Compressive behavior of Beaufort Sea ice under vertical and horizontal loading

(1)

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Compressive behavior of Beaufort Sea ice under vertical and horizontal

loading

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Ser

TH1

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1-1-92

1

31. National Research

Conseil national

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COMPRESSIVE BEHAVIOR OF BEAUFORT SEA ICE UNDER

VERTICAL AND HORIZONTAL LOADING

by

R.M.W. Frederking and G.W.

Timco

ANALYZED

'- I

Reprinted from

Proceedings of the Third International Offshore Mechanics

and Arctic Engineering Symposium, Volume 11

1, 1984

p. 145

-

149 L I B R A R Y

DBR Paper No. 1192

Division of Building Research

(3)

Le p r e s e n t r a p p o r t f a i t B t a t d ' e x p e r i e n c e s s u r l e t e r r a i n

e f f e c t u ' e e s s u r d e s k c h a n t i l l o n s c y l i n d r i q u e s e t p r i s m a t i q u e s

o r i e n t b p a r a l l e l e m e n t e t p e r p e n d i c u l a i r e m e n t

1 l a couche d e

g l a c e .

On

a f a i t v a r i e r l a v i t e s s e d e deformation d e

2 x 105 s-1

1

5

x s-l;

l a c h a r g e

e t l a d'eformation e t a i e n t

c o n t r a l ' e e s d e f q o n continue.

La r e s i s t a n c e d e s B c h a n t i l l o n s

v e r t i c a u x d e g l a c e columnaire 6 t a i t e n v i r o n t r o i s f o i s p l u s

grande que c e l l e d e s B c h a n t i l l o n s h o r i z o n t a w .

Pour l e s deux

6 c h a n t i l l o n s , l a r b i s t a n c e augmentait d e l a mSme £%on l o r s q u e

l a v i t e s s e d e d d f o r m a t i o n a u g m e n t a i t .

P a r c o n t r e , l a

ddformation a u p o i n t d e r u p t u r e d t a i t s i m i l a i r e pour l e s d e w

o r i e n t a t i o n s

e t

n e d e p e n d a i t p a s d e l a v i t e s s e d e d s o r m a t i o n .

La r i g i d i t ' e du s y s t b e d ' e s s a i a 8tB mesur*& e t une t e c h n i q u e

d e p r g v i s i o n d e s d e f o r m a t i o n s e s t d d c r i t e .

On

s e s e r t d e s

v a l e u r s mesur'ees d e l a r ' e s i s t a n c e u n i a x i a l e pour p r s v o i r l a

r e s i s t a n c e dans l e c a s d'une c h a r g e a p p l i q u k e s o u s 6 t r e i n t e .

(4)

COMPRESSIVE BEHAVIOR OF BEAUFORT SEA ICE UNDER VERTICAL AND HORIZONTAL LOADING

R. M. W. Fredgrking Division of Building Research

G. W. Timw

Division of Mechanical Engineering National Research Council Canada

Onawa. Ontario. Canada

ABSTRACT

F i e l d e x p e r i m e n t s on c y l i n d r i c a l and p r i s m o i d a l specimens o r i e n t e d i n t h e p l a n e of t h e i c e c o v e r and p e r p e n d i c u l a r t o i t a r e r e p o r t e d . Nominal s t r a i n r a t e was v a r i e d from 2 x l o m 5 s - I t o 5 x s-I; b o t h l o a d and s t r a i n were monitored c o n t i n u o u s l y . The s t r e n g t h of v e r t i c a l specimens of u n a l i g n e d c o l u m n a r g r a i n e d i c e was about t h r e e t i m e s t h a t of h o r i z o n t a l specimens. Both o r i e n t a t i o n s showed s i m i l a r i n c r e a s e i n s t r e n g t h w i t h i n c r e a s i n g s t r a i n r a t e . On t h e o t h e r hand, s t r a i n a t y i e l d f o r b o t h specimen o r i e n t a t i o n s was s i m i l a r and showed no dependence on s t r a i n r a t e . T e s t s y s t e m s t i f f n e s s was measured and a t e c h n i q u e f o r p r e d i c t i n g s t r a i n s i s d e s c r i b e d . The measured u n i a x i a l s t r e n g t h r e s u l t s a r e u s e d t o p r e d i c t s t r e n g t h u n d e r t h e c o n f i n e d l o a d i n g c o n d i t i o n . INTRODUCTION Knowledge of t h e mechanical p r o p e r t i e s of s e a i c e p r o v i d e s a b a s i s f o r e s t i m a t i n g d e s i g n i c e l o a d s on o f f s h o r e s t r u c t u r e s . When a n i c e c o v e r impinges on any s t r u c t u r e a complex s t r e s s f i e l d i s s e t u p w i t h i n t h e i c e , s o t h a t a f a i l u r e c r i t e r i o n f o r i c e under m u l t i - a x i a l l o a d i n g i s e s s e n t i a l . R a l s t o n

