Ice loads on a rigid structure with a compliant foundation

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Ice loads on a rigid structure with a compliant foundation

Frederking, R. M. W.; Timco, G. W.

https://publications-cnrc.canada.ca/fra/droits

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Construction construction

Ice Loads on a Rigid Structure with a

Compliant Foundation

by R. Frederking and G.W. Timco

Reprinted from

Proceedings

of

the

Nineth Conference

(POAC-87) University of Alaska Fairbanks, Fairbanks, Alaska August f 7-21, 1987

Port and Ocean Engineering

Under

Arctic Condftions Vol. 111, 1988. p. 409418.

(IRC Paper No. f 624)

Reprinted with permission

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On a dalid une s6rie d'essais afin d'etudier le c o m m m e n t d'une structure rigide

reposant sur une fondation souple.

Le

&le,

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&

60 mm de diamktre,

a Ct6

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_&re

_modifik.

_{Les charges exercks par la glace}

sur la strucm ont it6 mesdes en fonction de la

rigidid

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la fondation (Mquences

naturelles

de

9 B

50 Hz) et

de

la vitesse (10 h 270 d s ) .

On

a etilis6 de la glace type

EG/DA/S

dont

la

dsistance en flexion et 19$aisseur nominales etaient respectivement de

50 kPa et

de

40 mm. On a m e s d les charges longitudinaies et transversales. Les

cmdristiques dynamiques du sys&me ono dt6 mesunks et la fonction de mmsfen a

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ICE

LOADS ON A RIGID STRUCTURE WITH A COMPLIANT FOUNDATION

R. Frcderking G. W . Tirnco

National Research Council of Canada, Ottawa. Ontario, CANADA

A b s t r a c t

-

A t e s t s e r i e s h a s been c a r r i e d o u t t o s t u d y t h e b e h a v i o u r o f a r i g i d s t r u c t u r e o n a c o r e p l i a n t f o u n d a t i o n . The model, a 6 0 a m diam c y l i n d e r , w a s a t t a c h e d t o a b a s e vhose compliance c o u l d be v a r i e d . I c e l o a d s on t h e s t r u c t u r e were measured a s a f u n c t i o n o f f o u n d a t i o n s t i f f n e s s ( n a t u r a l f r e q u e n c i e s 9 t o 50

Hz)

and v e l o c i t y ( 1 0 t o 270 mm/s). EG/AD/S model i c e v i t h a n a v e r a g e f l e x u r a l s t r e n g t h o f 50 kPa and t h i c k n e s s 40 mm was used. Both l o n g i t u d i n a l and t r a n s v e r s e l o a d s v e r e measured. The dynamic c h a r a c t e r i s t i c s o f t h e s y s t e m were measured and t h e t r a n s f e r f u n c t i o n d e t e r m i n e d and s u b s e q u e n t l y used t o o b t a i n c o r r e c t e d i c e l o a d s u s i n g F o u r i e r t e c h n i q u e s . The mode of i c e f a i l u r e v a s f o u n d t o b e a f u n c t i o n p r i m a r i l y of v e l o c i t y and t o a l e s a e r e x t e n t f o u n d a t i o n s t i f f n e s s . For h i g h v e l o c i t i e s and c o m p l i a n t f o u n d a t i o n s t h e i c e l o a d t r a n s f e r r e d t h r o u g h t h e f o u n d a t i o n v a s m a g n i f i e d by a s much a s o n e t h i r d . I n t r o d u c t i o n The f l e x i b i l i t y of a s t r u c t u r e h a s been i d e n t i f i e d a s o n i m p o r t a n t f a c t o r i n c h a r a c t e r i z i n g i t s r e s p o n s e t o dynamic i c e l o a d s . O s c i l l a t o r y i c e l o a d s w e r e r e c o r d e d on a t e s t s t r u c t u r e i n Cook I n l e t , Alaska ( P e y t o n 1966). B l e n k a n ( 1 9 7 0 ) l a t e r s u g g e s t e d t h a t t h e p e r i o d i c i t y o f t h e m e a s u r e d f o r c e s r e s u l t e d from t h e r e s p o n s e c h a r a c t e r i s t i c s o f t h e s t r u c t u r e . S e v e r e v i b r a t i o n s r e s u l t i n g f r o m d y n a m i c i n t e r a c t i o n s b e t w e n moving i c e c o v e r s and l i g h t h o u s e s h a v e b e e n d o c u m e n t e d i n t h e B a l t i c ( M u t t k e n 1975; E n g l e b r e k t s o n 1978). More r e c e n t l y dynamic o s c i l l a t o r y i c e l o a d s have been o b s e r v e d a t a m a s s i v e o f f s h o r e s t r u c t u r e i n t h e B e a u f o r t Sea (Wright e t a l . 1986). I n a d d i t i o n t o f i e l d measurements and a n a l y s i s , t h e problem o f dynamic i c e l o a d s h a s been s t u d i e d u s i n g m o d e l l i n g t e c h - niques. m t t ' h e n (19811, Toyama e t a l . (19831, Tsuchiya e t a l . (1985) and S o d h i and Morris (1986) a l l c a r r i e d o u t model e x p e r i m e n t s i n which t h e e f f e c t s of s t r u c - t u r e d i a m e t e r , i c e t h i c k n e s s , r e l a t i v e v e l o c i t y and s t r u c t u r a l s t i f f n e s s w r e s t u d i e d . There a r e c e r t a i n c o n t r a d i c t i o n s

This is a reviewed and edited version of a paper presented i n t h e c o n c l u s i o n s o f t h e s t u d i e s , h o v e r

at the Ninth Infernational Con fmenn on Port and & a n e r , and, a s Daoud and Lee (1986) p o i n t

E n g i m ' n g Under Arctic Conditions, Fairtmnks, Alaska, o u t , e x p e r i m e n t a l d a t a f o r s t r u c t u r e s w i t h

USA. August 17-22. 1987. v a r i o u s s t i f f n e s s e s a n d i m p r o v e d a n a l y t i c a l models a r e s t i l l needed.

