Confined Compression Tests Outlining the Failure Envelope of Columnar Sea Ice

8/11/2019 Confined Compression Tests Outlining the Failure Envelope of Columnar Sea Ice

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Cold Regions Science and Technology 1 2 ( 1 9 8 6 ) 1 3 - 2 8 1 3

E l s e vi e r S c i e n c e P u b l is h e r s B .V . , A m s t e r d a m - P r i n t e d i n T h e N e t h e r l a n d s

C O N F I N E D C O M P R E S S IO N T ES TS : O U T L I N I N G T H E F A I L U R E E N V E L O P E O F

C O L U M N A R S E A I C E

G W T i m c o a nd R M W F r e d er k in g

National Research Council o f Canada, Ottawa, Ontario K IA OR6 Canada)

(Received M arch 14, 19 85; accepted in rev ised form June 19 , 1985)

ABSTRACT

A ser ies o f con f ined comp ress ion tes t s has been

p e r f o r m e d o n c o l u mn a r s e a i c e o v e r a r a ng e o f n o mi -

na l s tra in ra tes o f 10 -s to 10 -3 s -x a t a t em pera ture

o f -2 C . B o t h t h e a p p l i e d l o ad a n d s id e c o n fi n i n g

load were measured . These are used to ou t l ine th e fu l l

3 -d imens iona l fa i lu re enve lop e o f the i ce. T he resu l ts

are d i scussed in t erm s o f load ing ra te e f f ec t s t em -

pera ture br ine vo lu me and a ir poros i ty . A s t reng th

i n d e x i s i n t r o d u c e d w h i c h c o r re l at e s th e p r e s e n t

resu l t s in t erms o f these parameters . Th is leads to an

empir ica l re la t ionsh ip wh ich g ives the func t iona l

d e p e n d e n c e o f t h e u n i -a x i a l c o mp r e s s i v e s t r e n g t h i n

terms o f st ra in ra te load ing d i rec t ion sa l in ity t em -

p e r a t u r e a n d i c e d e n s it y . A ma t h e m a t i c a l d e s c r i pt i o n

o f t h e f a i l u r e e n v e l o p e i s p r e s e n t e d u s i n g a mo d i f i e d

n - t y pe y i e M f u n c t i o n .

INTRODUCTION

W h e n a n i c e b r e a k e r t r a v e l s t h r o u g h a f lo a t i n g i c e

s h e e t , o r w h e n a m o v i n g i c e s h e e t i n t e r a c t s w i t h a

s t a t i o n a r y s t r u c t u r e , t h e b r e a k i n g o f th e i c e i s a n im -

p o r t a n t p a r t o f t h e i n t e r a c t i o n p r o c e s s . T h e s tr e s s

l e v e l s a t w h i c h t h e i c e f a i l s c a n i n f l u e n c e b o t h t h e

g l o b a l l o a d s a n d l o c a l p r e s s u r e s o n t h e s t r u c t u r e . T h i s

f a i l u r e s t r e s s i s c o n t r o l l e d b y 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 t h e i c e . I c e , h o w e v e r , c a n e x h i b i t a v a r i e t y o f

b e h a v i o u r s u c h a s e l a s t i c i t y , b r i t t l e f r a c t u r e , v i s c o -

e l a s t i c i t y , p l a s t i c i t y , e t c . M o r e o v e r , f o r s e a i c e , t h e

m e c h a n i c a l p r o p e r t i e s a r e i n f l u e n c e d b y t h e l o a d i n g

s t r a i n r a t e , l oad i ng s t r ess r a t e , i ce sa l i n i t y , i ce t em-

p e r a t u r e , g r a i n s t r u c t u r e , g r a i n s i ze , g r a in o r i e n t a t i o n ,

b r i n e p o r o s i t y a n d a i r c o n t e n t . T h u s , i n o r d e r t o b e

a b l e t o u n d e r s t a n d t h e i n t e r a c t i o n p r o c e s s , it is n e c e s -

s a r y t o s t u d y 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 i c e f o r a

w i d e r a n g e o f c o n d i t i o n s . B e c a u s e o f i ts i m p o r t a n c e ,

t h e r e h a v e b e e n s e v e r a l i n v e s t i g a t i o n s 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 i c e . T h e s e a r e u s u a l l y p e r f o r m e d b y

t a k i n g a s a m p l e o f i c e a n d , u n d e r a w e l l- d e f i n e d lo a d -

i n g a r r a n g e m e n t , s u b j e c t i n g i t t o a n i n c r e a s i n g l o a d

un t i l i t f a i l s . For s i mpl i c i t y i n t es t i ng and ana l ys i s ,

t he s t r ess f i e l d i s u sua l l y appl i ed on l y i n one d i r ec-

t i o n , f o r e x a m p l e , i n u n i - a x i a l t e s t i n g o f t h e c o m p r e s -

s iv e s t r e n g t h o f i c e ( P e y t o n , 1 9 6 6 ; S c h w a r z , 1 9 7 0 ,

1983 ; Wang, 1979 ; S i nha , 1983a , 1983b , 1984;

F r e d e r k i n g a n d T i m c o , 1 9 8 0 , 1 9 8 3 , 1 9 8 4 a ) .

I n n a t u r e , h o w e v e r , t h e s t r e s s f i e l d i n t h e i c e c a n

b e v e r y c o m p l e x a n d t h e r e s p o n s e o f t h e i c e c a n n o t ,

t h e r e f o r e , b e d e s c r i b e d u n i q u e l y b y t h e u n i - a x i a l

s t r e s s p r o p e r t i e s o f t h e i c e . B e c a u s e o f t h i s , i n f o r m a -

t i o n i s r e q u i r e d o n t h e b e h a v i o u r o f i ce u n d e r c o m -

pl ex s t r ess s t a t es . Th i s behav i ou r i s u sua l l y descr i bed

i n t e r m s o f t h e

fa i lu re enve lope

f o r t h e m a t e r i a l ( P a u l ,

1968) . Th i s i s a descr i p t i on of t he s t r ess l eve l s a t

w h i c h t h e ic e y i e ld s f o r a n y c o m b i n a t i o n o f c o m p r e s -

s i ve or t ens i l e s t r ess s t a t es . One t echn i que for i nves -

t i g a t i n g t h e f a i l u r e e n v e l o p e o f a m a t e r i a l i s t h r o u g h

t h e u s e o f c o n f i n e d c o m p r e s s i o n t e s t s . I n t h e s e t e s t s ,

t h e m a t e r i a l i s l o a d e d i n o n e d i r e c t i o n w h i l e c o n f i n e d

i n a s e c o n d d i r e c t i o n . T h i s a l lo w s d e f o r m a t i o n o f t h e

m a t e r i a l i n o n l y o n e d i r e c t i o n . B y m e a s u r i n g b o t h t h e

a p p l i e d a n d c o n f i n i n g l o a d s , a n d k n o w i n g t h e o r i e n t a -

t i o n o f t h e i c e i n t h e c o n f i n e m e n t a p p a r a t u s , t h e

f a i l u r e s t r e s s e s f o r t h e i c e c a n b e d e t e r m i n e d f o r

v a r i o u s c o m b i n a t i o n s o f s t re s s s ta t e s . T h e s e d e f i n e t h e

f a i l u r e e n v e l o p e f o r t h e i c e i n t h e 3 - d i m e n s i o n a l c o m -

p r e s s i o n - c o m p r e s s i o n - c o m p r e s s i o n o c t a n t . A k n o w l -

e d g e o f t h e f a i l u r e e n v e l o p e f o r i c e i s i m p o r t a n t s i n c e

i t i n d i c a t e s t h e m a x i m u m s t r e s s w h i c h t h e i c e c a n


2/16

14

s u s t a i n b e f o r e f a i lu r e . I n a d d i t i o n , i f i t i s d e s c r i b e d in

a c o n v e n i e n t m a t h e m a t i c a l f o r m i n t e r m s o f t h e p r in -

c i p a l a n d s h e a r s t r e s s e s , i t c a n b e u s e d t o p r e d i c t

a n a l y t i c a l l y t h e i ce l o a d s f o r v a r io u s i c e - s t r u c t u r e

i n t e r a c t i o n s c e n a r i o s . T h e f a i l u r e e n v e l o p e f o r colum

nar

s e a i c e is p a r t i c u l a r l y i m p o r t a n t s i n c e c o l u m n a r -

s t r u c t u r e d i ce is p r e d o m i n a n t i n m a n y a r e a s o f t h e

A r c t i c .