(1)

and R e i n i k e

(2)

have d e m o n s t r a t e d t h e a p p l i c a t i o n of a f a i l u r e c r i t e r i o n , t o g e t h e r w i t h p l a s t i c i t y t h e o r y , t o t h e e s t i m a t i o n of i c e l o a d s f o r p a r t i c u l a r c o n d i t i o n s . More r e c e n t l y , Timco and F r e d e r k i n g

(3,

6 )

have determined s t r e n g t h f o r c o n f i n e d compression of b o t h c o l u m n a r g r a i n e d and g r a n u l a r s e a i c e and have e v a l u a t e d t h e c o r r e s p o n d i n g f a i l u r e c r i t e r i a . E v a l u a t i n g a f a i l u r e c r i t e r i o n g e n e r a l l y r e q u i r e s u n i a x i a l s t r e n g t h d a t a f o r specimens o r i e n t ' e d i n s e v e r a l d i r e c t i o n s i n t h e i c e c o v e r a s w e l l a s s t r e n g t h d a t a from b i a x i a l l o a d i n g . Only l i m i t e d b i a x i a l l o a d i n g d a t a a r e a v a i l a b l e , however, b e c a u s e of t h e e x p e r i m e n t a l d i f f i c u l t i e s of performing s u c h t e s t s . As a f i r s t a p p r o x i m a t i o n u n i a x i a l compressive t e s t s on v e r t i c a l and h o r i z o n t a l specimens can g i v e some i n d i c a t i o n of e x p e c t e d m l t i - a x i a l s t r e n g t h . T e s t r e s u l t s of s t r e n g t h a s a f u n c t i o n of s t r a i n r a t e f o r v e r t i c a l and h o r i z o n t a l specimens of f i r s t - y e a r s e a i c e

w i l l b e p r e s e n t e d and a p p l i e d t o a n e s t i m a t i o n of t h e c o n f i n e d compressive s t r e n g t h .

The mechanical p r o p e r t i e s measured a r e a f u n c t i o n of b o t h t h e t e s t i n g methods and t h e m a t e r i a l

c h a r a c t e r i s t i c s of t h e i c e . Two d i f f e r e n t l o a d i n g systems and specimen c o n f i g u r a t i o n s were u s e d , t h e b e t t e r t o d e f i n e t h e i r e f f e c t on measured s t r e n g t h p r o p e r t i e s . Loading s y s t e m s t i f f n e s s was measured i n b o t h c a s e s . A t e c h n i q u e f o r e s t i m a t i n g specimen s t r a i n from t h e load-time h i s t o r y of t h e specimen and t h e l o a d i n g s y s t e m s t i f f n e s s w i l l b e p r e s e n t e d .

SPECIMEN ACQUISITION AND PREPARATION

During a f i e l d t r i p t o t h e B e a u f o r t Sea, 3-6 May 1982, a number of b l o c k s and v e r t i c a l a n d h o r i z o n t a l c o r e s were c u t from a l a r g e r a f t e d p i e c e of i c e i n t h e r u b b l e f i e l d a b o u t 40 rn w e s t of T a r s i u t I s l a n d , a c a i s s o n - r e t a i n e d i s l a n d i n t h e B e a u f o r t Sea. Daytime maximum a i r t e m p e r a t u r e s were -5OC. The samples were packed i n p l a s t i c bags and c a r d b o a r d boxes and flown by h e l i c o p t e r t o Tuktoyaktuk, where t h e y were t a k e n t o a s m a l l l a b o r a t o r y and s t o r e d a t a t e m p e r a t u r e of - l l ° C f 1°C.