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It would be d e s i r a b l e t o c a r r y o u t i n v e s t i g a t i o n s of a s t r u c t u r e v h e r e i c e l o a d s , i c e p r o p e r t i e s , i c e b e h a v i o u r and s t r u c t u r e r e s p o n s e c h a r a c t e r i s t i c s a r e known. One s u c h s i t e is t h e l i g h t p i e r a t Y a m c h i c h e i n t h e St. Lawrence River. The l i g h t p i e r i s i n s t r u m e n t e d t o measure i c e f o r c e s (Danys 1975; F r e d e r k i n g e t a l . 1 9 8 5 ) . I n f o r m a t i o n o n i t s r e s p o n s e c h a r a c t e r i s t i c s h a s been o b t a i n e d (Haynes 1986) and now s m a l l - s c a l e e x p e r i m e n t s a r e b e i n g c a r r i e d o u t t o i n v e s t i g a t e t h e e f f e c t of f o u n d a t i o n s t i f f n e s s o n ice l o a d s t r a n s m i t t e d t h r o u g h t h e s t r u c t u r e . Note t h a t t h e work t o be r e p o r t e d h e r e is n o t a d i r e c t model s t u d y o f t h e Y a m c h i c h e p i e r , b u t was i n s p i r e d by it. T h i s p a p e r w i l l p r e s e n t t h e r e s u l t s o f a n i n i t i a l test s e r i e s c a r r i e d o u t i n a n i c e model b a s i n t o i n v e s t i g a t e f o u n d a t i o n s t i f f n e s s e f f e c t s . The a n a l y s i s method used w i l l b e d e s c r i b e d a n d some o f t h e p i t f a l l s e n c o u n t e r e d w i l l be d i s c u s s e d . Theory A s t r u c t u r e s u c h a s a l i g h t p i e r o n a f l e x i b l e f o u n d a t i o n c a n be assumed t o b e h a v e a s a s i n g l e d e g r e e o f - f r e e d o m s y s t e m modelled by a m a s s d a m p e r s p r i n g o s c i l l a t o r . It c a n b e r e p r e s e n t e d by t h e f o l l o w i n g d i f f e r e n t i a l e q u a t i o n o f motion: where u ( t ) = time s e r i e s of d i s p l a c e m e n t o f s t r u c t u r e r e l a t i v e t o i t s b a s e

In11

k = s t i f f n e s s o f t h e s t r u c t u r e [N/m] m

-

mass o f t h e s t r u c t u r e

-

[kg1 f n = o n / 2 n = 1 1 2 % /

&

= n a t u r a l f r e q u e n c y [Hz] c = damping c o n s t a n t [Ns/ml

C

= ~ 1 2 % = c r i t i c a l damping r a t i o [-I f ( t ) = t i m e - s e r i e s of t h e i c e i n p u t f o r c e [Nl I n i c e e n g i n e e r i n g t h e i c e i n p u t f o r c e f ( t ) , t h e r e s p o n s e f o r c e r ( t ) a t t h e f o u n d a t i o n , t h e movement u ( t ) of t h e s t r u c t u r e r e l a t i v e t o t h e f o u n d a t i o n , and i t s f i r s t and second t i m e d e r i v a t i v e s S ( t ) and 3 ( t ) , a r e a l l of i n t e r e s t . The n a t u r e o f t h e r e s p o n s e i s dependent upon t h e d y n a a f c c h a r a c t e r i s t i c s o f t h e s t r u c t u r e and c a n be r e l a t e d t o t h e f o r c i n g f u n c t i o n by t h e impulse r e s p o n s e f u n c t i o n o f t h e s t r u c t u r e , h( t )

,

by t h e c o n v o l u t i o n i n t e g r a l To e s t a b l i s h t h e r e l a t i o n b e t v e e n t h e f o r c e and t h e r e s p o n s e i t i s more c o n v e n i e n t t o t r a n s f o r m t h e above r e l a t i o n i n t o t h e f r e q u e n c y domain: w h e r e o i s c i r c u l a r f r e q u e n c y . T h e f r e q u e n c y r e s p o n s e f u n c t i o n , H(o), c a n b e d e r i v e d from measured c h a r a c t e r i s t i c s of t h e s y s t e m . T h i s c a n b e d o n e by p e r f o r p i n g a ' p l u c k i n g ' o r s t e p u n l o a d i n g e x p e r i m e n t f r o m w h i c h f n a n d 5 a r e determined. Once t h e s e f a c t o r s a r e known f o r t h e s i n g l e d e g r e r o f - f reedom s y s t e m d e s c r i b e d by E q u a t i o n (11, t h e a m p l i t u d e o f t h e f r e q u e n c y r e s p o n s e f u n c t i o n , a l s o r e f e r r e d t o a s t h e ' t r a n s f e r f u n c t i o n , ' c a n be 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 (Thoaeon 1981): The F o u r i e r t r a n s f o r m method p r o v i d e s a means of c o n v e r t i n g f u n c t i o n s from t h e t i n e domain t o t h e f r e q u e n c y domain and v i c e versa. When s i g n a l s a r e r e c o r d e d i n d i g i t a l form a t e q u a l t i m e i n t e r v a l s , A t , t h e d i s c r e t e F o u r i e r t r a n s f o r m o f a t i m e series x(kAt) of N p o i n t s i n t o a f u n c t i o n X(nAf

1

i n t h e f r e q u e n c y domain i s f o r n = 0,1,2,... N-1. In a s i m i l a r m a n n e r , t h e i n v e r s e d i s c r e t e F o u r i e r t r a n s f o r m is I n a set o f e x p e r i m e n t s t h e r e s p o n s e i n t h e time domain, i n t h i s c a s e t h e f o r c e , r ( t ) , i s measured. The measured r e s p o n s e f u n c t i o n c o u l d a l s o be a t i m e