T o d a t e , t h e re h a s b e e n o n l y a h a n d f u l o f c o n f i n e d

c o m p r e s s i o n t e s t s o n s e a i c e . T h e s e i n c l u d e t e s t s b y

T i m c o a n d F r e d e r k i n g ( 1 9 8 3 ) a n d B l a n c h e t a n d

H a m z a ( 1 9 8 3 ) w h o m e a s u r e d t h e c o n f in e d c o m p r e s -

s iv e s t r e n g t h o f i c e w i t h h o r i z o n t a l l o a d i n g a t o n e

t e m p e r a t u r e a n d o v e r a v e ry l i m i t e d r a n ge o f st r ai n

r a t e s . A m o r e t h o r o u g h i n v e s t i g a t i o n w a s c a r r i e d o u t

b y T i m c o a n d F r e d e r k i n g ( 1 9 8 4 a ) w h o m e a s u r e d t h e

f u l l f a il u r e e n v e l o p e u s i n g b o t h v e r t i c a l a n d h o r i -

z o n t a l l o a d i n g a r r a n g e m e n t s f o r g r a n u l a r /d i s c o n t i n -

u o u s c o l u m n a r s e a ic e a t o n e t e m p e r a t u r e o v e r a

r a n g e o f l o a d i n g r a t e s. T h e i r t e s t s w e r e a n a l y s e d u s i n g

p l a s t ic i t y t h e o r y a n d f i t t e d s u c c e s s f u ll y t o a n n - t y p e

y i e ld f u n c t i o n . T h e p r e s e n t t e s t s a r e c o n c e r n e d w i t h

t h e f a i l u r e e n v e l o p e o f columnar s e a i c e . T h e t e s t s

w e r e p e r f o r m e d i n th e f i e l d o n w a r m ( T = - 2 C )

c o l u m n a r s e a ic e f r o m N o r t h e r n L a b r a d o r a l on g t h e

e a s t c o a s t o f C a n a d a . I n t h is p a p e r , th e t e c h n i q u e s

u s e d f o r m e a s u r i n g t h e s t r e n g t h a r e d e s c r i b e d a n d t h e

r e s u l ts f o r f iv e d i f f e r e n t c o n f i n e m e n t c o n d i t i o n s a r e

g i v e n i n r e l a t i o n t o l o a d i n g r a t e a t c o n s t a n t t e m p e r a -

t u r e . I n a d d i t i o n , a s e ri e s o f u n i - a x i a l te s t s w e r e p e r -

f o r m e d a t d i f f e r e n t t e m p e r a t u r e s , a n d t h e r e s u l t s a r e

p r e s e n t e d i n t e r m s o f t e m p e r a t u r e , l o a d i n g r a te , b r in e

v o l u m e a n d t o t a l p o r o s i t y o f t h e i c e . T h e r e s u l t s f r o m

a l l o f t h e t e s t s a re u s e d t o o u t l i n e t h e 3 - d i m e n s i o n a l

f a i lu r e e n v e l o p e f o r w a r m c o l u m n a r s e a i c e , a n d t h e

c o r r e s p o n d i n g e n v e l o p e a t - 1 0 C i s i n f e r r e d . F i n a l l y ,

t h e r e s u l t s a re a n a l y s e d t o f i t a m o d i f i e d n - t y p e y i e l d

f u n c t i o n f o r th e i c e at b o t h t e m p e r a t u r e s .

r a t i o n . T o g e t s p e c i m e n s o f ic e , a la r g e b l o c k 1 . 2 m

1 . 2 m 1 . 0 m ( i c e t h i c k n e s s ) w a s c u t f r o m t h e ic e

c o v e r w i t h a c h a i n s a w , a n d b r o u g h t o n b o a r d u s i n g

t h e c r a n e o f t h e v e s s e l. T h e r e , t h e b o t t o m h a l f w a s

i m m e d i a t e l y c u t i n t o s m a l l e r p i e c es , 3 0 c m 5 0 c m

X 3 0 c m , l a b e ll e d a n d p u t i n a n o n b o a r d c o l d c h a m -

b e r a t a t e m p e r a t u r e o f - 1 5 C . T h e s e b l o c k s w e r e

t h e n c u t i n t o 1 9 c m 8 c m 5 c m s a m p l e s u s i n g a

b a n d s a w . T h e l a r g e f a c es o f e a c h s a m p l e w e r e s m o o t h -

e d u s i n g a p o w e r p l a n e r . O n c e c u t t o s a m p l e d i m e n -

s i o n s , th e i c e w a s tr a n s f e r r e d t o a s e c o n d c o l d r o o m

a n d a l l o w e d t o s i t o v e rn i g h t a t t h e a m b i e n t t e m p e r a -

t u r e o f t h e t e s t . A l l s a m p l e s t e s t e d c o n s i s t e d o f s tr i c t -

l y c o lu m n a r $ 2 i c e w i t h r a n d o m o r i e n t a t i o n o f th e

c - a x i s i n t h e h o r i z o n t a l p l a n e ( s e e F i g . 1 ) . F o r t h i s

t e s t s e r ie s , t h e m a j o r i t y o f t e s t s w e r e p e r f o r m e d a t

- 2 C , a l t h o u g h a s m a l l n u m b e r o f s a m p l e s w e r e

t e s t e d i n u n i- a x i al c o m p r e s s i o n a t - 4 C a n d - 1 2 C .

E X P E R I M E N T L

T h e t e s t s d e s c r i b e d h e r e w e r e c a r r i e d o u t i n l a t e

M a y , 1 9 8 4 i n n o r t h e r n L a b r a d o r , C a n a d a d u r i n g t h e

i c e b r e a k e r t r ia l s o f t h e G e r m a n i c e b r e a k i n g re s e a r c h

v e s s el P o l a r s t e r n . S i n c e t h e t e s t s w e re c a r r i e d o u t l a t e

i n t h e s p r i n g , t h e a i r t e m p e r a t u r e w a s r e l a t i v e l y h i g h

( - 5 t o + 5 C ) a n d t h e i c e h a d u n d e r g o n e s o m e d e t e r i o -

Fig. 1 . Thin sect ion of ice through crossed polaroids showing

the column ar s t ructure of the ice . The width of the sample i s

approx i ma t e l y 10 cm.


3/16

T h e t e m p e r a t u r e o f - 2 C w a s c h o s e n t o c o rr e s p o n d

t o t h e a v e r ag e t e m p e r a t u r e o f t h e i ce i n t h e L a b r a d o r

S e a a t t h a t t i m e . F o r a l l ic e s p e c i m e n s , t h e s a l i n i t y

a n d d e n s i t y w e r e d e t e r m i n e d . T h e a v e r a g e s a l i n i t i e s

w e r e 1 . 6 -+ 0 . 4 % 0 a n d 1 . 7 + 0 . 4 % 0 , a n d t h e a v e r a g e

d e n s i t i e s w e r e 0 . 8 4 7 -+ 0 . 0 3 6 g c m 3 a n d 0 . 8 2 9 -+

0 . 0 3 1 g c m - 3 a t - 1 2 C a n d - 2 C r e s p e c ti v e l y. S a l i n it y

a n d d e n s i t y h i s t o g r a m s a r e s h o w n f o r b o t h t e m p e r a -

t u r e s i n F i g s . 2 a n d 3 r e s p e c t i v e l y . T h e r e w e r e s e v e r a l

b r i n e d r a i n a g e c h a n n e l s a n d l a rg e v o i d s e v i d e n t

t h r o u g h o u t t h e i ce . T h e r e l a ti v e l y l o w v a l ue s f o r b o t h

s a l i n i t y a n d d e n s i t y , a s w e ll a s t h e g e n e r a l a p p e a r a n c e

o f t h e i c e , c o n f i r m t h a t i t h a d u n d e r g o n e c o n s i d e r a b le

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

i f t h e y c o n t a i n e d l a r g e d r a i n a g e c h a n n e l s , v o i d s , e t c .

I n t o t a l 9 3 s a m p l e s w e r e t e s t e d .

T h e t e s t s w e r e p e r f o r m e d u s i n g a 0 . 0 5 M N c a p a c -

i t y S o i l te s t C T - 4 0 5 c o m p r e s s i o n t e s t e r w h i c h h a s a

s c r e w - d ri v e n a c t u a t o r p o w e r e d b y a 1 /4 H . P . m o t o r .

