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Model tests of the ridge-building process in ice
Timco, G. W.; Sayed, M.
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Model Tests of the Ridge-Building
Process in Ice
by G.W. Timco and M. Sayed
Appeared in
Proceedings of IAHR Ice Symposium 1986
lowa City, lowa, 18-22 August 1986
Vol,
I,
p. 591 -682
(IRC Paper No. 1425)
I
L I B R A R Y
Reprinted with permission
Price $2.00
NRCC 2671
7
B I B L I O T H ~ Q U E
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l e s
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h o r i z o n t a l e m e n t .
1,a h a u t e u r s u r g l a c e l i m i t e (VISA) e t
1
a p r o f o n d e u r s o u s g l a c e l i m i t e (HkR) G t a i e n t p r o p o r t i o n n e l l e s
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e s s a i s d e s r a p p o r t s HsR/h
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=17,9
+
1,4.
IAHR Ice Symposium 1986
Iowa City, Iowa
HODEL TESTS OF THE RIDGE-BUILDIIG PROCESS IN ICE
G. W. Timco and M. Sayed Research O f f i c e r s
N a t i o n a l Research C o u n c i l Canada o f Canada
A model t e s t s t u d y h a s been done t o i n v e s t i g a t e t h e r i d g e - b u i l d i n g p r o c e s s -
es i n ice. Ridge g e o m e t r i e s and t h e a s s o c i a t e d f o r c e s have been d e t e r m i n e d t h r o u g h o u t t h e f o r m a t i o n o f p r e s s u r e r i d g e s . The r e s u l t s i n d i c a t e t h a t t h e f o r c e s appear to be p r o p o r t i o n a l t o t h e s a i l and k e e l h e i g h t s o f t h e r i d g e r a i s e d to a power g r e a t e r t h a n one. I n i t s f o r m a t i o n , t h e s a i l h e i g h t and k e e l d e p t h i n c r e a s e d u n t i l t h e y r e a c h e d l i m i t i n g v a l u e s whereupon t h e y grow h o r i z o n t a l l y . The l i m i t s a i l h e i g h t (H,Q) and l i m i t k e e l d e p t h (HkQ) were p r o p o r t i o n a l t o t h e ice t h i c k n e s s (h) w i t h r a t i o s averaged o v e r a l l t e s t s o f Hsk/h = 3.5 20.7 and HkR/h = 17.9 f 1.4.
1.0 Introduction
The mechanics o f t h e f o r m a t i o n o f p r e s s u r e r i d g e s i n ice i s p o o r l y under- s t o o d due t o i t s c o m p l e x i t y , t h e d i f f i c u l t y i n f i e l d o b s e r v a t i o n s o f t h e b u i l d i n g p r o c e s s , and t h e i n a b i l i t y t o measure t h e r i d g e - b u i l d i n g f o r c e s i n n a t u r e . lb d a t e , f i e l d s t u d i e s (e.g. Wright and McGonigal, 1980; Tucker and Govoni, 1981) have been c o n d u c t e d t o d e t e r m i n e t h e morphology o f e x i s t - i n g r i d g e s . There have been no r e p o r t e d s t u d i e s o f (measured) l o a d s a s s o - c i a t e d w i t h i c e r i d g i n g i n n a t u r e o r i n t h e l a b o r a t o r y . Knowledge i n t h i s a r e a is i m p o r t a n t , s i n c e t h e r i d g e b u i l d i n g p r o c e s s may l i m i t t h e l o a d which an ice s h e e t c a n e x e r t on a s t r u c t u r e .
To g a i n some i n s i g h t i n t o t h i s problem, a s e r i e s o f t e s t s were performed t o model t h e r i d g e b u i l d i n g p r o c e s s e s . The development o f r i d g e p r o f i l e s , p o r o s i t y and a s s o c i a t e d f o r c e s were examined. The p a r a m e t e r s which were v a r i e d i n c l u d e t h e ice t h i c k n e s s and t h e ice s t r e n g t h . I n t h i s p a p e r , t h e e x p e r i m e n t a l p r o c e d u r e s a r e d e s c r i b e d , and t h e r e s u l t s o f t h e t e s t series a r e p r e s e n t e d i n both g r a p h i c a l and t a b u l a r form. The r e s u l t s g i v e i n f o r m a t i o n on t h e shape, geometry and b u i l d i n g f o r c e s o f f l o a t i n g ice
r i d g e s .