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s e r i e s of t h e a c c e l e r a t i o n , B(t). The r e s p o n s e f u n c t i o n r ( t ) i n t h e t i m e domain i s c o n v e r t e d i n t o t h e f r e q u e n c y domain, R ( ~ ) , by a p p l y i n g t h e d i s c r e t e F o u r i e r transform- t o it. b o w i n g t h e t r a n s f e r f u n c t i o n A(w) from E q u a t i o n (51, t h e i c e f o r c i n g f u n c t i o n i n t h e f r e q u e n c y domain, F ( w ) , i s c a l c u l a t e d by t r a n s p o s i n g E q u a t i o n ( 4 )

me

i n v e r s e d i s c r e t e F o u r i e r t r a n s f o r m i s t h e n a p p l i e d t o F ( w ) t o o b t a i n a compensated time s e r i e s f o r t h e i c e f o r c e f ( t ) . The term compensated f o r c e v i l l b e used throughout t h i s p a p e r f o r f ( t ) , t h e c a l c u l a t e d i c e i n p u t f o r c e o n t h e t i m e domain. A s may be s e e n , t h e b a s i c methods f o r c a r r y i n g o u t t h i s a n a l y s i s a r e r e l a t i v e l y s t r a i g h t f o r w a r d , p a r t i c u l a r l y v i t h t h e r e a d y a v a i l a b i l i t y o f s o f t v a r e t o d i g i t i z e a n a l o g u e s i g n a l s a n d t o p e r f o r m t h e F o u r i e r t r a n s f o r m s . It must be k e p t i n mind, h w e v e r , t h a t t h e r e a r e c e r t a i n limitations i n a c t u a l a p p l i c a t i o n s ( R a i n e r 1 9 8 6 ) . The f i r s t i s t h e s a m p l i n g frequency. To a v o i d ' a l i a s i n g ' of a time

series s i g n a l i t must be sampled a t t h e N y q v i s t f r e q u e n c y

,

t v i c e t h e h i g h e s t f r e q u e n c y o f i n t e r e s t . To d e f i n e f r e q u e n c y response c u r v e s a d e q u a t e l y t h e s a m p l i n g frequency s h o u l d be a t l e a s t s i x t i m e s , and p r e f e r a b l y t e n times, t h e h i g h e s t f r e q u e n c y component i n t h e s i g n a l . T h e r e is a l s o t h e requirement t h a t t h e number o f samples N be e q u a l t o 2', v h e r e m i s a n i n t e g e r . I f t h e sample l e n g t h is l o n g e r t h a n N , t h e n i t may b e broken i n t o a number of o v e r l a p p i n g segments o f t h e r e q u i r e d length. A l t e r n a t i v e l y , i t c a n b e

augmented by adding zeros. The d i s c r e t e

F o u r i e r t r a n s f o r m i s a c i r c u l a r f u n c t i o n t h a t r e p e a t s i t s e l f e a c h N set of p o i n t s . I f t h e end and s t a r t v a l u e s of t h e r e c o r d a r e n o t t h e same, a f i c t i t i o u s i m p u l s e is imposed on t h e s i g n a l t h a t r e s u l t s i n a phenomenon known a s 'vrap-around.'

Apparatus

The t e s t s were conducted i n t h e i c e model b a s i n of t h e H y d r a u l i c s L a b o r a t o r y o f t h e N a t i o n a l Research Council o f Canada i n O t t a v a ( P r a t t e and Timco 1981). The b a s i n i s 2 1 m l o n g by 7 m wide by 1.2 m

d e e p and i s spanned by a t o v i n g c a r r i a g e t h a t c a n t r a v e l t h e l e n g t h o f t h e b a s i n . The model i c e used i n t h e t e s t s v a s

EG/AD/S (Timco 1986a).

A t e s t a p p a r a t u s was d e s i g n e d t o r e p r e s e n t a r i g i d s t r u c t u r e ( i n t h i s c a s e t h e Yamachiche l i g h t p i e r ) t h a t t r a n s l a t e s h o r i z o n t a l l y o n a c o m p l i a n t f o u n d a t i o n and b e h a v e s a s a s y s t e m w i t h a s i n g l e d e g r e e o f - f r e e d o m ( F i g u r e 1). The p i e r i s r e p r e s e n t e d by a 60-m diam s t e e l p i l e and i s r e s t r i c t e d t o move i n t h e h o r i z o n t a l p l a n e by a p a i r of p a r a l l e l h i n g e d l i n k s . A c a n t i l e v e r beam, f i x e d t o t h e u p p e r c a r r i e r and pinned t o t h e l o w e r c a r r i e r , i s u s e d a s t h e s p r i n g e l e m e n t . By c h a n g i n g t h e t h i c k n e s s of t h e beam and c l a t l p i n g it a t v a r i o u s e f f e c t i v e l e n g t h s , i t s s t i f f n e s s c a n be changed e a s i l y . Two thicknesses and f i v e e f f e c t i v e l e n g t h s o f t h e c a n t i l e v e r beam c o u l d b e s e l e c t e d . Knoving t h e v e i g h t o f t h e a p p a r a t u s and t h e dimenrions . o f t h e bearm,, n a t u r a l f r e q u e n c i e s c a n b e c a l c u l a t e d . Ten n a t u r a l f r e q u e n c i e s c o u l d be s e l e c t e d to r e p r e s e n t d i f f e r e n t d e g r e e s o f s t i f f n e s s o f t h e foundation. I n a c t u a l f a c t o n l y u w m c n r n t ~ m ~ l

\!!/_>I-

...

Y l ~ r n l I Y C I

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F i g u r e 1. Schematic of t e s t s e t - u p .

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f i v e f r e q u e n c i e s v e r e u s e d d u e t o zoo p r a c t i c a l l i m i t a t i o n s . No s p e c i a l ₁₁₁ m e a s u r e s w e r e t a k e n t o p r e d e t e r m i n e r e l a t i v e damping. f

-

loo 50 d The test a p p a r a t u s v a s a t t a c h e d t o a 2 0 1 0 kN c a p a c i t y six-component l o a d c e l l d -50 h a v i n g a m i n i m a n a t u r a l f r e q u e n c y of Zz 320 Hz. The l o a d c e l l was a t t a c h e d by .n -100 means of a s t i f f b r a c k e t t o t h e f r o n t f a c e

=

-

130 o f t h e t o w i n g c a r r i a g e , v h i c h h a s a -200 o P Z a 4 n~ 1.0 LZ 1.4 minimum n a t u r a l f r e q u e n c y o f a b o u t 40 Hz. _{r ! H t} _I T e s t Procedure P l u c k i n g tests

