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The failure of ice
Gold, L. W.
https://publications-cnrc.canada.ca/fra/droits
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NRC Publications Record / Notice d'Archives des publications de CNRC:
https://nrc-publications.canada.ca/eng/view/object/?id=e0e2941f-c59c-41ea-9112-244b716da462 https://publications-cnrc.canada.ca/fra/voir/objet/?id=e0e2941f-c59c-41ea-9112-244b716da462
ICE SYMPOSIUM 1970
REYKJAVIK
THE FAILURE O F ICE LA RUPTURE DE LA GLACE
D r . L . W . Gold, R e s e a r c h O f f i c e r , Division of Building R e s e a r c h , National R e s e a r c h Council of C a n a d a , O t t a w a , C a n a d a . I n f o r m a t i o n i s p r e s e n t e d on t h e c r a c k i n g a c t i v i t y t h a t o c c u r s i n c o l u m n a r
-
g r a i n e d i c e d u r i n g c r e e p and c o n s t a n t r a t e of s t r a i n t e s t s , when t h e l o a d i s applied p e r p e n d i c u l a r t o t h e long d i r e c t i o n of t h e g r a i n s . T h i s c r a c k i n g a c t i v i t y i s r e s p o n s i b l e f o r t h e o c c u r r e n c e of t e r t i a r y c r e e p o r f a i l u r e in u n i a x i a l c o m - p r e s s i o n t e s t s when t h e s t r e s s e x c e e d s about 1 2 b a r s . T h e b e h a v i o u r of i c e a r o u n d s t r u c t u r e s i s d i s c u s s e d w i t h r e f e r e n c e t o t h e r e s u l t s of t h e l a b o r a t o r y s t u d i e s . On prCsente d e s donnges s u r l a f i s s u r a t i o n de l a g l a c e5
s t r u c t u r e colonnaire a u c o u r s d ' e s s a i s d e fluage e t d e dCformations2
t a u x c o n s t a n tl o r s q u e l a c h a r g e e s t appliqu6e p e r p e n d i c u l a i r e m e n t
2
l a l o n g u e u r d e s g r a i n s .L a f i s s u r a t i o n e s t r e s p o n s a b l e du fluage t e r t i a i r e ou d e l a r u p t u r e a u c o u r s d e s e s s a i s s o u s c o m p r e s s i o n uniaxiale l o r s q u e l e s c o n t r a i n t e s e x c s d e n t 1 2 b a r s . On d i s c u t e du c o m p o r t e m e n t d e l a g l a c e a u t o u r d e s s t r u c t u r e s e n r a p p o r t a v e c l e s r e s u l t a t s obtenus e n l a b o r a t o i r e .
The determination of the maximum f o r c e that i c e can e x e r t against a s t r u c t u r e r e q u i r e s knowledge of the strength of i c e under various conditions of loading. F a i l u r e of i c e , under m o s t design loads of i n t e r e s t t o e n g i n e e r s , i s due t o a breakdown of i t s s t r u c t u r e by the formation of c r a c k s . A s e r i e s of observa- tions have been c a r r i e d out on the f a c t o r s controlling c r a c k formation in i c e , and the r o l e that i t plays in deformation and f a i l u r e (1, 2, 3 ) . T h e s e observations w e r e m a d e on columnar-grained i c e , subjected t o simple compression i n the d i r e c t i o n perpendicular t o the long direction of the g r a i n s . T h e r e was a m a r k e d tendency f o r the crystallographic b a s a l planes t o be p a r a l l e l t o the long direction of e a c h grain. This note p r e s e n t s some of the r e s u l t s of t h i s study that a r e of significance f o r both l a b o r a t o r y and field investigations of i c e p r e s s u r e s . CRACK FORMATION DURING C R E E P
C r a c k s w e r e observed t o f o r m in i c e when the constant c o m p r e s s i v e s t r e s s w a s gr,eater than about
6
b a r s . The c r a c k s w e r e long and n a r r o w , and usually a s s o c i a t e d with only one o r two g r a i n s . The plane of the c r a c k s tended to be p a r a l l e l to the applied s t r e s s , with the long direction in the long directionof the g r a i n s . When the s t r e s s w a s l e s s than about 10 b a r s , the cracking activity w a s confined mainly t o the p r i m a r y stage of c r e e p .
