Continuous records have been made during the passage of dry–snow avalanches of both seismic signals, which allows the avalanche speed to be estimated, and impact pressures on load cells with surface areas of 645 and 6 450 mm2. The impact pressure recordings show an initial peak followed by a base pressure. The observed initial and base pressures vary strongly within avalanches and from one avalanche to another, but, on average, they can be correlated with the frontal speed and the density of the deposited avalanche snow. It is concluded that well–developed dry–snow avalanches have an unsteady wave motion similar to the slug flow observed in ultra–rapid flow of water, and that they consist of three stratified components: dense flowing snow at the bottom, light flowing snow, and powder snow.

Small–scale modeling of flow and impact of snow avalanches is demonstrated to be both feasible and accurate. Geometric, kinematic, and force variables are scaled correctly under equivalence of Froude number between prototype and model using sifted snow as the model fluid. Physical and computer–simulated impact processes show correspondence, so that computer modeling is demonstrated to be a viable tool in flow and impact predictions.

Voellmy’s (1955) method for computing the run-out distance of a snow avalanche includes an unsatisfactory feature: the a priori selection of a midslope reference where the avalanche is assumed to begin decelerating from a computed steady velocity. There is no objective criterion for selecting this reference, and yet the choice critically determines the computed stopping position of the avalanche. As an alternative, a differential equation is derived in this paper on the premise that the only logical reference is the starting position of the avalanche. The equation is solved numerically for paths of complex geometry. Solutions are based on two parameters: a coefficient of friction μ; and a ratio of avalanche mass–to–drag, M⁄D. These are analogous to the two parameters in Voellmy’s model, μ and ξH. Velocity and run-out distance data are needed to estimate μ and M⁄D to useful precision. The mathematical properties of two–parameter models are explored, and it is shown that some difficulties arise since similar results are predicted by dissimilar pairs of μ and M⁄D.

In this work a model of the ultrasonic acoustic emission response in snow is developed. The model derived considers the acoustic emission response in snow as a function of stress and strain. It is suggested that the acoustic emission activity in snow is a quantitative indication of the creep rupture taking place in the material. The governing differential equation is developed; an example is then presented that considers the applicability of this equation to the release of certain types of avalanche.

Snow is variable in both time and space. Because of this fact, a complete understanding of snow strength must include statistical strength analyses. Two types of statistical strength theories are the series-element, or weakest-link theories and the parallel-element theories. In the case of snow in shear, Daniels’ (1945) parallel-element theory provides a quantitative explanation of the size and stress-rate relationships of snow, which are at least as accurate as presently available data. In the case of tensile tests, a combination of the two types of theories is proposed which also provides a quantitative explanation which is as accurate as present data. In each case large-volume, low-stress-rate strengths are predicted using small-volume, high-stress-rate data. More data are necessary to provide definitive tests of the proposed hypotheses.

This paper reports on research on the relationship between the electromagnetic scattering properties and physical properties of snow-pack. An FM-CW active microwave radar system operating in the frequency range 8-12 GHz is used to scatter electromagnetic radiation from surface and subsurface stratigraphic layers in the snow-pack. The amplitude of the scattered radiation as a function of depth in the snow-pack can be correlated with such physical characteristics as density, hardness, stratigraphy, and moisture content. A direct determination of snow-pack water equivalence can be made from these observations.

The propagation of pressure waves in low-density snow is investigated analytically to determine the variation of wave pressure and wave speed with density and frequency. The results show that, for pressure waves that produce finite volumetric deformations, both pressure jump across the wave and wave-speed increase with initial density and final density. The pressure jump was also found to increase with the wave frequency if other parameters were held constant, although the dependence on frequency is not as strong as the dependence on the initial and final densities. The relationship between pressure jump and frequency implies that high-frequency waves would tend to dissipate more quickly than lower-frequency waves, although like pressure, the attenuation rate would not be strongly frequency dependent.