W i t h t h i s m o t o r d r iv e , a c t u a t o r s p e e d s 0 ( ) o f 3 X

1 0 - 3 t O 7

X

1 0 - 2 m m s - 1 a r e o b t a i n a b l e . D u r i n g t h i s

t e s t se ri es , i n t e r m i t t e n t p r o b l e m s w i t h t h e m o t o r

n e c e s s i t a t e d c o n v e r s i o n o f t h e p r e s s t o a h a n d - d r i v e n

m a c h i n e . T h i s m o d i f i c a t i o n w o r k e d v e r y w e l l a n d i t

a l l o w e d h i g h e r c r o s s - h e a d s p e e d s u p t o 1 . 9 X 1 0 1

2 0

> 15

O

Z

ILl

::D 10

O

#

u_ 5

n = 4 6 [ ~ T = 2 C

0 . 8 1 . 0 1 . 2 1 . 4 1 , 6 1 . 8 2 . 0 2 . 2 2 . 4 2 . 6 2 . 8

S A L I N I T Y [ / - 3

2O

n = 1 2

Z

~ 1 0

u. 5

I I I I I I I

0 . 8 1 . 0 1 .2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2

T = - 1 2 o C

I

2 . 4 2 . 6 2 . 8

S A L I N I T Y [ * /* o )

Fig. 2. Salinity histogram for all i c e s a m p l e s a t T - 1 2 C a n d

T = -2C .

15

3 0

2 0

1 0

O

3 0

n = 6 0

0 . 7 6 0 . 7 8 0 . 8 0

T = - 2 C

i I I ] I I I I

0 . 8 2 0 . 8 4 0 . 8 6 0 . 8 8

I

0 . 9 0

D E N S I T Y [ g - c m - 3 ]

> .- 20

O

Z

LU

:3

O 1 0

U.I

CE

U-

0

n = 1 2

m

I I i

0 . 7 6 0 . 7 8

T = - 1 2 C

p = 0 , 8 4 7

I I I I I l I l I I I

0 . 8 0 0 . 8 2 0 . 8 4 0 . 8 6 0 . 8 8 0 . 9 0

D E N S I T Y ( g - c m -3 )

Fig. 3. D ensity histogram fo r all ice samples at T = -12 C and

T = -2C .

m m s - 1. W i t h s a m p l e s o f l e n g t h L = 1 9 c m , t h i s g i v es

a r a n g e o f n o m i n a l s t r a i n r a t e s ( e n =

x/L

o f 1 1 0 s

t o 1 1 0 - a s - 1. T h e t e s t i n g f r a m e s t i f fn e s s a n d l o a d -

i n g s y s t e m s t i f f n e s s w e r e m e a s u r e d u s i n g t h e a p -

p r o a c h d e s c r ib e d b y F r e d e rk i n g an d T i m c o ( 1 9 8 3 ) t o

b e 2 0 0 a n d 1 0 0 M N m - 1 , r e s p e c t i v e l y . I n o r d e r t o

c r e a t e t h e c o n f i n e d c o n d i t i o n s f o r t h e i c e, a s p e c i a l l y

b u i l t a l u m i n u m s u b - p r e s s w a s u s e d ( s e e F i g . 4 ) . I n c o n -

f i n e m e n t , t h e i ce s p e c i m e n w a s p u t b e t w e e n t h e tw o

c o n f i n i n g w a l ls o f t h e s u b - p r e s s w h i c h w e r e f i r m l y

r e t a i n e d w i t h a n i n i ti a l p r e s s u r e o f 0. 1 M P a u s in g f o u r

l a r ge t h r e a d e d r o d s w i t h n u t s . T h i s r e s t r a i n i n g s y s t e m

i s s ti f fe r t h a n t h e s y s t e m o f C - c l a m p s u s e d b y t h e

a u t h o r s i n e a r l i e r t e s t s ( T i m c o a n d F r e d e r k i n g , 1 9 8 3 ,

1 9 8 4 a ) . B o t h t h e a p p l i e d l o a d a n d s id e c o n f i n i n g l o a d

w e r e m e a s u r e d u s i n g t w o d i f f e r e n t l o a d c e l l s . T h e

o u t p u t f r o m t h e l o a d c e l ls w a s f e d i n t o a s tr i p - c h a r t

r e c o r d e r . F r o m t h e l o a d - t i m e c u r v e s , t h e s t r e s s e s a n d

s t r e n g t h s w e r e d e t e r m i n e d a s th e l o a d d i v id e d b y th e

i n i ti a l c r o s s - s e c t i o n a l a r e a o f t h e s a m p l e . T h e a v e r a g e

s t r e s s - r a t e ( 6 a ) w h i c h i s d e f i n e d a s t h e s t r e s s a t y i e l d

d i v i d e d b y t h e t i m e t o f a il u r e w a s a l s o d e t e r m i n e d

f r o m t h e c u r v e s.

F o r t h i s c o l u m n a r - s t r u c t u r e d i c e , t h e r e i s a h i g h

d e g r e e o f a n i s o t r o p y . I n t h e p l a n e o f th e i c e c o v e r ,


4/16

16

Fig. 4 . Pho tograph of an ice piece sandw iched between th e

confining plates in the sub-press. No te the two load cells

which measure th e app l ied and confining loads . Th e c loth a t

t he bo t t om was used t o abso rb t he l a rge amou nt o f l i qu id

br ine squeezed from the sam ple in the A - type tes t s .

t h e i c e c a n b e c o n s i d e r e d t o b e i s o t r o p i c s i n c e t h e r e

w a s r a n d o m o r i e n t a t i o n o f t h e c - a x i s o f th e i c e g r a i n s

i n t h is p l a n e . B e c a u s e o f t h e v e r t ic a l c o l u m n a r s t r u c -

t u r e , t h e r e i s a u n i q u e d i r e c t i o n w h i c h i s i n t h e l o n g

d i r e c t i o n o f t h e g r a i n s ( i. e . i n th e d i r e c t i o n o f g r o w t h

o f t h e i c e c o v e r ) . W i t h th i s i c e s t r u c t u r e , t h e r e a r e f i v e

d i f f e r e n t t e s t c o n f i g u r a t i o n s t h a t c a n b e u s e d . T h e s e

a r e s h o w n i n F i g . 5 a s :

T y p e A : B o t h l o a d i n g a n d c o n f i n e m e n t i n t h e

p l a n e o f t h e i c e c o v e r . T h is m e a s u r e s t h e c o n f i n e d

s t r e n g t h i n t h e x - d i r e c t i o n a n d s i d e - l o a d i n g i n th e y -

d i r e c t i o n , o r , s i n c e t h e i c e is is o t r o p i c i n th i s p l a n e ,

t h e s t r e n g t h i n t h e y - d i r e c t i o n a n d t h e s id e - l o a d i n g i n

t h e x - d i r e c t i o n .

T y p e B : L o a d i n g in t h e p l a n e o f th e i c e c o v e r w i t h

c o n f i n e m e n t i n t h e v e r t ic a l d i r e c ti o n . Th i s m e a s u r e s

t h e s t r e n g t h i n e i t h e r t h e x o r y d i r e c t i o n , a n d t h e

s i d e lo a d i n g i n t h e z - d i r e c t i o n .

T y p e C : L o a d i n g in t h e p l a n e o f th e i c e c o v e r w i t h

n o c o n f i n e m e n t . T h i s t e s t m e a s u r e s t h e u n i - a x i a l c o m -

p r e s s i v e s t r e n g t h f o r h o r i z o n t a l l o a d i n g ( i .e . p e r p e n -

d i c u l a r t o t h e l o n g d i r e c t i o n o f t h e g r a i n s ).

T y p e D : L o a d i n g p a r a l l e l t o t h e g r o w t h o f t h e ic e

c o v e r w i t h c o n f i n e m e n t i n t h e p l a n e o f t h e ic e c o v e r .

T h i s m e a s u r e s t h e c o n f i n e d s t r e n g t h i n t h e z - d i r e c t i o n

a n d t h e s i d e l o a d i n g in e i t h e r t h e x o r y d i r e c t i o n .

T y p e E : L o a d i n g i n t h e d i r e c t i o n o f g r o w t h o f t h e

i c e w i t h n o c o n f i n e m e n t . T h i s m e a s u r e s t h e u n i - a x i a l

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

t o t h e l o n g d i r e c t i o n o f t h e g r a i n s ).

U s i n g t h e s e f iv e d i f f e r e n t l o a d i n g a r r a n g e m e n t s ,

A PPL IE D

LO A D

APPLIED CONFINING .,,1~ ~, ) ICE f I

LO AD P LA1. E ~ ~. B LO OK X ~ - - - y ~ 1

A PPL IE D

LO A D

Fig. 5 . Geom etry for confined com press ion tes t s showing the f ive confine men t ar rangements .

CO NF IN ING

PLA TE S

A PPL IE D

LO A D


5/16

17

t h e s iz e a n d g e n e r a l s h a p e o f t h e f a il u r e e n v e l o p e c a n

b e d e t e r m i n e d f o r c o l u m n a r i ce f o r t h e x - y x - z a n d

y - z

p l a n e s i n t h e c o m p r e s s i o n - c o m p r e s s i o n q u a d -

r a n t s . W h e n c o m b i n e d , t h e y o u t l i n e t h e f a i l u r e e n -

v e l o p e o f t h e i c e in 3 - d i m e n s i o n a l s t r e s s s p a c e .