A m a r k e d change in c r e e p behaviour w a s observed over the s t r e s s range 10 t o 12 b a r s . The secondary c r e e p stage developed if the s t r e s s w a s l e s s than 10 b a r s . If the s t r e s s was g r e a t e r than about 12 b a r s , the t e r t i a r y o r a c c e l e r a t i n g c r e e p - r a t e stage developed d i r e c t l y f r o m the p r i m a r y stage within a c r e e p s t r a i n of 0.25 p e r cent. Cracking activity f o r t h e s e loads w a s continuous in the t e r t i a r y stage, and m a n y specimens developed fault zones approximately p a r a l l e l t o the planes of maximum s h e a r . The cracking activity appeared t o
concentrate within the fault zones, a s shown in f i g u r e 1.
The s t r a i n dependence of the a v e r a g e r a t e of cracking i s shown in figure 2 f o r t e s t s c a r r i e d out a t various s t r e s s e s a t a t e m p e r a t u r e of
-9.
5f.0. 5°C. The corresponding a v e r a g e c r e e p behaviour i s shown in figure 3. S i m i l a r cracking activity and c r e e p behaviour w a s observed a t t e m p e r a t u r e s of -4.8, -14.8 and -31.0°C.The observations indicated that the onset of the t e r t i a r y stage of c r e e p f o r s t r e s s g r e a t e r than 12 bars, w a s due t o the breakdown of the s t r u c t u r e by cracking activity. The c r a c k density observed a t the beginning of t h e secondary c r e e p stage f o r s t r e s s of 10 b a r s , was about 1.4 p e r cma. I t w a s about
1 . 6
1 F i g . 1. C r a c k f o r m a t i o n i n c o l u m - n a r - g r a i n e d i c e d e f o r m e d 1 p e r cent; s t r e s s = 1 9 . 6 b a r s . T e m p e r a t u r e = - 9 . 5 " C . F i g . 2. S t r a i n dependence of c r a c k - a N ing r a t e ,
-
,,
,
f o r given s t r e s s 0, b a r s . T e m p e r a t u r e = - 9 . 5 " C . F o r (T = 1 9 . 6 B a r s M a x i m u m C r a c k i n g R a t e = 3 9 4 0 ~ r a c k s l c m 2 / ~ n i t S t r a i n a t & = 1 4 . 5 ~ 1 0 - 4 0 1 0 20 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 S T R A I N x 1 0 4 3C R E E P S T R A I N
F i g . 3. S t r a i n dependence of a v e r a g e c r e e p r a t e f o r given s t r e s s . T e m p e r a t u r e = -9.5"C.
(Note the t r a n s i t i o n in behaviour in the s t r e s s range of 10 t o 12 b a r s .
p e r c m 2 a t the onset of the t e r t i a r y stage f o r s t r e s s of 1 1 . 8 b a r s
,
and about 0. 5 p e r c m 2 f o r the s a m e condition when the s t r e s s w a s 15.7 b a r s .CRACK FORMATION DURING CONSTANT RATE O F STRAIN
O b s e r v a t i o n s have a l s o been m a d e on the behaviour of columnar -grained i c e u n d e r conditions of constant r a t e of c r o s s - h e a d m o v e m e n t of the testing m a c h i n e . A s in the constant-load t e s t s , loads w e r e applied perpendicular t o the long d i r e c t i o n of the g r a i n s . The s t r e s s developed had a m a x i m u m in the range of s t r a i n of 5 x t o 1 5 x ( i . e . a n u p p e r yield s t r e s s ) . A second upper yield s t r e s s w a s o b s e r v e d f o r s t r a i n r a t e s i n the s a m e range a s those a s s o c i a t e d with constant c o m p r e s s i v e l o a d s of l e s s than 10 b a r s The second m a x i m u m i n the s t r e s s o c c u r r e d in t h e s t r a i n r a n g e of 1 t o 2 p e r cent; this range i s about the s a m e a s t h a t a s s o c i a t e d with the t r a n s i t i o n of the s e c o n d a r y c r e e p stage t o t h e t e r t i a r y s t a g e f o r constant c o m p r e s s i v e loads.
