . Only one panel, l o c a t e d a p p r o x i m a t e l y 1 0 m f r o m t h e f i e l d ' s o u t e r edge, responded t o t h e a c t i o n o f f l o a t i n g i c e . It measured a maximm s t r e s s o f 200 kPa. The c o r r e s p o n d i n g f o r c e p e r u n i t l e n g t h was e s t i m a t e d t o b e 500 kN/m. P a r t o f t h e s t r e s s - t i m e r e c o r d ( f r o r n Croasdale, 1985) i s shown i n F i g u r e 5. The o t h e r p a n e l s were i n s t a l l e d f u r t h e r i n s i d e t h e f i e l d a t d i s t a n c e s o f more t h a n 7 5 m f r o m t h e o u t e r edge. Those p a n e l s measured n e g l i g i b l e s t r e s s e s . E v i d e n t l y
b
g r o u n d i n g r e s i s t a n c e was s u f f i c i e n t t o t r a n s m i t a l l o f t h e f l o a t i n g i c e f o r c e s t o t h e o u t e r p a r t o f t h e berm.
A P R I L 1 9 8 5
F i g u r e 5: Normal s t r e s s n e a r t h e edge o f t h e r u b b l e f i e l d a t Arnerk, 1985 ( f r o m Croasdale, 1985).
S e v e r a l s t r e s s panels were a l s o i n s t a l l e d i n t h e r u b b l e f i e l d a t K a u b v i k d u r i n g 1986-87 w i n t e r ( F r e d e r k i n g , 1988). The maxirnrrn normal s t r e s s measured n e a r t h e f i e l d ' s o u t e r edge was 600 kPa. S t r e s s e s a t o t h e r l o c a t i o n s i n s i d e t h e f i e l d were n e g l i g i b l e .
The l o w s t r e s s e s i n s i d e t h e r u b b l e f i e l d ( a t b o t h Arnerk and K a u b v i k l o c a t i o n s ) were t o o s c a t t e r e d t o show any p a t t e r n o f s p a t i a l s t r e s s d i s t r i b u t i o n . The s i z e s o f a l l s t r e s s sensors used so f a r a r e s m a l l compared t o i c e b l o c k dimensions. T h i s can f u r t h e r c o m p l i c a t e a t t e m p t s t o c o r r e l a t e t h e s t r e s s e s measured a t v a r i o u s p a r t s o f a f i e l d .
O t h e r r e l e v a n t s t r e s s measurements were conducted i n t h e f l o a t i n g i c e s u r r o u n d i n g a number o f r u b b l e f i e l d s . A comprehensive r e v i e w o f t h i s s u b j e c t was g i v e n by Sanderson (1984). Measurements a t Kadluk w e r e a l s o
3. PHYSICAL MODELS
3.1 H o r i z o n t a l l o a d i n g o f grounded r u b b l e:
1
I
Experiments c o n c e r n i n g grounded r u b b l e s t a b i l i t y w e r e c o n d u c t e d by
Wards (1984) ( o t h e r t e s t s were a l s o r e p o r t e d by Wards i n APOA r e p o r t #186). I I H o r i z o n t a l f o r c e s were a p p l i e d t o p r e c o n s t r u c t e d r u b b l e p i l e u p s i n a n i c e
b a s i n . Two p i l e u p s w e r e used; t h e f i r s t c o n s i s t e d o f a t r i a n g u l a r s a i l and k e e l w i t h a n average s a i l h e i g h t o f 0.79 m, k e e l d e p t h o f 0.84 rn and w i d t h o f 1.82 m. The second p i l e u p a l s o had a t r i a n g u l a r s a i l a n d k e e l c r o s s - s e c t i o n w i t h a n a v e r a g e h e i g h t o f 0.43m, d e p t h o f 0.87 m a n d w i d t h o f 2.42 m. Two t y p e s o f t e s t s were conducted as i l l u s t r a t e d i n F i g u r e 6 ( a ) . A b a r r i e r supported t h e p i l e