2.0 Experimental
The t e s t s were conducted i n t h e ice t a n k i n t h e H y d r a u l i c s I i r b o r a t o r y o f
NRC i n Ottawa ( P r a t t e and Timco, 1981). The t a n k is 21 m l o n g by 7 m wide by 1.2 m deep. An 8-tonne c a r r i a g e s p a n s t h e width o f t h e tank and pro- v i d e s a means o f moving a s t r u c t u r e r e l a t i v e t o t h e ice a t a uniform r a t e . The t a n k is housed i n a l a r g e c o l d chamber and r e f r i g e r a t e d model ice is
used. I n t h i s test s e r i e s , a new t y p e o f model ice was used. T h i s new model i c e
-
termed EG/AD/S ice-
is grown from an aqueous s o l u t i o n con- t a i n i n g t h r e e c h e m i c a l s-
e t h y l e n e g l y c o l ( E G ) , a l i p h a t i c d e t e r g e n t (AD)and s u g a r ( S ) . Each o f t h e s e c h e m i c a l s p l a y s an i m p o r t a n t r o l e i n g i v i n g t h e model i c e its s p e c i a l p r o p e r t i e s . The ice is s i n g l e - l a y e r e d and columnar i n s t r u c t u r e with e x c e l l e n t s c a l i n g o f t h e mechanical p r o p e r t i e s o f s e a ice i n c l u d i n g f l e x u r a l p r o p e r t i e s , u n i - a x i a l and 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 , f a i l u r e e n v e l o p e and f r a c t u r e t o u g h n e s s (see Timco, 1986 f o r f u l l d e t a i l s ) .
For t h e t e s t program, it was d e c i d e d t o s i m p l i f y t h e geometry t o r e p r e s e n t a 2-dimensional s i t u a t i o n (see F i g u r e 1 ) . The a p p a r a t u s c o n s i s t e d o f a
Figure 1 Schematic o f test set-up i n plan view showing the *sided .chutem and the p o s i t i o n of video cameras, etc.
3-sided " c h u t e " which was mounted on t h e f r o n t f a c e o f t h e main c a r r i a g e . The backboard of t h e c h u t e , c o n s t r u c t e d from p a i n t e d plywood, was 1.27 m wide and 1.27 m high and was i n s t r u m e n t e d t o measure t h e t o t a l h o r i z o n t a l l o a d a c t i n g on it. The backboard s e r v e d a s an o b s t a c l e i n i t i a l l y t o form t h e r i d g e , and was c o n s i d e r e d t o be a p l a n e o f symmetry f o r t h e r i d g e . The two s i d e s o f t h e c h u t e were c o m p l e t e l y s e p a r a t e from t h e backboard and were c o n s t r u c t e d from 1.22 m x 1.22 m s h e e t s o f p l e x i g l a s s (marked w i t h a 5 c m x 5 cm g r i d ) a l l o w i n g a c l e a r view of h t h t h e s a i l and k e e l o f t h e r i d g e t h r o u g h o u t t h e whole r i d g e b u i l d i n g p r o c e s s ( s e e F i g u r e 2 ) . With t h i s a p p a r a t u s i t was p s s i b l e t o measure t h e r i d g e - b u i l d i n g l o a d s a c c u r a t e l y ,
t o p r o v i d e a means o f p r o f i l i n ; t h e r i d g e with t i n e , and t o overcome prob- lems due t o i c e r a f t i n g .
Figure 2 Photograph o f t e s t set-up showing a ridge firming i n the 'chutem.
