On measuring the shear strength of ice

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On measuring the shear strength of ice

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TH1

~ 2 1 d National Research

Conseil

natsonai

no. 1612

1 *

1 Council Canada

de

mhetches

Canada

c , 2

BLDG Institute for lnstitut de

-- .- Research in recherche en

Construction construction

On Measuring the Shear Strength

of

Ice

by R.M.W. Frederking, O.J. Svec and G.W.

T

imco

Appeared in

Proceedings of the 9th International Symposium on Ice

Sapporo, Japan, August 23-27,1988 IAHR Committee on Ice Problems, Vol. 3 p. 76-88

(IRC Paper No. 1612)

Reprinted with permission NRCC 30756

L I B R A R Y

B I B L I O T H ~ Q U E

I R C

(3)

L'analyse par la mCthode des ClCments finis de poutres soumises Zi des charges en quaue

points asyxnktriques a 6tC utilistk pour calculer les champs

de

contraintes internes

pour

d8fChents Cchantillons et diffkrentes gbmCmes d'application des charges. Les contraintes de

cisdement dCtamh&s d'aprks ces champs

de

contrahe diffdraient nettement de celles

cdcdies &ap& la thCorie de la poutre unique. Des exp5riences effectu6es en labratoire

avec des Cchantdlons de glace d'eau douee

h

gains columnaires ont montr6 que des valeurs

cshhntes Ctaient obtenues pourvu que les Cchantillons ~t les g&&tries &application des

charges ne varient pas au-del8 d'une plage pdcub2re. A

-10

OC

une dsistance au

cisaillement moyenne de

600 kPa a it6 dCt-k.

Des mesures sp&iales

adoptks

afin

de

r6duire la concentration des contraintes aux points d'application des charges ont entrahi un

accroissement de la dsistance au cisaillement moyenne qui est passee

B

1100

kPa. Une

m6thode d'essai de cisaillement dans la glace bade sur

cette

e&rience est proposCe.

(4)

Sapporo

ON MEASURING THE SHEAR STRENGTH OF I C E

R e Frederking and O.J. Svec Geotechnical Section

I n s t i t u t e f o r Research i n Construction G.W. Timco D i v i s i o n o f Mechanical Engineering

National Research Council of Canada Ottawa, Ontario, CANADA

K I A OR6 ABSTRACT

F i n i t e element a n a l y s i s o f beams subjected t o f o u r c p o i n t asymmetric l o a d i n g has been used t o c a l c u l a t e t h e i n t e r n a l s t r e s s f f e l d s f o r d i f f e r e n t specimen and 1 oading geometries. The shear stresses determi ned from these s t r e s s f i e l d s were s i g n i f i c a n t l y d i f f e r e n t from those c a l c u l a t e d from s i m p l e beam t h e o r y . L a b o r a t o r y experiments done on samples o f columnar-grained f r e s h w a t e r i c e showed t h a t consistent values o f shear s t r e n g t h were obtained provided specimen and 1 oading geometries d i d n o t vary beyond a p a r t i c u l a r range. A t - 1 r C an average shear s t r e n g t h o f 600 kPa was determined. Special measures taken t o reduce s t r e s s concentrations a t t h e l o a d a p p l i c a t i o n p o i n t s r e s u l t e d i n an increase o f t h e average shear s t r e n g t h t o 1100 kPa. Based on t h i s experience, a shear t e s t i n g method f o r i c e i s proposed.

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IAHR Ice

Symposium 1988

Sapporo

I n t r o d u c t i o n

A n a l y t i c a l models o f i c e forces on s t r u c t u r e s have generally considered t h e i c e i n t h e i n t e r a c t i o n zone t o be under a u n i a x i a l o r m u l t i a x i a l compressive s t r e s s condition. It i s q u i t e possible, however, t h a t s i g n i f i c a n t p a r t s o f t h e i n t e r a c t i o n zone may be subjected t o b i a x i a l s t r e s s c o n d i t i o n s i n v o l v i n g t e n s i l e i n a d d i t i o n t o compressive stresses. Measurements o f shear s t r e s s a r e r e l e v a n t t o d e f i n i n g t h i s s t r e s s condition. Therefore i n f o r m a t i o n on shear s t r e n g t h i s necessary i n a n a l y t i c a l p r e d i c t i o n s o f i c e loads where t h i s t y p e o f f a i l u r e behaviour i s occurring. Shear-strength data a r e a l s o u s e f u l i n determining t h e f a i l u r e envelope o f i c e under m u l t i a x i a l s t r e s s conditions.