u p d u r i n g t h e " c o n s t r a i n e d " t e s t s . The " u n c o n s t r a i n e d " t e s t s were conducted w i t h o u t a l a t e r a l s u p p o r t t o d e t e r m i n e t h e maximm g r o u n d i n g s h e a r r e s i s t a n c e . u n c o n s t r a i n e d t e s t s gave f r i c t i o n c o e f f i c i e n t v a l u e s ( t a k e n a s t h e r a t i o o f s h e a r t o normal f o r c e s o n t h e berm) o f 0.63 a n d 1.58. C o n s t r a i n e d t e s t r e s u l t s a r e e x p r e s s e d a s t h e r a t i o o f t h e h o r i z o n t a l f o r c e a c t i n g o n t h e berm t o t h a t a c t i n g o n t h e b a r r i e r . T h i s r a t i o d e c r e a s e d w i t h t i m e d u r i n g each t e s t . F o r t e s t s p e r f o r m e d u s i n g t h e f i r s t p i l e u p , t h e r a t i o v a r i e d f r o m 0.29 t o 0.09 d u r i n g one t e s t and f r o m 0.26 t o 0.24 d u r i n g a n o t h e r t e s t . A t e s t p e r f o r m e d u s i n g t h e second p i l e u p r e s u l t e d i n r a t i o s s t a r t i n g a t 1.44 and d e c r e a s i n g t o 0.31 by t h e end o f t h e t e s t . I n f o r m a t i o n r e g a r d i n g r u b b l e d e f o r m a t i o n and r u b b l e / b e d c o n t a c t c o n d i t i o n s i s n o t a v a i l a b l e , w h i c h 1 i m i t s p o s s i b l e i n t e r p r e t a t i o n o f t h e measurements. D e f o r m a t i o n o f t h e p i l e u p may have i m p r o v e d t h e r u b b l e c o n t a c t w i t h t h e b a r r i e r a s a t e s t p r o g r e s s e d and t h u s reduced t h e p o r t i o n o f t h e h o r i z o n t a l f o r c e t r a n s m i t t e d t o t h e berm. The l a r g e r g r o u n d i n g r e s i s t a n c e o f t h e second p i l e u p ( i n s p i t e o f i t s l o w e r s a i l ) was p r o b a b l y caused by i t s 1 a r g e r w i d t h w h i c h m i g h t have produced a 1 a r g e r c o n t a c t a r e a w i t h t h e berm.
One s i g n i f i c a n t c o n c l u s i d n t h a t c a n be i n f e r r e d f r o m t h e r e s u l t s i s t h a t a grounded r u b b l e p i l e u p does n o t behave as a r i g i d b l o c k . A " r i g i d
RUBBLE PILEUP
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RUBBLE PILEUP ICE SHEET WATER LEVEL F-
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61
Schematics o f i c e b a s i n e x p e r i m e n t s ( a ) Ward (1984), ( b ) Timco e t a l . (1989)t h e normal f o r c e ( o n t h e bed) m u l t i p l i e d by a f r i c t i o n c o e f f i c i e n t . Such a n approach cannot e x p l a i n t h e v a r i a t i o n s o f g r o u n d i n g r e s i s t a n c e d u r i n g each t e s t and between v a r i o u s t e s t s .
A n o t h e r program was r e c e n t l y conducted by Timco e t al. (1989) t o measure g r o u n d i n g f o r c e s d u r i n g a c t i v e r u b b l e p i l e u p , and d u r i n g l o a d i n g o f a n e x i s t i n g c o n s o l i d a t e d r u b b l e p i l e u p . A two-dimensional chute,
i n s t r u m e n t e d t o measure f o r c e s o n a berm and a v e r t i c a l back board, was u s e d i n a model i c e b a s i n a s i l l u s t r a t e d i n F i g u r e 6 ( b ) .