Both p r i s m o i d a l and c y l i n d r i c a l specimens w e r e made. The c y l i n d r i c a l ones were p r e p a r e d by c u t t i n g t h e c o r e samples t o p a r t i c u l a r l e n g t h s . They had

a

d i a m e t e r of 75 mm and p r e f e r r e d l e n g t h of 250 mm, b u t some s h o r t e r specimens were c u t t o t a k e a d v a n t a g e of t h e a v a i l a b l e p i e c e s of c o r e . The h o r i z o n t a l c o r e samples ( l o n g a x i s p a r a l l e l t o t h e i c e s u r f a c e ) were t a k e n a t a d e p t h of 0.55 m, where t h e g r a i n s t r u c t u r e was columnar. T h i n s e c t i o n s of t h e s e c o r e s s h a v e d t h a t t h e i c e had random c-axis o r i e n t a t i o n i n t h e h o r i z o n t a l p l a n e , i . e . u n a l i g n e d columnar g r a i n s , and a n a v e r a g e g r a i n s i z e of 3

-

5 mm. The v e r t i c a l c y l i n d r i c a l specimens were o b t a i n e d from v e r t i c a l c o r e s ( l o n g a x i s p e r p e n d i c u l a r t o i c e s u r f a c e ) and comprised e i t h e r g r a n u l a r o r c o l u m n a r g r a i n e d i c e , depending on t h e d e p t h from which t h e y were t a k e n i n t h e i c e cover. T h i n s e c t i o n s of t h e g r a n u l a r i c e s h a v e d t h a t i t had random c-axis o r i e n t a t i o n and g r a i n s i z e r a n g i n g from 1

-

2 mm. P r i s m o i d a l specimens were c u t from t h e b l o c k samples w i t h a band saw t o nominal dimensions of 190 mm

(5)

long, 100 mm wide, and 60 mm t h i c k . The l o n g a x i s of t h e v e r t i c a l specimens was p e r p e n d i c u l a r t o t h e i c e s u r f a c e and t h e l o n g a x i s of t h e h o r i z o n t a l specimens p a r a l l e l t o it. The p r i s m specimens were from a d e p t h of 0.45

-

0.65 m and were u n a l i g n e d columnar g r a i n e d . TEST PROCEDURE

A m o t o r i z e d , 60 kN c a p a c i t y , s c r e w - d r i v e compression t e s t machine ( T r i - T e s t 50) was u s e d f o r t e s t i n g . A c t u a t o r r a t ; s were s e l e c t e d i n t h e range 0.2 t o 5 mm/min, p r o d u c i n g nominal s t r a i n r a t e s i n t h e range 2 x t o 5 x s'l. "Maraset" c o m p l i a n t p l a t e n s were u s e d t o e l i m i n a t e t h e e f f e c t of i r r e g u l a r i t i e s and reduce r a d i a l s t r e s s e s a t t h e e n d s of t h e c y l i n d r i c a l specimens. F o r t h e c y l i n d r i c a l specimens t h e ends were c u t w i t h t h e band saw, w i t h no f u r t h e r end p r e p a r a t i o n ; two e x t e n s o m e t e r s were f i t t e d d i r e c t l y t o e a c h specimen and t h e o u t p u t a v e r a g e d f o r s t r a i n . The p r i s m o i d a l specimens w e r e l o a d e d between s t e e l p l a t e n s and t h e i r ends f i n i s h e d w i t h f i n e emery p a p e r t o p r o v i d e a f l a t s u r f a c e ; s t r a i n s were n o t measured.

Loading was monotonic t o y i e l d , when t h e specimen was unloaded. T y p i c a l s t r e s s - t i m e and s t r a i n - t i m e c u r v e s from v e r t i c a l and h o r i z o n t a l c y l i n d r i c a l and p r i s m o i d a l specimens under a nominal s t r a i n r a t e of

2 x s-I a r e p r e s e n t e d i n F i g . 1. I n a l l c a s e s t h e f a i l u r e mode was d u c t i l e . D e f i n i t i o n s of y i e l d s t r e s s , oy, time t o y i e t d , t f , s t r a i n a t y i e l d , cy, and s t r a i n r a t e a t y i e l d ,

5 ,

a r e a l s o shown. Average s t r e s s r a t e ,

kv,

i s a y / t f , and nominal s t r a i n r a t e ,

,,

i s

nominal machine s p e e d d i v i d e d by specimen l e n g t a . T e s t i n g was done a t a t e m p e r a t u r e of - l l ° C f 1°C. Specimen s a l i n i t y v a r i e d f r o m 3.2 t o 4.5 X O , w i t h a n a v e r a g e of 4

X O .