The shear s t r e n g t h o f i c e i s a d i f f i c u l t p r o p e r t y t o measure i n an unambiguous fashion. The techniques commonly used, d i r e c t shear, punching, o r torsion, create s t r e s s f i e l d s t h a t cannot be q u a n t i f i e d simply. Normally i t i s assuned t h a t a uniform shear s t r e s s i s generated on a plane o f f a i l u r e , b u t i n

many

instances indeterminate normal stresses a r e a l s o generated on t h e plane o f f a i l u r e . For example, Butkovich (1956) obtained values i n t h e ranges 500 t o 1200 kPa u s i n g t h e double shear technique, w h i l e Paige and Lee (1967) and Dykins (1971) obtained values i n t h e ranges 500 t o 1200 kPa and 100 t o 250 kPa r e s p e c t i v e l y f o r s i n g l e shear. I n a l l t h r e e cases, r e s u l t s were f o r f i r s t - y e a r sea i c e o f s i m i l a r s a l i n i t y and temperature. This l a r g e d i s p a r i t y i n r e s u l t s brings i n t o question t h e v a l i d i t y of t h e t e s t methods used i n t h e past. The o f f - a x i s s t r e n g t h t e s t (Pipes, 1973), i n which t h e specimen a x i s i s o r i e n t e d a t some angle t o t h e m a t e r i a l coordinate systems, has been used t o o b t a i n s t r e n g t h data under a l o a d i n g c o n d i t i o n w i t h t e n s i l e and compressive p r i n c i p a l stresses (shear).

It produces b o t h normal and shear stresses on t h e f a i l u r e plane.

The asymmetric f o u r - p o i n t l o a d i n g method has been proposed as a means o f performing improved shear t e s t s (Iosipescu, 1967). This method was a p p l i e d t o an i n v e s t i g a t i o n o f g r a n u l a ~ s t r u c t u r e d f i r s t - y e a r i c e from t h e Beaufort Sea (Frederking and Timco, 1984) and t o columnarcgrained and f r a z i l sea i c e from Labrador (Frederking and Timco, 1986). Consistent r e s u l t s were obtained. This paper w i l l present t h e r e s u l t s o f f i n i t e element (FE) c a l c u l a t i o n s o f beam subjected t o fourcpoint asymmetric

loading. Strengths c a l c u l a t e d from t h e FE a n a l y s i s and simple beamtheory

(6)

supporo

w ~ l l

be conpared w i t h r e s u l t s o f l a b o r a t o r y t e s t s and a recommended c a l c u l a t i o n and t e s t method f o r shear proposed.

Asymnetrical Four-point Bending Method f o r Shear

The asymmetrical f o u r - p o i n t bending method was used i n p e r f o r m i n g t h e shear t e s t s . Load i s appl i e d a t f o u r p o i n t s on a beam so t h a t a r e g i o n o f h i g h shear s t r e s s and low bending s t r e s s i s generated a t t h e m i d - s e c t i o n of t h e beam. The geometry o f l o a d a p p l i c a t i o n and r e s u l t i n g i d e a l i z e d shear forces and bending moments a r e i l l u s t r a t e d i n F i g u r e 1. The s h e a r c s t r e s s d i s t r i b u t i o n a t t h e c e n t r e plane, x

=

0,

i s assuned t o be p a r a b o l i c w h i c h gives a maximm shear s t r e s s ,

+,

a t t h e mid h e i g h t o f t h e beam

where P i s t o t a l a p p l i e d load, b i s specimen thickness, h i s specimen

1111,

/')Ir,

B A R U P P E R PLATE

c

S P E C I M E N

l

x

I I I / J LOWER P P L A T E - a

-

P _-_&_P S H E A R FORCE D I A G R A M I + = B E N D I N G M O M E N T D I A G R A M

F i g u r e 1. Asymmetric f o u r - p o i n t l o a d i n g apparatus and shear f o r c e and bending moment diagrams (from Frederk i n g and Timco, 1984).

