Proceedings of a Conference on Ice Pressures Against Structures

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Proceedings of a Conference on Ice Pressures Against Structures

CANADA

NATIONAL RESEARCH COUNCIL

Associate Committee on Geotechnical Research

ICE PRESSURES AGAINST STRUCTURES

Proceedings of a Conference

at

Laval University, Quehec, 10-11 November 1966

ＮｾＢＢｾ

oti-';;Y': .

Sponsored by the Subcommittee on Snow and Ice, NRC Associate Committee on Geotechnical Research

With the papers and discussion presented at the Seminar on lee Formation on Lakes and Rivers, sponsored by the Canadian National Committee of the

Interna-tional Hydrologic Decade and held at Laval University, Quebec, 9November 1966

Technical Memorandum No. 92

PREFACE

The force exerted by ice is a factor that must be taken into consideration in the design of many structures in Canada. Although the problem has been with us for many years, there is still not available to engineers the information required to predict these forces with a satisfactory degree of confidence. During the past few years, considerable knowledge and experience has been accumulated concerning the properties of ice and the forces that it can exert. The Snow and Ice Subcom-mittee of the National Research Council's Associate ComSubcom-mittee on Geotechnical Research considered that it would be useful to bring this knowledge and experience together through the holding of a conference. The papers and discussion presented to the conference are contained in this proceedings.

The conference was held at Laval University immediately following a seminar on ice formation on lakes and rivers sponsored by the Canadian National Com-mittee for the International Hydrologic Decade. The Canadian National ComCom-mittee for the IHD kindly agreed to allow the Associate Committee on Geotechnical Research to include in this proceedings the three papers and associated discussion presented to the seminar. As a result, this Technical Memorandum is a useful summary of what is now known in Canada concerning ice pressures on structures and the characteristics of the ice causing the pressures. The Associate Committee is indeed grateful to Laval University for providing the excellent facilities and support so necessary for the success of the conference; and to the Canadian National Committee for the IHD for allowing the information presented at its seminar to be included in this proceedings.

The Associate Committee also wishes to express its appreciation to the authors of papers, discussors, and all others who participated in the conference; and to its Secretary, Mr. M. K. Ward, and the Secretary of the Snow and Ice Subcommittee,

Miss J. Butler, for their assistance to Messrs. Gold and Williams in the

prepara-tion of this Technical Memorandum.

Ottawa

C. B. Crawford, Chairman,

Associate Committee on Geotechnical Research

R.

F.

TABLE OF CONTENTS

Page

Ice Pressure on Structures - A Canadian Problem .... 1

Plastic Deformation of Fresh Water Ice 5

Elastic and Strength Properties of Fresh Water Ice

13

The Mechanical Properties of Sea Ice 25

A. S. Krausz L. W. Gold W. F. Weeks and A. Assur G. E. Frankenstein G. R. Kendall M. Drouin N. Y. Lavoie H. R. Peyton J. Nuttall and L. W. Gold M. C. van Wijk L. W. Gold R. C. Sommerville and G. E. Burns D. E. Nevel B. Michel P. Donnelly L. Herr and J. L. Dery Appendix I Appendix II

Strength of Ice Sheets .... . .

Meteorological Information Relevant to Ice Pressures

Static Ice Forces on Extended Structures .

Ice Effects on Structures In the Northumberland

Strait Crossing .

Sea Ice Forces ..

Model Study of Ice Pressures .

The Use of Photogrammetry for Measuring the

Movement of Ice Covers ..

Observations on the Movement of Ice at a Bridge

Pier .

Damage to a Winnipeg Reservoir Due to Ice .

Lifting Forces Exerted by Ice on Structures .

Thrust Exerted By An Unconsolidated Ice Cover

on a Boom .

An Outline of the Design and Operation of the

Montreal Ice Control Structure ..

General Discussions .

On the Expansion of a Floating Ice Sheet With

Temperature Change - by R. J. Kennedy ..

Montreal Ice Control Structure Failure of Four Stop-Logs During Winter 1966-67 - by P. Donnelly

79 89 95 109 117 125

131

Page

Appendix III Statements of Research Problems Pertaining to Ice

Pressures:

Introduction

191

(A) C. Neill - Bridge Piers and Similar

Isolated Structures

191

(B) M. Drouin - Forces Exerted by Static Ice

Covers on Extended

Structures

194

(C) B. Michel - Ice Formation and Break-Up

in Rivers

196

(D) L. W. Gold - The Forces That Ice Can

Exert on Structures

199

Appendix IV Papers Presented to Seminar on Ice Formation:

(A) G. P. Williams - Freeze-Up and Break-Up

of Fresh-Water Lakes ....

203

(B) C. E. Deslauriers - Ice Break-Up In Rivers

217

ICE PRESSURES ON STRUCTURES: A CANADIAN PROBLEM

by

R. F. LEGGET AND L. W. GOLD

Division of Building Research, National Research Council, Ottawa

The pressure of ice is one of the "forces of nature" that engineers and builders in Canada have had to resist with their shore-line or mid-stream structures ever since the first small wharf and the first bridge pier were constructed in the early days of the development of this country.

It was a factor of importance as soon as dams

came to be constructed. In early records one can read of "cribs being taken out by the ice" so that the effect of ice pressure has been well recognized from the earliest days of Canadian building.

Robert Stephenson made judicious local in-quiries in Montreal when he came to design the piers of the Victoria Bridge, now a century ago. His solid masonry piers stand today, just as they were built (apart from some grouting of the masonry), tribute indeed to the skill of this great engineer. Many other early structures give similar silent testimony to sound construction, although their conservative design probably more than ensured their safety against ice pressure, the magnitude of which could then only be guessed. There has been an increasing demand in recent years for information on the forces that ice can exert against structures. This demand has not arisen because of failures, but rather because of the lack of information. At least two bridge projects, known to the authors, are believed to have been abandoned in favour of embankments because, so it was said, the effect of ice pressure against the piers could not be calculated with

certainty. Ithas often been suggested that because

of lack of information design loads chosen have been excessive, but there is little factual informa-tion to justify these claims other than satisfactory performance of structures. With the current in-crease in the number of structures that are being constructed at locations subject to the action of ice, the lack of accurate information on the magnitude of the forces that can be exerted by ice

is proving to be a serious handicap.Ithas resulted

not only in a possibly unnecessary increase in cost but also, in some instances, in the rejection of what might have been suitable and more economical designs. In cases where lower than usual design values have been chosen, there has always been the disturbing thought that the values chosen might be too low.

The ice pressure problem has received sound attention in recent years. In 1947, the American Society of Civil Engineers formed a subcom-mittee under Dr. R. L. Hearn to consider the current state of knowledge on predicting forces that ice can exert against dams. Inquiries by the subcommittee indicated a dearth of factual data on the subject. The work of this committee cul-minated in 1950 with a symposium to which were presented three papers by experts in the field. The Proceedings of this Symposium (1954) with the discussion, and an earlier paper by Rose (1947), provide the basis for present

esti-mates of ice pressures against dams. It is of

interest to quote the opinion of the committee given in the final paragraph of the Foreword to the Symposium:

"It will be several years before enough information is obtained from field observations in particular, to make possible a further advance toward a complete solution of the problem. The Subcommittee, therefore, recommends that the interested organ-' izations be encouraged to develop their work in connection with ice pressures against dams, and be urged to maintain mutual liaison in this field."