TEST RESULTS AND DISCUSSION

Complete t e s t r e s u l t s a r e t a b u l a t e d i n T a b l e s 1 and 2 f o r c y l i n d r i c a l and p r i s m o i d a l specimens,

r e s p e c t i v e l y . S t r e n g t h v e r s u s a v e r a g e s t r e s s r a t e f o r a l l t h e t e s t s i s p l o t t e d i n Fig. 2. The r e s u l t s f a l l i n t o t h r e e c a t e g o r i e s : one f o r t h e h o r i z o n t a l specimens of columnar-grained i c e , t h e second f o r v e r t i c a l specimens of g r a n u l a r i c e , and t h e t h i r d f o r v e r t i c a l specimens of columnar-grained i c e . C l e a r l y t h e v e r t i c a l l y o r i e n t e d specimens of u n a l i g n e d columnar-grained i c e a r e a b o u t t h r e e t i m e s s t r o n g e r t h a n t h e h o r i z o n t a l specimens, s i m i l a r t o t h e e a r l i e r f i n d i n g s of Peyton

(2).

T h i s c a n b e r e l a t e d t o t h e columnar-grain s t r u c t u r e of t h e i c e , i n which t h e l o n g a x i s of t h e columnar g r a i n s i s p a r a l l e l t o t h e l o n g a x i s of t h e v e r t i c a l specimen. Compared on a s t r e s s r a t e b a s i s , t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between t h e s t r e n g t h of p r i s m o i d a l specimens t e s t e d on s t e e l p l a t e n s and t h a t of c y l i n d r i c a l specimens t e s t e d o n compliant p l a t e n s . T h i s s u g g e s t s t h a t f o r f i e l d t e s t s average stress r a t e c a n be u s e d a e a n i n d e p e n d e n t variable t o compensate f o r d i f f e r e n c e 8 i n the stiffness

of t h e l o d d i n g aystem. bs mentioned e a r l i e r ,

a

number

of

t h e v e r t i c a l specimens comprised g r a n u l a r s e a ice, and r e s u l t s f r o m t h e s e are also i n c l u d e d i n t h e p l o t .

They f a l l a p p r o x i m a t e l y midway between t h e results f o r

v e r t i c a l a n d h o r i z o n t a l columnargraFned specimens.

Also p l o t r e d is t h e r e g r e s s i o n l i n e f o r t h e f i t of a

power l a w t o strength r e ~ u l t a

f o r

horizontal specimens of g r a n u l a r ice

(53.

There i s v e r y l i t t l e d i f f e r e n c e i n s t r e n g t h

f o r

v e r t i c a l and h o r i z o n t a l epecimena

of

g r a n u l a r

ice.

Given t h e e q u i a x i a l g r a i n s t r u c t u r e a n d t h e n e a ~ r a n d o m o r i e n t a t i o n o f the symmetry a x i s o f t h e g r a i n s , t h i s is t o be e x p e c t e d ,

----

VERTICAL SPECIMEN q -

-

HORIZONTAL S P E C I M N vy 8

-

/

,+--

-

7

-

/ 6

-

5

-

4

-

/

-

f

i

3 - / /

-

( a 1 2

-

/ u~ - 1

-

6

-

1 ?

-I

0 50 100 T I M E , s F i g u r e 1. S t r e s s - t i m e and s t r a i n - t i m e c u r v e s f o r v e r t i c a l and h o r i z o n t a l c y l i n d r i c a l specimens of columnar-grained i c e ;

c

= z X 1 o - 4 , nom t e s t t e m p e r a t u r e =

-

l l ° C f 1°C;

iyv

= 1.1 x s-I ( v e r t i c a l specimen)

E~~ = 1.0 x s - I ( h o r i z o n t a l specimen) 20 r ' " I I

'

' l " r ' l I I VERTICAL HORIZONTAL

---

• -0 CYLINDER -+ ---a P R I S M z- C 0 Z

z

5 -

___---

+ VI a 0 u _0,002l _0.005 _0.01 _0.02 _0.05 _0.1 _0.2 _0.5 A V E R A G E S T R E S S R A T E . M P a s-' F i g u r e 2. S t r e n g t h of v e r t i c a l and h o r i z o n t a l specimens of c o l u m n a r g r a i n e d i c e ( e x c e p t a s n o t e d ) a s a f u n c t i o n of a v e r a g e s t r e s s r a t e a t - l l ° C

+

1°C

(6)

