The flexural behaviour of ice from in situ cantilever beam tests

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The flexural behaviour of ice from in situ cantilever beam tests

Frederking, R. M. W.; Hausler, F.-U.

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IAHR INTERNATIONAL ASSOCIATION FOR HYDRAULIC RESEARCH

THE FLEXURAL BEHAVIOUR OF ICE FROM IN SITU CANTILEVER BEAM TESTS

R . F r e d e r k i n g

D i v i s i o n o f B u i l d i n g Research

N a t i o n a l Research Council of Canada Ottawa, O n t a r i o , Canada, KIA OR6 F

.

-U

.

Haus l e r

Hamburgische S c h i f f b a u - V e r s u c h s a n s t a l t GmbH Hamburg, Germany

SYNOPSIS

The c a n t i l e v e r beam t e s t h a s been u s e d v e r y e x t e n s i v e l y i n b o t h t h e f i e l d and l a b o r a t o r y t o i n v e s t i g a t e t h e f l e x u r a l s t r e n g t h and s t r a i n modulus of s e a i c e . Shortcomings i n t h e t e s t a r e g e n e r a l l y r e c o g n i z e d , hence t h e s e measurements a r e used o n l y a s i n d e x v a l u e s . One problem w i t h f l e x u r a l t e s t s i s t h a t some p r i o r knowledge about t h e m a t e r i a l p r o p e r t i e s i s

r e q u i r e d b e f o r e t h e y c a n b e a n a l y z e d .

The f i r s t p a r t of t h i s p a p e r c o n s i d e r s t h e e l a s t i c t h e o r y of a beam on an e l a s t i c f o u n d a t i o n . V a r i o u s f a c t o r s t h a t a f f e c t t h e i n t e r p r e t a t i o n of c a n t i l e v e r beam t e s t s a r e examined, i . e . , beam geometry, e l a s t i c founda- t i o n e f f e c t , and nonhomogeneity o f e l a s t i c modulus through beam t h i c k n e s s . The second p a r t of t h e p a p e r p r e s e n t s r e s u l t s from i n s i t u c a n t i l e v e r beam t e s t s i n I s f j o r d e n , S p i t s b e r g e n , conducted d u r i n g f u l l s c a l e t r i a l s w i t h t h e o f f s h o r e s u p p l y v e s s e l M . V . "Werdertor" by a German group o f i n v e s t i - g a t o r s under t h e management of t h e Hamburgische S c h i f f b a u - V e r s u c h s a n s t a l t

.

F i e l d t e s t s were c a r r i e d o u t on 0 . 4 m t h i c k s e a i c e w i t h beam l e n g t h s up t o 1 2 m . Load and beam d e f l e c t i o n s a t up t o t h r e e p o i n t s were measured v e r s u s t i m e . From t h e s e measurements s t r e n g t h and modulus i n d e x v a l u e s were determined and t h e b e h a v i o u r o f a l o n g c a n t i l e v e r beam on a founda-

t i o n was c o n f i r m e d . F r a n k e n s t e i n ' s approach o f r e l a t i n g s t r e n g t h and s t r a i n modulus t o t h e b r i n e volume o f s a l i n e i c e was found t o b e q u i t e a p p l i c a b l e .

THE FLEXURAL BEHAVIOUR OF ICE FROM IN SITU CANTILEVER BEAM TESTS

INTRODUCTION

The i n t e r a c t i o n mechanism between a f l o a t i n g i c e c o v e r and s t r u c t u r e i s

complex, i n v o l v i n g m u l t i a x i a l nonuniform s t r e s s s t a t e s , f r i c t i o n , buoyancy, d r a g and i n e r t i a l e f f e c t s . A n a l y t i c a l , model and f i e l d s t u d i e s have a l l been a p p l i e d t o o b t a i n s o l u t i o n s t o t h i s problem w i t h v a r y i n g d e g r e e s of

s u c c e s s . I n t h e c a s e o f h y d r a u l i c s t r u c t u r e s w i t h i n c l i n e d f a c e s t h e f l e x u r a l b e h a v i o u r of t h e i c e c o v e r i s an i m p o r t a n t f a c t o r i n e s t a b l i s h i n g i c e l o a d i n g s .

The i n s i t u c a n t i l e v e r beam t e s t h a s been used e x t e n s i v e l y i n b o t h f i e l d and l a b o r a t o r y ( F r a n k e n s t e i n , 1968; Tabata e t a l , 1975; Lavrov, 1969; Mzzttznen, 1975; Schwarz, 1975) t o i n v e s t i g a t e f l e x u r a l s t r e n g t h and

s t r a i n modulus o f f l o a t i n g i c e c o v e r s . I n s i t u t e s t i n g m a i n t a i n s t h e t e s t beam under t h e same c o n d i t i o n s a s t h o s e o f t h e i c e c o v e r , i . e . , b u o y a n t l y s u p p o r t e d b y t h e w a t e r and w i t h a t e m p e r a t u r e v a r i a t i o n t h r o u g h t h e

t h i c k n e s s of t h e i c e . F l e x u r e t e s t i n g , however, h a s t h e d i s a d v a n t a g e of b e i n g an i n d i r e c t t e s t , i . e . , b e f o r e t h e r e s u l t s c a n be i n t e r p r e t e d , a number o f assumptions must b e made c o n c e r n i n g t h e m a t e r i a l b e h a v i o u r . These assumptions i n c l u d e , (1) p l a n e s e c t i o n s remaining p l a n e , ( 2 )

d e f l e c t i o n s s m a l l compared w i t h t h i c k n e s s o f beam, and ( 3 ) l i n e a r e l a s t i c o r v i s c o e l a s t i c b e h a v i o u r . I n t h e c a s e of i c e i t i s known t h a t t h e l a s t assumption i s n o t always s a t i s f i e d . N e v e r t h e l e s s t h e f l e x u r a l t e s t i s a u s e f u l a n a l o g u e o f i c e b e h a v i o u r on a s l o p i n g s t r u c t u r e and i s a c c e p t e d a s an i n d e x t e s t (Schwarz and Weeks, 1977).