During t e s t i n g , t h e c a r r i a g e was advanced t h e f u l l l e n g t h o f t h e i c e t a n k i n one c o n t i n u o u s run a t a c o n s t a n t r a t e o f 0.01 IPS-'. The i c e i n f r o n t was c u t t o t h e width of t h e c h u t e immediately p r i o r t o e n t e r i n g it. The i c e d e b r i s o u t s i d e t h e c h u t e was pushed c l e a r t o p e r m i t o b s e r v a t i o n below t h e f l u i d s u r f a c e . T m video cameras were used t o r e c o r d t h e t e s t s . One camera was mounted t o g i v e a s i d e view t h r o u g h one o f t h e p l e x i g l a s s
s h e e t s , and t h e o t h e r camera was mounted on t h e s e r v i c e c a r r i a g e ( i n f r o n t o f t h e main c a r r i a g e ) t o g i v e a f r o n t a l view. Both cameras were used t o i d e n t i f y t h e d i f f e r e n t r i d g e - b u i l d i n g p r o c e s s e s and had t i m e i n d i c a t o r s t o monitor t h e development o f t h e r u b b l e p r o f i l e s a s a f u n c t i o n o f t i m e . A t o t a l o f seven d i f f e r e n t ice s h e e t s were grown with d i f f e r e n t t h i c k n e s s e s and s t r e n g t h s ( T a b l e 1). For one t e s t , a number o f 10 c m l o n g " f l a w s " were c u t i n t h e i c e t o a d e n s i t y o f 16 m-2. T h i s allowed a comparison o f t h e r i d g e b u i l d i n g f o r c e s o f a "flawed" i c e s h e e t w i t h t h o s e o f uniform l e v e l ice s h e e t s o f t h e same t h i c k n e s s e s and s t r e n g t h s .
T e s t Ice T h i c k n e s s F l e x u r a l S t r e n g t h ( m ) (kPa) 1
.
0 3 2 12 2 . 0 4 7 5 4 3 . 0 2 8 6 0 4 . 0 1 3 36 5 . 0 4 9 4 1 6 0 2 9 9 6 7 * . 0 3 0 4 8*
Ice s h e e t was flawed w i t h 10 c m l o n g c u t s . 3.0 Results and DiscussionAt t h e s t a r t o f a t e s t , t h e ice s h e e t f a i l e d a g a i n s t t h e v e r t i c a l back- p l a t e , u s u a l l y i n buckling. Broken ice b l o c k s moved m o s t l y under t h e ice s h e e t i n f r o n t of t h e advancing p l a t e . The b l o c k s wsuld t h e n g r a d u a l l y a c c u m u l a t e t o form a k e e l and a r e l a t i v e l y s m a l l s a i l . A f t e r t h a t i n i t i a l s t a g e , t h e ice s h e e t f a i l e d sometimes a g a i n s t t h e r u b b l e i n b u c k l i n g o r bending downwards. A t o t h e r t i m e s t h e ice s h e e t s l i d (or r o d e ) o v e r t h e r u b b l e t o f a i l a g a i n s t t h e b a c k p l a t e i n b u c k l i n g , c r u s h i n g , bending upwards o r bending downwards. F a i l u r e o f t h e ice s h e e t was uniform a c r o s s t h e w i d t h o f t h e chute. Although b u c k l i n g o r bending o c c u r r e d o v e r p a r t o f t h e width a few t i m e s , no p a t t e r n of "nonsimultaneous" o r multi-mode f a i l u r e was observed. P r o f i l e s o f t h e r u b b l e were a l s o m o s t l y t m - d i m e n s i o n a l .