R e s u l t s i n d i c a t e t h a t t h e r a t i o o f h o r i z o n t a l t o v e r t i c a l f o r c e s a c t i n g on t h e berm, q, depends o n w a t e r depth, p i l e u p s i z e , and 1 e n g t h o f t h e p i l e u p between t h e v e r t i c a l s t r u c t u r e and f l o a t i n g i c e . As a n example, t h e l o a d a p p o r t i o n i n g r a t i o (q) i s p l o t t e d v e r s u s t h e r a t i o o f v e r t i c a l f o r c e o n t h e b e r m ( V B ) t o t h e h o r i z o n t a l f o r c e ( H T ) , i n F i g u r e 7. The shown curves r e p r e s e n t v a r i o u s t e s t r u n s t h a t c o r r e s p o n d t o t w o v a l u e s o f r u b b l e l e n g t h ( L ) t o w a t e r d e p t h ( d ) r a t i o . The t e s t s w e r e a l s o c o n d u c t e d u s i n g rough and smooth berms.
-
+ EQUATION ( 1 )
(a) ROUGH BERM
I I t
-
EQUATION (1) WITH (P 125'-
-
i (b) SMOOTH BERM I 1 F i g u r e 7: F o r c e a p p o r t i o n i n g 11 v e r s u s v e r t i c a l ' t o h o r i z o n t a l f o r c e r a t i o ( V B / H T ) f o r ( a ) r o u g h berm, L / d = 4.5 a n d ( b ) s m o o t h berm, L l d = 4.5 f o r t e s t # 2 and #4, L / d = 9 f o r t e s t#7
( f r o m Timco e t a l . , 1989)Again, t h e s e t e s t s i n d i c a t e t h a t grounded r u b b l e b e h a v i o u r i s more complex t h a n t h a t o f a r i g i d b l o c k . The measurements s h w t h a t g r o u n d i n g r e s i s t a n c e can be o v e r e s t i m a t e d i f s i m p l y t a k e n as t h e v e r t i c a l f o r c e o n t h e berm m u t i p l i e d by a f r i c t i o n c o e f f i c i e n t .
)
3.2
Growth o f t h e c o n s o l i d a t e d 1 ayer:D e f i n i t i o n and d e s c r i p t i o n o f t h e cons01 i d a t e d 1 a y e r were g i v e n e a r l i e r i n t h i s r e v i e w ( s e c t i o n 2.1). Timco and G o o d r i c h (1988) measured t h e r a t e o f c o n s o l i d a t i o n ( o r f r e e z i n g ) o f i c e r u b b l e . Experiments were conducted i n a model i c e b a s i n t o examine t h e i n f l u e n c e o f b l o c k s i z e , a i r t e m p e r a t u r e , and w i n d c h i l l on f r e e z i n g r a t e . The r e s u l t s showed t h a t f r e e z i n g r a t e o f i c e r u b b l e i s a p p r o x i m a t e l y t w i c e a s h i g h a s t h a t o f 1 eve1 i ce.
4 . MECHANICAL PROPERTIES OF I C E RUBBLE
K n o w l e d g e o f t h e m e c h a n i c a l p r o p e r t i e s o f b u l k r u b b l e i s a p r e r e q u i s i t e f o r a n a l y s i s o f r u b b l e f i e l d behaviour. The m a i n f e a t u r e s o f t h e s e p r o p e r t i e s a r e b r i e f l y reviewed. More d e t a i l e d i n f o r m a t i o n c a n b e f o u n d i n t h e c i t e d r e f e r e n c e s .
P r o d a n o v i c (1979) t e s t e d submerged r u b b l e samples i n a d i r e c t s h e a r box. H i s r e s u l t s i n d i c a t e d t h a t t h e b u l k r u b b l e obeys t h e MohrCoulomb c r i t e r i o n , u n d e r a c e r t a i n range o f s t r e s s e s and d i s p l a c e m e n t r a t e s . O t h e r e x p e r i m e n t s by T a t i n c l aux and Cheng (1978), K e i nonen and Nyma n (1978), H e l l m a n (1984), and F r a n s s o n and S a n d k v i s t (1985) were i n agreement w i t h t h i s c o n c l u s i o n . G a l e e t a l . (1985) used b o t h d i r e c t s h e a r and a s m a l l
t r i a x i a l c e l l t o t e s t s m a l l r u b b l e samples.