F I G U R E 1

S C H E M A T I C O F B U O Y A N T L Y SUPPORTED I N S I T U C A N T I L E V E R B E A M

wb/w, i s p l o t t e d a s a f u n c t i o n o f nondimensional beam l e n g t h , XR, i n F i g u r e 3 . Provided beam l e n g t h X R i s l e s s t h a t 0 . 5 t h e r e i s l i t t l e d i f f e r e n c e i n t h e d e f l e c t i o n s . Both i n n a t u r e and i n t h e model t a n k a beam l e n g t h t o i c e t h i c k n e s s r a t i o of 10 c o r r e s p o n d s t o a nondimensional beam l e n g t h o f a b o u t 0 . 5 . T h e r e f o r e a s long a s beam l e n g t h i s no more t h a n 10 t i m e s t h e i c e t h i c k n e s s s i m p l e c a n t i l e v e r beam t h e o r y c a n b e

s a t i s f a c t o r i l y u s e d t o c a l c u l a t e t h e b u l k e l a s t i c modulus, Eb. For l o n g e r beams t h e e f f e c t o f i g n o r i n g buoyancy would r e s u l t i n t h e d e t e r m i n a t i o n o f a t o o l a r g e v a l u e o f s t r a i n modulus. T h e r e f o r e E q u a t i o n ( I ) , which

i n c l u d e s buoyancy e f f e c t s , must b e used t o s o l v e f o r Eb.

The bending moment d i s t r i b u t i o n a l o n g t h e l e n g t h o f t h e beam i s g i v e n by

Mb (XI

- -

- - -

1 cosh A(R-x) s i n Xx c o s h X R + c o s A(&-x) s i n h Xx c o s XR

PR XR ( 2)

cosh2 A R + c o s 2 AR

Nondimensional moment d i s t r i b u t i o n s f o r 4, 8 and 12 m long b u o y a n t l y s u p p o r t e d beams ( s o l i d 1 i n e s ) ' a n d s i m p l e c a n t i l e v e r beams (dashed l i n e s ) a r e p l o t t e d i n F i g u r e 4 . The nondimensional moment i s 1 a t t h e r o o t of a n unsupported c a n t i l e v e r beam. Buoyancy r e d u c e s t h e r o o t bending moment by o n l y a b o u t 3% f o r a 4 m long beam b u t f o r 8 and 1 2 m beams it l e a d s t o a s u b s t a n t i a l r e d u c t i o n i n t h e bending moment, a b o u t 35% and 75% r e s p e c - t i v e l y , a t t h e beam r o o t . A l s o n o t e t h a t f o r t h e 1 2 m beam t h e bending moment i s s u b s t a n t i a l l y c o n s t a n t w i t h i n 4 m o f t h e r o o t . I n n a t u r e one would e x p e c t a beam could f a i l anywhere i n t h i s s e c t i o n .

I t h a s b e e n shown by Schwarz and Kloppenburg (1976) t h a t f o r nondimen- s i o n a l beam l e n g t h s , XR, up t o

IT/^

t h e maximum moment o c c u r s a t t h e beam r o o t . For g r e a t e r beam l e n g t h s t h e p o s i t i o n of maximum moment moves away from t h e beam r o o t back towards t h e t i p . The a c t u a l p o s i t i o n of t h e maximum bending moment i s p l o t t e d i n F i g u r e 5 . For a nondimensional beam l e n g t h , XR, o f 2 t h e maximum moment p o s i t i o n has a l r e a d y moved t o t h e p o s i t i o n o f a s e m i - i n f i n i t e beam, i . e , , Axc = ~ / 4 . The maximum

nondimensional bending moment i s p l o t t e d v s nondimensional beam l e n g t h X R

i n F i g u r e 6 . For l e n g t h s g r e a t e r t h a n

IT/^

t h e dashed l i n e r e f e r s t o t h e bending moment a t t h e r o o t , i . e . , h e r e t h e maximum bending moment i s n o t a t t h e r o o t b u t a t some i n t e r m e d i a t e p o i n t a l o n g t h e beam.

Nonhomogeneous Beam on a n E l a s t i c Foundation

The f o r e g o i n g h a s assumed t h a t t h e i c e c o v e r i s homogeneous and i s o t r o p i c . T h i s i s i n f a c t n o t t h e c a s e . Normally a n i c e c o v e r i n n a t u r e has a

v a r i a t i o n o f t e m p e r a t u r e through t h e d e p t h and t h e r e f o r e i s nonhomogeneous i n t h e d i r e c t i o n normal t o t h e s u r f a c e . Kerr and Palmer (1972), however, have shown t h a t a nonhomogeneous beam c a n b e t r e a t e d a s a homogeneous beam p r o v i d e d a m o d i f i e d f l e x u r a l r i g i d i t y i s employed. The modified f l e x u r a l r i g i d i t y , D l , i s c a l c u l a t e d from t h e f o l l o w i n g e x p r e s s i o n

T h i s p a p e r d e a l s w i t h t h e t h e o r y o f homogeneous and nonhomogeneous e l a s t i c , beams on an e l a s t i c f o u n d a t i o n . T h i s i s followed by t h e r e s u l t s of i n s i t u s e a i c e c a n t i l e v e r beam t e s t s t h a t a r e a n a l y z e d u s i n g t h e appraoch out 1 ined

.