E a r l y i n t h e t e s t , both t h e s a i l and k e e l grew i n t h e v e r t i c a l and h o r i z o n -
t a l d i r e c t i o n s . I n l a t e r s t a g e s , v e r t i c a l growth became n e g l i g i b l e whereas
h o r i z o n t a l growth c o n t i n u e d . T h i s produced a l i m i t i n g s a i l h e i g h t (H,Q)
and a l i m i t i n g k e e l depth (HkQ) a s shown i n F i g u r e 3. Because o f s p a c e
l i m i t a t i o n s , examples o f t h e development o f t h e r u b b l e p r o f i l e s from o n l y two t e s t s a r e shown. These two s e t s c l e a r l y i l l u s t r a t e most o f t h e f e a - t u r e s o b s e r v e d i n o t h e r t e s t s and r e p r e s e n t t h e c a s e s o f i n t a c t and p r e c u t
i c e s h e e t s . The k e e l was always much l a r g e r t h a n t h e s a i l and e x t e n d e d
h o r i z o n t a l l y below t h e i c e s h e e t . S l o p e s o f t h e k e e l changed f r e q u e n t l y
d u r i n g t h e t e s t . A s t e e p s l o p e would u s u a l l y d e v e l o p , t h e n r u b b l e would
flow suddenly t o form a f l a t t e r slope. Sometimes t h e k e e l had a s t e p p e d
s h a p e w i t h s t e e p and f l a t p a r t s . S a i l h e i g h t and h o r i z o n t a l e x t e n t were
always s m a l l ( r e l a t i v e t o t h e i c e block s i z e ) which made it d i f f i c u l t t o
d e t e r m i n e a c c u r a t e l y its geometry. T h i s a l s o c a u s e d a n o c c a s i o n a l momen-
t a r y i n c r e a s e i n t h e s a i l h e i g h t above its l i m i t i n g value. The v a l u e s o f
l i m i t i n g s a i l h e i g h t and k e e l d e p t h show c o n s i s t e n t dependence o n ice s h e e t
t h i c k n e s s ( s e e Table 2 ) . The r e s u l t s a r e i n good agreement w i t h f i e l d
measurements o f Wright and McGonigal (1980) and Tucker and Govoni (1981). The p r e s e n t r a t i o o f k e e l d e p t h t o s a i l h e i g h t may be a f f e c t e d by both t h e d i f f i c u l t y i n t h e measurement o f t h e s a i l h e i g h t and t h e s p e c i f i c g r a v i t y
o f model ice (0.95) which is l a r g e r t h a n t h a t o f s e a ice.
The volume c o n c e n t r a t i o n
(5) o f t h e r i d g e c a n be d e t e r m i n e d a t any
t i m e ( t )by 6 = shwt/V u s i n g t h e r i d g e p r o f i l e (or measured volume V), t h e ice
t h i c k n e s s ( h ) , t h e width o f t h e c h u t e ( w ) and t h e speed (s) o f t h e c a r -
r i a g e . E s t i m a t e s of t h e a v e r a g e ice c o n c e n t r a t i o n o f t h e r i d g e a r e g i v e n
f o r each test i n T a b l e 2. The most r e l i a b l e e s t i m a t e s were o b t a i n e d d u r i n g
t h e i n t e r m e d i a t e s t a g e s o f each t e s t , but t h e s e s t i l l showed some s c a t t e r .
For t h e s e t e s t s , 6 ranged from 0.55 t o 0.89 w i t h a n a v e r a g e v a l u e o f 0.73
.
F i g u r e 4 shows t h e f o r c e r e c o r d e d o n t h e b a c k p l a t e d u r i n g t h e two t e s t s i n d i c a t e d i n F i g u r e 3. These r e c o r d s r e p r e s e n t r i d g e b u i l d i n g f o r c e s a n d t h e f o r c e s a s s o c i a t e d with t h e i c e s h e e t s l i d i n g o v e r t h e r u b b l e t o f a i l a g a i n s t t h e b a c k p l a t e . A l l o f t h e l a r g e s p i k e y f o r c e s belong t o t h e l a t t e r
c a s e . S i n c e t h e s e high f o r c e s a r e an a r t i f a c t o f t h e test p r o c e d u r e (and
a r e u n l i k e l y t o o c c u r i n n a t u r e ) t h e y were n e g l e c t e d i n t h e a n a l y s i s . T h i s d o e s not i n f l u e n c e t h e modelling o f t h e r i d g e - b u i l d i n g p r o c e s s .
W A T E R L E V E L
Figure 3 S a i l aod keel p r o f i l e s a s a function of time ( i n minutes)
5 1 0
TlME ( M I N U T E S )
0 5 10 15 20
TlME ( M I N U T E S )
Figure 4 Force-time records ( t o t a l force divided by chute width) for
(a) Test #3 and @) Test #7 showing the f o r c e s a s s o c i a t e d with t h e various f a i l u r e modes o f the ice. The e l l i p s e s i n d i c a t e the values chosen for the ridge building forces.