A stress-wave model is used to describe snow-slab failure under dynamic loading conditions. This model indicates that dilational waves and shear waves can interact with a thin, weak bedding layer underlying a snow slab causing dilatational and shear stresses in the layer. The magnitude and distribution of stresses in the layer are shown to depend strongly on the height of the loading source above the bedding plane, the difference in impedance between the slab and the loading source, the difference in impedance between the slab and its substratum, and the initial stress magnitude of the loading source. Failure occurs in the bedding layer when the generated stresses exceed the strength of the layer. This causes a loss of shear strength capacity at the bedding plane and a re-distribution of stress in the slab. If the shear capacity is reduced sufficiently the body-force loading of the slab will cause snow-slab failure.

Measurements over several hours of the tensile strain of snow have been carried out, and the strain-rate e can be expressed in terms of stress σ, elapsed time t, and (Celsius) snow temperature T as . It is evident from this expression that a creep fracture does not happen without either an increase of stress or a rise of temperature. We observed the phenomenon of creep fracture of snow by these two methods.

Fluidized snow was produced in a cold laboratory and its viscosity and heat transfer were studied. The viscosity of the fluidized snow was measured with a modified Stormer-type viscometer. It was found that the apparent viscosity decreased with increasing air velocity and decreasing particle diameter. Two mechanisms were suggested as producing the viscosity of the fluidized snow on the basis of the plot of the viscosity against the reciprocal of the air velocity.

The heat-transfer coefficient was obtained by measuring the temperature of a cooled brass sphere suspended in the fluidized snow. The heat-transfer coefficient in the fluidized snow was three or four times larger than that in an air flow containing no snow particles. The increase was attributed to the enhanced turbulence of air flow and the collision of snow particles; the contribution of the latter was estimated to be 80 to 90% of the total increase due to the fluidization of snow. These results were also confirmed in an artificial blowing snow produced in a cold horizontal wind-tunnel by measuring the heat-transfer coefficient, wind velocity, and drift density.

The mechanical behaviour of snow was studied at — 10°C under uniaxial tensile stress in a range of cross-head speed 6.8 - 10–8 to 3.1 - 10–4 ms–1 and snow density 240-470 kg m–3.It was found from the resisting force-deformation curves that the snow was deformed in two different ways: namely, brittle and ductile deformation at high and low strain-rates, respectively. The critical strain-rate dividing the two deformation modes was found to depend on the density of snow. In ductile deformation, many small cracks appeared throughout the entire specimen. Their features were observed by making thin sections and they were compared with small cracks formed in natural snow on a mountain slope.

The maximum strength of snow was found to depend on strain-rate: at strain-rates above about 10–5 s –1, the maximum strength increased with decreasing strain-rate but below 10–5 s–1 it decreased with decreasing strain-rate.

Compressive strain-rates in discrete layers of a sub-alpine snow cover are analyzed. Individual layers are identified according to density and the dominant type of metamorphism which contributed to their formation. Data were collected during four winter seasons at the Institute of Arctic and Alpine Research (INSTAAR) snow-study site (3 400 m), Red Mountain Pass, south-western Colorado, U.S.A. At average densities of less than 250 kg m₋3 the influence of metamorphism on strain-rate is not apparent. However, at densities greater than 250 kg m₋3, two separate relationships emerge for strain as a function of crystal type and density. While two adjacent layers may exhibit comparable densities, a layer of sintered, fine grained (ET) snow indicates a strain-rate approximately one order of magnitude greater than an adjacent layer of cohesionless, coarse-grained (TG) snow.

In the absence of imposed temperature gradients, the metamorphism of dry snow is dominated by the slow process of vapor diffusion between surfaces of different radii of curvature. This process is so slow in a seasonal snow cover (where temperatures normally change on the scale of hours or days) that vapor migration is usually dominated by the imposed temperature gradient. Thus radius of curvature contributes to but does not control metamorphism except for short periods in very fresh snow. As opposed to dry snow, liquid-saturated snow (i.e. pore space filled by the melt) is metamorphosed by heat flow arising from relatively large temperature differences among the particles. Grain growth in liquid-saturated snow is rapid because of the large temperature differences at nearly constant liquid pressure. In wet snow with low liquid content (2-5% by volume), grain growth is dominated by vapor diffusion (as in dry snow) so grain growth is much slower than under conditions of liquid saturation.