R S U L T S

f f e c t s o f c o n f i n e m e n t

F i g ur e 6 s h o w s t y p i c a l s t r e s s - t i m e c u r ve s f o r e a c h

o f t h e f i v e t y p e s o f c o n f i n e m e n t a t a n o m i n a l s t r a i n

r a t e o f 2 X 1 0 4 s 1 a n d t e m p e r a t u r e o f - 2 C . F o r

c o n f i n e d c o n d i t i o n s , b o t h t h e a p p l i e d s t r e ss a n d s id e -

c o n f i n i n g s t r e s s a r e s h o w n . A c o m p a r i s o n o f t h e i r

va l ues a t y i e l d for a l l i nves t i ga t ed l oad i ng r a t es i s

s h o w n i n F ig . 7 f o r A , B a n d D t y p e c o n f i n e m e n t .

F r o m t h e s e f i g u r e s , t h e r e a r e s e v e r a l t h i n g s t o n o t e .

F o r C - t y p e c o n f i n e m e n t , w h i c h i s t h e c o n v e n t i o n a l

u n i - a x i a l l o a d i n g i n t h e h o r i z o n t a l d i r e c t i o n , t h e

s t r e s s - t i m e c u r v e i l l u s t r a t e s t y p i c a l d u c t i l e f a i l u r e a t

t h i s s t r a i n r a t e a n d t e m p e r a t u r e . F o r B - t y p e c o n f i n e -

m e n t , t h e l o a d i n g c h a r a c t e r i s t i c s a r e s i m i l a r w i t h o n l y

v e r y s m a l l ( < 0 . 2 M P a ) s i d e c o n f i n i n g s t r e s s, e v e n a t

y i e l d . A - t y p e c o n f i n e m e n t , o n t h e o t h e r h a n d , p r o -

d u c e s s t r a i n - h a r d e n i n g a n d a p p r e c i a b l y h i g h e r st r e s se s

a t y i e l d f o r b o t h t h e a p p l i e d a n d s i d e -l o a d i n g d i r e c -

t i o n s . I n a d d i t i o n , t h e t i m e t o f a i l u r e i s c o n s i d e r a b l y

l o n g e r t h a n f o r e i t h e r t h e B - t y p e o r C - t y p e c o n f i n e -

m e n t . F o r t h is c o l u m n a r i c e , A - t y p e c o n f i n e m e n t

p r o d u c e s y i e l d s t r e s s e s w h i c h a r e 4 - 5 t i m e s h i g h e r

t h a n t h e s t r e s s n e c e s s a r y f o r i c e f a i l u r e i n u n c o n f i n e d

c o n d i t i o n s . I n a d d i t i o n , t h e c o n f i n e m e n t s t r e s s i s

t y p i c a l l y 5 0 % o f t h e a p p l i e d s t r e ss .

$ 2 c o l u m n a r i c e is c h a r a c t e r i z e d b y a p r e f e r r e d

b a s a l - p l a n e o r i e n t a t i o n a n d g r a i n b o u n d a r y d i r e c t i o n

s u c h t h a t t h e " e a s y - f a i l " d i r e c t i o n i s i n t h e p l a n e o f

t h e i c e c o v e r . I n A - t y p e c o n f i n e m e n t , t h e c o n f i n i n g

p l a t e s a n d l o a d i n g p l a t e n s a r e o r i e n t e d i n s u c h a w a y

t h a t t h e y p r e v e n t d e f o r m a t i o n i n t h i s p l a n e . A s s u c h ,

t h i s d e f o r m a t i o n i s r e s t r i c t e d , a n d t h e i c e m u s t d e -

f o r m i n t h e l o n g d i r e c t i o n o f t h e g r a i n s . T h i s i s o b -

s e r v e d a f t e r a t e s t b y e x a m i n i n g t h e i c e s u r f a c e i n t h e

u n c o n f i n e d d i r e c t i o n . I n m a n y c a s e s, t h e i c e d e f o r m -

e d t o g i v e a " m o t t l e d " a p p e a r a n c e i n w h i c h i n d i v i d u a l

g r a i n s w e r e c l e a r l y e v i d e n t . B e c a u s e o f t h e o r i e n t a t i o n

o f t h e g r a i n b o u n d a r i e s a n d b a s a l p l a n e s f o r $ 2

c o l u m n a r i ce , th i s t y p e o f d e f o r m a t i o n b y e l o n g a t io n

o f t h e c o l u m n s r e q u ir e s s o m e t y p e o f n o n b a s a l -p l a ne

g l id e . T h e s t re s s f o r t h i s is m u c h g r e a t e r t h a n t h a t

assoc i a t ed wi t h basa l -p l ane g l i de (Hi gash i , 1967) .

4

3

2

1

0

5

~ 4

3

2

i i i

O3

0

5

4

3

2

1

0

5

4

3

2

1

0

m

\ _ ~ - / CO NF IN ING

- - J / / ST R ESS

A T Y P E

V I I I I 1 I I I I I I

0 200 400 600 80 0 1000

/APPLIED STRESS

/

/

/CONFINING STR ESS B-TYPE

200 400 600 800 1000

APPLIED STRESS

I I I I I I I I

0 200 400 600 800

/ APPLIED STRESS

~ 11 CO NF IN ING ST RESS

I I I I I I

0 200 400 600 800

r//APPLIED STRESS

0 200 400 600 800

C- T YPE

I I I

1000

D-TYPE

I I I

1000

E T Y P E

1000

LOADING TIME (seconds)

Fig. 6. Stress-time curves for each of the five confinement

condit ions showing bo th the applied and confining stress in

eac h ca se at i n = 2 X 10 -4 s-1 and T = --2C.


6/16

1 8

3 5

3 0

~- 2.5

w 2.0

12

1.5

z

z

ta_

Z

0 1 . 0

O

0 5

I I

A = A - T Y P E

- - B = B - T Y P E

D = D - T Y P E

AA

A A

A

A

A A

~A

I

a ~ B

1

D i ~ D D D

I B B f f B ~ b I I

2 3 4 5 6 7

A P P L I E D S T R E S S ( M P a ]

Fig. 7. Applied stress versus side-confining stress at yield for

A, B and D-type confinement.

T h e r e f o r e , t h e s t r e s s e s n e c e s s a r y f o r y i e l d o f t h e

c o l u m n a r i c e w i t h A - t y p e c o n f i n e m e n t a r e s i g n if ic a n t -

l y h ig h e r th a n f o r u n c o n f i n e d o r B - t y p e c o n f i n e m e n t

w h e r e d e f o r m a t i o n w i t h b a s a l g l i d e is a l l o w e d . T h i s

a l s o e x p l a i n s t h e s i m i l a r i t y in s t r e n g t h b e t w e e n B a n d

C - t y p e c o n f i n e m e n t f o r t h i s c o lu m n a r ic e . F o r th e

s a m e r e a s o n s , l o a d i n g p e r p e n d i c u l a r t o t h i s d i r e c t i o n ,

w i t h e i t h e r D o r E - t y p e c o n f i n e m e n t r e s u l ts in f a i lu r e

s t r e ss e s w h i c h a r e c o n s i d e r a b l y h i g h e r t h a n f o r h o r i -

z o n t a l C - t y p e l o a d i n g , b u t v e r y s i m i l a r t o s t r e n g t h s

f o r A - t y p e l o a d i n g . W i t h r e g a r d t o t h e c o n f i n i n g

s t r e s s , i t i s r e l a t i v e l y s m a l l f o r D - t y p e l o a d i n g .