(7)

IAHR

Ice Symposium 1988

Sappon,

h, and a r e l a t e s t o t h e l o a d i n g geometry. The specimen geometry proposed by Iosipescu, (1967) included notches i n t h e t o p and bottom surfaces of t h e beam a t t h e mid-plane, x = 0. This procedure has t h e e f f e c t of reducing t h e cross-sectional area subjected t o t h e shear s t r e s s and o f producing a nearly uniform shearcstress d i s t r i b u t i o n , provided t h a t each notch depth i s between 20

-

25% o f t h e specimen heigtit, h. For t h e notched beam, maxirmm shear s t r e s s i s g i v e n by

where P,- a, and b a r e as defined f o r equation (1) and ho i s t h e n e t h e i g h t of t h e beam across t h e notches.

F i n i t e

Element

Analysis

A f i n i t e element analysis, u s i n g q u a d r i l a t e r a l 1 in e a r elements, was

employed t o examine t h e s t r e s s f i e l d i n t h e c e n t r a l r e g i o n of t h e t e s t specimens. L i n e a r e l a s t i c behaviour was assuned f o r t h e i c e ( e l a s t i c modulus 10 GPa and P o i s s o n ' s r a t i o 0.3) and t h e p l a n e s t r e s s (az

=

o) c o n d i t i o n appl ied. The factors of specimen depth, h, l o a d i n g p o s i t i o n , a

and notch o r saw cut a t t h e c e n t r a l plane o f t h e beam were treated. A standard mesh of 66 elements along t h e l e n g t h of t h e beam and 20 elements over t h e depth was used f o r a l l t h e cases investigated. Only element s i z e and shape ( t r a p e z o i d a l f o r t h e notch and saw-cut) were varied. The stresses i n a l l cases a r e f o r an a p p l i e d l o a d o f P = 1080 N.

The r e s u l t s o f t h e f i n i t e element c a l c u l a t i o n s a r e summarized i n Table 1. Maximum v a l u e s of s h e a r s t r e s s , .cmax, and t e n s i l e stress, ul, a t t h e c e n t r e plane (x = 0) and l o a d i n g plane ( x = a x ) a r e presented f o r a v a r i e t y o f cases. F o r comparison s h e a r stress, .c c a l c u l a t e d from simple beam

XY

'

theory i s a l s o included. It can be seen t h a t t h e r e s u l t s f o r maxinum shear s t r e s s , s and a r e i n reasonable agreement f o r t h e two c a l c u l a t i o n

x Y

methods, i n t h e case of p l a i n beams.

F i g u r e 2 presents t h e s t r e s s d i s t r i b u t i o n s a t t h e c e n t r a l plane

( x = 0) of t h e beam f o r t h e case of beam depth h 100 mm and l o a d p o s i t i o n

a = 0.1. The l e f t hand p a r t o f t h e f i g u r e shows t h e stresses i n terms o f t h e Cartesian coordinate system (x, y ) and i n t h e r i g h t hand p a r t t h e same

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s@poro

b l e

1

Calculated maxlmrrn shear and t e n s i l e s t r e s s u s i n q f i n i t e element a n a l y s i s (FE) and simple beam theory (SB) f o r v a r i o i s beam geometries and l o a d i n g p o s i t i o n s . Stresses, i n kPa, a r e f o r 50 mm t h i c k beams w i t h a nominal l o a d P = 1080 N. + h=70 mm h=100 mm h=140 mm p l a i n p l a i n V-notch saw-cut p l a i n eO.1

SB

%y 3 90 27 0

-

240 180 F E h x , x = O 340 2 50

--

1780 ' 210 %ins x'QR 380 380

--

350 350 ul, x-0 360 220

..