U r r o z and Ettema (1987) used a " t r u e " s i m p l e s h e a r a p p a r a t u s t o t e s t f l o a t i n g r u b b l e . T h e i r s e t - u p overcame many o f t h e problems a s s o c i a t e d w i t h d i r e c t s h e a r t e s t s . Sayed (1987) t e s t e d d r y r u b b l e i n a p l a n e s t r a i n apparatus, and examined s t r a i n r a t e and t e m p e r a t u r e i n f l u e n c e on t h e s t r e n g t h . I n a n o t h e r r e l a t e d s t u d y , E t tema and S c h a e f e r ( 1 986) measured freeze-bonding s t r e n g t h between i c e b l o c k s . The s h e a r f o r c e a t t h e c o n t a c t was found t o depend o n f r e e z i n g t i m e , t e m p e r a t u r e and normal s t r e s s .
The m a i n outcome o f t h e above experiments i s t h a t b u l k r u b b l e obeys . t h e Mohr-Coulomb c r i t e r i o n . Values o f t h e a n g l e o f i n t e r n a l f r i c t i o n v a r y
f r o m 30' t o 50', and cohesion i s n e g l i g i b l e . S t r e n g t h decreases w i t h i n c r e a s i n g s t r a i n r a t e s ( U r r o z and ~ t t e m a , 1987, and Sayed, 1987), and w i t h d e c r e a s i n g t e m p e r a t u r e (Sayed, 1987). These r e s u l t s a r e t r u e f o r a r a n g e
o f s t r e s s e s and d e f o r m a t i o n modes t h a t appear t o b e r e l e v a n t t o f i e l d c o n d i t i o n s , i.e. d e f o r m a t i o n c o n s i s t s o f b l o c k re-arrangement, b l o c k f r a c t u r e and s l i g h t i c e c r u s h i n g . It s h o u l d b e n o t e d t h a t , u n d e r c e r t a i n - c o n d i t i o n s (e.g. h i g h c o n f i n i n g s t r e s s e s ) , t h e b u l k r u b b l e may f r e e z e and deform as a s i n g l e b l o c k o f s o l i d i c e , w h i c h i s n o t i n accordance w i t h f i e l d o b s e r v a t i o n s . A l l d a t a on mechanical p r o p e r t i e s a r e f r o m s m a l l s c a l e l a b o r a t o r y t e s t s . U n c e r t a i n t i e s r e m a i n r e g a r d i n g t h e e x t r a p o l a t i o n o f s m a l l s c a l e d a t a t o f i e l d c o n d i t i o n s . Also, no i n f o r m a t i o n i s a v a i l a b l e c o n c e r n i n g t h e p r o p e r t i e s o f f r o z e n ( c o n s o l i d a t e d ) r u b b l e . 5. ANALYTICAL METHODS 5.1 Grounding r e s i s t a n c e :
Only v e r y l i m i t e d p r o g r e s s has s o f a r been a c h i e v e d i n m o d e l l i n g l o a d t r a n s f e r t h r o u g h t h e k e e l o f a grounded p i l e u p t o t h e berm. A s i m p l e method f o r e s t i m a t i n g g r o u n d i n g r e s i s t a n c e , however, has b e e n i n use. It assumes t h a t t h e h o r i z o n t a l f o r c e a t t h e rubble/berm i n t e r f a c e i s e q u a l t o a f r i c t i o n c o e f f i c i e n t m u l t i p l i e d by t h e normal f o r c e ( s e e f o r example K r y , 1977). The h o r i z o n t a l f o r c e p e r u n i t a r e a o f t h e berm w o u l d b e g i v e n by w h e r e p i s a f r i c t i o n c o e f f i c i e n t , y i s t h e s a i l ' s b u l k u n i t w e i g h t ,
q
i s s t h e k e e l ' s b u l k u n i t w e i g h t , yw i s w a t e r u n i t w e i g h t , HS i s t h e average s a i l h e i g h t , and H i s t h e average k e e l depth. The f r i c t i o n c o e f f i c i e n t pk
i s u s u a l l y c o n s i d e r e d t o b e e q u a l t o t a n 4, where 4 i s t h e a n g l e o f i n t e r n a l f r i c t i o n o f b u l k rubble. T h i s method has been e l u c i d a t e d i n numerous pub1 i c a t i o n s . S i nce t h e approach i s obvious, a 1 i s t i n g of t h a t l i t e r a t u r e i s n o t g i v e n here.