E f f e c t s o f l o a d i n g r a t e

F i g u r e 8 s h o w s t h e c h a n g e i n y i e l d s t r e ss a s a f u n c -

t i o n o f n o m i n a l s t r ai n ra t e e n ) f o r a c o n s t a n t t e m -

p e r a tu r e o f - 2 C f o r e a ch o f th e f i v e t y p e s o f c o n f i n e -

m e n t . F o r b o t h B a n d C - t y p e c o n f i n e m e n t , t h e r e i s

a d e f i n i te 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 in g l o a d i n g

r a te w i t h a f u n c t i o n a l f o r m

o

=

5 5 ( ~ n ) ' 46 f o r B - t y p e ( 1 )

a n d

o = 8 . 9 @ n ) O ' 26

f o r C - t y p e

( 2 )

w h e r e o i s t h e M P a a n d ~ n i s i n s ~ a . F o r t h e o t h e r

t h r e e t y p e s o f c o n f i n e m e n t , h o w e v e r , t h e r e is l it t le

LU 1 . 0

GO

C~

U

LU

>

1 0

0 . 1

1 0 - 5

I I I I

I I1 1 1

D

A D

E A

E D A

D

I I I i 1 1 1 1 1

D A

o

D

A

B

B

B C

C c C C ~ , , ~ ' ~

B ~ ~ -

. c : _

C

0 2 6

B c ~ = 8 . 9 ( E n ) - -

F O R C - T Y P E

= B R I T T L E F A I L U R E

I I I I I I I I I I I

I I I I I I I

-4

1 0 1 0 3

N O M I N A L S T R A I N R A T E ( S - 1 )

Fig. 8. Strength versus nom inal strain rate for each o f the five

conf inement conditions at T = -2C .

e v i d e n c e o f a n y l o a d i n g r a t e e f f e c t s f o r t h i s i c e . T h e

s t r e n g t h v a l u e s f o r A , D o r E - t y p e c o n f i n e m e n t a r e

v e r y s i m i l a r f o r a l l s t r a i n r a t e s. F i g u r e 8 s h o w s t h a t

w i t h i n t h e r a n g e o f l o a d i n g r a t e s i n v e s t i g a t e d , t h e d i f -

f e r e n c e b e t w e e n s t r e n g t h v a l u e s d e c r e a s e s w i t h e i th e r

t h e t y p e o f c o n f i n e m e n t o r l o a d i n g d ir e c t io n a s t h e

l o a d i n g r a te i s i n c r e a s e d . A s i m i l a r t r e n d h a s b e e n

n o t e d b y F r e d e r k i n g 1 9 7 7 ) i n h i s l a b o r a t o r y te s t s

s t u d y i n g t h e 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 th o f f r es h -

w a t e r i c e . N o t e t h a t a t t h e h i g h e r s t r a i n r a t e s i n t h i s

t e s t s e r i e s, t h e E - t y p e t e s t p r o d u c e b r i t t l e fa i lu r e o f

t h e i c e .

T h e r e s u l t s h a v e a l s o b e e n i n t e r p r e t e d i n t e r m s o f

a v e r a g e s t r e s s r a t e t o f a i l u r e , i . e . d a = o / t f w h e r e o i s

t h e s t r e ss a t y i e l d a n d t f is t h e t i m e t o f a i l u re . T h i s

w a s d o n e s i n c e a c o m p a r i s o n o n a s t r e ss r at e b as i s

l a r g e l y e l i m i n a t e s t h e i n f l u e n c e o f t h e t e st m a c h i n e

s t if f n e ss t h e r e b y a l l o w i n g a r e a d y c o m p a r i s o n w i t h

p r e v i o u s t e s t s r e p o r t e d i n t h e li t e ra t u r e S i n h a a n d

F r e d e r k i n g , 1 9 7 9 ) . F i g u r e 9 s h o w s t h e y i e l d s t r e s s a s

a f u n c t i o n o f a v e r a g e s t r e s s r a t e f o r a l l f i v e t y p e s o f

c o n f i n e m e n t f o r T = - 2 C . N o t e t h e re l a ti v e ly l o w

s t r es s -r a t e s f o r t h e A - t y p e l o a d i n g . T h i s is a r e f l e c t i o n

o f t h e v e r y l o n g t i m e s - t o -f a il u r e f o r t h is t y p e o f c o n -

f i n e m e n t . I n g e n e r a l , t h e r e s u l ts i n t e r p r e t e d i n t e r m s

o f s t r e s s r a t e s h o w t h e s a m e t e n d e n c i e s e x h i b i t e d i n

F i g u r e 8 i n t e r m s o f s t r a i n r a t e ; v i z d e p e n d e n c e o f

s t r e n g t h o n s t r es s r a t e f o r b o t h B a n d C t y p e c o n f i n e -


7/16

1 9

m e n t w i t h f u n c t i o n a l f o r m s

O 3 . 3 ( O a ) 0 2 9 f o r B-type 3)

a n d

a = 1 . 9 ( 6 a ) 2 2 f o r C - t y p e ( 4 )

w h e r e a i s i n M P a a n d

a

is

i n

M P a s - 1 ; n o s t r e s s r a t e

e f f e c t f o r a n y o f t h e o t h e r th r e e t y p e s o f c o n f i n e m e n t ;

s i m i l a r s t r e n g t h v a l u e s f o r A , D a n d E - t y p e c o n f i n e -

m e n t o v e r t h e w h o l e r a n g e o f st r e s s r a t es a n d a

g r a d u a l d e c r e a s e i n t h e d i f f e r e n c e o f t h e s tr e n g t h w i t h

t y p e o f c o n f i n e m e n t o r l o a d i n g d i r e ct i o n w i t h i n -

c r e a s i n g s t r e s s r a t e .

q ,

1 0

Z I

A ~

I I I l l l l l I I I I I I II I I I I I I I

' ~ A ~ A A A D D D E D D ~

D EA D D E E D D E D ~ D D E

A D

B B

03 B C

~ C Z

m

, - ,

_

, ~ = '1 9 ( o - ' a ~ c ~ ~ -

u J - - F O R C - T Y P E

> - _ _ ~

I - : : B R I T T L E F A I L U R E

0 . 1 I I i I I I I I I I I I l i l l l l i I I f l l l l J

-3 0 2

1 0 1 1 0 - 1 1 0 0

A V E R A G E S T R E S S R A T E [ M P a - s - ~ )

Fi g . 9 . Streng th v ersus a v era g e s tress ra te fo r ea ch o f the f i v e

c o n f 'm e m e n t c o n d i t i o n s a t T = - 2 C .

E f f e c t s o f t e m p e r a t u r e

I n a d d i t i o n t o t h e f u l l s e t o f t e s t s f o r t h e f i v e d i f -

f e r en t c o n f i n e m e n t c o n d i t i o n s f o r th e w a r m c o l u m -

nar i c e a t - 2 C , a s e p a r a te s e ri es w a s p e r f o r m e d a t

- 1 2 C

f o r th e u n c o n f i n e d ( C an d E - t y p e ) c o n d i t i o n s .

T h i s w a s d o n e p r i m a r i l y fo r c o r re l a t io n w i t h t h e e x -

i s t i n g i n f o r m a t i o n o n c o l u m n a r s e a i c e a t t h a t t e m -

p e r a t u r e . T h e r e s u lt s a r e p r e s e n t e d i n t e r m s o f a v e r a g e

s t r e ss r a t e i n F i g s . 1 0 a n d 1 1 f o r C - t y p e a n d E - t y p e

r e s p e c t i v e ly . F o r b o t h l o a d i n g d i r e c t i o n s , t h e s t re n g t h

o f t h e i c e is h i g h e r fo r t h e c o ld e r t e m p e r a t u r e s o v e r

t h e w h o l e r a n ge o f s t r e ss r a t e s, a s e x p e c t e d . A t th e

c o l d e r t e m p e r a t u r e s , r e l a t i v e l y f e w t es t s w e r e d o n e ,

s o c u r v e f i t t in g o f t h e t e st d a t a is n o t c o n s i d e r e d t o

b e r e li a b le . T h e s e d a t a a re c o m p a r e d t o p r e v i o u s l y

p u b l i s h e d r e s u lt s a t a s i m i la r t e m p e r a t u r e . F o r t h e C-

t y p e t e s ts , p r e v i o u s t e s t s in w h i c h t h e s t r e n g t h i s

p r e s e n t e d i n t e r m s o f a v e ra g e s tr e s s ra t e i n c l u d e t h o s e

o f S i nh a ( 1 9 8 3 a , 1 9 8 4 ) a n d F r e d e rk i n g a n d T i m c o

( 1 9 8 3 , 1 9 8 4 a ) , g i v en i n T a b le I , a n d p l o t t e d i n Fi g .

1 0 . T h e p r e s e n t t e s t s a t - 1 2 C a r e i n r e a s o n a b l e a g r e e -

m e n t w i t h t h e s e c u r v e s . N o t e t h a t f o r b o t h t e m p e r a -

t u r e s , al l C - t y p e f a i lu r e s w e r e d u c t i l e i n n a t u r e . F o r

t h e E - t y p e t e s t , t h e r e s u lt s c a n b e c o m p a r e d t o p r e v -

i o u s t e st s o f t h e s t r e n g t h o f v e r t ic a l ly l o a d e d c o l u m n -

n a r s e a i c e b y S i n h a ( 1 9 8 3 b ) a n d F r e d e r k i n g a n d

T i m c o ( 1 9 8 4 a ) . T h e p r e s e n t te s t s a re a l s o i n r e a s o n -

a b l e a g r e e m e n t w i t h t h e s e r e s u l t s . N o t e t h a t f o r t h e

E - t y p e l o a d i n g , t h e f a i lu r e o f t h e i c e w a s d u c t i l e f o r

6 a ~ < 0 . 1 M P a s - 1 a n d b r i t t l e f o r s t r e s s r a t e s a b o v e t h i s

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

z 4

LU

CC

CO

3

w 2

1

o

0

I I I t I I I I l l l l I I I I I I I I

C - T Y P E

T : 1 1 D

I z : 2 c , F E O E R K ,N G A N D - -

T I M C O

1 9 8 4 '

, - T = - 1 0 o C

( S I N H A 1 9 8 3 a }

I I l i l t I I I 1 1 1 1 11 [ I I I I l l

; , n

10 10 10

A V E R A G E S T R E S S R A T E ( M P a - s ~ )

Fi g . 1 0 . Streng th v ersus a v era g e s tre ss ra te fo r tw o di f ferent

t e m p e r a t u r e s f o r C - t y p e l o a d i n g .