130 150 ' h0.2 SB 310 220 300 300 150 FE

hx,

F O

310 210 230 910 140 %i n* X" 270 310 300 310 3 10 ul, x=O 490 250 160 240 150

s t r e s s e s have been converted t o p r i n c i p a l stresses, q a n d

%,

and maxinum s h e a r s t r e s s , rma, =

( 4

-

u22)12. Note, t e n s i l e s t r e s s e s a r e t a k e n as p o s i t i v e . The FE a n a l y s i s produces values o f -40 kPa f o r s a t t h e beam

XY

surface, whereas t h e v a l u e here should be zero. T h i s anomaly i n d i c a t e s t h a t t h e r e s u l t s o f t h e a n a l y s i s a t o r near a f r e e surface have t o be

STRESS, kPa STRESS

(COMPRESSION) (TENSION)

F i g u r e 2. Stress d i s t r i b u t i o n p l o t s a t c e n t r a l p l a n s (x

=

0)

o f a 100 mm deep beam i n t e r n o f ( a ) specimen coordinates

(%,

and ), and ( b ) p r i n c i p a l s t r e s s coordinates (=,

q

and

%3.

~ o a n g p o s i t i o n a = 0.1.

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IAHR

Ice SymPosium

1988

Snpporo

r n t e s p r c t e d w i t h some caution, F i g u r e 2 shows t h e s h e a r s t r e s s , r XY

'

d i s t r i b u t i o n detennined from t h e FE a n a l y s i s d i f f e r s s u b s t a n t i a l l y from t h e p a r a b o l i c d i s t r i b u t i o n assuned i n t h e simple beam theory (Equation I ) , even though t h e maxirmm values o f shear s t r e s s a r e s i m i l a r f o r t h e two c a l c u l a t i o n methods. The r e s u l t s a l s o s h w t h a t a c o n d i t i o n o f pure shear (ax

= u =

0 o r

q

=

- ? )

does n o t e x i s t a t t h e c e n t r a l plane, t h e r e

Y

i s i n f a c t a mean compressive s t r e s s o f 140 kPa on t h e plane o f l a r g e s t

s _{ma x}(260kPa).

I n F i g u r e 3 t h e p r i n c i p a l stresses,

9

and

4 ,

and zmx a r e p l o t t e d f o r two l o a d i n g positions, a = 0.1 and 0.2, f o r a 100 mm deep beam. F i g u r e 3a, f o r t h e stresses a t t h e centre plane, s h w s t h a t t h e s t r e s s d i s t r i b u t i o n s change s l i g h t l y and t h a t t h e maxirmm shear s t r e s s on t h e centre plane (x = 0) i s 250 kPa i n t h e case o f l o a d p o s i t i o n a = 0.1 versus 200 kPa f o r load p o s i t i o n 0.2. Figure 3b, f o r stresses a t t h e plane of l o a d a p p l i c a t i o n (x

=

d), i n d i c a t e s t h a t b o t h d i s t r i b u t i o n s a r e generally s i m i l a r b u t t h a t , again, -rmax i s l a r g e r f o r l o a d p o s i t i o n a

=

0.1. Note t h a t F i g u r e 3b a l s o i n d i c a t e s t h e presence o f a high shear s t r e s s j u s t b e l m t h e surface o f t h e beam and a high t e n s i l e s t r e s s on t h e opposite s i d e o f t h e beam a t t h e l o a d a p p l i c a t i o n plane (x

=

aA).

The s t r e s s d i s t r i b u t i o n s a t t h e c e n t r e plane f o r a 20 mm deep

90'

V-notch i n a beam o f depth 100 mm a r e presented i n F i g u r e 4. Note t h a t t h e n e t s e c t i o n d e p t h a t t h e notch, ho, i s 6 0 m I n t h i s case, rmX i n t h e notch i s uniform w i t h a maxirmm value o f 230 kPa. This s t r e s s i s s l i g h t l y l a r g e r t h a n t h e value o f 210 kPa obtained f o r an unnotched beam w i t h l o a d p o s i t i o n a = 0.2 (see Table 1). The s t r e s s d i s t r i b u t i o n s a t t h e l o a d i n g plane ( x

=

UA) were s i m i l a r t o those o f t h e un-notched beam.