THEORETICAL CONSIDERATIONS C a n t i l e v e r Beam on a n E l a s t i c Foundation

The t h e o r y o f beams on a n e l a s t i c f o u n d a t i o n has been t r e a t e d by Hetenyi (1946) and t h e p a r t i c u l a r c a s e o f c a n t i l e v e r i c e beams s u p p o r t e d e l a s t i - c a l l y by t h e buoyant a c t i o n of t h e water h a s been c o n s i d e r e d b y Schwarz and Kloppenburg (1976)

.

The c a s e o f a n i n s i t u c a n t i l e v e r i c e beam w i l l now b e t r e a t e d i n d e t a i l . The i c e i s assumed t o b e p e r f e c t l y e l a s t i c ,

i s o t r o p i c and homogeneous. The problem b e i n g c o n s i d e r e d is shown

s c h e m a t i c a l l y i n F i g u r e 1. The e q u a t i o n f o r t h e d e f l e c t i o n l i n e wb(x) is g i v e n by

B 2X s i n h X(R-x) c o s Xx cosh XR

-

s i n A(R-x) cosh Ax c o s X R

W ( x )

P

=

k

b (1)

cosh2 XR + cos2 X R

where P = load a p p l i e d t o f r e e end o f beam [kN]

B = Beam width [ml

k = _{pwg = subgrade r e a c t i o n (weight d e n s i t y o f water) [kN/m3]} Ebh D = - 1 2 f l e x u r a l r i g i d i t y [ kN/ml Eb = b u l k s t r a i n modulus [kPa* ] h = i c e t h i c k n e s s

R

= beam l e n g t h T y p i c a l d e f l e c t i o n c u r v e s f o r v a r i o u s beam l e n g t h s a r e p l o t t e d i n F i g u r e 2, assuming E = 1.4 GPa, k = 10 k ~ / m ~ and h = 0.4 m. The s o l i d l i n e s r e p r e s e n t b u o y a n t l y s u p p o r t e d c a n t i l e v e r beams and t h e dashed l i n e s

r e p r e s e n t unsupported c a n t i l e v e r beams. For t h e 4 m long beam t h e buoyant e f f e c t i s n e g l i g i b l e , however, f o r t h e 8 and 12 m long beams, t h e buoyant e f f e c t l e a d s t o a s u b s t a n t i a l r e d u c t i o n i n t h e d e f l e c t i o n s . I t i s u s e f u l t o p l o t t h e r a t i o of t h e t i p d e f l e c t i o n of a buoyantly s u p p o r t e d c a n t i - l e v e r beam t o t h e t i p d e f l e c t i o n o f a simple c a n t i l e v e r beam. T h i s r a t i o ,

B E A M P O S I T I O N , rn 0 2 4 6 8 1 0 1 2 F I G U R E 2 D E F L E C T I O N L l N E S O F B U O Y A N T L Y S U P P O R T E D (-1 A N D U N S U P P O R T E D (---I B E A M S O F V A R I O U S L E N G T H S . 1 0 0 0.2 0.4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 l . . 8 2 . 0 N O N D I M E N S I O N A L B E A M L E N G T H , F I G U R E 3 R A T I 0 O F B U O Y A N T L Y S U P P O R T E D B E A M D E F L E C T I O N T O S I M P L E C A N T I L E V E R B E A M D E F L E C T I O N

n Z 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 0 z _{B E A M P O S I T I O N , m} F I G U R E 4 N O N D I M E N S I O N A L B E N D I N G M O M E N T D l S T R l B U T I O N F O R B U O Y A N T L Y S U P P O R T E D (-) A N D U N S U P P O R T E D (---I B E A M S OF V A R I O U S L E N G T H S ,

I

N O N D I M E N S I O N A L B E A M L E N G T H , F I G U R E 5 P O S I T I O N O F M A X I M U M B E N D I N G M O M E N T , X c , A S A F U N C T I O N O F L E N G T H O F B U O Y A N T L Y S U P P O R T E D B E A M

which when s o l v e d h a s t h e form

where D i s t h e f l e x u r a l r i g i d i t y o f a homogeneous beam w i t h a c o n s t a n t s t r a i n modulus. Before t h e r i g i d i t y f a c t o r , K, c a n b e e v a l u a t e d , however, t h e p o s i t i o n of t h e n e u t r a l a x i s , zo, ( s e e F i g u r e 1) must be e s t a b l i s h e d . The c o n d i t i o n t h a t t h e r e b e n o r e s u l t a n t f o r c e i n t h e x - d i r e c t i o n on a n y p l a n e x = c o n s t a n t y i e l d s t h e e x p r e s s i o n

from which t h e p o s i t i o n o f t h e n e u t r a l a x i s c a n be c a l c u l a t e d . A t t h i s s t a g e i t i s u s e f u l t o e v a l u a t e K f o r some t y p i c a l s t r a i n modulus d i s t r i b u - t i o n s , E ( z ) . Kerr and Palmer (1972) have proposed a g e n e r a l e x p r e s s i o n of t h e form

where n and

a

_{a r e a r b i t r a r y c o n s t a n t s s e l e c t e d t o g i v e a n approximation of}