The present study was carried out with a view to quantifying the effects of the main parameters ot temperature-gradient metamorphism. Cold-room simulation tests showed crystal growth to be an increasing function of the temperature-gradient modulus with a lower limit of around 0.25 deg/cm. This growth also proved to be a function of temperature itself reaching a maximum at around –5°C Furthermore the shape of depth-hoar crystals was also shown to depend on temperature and to resemble approximately that obtained when crystals are formed in the atmosphere. Temperature-gradient metamorphism is observed to take place at constant density. Increase in crystal size is a decreasing function of density with a lower limit of around 150 kg/m3, below which destructive metamorphism occurs accompanied by packing (similar to ET metamorphism): the upper limit is situated at approximately 350 kg/m3 and no depth-hoar crystals occur above this value. The series of Cold-room simulations enabled a highly simplified model of crystal growth to be constructed.

Tourism in the Swiss Alpine region has developed rapidly in the last 20 years. Many new routes transport systems, and tourist resorts have appeared for which the planning and construction have inadequately considered the avalanche danger. The local authorities are responsible for the safety and welfare of the inhabitants and visitors. This is especially true with respect to land-use control and the issue of building permits. Since property values have risen considerably since the second World War, speculation in land that is not safe from hazard has become widespread. This speculation has led to numerous conflicts between property owners and the municipal government as well as between sellers and buyers of land which is later found to have an avalanche hazard. In Swiss law a legal basis is required to prohibit building in unsafe places. This basis did not exist in many Swiss cantons when these fateful developments began. This study will show how the legal basis for avalanche zoning has been developed at the federal, cantonal and communal levels and what the actual state of jurisdiction is. Of special interest are the “precedents” or “case law” which are presented and discussed in this paper. It also gives definitions of the terms “zone”, “avalanche zoning”, “avalanche hazard map”, and “avalanche zone plan”.

Avalanche zoning in France comprises two main parts:

1. A map of the probable location of avalanches was produced between 1970 and 1976, at a scale of 1 : 20000, and covering nearly 600000 ha. This was prepared by using a novel method based on:

1. (i) the photo-interpretation of air photographs: the relief, extent of vegetation, notably forests the structure of deposits and alluvia, the comparison of several areas, thus enabling the zones …. which appear to have been struck by avalanches in the past to be identified;

2. (ii) information acquired from inhabitants and the study of archives;

3. (iii) a detailed inspection of the ground which can reveal physical or anthropogenic signs not disclosed by photo-interpretation.

This map is only concerned with the past and gives no indication of frequencies.

2. French law places an obligation on the State to define the limits of the zone subject to natural risk betore a building permit can be obtained.

Consequently, since 1974 when France ventured into zoning, plans have been made on a large scale (1 : 2000) showing the zones exposed to avalanches. Plans are made in three colours: white presumed to be without danger, red dangerous and therefore prohibited to constructors, and blue zones, doubtful.

Blue zoning, the most difficult to establish, relics on the evaluation of specialists, supported by the classical calculation of Voellmy, as well as by some first results received from experiments in a water channel for powder-snow avalanches, or from numerical simulations for other avalanches.

The blue zone includes heavy avalanches with a time of return greater than 300 years and slightly more frequent avalanches (return time 30-50 years) but of very little importance.

According to circumstances in every blue zone, several types of measure are recommended: police measures (evacuation or regulation in the home), architectural measures of reinforcement protective structure construction or annual checking by the authorities that natural (forest) or artificial (structures) defences are in a good state.