In 1964, the Snow and Ice Subcommittee

of the Associate Committee on Geotechnical

Research of the National Research Council

decided to give attention to the problem. As a first step, a meeting was held in that year to review the current state of knowledge. Those present were invited to present to the Subcom-mittee their experience and opinion concerning

the need for information on the forces that ice

could exert against structures. This meeting

brought out clearly the lack of knowledge that still exists on the subject and, therefore, the unsatisfactory state of current practice in the design of structures subject to the action of ice. As a result of the meeting the Subcommittee pre-pared statements of the research that should be encouraged in order to establish the information required for estimating the maximum force that ice can exert on structures, These statements are

presented in Appendix III of these Proceedings.

A study of ice formations and their effect on bridges was carried out by McClure and Herman (1965) for the Montana State Highway Com-mission and the Bureau of Public Roads of the

United States Department of Commerce. In the

introduction to their report McClure and Herman quote the criteria specified by the American State Highway Officials for the design of bridges subject to the action of ice, namely: "Pressures of ice on piers shall be calculated at 400 psi. The thickness of the ice and the height at which it applies shall be determined by investigation at the site of the structure." They then go on to state "Such a requirement does nothing more than to make the engineer aware of the fact that there might be an ice load which should be included in the

design. It does not even indicate whether or not

the pressure should be applied in both direc-tions on the pier. The best that a bridge engineer can do, using such a criteria and other presently available knowledge, is to make an educated guess based on past experience. With the increas-ing cost of bridge construction and the increase in the number of bridges being built, it seemed that a better understanding of the nature of ice formation and the forces exerted on bridges by the ice was necessary." After a careful review of available knowledge these authors state, in their

concluding summary, that "It is not possible at

this time, with the present available information, to develop rational design criteria for determining of forces of ice on bridges."

At first glance, it may seem surprising that information that is required concerning ice pres-sures has not been accumulated, although the problem has been with us for many years. There

are reasons for this. It may be instructive to

con-sider why this area of engineering practice has not developed to the level of preeision desired by the profession.

The force that ice will exert against a structure is determined by four factors. These are: the characteristics of the ice cover and properties of the ice; the relative motion between the ice and the structure; the response of ice to stress; and the response of the structure to an imposed load. The latter factor is determined primarily by the design, but the engineer has little control over the first three, and it is about these that additional knowledge is required.

Ice covers are a product of the weather. Their characteristics, such as thickness, quality of the ice and type of grain structure, are subject to a variability that is typical of weather. Ice is normally at a temperature very close to that at which it melts. Because of this, some of its

properties, such as elasticity, plasticity and

strength, are sensitive to temperature. These

properties depend also on the quality of the ice, the type of grain structure and the stress distribu-tion. The naturally varying characteristics of ice covers and properties of ice as a material intro-duce into design calculations uncertainties that can only be handled through the use of statistics and the theory of probability. For a particular site, several years of observations on the char-acteristics of the ice cover and the weather are usually necessary to establish the statistical in-formation required. Because of the size of the country and limitations imposed by time and human resources, these observations are usually not available, and so the engineer must make do with the more general information that is already available.

A force is developed at a structure when the ice cover moves or attempts to move relative to it. This motion may be due, for example, to changes in temperature, changes in water level, or the drag forces induced by water currents or wind. The movements of the cover will be determined not only by these capricious events, but also by the degree of restraint imposed by the shoreline and by the structure. A large structure, such as a dam, can have a considerable influence on ice movement, whereas a relatively small structure such as a bridge pier, may not. Few field observa-tions have been made that provide the informa-tion necessary for predicting the moinforma-tion that can be expected about a structure under given field conditions.

Another important aspect of the ice pressure problem about which little is known is the

ques-tion, "What determines the maximum load that will be exerted?" Is it the strength properties of ice for situations involving compression or ten-sion? Is it buckling of the cover, plastic flow, or the properties of the shoreline? This information is required by engineers to estimate the maximum force that can be expected under given conditions. When an ice cover breaks up, floes of variable size are formed. These floes move with a speed that is determined primarily by the water cur-rents for inland situations, but they may be in-fluenced also by the speed and direction of the wind, particularly on large bodies of water. Floes may override each other and so create floes that are considerably thicker than the original thick-ness of the cover. Collision of floes may result in the formation of large ridges. These unusual ice conditions, about which very little information is available, can be responsible for the most severe load that a structure is required to with-stand. Information on such conditions can only be accumulated by making the appropriate field observations whenever the opportunity arises.

Because of the lack of the information required for estimating ice pressures, the time necessary to

collect this information and the number of

variables involved, the direct measurement of forces in the field will probably provide the most immediate method of obtaining the design criteria required by engineers. Such measurements need, however, structures sufficiently strong to with-stand ice forces, and rather sophisticated instru-mentation. Observations must be carried out over a number of years, furthermore, to establish the correlation between relevant factors and to pro-vide the statistical basis required for the predic-tion of extreme values. There have been few possibilities for this approach in the past, but several interesting opportunities may be available in the future.

Following the meeting in 1964, the Snow and

Ice Subcommittee decided that sufficient

inforrna-tion had accumulated since the 1950 Conference sponsored by the American Society of Civil Engineers to justify holding a two-day

con-ference on ice pressures. It was considered that

a conference on ice pressures would not be com-plete without consideration being given also to

ice formation on lakes and rivers. The Canadian National Committee for the International Hydro-logic Decade, recognizing the role that the forma-tion of ice covers plays in the hydrologic cycle, had decided to hold a "Workshop" on this

subject. It was possible to bring these two

meet-ings together.

It is a pleasure to acknowledge the generosity of the I.H.D. Canadian National Committee in

allowing the papers and written discussion

presented at the Workshop to be included in the Proceedings of the Conference on Ice Pres-sures. The Proceedings now provide a useful summary of what is now known in Canada about pressures due to icc, about the ice covers respon-sible for these pressures and the conditions to

which they are subject. It should also provide a

useful starting point and give direction to those field and laboratory studies still required to pro-vide the information on ice pressures necessary for design purposes.

The problem is a complex one, a fact which the discussions at the seminar and conference clearly demonstrated. But it is important and its solution is equally urgent in view of all the new dam, bridge and wharf construction that can even now be predicted for the years immediately

ahead. It is peculiarly a Canadian problem so

that it was appropriate that the meetings were held in the ancient city of Quebec, site of so much of Canadian history and also of some of the very earliest experiments on the strength of ice carried out in North America.

REFERENCES

Ice Pressures Against Dams-A Symposium.

(1954). Trans. A. Soc. Civil Eng., 119,

p. 1-42.

McClure, G. S. and G. J. Herman (1965). A

Study of Ice Formations and their Effect on Bridges. Highway Research Report, Mon-tana State Highway Commission in Coopera-tion with United States Dept. of Commerce, Bureau of Public Roads.

Rose, E. (1947). Thrust Exerted by Expanding

Ice Sheet. Trans. A. Soc. Civil Eng. 112,

dam, bridge and wharf construction that can even now be predicted for the years immediately

ahead. It is peculiarly a Canadian problem so

that it was appropriate that the meetings were held in the ancient city of Quebec, site of so much of Canadian history and also of some of the very earliest experiments on the strength of ice carried out in North America.

REFERENCES

Ice Pressures Against Dams-A Symposium.

(1954). Trans. A. Soc. Civil Eng., 119,

p.

McClure, G. S. and G. J. Herman (1965). A Study of Ice Formations and their Effect on Bridges. Highway Research Report, Mon-tana State Highway Commission in Coopera-tion with United States Dept. of Commerce, Bureau of Public Roads.