t h e s t r a i n modulus d i s t r i b u t i o n and Et i s t h e s t r a i n modulus on t h e t o p s u r f a c e of t h e i c e c o v e r . Applying Weeks and A s s u r l s (1967) r e l a t i o n between b r i n e volume and s t r a i n modulus t o f i r s t y e a r s e a i c e t h e

parameters

a

and n i n Equation (6) would b e approximately 0.4 and 4

r e s p e c t i v e l y . The r i g i d i t y r e d u c t i o n f a c t o r , K, i s p l o t t e d i n F i g u r e 7 f o r a range o f v a l u e s o f

a

_{and n .}

The e q u a t i o n s f o r t h e d e f l e c t i o n l i n e , wn, and bending moment, Mn of a nonhomogeneous beam a r e given, i n terms o f t h o s e f o r a homogeneous beam, by

and

The d e f l e c t i o n s and moments a r e s e e n t o be d i r e c t l y p r o p o r t i o n a l t o t h o s e

of a homogeneous beam. Because K i s always l e s s t h a n 1, t a k i n g t h e f o u r t h

r o o t o f i t b r i n g s i t c l o s e r t o 1 and t h u s a t t e n u a t e s t h e e f f e c t s of t h e

nonhomogeneity o f t h e beam. The p r e c e d i n g example of f i r s t y e a r sea i c e

y i e l d s a K o f 0.75 and

~4

of 0.93. I t must a l s o b e k e p t i n mind t h a t because t h e s t r a i n modulus v a r i e s through t h e i c e t h i c k n e s s , t h e s t r e s s

N O N D I M E N S I O N A L B E A M L E N G T H , XL F I G U R E 6 M A X I M U M B E N D I N G M O M E N T A S A F U N C T I O N O F B E A M L E N G T H F I G U R E 7 R I G l D I T Y R E D U C T I O N F A C T O R , K. O F A N O N H O M O G E N E O U S B E A M A S A F U N C T I O N O F S T R A I N - M O D U L U S D I S T R I B U T I O N P A R A M E T E R S , Q A N D n

d i s t r i b u t i o n w i l l n o t b e l i n e a r . I t i s p o s s i b l e , depending upon t h e n a t u r e of E ( z ) , f o r t h e maximum s t r e s s t o b e a t a l o c a t i o n o t h e r t h a n t h e extreme f i b r e s o f t h e beam.

The g e n e r a l t r e a t m e n t of a nonhomogeneous p l a t e by Kerr and Palmer (1972) was a c t u a l l y preceded by F r a n k e n s t e i n (1970) who p r e s e n t e d a t e c h n i q u e f o r a n a l y z i n g t h e s t r e n g t h o f i n s i t u c a n t i l e v e r beams w i t h b r i n e volume

v a r i a t i o n t h r o u g h t h e t h i c k n e s s o f t h e beam. He u s e d t h e b r i n e r e l a t i o n s f o r s t r e n g t h and e l a s t i c i t y developed by Weeks and Assur (1967).

where v i s t h e b r i n e volume and

a,

and Eo a r e c o r r e s p o n d i n g v a l u e s f o r f r e s h w a t e r i c e , i . e . , v = 0 . B r i n e volume i s a f u n c t i o n of s a l i n i t y and t e m p e r a t u r e . The f o l l o w i n g apprc .imate e x p r e s s i o n

where S i s s a l i n i t y i n u n i t s of p a r t s p e r thousand (mass) and 8 i s temper- a t u r e i n d e g r e e s C e l s i u s , was developed by F r a n k e n s t e i n and Garner (1967). T h i s e q u a t i o n i s v a l i d f o r t h e r a n g e -O.S°C > 8 > -23°C. Temperature and s a l i n i t y a r e measured a t d i s c r e t e p o i n t s through a n i c e c o v e r and hence t h e b r i n e volume a n d s t r a i n modulus p r o f i l e c a n b e approximated b y a f u n c t i o n l i k e t h a t o f Equation (6) o r r e p r e s e n t e d n u m e r i c a l l y .

Assuming p l a n e s e c t i o n s remain p l a n e , t h e s t r e s s p r o f i l e through t h e beam i s g i v e n by

where r i s t h e r a d i u s o f c u r v a t r , L d , and z = 0 i s t h e n e u t r a l a x i s o f t h e beam. The p o s i t i o n o f t h e neuty- t a x i s o f a beam f o r which t h e b r i n e volume p r o f i l e i s known i s deterlnined by s u b s t i t u t i n g Equation (10) i n t o Equation (5) and s o l v i n g f o r zo. The bending moment on a c r o s s - s e c t i o n of t h e beam, i n t e r m s o f t h e s t r e s s developed on it i s g i v e n b y

Knowing t h e a p p l i e d moment Mb f - 2 - n Equation (2) and s u b s t i t u t i n g E q u a t i o n s

s t r e n g t h i s f i n a l l y c a l c u l a t e d by s u b s t i t u t i n g t h e v a l u e s of E o / r and Equation (10) i n t o Equation (12), i . e . ,

where v and z 1 a r e a t t h e p o i n t of f a i l u r e ( z ' =

-zo

o r h - z o ) . Once

a

i s

known, t h e n

a.

can be c a l c u l a t e d from Equation ( 9 ) . Frankenstein f u r t h e r

suggested t h a t i f t h e v a l u e s of

a.

were v e r y s i m i l a r f o r v a r i o u s beam t e s t s then a r e l a t i v e l y simple b r i n e volume d e t e r m i n a t i o n i n t h e f i e l d and i t s a p p l i c a t i o n t o Equation (9) could y i e l d a c c e p t a b l e f l e x u r a l s t r e n g t h v a l u e s without going t o t h e e f f o r t of l a r g e - s c a l e i n s i t u c a n t i l e v e r beam t e s t s .

