R.L. Brown

The spatial variability of snow resistance on potential avalanche slopes

Since snow avalanches are believed to release from zones of localized weakness, knowledge of snow-strength patterns is important for determining slope stability and for applying effective avalanche-control measures. In this study, the spatial variability of snow resistance (an index of snow strength) and depth were measured and compared with terrain features on two inclined slopes. A refined instrument allowed the strength of an entire snow slab to be characterized in a short time. The spatial pattern of trees appeared to affect the pattern of snow depth at one site, where a significant linear relationship was found between snow depth and average snow resistance. These results suggest that localized snow-depth variations may be important in snow-strength genesis. Although a linear relationship existed at that site, additional factors may be critically relevant. A second site with more complex terrain features and less localized wind drifting did not show a linear relationship between depth and average resistance. Instead, complex patterns of resistance demonstrated that many factors contribute to snow resistance. In particular, the snow overlying rocks was found to have significantly weaker resistance than that in adjacent areas not over rocks

Metamorphism of Dry Snow as a Result of Temperature Gradient and Vapor Density Differences

A heat conduction equation for the determination of the temperature profile in a snowpack is developed. The magnitude of the temperature gradient tends to increase as the snow surface is approached, with local minima through layers of high snow density and local maxima above and below these layers. Calculations are made of the difference in varor density in the pore and over the ice grain surfacps which border the pore. In the presence of sufficient temperature and temperature gra~ient, faceted crystals will develop near the top of the pore, as ice is sublimed away from the surfaces in the lower region. There will be a reduction in the percentage of rounded grains as the faceted form develops. The process is demonstrated to be enhanced at warm temperatures and large temperature gradients in low density snow. I NTRODUCTI 0 t~ Temperatures at the base of a seasonal snowpack usually remain just below O·C throughout the winter. Snow is warmed from below, as the ground gives up heat accumulated during the warmer months. If this geothermal heating coincides with cooler ambient air temperatures, characteristic of the winter months, a temperature gradient is established across the snowpack. . A variation in vapor pressure, resultlng from the temperature differential, will cause a mass flux of vapor from the zone of high vapor pressure (the deeper warmer region) to the zone of lower vapor pressure. Since dry snow, in which this mechanism is most effective, consists of a solid and a vapor phase of.the same material, the transfer can act as though lt partly takes place through the solid matrix itself, as a hand-to-hand transfer of mass (Yosida and Kojima (1950), described in Akitaya 1974). Yapor will evaporate from the top of an ice grain, diffuse across the pore and deposit as a solid on the bottom of the grain above. The ice molecules on the top of this grain will sublime and redeposit in a similar fashion. When snow of low to medium density is subjected to the correct combination of temperature and temperature gradient, angular flat-surfaced crystals, known as depth hoar, will develop at the expense of those grains with a more rounded configuration. This effect is most prevalent in low-density snow at relatively warm temperatures subjected to large temperature gradients. Snowpack development in which faceted crystal growth predominates is known as temperature gradient metamorphism. At low temperature gradients, rounded grains are observed to form, in a process known as equitemperature metamorplli srn. Col beck (1982) refers to the crystals which develop as a result of equitemperature metamorphism as the equilibrium growth form. In the proper conditions this equilibrium form may be other than spherical. Colbeck terms the faceted crystals which develop as a result of temperature gradient metamorpnism the kinetic growth form. A satisfactory value for the temperature gradient at which the transition from the equilibrium to the kinetic growth form takes place has not been established; this is because of the dependency on temperature and snow density. The point at which this transition occurs is an important topic which requires further investigation. This paper deals with processes involved during kinetic growth. Two general types of depth hoar are recognized (Akitaya 1974): a solid type, which develops under smaller temperature gradients, and a skeleton type, which predominates under large temperature gradients. Skeleton-type depth hoar is composed of large faceted crystals, which are poorly bonded together and form a weak snow 1 ayer. The soli d type cons is ts of sma 11 faceted crystals which do not show the marked reduction in strength characterized by the skeleton type. Akitaya (1974), in what is perhaps the most complete experimental work carried out on the topic of temperature gradient metamorphism, has shown that pore size, initial ice-grain size and geometry affects depth-hoar development. A large pore will enhance the rate of growth and the size of the crystal which will develop. This is in agreement with Marboutys (1980) observation that fine-grained snow with a density in excess of approximately 350 kg 013 subjected to a large temperature gradient will develop depth hoar of a solid type. Lower density snow, which has a large pore size, tends toward developing the skeleton type in the presence of a sufficient temperature gradient. Faceted crystals grow toward the direction of higher temperature in the snow. The direction of crystal growth Was observed to be dependent on the thermal gradient and not on gravity (Akitaya 1974).