An i n i t i a l set o f tests was c a r r i e d o u t t o e v a l u a t e t h e n a t u r a l f r e q u e n c i e s and r e l a t i v e damping o f t h e system i n v a r i o u s c o n f i g u r a t i o n s by means o f ' p l u c k i n g ' t e s t s . The a p p a r a t u s was a s shown i n F i g u r e 1, w i t h a s t a t i c l o a d a p p l i e d a t a p o i n t a b o u t 1 cm above t h e v a t e r l i n e by means o f a f i n e wire. The l o a d was t h e n r e l e a s e d q u i c k l y by c u t t i n g t h e wire, t h e r e b y a c h i e v i n g a s t e p u n l o a d i n g t h a t c a u s e s t h e s t r u c t u r e t o v i b r a t e a t i t s n a t u r a l f r e q u e n c y ( F i g u r e 2). A l l t e s t s were c a r r i e d o u t w i t h t h e p i l e immersed i n w a t e r a t t h e t e s t d e p t h b u t v i t h no i c e p r e s e n t . The time series s i g n a l o f t h e r e s p o n s e f o r c e , measured w i t h t h e l o a d c e l l , was d i g i t i z e d a t a f r e q u e n c y of 1000 Hz. I c e t e s t s A s e p a r a t e s h e e t of c o l u m n a r - g r a i n e d EG/AD/S i c e v a s g r o w f o r e a c h of t h e f i v e s t i f f n e s s c a s e s t e s t e d . The nominal i c e t h i c k n e s s v a s 40 mm and t h e f l e x u r a l s t r e n g t h 50 kPa. T h i s v o u l d c o r r e s p o n d t o a u n i a x i a l compressive s t r e n g t h of a b o u t

100 kPa (Timco 1986a). Average i c e s h e e t

t h i c k n e s s e s ranged from 37 t o 40 mm and a v e r a g e f l e x u r a l s t r e n g t h s from 49 t o

55 kPa. For e a c h s t i f f n e s s c a s e ( i c e s h e e t ) t e s t r u n s were made i n sequence a t f o u r d i f f e r e n t v e l o c i t i e s , namely, 3, 9, 27 and 1 cm/s. The l e n g t h o f t h e measured p a r t of e a c h test r u n was g e n e r a l l y 2 t o 3 m, a d i s t a n c e r e p r e s e n t i n g more t h a n 30 t i m e s t h e s t r u c t u r e d i a m e t e r . In a d d i t i o n t o t h e l o n g i t u d i n a l f o r c e , t r a n s v e r s e and v e r t i c a l f o r c e s , t h e t h r e e moments, and t h e a c c e l e r a t i o n o f t h e p i l e v e r e a l s o measured and r e c o r d e d , a l t h o u g h o n l y t h e loo0 100

-

f

r

u 600

-

"4 0 e E A00

-

% ZOO

-

C 0 5 I0 15 20 25 30 F R E O U E N C I f Hz F i g u r e 2. T i m e s e r i e s o f m e a s u r e d r e s p o n s e l o a d , r ( t ) , from p l u c k i n g t e s t and i t s power spectrum.

l o n g i t u d i n a l f o r c e s v i l l be p r e s e n t e d i n t h i s p a p e r . F o r t h e s e t e s t s t h e d i g i t i z i n g f r e q u e n c y was 100 Hz. T e s t R e s u l t s and D i s c u s s i o n P l u c k i n g tests A t y p i c a l r e s u l t from a p l u c k i n g t e s t i s i l l u s t r a t e d i n F i g u r e 2, showing t h e s t r u c t u r e v i b r a t i n g a t i t s n a t u r a l f r e q u e n c y f o l l o w i n g s t e p u n l o a d i n g o f t h e a p p l i e d f o r c e . The r a t e a t v h i c h t h e s i g n a l d e c a y s i s a measure o f t h e damping o f t h e s t r u c t u r e . T h u s , f r o m t h e s e p l u c k i n g t e s t s t h e n a t u r a l f r e q u e n c y and

,

r e l a t i v e damping c o u l d be d e t e r m i n e d by a p p l y i n g a s t a n d a r d a n a l y s i s program t o t h e d i g i t i z e d s i g n a l . The r e s u l t s o f t h e p l u c k i n g tests and t h e p r e d i c t e d n a t u r a l f r e q u e n c i e s a r e shown i n T a b l e 1. It may b e s e e n t h a t a t Lou f r e q u e n c i e s t h e p r e d i c t e d a n d m e a s u r e d v a l u e s o f f r e q u e n c i e s a g r e e q u i t e v e l l . The f i v e f o u n d a t i o n s t i f f n e s s c a s e s f o r v h i c h t e s t s

(8)

i n i c e were c a r r i e d o u t a r e marked by a s t e r i s k s . It was n o t p o s s i b l e t o c a r r y o u t tests a t t h e two lowest f r e q u e n c i e s because t h e i c e l o a d s would have caused p l a s t i c deformation of t h e c a n t i l e v e r - b e - a t t h o s e clamping lengths.

G i v e n t h e n a t u r a l f r e q u e n c y and r e l a t i v e damping and aesuming a l i n e a r system, t h e t r a n s f e r f u n c t i o n can be determined f o r each foundation s t i f f n e s s

by u s i n g Equation (5). The t r a n s f e r

f u n c t i o n s f o r a l l t h e test c o n f i g u r a t i o n s used i n t h e s e experiments a r e p l o t t e d i n F i g u r e 3. Note t h a t t h e v a l u e of t h e s i n g l e d e g r e e o f - f r e e d o a t r a n s f e r f u n c t i o n becomes less t h a n one once a p a r t i c u l a r v a l u e of frequency i s exceeded. Since t h e t r a n s f e r f u n c t i o n is deconvolved w i t h t h e f r e q u e n c y domain r e s p o n s e f u n c t i o n ( E q u a t i o n 81, i t may be s e e n t h a t t h e a m p l i t u d e o f t h e h i g h e r f r e q u e n c y components would be a m p l i f i e d i n t h i s region. A c u t - o f f frequency h a s t h e r e f o r e been s e l e c t e d beyond which t h i s e f f e c t c a n b e neglected. For t h e t h r e e lower n a t u r a l frequency c a s e s , t h i s i s t h e frequency a t which t h e v a l u e of t h e t r a n s f e r f u n c t i o n r e t u r n s t o one. The v a l u e of t h e t r a n s f e r f u n c t i o n i s a r b i t r a r i l y set a t one f o r f r e q u e n c i e s g r e a t e r t h a n t h e c u t - o f f frequency i n t h e t h r e e cases. Ihis p o i n t , which is marked on F i g u r e 3, i s about 413 o f t h e n a t u r a l frequency. For t h e two h i g h e r n a t u r a l f r e q u e n c i e s a c u t - o f f frequency of 36 Hz h a s been s e l e c t e d t o f i l t e r o u t t h e e f f e c t s of c a r r i a g e frequency. I n t h e s e c a s e s t h e v a l u e of t h e t r a n s f e r f u n c t i o n i s t a k e n t o be one f o r f r e q u e n c i e s h i g h e r t h a n 36 Hz. 2 0