T h i s approach of Frankenstein w i l l be used i n analyzing t h e r e s u l t s f o r

f l e x u r a l s t r e n g t h of a s e r i e s of c a n t i l e v e r beam t e s t s c a r r i e d out i n t h e f i e l d . Also buoyancy e f f e c t s w i l l be considered i n c a l c u l a t i n g s t r a i n modulus.

EXPERIMENTAL RESULTS F i e l d T e s t s i n S ~ i t s b e r e e n

I n A p r i l 1977 a program of i n s i t u c a n t i l e v e r beam t e s t s was c a r r i e d o u t i n I s f jorden, Spitsbergen, a s p a r t of t h e A r c t i c icebreaking t r i a l s of t h e

o f f s h o r e supply v e s s e l M.V. "Werdertor". The t o t a l icebreaking program

was c a r r i e d out by t h e German Companies, Hamburgische Schiffbau- V e r s u c h s a n s t a l t (management), V e r e i n i g t e Tanklager-Gesellschaft,

Germanischer Lloyd and J a s t r a m ( s e e Schwarz and Hoffman, 1978). Maximum information on t h e f l e x u r a l behaviour of t h e i c e was d e s i r e d s o a

comprehensive beam t e s t program was planned. Continuous r e c o r d s of load and d e f l e c t i o n s were i n d i c a t e d a s well a s d e t a i l e d temperature and

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

Following s e l e c t i o n of a t e s t s i t e deemed t o have i c e t y p i c a l of t h a t through which a s e r i e s o f icebreaking t r i a l s would be run, a small camp was s e t up on t h e i c e . A t e n t was p i t c h e d t o provide s h e l t e r f o r t h e r e c o r d i n g and s i g n a l c o n d i t i o n i n g i n s t r u m e n t a t i o n and personnel.

E l e c t r i c a l power f o r t h e instruments came from a p o r t a b l e g e n e r a t o r . The camp was maintained f o r s e v e r a l days while a s e r i e s of beam t e s t s and i c e c o r e samplings were c a r r i e d out i n t h e v i c i n i t y .

Beam p r e p a r a t i o n was a i d e d by t h e f a c t t h a t i c e t h i c k n e s s was i n t h e range of 0.4 m t o 0 . 5 m . A c h a i n saw, p i v o t i n g about a h o r i z o n t a l a x i s , and mounted on a l i g h t s l e d g r e a t l y f a c i l i t a t e d t h e sawing of t h e beams. For s i m p l i c i t y , f o r c e was a p p l i e d manually from a sled-mounted f o r c e -

m u l t i p l y i n g l e v e r system. A load c e l l l o c a t e d a t t h e p o i n t of f o r c e a p p l i c a t i o n t o t h e beam produced a continuous analogue r e c o r d of f o r c e v s time. A t t h r e e p o i n t s along t h e beam ( t i p , midpoint and n e a r t h e r o o t ) displacement t r a n s d u c e r s measured v e r t i c a l d e f l e c t i o n of t h e beam

r e l a t i v e t o t h e a d j a c e n t i c e cover. These d e f l e c t i o n measurements yielded an experimental approximation of t h e d e f l e c t i o n l i n e . The t e s t s e t - u p i s i l l u s t r a t e d i n Figure 8 . Snow was l e f t on t h e i c e s u r f a c e t o minimize d i s t u r b a n c e t o t h e h y d r o s t a t i c e q u i l i b r i u m and temperature p r o f i l e of t h e i c e c o v e r .

I C E 'O V E R r B E A M R E A D Y F O R T E S T D I S P L A C E M E N T TRANSDUCERS TESTED B E A M X

X

F O R C E A P P L I C A T I O N P O I N T A N D L O A D C E L L - L E D W I T H LEVER A R M F I G U R E 8 S C H E M A T I C O F SET-UP F O R I N S l T U C A N T I L E V E R B E A M T E S T S

The t e s t procedure was a s f o l l o w s :

a ) The i c e c o v e r was c u t completely through a l o n g a l i n e XX ( s e e .

F i g u r e 8) approximately 10 m long. T h i s i s o l a t e d t h e beam t o be t e s t e d and t h e anchor p o i n t s of t h e displacement t r a n s d u c e r s from t h e i n f l u e n c e of t h e r e a c t i o n l o a d s developed b y t h e l e v e r arm while a p p l y i n g l o a d t o t h e beam t i p .

b) P e r p e n d i c u l a r c u t s , AA, BB, e t c . , were made t o i s o l a t e s u c c e s s i v e beams f o r t e s t i n g .

c ) The l o a d i n g s l e d was anchored t o t h e i c e c o v e r s o t h a t a down- wards a c t i n g f o r c e could b e a p p l i e d t o t h e t i p of t h e beam.

d) An i n c r e a s i n g f o r c e was a p p l i e d t o t h e beam t i p b y d e f l e c t i n g i t downwards u n t i l f a i l u r e o c c u r r e d .

e ) The beam dimensions were t h e n measured.

f ) An i c e c o r e was r e c o v e r e d a t t h e beam r o o t , t h e t e m p e r a t u r e p r o f i l e measured and samples t a k e n f o r s a l i n i t y d e t e r m i n a t i o n . A s a n example t h e f o r c e and d e f l e c t i o n r e c o r d s , beam dimensions and corresponding t e m p e r a t u r e and s a l i n i t y p r o f i l e f o r Beam T e s t No. 5 a r e shown i n F i g u r e 9 . I t can b e s e e n t h a t f o r c e a p p l i c a t i o n r a t e was n o t s t e a d y and t h a t i n i t i a l l y t h e beam d e f l e c t i o n s lagged behind t h e f o r c e .