A power f u n c t i o n h a s been f i t t e d t o e a c h s e t of s t r e n g t h v e r s u s average s t r e s s r a t e r e s u l t s . The r e s u l t i n g e q u a t i o n s , w i t h c o r r e s p o n d i n g c o r r e l a t i o n c o e f f i c e n t s , r , a r e a s f o l l o w s : Columnar-grained i c e

-

v e r t i c a l specimens h o r i z o n t a l specimens Granular i c e

-

v e r t i c a l specimens h o r i z o n t a l specimens (The r e a d e r i s c a u t i o n e d n o t t o e x t r a p o l a t e t h e p r e c e d i n g e m p i r i c a l e x p r e s s i o n s beyond t h e range of t h e e x p e r i m e n t a l d a t a . ) Although n o t p l o t t e d , t h e s t r e n g t h r e s u l t s were examined i n terms of t i m e - t o y i e l d t o v e r i f y t h e s a t i s f a c t o r y performance of t h e t e s t machine

(1).

A l l

showed a t r e n d towards i n c r e a s i n g y i e l d time w i t h d e c r e a s i n g s t r e n g t h , confirming t h e s a t i s f a c t o r y performance of t h i s f i e l d t e s t system.

From Fig. 1 i t may be s e e n t h a t a l t h o u g h t h e t e s t s were run a t a c o n s t a n t nominal s t r a i n r a t e of

2

x s-I, s t r a i n r a t e i s f a r from c o n s t a n t . I n i t i a l l y i t i s much l e s s t h a n t h e nominal r a t e , and only begins t o approach t h e nominal s t r a i n r a t e a t y i e l d . There i s undoubtedly some e x p e r i m e n t a l

measurement e r r o r a t s m a l l s t r a i n s . The average s t r a i n a t y i e l d f o r b o t h t h e v e r t i c a l and h o r i z o n t a l specimens was about

3

x A very weak t r e n d towards

i n c r e a s i n g s t r a i n w i t h i n c r e a s i n g t i m e - t c r y i e l d was a p p a r e n t .

Measurements were made of t h e s t i f f n e s s of b o t h t h e t e s t machine and t h e l o a d i n g system; s t i f f n e s s of t h e e n t i r e l o a d i n g system can be q u i t e d i f f e r e n t from t h a t of t h e b a s i c t e s t machine owing t o t h e s e p a r a t e e f f e c t s of l o a d c e l l , p l a t e n s , alignment j o i n t s , e t c . I n t h i s c a s e t h e system s t i f f n e s s was determined by l o a d i n g a specimen of known c o n s t a n t e l a s t i c i t y and measuring l o a d , movement of screw j a c k , and load frame d e f l e c t i o n

(6).

The f o l l o w i n g e x p r e s s i o n was used t o determine t h e l o a d i n g system s t i f f n e s s , KLs, AP K Q s ( P ) =

-

AF'L 6,

- -

E

A

where AP i s l o a d increment, 6 i s t h e corresponding

j

displacement increment of t h e j a c k , A i s t h e cross- s e c t i o n a l a r e a of t h e specimen, L i s l e n g t h , and

E

e l a s t i c modulus. KLs was determined by l o a d i n g a

75-m

diam by

200

mm l o n g aluminum specimen. The r e s u l t i n g l o a d i n g system s t i f f n e s s e s d e r i v e d from such t e s t s on t h e Tri-Test

50

machine w i t h compliant p l a t e n s and s t e e l p l a t e n s a r e p r e s e n t e d i n Fig.

3.

Loading system s t i f f n e s s i s n o t a c o n s t a n t , b u t a f u n c t i o n of l o a d , P. A s expected, s t i f f n e s s was g r e a t e r f o r t h e s t e e l p l a t e n s t h a n f o r t h e compliant p l a t e n s . J a c k speed was r e l a t i v e l y c o n s t a n t a t about

75%

of t h e nominal r a t e . The b a s i c frame s t i f f n e s s of t h e machine i s about

150

M N / ~ , which i s s u b s t a n t i a l l y h i g h e r t h a n t h e system s t i f f n e s s .

Having determined l o a d i n g system s t i f f n e s s , i t i s p o s s i b l e t o e s t i m a t e t h e s t r a i n i n a specimen of a n o t h e r m a t e r i a l by t r a n s p o s i n g e q u a t i o n

(5)

t o make E t h e dependent v a r i a b l e :

TABLE

1.