Rose, E. (1947). Thrust Exerted by Expanding

Ice Sheet. Trans. A. Soc. Civil Eng. 112,

PLASTIC DEFORMATION OF FRESH·WATER ICE

by

A. S. KRAUSZ

Snow and lee Section, Division of Building Research, National Research Council, Ottawa

ABSTRACT

In this review the results of laboratory experi-ments on the plastic deformation of ice are presented from the engineering point of view. A discussion is also presented on the creep be-haviour of columnar-grained and snow ice in tension, compression, bending and shear empha-sizing the effect of the crystal structure. The

relationship between strain rate f, creep time,

stress a and temperature are represented by the

simple expression

where the factors A and n are functions of the creep time and temperature.

To illustrate the significance of the deforma-tion history on the creep properties of ice, in-formation obtained in repeated loading tests is presented. The effect of variable stress as well as non-uniform and complex stress fields on the plastic deformation process is briefly reviewed.

Laboratory measurements on ice are usually made under the simplest possible test conditions. Most of the tests are carried out under uniaxial load conditions with small stresses, and the meas-urements are made in the large strain region. Conditions encountered in engineering problems are usually just the opposite. The load level of interest is usually high and the strains relatively small. Complex stress fields are common and, with continued deformation, the load acting on the ice changes as contact with different obstacles and with the shoreline changes. The dynamic effects associated with the changing stress field are also of importance as the deformation of ice is sensitive to the rate of change of the load. The temperature can change within a short period of time producing a significant effect on the

RESUME

L'auteur presente une recapitulation des

resul-tats obtenus

a

labora-toire sur la deformation plastique de la glace, du point de vue de l'ingenieur. II etudie egalement le comportement de fluage de la glace colonnaire et de la glace de neve en traction, compression, flexion et cisaillement, specialement au point de vue de la structure cristalline. Les relations entre

vitesse de deformation

i ,

con-trainte et temperature sont representes par l'equa-tion simple

dans laquelle les facteurs A et n sont fonctions

de la duree du fluage et de la temperature.

L'auteur presente des donnees obtenues au cours d'essais repetes de chargernent pour souli-gner l'importance de la deformation passee sur les caracteristiques de fluage de la glace. Il reca-pitule brievernent l'effet d'une contrainte variable et d'un champ non uniforme et complexe de contraintes sur le phenornene de deformation plastique.

elastic and plastic properties of ice. In con-sequence, the information that is available from laboratory tests must be carefully scrutinized with consideration given to the stress distribution, load rate, extent of deformation, type and crystal structure of ice under consideration, thickness, previous deformation history, temperature level, and temperature variation. Some of the available information on these aspects of plastic deforma-tion of ice will be discussed in this review.

STRUCTURAL PROPERTIES OF ICE Ice is a crystalline material and its plastic behaviour is directly related to the crystal struc-ture. Natural fresh-water ice, when formed uni-directionally and free of snow, usually consists

of long, pencil-like grains. The cross-sectional area of a grain perpendicular to its long direc-tion can vary from a fracdirec-tion of a square inch to 20 sq. in. or more. Each grain is one crystal in which the oxygen and hydrogen atoms are arranged in a regular geometrical pattern. This pattern is built up from simple hexagonal prism units, one of which is shown in Figure 1. The oxygen atoms occupy the corners of the hexa-gonal prisms forming the crystal lattice. The plane perpendicular to the axis of hexagonal symmetry, i.e., the C axis, is called the basal plane and plays an important role in the plastic deformation of ice.

C AXIS

BASAL PLANE.

Fig. 1. A Simplified Model of a Hexagonal Prism Unit. The Circles Represent the Oxygen Atoms

tion of time t was measured during the test

for different temperatures, T, and stress levels a,

and the results are presented as

f=f(t,T,a)

or in terms of the strain rate

df=f=(t,T,a) dt

Creep tests have beer. carried out on columnar-grained ice in compression (Gold, 1965) and tension (Krausz, to be published) at 15°F in the

stress range of a

=

=

The orientation of the grains and the basal planes with respect to the compression or tensile axis are shown in Figure 3. The ice from which the specimens were cut was formed from deaerated tap water. Growth was in the direction perpen-dicular to the water surface. The grain size was

between

i-

Fig. 3. A Columnar-Grained Ice Plate. The Solid Lines Indicate the Grains. The Shaded Hexagons Indicate the Orientation of the Basal Planes in Some of the Grains

The tests were continued to about 1 per cent

strain. It was observed in these tests that some

of the specimens deformed in the manner shown in Figure 4 (a) and others as illustrated schema-tically in Figure 4 (b). This result is important

Itis now a well-substantiated fact that

crystal-line materials, including ice, deform plastically by slip on preferred crystallographic planes. Slip in ice occurs most easily on the basal plane in the manner illustrated in Figure 2. Experimental evidence indicates that a considerably higher shear stress is required to induce slip on non-basal planes. This is of great significance in the understanding of the plastic behaviour of

poly-crystalline ice. In each grain there is only one

system of slip planes (the basal planes) and the deformation will depend on the shear stress component in this plane rather than on the maximum shear stress.

ｾ

ｾ ｣ ｾ ｳ

8---L.-.

ＭＭﾱＭ｟ｾ｟｣

----l.-_. _

rr:

Fig. 2. The Figure Illustrates the Process of Plastic Deformation Under the Effect of the Shear Stress T

TI ME

(a)

TI ME lbl

CREEP TESTS

Most of the deformation studies on ice have been carried out in creep, i.e., under constant

load or constant stress. The strain c as a

func-Fig. 4. The Two Types of Behaviour Observed in the Creep Tests on Columnar-Grained Ice Specimens

because it indicates that the plastic behaviour of previously undeformed ice can vary within a

Fig. 5. The Variation of the Constants A and n in Eq. (l) During Creep (Gold, 1965)

where the value of A and n as a function of

time is shown in Figure 5 for a in psi. The

(3)

'R

f

R

ＨｾＩｭｒ

R 14·2

rn_R

The specimens were unloaded and allowed to

recover at 15 OF for periods of up to 3 days and were then reloaded to the same stress level. All of the creep curves obtained after recovery were of the type shown in Figure 4 (b). In

compres-sion the creep strain rate fRon reloading was

where the value of Band m as a function of time t is given in Figure 6. The tests were usually carried out for 5 to 6 hours.

The relationships BR (t ) and mR (t ) are shown

in Figure 7. (1) 300 100

."

wide range. The average creep behaviour in com-pression could be represented by the relationship (Gold, 1965)

(

a

)n(l)

-14·2

alternative expression giving the strain rate in terms of time and stress is also of interest

rn_R ( a

)m(l)

Fig. 7. The Variation of the Constants BR and mR in Eq .. (3) in Reloading (Gold, 1965)

m

."

Fig. 6. The Variation of the Constants Band m in Eq. (2) During Creep (Gold, 1965)

It is now well established that, on reloading, previously deformed ice specimens behave in a harder, stronger manner than in first loading. The first loading results showed considerable scatter but good reproductibility has been observed in repeated loading tests. It can be concluded from these results that the deformation history of ice covers has a significant effect on how the cover responds to an applied load.

Four-point bending tests in creep (Figure 8) were carried out on columnar-grained ice speci-mens (Krausz, 1963). In these tests the long axis of the grains was parallel to the direction of the applied load F as indicated in the figure.

where I. is the distance between the supports, x is the distance from the middle of the beam meas-ured in inches, A and a, given in Table I, are constants for a given beam thickness. All tests were carried out with a constant load of 33.3 lb at 15°F.