T h e s t r a i n r a t e s that w e r e applied covered t h e r a n g e of 1 . 2 x 10- S ~ C - ' to
1 . 7 x sec-'. A h c t i k - t o - b r i t t l e t r a n s i t i o n w a s o b s e r v e d f o r s t r a i n r a t e s of about 8 . 3 x
set-l.
The yield s t r e s s in t h i s range of s t r a i n r a t e w a s 70 t o100 b a r s .
-7 Crack formation occurred when the strain r a t e exceeded about 10
s e c l'
,
a rate that i s about equal to that associated with a constant compressives t r e s s of
6
b a r s . There was very considerable cracking activity p r i o r to and during yield for s t r a i n r a t e s giving an upper yield s t r e s s g r e a t e r than 12 b a r s .Cracking activity p r i o r t o yield in the constant s t r a i n rate t e s t s , and p r i o r to the t e r t i a r y stage in the c r e e p t e s t s , appeared to be distributed relativ- ely uniformly throughout the specimens. Yield in the constant-strain r a t e t e s t s appeared to be associated with the development of fault zones in the s a m e way a s for the t e r t i a r y stage during c r e e p ( s e e figure 1). These observations demon- strated that the s t r u c t u r a l instability associated with failure was induced by the breakdown of the structure by cracking activity. This fact has implications f o r the failure behaviour of ice around s t r u c t u r e s , and the use of laboratory r e s u l t s on the strength of ice f o r predicting the maximum f o r c e s that can occur.
IMPLICATIONS FOR LABORATORY AND FIELD TESTS.
Almost all information concerning the strength of i c e has been obtained f r o m unconfined compression t e s t s . The behaviour of columnar-grained ice for this condition of loading i s such a s to cause the s t r a i n during deformation and failure to be primarily perpendicular to the long direction of the grains. This strain behaviour would be inhibited under m o s t field conditions because of the biaxial s t r e s s state that would be induced. Such a biaxial s t r e s s would also inhibit the type of cracking activity causing failure in the c a s e of unconfined compression. F o r the case of complete l a t e r a l constraint, f o r example, c r u s h - ing failure would require crack formation perpendicular a s well a s p a r a l l e l t o the long axis of the columnar-grains if the failed ice i s to be displaced to the upper and bottom surfaces of the ice cover. Crushing strengths for complete l a t e r a l constraint would be g r e a t e r than those observed in unconfined c o m p r e s -
sion.
There appears t o be little evidence that the relatively l a r g e s t r e s s e s required t o fail ice in the laboratory a r e induced near s t r u c t u r e s . F r o m a design point of view, however, the possibility of such l a r g e s t r e s s e s under some field conditions cannot be ruled out a t this time. Ice covers would probably develop their maximum load on a structure when moving relative to i t a t a speed causing a r a t e of strain in the ductile-to-brittle transition range. A s e r i o u s load condition might develop, for example, at an isolated s t r u c t u r e frozen into the ice cover, i f the cover i s suddenly subjected t o a significant l a t e r a l displacement.
REFERENCES
( 1 ) Gold, L. W.
,
The Initial Creep of Columnar-Grained I c e , Can. Jour. P h y s . , 43, 1965, 1414-1422.-
(2) Gold, L. W . , Dependence of Crack Formation on Crystallographic Orientation for I c e , Can. Jour. P h y s . ,
-
4 4 , 1966, 2757-2764. ( 3 ) Gold, L. W.,
Crack Formation in Ice During C r e e p , Scripta Metall.,
3, 1969, 367-370.
-
D i s c u s s i o n by B. Ross on paper by L.W. Cold.
Are t h e c r a c k s observed i n t h e t e s t s n o t e d t o occur i n t h e c e n t r a l r e g i o n s of t h e specimens o r a r e t h e y i n i t i a t e d a t t h e l o a d i n g heads of t h e t e s t machine?
Reply t o q u e s t i o n by B. Ross.
