The general properties of snow are described with a view to engineering applications of data. Following an introduction and a short note on the origins of snow, data are given for fall velocities of snow particles, and for mass flux and particle concentrations in falling snow and blowing snow. Notes on the structural properties of deposited snow cover grain size, grain bonds, bulk density, overburden pressure, and permeability. A section on impurities deals with stable and radioactive isotopes, chemical impurities, insoluble particles, living organisms, acidity, and gases. Mechanical properties are treated only selectively, and the reader is referred to another paper for comprehensive coverage. The selective treatment deals with stress waves and strain waves, compressibility, effects of volumetric strain on deviatoric strain, and specific energy for comminution. The section on thermal properties covers heat capacity, latent heat, conductivity, diffusivity, heat transfer by vapor diffusion, heat transfer and vapor transport with forced convection, and thermal strain. The section on electrical properties opens with a brief discussion on dielectric properties of ice, and proceeds to a summary of the dielectric properties of snow, including dielectric dispersion, permittivity, dielectric loss, and d.c. conductivity. There are also notes on the thermoelectric effect and on electrical charges in falling and blowing snow. The section on optical properties deals with transmission and attenuation of visible radiation, with spectral reflectance, and with long-wave emissivity. The review concludes with some comments on engineering problems that involve snow, and the requirements for research and development.

Snow forces are understood as forces originating from a very slow motion of the seasonal snow cover and acting on boundaries confining it. They depend on the total water-equivalent (a statistical magnitude with a certain probability of occurrence) and on mechanical characteristics of snow. The approximation of considering of snow as a Newtonian liquid fits the requirements for applications best. In this the only mechanical characteristics to be taken into account, besides density, are shear viscosity and Poisson’s ratio. They depend strongly on the snow structure. Generalizations are shown in which the snow cover is subdivided into layers having constant (Newtonian) properties. Non-Newtonian behaviour is also mentioned.

Many slab avalanches can be attributed to shear failure in a weak, thin basal layer at the slab base. A reasonable starting point for evaluation of the conditions prior to fracture is, therefore, an investigation of shear failure in thin samples of snow. This paper gives the experimental procedure and data on measurements of shear stress versus displacement for thin samples of snow under plane strain and approximately simple shear conditions. The data are given under varying conditions of strain-rate, normal stress, density and snow type. The results show that the samples exhibited strain-softening provided they were sheared faster than they gained strength by settlement under the chosen conditions. If snow fails at the base of a slab in the way in which it fails in the laboratory, then a mechanism is provided whereby tensile stresses would be produced in the slab and whereby the corresponding maximum principal stresses would be rotated toward a direction parallel to the slope, thereby promoting avalanche release.

A fracture criterion is developed for fine-grained granular snow and is shown to predict accurately the conditions required for fracture under multiaxial states of stress. The criterion is applied to two specific types of deformation histories. The first deformation path involves an initial high strain-rate to produce fracture from an unstressed rest configuration, and the second path involves multiple strain-rate paths. The criterion expresses the critical value of deviatoric free energy in terms of the volumetric free energy and internal energy dissipation, and it was found to predict fracture accurately for tension, compression, and shear.

Wind-blown snow represents an age-old problem in the applied glaciology of most higher-latitude regions, but its physical intricacies first received attention in esoteric discussions on the long-term mass balance of polar ice sheets (Loewe, 1933, 1956). Measurements on the uniform unlimited surface of such ice sheets have shown good agreement, at least over a limited height range, with estimates for the concentration and flux of drift snow as a function of height and wind velocity based on turbulence theory. An alternative theory, developed concurrently from wind-tunnel results and field observations in Siberia, is discussed on the basis of its most recent exposition (Dyunin, 1974). Basic questions requiring further study include drift-snow concentrations at considerable heights, drift evaporation, and electrical phenomena. The main practical aspects of snow drift relate to the prevention of excess accumulation on roads, railway lines, and avalanche slopes; and to the encouragement of accumulation in fields and forests, and other locations where frost protection and/or storage of water is desired. The methods used are reviewed; they are beginning to rely on physical concepts and theories rather than solely on empirical formulae derived from engineering experiments.