The creep curves were of the types shown in Figures 4 (a) and (b). The deflection 8 of the beams was measured as a function of time, beam size and load. The deflected shape of the beams after 5 hours of creep time could be described by the expression

0= A X 10-3 [(O.5l)a - x "] in.

Fig. 8. Four-Point Bending Test in Creep

These investigations also showed that the stress distribution changes with time. There is an initial, short-term, elastic deformation with a high maxi-mum stress which decreases with time as the deformation gradually becomes plastic. A similar behaviour can be expected for an ice cover subject to a given bending moment. Because of the elastic and creep properties of ice, the stress is the highest at the very early stage of deforma-tion. The subsequent plastic deflection for a given load will be strongly dependent on the thickness of the cover.

Substituting this relationship into Eq. (1) the strain is expressed as a function of h

( oxh- 3

indicating that the deflection is strongly dependent on the beam thickness as was indeed found.

Butkovich and Landauer (1960) carried out compression tests on granular and columnar-grained ice specimens at very low values of the stress. They found that after a short initial period the strain was a linear function of time. The strain rate ; measured in these tests could be

rep-resented as a function of stress (J by an

expres-sion of the following type

C₁(J + C 2a 3

-x

F

F

ｉｾ

!

Inspection of Table I shows that the creep behaviour is very strongly influenced by the beam thickness. The 1.0-in.-thick beams had 100 per cent greater deflection after 2t hours of creep than the 1.055-in.-thick beam. Beams 0.90 in.

thick failed under the applied load within t hour

while the 1.00-in.-thick beam supported the same load for 7 hours without developing any cracks. This behaviour was explained by Gold (1965)

as follows. It can be shown that the stress is

approximately inversely proportional to the

square of the beam thickness h

in the temperature range of 30°F to - 2 OF up to

a stress level of a = 3 psi.

Creep tests in shear were also conducted by Butkovich and Landauer (1959). Both columnar-grained and granular ice specimens were tested.

The grain diameter was small, less than t in. in

both cases. The tests were carried out in the shear

stress range of T

=

=

a temperature of about 23 oF. The creep shear

strain y was observed to depend on the time

according to

where t is the time and m to one per cent.

Butkovich and Landauer pointed out, however, that this result is only a rough approximation and should, therefore, be used with caution. A

typical creep curve is shown in Figure 9. Inthese

tests the strain rate decreased in the first stage and, after going through a minimum, increased in the final stage. The stress dependence of the

minimum shear strain rate

Y

1.0

TABLE II

100 '0

The creep behaviour of snow ice in tension was investigated by Jellinek and Brill (1956). The tests were carried out in the stress range of

a

=

=

tempera-tures of 23°F, 14°F, and 5°F. The empirical relation

Fig. 10. The Creep Behaviour of Granular-Grained Ice (Glen, 1955) PI/I MARY CREEP 0.100 ) i ... ｓｅｃｏｾｄａｒｙ ｾｔｅｒｔｉａｒｙ : CHO.P ! cettr ｾ 0.050

tion of the uncertainty that is still present in the interpretation of creep test results.

was obtained with n = 1 to 1.4, m

=

0.53. The stress was measured in 10-3 psi and

the time in minutes. A comparison of these results with that obtained by Glen shows signi-ficant discrepancies in the constants of the strain-time-stress relationship. Jellinek and Brill point out that these differences are due to several causes: the snow-water compositions of the speci-mens were not the same and the strain and stress ranges were also different. All these factors should be carefully weighed when the creep behaviour of ice covers has to be predicted.

Tensile and compression creep tests were

carried out by Steinemann (1958) on snow ice. The creep curves were similar to that obtained by Glen and consisted of the usual primary, sec-ondary, and tertiary stages as shown in Figure 10.

f = aant m + ba

TI ME. HOlJRS (3)

Fig. 9. A Typical Creep Curve in Shear (Butkovich and Landauer, 1959)

10 2 103 IOd II M:, MIN

The creep behaviour of granular-grained ice has been investigated by Glen (1955). The speci-mens were prepared by mixing hoar frost with de aerated water. The ice was only slightly cloudy and its density was approximately the same as that of clear ice.

The tests were carried out in compression in

the stress range of a = 10 psi to 135 psi. A

typical creep curve is shown in Figure 10. In all of these tests the strain rate decreased at first and was followed by a steady state (constant strain rate) period. At the high stress level an accelerating strain rate stage was also observed.

The minimum strain rate _min was observed

to satisfy the equation

where T is the shear stress in lba/sq in. and

the value of the constants were: n '" 3, k '" 2.85

x 10 -12/sec. Because of the large scatter in

the test results, the above expression can be considered only as an approximation.

c;10

The constants k and n are given in Table II for stresses in psi.

where n is given in Figure 11 and E in Figure 12. Although it is clear that the complexity of the behaviour and the large scatter in the experi-mental results require great care in calculating creep strain, Eq. (5) does allow some estimate to be made of the effect of the temperature level. Equation (5) was obtained for constant tempera-ture and because of transient effects it is not valid for variable temperature. When using these results for determining the deformation of ice I I Temperature, I k x 109 , n OF hours - 1 I I I 31.6 4.25 I 3.17 29.5 0.57 3.17 I

It was observed that for small strains near to the melting point (31.96°F) the creep curves could also be expressed by the equation

f_/3t1/3+kt (4)

where k ex0 4• 2• Equations (3) and (4) were

determined by different methods and the dis-agreement in the stress exponent is a good

indica-The strain rate f could be expressed

function of the stress a and temperature T

by the following equation

• n(a T) [ E (a, T) ]

f exa . exp -

covers, it should be realized that ice in natural environment is subjected to temperature changes large enough to invalidate the calculations.

While all of the creep calculations are valid primarily for a uniform, uniaxial stress field it has been demonstrated for four-point bending tests that when the creep data is properly applied, correct predictions can be obtained for nonuni-form stress distribution. Serious difficulty arises, however, when the effect of a variable or complex stress field has to be considered.

The load acting on the ice cover usually varies

with time. It is well known that ice behaves

elastically under the effect of a load of short duration and begins to deform plastically only 5 to 15 seconds after the application of the load. The plastic deformation process is also strongly dependent on the stress change. Experiments in which the stress was varied are therefore of interest.

VARIABLE STRESS TESTS

300 100 100 ｾｉｉｆ 00LＭＭｾＭＭＭＧＭＭＭＭＭＧ 10ｉ｟ＭＭＺＺＺＺ］］］］］］ＺＺＺＺＺ［ＺＺＺ］ＺＺｾ STRESS, P51

Fig. 11. The Stress Exponent n in Eq. (5) (Steinemann,

1958)

Fig. 12. The Exponent E in Eq. (5) (Steinernann,

1958)

f =

A

ｾｅＩ

In this section a number of creep equations obtained by several investigators were reviewed. Despite the apparent variety all of these equations can be expressed by the single formal relationship

Glen (1955) carried out this type of test on snow ice in compression at 29.5°F. It was found that after the load was increased the deforma-tion continued with a transient, decreasing strain rate, similar to that observed at the beginning of the test. When the load was decreased an instan-taneous strain drop occurred. This was followed by an increasing strain rate in some of the tests and by a decreasing transient stage in other cases. The behaviour in the period immediately follow-ing the load drop was complex and for a detailed discussion Glen, 1965 should be consulted. In all cases the transient stage was followed by a creep behaviour similar to that observed in the uninterrupted tests.