The c r a c k s t h a t a r e formed p r i o r t o t h e o n s e t of t h e f a i l u r e c o n d i t i o n a r e uniformly d i s t r i b u t e d throughout t h e c e n t r a l r e g i o n of t h e specimen. It
was c l e a r t h a t t h e c o n s t r a i n t s imposed by t h e l o a d i n g p l a t e n s a f f e c t e d t h e d i s t r i b u t i o n of t h e c r a c k s n e a r t h e ends of t h e specimens. Some evidence was a l s o o b t a i n e d of a n edge e f f e c t ( i . e . t h e c r a c k d e n s i t y was s m a l l e r n e a r t h e edge t h a n i n t h e c e n t r a l r e g i o n ) . The o b s e r v a t i o n s on t h e c a r c k i n g a c t i v i t y were made over t h e c e n t r a l p o r t i o n of each specimen where t h e c r a c k i n g a c t i v i t y appeared t o be uniform.
D i s c u s s i o n by C. F r a n k e n s t e i n on paper by L.W. Cold.
Did t h e c r a c k s occur a l o n g t h e Grain, Boundries?
Reply t o q u e s t i o n by C. F r a n k e n s t e i n .
We observed b o t h t r a n s c r y s t a l l i n e and g r a i n boundary c r a c k s . The r e l a t i v e p r o p o r t i o n of t h e s e two t y p e s of c r a c k s a p p e a r s t o depend upon t h e s t r a i n r a t e and a s s o c i a t e d s t r e s s .
D i s c u s s i o n by S. Hanagud on paper by L.W. Cold.
I n y o u r p a p e r you mentioned t h a t c r a c k s a r e i n i t i a t e d under t e n s i l e l o a d i n g
at a s t r e s s below t h e l e v e l a t which complete f a i l u r e would t a k e p l a c e . I
would l i k e t o h o w t h e s t r e s s a t which t h e s e c r a c k s a r e i n i t i a t e d a r e t h e i r s i z e . Is t h e r e any e f f e c t of t h e s e c r a c k s ?
Also I s h a l l a p p r e c i a t e i f you can e l a b o r a t e on t h e f a i l u r e s t r e s s under s t r e a m r a t e .
Reply t o q u e s t i o n by S. Hanagud.
I n t e n s i l e t e s t s , c r a c k s were observed t o form f o r s t r e s s equal t o These c r a c k s were small, u s u a l l y l e s s t h a n 1 mm by 1 cm i n
a r e a . Some c r a c k s were observed t o d e g e n e r a t e i n t o a p l a n e of small
c a v i t i e s w i t h c o n t i n u e d deformation. The c r a c k s d i d not appear t o p a r t i c i p a t e i n t h e f i n a l f a i l u r e e v e n t , a l t h o u g h t h i s o c c u r r e d s o r a p i d l y t h a t i t w a s not p o s s i b l e t o s t a t e p o s i t i v e l y t h a t f a i l u r e was n o t due t o t h e p r o p a g a t i o n of a p r e - e x i s t i n g crack.
A l l of our t e s t s at c o n s t a n t r a t e of s t r a i n have been c a r r i e d out i n compression. I n t h e d u c t i l e r a n g e of behaviour, t h e maximum y i e l d s t r e s s i n c r e a s e d w i t h r a t e of s t r a i n a c c o r d i n g t o a power l a w
r e l a t i o n s h i p . T h i s dependence w a s found t o b e t h e following:
-1
where
i
i s i n min..
We have not extended our o b s e r v a t i o n s f a r enough i n t h e b r i t t l e r a n g e of behaviour t o determine t h e s t r a i n r a t e dependence of t h e b r i t t l e s t r e n g t h .D i s c u s s i o n by C. Cochard on paper by L.W. Gold.
Can you t e l l me i f t h e c r o s s - s e c t i o n a l dimension of t h e c r y s t a l s h a s an i n f l u e n c e on t h e number and t h e r e p a r t i t i o n of t h e cracks?
Reply t o q u e s t i o n by C. Cochard.
Most of o u r s t u d i e s have been c a r r i e d out on i c e w i t h g r a i n s i z e of 1 t o 3 mm. A s t h e c r a c k s a r e a s s o c i a t e d w i t h e i t h e r one o r two g r a i n s ,
i t would b e expected t h a t as t h e g r a i n s i z e i n c r e a s e d , t h e number of c r a c k s p e r u n i t a r e a would d e c r e a s e and t h e i r s i z e i n c r e a s e . T h i s appeared t o b e t h e c a s e f o r specimens t h a t we p r e p a r e d from n a t u r a l columnar-grained i c e of l a r g e r g r a i n s i z e .