TABLE 2
T e s t L i m i t i n g L i m i t i n g L i m i t i n g Normalized Values Average
F o r c e S a i l Height Keel Depth Ice
*
* *
***
Concen- (N/m) Hsp. (m) Hki (m) H s a h H k a h Hkg/Hsa t r a t i o n 1 512 . 1 5 . 6 5 4. 7 20.3 4. 3 0.79 2 787 - 1 7 . 8 0 3. 6 17. 0 4. 7 0.65 3 102 .075 50 2. 7 18.2 6. 7 0.68 4 7 9 . 0 5 . 2 3 3.8 17.7 4. 6 0.78 5 433.
175 . 8 0 3. 6 16.5 4. 6 0.89 6 27 6 . 1 0 . 5 5 3. 4 19.0 5. 5 0.55 7 138 . 0 7 5 . 5 0 2. 5 16.7 6. 7 0.75 Average Values 3. 5 17.9 5. 3 0.73*
R a t i o o f l i m i t i n g s a i l h e i g h t t o i c e s h e e t t h i c k n e s s .**
R a t i o o f l i m i t i n g k e e l d e p t h t o ice s h e e t t h i c k n e s s .***
R a t i o o f l i m i t i n g k e e l d e p t h t o l i m i t i n g s a i l h e i g h t .Each f o r c e r e c o r d was examined t o g e t h e r w i t h t h e v i d e o r e c o r d i n o r d e r t o
r e l a t e t h e f o r c e s t o t h e modes o f ice d e f o r m a t i o n . R i d g e - b u i l d i n g f o r c e s were c h o s e n a s t h o s e o c c u r r i n g when t h e ice s h e e t was pushing a g a i n s t t h e rubble. The a v e r a g e o f t h e f o r c e r e c o r d e d o v e r a few s e c o n d s was t a k e n a s t h e a p p r o p r i a t e v a l u e t h a t c a u s e d t h e d e f o r m a t i o n o f t h e rubble. A number o f t h e s e r i d g e - b u i l d i n g e v e n t s were c h o s e n from each test. When combined w i t h t h e r i d g e p r o f i l e a t t h e same t i m e , t h e s e measured l o a d s g i v e t h e r e l a t i o n s h i p between f o r c e , s a i l h e i g h t and k e e l depth. The r e s u l t s from a l l tests a r e shown i n F i g u r e 5. Although t h e r e is s c a t t e r ( p r o b a b l y due
t o d i f f e r e n c e s i n ice s t r e n g t h , ice t h i c k n e s s and s i d e - w a l l f r i c t i o n ) , t h e r e s u l t s i n F i g u r e 5 i n d i c a t e t h a t ice f o r c e is p r o p o r t i o n a l t o r u b b l e d e p t h and h e i g h t r a i s e d t o a power g r e a t e r t h a n one. To a v o i d o b s c u r i n g t h e r e - s u l t s , no c u r v e f i t t i n g o r n o r m a l i z a t i o n o f t h e measurements was attemp- ted. I t s h o u l d be noted though t h a t r u b b l e bulk d e n s i t y o r u n i t weight c o u l d be used i n n o r m a l i z i n g t h e f o r c e s ( b u t not t h e f l e x u r a l s t r e n g t h o f t h e ice s i n c e it h a s no d i r e c t p h y s i c a l s i g n i f i c a n c e i n t h e p r e s e n t c a s e ) .
0
0 0.1 0 . 2 0.3 0.4 0.5 0.6 0.7 0.8 K E E L D E P T H ( X I O R S A l L H E I G H T
(a)
(rn)Figure 5 Force versus keel depth (x) and sail height (m). The test
numbers are indicated beside each data point.
1 0 0 0
L I M I T I N G K E E L D E P T H ( X ) O R S A l L H E I G H T
(a)
( m )Figure 6 Force versus l i m i t i n g k e e l depth (x) and sail height (m)
.