Data and r e s u l t s of t e s t s on c y l i n d r i c a l specimens

(76

mm 4 ) a t

-ll°C

+

1°C

Time S t r a i n O r i e n t a t i o n Specimen J a c k Y i e l d t o a t

Length, Speed, S t r e s s , Y i e l d , Yield, mm mm/min MPa s 10- 3 h o r i z o n t a l

248

1.5

1.84 9 3

3.8 2 24

4.5

2.25 2 8

3.2

225

0.5

1.22

258

3.6

170

2.0

1.90 5 8

2.5

206

0.6

1.44

222

2.3

205

0.25

1.66

550

3.9

206

1.8

2.36

82

2.7

205

5.0

3.22 2 7

2.5

157

5.0

3.17

25

2.7

153

1.2

1.55

102

2.4

145

0.5

1.77

312

4.8

140

0.2

1.62

606

4.0

v e r t i c a l *

252

0.5

3.43

318

3.2 -

*

251

1.5

2.89

177

6.3

,#

*

248

3.0

3.85

55

2.9 -

*

250

5.0

4.75 3 0

2.3 -

x

230

0.69

3.61

237 3 .O

'a

*

250

0.30

2.89

528

2.8

,# x

172

0.70

3.96

212

1.1

.a

*

179

1.6

4.00 6 0

2.5

178

1.6

8.03

80

2.8

179

1.6

7.74 8 7

5.3

179

1.6

8.29 7 8

2.9

178

1.6

8.71 8 0

1.3

192

0.25

4.29

549 -

191

0.25

5.23

570 -

186

0.6

6.02

228 -

192

0.6

3.24

210 -

* g r a n u l a r i c e

TABLE

2.

Data and r e s u l t s of t e s t s on prismoidal specimens a t - l l ° C

+

1°C

J a c k Y i e l d Time t o O r i e n t a t i o n Length, Speed, S t r e s s . Y i e l d , mm mm/min MPa s h o r i z o n t a l v e r t i c a l

(7)

10 _I _' _I _' _I _I _I _I

stresses and loading only in the compression-

compression quadrants, these assumptions are

5 80

-

I

5

/ S T E E L P L A T E N S

-

acceptable. Taking x, y and z to be a right cartesian

coordinate system, with x and y in the plane of the ice

-

cover and z normal to it, and principal stresses to

correspond to this coordinate system, F, G and H can be

determined from the results of uniaxial compressive

tests on specimens oriented in the three coordinate

-

directions.

For an unaligned columnargrained ice cover the

-

structural and mechanical properties are usually

isotropic in the plane of the ice cover. The uniaxial

-

strength of a specimen oriented in the plane of the ice

-

cover (horizontal) is ox

=

o

=

X; for one oriented

perpendicular to the plane of the ice cover (vertical)

10 20 30 40 50

it is oz

= Z .

Substituting these values for uniaxial

yield strength in equation (8) gives

LOAD kN

and

Figure

3.

Loading system stiffness of Tri-Test 50 at

1

mm/min nominal actuator rate

E = II

(6

Taking the jack displacement increment, 6j, as equal to

75% of the nominal jack rate, Bj, times a correspon&

ing time increment, At, and substituting in

equation (6) gives

E(p) =

a

3 '

(7)

A ( ~

d j

$-

A)

KQe(P)

From a load-time plot of a test on an ice specimen of

known dimensions, modulus

E can be determined as a

function of load P (or stress).

Strain can also be

determined. Such a calculation was made for the two

cases shown in Fig.

1.

The smoothed curves for loading system stiffness

in Fig. 3 were used in the calculation. In a

quantitative sense the correspondence of the predicted

strain-time curves to the measured curves is not

particularly close. The form of equation (7), with a

difference in two small terms of the denominator, makes

the modulus

E(P)

quite sensitive to any uncertainties

in values for loading system stiffness and jack rate.

Nevertheless, the predicted strains are an indication

of actual strain at yield. In the two cases the

predicted strain at yield is about twice the measured

value.