The s t r e s s d i s t r i k r t i o n s c a l c u l a t e d f o r t h e saw c u t case a r e n o t plotted, b u t i t can be seen i n Table 1 t h a t they gave a very high v a l u e f o r

r

max' There i s some q u e s t i o n as t o t h e accuracy o f t h e stresses c a l c u l a t e d a t t h e t i p o f t h e cut. It i s planned f o r f u t u r e research t o use h i g h e r o r d e r elements and a more r e f i n e d FE mesh, p a r t i c u l a r l y i n l o c a t i o n s o f s t r e s s concentration. Developnent o f a FE model capable o f approximating nonl i n e a r behaviour o f i c e might a l s o become necessary.

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Sapporo

q

,

kPa a2, @a %OX 9 IcF'a

-0 300 -300 0 -300 0

a) STRESSES AT CENTRAL PLANE ( x = 0 )

q,

kPa %, kpa T , , , ~ , kpa

b) STRESSES AT LOAD PLANE ( x = a

I )

F i g u r e 3. D i s t r i b u t i o n s o f p r i n c i p a l s t r e s s e s ,

q

and 42, a n d maximm s h e a r s t r e s s , f o r a p l a i n 1 0 0 mm d e e p beam w i t h l o a d F = 1080N.

Test Method and Specimen Preparation

A t e s t apparatus has been b u i l t t o rep1 i c a t e t h e c o n d i t i o n s i n d i c a t e d i n F i g u r e 1. The d i s t a n c e of t h e o u t e r l o a d i n g p o i n t s (a b a l l i n each

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IAHR Ice Sym~osium

1988

Sapporo

STRESS, kPa

' i g u r e 4. D i s t r i b u t i o n s o f p r i n c i p a l s t r e s s e s ,

q ,

and

9 ,

and maximm shear stress,

ha,

a t t h e c e n t r a l plane (x = 0) of a 100 mm deep beam w i t h 2 20 mm deep 90' notches.

case), A, i s 150 mm from t h e c e n t r e 1 ine, x

=

0, Two s e t s o f notches a r e provided i n each p l a t e a t 1 5 and 30

mm

d i s t a n c e ( a = 0.1 and 0.2 r e s p e c t i v e l y ) from t h e centre. A t these i n n e r l o a d i n g p o s i t i o n s a b a r i s used t o d i s t r i b u t e t h e l o a d across t h e w i d t h o f t h e specimen. The upper p l a t e , through which t h e l o a d P i s applied, i s f r e e t o r o t a t e about t h e 1 oad-appl i c a t i o n point. Loading was c a r r i e d o u t u s i n g a 50-kN capacity f i e l d p o r t a b l e conpression t e s t e r designed and b u i l t a t t h e National Research Council o f Canada. The machine has a screw d r i v e actuator. A1 1 t e s t i n g was done a t a nominal a c t u a t o r r a t e o f 0.5 mm sml.

Continuous records o f l o a d versus time were made f o r each test. I n a few cases, high speed 16 mm movie f i l m were a l s o taken, a t a r a t e o f 400 frames/s. The purpose o f t h e f i l m i n g was t o d e t e c t t h e l o c a t i o n of f a i l u r e i n i t i a t i o n and t o f o l l o w i t s progress.