A few measurements have been made under the conditions which are usually called "tensile" or "compression" tests. These measurements are carried out with a testing machine under condi-tions of constant cross-head speed, and are often referred to as constant strain rate tests. Theore-tical considerations show that the behaviour of materials in creep and constant strain rate tests is controlled by the same deformation mechanism. This fact allows a close correlation to be made between the two kinds of tests. The creep curve of the columnar-grained ice (Figure 13 (a)) indicates that the stress-strain curve should be of the type shown in Figure 13 (b). Preliminary tests by Krausz (to be published) in tension and by Gold (1967) in compression substantiated this prediction for fresh-water ice. The creep

100 STRESS a,PS I 100

where A, n, c, and E can be functions of the

stress a, strain €, temperature T, and time t.

In general it is not possible to express A, n, c, and E by one simple function covering the whole spectrum of engineering interest.

The creep behaviour of ice can be estimated for uniaxial stress conditions if the values of A, n, c, and E are known. To determine these values, it is first necessary to establish the crystal

structure of the ice (i.e., whether it is

columnar-grained or granular). The values can then be estimated for the stress condition and temperature desired from the papers referred to in this review. As mentioned earlier, it may be important to distinguish between "first load" and "reload" conditions, particularly for columnar-grained ice.

V'! V'! l.LJ (b) e:::: l -V'!

COMPLEX STRESS FIELD

Andersland (1966). While the qualitative cor-relation seems to be quite satisfactory, numerical information on the behaviour of ice in constant strain rate tests is scarce.

Very few experiments have been carried out on the effect of a three-dimensional stress field on the plastic deformation of ice. Tamman and Salge (1928) found that when uniaxial compres-sion was applied perpendicular to the basal plane a smaller shear stress was necessary to deform the specimen. A similar observation was reported by Steinemann (1958). According to his results the simultaneous action of uniaxial pressure along the axis of a torsion specimen increases the shear velocity of snow ice.

Hydrostatic pressure of up to 90 atmosphere superimposed on torsion does not appear to influence the shear velocity of snow ice (Steine-mann, 1958). Similar results were obtained by Rigsby (1957) with pressures up to 300

atmo-sphere when corrections were made for the

change in the melting point. Recent experiments (Halbrook, 1962) on snow ice indicate that con-fining pressure may increase the steady state creep rate in compression. At the present time the effect of the three-dimensional stress field on the plastic deformation of ice is not known well enough and much further work is needed.

TERTIARY

i

I

(

I

I

I

I

I

Fig. 13. The Figure Illustrates the Relationship Between Creep Test (a) and Constant Strain Rate Test (b) for

Granular-Grained Ice

Fig. 14. The Figure Illustrates the Relationship Between Creep Test (a) and Constant Strain Rate Test (b) for

Granular-Grained Ice.

CONCLUSIONS

These variables have been studied separately in laboratory experiments to facilitate the under-standing of the deformation process and signi-ficant progress has been made over the last decade. It is now possible to estimate the plastic deformation of ice due to a uniaxial constant

In most engineering situations the plastic

deformation of ice occurs under the effect of a high, continuously varying stress field. This stress field is sometimes uniaxial but most often it is complex. The ice can vary in structure and quality from air-free, transparent, columnar-grained ice to

porous, granular, snow ice. The plastic deforma-tion may occur at significantly different and changing temperature levels depending on the weather conditions and on the length of time over which the load is applied. All of these factors have a significant influence on the plastic behaviour and have to be considered when pre-dicting or calculating the deformation of ice covers.

STRAIN Ib I TI ME

(0)

curve of snow ice (Figure 14 (a)) indicates that the constant strain rate curve should be similar to that shown in Figure 14 (b). This type of

load. Very little is known, however, about the behaviour of ice when either the stress or tem-perature or both vary during deformation. The effect of three-dimensional stress fields has not yet been investigated in sufficient detail either. The absence of this essential information clearly indicates the need for additional research on the deformation behaviour of ice.

ACKNOWLEDGMENT

The author is indebted to Mr. L. W. Gold for his comments and for the discussions which contributed greatly to this review.

REFERENCES

Andersland, O. B. and H. B. Dillon (1966). Deformation Rates of Polycrystalline Ice. Presented at the International Conference on Physics of Snow and Ice, Hokkaido Uni-versity, Japan.

Butkovich, T. R. and J. K. Landauer (1959). The Flow Law for Ice. Snow, Ice and

Permafrost Res. Establishment, Research

Report No. 56.

( 1960). Creep of Ice at Low Stresses. Snow, Ice and Permafrost Res. Establish-ment, Research Report No. 72.

Glen, J. W. (1955). The Creep of Polycrystalline

Ice. Proceedings, Royal Society, Ser. A, Vol. 228, p. 519-538.

Gold, L. W. ( 1965 ) . The Initial Creep of

Columnar-Grained Ice. Can. J. Phys., Vol. 43, p. 1414.

( 1967) . The Elastic and Strength Properties of Fresh-Water Ice. Proc. Conf. Ice Pressures, against Structures, N.R.C. Associate Committee on Geotechnical

Re-search, Tech. Memo. No. 92, p. 13,

Ottawa.

Halbrook, T. R. (1962). Mechanical Properties

of Ice. M.Sc. Thesis, Michigan State

Uni-versity.

Jellinek, H. H. G. and R. Brill. (1956). Visco-elastic Properties of Ice. J. Appl. Phys., Vol. 27, No. 10, p. 1198.

Krausz, A. S. (1963). The Creep of Ice in Bending. Can. J. Phys., Vol. 41, No.1, p. 167.

The Mechanism of Initial Plastic De-formation of Ice. To be published.

- - - - The Creep of Ice in Tension. To be published.

Rigsby, G. P. (1957). Effect of Hydrostatic Pressure on the Velocity of Shear Deforma-tion of Single Crystals of Ice. Snow, Ice

and Permafrost Research Establishment,

Research Report No. 32.

Steinemann, S. (1958). Experimentelle Unter-suchungen zur Plastizitat von Eis. Beitrage zur Geologischen Karte der Schweiz, Geo-technische Series Hydrologie, No. 10.

Tamman, G. and W. Salge. (1928). Der Einflus

des Druckes auf die Reibung beim Gleiten

langs der Gleitebenen von Kristallen. Neues

Jb. Min. Geol. Palaont, Beil., Vol. 57A, p. 117.

ELASTIC AND STRENGTH PROPERTIES OF FRESH WATER ICE

by

L. W. GOLD

Division of Building Research, National Research Council, Ottawa

ABSTRACT

Information on the elastic and strength proper-ties of ice is reviewed. Representative" values for the ultimate strength of ice in shear, tension and compression are presented. The failure behaviour of ice during creep and constant load rate tests, and the internal cracking activity that occurs

during such tests, are discussed. It is suggested

that the failure behaviour of ice in uniaxial tests can be explained on the basis of the behaviour of imperfections associated with plastic

deforma-tion. It is pointed out that caution should be

used when applying the results of uniaxial tests to biaxial and triaxial conditions encountered under field conditions, because of the role that the shear stress plays in the deformation and failure behaviour of ice.

Ice normally exists at a temperature within 50°F of that at which it melts. During deforma-tion and failure it exhibits a behaviour that is characteristic of materials in this thermal state. Lack of knowledge of the behaviour of ice when stressed, and of the factors upon which this behaviour depends, has contributed to the diffi-culties encountered by engineers when predicting the forces exerted by ice on structures. Con-siderable information has been published on the elastic and strength properties of ice during the

past few years. It is the purpose of this paper to

review some of this information with particular reference to the ice pressure problem.