Problems concerning natural-hazard mapping have been discussed by the Norges Geotekniske Institutt in pilot projects sponsored by the National Fund for Natural Disaster Assistance. Hazard-registration maps, geomorphic hazard maps and hazard-zoning maps are defined. Hazard-zoning maps are preferable in land-use planning. Both survey maps (1 : 50000) and detailed maps (1:5000) are of interest. A survey map (c. 600 km2) would be mainly based on airphoto interpretation and could be prepared in about 150 h. Detailed mapping is more time consuming and should be limited to development areas.

Mapping of “marine deposits” and “other areas” are handled by separate groups, mainly because of differences in technical and professional problems. This gives rise to two parallel series of survey maps and detailed maps.

The proposed programmes for survey mapping states that 80% of the marine areas should be evaluated in 5 years (1980-84), and that one-third of the country should be examined for rockfalls, rock slides, and snow avalanches in 10 years. Other hazard types are impossible to identify by survey mapping. There is a rising demand for detailed maps but as yet there has been no research project to standardize methods.

The hazard maps are intended primarily to be an aid in land-use planning.

Many developed areas in British Columbia are exposed to snow-avalanche hazards. Avalanche-hazard zoning has been undertaken by the British Columbia Ministry of Transportation, Communications, and Highways during the past five years. Recommendations from these zoning studies are forwarded to those agencies responsible for land-use zoning and development approval. Existing and possible legislation are described, as well as problems associated with implementation of the legislation. Technical considerations are outlined; interpretation of vegetation is a very important factor in evaluating each avalanche site. Calculation of run-out distances and consideration of other factors serve as a check on the vegetation interpretation. A special safety factor has been developed.

Socio-political considerations with respect to British Columbia are described. Existing developments have the most wide-ranging implications.

Four communities in the western United States (Vail, Colorado; Ketchum, Idaho; Ophir, Colorado; and Juneau, Alaska) have detailed avalanche–hazard mapping available. In response to this detailed information, Vail restricts building in a red (high hazard) zone but permits specially designed buildings in the blue (moderate hazard) zone. Ketchum allows single–family dwellings in red or blue zones regardless of design but will not permit such structures to be rented from the period 15 November through 15 April of each year. Multi–family dwellings in Ketchum hazard zones must be designed for avalanche forces. Ophir will restrict buildings from the red zone and permit specially designed structures in the blue zone. Juneau does not restrict development in any avalanche–hazard zone.

Avalanche-hazard mapping as a basis for land-use decision-making was not undertaken systematically in Colorado until 1974. Passage of Colorado House Bill 1041 required counties to map areas subject to snow avalanche, landslide, debris flow, and mountain flood at 1 : 24 000, and funds were provided. This legislation induced several approaches: work undertaken directly by the Colorado Geological Survey; private contract work; mapping by the Institute of Arctic and Alpine Research (INSTAAR) funded by a NASA research grant. This latter effort produced 37 individual 1 : 24 000 map sheets of Hinsdale, Ouray, San Juan, and San Miguel counties, San Juan Mountains. This emphasized problems of scale and degree of cartographic accuracy. Swiss, Austrian, and French experience, together with the actual Colorado mapping experience, facilitated further definition of problems facing the Rocky Mountains slates, both in terms of resolution of actual mapping problems, and of using such developing experience to influence the decision-making process.

Two mapping attempts are described: (i) development of a combined hazard map for a mountain type area, indicating the difficulties of, and need for, combining hazard assessment of avalanche and other physical processes that frequently overlap; (ii) consideration of avalanche-zoning problems in a wilderness area.

Finally, scale limitations and the need to define rigorously “hazard” are discussed. Definition of hazard must include consideration of recurrence interval, impact pressures in the run-out zone, and limitations of displaying this type of data on available topographic maps, all in relation to types of impact, i.e. to moving or stationary objects in relatively sparsely populated terrane. Additional critical needs facing Rocky Mountains states are itemized: (i) standardized mapping legends for different scales; (ii) establishment of an avalanche cadastre; (iii) systematic reporting of climax events; (iv) development of an historical archive; (v) public awareness; (vi) attention to legal aspects of the avalanche equivalent of the hundred-year flood, and its legal testing.