I n
a r e p o r t by Canada M a r i n e E n g i n e e r i n g Ltd. e t a l . (1986), s e v e r a l c a l c u l a t i o n methods were given. It i n c l u d e s a f i n i t e e l e m e n t a n a l y s i s o f 1 a t e r a l r u b b l e 1 oading. P r e l i m i n a r y r e s u l t s i n d i c a t e d t h a t e x t e n s i v e computing w i l l b e r e q u i r e d t o d e a l w i t h t h i s problem. A v a i l a b l e 1 i m i t e d r e s u l t s , however, g i v e v a l u e s o f f o r c e s on t h e berm and t h e s t r u c t u r e t h a tdo n o t appear t o e x h i b i t t h e t r e n d s observed i n t h e f i e l d (Croasdale, 1985;
and F r e d e r k i n g , 1988) o r t h e l a b o r a t o r y (Ward, 1984; and Timco e t a l . 1989).
A n o t h e r f i n i t e element a n a l y s i s by E v g i n and Morgenstern (1984) examined t h e s t a b i l i t y o f o f f s h o r e caissons. The a n a l y s i s showed t h a t t h e r e l a t i v e s t i f f n e s s o f r u b b l e k e e l , compared t o t h a t o f t h e f r o z e n r u b b l e l a y e r , c a n have s i g n i f i c a n t e f f e c t o n l o a d t r a n s f e r t h r o u g h t h e rubble.
5.2 S t r e s s d i s t r i b u t i o n i n r u b b l e f i e l d s
Geometry o f most r u b b l e f i e l d s and l o a d i n g c o n d i t i o n s a t t h e i r b o u n d a r i e s w o u l d g i v e r i s e t o complex s t r e s s d i s t r i b u t i o n s . I n a d d i t i o n t o e s t i m a t e s o f l o c a l g r o u n d i n g r e s i s t a n c e , knowledge o f s p a t i a l s t r e s s v a r i a t i o n s i s needed t o examine s t a b i l i t y o f t h e . - s t r u c t u r e and t h e r u b b l e f i e l d .
The a n a l y s i s o f Sayed and F r e d e r k i n g (1984) t r e a t s t h e b u l k r u b b l e a s a Mohr-Coulomb m a t e r i a l a t c r i t i c a l e q u i l i b r i u m . S o l u t i o n s o f t h e e q u i l i b r i u m e q u a t i o n s and y i e l d c o n d i t i o n gave s t r e s s d i s t r i b u t i o n s f o r a
r a n g e o f boundary g e o m e t r i e s and g r o u n d i n g forces.
A n o t h e r s i m p l e r approach c o n s i d e r s t h e e q u i l i b r i u m o f a r i g i d body, r e p r e s e n t i n g t h e r u b b l e . D e t a i l s o f complex g e o m e t r i e s can b e t a k e n i n t o account, and r e s u l t i n g f o r c e s can be checked f o r f a i l u r e c o n d i t i o n s . C a l c u l a t i o n s based o n t h i s approach were d e s c r i b e d by A1 l y n and W a s i l e w s k i
(1979), A l l y n (1982), and Canada M a r i n e E n g i n e e r i n g Ltd. e t a l . (1986). A t p r e s e n t , t h e r e a r e no a v a i l a b l e d a t a p e r t a i n i n g t o t h e s p a t i a l s t r e s s d i s t r i b u t i o n f r o m e i t h e r f i e l d o b s e r v a t i o n s o r l a b o r a t o r y t e s t s . The models and c a l c u l a t i o n s cannot be c o r r o b o r a t e d .