-

t l - I 6

-

_I_I - C .ma- C.0.n

-

F R E Q U E N C Y . HZ F i g u r e 3. Amplitude of t r a n s f e r f u n c t i o n , H(v), f o r t h e f i v e f o u n d a t i o n s t i f f n e s s e s t e s t e d . F i g u r e 3 a l s o s h w s t h e e f f e c t of r e l a t i v e damping; l o v e r v a l u e s r e s u l t i n h i g h e r p e a k a m p l i t u d e s i n t h e t r a n s f e r f u n c t i o n s . Ice t e s t s R e p r e s e n t a t i v e s a m p l e s o f b o t h measured time series r e c o r d s , r ( t ) , and cogpensated time series r e c o r d s , f ( t ) , a r e s h o w n i n F i g u r e s 4 , 5 a n d 6 f o r

comparative purposes. Note t h a t t h e

samples a r e s e l e c t e d from w i t h i n t h e ( 3 t o 5 times) l o n g e r r e c o r d analyzed. F i g u r e 4 i l l u s t r a t e s t h e c a s e of l w v e l o c i t y ( 3 cmls) i c e breaking f o r ' both a s t i f f

( 5 0 Hz) and a more compliant ( 9 Hz)

foundation. It may be s e e n t h a t i n e a c h c a s e t h e measured and compensated v a l u e s

Table 1

C a l c u l a t e d and measured n a t u r a l f r e q u e n c i e s of t e s t a p p a r a t u s s i r a u l a t i n g f o u n d a t i o n s t i f f n e s s

S t i f f beam A F l e x i b l e beam

Frequency En [Hz] R e l a t i v e Frequency f n [Hz] R e l a t i v e

( p r e d i c t e d ) (measured) damping, C ( p r e d i c t e d ) (measured) damping, C

18.3 17.7* 0.025 3.1 4.0 0.28 37.5

-

6.3 5.8 0.056 6 5 31.8" 0.059 11.0 9.0* 0.043

.

157

-

26.5 16.8* 0.066 1760

-

296 50* 0.19 * S t i f f n e e s e e a c t u a l l y t e s t e d

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of t h e i c e f o r c e i n t h e time domain a r e v i r t u a l l y i d e n t i c a l . The main e f f e c t of t h e compensation is t o e l i m i n a t e t h e s p u r i o u s ' n e g a t i v e ' response f o r c e s i n t h e time domain f o r t h e compliant ( 9 Hz) foundation. m e f o r c e s i n t h e time domain a l s o i n d i c a t e t h a t t h e more compliant f o u n d a t i o n e x h i b i t s h i g h e r f r e q u e n c i e s t h a n t h e s t i f f e r foundation, but t h e r e a r e no s i g n i f i c a n t frequency components above

about 5 Hz. For f r e q u e n c i e s less than

5 Hz ( F i g u r e 3) t h e t r a n s f e r f u n c t i o n i s one ( 5 0 Hz foundation) o r s l i g h t l y g r e a t e r t h a n o n e ( 9 Hz f o u n d a t i o n ) . T h e s i m i l a r i t y b e t w e e n t h e measured and compensated v a l u e s of t h e i c e f o r c e i n t h e time domain i s t h e r e f o r e n o t s u r p r i s i n g . The f a i l u r e behaviour of t h e i c e s h e e t c a n be d e s c r i b e d a s mixed mode, comprising b o t h c r u s h i n g and buckling w i t h a t t e n d a n t r a d i a l and c i r c u m f e r e n t i a l cracking. I n

t h e time series record of Figure 4 t h e

0 2 1 b 6 10 I ? 18 I6 18 10

TIME. I s

I I STIFF I50 Hz1 FOUNDATION

0 ? 4 6 8 10 I ? 14 16 I 8 20 TIME. I. s

b l COMPLIANT I( WIt FOUNDATION

F i g u r e 4. Comparison of measured response

f o r c e , r ( t ) , and compensated i c e f o r c e , f ( t ) , f o r s t i f f and compliant foundations, t e s t v e l o c i t y 3 cmls.

s e c t i o n w i t h l a r g e a m p l i t u d e l o a d v a r i a t i o n s r e p r e s e n t s a mixed c r u s h i n g and f i n a l buckling f a i l u r e , followed by a z e r o l o a d s e c t i o n d u r i n g which t h e buckled segments ;are r o t a t e d and t r a n s l a t e d o u t of t h e p a t h of t h e p i l e . The second peak i s

a p u r e buckling f a i l u r e , a g a i n followed by a z e r o load s e c t i o n . Very s i m i l a r f a i l u r e behaviour and time s e r i e s of f o r c e were observed f o r both 1 and 3 cm/s v e l o c i t i e s . F i g u r e 5 r e p r e s e n t s t h e h i g h v e l o c i t y ( 2 7 cm/s) c a s e f o r both s t i f f ( 5 0 Hz) and

compliant (9 RE) foundations. In t h i s

c a s e i t may be s e e n t h a t t h e r e a r e e i g n i f i c a n t d i f f e r e n c e s b e t w e e n t h e measured and compensated v a l u e s of f o r c e s

i n t h e time domain. For t h e compliant

( 9 Hz) foundation a measured maximum r e s p o n s e f o r c e peak h a s been s u b s t a n t i a l l y

reduced, almost by h a l f . The compensated

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

TIME. I 5

a t STIFF I50 Hz1 FOUNOhTION

I

1 1 1 1 1 1 1 1 1 1 1 1 o ar an 1.2 1.b 2.0

TIME. t s

) I COMPLIANT 1 9 nzl F O U N O A T I O N

F i g u r e 5. Comparison of measured response

f o r c e , r ( t ) , and compensated i c e f o r c e , f ( t ) , f u r s t i f f and compliant f o u n d a t i o n s , t e s t v e l o c i t y 27 c m l s .