The r e s u l t s r e p r e s e n t i n g o n l y t h e l i m i t i n g s a i l h e i g h t and k e e l d e p t h a r e shown i n F i g u r e 6. The f o r c e s c o r r e s p o n d t o c a s e s when r u b b l e a p p e a r e d t o grow h o r i z o n t a l l y . These f o r c e s show l i t t l e s c a t t e r and form a lower bound t o t h e f o r c e s measured d u r i n g v a r i o u s s t a g e s o f r i d g e d e v e l o p n e n t (i.e. t h o s e shown i n F i g u r e 5).
4.0 Concluding Remarks
Model t e s t s were c o n d u c t e d t o o b s e r v e t h e p r o c e s s e s o f ice r u b b l e r i d g i n g . Ridge g e o m e t r i e s , and t h e a s s o c i a t e d f o r c e s were determined. The s a i l and k e e l s h a p e s underwent s i g n i f i c a n t c h a n g e s a s t h e y developed. One p a t t e r n a p p e a r e d t o be t h e p e r i o d i c change o f k e e l s l o p e . Also
a
s t e p p e d k e e l w i t h s t e e p and f l a t p a r t s was common. No c l e a r s h a p e s o f t h e s a i l s were d i s - c e r n e d because o f t h e i r r e l a t i v e l y s m a l l s i z e s .The ice s h e e t f a i l e d i n a number o f modes, sometimes a g a i n s t t h e r u b b l e , whereas i n o t h e r i n s t a n c e s it s l i d over t h e s a i l to f a i l a g a i n s t t h e back- p l a t e . The s a i l h e i g h t and k e e l d e p t h i n c r e a s e d i n each test t o r e a c h l i m i t i n g v a l u e s whereupon t h e y a p p e a r e d t o grow h o r i z o n t a l l y .
F o r c e s c o r r e s p o n d i n g t o r u b b l e d e f o r m a t i o n were o b t a i n e d by examining t h e f o r c e - t i m e and video r e c o r d s . Only f o r c e s r e c o r d e d when t h e ice s h e e t was p r e s s i n g a g a i n s t t h e r u b b l e were used. These f o r c e s appear t o be pro- p o r t i o n a l t o t h e k e e l d e p t h and s a i l h e i g h t r a i s e d t o a power g r e a t e r t h a n one.
I c e t h i c k n e s s and s t r e n g t h were changed between tests i n o r d e r t o produce a wide range o f f o r c e s . There was no c l e a r dependence o f r u b b l e b e h a v i o u r o n t h e s e v a r i a b l e s . The l i m i t s a i l h e i g h t and k e e l d e p t h , however, were pro- p o r t i o n a l t o ice t h i c k n e s s i n agreement w i t h f i e l d o b s e r v a t i o n s .
5.0 k k n o w l e d g e m e n t s
The a u t h o r s m u l d l i k e t o thank R. F r e d e r k i n g f o r h e l p f u l d i s c u s s i o n s . The t e c h n i c a l a s s i s t a n c e o f R. Bowen and J. N e i l t h r o u g h o u t t h e whole t e s t program is g r e a t l y a p p r e c i a t e d .
6.0 References
P r a t t e , B.D. and GW. Timco, 1981. "A new model b a s i n f o r t h e t e s t i n g o f i c e - s t r u c t u r e i n t e r a c t i o n s " . Proc. POAC 81, WIL 11, Quebec C i t y , Canada, p. 857-866.
Timco, GW., 1986. "EG/AD/S: A new t y p e o f model ice f o r r e f r i g e r a t e d towing tanks". Cold Regions S c i e n c e and Technology
2,
p. 175-195. Tucker, W.B. I11 and J.W. Govoni, 1981. "Morphological i n v e s t i g a t i o n s o ff i r s t - y e a r s e a ice p r e s s u r e r i d g e s a i l s " . Cold B g i o n s S c i e n c e and Technology
5,
p. 1-12.Wright, B.R and R McGonigal, 1980. " F e a t u r e s o f f i r s t and m u l t i - y e a r r i d g e s " . Proc. o f Workshop on Sea Ice Ridges and P i l e - u p , C a l g a r y , A l t a . , 22-24 O c t o b e r , NRC Tech. Memo No. 134, J a n u a r y , 1982, p. 2-8.