A 60 mm t h i c k columnar-grained f r e s h w a t e r i c e sheet (C2, according t o IAHR, 1986 c l a s s i f i c a t i o n o r S2 according t o Michel and Ramseier, 1971) was g r w n i n t h e I c e Test Basin o f NRC's Hydraulics Laboratory i n Ottawa. The t o p 10 mm o f t h e i c e sheet was discarded, l e a v i n g uniform columnar i c e w i t h an average g r a i n diameter o f 3 mm. Specimens were c u t t o rough dimensions on a band saw and t h e n planed on a power p l a n e r t o f i n a l nominal dimensions

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**s*m**

350 nun length, 50 mm thickness and 70, 100 o r 140 mm depth. A d d i t i o n a l l y , some o f t h e 100 mm deep specimens were prepared w i t h a p a i r of 90' notches o r 2 mm wide saw cuts a t t h e c e n t r a l plane of t h e beam

( x

=

0). These notches o r c u t s each extended t o a depth o f about 20 mm, l e a v i n g a net s e c t i o n depth o f about 60 mm. The l o n g a x i s o f t h e columnar g r a i n s were always normal t o t h e l a r g e s t faces. Specimen p r e p a r a t i o n and t e s t i n g was c a r r i e d out a t a temperature o f -10'C

+

1'C.

Test Results and Discussion

Tests were performed on a t o t a l o f 57 beams. Table 2 summarizes a l l t h e cases examined. The main parameters v a r i e d were beam depth, h, l o a d position, a, notching and saw c u t s o f beams, and t h e absence o r presence of s t r e s s r e l i e f m a t e r i a l under t h e l o a d i n g bars. Force time curves f o r

repeat t e s t s done on a 100 mm deep beam w i t h l o a d p o s i t i o n a = 0.1 a r e presented f n F i g u r e S(a). The general consistency of t h e t e s t r e s u l t s can be seen. These curves a l s o shcw t h e e f f e c t s o f l o c a l cracking and spa11 i n g o f t h e specimen a t t h e l o a d i n g p o i n t s when no s t r e s s r e l i e f i s used a t t h e l o a d i n g bars. The small decreases i n l o a d occur due t o r e l a x a t i o n i n t h e t e s t system which i s l o a d i n g a t a nominally constant r a t e o f displacement. T h i s behaviour was not noted i n a previous a p p l i c a t i o n o f t h i s t e s t method t o s a l i n e i c e ( F r e d e k i n g and Timco, 1984, 1986). Figure 5(b), by contrast, presents r e s u l t s w i t h a l o c a l s t r e s s r e l i e f m a t e r i a l under t h e l o a d i n g points. The f i r s t obvious f a c t o r i n t h i s case i s t h e smooth monotonic increase i n l o a d up t o f a i l u r e . Also, s i g n i f i c a n t l y h i g h e r f a i l u r e loads were obtained. This d i f f e r e n c e i n l o a d i n g behaviour was a l s o observed i n t h e high speed 16 mm filming, i n which small pieces o f i c e Table 2 Summary o f cases examined i n t e s t program

X, tested; S, t e s t e d w i t h s t r e s s r e l i e f m a t e r i a l

-

84

-

Beam h=70 mm p l a i n a

=

0.1 X, S a = 0.2 X <

-

h=140 mm p l a i n X X h=100 mm p l a i n X,

s

X V-notch

--

X,S saw-cut X,S

x,s

(13)

-- --

IAHR

Ice

Symposium 1988

Sapporo

6000

a) I

TIME,

s

F i g u r e 5. P l o t s o f f o r c e versus time f o r 100 mm deep beams w i t h l o a d

p o s i t i o n a

=

0.1; (a) no s t r e s s r e l i e f m a t e r i a l under l o a d i n g bars, (b) stress r e l i e f m a t e r i a l under b a n , ( s o l i d l i n e s

-

bake1 i t e )

,

(dashed 1 ines

-

cardboard).

c o u l d be seen s p a l l i n g o f f t h e beam when no s t r e s s r e l i e f m a t e r i a l was used.