Q-

5 : 1 2

T

(.3 10

Z

~ 8

~ 6

r r

13

~ 4

0

0

~ 2

-L

Z

D 0

t t l l l l t I t I I I I I I I I I I l l l l

D U C T I LE BRI T T L E T E MP O - -

FAILURE FAILURE [C ) J

O 1 2 o

E - T Y P E

I L I I L i I I I I ] i I I L J i l l

1 0 2 1 0 ~ 1 0 o

A V E R A G E S T R E S S R A T E ( M P a s i )

Fi g . 1 1 . Streng th v ersus a v era g e s tre ss ra te fo r tw o di f ferent

t e m p e r a t u r e s f o r E - t y p e l o a d i n g .


8/16

20

TABLE 1

Summary of previous tests

Temperature Ice Average

salinity density

(C) (700) (Mg m -3)

Test

type

Number Results* Investigators

of tests

-26 3- 5 (0.90) C

-10 6- 9 0.91 C

-11 4.5 +-0.5 0.90 C

-11 3.2-4.5 (0.85) C

-10 4- 7 0.91 C

-26 3 5 (0.90) E

-11 3.2-4.5 (0.85) E

-10 3.0 -4.5 0.90 E

7 J =3.9 at Frederking and

6a = 0.074 Timco (1980)

30 a = 4.5 Sinha (1983a)

( h a ) 2

10 a = 5.2 Frederking and

(ha) '36 Timco (1983)

18 cr = 4.1 Frederking and

(ha) '2 Timco (1984a)

10 cr = 4.6 Sinha (1984)

(6a) '29

16 ~ = 13 at Frederking and

6a = 0.27 Timco (1980)

13 a = 14 Frederking and

(ha) '22 Timco (1984a)

20 a = 25 Sinha (1983b)

(ha) '34

*o = MPa, 6a = MPas 1

f fects of brine volume and porosity

Results of strength tests on sea ice are frequently

presented in terms of the brine volume (or square

root of the brine volume fraction) of the ice. This is

done since sea ic e consists of a comple x mixture of

ice, air, salts and liquid brine such that the relative

amount of each of these constituents is determined

by the tempe rature , salinity, density and the cor-

responding phase diagrams of the various salts in the

ice (see e.g. Weeks and Ackley, 1982). With increasing

tempe rature , the liquid brine inclusio ns within the ice

increase in size. Since this increases the total p orosity

of the ice, the strength of the ice should exhibit a

functional dependence on brine volume such that it

decreases with increasing brine volume. When inter-

preting the test results in terms of brine volu me, how-

ever, it is not always possible to do this directly since

the strength of the ice is also a funct ion of the rate of

loading. As a first approximation to eliminate this ef-

fect, the present test results were normaliz ed with

respect to average stress rate. This produces a stre ngth

numbe r (On) which is indepe ndent of loading rate

and defined as

n = O 6 a ~ / a a ) ~

S )

where o is the measure d compressive strength, 6a the

corr esp ond ing average stress rate, ba is a reference

average stress rate, and b is some exponent. Based on

the tests for the warm sea ice, and cons iderin g past

tests on sea ice (see Figs. 10 and 11), a value of b =

0.22 for the exponent seems reasonable. As a refer-

ence stress rate , ba,r = 1 MPas -1 is chosen for simplic-

ity in comparison, even though it is beyond the range

of actual measurements. Using this approach, the ef-

fects of loading rate are largely eliminated, thereby

allowing an evaluatio n of the influence of brine

volume and total porosity o n the s trength o f the ice.

It should be noted that Peyton (1966 ) has introduced

a similar approach to eliminate stress rate effects (as

discussed by Weeks and Assur (1967), Schwarz and

Weeks (1977)). His results have been normalized

using a multi ple linear regression analysis and the y are

therefore not compatible with the present approach.

The reader is cautioned not to confuse the present

strength numbe r (On) with Peyton's strength index.

Figure 12 shows the strength number (an) versus

the brine volume in the ice for the present tests. In-

cluded in these results are a few tests which were per-


9/16

21

f o r m e d a t a t e m p e r a t u r e o f - 4 C . I n g en e r a l , t h e r e i s

a d e 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 b r i n e v o l u m e ,

w i t h l a r ge s c a t t e r i n t h e d a t a . F o r t h i s i c e , w h i c h h a d

u n d e r g o n e s o m e d e t e r i o r a t io n , i t w a s e v i d e n t t h a t

t h e r e w a s a c o n s i d e r a b l e v o l u m e o f ai r w i t h i n t h e i c e .

A s s u c h , t h e t o t a l p o r o s i t y o f t h e ic e w o u l d b e m u c h

h i g h e r t h a n t h a t p r e d i c t e d s o l e l y o n t h e b a s i s o f b r i n e

v o l u m e a l o n e i . e. l iq u i d i n c l u s i o n s ) . R e c e n t l y , C o x

a n d W e e k s 1 9 8 3 ) h a v e d e r iv e d s i m p l e e x p r e s s i o n s

w h i c h c a n b e u s ed t o d e t e r m i n e t h e a m o u n t o f b o t h

b r i n e a n d a i r w i t h i n t h e i c e , if t h e t e m p e r a t u r e , sa l i n -

i t y a n d d e n s i t y a r e k n o w n . U s in g t h e se e q u a t i o n s a n d

t h e s e m e a s u r e d q u a n t i t ie s , t h e a i r a n d b r in e c o n t e n t

w e r e d e t e r m i n e d f o r e a c h s a m p l e t e s t e d i n t h e p r e s e n t

t e s t s e r ie s . T h e r e s u lt s o f t h e C - t y p e c o m p r e s s i o n t e s ts

a r e s h o w n i n F i g . 1 2 a s a f u n c t i o n o f t h e t o t a l p o r o s -

i t y a i r p lu s b r i n e ) i n t h e i c e . F r o m t h i s f i g u r e , t h e r e

a re t w o t h i n g s t o n o t e . F i r s t l y , t h e r e is a m u c h b e t t e r

c o r r e l a t i o n o f t h e s t r e n g t h d a t a w i t h t o t a l p o r o s i t y

t h a n w i t h t h e b r in e p o r o s i t y . S e c o n d l y , t h e a m o u n t

o f a ir p o r o s i t y f o r t h i s i c e w a s h i g h e r b y a f a c t o r o f

3 t o 4 t h a n t h e b r i n e p o r o s i t y . T h i s r e f l e c t s t h e r e -

l a t i v e l y l o w s a l i n i t i e s a n d d e n s i t i e s m e a s u r e d F i g . 2

a n d 3 ) . T h e r e s u lt s o f F i g . 1 2 e m p h a s i z e t h e n e e d t o

k n o w t h e t o t a l p o r o s i t y o f t h e i c e i n o r d e r t o b e a b l e

t o in t e r p r e t p r o p e r l y t h e s t r e n g t h m e a s u r e m e n t .

C l e a rl y , t h e d e n s i t y o f t h e ic e s h o u l d b e m e a s u r e d

f o r a n y s t r e n g t h t e s t o n s e a i c e .

S i n c e t h e r e w a s a n a p p a r e n t s t r o n g c o r r e l a t i o n b e -

t w e e n t h e u n i -a x i al c o m p r e s s i v e s t r e n g th a n d t h e t o t a l

T O T A L P O R O S I T Y ( B R I N E + A I R ) [ % o )

0 5 0 1 0 0 1 5 0 2 0 0

6 I ] ] I I I I

5 - . ~ . ~ ~ -

,~ ,

= \

b 4 - -

, , . .