A c a t e g o r y o f s t u d i e s addressed t h e r e l a t e d problem o f f o r c e s due t o f l o a t i n g rubble. M e l l o r (1980) c o n s i d e r e d b r a s h i c e t o deform as a Mohr-Coulomb m a t e r i a l and u t i l i z e d s o i l mechanics f o m l a s t o e s t i m a t e t h e r e s i s t a n c e t o ships. K r a n k a l a and Maattanen (1984) used a s i m i l a r approach t o c a l c u l a t e t h e f o r c e s on s t r u c t u r e s due t o moving r u b b l e f i e l d s and r i d g e s . Gurshunov (1987) used a method based o n " r i g i d body e q u i l i b r i u m " t o s t u d y s t r u c t u r e - f l o a t i n g r u b b l e f i e l d i n t e r a c t i o n .
5.3 Rubble consol i d a t i o n
K r y ( 1 9 7 7 ) d i s c u s s e d t h e problem o f c o n s o l i d a t e d 1 a y e r growth. Canada M a r i n e E n g i n e e r i n g Ltd. e t a l . (1986) l a t e r developed a model t h a t t a k e s i n t o account t h e i n f l u e n c e o f w i n d v e l o c i t y , snow d e p t h , and s a i l h e i g h t . P r e d i c t e d c o n s o l i d a t e d ' l a y e r t h i c k n e s s e s agreed w i t h f i e l d measurements.
6. CONCLUDING REMARKS
F i e l d and l a b o r a t o r y d a t a r e g a r d i n g g r o u n d i n g r e s i s t a n c e and s t r e s s d i s t r i b u t i o n i n r u b b l e f i e l d s a r e v e r y l i m i t e d , and can o n l y b e g i n t o
i n d i c a t e t h e c o m p l e x i t i e s o f r u b b l e behaviour. It c a n b e s e e n from f i e l d measurements, nonet heless, t h a t grounded r u b b l e f i e l d s r e d u c e t h e 1 oads a c t i n g o n t h e s t r u c t u r e s , r a t h e r t h a n i n c r e a s e them.
The s i m p l e method, c u r r e n t l y i n use ( e q u a t i o n
I ) ,
appears t o o v e r e s t i m a t e g r o u n d i n g r e s i s t a n c e t o a p p l i e d h o r i z o n t a l1
oads. More e l a b o r a t e m o d e l l i n g and measurements a r e needed i n o r d e r t o o b t a i nr e a l i s t i c p r e d i c t i o n s .
As f o r s p a t i a l s t r e s s d i s t r i b u t i o n , a number o f c a l c u l a t i o n methods a r e a1 ready a v a i l a b l e . F u r t h e r r e f i n e m e n t s o f i n p u t r u b b l e g e o m e t r i e s o r parameters a r e u n l i k e l y t o s u b s t a n t i a l l y improve p r e d i c t i o n s o f t h e " r i g i d body models". F i e l d and l a b o r a t o r y data, however, a r e needed t o v e r i f y t h e b a s i c assumptions.
Some 1 i m i t e d i n f o r m a t i o n f r o m model i c e b a s i n t e s t s i s now a v a i l a b l e . F u r t h e r t e s t s a r e needed t o examine t h e a p p r o p r i a t e s c a l i n g l a w s and t h e e f f e c t s o f r u b b l e c o n s o l i d a t i o n . O t h e r f a c t o r s r e q u i r i n g s t u d y i n c l u d e :
r u b b l e geometry, t h r e e - d i m e n s i o n a l e f f e c t s and t h e t y p e o f r u b b l e l b e r m
i n t e r f a c e .
An e f f o r t t o c o m p i l e and a n a l y z e d a t a a v a i l a b l e i n a number o f t h e A r c t i c P e t r o l eun O p e r a t o r s A s s o c i a t i o n (APOA) r e p o r t s woul d produce a m a n a g e a b l e and u s e f u l r e f e r e n c e . F u r t h e r f i e l d a n d l a b o r a t o r y i n v e s t i g a t i o n s s h o u l d i n c l u d e , i n a d d i t i o n t o s t r e s s measurements, r u b b l e c h a r a c t e r i z a t i o n and o b s e r v a t i o n o f d e f o r m a t i o n modes i n o r d e r t o g a i n a n u n d e r s t a n d i n g o f t h e r e 1 evant processes.
7. ACKNOWLEDGEMENTS
T h i s p a p e r i s a c o n t r i b u t i o n f r o m t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n , N a t i o n a l Reasearch C o u n c i l Canada.
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