As pointed out in the paper by Krausz (1967), ice crystals have a hexagonal symmetry with respect to the arrangement of the water molecules. Plastic deformation of the crystal occurs pri-marily by the movement of imperfections, i.e.,

RESUME

L'auteur recapitule les donnees qu'on possede sur les caracteristiques d'elasticite et de resistance de la glace d'eau douce, et il donne des valeurs-types pour la resistance de rupture en cisaille-ment, traction et compression. 11 etudie de quelle Iacon se produit la rupture de l'cchantillon de glace au cours des essais de fluage et des essais

a

pheno-menes de fissuration interne qui se produisent au cours de ces essais. 11 propose une explication de la rupture de la glace dans les essais de resis-tance unidimensionnels, basee sur le comporte-ment des imperfections de structure associees avec la deformation plastique. L'auteur souligne qu'il ne faut appliquer qu'avec prudence les re-sultats des essais unidimensionnels aux condi-tions reelles d'un champ bi ou triaxial de con-traintes en raison du role joue par les concon-traintes de cisaillement dans la deformation et la rupture de la glace.

dislocations, along the basal plane, the plane

perpendicular to the axis of symmetry. If the

basal planes of individual crystals are parallel or perpendicular to the principal stresses, that is if there is no shear stress acting on them, the imperfections in the plane will not move and the response of the crystal to stress is nearly

elastic. If there is a shear stress acting on the

planes, the imperfections will move and the crystal can undergo plastic deformation. For polycrystalline ice, the orientation of the basal plane changes from grain to grain. When a stress is applied, the degree to which the response of each grain is elastic or plastic will vary, depending on its orientation with respect to the stress and the time over which the stress is applied.

When a polycrystalline material undergoes de-formation, individual grains must conform with it.

This may require that the grains deform plas-tically. The sudden change in crystallographic orientation that occurs at grain boundaries can create a barrier to the movement of the

imper-fections associated with plastic deformation.

Constraints imposed in this way by grains on the change of shape of neighbouring grains cause nonuniform internal stresses to develop and make it more difficult for grains to conform with the deformation. The magnitude of the stresses devel-oped depends on the number of imperfections blocked by barriers and the shear stress acting on them. Similar stress concentrations may be established at the intersection of grains due to the tendency for grains to move relative to their neighbours because of variations in their response to the stress. The nonuniform internal stresses that are developed can become great enough to initiate new modes of deformation, ineluding cracks. Tn this way, deformation modifies the structures and can weaken it to the point where it yields or fractures.

Imperfections responsible for plastic flow move at a speed that depends on the temperature and the shear stress acting on them. If the stress is applied and released in a sufficiently short time as, for example, during the passage of a sound wave, the imperfections have little opportunity to move, and the deformation response is primarily elastic. As the time over which the load is applied is increased, there is greater opportunity for imperfections to move and contribute to the deformation. For periods of loading less than about 10 seconds, and depending on the tempera-ture, the deformation of ice is almost entirely recoverable and can be considered elastic. For periods greater than about 10 seconds, some of the deformation due to the movement of imper-fections will be irrecoverable, that is, the ice

will undergo plastic deformation. Thus both

orientation of grains and duration of loading tnfluence the degree to which their response to load is elastic or plastic, and affect the magnitude of the nonuniform internal stresses that develop. This behaviour has a significant effect on the elastic and strength properties of polycrystalline ice.

ELASTIC MODULI

Estimates of the force that ice might exert against a structure are often based on elastic theory. For this reason, it is useful to have a

knowledge of the value of the elastic moduli for ice and the factors that influence them.

It appears that stress-induced movements of

imperfections in ice can contribute to the elastic strain. Each type of imperfection has associated with it a characteristic time that it takes to attain a new equilibrium position. Some imperfec-tions, such as dislocaimperfec-tions, move through the structure with a speed that depends on the stress. If the stress is applied for a sufficiently long period of time, imperfections may be incorporated into the structure at new equilibrium positions. Thus the strain associated with their motion be-comes irrecoverable. Because of this behaviour, the elastic moduli of ice depend upon the rate at which the stress changes and the length of time during which it is imposed.

Yamaji and Kuroiwa (1956), Kuroiwa

(1964), and N akaya (1959) have presented

in-formation on the frequency dependence of

Young's modulus of polycrystalline ice for fre-quencies greater than 100 cycles/sec. They also present information on the temperature depend-ence of the "dynamic" Young's modulus. For a frequency of 500 cycles/sec, Young's modulus

increases about 5 per cent between 32 OF and

- 40°F. For most engineering calculations, the dependence of the "dynamic" moduli on tem-perature and frequency can probably be ignored. Characteristic values of the "dynamic" Young's modulus, rigidity modulus and Poisson's ratio are

presented in Table 1. Nakaya (1959) gives

in-formation on the dependence of the "dynamic" Young's modulus on density.

Numerous observations have been made on

the "static" clastic moduli of columnar and

granular ice. See for example, Gold (1958), Voitkovskii (1960), Mantis (1951), and Dorsey (1940). Observations indicate that when the stress changes relatively slowly (e.g., load applied and removed in about 5 to 10 seconds) recover-able relative movement between grains contributes significantly to the elastic strain. Under these conditions of loading, the elastic moduli of ice are quite dependent on temperature. Gold (1958) observed for columnar-grain icc stressed per-pendicular to the long direction of the columns that Young's modulus increased from about 0.8 x

106 _{psi at 32 OF to within 10 per cent of the}

sonic value (about 1.2 x 106 _{psi) at - 40 of.}

Poisson's ratio was observed to decrease from

close to its theoretical maximum value at 32 OF

TABLE I

SONIC VALUES FOR YOUNG'S MODULUS, E; RIGIDITY MODULUS, G;

AND POISSON'S RATIO a ; FOR MULTIGRAIN ICE AT

A TEMPERATURE OF _5° C Source Young's Modulus E, psi x 106 Rigidity Modulus G, psi x 106 Poisson's Ratio, a

Boyle and Sproule (1931) Ewing, Craig and Thorne (1934) Jona and Scherrer (1952)

Gold (1958) Nakaya (1959) 1.30 1.33 1.35 1.44 1.26 *0.49 *0.50 0.55 0.365 0.33 *0.31

':' Calculated from the relationship between E, G and a for isotropic malerials.

CRUSHINGSIRENGTH,CLEAR

LHE ICE; ORIENTATION NOT SPECIFIED, T' -2D'F· BUTKOVICH 11955)

BOO 90'

Brown (1926), in his classic study of the strength properties of ice undertaken for the St. Lawrence Waterway Project, pointed out that the term "compression or crushing strength of ice is meaningless in itself ... The behaviour of ice in compression is different at the same rates of loading at different temperatures, and at dif-ferent rates of loading at the same temperature ... to obtain characteristic compression fractures the load must be applied rapidly, so that the ice has no opportunity to flow."

Jellinek (1958), in a study of the strength of the adhesive bond between granular ice and

various solids, obtained information on the

dependence of strength in tension on the rate of loading. His results for granular icc cylinders are shown in Figure 2, which shows that the failure

0.5 ｾ o 0,4", 0.' 20 30 TEMPERATURE, F

,-AVERAGE YOUNG'S MODULUS FOR SINGLE CRYSTAL LOA 0ｐｅｾ PEN 0 I CULAR TO CRYSTALLOGRAPHI C AXIS OF SYMMETRY

ＭＭＭＭＭｾＭＭＭＭＭＭＭＭｾ［ｾｾｾｾﾭ ｾｯｾ _ - - - - - YOUNG'S MODUlUS -40 -30 -20 0.' 0./ _ 1.4 ｾ l.l ｾ 1.0 ｾ 0.9

at -40°F. The results of this study are shown in Figure 1.