**t* ell

2

~,~,~ ~

I--

0 I I I I L I I I

0 5 0 1 0 0 1 5 0 2 0 0

B R I N E V O L U M E [ % 0 )

F i g . 1 2 . S t r e n g t h n u m b e r ( O n ) v e r s u s b r i n e v o l u m e ( a s t e r i s k s

- l o w e r a x i s ) a n d t o t a l p o r o s i t y ( c ir c l e s - u p p e r a x is ) f o r t h e

present te s t s .

p o r o s i t y , t h e s t r e n g t h n u m b e r w a s p l o t t e d v e rs u s t h e

s q u a r e r o o t o f t h e t o t a l p o r o s i t y f o r b o t h C - a n d E -

t y p e l o a d i n g . T h e s e a r e s h o w n i n F ig s . 13 a n d 1 4

r e s p e c t i v e l y . F o r b o t h t e s t t y p e s , t h e r e a p p e a r s to

c

b

rr

f ~

Z

7 -

( -9

z

LU

n

o3

8 ~ I I I I 1 I I I

7 _ _ ~ E C ] . ~ ~ z C -T Y P E _

6 - - - O - R : 8 4 1 4 9 ~ T - -

5 - - E ~ I o - -

lO

4 - i ~ , ~ o -

T z 1 2 0 C ( P R E S E N T S T U D Y )

T = 4 C ( P R E S E N T S T U D Y ) ~ I

2 ~ T - _ ~ 6 C c ( I ~ R E S E N T S N T U D A Y ) D T I M C O 1 9 8 0 ~ . . q

[ ] ]] Z ~ T : - 1 0 C ( S I N H A , 1 9 8 3 a ) & ~ |

T : - 1 l e D ( F R E D E R K t N G A N D T ~ M C O 1 9 8 3 1 ~ [

1 ~ T : 1 l e D ( F R E D E R K I N G A N D T F M C O 1 E 8 4 a I

T : 1 0 o c ( S I N H A , 1 9 8 4 ]

o I I I I L I I I I J

0 0 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0

+ - ] 1 1 2

r T O T A L P O R O S I T Y [ B R I N E A I R )

F i g . 1 3 . S t r e n g t h n u m b e r v e rs u s t h e s q u a r e r o o t o f t h e t o t a l

p o r o s i t y f o r t h e p r e s e n t t e st s f o r C - t y p e l o a d i n g . I n c l u d e d o n

t h i s f i g u r e a r e t h e e n v e l o p e s o f d a t a f r o m p r e v i o u s l y p u b -

l i s h e d r e s u lt s e x p r e s s e d i n t e r m s o f t h e s t re n g t h n u m b e r . T h e

n u m b e r b e s i d e e a ch b o x r e p r e s en t s t h e n u m b e r o f d a t a p o i n t s

f o r e a c h o f t h e s e s t u d i e s .

rr

IdJ

t~3

Z

~ , , I I I I I I I I

E - T Y P E _

2 4 [ ' - ] 2 o

2 0 - -- - - s = 3 2 6 E I 8 ~ - T - -

- - 1 - 1 o ~ - -

1 6 - - ~ 6 o

8 O T : - 1 2 e C ( P R E S EN T S T D D Y J Q

-- ~ Tu-4etJ (PRESENT STUDY)

- - T : - 2 G ( P RE S EN T S T U D Y ] & ~ - -

T :-2 60C (FREDERKING AND T lMCC ,1980)

4 - - ~ T =- 11 eC (F RED ERK qN G,TIMCO , 1 98 4 a) ~ - -

__ ~ T : -10eC (S INHA, 1983b)

o ] I I I I I I I L

0 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0

F T O T A L P O R O S I T Y ( B R I N E + A I R ) - ] 1 / 2

F i g . 1 4 . S t r e n g t h n u m b e r v e rs u s t h e s q u a re r o o t o f t h e t o t a l

p o r o s i t y f o r t h e p r e s e n t t e s t s f o r E - t y p e l o a d i n g . I n c l u d e d o n

t h i s f i g u r e a re t h e e n v e l o p e s o f d a t a f r o m p r e v i o u s l y p u b -

f i s h e d r e su l t s e x p r e s s e d i n t e r m s o f t h e s t re n g t h n u m b e r . T h e

n u m b e r b e s id e e a c h b o x r e p r e se n t s t h e n u m b e r o f d a t a p o i n t s

f o r e a c h o f t h e s e s t u d i e s .


10/16

22

b e a g o o d c o r r e l a t i o n f o r a ll t h e t e s t d a t a w i t h a n

a p p a r e n t l in e a r d e p e n d e n c e b e t w e e n O n a n d X /U T .

T h e p r e s e n t a p p r o a c h , t h e r e f o r e , s ee m s t o p r ov i d e a

m e t h o d o f c o m p a r i s o n o f c o m p r e ss i v e b e h av i o u r o f

s e a i ce i n t e r m s o f b r i n e v o l u m e , a ir p o r o s i t y a n d

l o a d i n g r a t e . I t i s i n t e r e s t i n g t o i n c l u d e i n t h e s e

f i g u r es t h e r e s u l t s o f p r e v i o u s t e s t s w h i c h h a v e b e e n

m a d e o n c o l u m n a r s e a i c e w i t h d i f f e r e n t s a l in i t ie s a n d

d e n s i t ie s . F o r t h e C - t y p e l o a d i n g , t h is i n c l u d e s t h e

w o r k o f S i n h a ( 1 9 8 3 a , 1 9 8 4 ) , a n d F r e d e r k in g a n d

T i m c o ( 1 9 8 0 , 1 9 8 3 , 1 9 8 4 a ) as s u m m a r i z e d in T a b l e

1 . F o r t h e s e , i f t h e f u n c t i o n a l d e p e n d e n c e b e t w e e n

t h e s t r e n g t h a n d s t r e s s r a t e w a s g i v e n , t h e s t r e n g t h

n u m b e r w a s t a k e n a s t h e v a l u e a t 1 M P a s 1 u s i n g t h e

r e g r e s s io n e q u a t i o n . I f t h i s r e l a t io n s h i p w a s n o t g i v e n ,

t h e s t r e n g t h v a l u e s w e r e n o r m a l i z e d t o t h i s s t r e s s r a t e

v a l u e u s in g e q n . ( 5 ) a n d b = 0 . 2 2 . T h e r e s u l ti n g c o m -

p r e s s o n s t r e n g t h n u m b e r is p l o t t e d v e r su s t h e s q u a re

r o o t o f t h e t o t a l p o r o s i t y b a s e d o n t h e a v e r a g e s a l in i t y

a n d d e n s i t i e s f o r t h e i c e . I t s h o u l d b e n o t e d t h a t f o r

t h e t e s t s e ri es o f F r e d e r k i n g a n d T i m c o ( 1 9 8 0 ,

1 9 8 4 a ) , t h e d e n s i t y o f t h e i ce w a s n o t m e a s u r e d .

T h e r e f o r e , f o r t h e s e t e s t s e r i e s , t h e d e n s i t y w a s e s t i -

m a t e d b a s e d o n t h e t i m e o f t h e y e a r a n d t h e p h y s i c al

d e s c r i p t i o n o f t h e i c e . T h e t e s t r e s u l t s f o r v e r t i c a l l y -

l o a d e d ( E - t y p e ) c o m p r e s s i v e s t r e n g t h a r e s h o w n i n

F i g . 1 4 w i t h t h e a d d i t i o n a l t e s t r e s u lt s f r o m S i n h a

( 1 9 8 3 b ) a n d F r e d e r k i n g a n d T i m c o ( 1 9 8 0 , 1 9 8 4 a ) .

E x a m i n a t i o n o f t h e s e f i g u re s i n d i c a t e s t h a t t h e r e i s a

g o o d c o r r e l a t i o n f o r al l o f th e t e s t s e r ie s u s i n g t h is

a p p r o a c h . A l i n e a r r e g re s s i o n a n a l y s is o f t h e d a t a ,

w i t h a p p r o p r i a t e w e i g h i n g a c c o r d i n g t o t h e n u m b e r

o f d a t a p o i n t s f r o m e a c h t e s t s e r i e s y i e ld s , f o r t h e C -

t y p e

O n = 8 . 4 - 1 4 . 9 X ~ T ( 6 )

a n d , f o r t h e E - t y p e

O n = 3 2 . 6 - 6 1 . 8 V ~ T ( 7 )

T h e s e e q u a t i o n s c a n b e r e - a r r a n g e d a s

O n = 8 . 4 ( 1 - v r f f T / 3 2 0 ) f o r C - t y p e ( 8 )

O n = 3 2 . 6 ( 1 - ~ / V T / 2 8 0 ) f o r E - t y p e ( 9 )

w h e r e v T i s i n p a r t s p e r t h o u s a n d i n e q n s . ( 8 ) a n d ( 9 ) .