S t r a i n Modulus R e s u l t s

Force and c o r r e s p o n d i n g d e f l e c t i o n s a t up t o t h r e e p o i n t s a l o n g t h e l e n g t h of t h e beam were used i n c a l c u l a t i n g t h e b u l k s t r a i n modulus, Eb. A

computer program employing a n i t e r a t i v e t e c h n i q u e s o l v e d f o r t h e v a l u e of Eb which would b e s t f i t Equation (1) t o t h e measured d e f l e c t i o n s . The r e s u l t s of t h e c a l c u l a t e d modulus v a l u e s p l u s beam dimensions a r e p r e s e n t e d i n Table 1. The s t r a i n modulus r e s u l t s a r e a c t u a l l y i n i t i a l t a n g e n t moduli. The 4 m long beams had a n a v e r a g e b u l k s t r a i n modulus, Eb, o f 2 GPa. For purposes o f comp2 - ;on moduli v a l u e s assuming simple c a n t i l e v e r beam behaviour, Esb, (bw., ~ c y e f f e c t of t h e w a t e r ignored) a r e a l s o p r e s e n t e d . Although i n a few c,-ss t h e simple beam modulus v a l u e s were s m a l l e r , on a v e r a g e t h e y were ab~:s.t 10% g r e a t e r , a s would b e e x p e c t e d . The modulus r e s u l t s f o r t h e 8 and 12 rri beams a r e v e r y q u e s t i o n a b l e . The maximum v a l u e f o r s t r a i n modulus determined from dynamic measurements on s m a l l specimen i s 10 GPa (Langleben and Pounder, 1963), t h e r e f o r e it i s r e a s o n a b l e t o conclude t h a t t h e r e was some experimental e r r o r i n t h e measurements. I t i s p o s s i b l e t h a t t h e d e f l e c t i o n measurements were i n e r r o r due t o t h e l i n e a r v a r i a b l e d i f f e r e n t i a l t r a n s f o r m e r s n o t responding f u l l y t o d e f l e c t i o n s a s a r e s u l t of e i t h e r f r i c t i o n a l o r i n e r t i a l e f f e c t s o r b o t h .

F l e x u r a l S t r e n e t h

F l e x u r a 1 s t r e n g t h s were c a l c u l a t e d u s i n g F r a n k e n s t e i n

'

s (19 70) technique, which h a s a l r e a d y been d e s c r i b e d i n t h i s p a p e r . The e x p e r i m e n t a l l y determined b r i n e volume p r o f i l e of each beam y i e l d s t h e p o s i t i o n of t h e n e u t r a l a x i s , zo, and s u b s e q u e n t l y t h e s t r e s s d i s t r i b u t i o n through t h e

T I M E , s D E F L E C T I O N - A N D F O R C E - T I M E C U R V E S

1

1 4.04m BEAM DIMENSIONS 50 T E M P E R A T U R E A N D S A L I N I T Y P R O F I L E F I G U R E 9 R E S U L T S O F B E A M T E S T N O . 5

beam. The f a i l u r e moment o f t h e beam i s e s t a b l i s h e d from t h e f o r c e a t f a i l u r e and a l s o t h e buoyant e f f e c t o f t h e w a t e r and t h e s t r a i n modulus of t h e beam. S i n c e i n a l l c a s e s f o r c e was a p p l i e d downwards a t t h e t i p of t h e beam, t h e f l e x u r a l s t r e n g t h ,

a,

i s c a l c u l a t e d b y s u b s t i t u t i n g i n t o Equation (14) t h e c o n d i t i o n s a t t h e t o p f i b r e s of t h e beam. These r e s u l t s ; t h e v a l u e of

a,

c a l c u l a t e d from Equation ( 9 ) ; and t h e v a l u e of s t r e n g t h , osb, c a l c u l a t e d u s i n g simple c a n t i l e v e r beam t h e o r y a r e p r e s e n t e d i n Table 1 . The average v a l u e of f l e x u r a l s t r e n g t h ,

a,

from a l l t e s t s was

0.39 MPa. The average v a l u e o f ,

a,,

from a l l t h e 4 m-long beams, t e s t s was 0.70 MPa. T h i s i s i n r e a s o n a b l e agreement with F r a n k e n s t e i n ' s (1970) v a l u e of

a0

= 0.76 MPa found f o r beams having v e r y s i m i l a r dimensions t o t h o s e t e s t e d h e r e .

I n F i g u r e 10 f l e x u r a l s t r e n g t h c a l c u l a t e d from b r i n e volume measurements (Equation (9) w i t h

a,

= 0.70 MPa) a r e p l o t t e d v s f l e x u r a l s t r e n g t h

determined from bending moment a t f a i l u r e (Equations (13) and ( 1 4 ) ) . The average s t r e n g t h c a l c u l a t e d from b r i n e volume i s 0.32 MPa. With t h e e x c e p t i o n of a few h i g h f l e x u r a l s t r e n g t h s determined from long beam f a i l u r e moment measurements, t h e r e i s g e n e r a l l y a good one-to-one

correspondence between t h e two approaches t o f l e x u r a l s t r e n g t h determina- t i o n . Confirmation, however, i s needed f o r g r e a t e r i c e t h i c k n e s s e s and a t o t h e r t i m e s of t h e y e a r .