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I

,

(50 Az) foundation, but i t i s n o t n e a r l y s o d r a m a t i c . A t t h i s h i g h v e l o c i t y ( 2 7 cmls) f a i r l y s i g n i f i c a n t peaks were observed i n t h e 2 t o 20 Hz range of t h e t i m e domain records. Thus, 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 maximum i c e f o r c e c o u l d b e e x p e c t e d , p a r t i c u l a r l y f o r t h e

compliant ( 9 Hz) foundation. The f a i l u r e

of t h e i c e a t v e l o c i t i e s of 9 and 27 cm/s can be d e s c r i b e d a s crushing. F i g u r e 6 is an example of t h e e f f e c t of t a k i n g a time s l i c e , f o r a n a l y s i s purposes, from d i f f e r e n t i n t e r v a l s of t h e tima dumain, i n t h i s c a s e f o r t h e s t i f f ( 5 0

Hz)

foundation ( F i g u r e 4a). In t h e f i r s t i n s t a n c e ( F i g u r e 6 a ) t h e s t a r t and end v a l u e s of t h e time s e r i e s , r ( t ) , a r e c l o s e t o zero. It may be s e e n t h a t t h e

measured and compensated tiam domains a r e

i d e n t i c a l . I n t h e s e c o n d i n s t a n c e ( F i g u r e 6 b ) t h e t i m e s l i c e h a s b e e n 0 2 4 6 8 10 12 14 16 18 20 TIME, f s I I TIME INTIRVAL 12.5 TO 90.5 I TIME. I. r b l TIME INlERVAL 10.5 10 88.5 s F i g u r e 6. Example of ' w r a p a r o u n d ' e f f e c t r e s u l t i n g from a s l i g h t s h i f t i n time i n t e r v a l s e l e c t e d f o r a n a l y s i s , s t i f f (50 Hz) foundation and 3 cmls v e l o c i t y . s e l e c t e d s o t h a t t h e r e i s a m a j o r d i s c o n t i n u i t y between t h e s t a r t and end o f t h e record. & r e i t may be s e e n t h a t t h e r e i s a - 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 two time s e r i e s . N o t h i n g h a s p h y s i c a l l y changed, o n l y a s l i g h t (1.5 s ) s h i f t i n t h e 18 s time i n t e r v a l s e l e c t e d f o r a n a l y s i s . T h i s i s a good example of t h e e f f e c t of wrap-around. The r e s u l t s of a l l t h e t e s t s a r e summarized i n Table 2, which p r e s e n t s t h e

maximum measured f o r c e , r ( t ) max, t h e

compensated maxima f o r c e , f ( t ) max, t h e mean c o m p e n s a t e d f o r c e ,

f(

t ) , a n d t h e s t a n d a r d d e v i a t i o n of t h e compensated f o r c e , S.D.[f ( t )

1.

E x a d n a t i o n r e v e a l s t h a t t h e mean and s t a n d a r d d e v i a t i o n s of t h e compensated i c e f o r c e f a l l i n t o two c a t e g o r i e s , c o r r e s p o n d i n g t o a low v e l o c i t y f a i l u r e mode (mixed b u c k l i n g and c r u s h i n g ) and a h i g h v e l o c i t y f a i l u r e mode ( c r u s h i n g ) . In t h e low v e l o c i t y mode t h e c o e f f i c i e n t of v a r i a t i o n ( r a t i o o f s t a n d a r d d e v i a t i o n t o mean) i s a b o u t one, v h i l e i n t h e h i g h v e l o c i t y mode i t is about 0.3. There i s a c o n s i s t e n t r e l a t i o n

f o r t h e maximum, mean and s t a n d a r d

d e v i a t i o n s aa follows: low v e l o c i t y high v e l o c i t y r n t t ' h e n (1983) found a r e l a t i o n s i m l l a r t o t h a t of Equation ( 9 ) o v e r t h e v e l o c i t y range 1 t o 10 cm/s. F i g u r e 7

coapares t h e measured and compensated

maxiam i c e f o r c e s f o r e a c h of t h e t e s t

cases. If foundation s t i f f n e s s h a s no

e f f e c t on i c e f o r c e s , t h e compensated maximum f o r c e s should a l l have t h e same

value. This is n o t t h e c a s e , b u t i t may b e s e e n t h a t t h e a p p l i c a t i o n o f t h e c o m p e n s a t i o n d o e s r e s u l t i n g r e a t e r c o n s i s t e n c y i n t h e maximum v a l u e s . E x a d n a t i o n of F i g u r e 7 r e v e a l s a p a t t e r n i n t h e r e s u l t s . For t h e l o v v e l o c i t y ( 1 and 3 cmls) regime 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 m e a s u r e d and

compensated maximum i c e f o r c e s ; i .e.

foundation s t i f f n e s s (frequency) d o e s n o t p l a y a r o l e because i t is r e l a t i v e l y high compared t o t h e f r e q u e n c i e s e x c i t e d i n t h e s t r u c t u r e by t h e ice.' For t h e h i g h

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Table 2

Heasured r e s p o n s e f o r c e and compensated i c e f o r c e s , mean f o r c e and s t a n d a r d d e v i a t i o n s [ a ] f o r model t e s t s of a 60-mm d i a m e t e r p i l e i n EG/AD/S i c e V e l o c i t y , cmls Foundation s t i f f n e s s 1 3 9 2 7 f n = 9 Hz 790 710r 1065 1070 1495 1030 940 570 C 1 0.043 232 f 238 217 t 252 407 131 322 t 77 f = 17.7 Hz 850 850 970 970 825 810 1205 660