U s e c a n b e m a d e o f e q . ( 5 ) t o r e- e x p r e s s t h e s e

s t r e n g t h n u m b e r s ( e q n s . ( 8 ) a n d ( 9 ) ) in t e r m s o f t h e

u n i - a x ia l c o m p r e s s i v e s t r e n g t h o f c o l u m n a r s e a i c e

f o r t h e t w o l o a d i n g d i r e c t i o n s . T h a t is , s i n c e a n =

a 6 a , r / 6 a ) b a n d d a , r = 1 M P a s 1 , t h e s e e q u a t i o n s

b e c o m e

o = 8. 4( Oa 0.22 ( 1 - N / V T/ 3 20 ) ( 10 )

f o r C - t y p e , a n d

o = 3 2 .6 (d a) '22 (1 - X/f iT/28 0 ) (11 )

f o r E - t y p e , w h e r e o is M P a , O a is i n M P a s 1 s u c h t h a t

1 0 - 3 ~ O a ~ 1 0 a n d P T i s i n p a r t s p e r t h o u s a n d .

T h e s e e x p r e s s i o n s r e l a t e t h e u n i - a x i a l c o m p r e s s i v e

s t r e n g t h o f c o l u m n a r s e a ic e f o r b o t h h o r i z o n t a l a n d

v e r t ic a l l o a d i n g i n t e r m s o f t h e t o t a l p o r o s i t y o f t h e

i c e a n d t h e a v e r a g e s tr e s s - ra t e f o r l o a d i n g . T h e s e e q u a -

t i o n s i n d i c a t e t h a t t h e r a t i o o f t h e u n i- a x i a l c o m p r e s -

s i ve s t r e n g t h f o r v e r t i c a l a n d h o r i z o n t a l l o a d i n g is 3 . 9

i n d e p e n d e n t o f b o t h t h e p o r o s i t y o f t h e i ce a n d lo a d -

i n g r a t e. M o r e o v e r , e x t r a p o l a t i o n o f b o t h e q u a t i o n s

t o h i g h p o r o s i t i e s in d i c a t e s t h a t t h e s t r e n g t h o f t h e

i c e a p p r o a c h e s z e r o f o r p o r o s i t i e s a b o v e - ~ 3 0 0 % o .

E x t r a p o l a t i o n o f t h e e q u a t i o n s t o l ow p o r o si t ie s

sug g e s t s t ha t f o r V to = 0 , O = 8 .4 (d ra ) ' 22 a nd o =

3 2 . 6 ( d a ) '2 2 f o r C - t y p e a n d E - t y p e l o a d i n g r e s p e c t iv e -

l y . T h e f o r m e r is i n r e as o n a b l e a g r e e m e n t w i t h b u t

l e s s t h a n t h e s t r e n g t h m e a s u r e d o n c o l u m n a r

f r e s h -

w a t e r i c e l o a d e d h o r i z o n t a l l y a t T = - 1 0 C w h e r e a c

= 1 1 .7 (O a ) ' 3 (S inh a , 198 1 ) .

I n m a n y i n s t a n c e s , i t i s m o r e u s e f u l t o e x p r e s s t h e

u n i - a x ia l c o m p r e s s i v e s t r e n g t h i n t e r m s o f s t r a i n r a t e

r a t h e r t h a n s t r e ss r a t e . T h i s c a n b e d o n e f o r b o t h

l o a d i n g d i r e c t i o n s . F o r C - t y p e l o a d i n g , a c o m p a r i s o n

o f t h e r a t e - d e p e n d e n c e f o r b o t h n o m i n a l s t r a in r a te

( e q n . ( 2 ) ) a n d a v e r a g e s t r e s s - r a t e ( e q n . ( 4 ) ) g i v e s

o = 8 . 9 @ n ) 'z 6 = 1 . 9 ( d a ) '2 2 w h i c h , w h e n s u b s t i t u t e d

i n t o e q n . ( 1 0 ) y i e l d s

o = 3 9 ( g n ) ' ~ ( 1 - X / U T / 3 2 0 ) ( 1 2 )

w h e re o i s i n MPa , e n i s i n s a suc h tha t 10 - s ~< e n ~ / 7

f2 = o x - O y ) 2 + O x 2 + O y 2 _ 4 5 . 6

f o r Ox + oy < 3 ' (27 )

w h e r e 3 ' i s t h e s u m o f t h e a p p l i e d a n d c o n f i n i n g l o a d

f o r A - t y p e c o m p r e s s i o n ( = - 8 . 5 M P a i n t h is c a se ) .

T h i s e x p r e s s i o n w h i c h r e p r e s e n t s t h e c a s e o f p l a n e

s t r e ss i s s h o w n i n F i g . 1 5 a a s t h e h e a v y d a s h e d l i n e .

T h i s m o d i f i e d n - t y p e f u n c t i o n a p p e a r s t o b e a r e a s o n -


15/16

27

able representation of the failure envelope for plane

stress conditions. In a similar manner, the full failure

envelope for colder (T = -10C) columnar sea ice can

be determined as

fl = 0.04 [(Oy - Oz) 2 + (Oz - Ox) 21 + 0.43(0x - Oy)2

+ 2.52(ryz 2 +

r x z : )

+ 1.78rxy 2 + 0.78(ox + ay)

+ 0.74Oz - 1 for

Ox + Oy >1 3

f 2 = ( O x - O y ) 2 + O x 2 + O y 2 - 136

for

O x

+ o3, < 3' (28)

where 3' = -14.7 MPa in this case. This is shown in

Fig. 16.

CO NC L U S I O N S

The results of the present tests indicate the general

behaviour and strength of columnar sea ice under

confined conditions. The test results indicate:

(1) Confinement conditions do not appreciably

affect the strength of the ice if the confinement is of

either B or D-type. For A-type confinement, how-

ever, the stress level in the ice can be over four times

higher than the strength of the ice with no confine-

ment.

(2) A-type confinement on columnar sea ice pro-

duces strain-hardening with correspondingly longer

times to failure.

(3) The ratio of the confinement stress to applied

stress at yield for the test apparatus used is of the

order of 58%, 10% and 4% for A-type, B-type and D-

type confinement, respectively.

(4) Comparison of unconfined tests indicates that

the strength of columnar ice loaded vertically is ap-

proximately four times higher than the strength of

the ice loaded horizontall y.

(5) A strength number has been introduced

which ties together the results of the present tests and

a number of previous tests for uni-axial loading. This

leads to an empirical relationship which gives the

functional dependence of the uni-axial compressive

strength in terms of loading direction, loading rate,

temperature, salinity, density and total porosity.

(6) For columnar ice, over the range of loading

rates of 10 -s to

10 -3 S 1 ,

there is a power law depend-

ence of the strength of the ice for B and C-type load-

ing only. For the other three types of confinement,

there is no apparent loading rate effect.

(7) The three-dimensional yield surface for colum-

nar ice changes both size and shape with changes in

loading rate.

(8) With changes in temperature, the failure en-

velope remains similar in shape, but becomes appreci-

ably larger as the temperature decreases.

(9) The results of confined compression tests can

be used to evaluate the general applicability of vari-

ous formulations describing the failure envelope of

the ice. Moreover, the results can be used to evaluate

the coefficients which give the best description of the

yield surface.

(10) The results o f the present tests have been

analyzed and fit to a modified n-type yield function

for temperatures of -2 and -10C at en = 2 X 10 r4

s -1. These expressions, together with an appropriate

representation of the rheological behaviour of the ice

should provide a solid basis for the use of plasticity

theory to analyze various problems in ice mechanics

and Arctic engineering.

C K N OW L E D G EM E N T S

The authors would like to thank Joachim Schwarz

for the invitation to participate in these trials of the

Polarstern . Appreciation is also extended to Tony

Gow for the use of some of his equipment, and to

Guenther Hackbarth for technical assistance. The

voyage was funded by the German Ministry for Re-

search and Technology. The Polarstern was provided

for this mission of icebreaking research by the Alfred-

Wegener-lnstitute ffir Polarforschung. This paper is a

contribution of the Divisions of Mechanical Engineer-

ing and Building Research, and it is published with

the approval of the Directors of the Divisions.

R E F E R E NC E S

Blanchet, D. and Hamza, H. (1983). Plane-strain compressive

strength of first year Beaufort Sea ice. Proc. POAC 83,

Vol. 3, Helsinki, Finland, pp. 84-96.

Cox, G.F.N. and Weeks, W.F. (1983). Equations for deter-

mining the gas and brine volumes in sea ice samples. J.

Glaciol., 29: 306-316.

Croasdale, K.R., Morgenstern, N.R. and Nuttall, J.B. (1977).

Indentation tests to investigate ice pressures on vertical

piers. J. Glaciol., 19 (81): 301-312.

Frederking, R.M.W. (1977). Plane-strain compressive strength


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2 8

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Confined Compression Tests Outlining the Failure Envelope of Columnar Sea Ice

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