The p o s i t i o n o f f a i l u r e was always a t t h e r o o t of t h e beam, w i t h t h e e x c e p t i o n of t h e 1 2 m long beam where two f a i l u r e p l a n e s o c c u r r e d 4.75 m

from t h e r o o t and a t t h e r o o t t o o . T h i s i s n o t a t a l l unexpected when t h e t y p i c a l moment d i s t r i b u t i o n f o r long beams, a s shown i n Figure 4, i s

c o n s i d e r e d . Table 1 shows t h e t i m e t o f a i l u r e , t f . The a v e r a g e loading r a t e f o r t h e whole t e s t s e r i e s was about 0 . 5 MPa s - l . A t t h i s s t r e s s r a t e

f o r s i m i l a r s i z e d c a n t i l e v e r beams M a a t t h e n (1975) found t h a t no

c o r r e c t i o n was r e q u i r e d f o r dynamic e f f e c t s of e i t h e r t h e i c e o r w a t e r , consequently no such c o r r e c t i o n s were made t o t h e d a t a p r e s e n t e d h e r e .

CONCLUSIONS

A p p l i c a t i o n o f e l a s t i c i t y t h e o r y t o b o t h homogeneous and nonhomogeneous c a n t i l e v e r beams i n d i c a t e d t h a t t h e i n f l u e n c e o f a n e l a s t i c foundation c a n have a s u b s t a n t i a l e f f e c t on t h e d e f l e c t i o n s and bending moments when t h e beam l e n g t h i s more t h a n 1 0 t i m e s i t s d e p t h .

The r e s u l t s o f a s e r i e s of c a n t i l e v e r beam t e s t s have been a n a l y z e d t o o b t a i n index v a l u e s o f f l e x u r a l s t r e n g t h and s t r a i n modulus, t h e r e b y c h a r a c t e r i z i n g t h e mechanical b e h a v i o u r of s e a i c e s u b j e c t e d t o f l e x u r a l

l o a d i n g . An a v e r a g e s t r a i n modulus of 2.0 GPa and f l e x u r a l s t r e n g t h of 0.32 MPa were o b t a i n e d . L i t t l e i n f l u e n c e o f buoyancy was noted, provided t h e r a t i o o f beam l e n g t h t o i c e t h i c k n e s s was l e s s t h a n 10. The l i m i t e d r e s u l t s p r e s e n t e d i n t h i s paper s u g g e s t t h a t t h e c l a s s i c a l e l a s t i c t h e o r y of a beam o n , a n e l a s t i c f o u n d a t i o n c a n b e a p p l i e d t o t h e c a s e o f i n s i t u c a n t i l e v e r beams. F u r t h e r e v a l u a t i o n s of t h e d a t a , however, s u g g e s t t h a t p l a s t i c deformation i s beginning t o occur a t t h e r o o t of t h e beams.

F r a n k e n s t e i n ' s (1970) approach of i n c l u d i n g t h e i n f l u e n c e of b r i n e volume v a r i a t i o n (nonhomogeneity) through t h e t h i c k n e s s o f t h e beam h a s been

, found a s a t i s f a c t o r y approach t o t h e a n a l y s i s of t h e f l e x u r a l s t r e n g t h of

C I I 1

I

I I

-

*

3:

(

@.

-

.

.

_-

A V E R A G E S T R E N G T H

-

-

-

-

I

I

I

I

1

F L E X U R A L S T R E N G T H F R O M F A I L U R E M O M E N T M E A S U R E M E N T S , M P a F I G U R E 10 F L E X U R A L S T R E N G T H O F S E A I C E F R O M B R I N E V O L U M E M E A S U R E M E N T S V S F A I L U R E M O M E N T M E A S U R E M E N T S

ACKNOWLEDGEMENTS

The a u t h o r s o f t h i s p a p e r e x p r e s s a p p r e c i a t i o n t o t h e i r employers, t h e N a t i o n a l Research Council o f Canada, t h e I n s t i t u t ftr S c h i f f b a u , Hamburg, and t h e Deutsche Forschungsgemeinschaft f o r a u t h o r i z i n g t h e i r p a r t i c i p a - t i o n i n t h e f i e l d measurement program. The f i n a n c i a l a s s i s t a n c e o f t h e German M i n i s t r y o f S c i e n c e and Technology (BMFT) t h r o u g h C o n t r a c t No. MTK0055, which made t h e f i e l d program p o s s i b l e , i s g r a t e f u l l y

acknowledged. F i n a l l y , t h e c o n t r i b u t i o n s o f P r o f . Franz Nusser, D i e t e r Lemke and Rudolf Reymer, t o t h e s u c c e s s f u l conrpletion of t h e f i e l d t e s t s i s most g r a t e f u l l y acknowledged.

T h i s p a p e r i s a c o n t r i b u t i o n from t h e D i v i s i o n of Building Research,

N a t i o n a l Research Council o f Canada, and i s p u b l i s h e d w i t h t h e a p p r o v a l of t h e D i r e c t o r o f t h e D i v i s i o n .

REFERENCES

F r a n k e n s t e i n , G . E . 1968. S t r e n g t h o f i c e s h e e t s . N a t i o n a l Research

C o u n c i l o f Canada, A s s o c i a t e Committee on G e o t e c h n i c a l Research, T e c h n i c a l

Memorandum No. 92,

p .

79

-

8 7 .