2

= 0.025 153 2 181 264 t 249 349 f 133 266 t 77 f = 16.8 Hz 675

+

660 1090 1090 1200 790 1270 800

2

= 0.065 154 2 189 252 2 264 331 t 96 304 t 110 f

-

32 Hz 975 t 810 1430 1430 1125 f 1130 835 640

2

= 0.059 178 f 215 325 t 354 481 f 174 360 t 87 t

-

50 Hz 625 620 1165 1170 980 980 630 530

2

-

0.19 164 2 176 232

+

249 428 f 168 303 f 77 *Format of d a t a r(t),,, f ( t),, T ( t ) S.D.[f(t)]

v e l o c i t y (9 and 27 cm/a) regime f o u n d a t i o n s t i f f n e s s i s a s i g n i f i c a n t f a c t o r f o r t h e more compliant c a s e s ( f r e q u e n c i e s less

t h a n about 20 Hz), b u t n o t s o f o r t h e s t i f f e r f o u n d a t i o n s ( f r e q u e n c i e s g r e a t e r t h a n 30 Hz). The compliant f o u n d a t i o n ( s t i f f n e s s less t h a n 20 Hz) i n t h i s c a s e m a g n i f i e s t h e i c e l o a d s t r a n s f e r r e d t o t h e foundation. h t h i s h i g h e r v e l o c i t y regime i c e f a i l u r e e x c i t e s f r e q u e n c i e s i n t h e s t r u c t u r e up t o about 20 Hz. F i g u r e 8 is a p l o t of t h e compensated maximum i c e f o r c e s (averaged f o r a l l f o u n d a t i o n s t i f f n e s s e e ) v e r s u s v e l o c i t y . F i r s t l y , i t may be s e e n t h a t t h e r e a r e tw, r e g i o n s of f a i l u r e behaviour. These f o l l o w a s i m i l a r p a t t e r n , i f n o t an e x a c t correspondence t o t h e f a i l u r w o d e map p r e s e n t e d by Timco (1986b) f o r fresh-water i c e ; i.e., f o r a g i v e n a s p e c t r a t i o one vould e x p e c t a t r a n s i t i o n from buckling t o c r u s h i n g a s v e l o c i t y i n c r e a s e s . It may be s e e n t h a t i n t h e l o v v e l o c i t y r e g i o n ,

Where f a i l u r e is by a mixed mode of

b u c k l i n g a n d c r u s h i n g , t h e maximum c o r r e c t e d i c e f o r c e a p p e a r s t o i n c r e a s e w i t h i n c r e a s i n g v e l o c i t y . I n t h e h i g h e r v e l o c i t y r e g i o n (9 and 27 c m l s ) t h e maximum c o m p e n s a t e d f o r c e a p p e a r s t o d e c r e a s e w i t h i n c r e a e i n g v e l o c i t y . It i s

1 I

I

n o t p o s s i b l e t o p l a c e a g r e a t d e a l of s i g n i f i c a n c e on t h e s e t r e n d s , b u t i t is c l e a r t h a t i n s e e k i n g e x p l a n a t i o n s f o r v e l o c i t y e f f e c t s on i c e l o a d s i t i s n o t r e a s o n a b l e t o e x p e c t t h e same p r o c e s s ( f a i l u r e behaviour) t o p r e v a i l o v e r a wide range of v e l o c i t i e s . D e t a i l e d r e s u l t s of t h e frequency c o n t e n t of t h e measured o r compensated i c e l o a d r e c o r d s a r e not p r e s e n t e d h e r e , b u t i t was g e n e r a l l y o b s e r v e d t h a t a t v e l o c i t i e s of 1 and 3 cm/s t h e peak

frequency was about 1 Hz, a t 9 cm/s about

3 Hz, and a t 27 cm/s about 15 Hz. No

s y s t e m a t i c v a r i a t i o n w i t h f o u n d a t i o n s t i f f n e s s was noted. The g e n e r a l t r e n d of i n c r e a s i n g f r e q u e n c y w i t h i n c r e a s i n g v e l o c i t y is s i m i l a r t o t h a t r e p o r t e d by Sodhi and P b r r i s (19861, a l t h o u g h t h e p r e s e n t r e s u l t s a r e n o t s u f f i c i e n t l y c o n s i s t e n t t o permit any c o n c l u s i o n s about a damage zone s i z e .

T r a n s v e r s e l o a d s were a l s o measured. Again, d e t a i l s of t h e s e measurements a r e n o t p r e s e n t e d h e r e , b u t t h e a v e r a g e maxinum t r a n s v e r s e load was found t o be a b o u t 25X of t h e maximum compensated i c e l o a d , and i n a few i n s t a n c e s i t exceeded .

30%.

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F i g u r e 7. C o ~ p a r i s o n of maximum measured r e s p o n s e f o r c e , r ( t ) nax, and maximum compensated i c e f o r c e , f ( t ) max, a s a f u n c t i o n of f o u n d a t i o n s t i f f n e e s and test v e l o c i t y . 1500 BUCKLING

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1 0 za 3 0 T E S T V I L O C I T V . c m t s F i g u r e 8. I n f l u e n c e of t e s t v e l o c i t y o n a v e r a g e maximum compensated i c e f o r c e . Summary

1. Sempling r a t e s and time i n t e r v a l s f o r a n a l y s i s m a t be s e l e c t e d v i t h c a r e t o minimize t h e i n t r o d u c t i o n of a r t i f a c t s i n t o t h e r e s u l t s .