It was pointed out in the introduction that

strength measurements for vertically and horizontally

oriented, uniaxial specimens can be used in estimating

the confined compressive strength. This is not possi-

ble in a rigorous sense, but a qualitative estimate is

possible. The simplest yield criterion for an

anisotropic material, proposed by Hill

(c),

is assumed

to be a quadratic in terms of the stress components

This expression assumes similar yield stresses under

tensile or compressive loading, and assumes also that

hydzostatic stresses do not influence yield. Under the

test conditions, i.e. low effective hydrostatic

Having determined the constants F,

G

and H in equation

(81, it is possible to estimate the yield strength for

combined loading conditions. The loading case of

frequent interest is confined compression in the plane

of the ice cover, i. e., ax

=

aay

,

o

=

0. For ideal

confined compression, a

=

1 and

where oc is the confined compressive strength.

Substituting equation (9) in (8) for the loading

condition of equation (10) gives the confined

compressive strength.

At a nominal strain rate of

2 x

s-l the

uniaxial yield strengths from this test series were 8.4

and

2.65

MPa for vertical and horizontal specimens of

columnargrained ice, respectively. With these

results, a confined compressive strength of 8.4 MPa

would be the predicted value for biaxial loading in the

plane of the ice cover. Results of confined

compressive tests of columnargrained ice under similar

loading conditions gave an average confined compressive

strength of 9 MPa

(A).

CONCLUSIONS

1. On an average stress rate basis, the yield strength

of the ice measured in these field tests is

independent of the stiffness of the test system

(compliant platens versus steel platens).

2.

For unaligned columnar-grained ice, the uniaxial

compressive strength of vertical specimens is

slightly more than three times the uniaxial

compressive strength of horizontal specimens.

3.

For granular ice, the vertical strength is only

about 10% greater than the horizontal strength.

4. With knowledge of the stiffness of the loading

system, it is possible to estimate strain from the

load-time results.

5.

Uniaxial compressive strength results on vertical

and horizontal specimens can be used in estimating

confined compressive strength.

6. The strain at yield measured in these test for both

vertically and horizontally loaded columnargrained

specimens is about 3 x

(8)

NOMENCLATURE

REFERENCES

cross-sectional area of test specimen

elastic modulus

coefficients on yield function

loading system stiffness

specimen length

load

load increment

time to yield

time increment

uniaxial compressive strength in

plane of ice cover

uniaxial compressive strength normal

to plane of ice cover

ratio of biaxial stresses in plane of

the ice cover

displacement increment of

jack

nominal jack displacement rate

nominal strain rate

strain at yield

strain rate

a t

yield

confined compressive strength

normal stress components

uniaxial compressive yield strength

average stress rate

shear stress components

ACKNOWLEDGEMENTS

The authors would like to thank Gulf Canada and

Dome Petroleum for the opportunity to perform these

tests; the logistics, transportation, and accommodation

support provided by these companies is gratefully

acknowledged. The assistance of J.D. Neil, Technical

Officer, National Resarch Council of Canada, in

reducing the data is also acknowledged.

1. Ralston, T.D., "An analysis of ice sheet

indentation," Proc. IAHR Symposium on Ice Problems,

Vol. 1, 1978,

pp.

15-31.

2. Reinicke, K.M., "Analytical approach for the

determination of ice forces using plasticity

theory," &Physics

and Mechanics of Ice,

(Tryde, P., ed.), SpringerVerlag, New York, 1980,

p. 325-341.

3. Timco, G.W., and Frederking, R., "Confined

compressive strength of sea ice," Proc. 7th Int.

Conf. on Port and Ocean Eng. under Arctic

Conditions, POAC 83, Vol. 1, 1983, pp. 243-253.

4. Timco, G.W., and Frederking, R., "An investigation

of the failure envelope of granular/discontinuous

columnar sea ice," to be published.

5. Peyton, H.R.

"Sea ice strength," Geophysical

Institute University of Alaska, College, Alaska,

U.A.G.

R-182, 1966.

6.

Frederking, R., and Timco, G.W., "Uniaxial

compressive strength and deformation of Beaufort

Sea ice," Proc. 7th Int. Conf. on Port and Ocean

Eng. under Arctic Conditions, POAC 83, Vol. 1,

1983, pp. 89-98.

7. Sinha,

N.K., "Field Test

1

of compressYve strength

of first-year sea ice," Annals of Glacial., Vol. 4,

1983, 253-259.

8. Hill,

R., "The mathematical theory of plasticity,"

(PP. 318-320). Oxford University Press, 1950,

355p.

(9)

reprinted from

Proceedings of the Third International Offohore Mechanics and Arctic Engineering Symposium

-

Volume Ill

Editor: V. J. Lunardini (Book No. 100173) published by

THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 East 47th Street, New York, N. Y. 10017