F r a n k e n s t e i n , G.E. 1970. The f l e x u r a l s t r e n g t h o f s e a i c e a s d e t e r m i n e d from s a l i n i t y and t e m p e r a t u r e p r o f i l e s . N a t i o n a l Research Council of Canada, A s s o c i a t e Committee on G e o t e c h n i c a l Research, T e c h n i c a l Memorandum

NO. 98, p . 66 - 73.

F r a n k e n s t e i n , G . E . , and Garner, R . 1967. E q u a t i o n s f o r d e t e r m i n i n g t h e b r i n e volume o f s e a i c e from - 0 . 5 t o - 2 2 . g 0 c . J o u r n a l of G l a c i o l o g y ,

Vol. 6, NO. 48, p . 943

-

44.

Hetgnyi, M . 1946. Beams on e l a s t i c f o u n d a t i o n . Ann Arbor, The U n i v e r s i t y of Michigan P r e s s , 255 p .

Kerr, A . D . , a n d Palmer, W.T. 1972. The d e f o r m a t i o n s a n d s t r e s s e s i n f l o a t i n g i c e p l a t e s . Acta Mechanica, Vol. 15, p . 57 - 72.

Langleben, M.P., a n d Pounder, E . R . 1963. E l a s t i c p a r a m e t e r s o f s e a i c e . I n I c e and Snow-Processes, P r o p e r t i e s and A p p l i c a t i o n s (W.E. Kingery, Ed.), E m b r i d g e , Mass., MIT P r e s s , p. 69 - 78.

Lavrov, V . V . 1969. Deformation and s t r e n g t h o f i c e . Gidrometeorolog-

i c h e s k o e I s d a t e l ' s t v o , Leningrad, NSF-Translation (TT 70 501 30)

.

MZZttZnen, M. 1975. On t h e f l e x u r a l s t r e n g t h o f b r a c k i s h w a t e r i c e by i n s i t u t e s t s . Proceedings, T h i r d I n t e r n a t i o n a l Conference on P o r t and Ocean E n g i n e e r i n g under A r c t i c C o n d i t i o n s , F a i r b a n k s , p. 349

-

359.

Schwarz, J . '1975. On t h e f l e x u r a l s t r e n g t h and e l a s t i c i t y of s a l i n e i c e . Proceedings, T h i r d I n t e r n a t i o n a l Symposium on I c e Problems,

(G . E

.

F r a n k e n s t e i n , E d . ) , Hanover, -New Hampshire, p . 373 - 386.

Schwarz, J

.

,

and Hof fmann, L

.

1978. I c e b r e a k i n g t r i a l s around S p i t z b e r g e n , 4 t h IAHR Symposium on I c e Problems, ~ u l e z .

Schwarz, J . , and Kloppenburg, M . 1976. Untersuchung iiber das

W i d e r s t a n d s v e r h g l t n i s zwischen Model1 und GruBausfuhrung e i s b r e c h e n d e r S c h i f f e - S c h l u B b e r i c h t . Hamburgische Schiffbau-Versuchsanstalt, B e r i c h t No. E82/76.

Schwarz, J . , and Weeks, W.F. 1977. Engineering p r o p e r t i e s of s e a i c e . J o u r n a l o f Glaciology, Vol. 19, No. 81, p . 499 - 531.

Tabata, T., e t a l . 1975. I c e s t u d y i n t h e Gulf of Bothnia. 1 1 . Measurements o f f l e x u r a l s t r e n g t h . Low Temperature S c i e n c e , S e r . A, NO. 33, p. 199

-

206.

Weeks, W . , and Assur, A . 1967. The mechanical p r o p e r t i e s of s e a i c e . U .S

.

Army Materie 1 Command, Cold Reg i o n s Research and Engineering Laboratory, Hanover, New Hampshire, 80 p .

TABLE 1

RESULTS OF IN SITU CANTILEVER BEAM TEST, ISFJORDEN, SPITSBERGEN, APRIL, 1977

Beam Beam

I c e S t r a i n Modulus F l e x u r a l S t r e n g t h Length Width Thickness

h Eb sb 0 OO 0

Beam

R

B sb t f

THE FLEXURAL BEHAVIOUR OF ICE FROM IN SITU CANTILEVER BEILnI

TESTS

R

Frederking

Division of Buildinq Research

National Research Council of

Canada

Ottawa, Ontario

Canada, KIA OX6

Hamburgische Schiffbau-

Versuchsanstalt GmbH

Hamburg, Germany

Question from: K Karal, Norway

1

1) Vhat is the reason for using so large

ratios?

2)

Any effects of

on the results?

Answer: The larqe l/3 ratios were used to verify the theory

of a cantilever beam on elastic f.~undation

as well as to

achieve the situation of havina our beam break at some ~ o i n t

other than at the rest, therebv eliminat4ng any stress con-

centrations which might occur there.

The 1/B ratio was not in fact investigatec. basically we were

looking at beam length effects

- A .

relatior* to ic( thickness.

Question from: Pauli Jwppanen, F!.nland

Ffi.ich are the influences of ~lastic

and viscoelastic effects

on the flexural strengtk-

in your ,tests

and what was the basis

to neqlect these effects? Which were the loading speeds you

used?

Answer: Our meazurements suggested that there was some pl~stic

behaviour in ouz beams, however J u r deflection measurements

were n o r sufficientlv precise to allow a quankitative con-

siderat~an

of ~ t ,

Also nlastic and viscoelastic effects shcvld

than flexural

.

Our loading speeds were not nrecisely controlled, but

in

general our loading time to failure was of the order of one

second or less.

Question from: T Carstens Norway

Was your S ~ i t s b e r g e n

tes.t site in a fjord or offshore?