Fig. 1. Dependence of Young's Modulus and Poisson's Ratio on Temperature for Columnar Grain Ice, Gold

(1958).

A significant difference is often found between reported values of Young's modulus that have been measured at the same temperature. This is due, at least in part, to variation between tests in the rate of application and duration of the stress.

.. COMPRESSIVE YIELD STRESS; COLUMNAR GRAIN ICE, 100 STRESS PERPENDICULAR TO LONG DI RECIION Of

GRAINS T' -15f.

o0'--"---""---'-,---"--.--"'::-0ｾＱＱＺＭＺＧＺＱＴＭＺＭＺＱＶ --:,'::-.--:,,::---::,,:-:':,.-,:':-,--:,':-...:',,:-:':,,---'-,.-,:':-,--:,'--'."

RATEOFSTRfSSING, PSI/SEC

Fig. 2. Dependence of Strength or Yield Stress on Rate of Application of Stress.

TENSiLE STRENGTH GRANULAR ICE T'ｾＲＴｆ JElllN[1<. 11958) COMPRESSiVE YIELD ｓｔｒｾｓｓ［ SNOW I C[ T •ＭＲｾＧ F HALBROOK (1962 JOO 100 ::;:;100 ｾ 500 ｾ 400

'"

g

Strength is not a simple property to define. For some situations, it may designate the stress at which fracture occurs; for others, the condi-tion when the material is no longer able to sustain the applied stress but is in a state of yield. The particular type of failure behaviour that occurs depends in part on the properties of the material and, to a significant degree, on the stress condi-tions. This is particularly true for a material, such as ice, that responds plastically to a shear stress and whose behaviour in shear is greatly influenced by rate of loading, crystallographic orientation and grain structure.

stress increases to a maximum with increasing rate of loading and decreases thereafter to a relatively constant value. For the conditions of his test (temperature about 24°F), maximum strength was observed for a loading rate of about 3 psi/sec, and the strength was relatively constant for loading rates exceeding about 8 psi/sec.

On the basis of this work, Butkovich (1958) recommended that when measuring the strength of icc, the loading rate should be greater than 7 psi/sec. This has been adopted as standard for most tests since that time. There is evidence that for uniaxial compression strength tests, the loading rate must be greater than that recom-mended by Butkovich in order for the observed strength to be independent of the rate of loading. This is discussed later when consideration is given to the yield strength of ice. Brown adopted as standard in his tests a loading rate of about 20 psi/sec. Representative values of the strength of ice in tension, shear, and compression are given in Table II. These values were obtained from tests for which the rate of loading exceeded 7 psi/sec.

Brown (1926) observed that for columnar-grain ice failure behaviour in simple compression depended on orientation of the stress relative to

the long direction of the columns. If the load

was applied parallel to the long direction, a conical failure plane developed; if perpendicular, a tent-like failure occurred, with the crystals forming ridges parallel to the loaded faces. Similar behaviour has been reported by Bell

(1911). He observed that at 32of ice could

spread or flow without fracture for loads of 500

10 600 psi applied perpendicular to the long

direction of grains.

Butkovich (1954) found in a study of the strength of columnar-grain ice that the com-pressive strength perpendicular to the long direc-tion of the grains was about 75 per cent of that for the load applied parallel to that direction. The loading rate was about 70 psi/sec. Voitkov-skii (1960) also found the compressive strength parallel to the long direction of columnar grains usually greater than perpendicular to it. Wein-berg (1936) on the other hand, concluded after a statistical analysis of available strength observa-tions that there was no marked dependence on orientation. This question is perhaps academic since for most situations of interest to the engineer it is the strength for stress applied perpendicular to the long direction of the grains that is important.

Butkovich (1954) observed that the compres-sive, shear and tensile strengths increased with decreasing temperature. His results are shown in Figure 3 (a,b,c). The strength of columnar-grain ice was more strongly temperature dependent than snow ice, i.e., granular ice. Brown (1926) and Bell (1911) also report an increase in the crushing strength of ice with decreasing tempera-ture. Butkovich (1959) reports that the strength of coarse-grain ice in tension is lower than that of fine-grain icc, and in compression is greater

(Butkovich 1955).

Butkovich (1959) observed that the strength decreased linearly with density for densities close

TABLE II

REPRESENTATIVE VALVES OF STRENGTH OF ICE IN TENSION, SHEAR, AND COMPRESSION

Source Butkovich (1954) Temp., of 23°F -4°F 23°F 5°F 23°F -4°F Tension, psi *208 *229 Compression, psi *402 *622 408 493 Shear, psi t117 t202 *195 *277 142

₁

Clear Lake Ice

Natural Snow Ice

"Columnar-grain ice, stress applied perpendicular to the long direction of grains. tColumnar-grain ice, shear stress applied parallel to long direction of grains.

1- GRANULAR ICE

u-INITIAL CR[EP BEHAVIOUR, COlUMIriIAR-GRAIN ICE

TIME YIELD STRENGTH

to the maximum for ice. His results for the crushing strength give:

Ultimate strength

= ault = 1420 (y - 0.39) psi

where y is the specific gravity of ice.

Columnar-grain ice will usually have a density equal to the maximum for ice unless air bubbles are included during freezing. Granular ice, which

often has a whitish appearance due to the

presence of small air bubbles, has a more variable specific gravity but usually lies in the range of 0.80 to 0.917 (Ager 1962). Ice covers formed in rapidly flowing water by the consolidation of floes can be expected to have a highly variable density.

In summary, the results quoted show clearly that the strength of ice in uniaxial tension and compression depends on the rate of loading. In

general, the crushing strength increases with

decreasing temperature and increasing grain size, and decreases linearly with decreasing density. For columnar-grain ice, the characteristics of failure and strength depend on the direction of the stress relative to the grain boundaries.

When granular ice is subjected to a uniaxial constant compressive or tensile load, a

depend-ence of creep strain on time illustrated by

curve I of Figure 4 is usually observed (Glen 1955, Steinemann 1954, Halbrook 1962). On application of the load there is an initial period of decelerating creep rate. This is followed by a period in which the creep rate tends to a constant value and subsequently by one in which the creep rate continuously accelerates. These periods are referred to as the primary, secondary, and tertiary stages of creep. Halbrook's observations were made in a triaxial cell with compressive stresses of 130.7, 196.2, and 261.7 psi, and con-fining pressures of 0 and 45 psi. He found that

Fig. 4. General Dependence of Plastic Strain on Time for Constant Compressive Load.

(b) COLUMNAR ICE,LOAD PERPENDICULAR TO LONG DIRECTION OF GRAINS 10 0 -10 -20 -30 -40 -50 -60 TEMPERATURE, of (a) COLUMNAR I CE LOA D PARALLEL TO LONG DIRECTION OF GRAINS ARTIFICIAL COLUMNAR ICE LOAD PERPENDICULAR TO LONG DIRECTION OF GRAINS

30 20

o

""

o

""

""

Fig. 3. Dependence of Crushing, Tensile and Shear Strength on Temperature, Butkovich (1954).

Fig. 5. General Dependence of Stress on Strain for Constant Rate of Movement of Crosshead.

at the end of the tests the specimens were always badly cracked.