In regions of positive surface mass balance, buildings and other structures tend to become obliterated by snow drift. An important factor of this process is the fall-out of snow in the retarded flow on the windward side of the structure. Some recent attempts to measure and calculate that fall-out are discussed.

This paper presents many experimental data of friction between a slider and snow or ice in relation to ski-ing and skating. Measurements of the kinetic coefficient of friction μk for a metallic or plastic-resin ring in contact with a snow surface were made using an oscillograph. The mechanism of this friction was analysed through oscillograms showing frictional resistance between a slider and a snow surface together with observations of the real contact area between the surface of the slider and snow grains. It was shown that friction at low sliding speeds caused plastic deformation within snow, but, when sliding velocity was increased, a stick-slip friction occurred accompanying fractures and abrasions of snow grains. Since the laboratory experiment of friction on snow is limited to a range of low sliding speeds, the measurements of μk for high sliding velocities were made by the use of practical skis. The value of μK for practical skis increased from 0.03 to 0.1 as the speed increased from for velocities 5 to 22 m/s.

The measurements μk for skates were made using a specially designed device on skating rinks prepared both on natural lake ice and artificial ice. The temperature dependence of μk was studied for the blades of skates; μk showed a minimum value for both rinks around —1 to — °C, namely, 0.003 for the natural lake ice and 0.007 8 for the artificial rink ice.

The modeling of deformation in snow-pack of realistic geometry is reported. Experimentally measured deformation rates are compared with corresponding rates predicted from a finite-element model developed using local stratigraphy in the experimental area. Specifically designed deformation gages placed on an avalanche-sensitive snow slope at Berthoud Pass, Colorado, during the winter of 1972-73, were used to measure the experimental values. The finite-element code, based upon a plane-strain idealization, was used to model the steady-state flow of the slope. The program incorporates visco-elastic properties of the snow-pack, snow-layer stratigraphy, and the orthotropic properties of snow when both tension and compression components of stress act at a point. The degree of correlation between experimental and computed values of deformation rates is reported, and limitations of the analysis in conjunction with the type of experimental data taken are discussed.

This paper presents a numerical calculation procedure for the stress and deformation analysis of a snow mass which is creeping and gliding on an inclined surface and which may, in addition, be restrained by rigid obstacles. The analysis is based on the assumption that the velocity profile at any position in the snow-pack is linear, that is, that sections initially plane remain plane during deformation. Such motion has been observed to occur in the neutral zone and is certainly true at a rigid barrier; accordingly, it appears to be reasonable to restrict the velocity field to be plane everywhere. A constitutive law for steady creep is used which is consistent with the observed neutral zone motion. The solution procedure is illustrated by its application to some problems of avalanche defense barriers. The cases investigated include: continuous barriers, cylindrical barriers, and barriers of finite width. Barrier forces and the extent of back-pressure zones are given.

When snow is pushed very fast by a moving body a plastic wave is generated at the head of the body. If the velocity of the moving body becomes close to that of the plastic wave, the snow may exert a great resistive force against the body as predicted by Yosida. It is, therefore, very important to study the dynamic behaviour of snow at a high rate of deformation, such as takes place when a snow plough is used on the highway, a train runs on a railroad covered with snow, or an avalanche occurs. Hence, this study is concerned with the safety and maintenance of winter traffic and transportation, and also with the generation and propagation of an avalanche. In order to clarify the detailed processes of the deformation of snow at high rates, laboratory experiments were made by compressing snow at high speed. The propagation of a plastic wave through snow was observed by using a high-speed camera and a pressure-detecting device. Analyses of the data obtained gave the velocity of the plastic wave for various kinds of snow whose density ranged from 0.17 to 0.46 Mg m-3 and free-water content from o to 17%, whereby studies were made into the dependences on the density and free-water content of the velocity of the plastic wave. When the impact velocity was 4.3 ± 0.2 m s-1, the wave velocity ranged from 5 m s-1 for a new snow to 12 m s-1 for a fine-grained, well-settled snow. The plastic-wave velocity in wet snow was, in general, smaller than that in dry snow of the same density. Changes in density and structure of snow associated with the passage of a plastic wave were studied and discussed. The pressure at the wave front was measured; values of 0.1-0.3 bar were obtained, these are of the same order as the value estimated from theoretical formulae. The plastic-wave velocity was also observed for a confined snow, which showed a larger velocity and plastic strain than an unconfined snow.