2. For l o v v e l o c i t i e s (1-3 cm/s) o r f o r a s t i f f ( 5 0 Hz) f o u n d a t i o n t h e maximum measured and compensated i c e f o r c e s a r e q u i t e s i m i l a r . These a r e c a s e s where f o u n d a t i o n f r e q u e n c y r u b e c a n t i a l l y e x c e e d s t h e o b s e r v e d primary i c e f a i l u r e f r e q u e n c y o f 1 Hz. 3. For h i g h v e l o c i t i e s (9-27 cm/s) and f o u n d a t i o n f r e q u e n c i e s l e s s t h a n 32 Hz t h e maximum C o m p e n s a t e d i c e f o r c e i s s u b s t a n t i a l l y l e s s t h a n t h e m e a s u r e d maximum. I n t h e s e c a s e s r e s p o n s e f o r c e o n t h e f o u n d a t i o n is m a g n i f i e d by s t r u c t u r e c h a r a c t e r i s t i c s . 4. Mode of f a i l u r e i s a n i m p o r t a n t f a c t o r i n d y n a m i c i n t e r a c t i o n l o a d i n g ; f o r b u c k l i n g , t h e i c e f o r c e a p p e a r s t o i n c r e a s e w i t h i n c r e a s i n g v e l o c i t y , and f o r c r u s h i n g i t a p p e a r s t o d e c r e a s e w i t h i n c r e a s i n g v e l o c i t y . Acknovledgement

The a u t h o r s would l i k e t o acknowledge t h e t e c h n i c a l a s s i s t a n c e of R. Bowen and

J. Neil i n p e r f o r n i n g t h e t e s t s and of E. Funke a n d G. P e r n i c a f o r h e l p f u l d i s c u s s i o n s c o n c e r n i n g t h e a n a l y s i s .

R e f e r e n c e s

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.XI,

pp. 365-378. Danys, J.V. (1975). O f f s h o r e i n s t a l l a t i o n s t o measure i c e f o r c e s o n t h e l i g h t p i e r i n L a c S t . P i e r r e . 9 t h I n t . Conf. o n L i g h t h o u s e s and O t h e r Aids t o N a v i g a t i o n , O t t a w a ( I n t e r n a t i o n a l A s s o c i a t i o n o f Lighthouse A u t h o r i t i e s , P a r i s . ) D a o u d , N. a n d L e e , F.C. ( 1 9 8 6 ) . Ice-induced dynamic l o a d s on o f f s h o r e s t r u c t u r e s . h o c . 5 t h I n t . O f f s h o r e Mechanics and A r c t i c E n g i n e e r i n g ( O W )

Symp., Tokyo, 1986, Val. 4 , pp. 212-218.

Engelbrekrson, A. (L978). Dynantle Ice

l o a d s on a l i g h t h o u s e s t r u c t u r e . POAC177, M e m o r i a l U n i v . o f N e v f o u n d l a n d , St. J o h n ' s , Vol. 2, pp. 654-663.

Frederking, R., Sayed, M., Hodgson, T. and

B e r t h e l e t , U. (1985). I c e f o r c e r e s u l t s f r o m t h e m o d i f i e d Y a m a c h i c h e B e n d

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L i g h t p i e r , w i n t e r 1983-84. P r o c . Canadi an C o a s t a l Conference, St. J o h n ' s , ppe 319-331. Haynes, F.D. (1986). V i b r a t i o n a n a l y s i s of t h e Yamachiche L i g h t p i e r . I n t . J. A n a l y t i c a l a n d E x p e r i m e n t a l n o d e 1 Analysis, Vol. 1, No. 2, pp. 9-18.

MZitt'gnen, M. (1975). Experiences of i c e

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Fairbanks, Vol. 2, pp. 857-869.

M U t t g n e n , H. (1.981). I c e s t r u c t u r e dynamlc i n t e r a c t i o n

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ice f o r c e s v e r s u s v e l o c i t y , i c c i n d u c e d damping. Proc. Quebec 1981 I n t . A s s o c i a t i o n of Hydraulic

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27-31 J u l y , Lava1 U n i v e r s i t y , Quebec, pp. 783-796.

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continuous crushing. U.S. Army Cdld

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P r a t t e , B.D. and Timco, G.U. (1981). A new m o d e l b a s i n f o r t h e t e s t i n g o f i c e s t r u c t u r e i n t e r a c t i o n s . POAC'8 1, Qwbec C i t y , Val. 11, pp. 857-866. Rainer, J.H. (1986). A p p l i c a t i o n s of t h e F o u r i e r t r a n s f o r m t o t h e p r o c e s s i n g of v i b r a t i o n s i g n a l s . N a t i o n a l Research

Council Canada, Ottawa, BRN 233, 24 pp.

Sodhi, D.S. and E b r r i s , C.E. (1986).

C h a r a c t e r i s t i c f r e q u e n c y o f f o r c e v a r i a t i o n e i n c o n t i n u o u s c r u s h i n g of s h e e t i c e a g a i n s t r i g i d c y l i n d r i c a l s t r u c t u r e s . Cold R e g i o n s S c i e n c e a n d T e c h n o l o g y , Vol. 12, pp. 1-12. Thomson, W.T. (1981). Theory of v i b r a t i o n s w i t h a p p l i c a t i o n s . London, George Al Len and Unwin, 467 p.

Timco, G.W. ( 1 9 8 6 b ) . I n d e n t a t i o n and p e n e t r a t i o n of e d g e l o a d e d f r e s h w a t e r i c e s h e e t s i n t h e b r i t t l e range. Proc. 5 t h

OMAE Symp., Tokyo, J a p a n , Vol. 4,

pp. 4 4 4 4 5 2 .

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,

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D i s c u s s i o n

D. SODHI: Did you r e l a t e t h e dominant

frequency i n t h e i c e f o r c e record from t e s t s conducted a t low v e l o c i t i e s t o v e l o c i t y - t o - t h i c k n e s s r a t i o ?

R. FREDERSCING: We examined t h i s r e l a t i o n but d i d not f i n d c o n s i s t e n t r e s u l t s . For both a v e l o c i t y of 1 cm/s and 3 cm/s, t h e dominant frequency was between 1 and 1.5

H

w i t h no s y s t e m a t i c c o r r e l a t i o n t o f%undation s t i f f n e s s . A t v e l o c i t i e s of 9 and 27 cm/s. p r o g r e s s i v e l y h i g h e r dominant f r e q u e n c i e s were observed. s o o u r r e s u l t s shoved t e n d e n c i e s s i m i l a r t o your

f i n d i n g s (Sodhi and Morris 1986). Our

v a l u e s of v / f h were i n t h e range 0.2 t o 0.8 and averaged 0.6, c o n s i d e r a b l y h i g h e r than your average v a l u e of 0.3.

Timco, G.U. (1986a). EG/AD/S: A new type

o f model i c e f o r r e f r i g e r a t e d towing t a n k s . C o l d R e g i o n s S c i . e n c e a n d Technology, vol. 12, pp. 175-195.