Grain boundary ridge on sintered bonds between ice crystals

Well-sintered snow examined in a scanning electron microscope revealed a newly observed morphological structure that protrudes into the pore space along ice grain boundaries. We have termed this a “grain boundary ridge.” Grain boundary diffusion is a sintering process that occurs at the interface of two crystals, whereby mass migrates from the center of the contact to the surface of the bond. Since mass tends to sublimate from sharp features toward smaller curvature surfaces through vapor diffusion, a ridge developed by grain boundary diffusion will readily sacrifice mass to the surrounding ice surfaces. A mass balance between vapor and grain boundary diffusion based on the observed geometry is considered. This analysis indicates grain boundary diffusion may play a far more significant role than generally acknowledged. While this study was restricted to ice, it may have implications for other crystalline materials.

A constitutive theory for snow as a continuous multiphase mixture

Abstract Snow on the ground is viewed in this formulation, as a saturated two-phase granular material comprised of small grains of ice with interstitial pores filled by a single vapor. The snow is considered as a continuous mixture in which the ice and vapor constituents are themselves treated as individual but interacting continua. Mathematical modeling of the Snow is accomplished using a relatively recent continuum theory for mixtures where the individual constituents are physically separate. This approach considers the volume fraction occupied by each constituent as an additional kinematic variable. Therefore, in addition to the balance equations for mass, linear momentum, angular momentum and energy, usually applied in continuum mechanics, an equation which accounts for changes in the volume fraction, called the balance of equilibrated force, is included. Balance equations for each constituent as well as for the mixture are considered. The immiscible nature of the constituents allows constitutive equations to be developed which depend only on those variables which pertain to that constituent. Exchange between the ice and vapor is aecounted for by interaction terms which enter the theory through the balance equations for the constituents. Forms for these interaction terms are used which guarantee that the entropy inequality is not violated. A one-dimensional analysis of an isothermal homogeneous snow cover suddenly subjected to a colder surface temperature reveals a thermodynamically active zone associated with a large temperature gradient, initially located near the top surface, but which moves downward with time in a wavelike fashion decreasing in intensity. Slight differences in constituent temperatures are calculated during the more active transient phase in conjunction with a decrease in snow density.