Halbrook carried out tests for which the load was applied under the condition of a constant rate of movement of the crosshead. The general dependence of stress on strain that he observed for granular ice is shown in Figure 5. For the rate of movement used (0.54, 0.95, 1.67, and

3.33 per cent per min) the load increased rapidly

to a maximum or yield value that occurred for

strain between 1 and 2 per cent. It is this yield

value that is probably observed in measurements of the crushing strength of ice.

On comparing the behaviour of ice in the constant load tests with that in the constant strain rate tests, Halbrook observed that the amount of strain associated with yield was about the same as that associated with the transition from the secondary to the tertiary creep stage. The almost linear rise of stress with strain on the left of the yield point is thus associated with the primary and secondary creep stage, and the decrease after yield with the tertiary stage. The average value of the yield stress increased with increased rate of loading.

Gold (1960, 1965) carried out constant load creep tests on columnar-grain ice that had never been deformed before. Curve II of Figure 3 is typical of the dependence of creep strain on time that was observed for loads applied perpendicular

to the long direction of the columns. The

behaviour was unusual in that there was an initial decrease in strain rate followed by an accelerating stage within the first 0.5 per 'cent of the creep

strain. Thereafter, the creep behaviour was

similar to that observed for granular ice. If the

columnar-grain ice was reloaded after it had been strained about 1 per cent or more, the creep behaviour was always similar to that for granular

ice, even if the ice was annealed for several weeks. This behaviour was confirmed by Krausz (1963) in a study of the deflection of beams made from columnar-grain ice.

With increasing loads, crack formation

be-comes more severe (Gold 1960). If the load is

sufficiently great, it disrupts the structure to the extent that the first period of decreasing strain rate for both curves I and II in Figure 3 pass directly to the accelerating creep stage. For a temperature of 15 OF, this behaviour occurs for a constant compressive stress of about 200 psi.

It is of interest that Brown (1926) drew

atten-tion to a sudden change in the characteristics of the creep curve at about the same stress. Brown observed that this critical stress tended to in-crease with decreasing temperature.

Observations by Gold (1965) have shown that the first period of decelerating creep for curve II in Figure 4 is associated with structural changes

in the ice. If the stress exceeds about 80 psi,

the structural changes include crack formation. Brown (1926), Halbrook (1962) and Butkovich

(1954) have also noted crack formation in

similar tests. In the preliminary observations made under conditions of constant rate of cross-head movement, internal cracks were observed to form just prior to the attainment of the first

upper yield point. This provides additional

evidence of the correspondence of the first upper yield point with the initiation of the first accelerat-ing strain rate stage in the constant stress test.

The author has also carried out preliminary observations on the dependence of stress on strain for columnar-grain ice when the load is applied perpendicular to the long direction of the columns under the condition of constant rate of cross-head movement. For rate of movement equivalent

to a strain rate of about 0.5 x 10-2_{per cent per}

min., the dependence of stress on strain was as shown by curve II in Figure 5. The load increased to an upper yield value within the first 0.3 per

cent strain. Itdecreased thereafter to a lower yield

point and increased to a second upper yield value that occurred in about the same range of strain as that observed by Halbrook. As for the tests on granular ice, the behaviour under conditions approaching constant strain rate corresponds to that observed in the constant stress tests, that is a transition to an accelerating creep rate stage in the constant stress test corresponds to an upper yield point in a constant strain rate test.

3.0 1.0

I .ｇｉｬａｾｕｌａ RICE; TEMPERATUREＧｾＲＵ f RAn. Of CROSSHEAD MovEMENT EQUIVALENT TO STRAIN RATE -1.76" PER MIN. HALBROOK 119621

PLASTIC STRAIN, "

1.0

IT - COLUMNAR-GRAIN ICE, TEMPERATURE 15 F LOAD PERPENDICUlAR TO LONG DIRECTiON OF GRAINS

RATE OF CROSSHEAO MOVEMENT EQUivALENT TO STRAIN RATEｾｏＮＵ､ｏＢＢ PE.R MIN. ;00

ｾ 200

The author is at present conducting a series of experiments on crack formation in columnar-grain ice during compressive load and the factors that influence it. For the type of ice used, the cracks are observed to be long and narrow with their long direction parallel to the long direction of the grains, and their plane tending to be parallel to the stress. They usually involve only one or two grains and propagate parallel or pcr-pendicular to the basal planes. The number of cracks that form depends primarily on stress and amount of creep strain, but is largely independent of temperature. Onset of tertiary creep for the loads used appears to depend on the number of cracks formed and the stress. The failure process is time dependent. The time taken to form a given number of cracks for a given applied stress appears to depend on the factors controlling the strain rate. These observations raise questions concerning the dependence of strength on tem-perature that still have to be resolved by addi-tional measurements, The formation of internal cracks in a tensile test will probably result in failure. In a compression test, the formation of such cracks relieves the stress concentration re-sponsible for them and causes a redistribution of stress. The specimen is able to sustain a load, at least during the early part of the test, that is higher than that required to initiate crack

forma-tion. It would be expected, therefore, that the

dependence of maximum load on rate of loading for a compression test would be different from that observed for tensile tests.

In Figure 2 are plotted yield strengths versus rate of loading estimated from the results of Halbrook. Shown also are two results for the first yield point at low rates of loading obtained by the author for columnar-grain ice, and results obtained by Butkovich (1955) at higher rates. This plot indicates that for compressive loading, maximum yield values may not be obtained unless rates of loading are in excess of 16 psi/sec. The results plotted indicate that the yield strength of granular icc is appreciably less than the yield strength of columnar-grain icc.

The results of Butkovich indicate that strength drops off appreciably at higher rates of loading. Voitkovskii (1960) and Korzhavin (1955) re-port also that at higher rates of loading (2 ft/sec) the strength of ice is lower than at low rates. Not much information on this aspect of the behaviour of ice is as yet available. Results quoted by Voitkovskii for normal ice and river ice at the

time of break-up are given in Tables 111 and IV respectively.

In summary, studies of the strength of granular ice in uniaxial compression indicate that, under conditions of constant rate of crosshcad move-ment, the load builds up to an upper yield value that occurs for strain between 1 to 2 pcr cent. The yield stress depends upon the rate of strain-ing and, for a given rate, upon the temperature. Previously undeformed columnar-grain ice sub-jected to a compressive load perpendicular to the long direction of the columns can have two upper yield values. The first occurs within 0.3 per cent strain and is probably associated with the breakdown of the constraints imposed by grains on the deformation of neighbouring grains. The second corresponds to the upper yield value observed for granular ice. Yield under condi-tions approaching constant strain rate corresponds to the transition to accelerating creep rate in a constant stress test. With increasing rate of strain-ing, the yield stress goes through a maximum that is probably temperature dependent.

If the stress exceeds about 80 psi, yield in the constant strain rate test and accelerating strain rate in the constant load test are associated with the formation of internal cracks. The number of cracks that form in a given time depends primarily on stress and amount of strain. Formation of cracks results ultimately in the breakdown of

the structure of the ice and failure of the

specimen.

TABLE III

DEPENDENCE OF CRUSHING STRENGTH OF ICE (PSI) ON TEMPERATURE AND

RA TE OF MOVEMENT OF ICE (FROM VOITKOVSKII 1960). STRESS APPLIED PERPENDICULAR TO LONG DIRECTION

OF GRAINS Rate of Temperature, OF movement, in/min. 32 28.4 24.8 21.2 17.6 14 - _.._ -0.79 206 301 391 497 586 69.5 7.9 138 142 149 163 185 202