An assessment of snow loads in Switzerland was required for a revision of the building code. Settling curves of snow are used to compute water equivalents of snow if direct measurements are not available. Based on a frequency analysis, relations between the snow load and the altitude are given for various return periods. Problems of regional effects and of converting the snow-cover data to roof loads are outlined.

The principal engineering problems requiring knowledge concerning the properties of ice are prediction of the maximum force that ice might exert on a structure and determination of the load that can be placed safely on an ice cover. The properties of ice relevant to these problems are discussed. Particular attention is given to the dependence of Young's modulus on the frequency of the stress, strain-rate dependence of the yield and fracture strengths, and the ductile to brittle transition. It is shown that the strain-rate dependence of these properties is consistent with information on the stress dependence of dislocation velocity on the basal plane. The tensile and compressive strengths are also shown to be consistent with current theories of crack initiation and propagation.

An attempt was made to develop a simple but accurate method for making compressive strength tests on right circular cylinders. Compliant loading platens were designed to apply uniform normal stress without introducing significant interface radial shear stresses. The compliant platens gave reproducible results that agree well with results obtained by a precise conventional technique. Accurate results were obtained with simple specimen preparation, and with short specimens where the length-to-diameter ratio was less than unity. Platens were made from a rubber-like urethane which was molded in aluminum cylinders to provide lateral restraint. Uniaxial compression tests on cylindrical polycrystalline ice specimens were made to determine the characteristics of the platens. For 21 specimens with ends prepared on a lapping plate to obtain a mirror finish, the measured strength showed a variation of only 13% for length-to-diameter ratios from 0.74 to 2.5, with no systematic trend. Another 21 specimens with length-to-diameter ratios of about 2.35 were tested with various platens and various methods of specimen end preparation. The strength for specimens with saw-cut ends and for those with ends lapped showed very little difference when tested with the rubber platens.

This paper presents the results of a study carried out to explain the low friction on ice. Friction of a steel ball on a single crystal of ice was measured as a function of load, velocity, temperature, and diameter of slider. It was found that even when the velocity was very small (1.5 - 10-7 to 1.8-10–3 m/s) the coefficient of friction was very small ranging from 0.005 to 0.2, although friction on the prismatic plane was twice as large as that on the basal plane. The coefficient of friction increased with load, which means that Amonton’s classical law of friction is not applicable to ice. The coefficient of friction increased with decreasing velocity, which may result from the creep of ice in the contact area. The friction strongly increased as the temperature became close to °C. A minimum friction was observed for a definite temperature. It was found that the explanation of the results obtained is given satisfactorily neither by the classic pressure-melting theory nor by the friction-melting theory, but only by adhesion theory.

The safe bearing capacity of a floating ice sheet is usually determined by limiting the maximum tensile stress which occurs under the load at the bottom of the ice sheet. If the size of the load distribution is large compared to the ice thickness, the thin plate theory predicts these stresses correctly. However, if the size of the load distribution becomes small compared to the ice thickness, the plate theory overestimates the stresses. In this case the ice sheet should he treated as a three-dimensional elastic layer.

Previous investigators have solved the elastic-layer problem for loads distributed over a circular area, and have limited the results to the stress at the bottom of the ice sheet directly under the center of the load. In the present paper the stresses are evaluated at any radial position, and it is shown how these stresses approach those for the plate theory as the radial position becomes large. The solutions for the stresses are presented in integral form, as well as graphs from the numerical integration. These new results are significant for the superposition of stresses when two concentrated loads act near each other.

Similarly for loads distributed over a rectangular area, the plate theory will overestimate the stresses if the dimensions of the load becomes small compared to the ice thickness. For this case integral solutions are presented for the stresses, and are evaluated directly under the center of the load.