Further Results on Studies of Temperature-Gradient Metamorphism

A correlation between temperature gradient in snow-pack and material strength is found to exist in laboratory studies on temperature-gradient metamorphism of snow. These results are in agreement with earlier field investigations and eliminate diurnal solar and temperature variations as reasons for the existence of the maximum temperature gradient in the zone of minimum strength. Also the laboratory studies have indicated that locally dense layers such as ice crusts tend to enhance weakness directly below the crust due to local alteration of the thermal regimen. Further studies are continuing to describe the thermodynamic process of temperaturegradient metamorphism more exactly. RESUME. Nouveaux ri?Sltitats des etudes de metamorphose de gradient thermique. Au cours detudes en laboratoire sur la metamorphose de gradient thermique de la neige on a trouve une correlation entre le gradient thermique de la neige et la resistance mecanique du materiau. Ces resultats sont coherents avec des investigations de terrain anterieures et eliminent le rayonnement solaire diurne et les variations de temperatures comme causes de Iexistence dun gradient thermique maximum dans les zones de moindre resistance mecanique. Les etudes de laboratoire ont egalement montre que des niveaux localement denses comme les croutes de glace ten dent it engendrer une zone fragile directement sous la croute en raison de Ialteration locale des regimes thermiques. De nouvelles etudes sont poursuivies pour decrire plus exactement les processus thermodynamiques de la metamorphose de gradient. ZUSAMMENFASSUNG. Weitere Ergebllisse iiber den Metamorphismus unter einem Temperaturgradienten. Aus Laboruntersuchungen liber den Metarnorphismus von Schnee unter einem Temperaturgradienten geht hervor, dass eine Korrelation zwischen dem Temperaturgradienten in der Schneedecke und der Festigkeit des Material s besteht. Diese Ergebnisse stimmen mit frliheren Felduntersuchungen liberein ; sie schliessen tagliche Schwankungen der Sonneneinstrahlung und der Temperatur als Ursache des Auftretens des maximalen Ternperaturgradienten in der Zone geringster Festigkeit aus. Die Laborversuche haben weiter gezeigt, dass lokal dichte schichten. wie z.B. Eiskrusten. infolge lokaler Anderungen der Wiirmehaushalts zu einer Erhiihung der Nachgiebigkeit direkt unter der Kruste flihren. Weitere Studien werden unternommen, um den therrnodynami schen Vorgang des Metamorphismus unter einern Temperaturgradienten noch genauer beschreiben zu kiinnen. INTRODUCTION During the process of temperature-gradient metamorphism of a snow-pack, an intricate relationship exists between temperature gradient in the snow-pack and material density, strength, crystalline properties, and the transfer of heat and mass in the pack. In order to develop a mathematical formulation of this complicated thermodynamic problem, a better grasp of the physical processes taking place at the crystalline level is needed. For the past several years, field and laboratory studies (Bradley and others, 1977lal, Ibl; Armstrong, 1980) have been under way in order to gain a better understanding of this problem. In earlier papers (Bradley and others, 1977[a], I b]), field investigations of temperature-gradient metamorphism indicated that a temperature-gradient anomaly existed at the point of weakest strength in alpine snow-pack. In these papers, it was noted that the weakest snow was usually subhedral depth hoar rather than the fully developed euhedral depth hoar at the bottom of the snow-pack. This subhedral zone, was often found 100 to 150 mm above the ground surface, and in this zone both minimum strength and maximum temperature gradient occurred. These field observations were not fully verified by laboratory tests (Bradley and others, 1977[a]). The laboratory tests did indicate that the weakest snow was subhedral depth hoar located above the fully developed euhedral depth hoar, but no temperature-gradient anomaly was detected. The laboratory results did show a non-linear temperature gradient in the snow sample, but no local maximum in the temperature gradient was detected. This discrepancy was confusing, since under controlled laboratory conditions, a temperature-gradient anomaly such as seen in the field investigations should have been detected if it did

A method for evaluating shockwave propagation in snow

Abstract Shockwaves in snow are analyzed by developing and then solving a set of governing jump equations which are defined in terms of the jump in certain material parameters across the shockwave. This method represents an alternative means to studying shockwaves, since most previous solution techniques have involved direct integration of the governing differential wave equations. However, since this classical means is normally difficult, the use of jump equations represents a viable means of determining stress wave properties. The two methods are compared for propagation of plastic shockwaves in snow, and some comparison to data is made. The use of jump equations is shown to give results which are similar to those obtained with the direct method.

Preliminary experimental evidence of heating at the running surface of avalanching snow

At the Montana State University Avalanche Research Site, instrumentation has been installed to measure temperatures, flow depth, and velocities during an avalanche. Five thermocouples have been installed along a 30-m section of the avalanche running surface. Temperature time histories were collected during several avalanches at the flow running surface. The flowing snow at the running surface did show a temperature increase as it progressed down the slope, but did not frequently approach the melt temperature. Snow samples were collected before the tests in the release zone and after the avalanches in the debris for microstructural comparison. A computed tomography (CT) X-ray scanner was used to obtain images of the microstructural details of the pretest and debris snow samples. Using the microstructural parameters from the CT images, the growth of the new bonds in the debris was analyzed using a vapor diffusion sintering model. New bonds were shown to grow rapidly at the expense of small high-energy structures that resulted from the avalanche. The analysis showed vapor movement and sintering of new bonds due to surface curvature differences may be a significant debris bonding mechanism in snow that does not approach melt temperatures during an avalanche.

A numerical evaluation of flexible footing settlement into uniform snowcover

Abstract Finite difference equations are developed to analyze the deformation of snow subjected to flexible foundation loading. A constitutive equation which describes the response of snow to long term finite strains is used in the solution. The results are compared with the available experimental data. Effects of footing size and shape on the settlement of snow are discussed. Stress distribution in the snow-mass is plotted. The settlement and effect of load on settlement are found to agree with the experimental data. The stress distribution under the footing is similar to the stress distribution obtained by the Boussinesq solution and agrees with experimental data obtained by others. For a good quantitative agreement between theory and experiment, the effects of equitemperature metamorphism should be included in such solutions.