P l a i n specimens f a i l e d w i t h a s i n g l e crack which extended from l o a d b a r t o l o a d bar. The V-notched and saw-cut specimens f a i l e d w i t h two cracks, each extending from t h e l o a d b a r t o t h e opposite notch o r saw-cut t i p . The h i g h speed f i l m was examined t o see whether t h e p o i n t o f cradt

i n i t i a t i o n and d i r e c t i o n o f propagation could be detected, I n t h e case of t h e plane beam, crack i n i t i a t i o n and propagation occurred i n l e s s t i m e t h a n t h e 11400 s (2.5

ms)

between frames. I n t h e case o f t h e V-notch, i t appeared t h a t t h e crack i n i t i a t e d a t t h e b a r and then ran t o t h e notch t i p . Propagation t i m e i n t h i s instance was l e s s t h a n 5

ms.

The t e s t r e s u l t s were analysed f o r shear s t r e n g t h and t e n s i l e s t r e n g t h u s i n g simple beam theory (Equations(1) and ( 2 ) ) and f i n i t e element a n a l y s i s (Table 1). I n terms o f d e r i v i n g a shear s t r e n g t h from t h e data, t h e most c o n s i s t e n t r e s u l t s were o b t a i n e d u s i n g t h e maxim. shear strength,

bax,

determined from t h e f i n i t e element analysis. This can be seen i n Table 3 which summarizes a l l t h e t e s t results.

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**S*IO**

There were no instances o f t h e f a i l u r e plane propagating towards o r away from t h e zone o f high t e n s i l e s t r e s s opposite t h e l o a d i n g points. Therefore calculated t e n s i l e s t r e n g t h s a r e not presented here even though t h e f i n i t e element c a l c u l a t i o n s would i n d i c a t e t h a t they were high, p a r t i c u l a r l y f o r t h e 70 mm deep beams (see Table 1). F i g u r e 3 and Table 1

a l s o s h w high shear stresses under t h e l o a d i n g p o i n t s ( x

=

+ a ~ ) b u t these have been disregarded i n subsequent c a l cul ations o f shear strength. They were exami ned, but produced 1 ess c o n s i s t e n t results.

The r e s u l t s o f Table 3 shcw t h a t t h e r e i s b e t t e r consistency i n t h e shear strength values when they a r e evaluated u s i n g a f i n i t e element a n a l y s i s r a t h e r than simple beam theory, p a r t i c u l a r l y i n t h e case of plane beams and V-notched beams. The p l a i n beams o f depth 70, 100 and 140 mm and l o a d p o s i t i o n a = 0.1 as w e l l as t h e 100 mm deep beam w i t h l o a d p o s i t i o n

a

=

0.2 a l l had remarkably s i m i l a r r e s u l t s when evaluated u s i n g t h e f i n i t e element analysis. These r e s u l t s a r e u n d e r l i n e d i n Table 3. It can a l s o be seen t h a t i n t r o d u c i n g a s t r e s s r e l i e f m a t e r f a l r e s u l t s i n about a d o u b l i n g

o f t h e shear strength. T h i s r e s u l t i m p l i e s t h a t f o r no s t r e s s r e l i e f m a t e r i a l under t h e l o a d i n g p o i n t s d i f f e r e n t stresses a r e produced t h a n those fndicated by t h e f i n i t e element analysis. Some i n d e n t a t i o n of t h e bars i n t o t h e i c e was noted. This i n d e n t a t i o n could induce h i g h t e n s i l e stresses i n t h e beam and i n i t i a t e premature f a i l u r e under t h e l o a d i n g bars.

S u m

ry

a

nil

Rectnmiendat i

ons

, Shear strengths c a l c u l a t e d from f i n i t e element a n a l y s i s o r simple beam

theory give s i m i l a r r e s u l t s f o r plane and 90' V-notch beams. The shear s t r e s s d i s t r i b u t i o n s c a l c u l a t e d w i t h f i n i t e element analysis, however, a r e more accurate t h a n those c a l c u l a t e d u s i n g simple beam theory. Experiments

performed on columnar-grained f r e s h water i c e were used t o evaluate t h e c a l c u l a t i o n methods. Test r e s u l t s i n d i c a t e d t h a t keeping beam dimensions and loading p o s i t i o n s w i t h i n l i m i t s determined by t h e t e s t s allowed c o n s i s t e n t shear s t r e n g t h values t o be determined.