Large, simply supported beams of temperate lake ice generally yield significantly higher f1exural strengths than the same beams tested in the cantilever mode. Data support the view that a significant stress concentration may exist at the fixed corners of the cantilever beams. Maximum effects are experienced with beams of cold, brittle ice substantially free of structural imperfections; the stress concentration factor may exceed 2.0 in this kind of ice. In ice that has undergone extensive thermal degradation the stress concentration effect may be eliminated entirely. Simply supported beams generally test stronger when the top surface is placed in tension. This behavior is attributed to differences in ice type; the fine-grained, crack-free top layer of snow-ice usually reacting more strongly in tension than the coarse-grained bottom lake ice which is prone to cracking.

When large masses of ice, for example in the form of glaciers or floating ice fields, are moving against an obstruction, either natural or man-made, huge forces will develop. It is possible to derive formulae to estimate these forces from elementary mechanics of the rupture of ice. The basic formula may be written: F = ϕ(C)rced, where ϕ(C) is a function of the geometrical and physical parameters of the system, rc is the compression strength of the ice, e is the thickness of the ice, and d is the width of the structure. The paper deals with the different types of rupture patterns that may develop in front of either vertical or inclined faces, and formulae are given for some typical cases.

The paper describes the dynamic ice-structure interaction study of monopod platforms (fixed type) which are of considerable interest to the off-shore oil industry in cold regions. In view of the scantiness of continuous ice-force records, artificial-force records are generated from available small-scale field ice-force records using stochastic concepts. The method, based on the similarity between the fluctuating parts of randomly varying ice-force records and the seismic records uses a non-stationary random process obtained from filtering a shot noise through a second-order filter. The dynamic response analysis of a monopod structure located at Cook Inlet, Alaska, is carried out by hybridizing the relevant sub-routines of the computer programmes, SAP IV (Structural Analysis Programme) and EATSW (Earthquake response of Axisymmetric Tower Structures surrounded by Water). The work includes a study of the influence of soil properties on the frequencies and responses, and a comparison between the responses of fixed and elastically supported (by the soil foundation) monopod platforms.

This study gives the results and interpretation of tests made in a cold room on ice plates held vertically in a press and indented at various speeds with a rectangular indentor. These plates, 81 cm square, were held and frozen solid to a steel frame to represent semi-infinite ice sheets. The tests were carried out at — 10°C with indentation speeds varying from 6 × 10 -5 cm/s to 3 cm/s.

It was found that the nominal pressure of indentation varies as a function of loading rates in a manner similar to that of the strength of S2 ice in uniaxial compression. The pressure increases rapidly with loading rates up to its maximum value at a strain-rate of 5 × 10-4 S-1. From there on, the pressure decreases. In the ductile range and up to the point of maximum pressure, a theoretical model was proposed where the theory of Hill (1950) of indentation of an ideal plastic body can be applied to predict an indentation pressure close to three times that of the uniaxial crushing strength.

The tests did not show any so-called “ratio effect” caused by the ratio of the indentor width to the plane thickness. This effect could be explained by the influence of the geometry of the indentor on the strain-rate.

Controlled field and laboratory tests were performed to investigate the relationship between ice strength and the maximum ice pressures on vertical piers. The apparatus used in the field tests consisted of a flat indentor (75 cm wide) which was pushed through the ice by hydraulic rams. 27 tests were conducted on lake ice up to one metre thick. Ice pressures in the range 2.5 to 5.0 MPa were obtained for ice in good initial contact with the indentor. The ice pressures exhibited little sensitivity to variations in temperature, ice thickness and strain-rate for the range 7.5 × 10-7 to 4.4 × 10-3 s-1.

The average unconfined compressive strengths obtained in the laboratory were about 20% higher than the average field ice pressures. In addition, the laboratory strengths were found to be sensitive to temperature, and to strain-rate in the range 1 × 10-7 to 1 × 10-3 s-1. The confined compressive strength was two to three times the unconfined strength.

The failure modes observed in the indentation tests were similar to those predicted (before the tests) by an upper-bound plasticity model. The ability of the model to relate small-scale ice strength to field ice pressures is discussed.