Ice pressure on vertical structures

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Ice pressure on vertical structures

Afanas'ev, V. P.; National Research Council of Canada. Division of Building

Research

THIS IS THE TWO HUNDRED AND FOURTEENTH OF THE SERIES OF TRANSLATIONS PREPARED FOR THE DIVISION OF BUILDING RESEARCH

TECHNICAL TRANSLATION 1708 TRANSPORTNOE STROITEL'STVO, (3): 47 - 48, 1972 NRC TT - 1708 onAWA 1973 BY FROM V. POPPE TRANSLATED BY V. P. AFANAS'EV Conseil national de recherches Canada

ICE PRESSURE ON VERTICAL STRUCTUR"ES'

National Research Council Canada

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NRC TT·1708

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PREFACE

The maximum force which an ice cover can exert on a structure and the relative importance of the various factors which influence it cannot yet be established with the degree of confidence desired in engineering practice. The Division of Building Research is concerned with developing a greater understanding of ice forces through analytical, laboratory and field investigations. Other northern countries besides Canada are involved in similar investigations, and from time to time there are articles in their journals reporting on research which is of particular interest.

One factor assumed to influence the load developed on a structure is the ratio of the structure width to ice thickness. Closely allied to this is the degree of completeness of contact between the ice and the structure. This article, translated from the Russian, develops an analytical fr amewcr k within which field or laboratory observations on these factors can be

compared.

The Division of Building Research is pleased to express its appreciation to Mr. V. Poppe for preparing this translation and to Dr. R. Frederking of this Division who checked the translation.

Ottawa December 1973 N.B. Hutcheon Director

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NATIONAL RESEARCH COUNCIL OF CANADA Technical Translation 1708

Title: Ice pressure on vertical structures

(Davlenie l'da na vertikal'nye pregrady)

Author: V.P. Afanas'ev

Reference: Transportrtoe Stroitel'stvo, (3): 47-48, 1972

Translator: V. Poppe, Translations Section, National Science Library

ICE PRESSURE ON VERTICAL STRUCTURES

A method is suggested for calculating the ice loads on single marine hydroengineering structures with vertical surfaces (foundations of light-houses and navigational aids, island moorings, etc.) due to moving ice fields.

The method is based on the results of experimental and theoretical studies, as well as on data published in foreign literature.

It has been determined that the specific ice pressure q on a vertical structure depends not only on the ice strength, but also on the loading conditions, and is expressed by the empirical relationship:

q

=

ma k

c (1)

to:

B

For

h

=

1 to 6, as used in the experiments, k is approximately equal

(4 ) (3) (2)

P

=

qBh. The total pressure on the structure is:

Applying the Prandtl relationship to determine the bearing strength of

B

a blunt wedge (Figure la,

h

«1), we have

(1

+

sin p)e2116- 1

+

sinp

p= O'llp 2 sin P

where m is the shape coefficient of the frontal part of the structure in plan view equal to 1.0 for a flat face, and 0.9 for a semi-circular face;

cr is the uniaxial compression strength of ice (cubic strength);

c

k is a coefficient which depends on the ratio of the width of structure

B

to ice thickness h.

Since the experiments were conducted only within the range

*

=

J to fi,

values of q outside this range must be obtained 11y theoretical analysis or t i l ( '

corresponding loading regimes for ice plates.

from (8) (7) (6) q2

=

0.80_c ql

=

40 (5) c a a

=

15 to 25 , we have (1-+-sin p)･＿ｾｉｏ 1 ＺＺｾﾣＮＮＮＮＮ 2sin p

that follows, 0.8 0_c will be substituted for 0_{TIP ,}).

Under natural conditions the destruction of the ice cover does not occur Let '0'= ｾＭＬ then from (4) at p

2

whe r e

With allowances for this the average specific pressure can be found

simultaneously throughout the entire width of the vertical structure, hut only at some contact points (Figure lc).

4

-To determine the limiting pressure for

ｾ

»1, refer to Figure lb. Angle

-&

depends on the cracks formed in the plate by loads which are less

than the destructive load. The load on the marginal sections of width a can be determined approximately from (4), since these sections are subjected to conditions which resemble the working conditions of each half of the blunt wedge (see Figure la). The load on section B-2a is equal to Q2' since

the working conditions here correspond to the loading conditions in scheme h.

Assuming that the destructive load on individual sections of length R. can be determined from (7), we shall calculate the average specific

ｾ

pressure throughout the width B from

is the angle of inclination of the envelope of the !'lohr circle: u

=

tg O.

Applying the Prandtl formula in the case of an ice plate subjected to a uniformly distributed load, and assuming that ｾ

=

0, we obtain

Since in this case (and in subsequent cases) m

=

1, it is easily shown that in (5) k₁

=

4.

where 0 is the prismatic compression strength of ice (in the treatment

- 5

-In (9) _{k 4} can be expressed as follows:

(9)

(10)

k, = 0,8 {

ｾｾＭ ｛ｾＫ

N (£1 - 1) - 1]-i-s«.c. },

is the number of intervals between the contact points;

E, & ｾｬ｡ｲ･ found from (8) for -& and.J'l respectively;

H is the depth of breaking up equal to 1.5 - 2.0 h;

where N

is the coefficient of looseness of contact between the ice

kIf.C.= _ 1 -8- sheet and the vertical structure.

Let

ｾ ｾｰ

{} = T; i)'1 = {}2=" ='1'}i=aretg'2H ;

(1- kll ,c)B

[ c P = - - N - - '

(lOa)

The numher of intervals N is taken arbitrarily, for example, equal to 1,

B

since the analysis has shown that ｎＨｾｬ - 1) at

h

< 20 is practically independent of the numerical value of N.

The values of k₄ for

ｾ

2:- 6 are given in Figure 2 (curve 2). r:urve 1 in

the same figure has heen constructed with the help of equation (2). Point 3

was determined from (5).

*

Ekspress-informatsiya VINITI, Seriya PTV i SR, 1971, No. 6

B

of 1 •

,1 J)

for

h

_{S 2, kH. C.}

=

1; found by linear inter-the basis of observations it is assumed that

B 20, k_{H. C.}

=

0.5; and for 2 <

h

< 20 k_{H. C.} is On B for

h

2:-polation.

Recent foreign literature contains some clata concerning ice loads on marine hydroengineering structures*. For example, on the basis of

investigations under natural conditions, the ice pressure on a cylindrical structure was assumed to be 300 tons

1m

2 at

ｾ =

4 and 150 tons

1m

2 at

ｾ ｾ

15 (without allowances for a safety factor). The load ratio was equal to 2,

6

-Hence, the investigations yield a qualitative confirmation of the experimentally determined relationship q

=

f

ＨＭｨｂｾ

and disclose its physical

\ l ;

meaning. This makes it possible LO recommend equation (1) for the calcula-tion of loads exerted by uniform (non-hummocky) ice fields on single

vertical structures. Coefficient k should be determined as follows:

1.

2.

B

For - > 1 - from equation (2);

h

B

For 0.1 ｾ

h

ｾ 1 - from linear interpolation, assuming that at these

B k· 4 d 2 5 . 1

h'

1S an . respect1ve y. Fig. 1 4 -ＭｾＭＭＮ Ｍｾ --K., \-JII i i J \ - . \N-'i o I ' _ 1 I I II :I

,-Ll _

IJ 2 4 Fig. 2