The f o l l w i n g recomnendations a r e made f o r t e s t i n g and i n t e r p r e t i o n of shear strength:

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IAHR

Ice Symposium

1988

sapporn

Table

3

~um'ma ry o f average shear s t r e n g t h s i n kPa a t t h e c e n t r a l plane ( x = 0) c a l c u l a t e d u s i n g simple beam theory (SB) and f i n i t e element a n a l y s i s (FE). C o l u m n a ~ g r a i n e d f r e s h water i c e a t -10.C

1) Test Conditions

-

beam dimensions 100 mm deep, 50 mm t h i c k and 350

mm

l o n g

-

p l a i n beam cross s e c t i o n .

-

l o a d i n g p o s i t i o n a

=

0.1

-

use s t r e s s r e l i e f m a t e r i a l under l o a d i n g bars ( b a k e l i t e o r cardboard f o r exampl e)

2) I n t e r p r e t a t i o n o f shear s t r e n g t h

-

f o r i n d e x shear s t r e n g t h use r c a l c u l a t e d u s i n g simple beam theory, XY

Equation

( I ) ,

provided t h e t e s t c o n d i t i o n s above a r e f o l l w e d .

-

f o r f a i l u r e envelope determinations use a c t u a l b i a x i a l stresses

u1

and

u2

as determined from FE cal culations.

Ack now1 edgements

The authors would l i k e t o acknwledge t h e assistance o f F r a r q o i s C a r r i e r , Summer Assistant, i n performing t h e f i n i t e element c a l c u l a t i o n s , and J. N e i l and R. Bowen, Technical O f f i c e r s , National Research Council o f Canada i n a s s i s t i n g w i t h t h e testing.

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Sapporo

Butkovich, T.C. 1956. S t r e n g t h o f sea ice. Snow, I c e and Permafrost Research Establishnent, Research Report RR-20. W i 1 lamette, I 1 1 i nois, 15 p.

Dykins, J.E. 1971. I c e e n g i n e e r i n g

-

m a t e r i a l p r o p e r t i e s o f s a l i n e i c e f o r a l i m i t e d range o f conditions. Naval C i v i l Engineering Laboratory, Technical Report R720, P o r t Hueneme, C a l i f o r n i a , 96 p.

Frederking, R.M.W. and Timco, G.W. 1984. Measurement o f shear s t r e n g t h o f granul ar/discontinuous-columnar sea ice. Cold Regions Science and Technology, Vol. 9, pp. 215-220.

F r e d e h i n g , R., and Timco, G.W. 1986. F i e l d measurements o f t h e shear s t r e n g t h o f columnar-grai ned sea ice. Proceedings of I A H R I c e Symposium 1986, Iowa C i t y , Iowa, 18-22 August 1986, Vol. 1, pp. 279-292.

IAHR, 1986. IAHR

-

Recommendations on t e s t i n g m e t h o d s o f ice, 5 t h r e p o r t o f Working Group on T e s t i n g Methods i n Ice. IAHR I c e Symposium, Iowa C i t y , Iowa, 18-22 August 1986, Vo1. I I I, pp. 595-599.

Iosipescu, N. 1967. New a c c u r a t e method f o r s i n g l e shear t e s t i n g o f metals. Journal o f M a t e r i a l s , Vol. 2 ( 3 ) , pp. 537-566.

Michel,

B.,

and Ramseier, R. 1971. C l a s s i f i c a t i o n of r i v e r and l a k e ice. Canadian Geotechnical Journal, Vol. 8, No. 1, pp. 36-45.

Paige, R.A. and Lee, C.W. 1967. P r e l i m i n a r y s t u d i e s on sea i c e i n Mdtlurdo Sound, A n t a r c t i c a , d u r i n g "Deep Freeze 65". Journal of Glaciology, Vol. 4

(46), p. 515-528.

Pipes, R. 1973. The o f f - a x i s s t r e n g t h t e s t f o r a n i s o t r o p i c m a t e r i a l s . J. Comp. Mat., Vol. 7, p. 246-256.