FAILURE OF SNOW SLOPES
Snow is a complex material with unique properties such as high compressibility and thermodynamic instability. It is, therefore, not surprising that the failure mechanisms of avalanche slopes are not well understood, and are in fact, controversial.
Observations made in the starting zone of slab avalanches are as follows: slabs occur almost exclusively on planar slopes, inclined between 30 and 50 degrees with a strong peak occurrence at about 40 degrees. The upslope tensile fracture (crown surface) is nearly perpendicular to the main shear plane (bed surface). The side fractures (flanks) tend to zigzag downslope, oscillating between tensile and shear fractures. Unstable slabs usually consist of a strong, stiff layer resting on a weak substratum; thickness of the weak layer varies from less than 1 cm to over 10 cm. Computed strength/load ratios evaluated at observed bed surfaces have a wide variance; some of the variance may be removed with improved in-situ tests.
A broad model of slab instability is proposed as follows: if the slab substratum is weak, tensile stress and hence elastic energy will increase substantially in the slab, which becomes primed for tensile fracture. Any tensile disturbance will jar the already weakened substratum and initiate shear fractures; in turn, the shear fractures cooperate to drive the tensile fractures. Thus, fracture will propagate catastrophically over a wide area before the snow can rebond to heal substratum weakness.
It is customary to consider that a snow avalanche path consists of three zones: starting zone, track, and runout-deposition zone. The failure process begins in the starting zone, and then - similar to all rock slides - the developed energy and other dynamic characteristics depend on the relief of the track and the amount of material that can be entrained into the avalanche as it gains momentum. A comprehensive discussion with a substantial bibliography of the overall avalanche phenomenon, including starting zone failure, avalanche motion, ice avalanches, avalanche control, etc., is given by Mellor (1968). The present discussion will be restricted to a study of the failure processes that occur in the starting zone, and will not touch upon the interesting work on avalanche motion and destructive forces. (For a discussion of avalanche dynamics, the reader is referred to a companion paper by Mellor in this volume, Chapter 23.)
Snow slope failure is far from completely understood, and all present work is in part speculative and controversial. This chapter will attempt to bring together the various schools of thought, and to tie observations and existing theories together into a broad qualitative model.
THE MOUNTAIN SNOWPACK
The two main boundaries of the snowpack are the snow-atmosphere interface, and the snow-ground interface; these are referred to, respectively, as the snow surface and the ground surface. The snow surface is a moving boundary that rises during periods of snow deposition and falls as the snowpack ablates or densifies. Most layers within the mountain snowpack densify by several hundred percent in the time between deposition and ablation. The high compressibility of snow is a rare property not generally found in solid earth materials.
Depending on atmospheric conditions at time of deposition, layers of new snow range in density from 30 to 300 kg/m3. Density of new snow increases with windspeed measured in the vicinity of the deposition area. During relatively light winds (1-10 m/s), snow crystals are deposited nearly intact in a rich variety of hexagonal forms (LaChapelle, 1969). These light-wind specimens have typical dimensions on the order of 1 mm. As the windspeed increases, the crystals are transported considerable distances before becoming permanently attached to the snow surface. During the transport process, the crystals bounce along near the snow surface, and are therefore subject to erosion, fragmentation, and sublimation. The vast majority of wind-deposited particles are irregularly shaped ice grains with maximum dimensions on the order of 0.1 mm. These small grains pack into relatively dense layers.
Although large-grained, low-density snow is often found in the starting zones of avalanche paths, most of the new snow deposited in starting zones is wind-transported and therefore tends to be small-grained and dense. It is also evident that wind transport will not build purely homogeneous layers; significant variations (order 10%) in density and thickness are observed at all stratigraphic levels in the starting zone snowpack.
As soon as a snow crystal is incorporated into the pack, it fastens to its neighbors and participates in several dissipative processes that occur continuously throughout the ice-pore structure. These processes are due to the freedom of the ice grains to move into pore space, and to the thermodynamic instability of the ice-pore structure at temperatures normally encountered in the mountain snowpack (-40 degrees C < T < 0 degrees C). At first, the dominant process is an incremental collapse of the ice-pore structure caused by the transformation of snowpack weight (body force) into high-stress concentrations at the grain-to-grain contacts. The grains slide and rotate into the available pore space, although neighboring grains remain more or less linked. These grain motions may increase new snow density by 50% in 24 hours (for example from 100 to 150 kg/m3.) As the density increases, incremental collapse is replaced by viscous (or plastic) flow of the ice skeleton. As the density continues to increase, pore vacancies become less available until bulk shrinkage is no longer possible, and the layer reaches a fairly stable density.
In seasonal snowpacks, densification beyond about 500 kg/m3 is seldom observed in response to overburden loads alone, although melting and refreezing may produce high-density crusts. When the pores within a crust or layer no longer "communicate", the snow layer has transformed to ice, by definition. Pores cease to "communicate" at about 800 kg/m3.
At the same time that collapse and viscous flow are densifying the snowpack, other dissipative processes are altering the ice-pore texture. This second set of processes involves H20 molecular transport through pore space, over ice surfaces, and through the bulk of the ice grains. Recent studies summarized by Yen (1969) show that H20 transport occurs mostly by vapor diffusion in the pore space, and to a lesser degree by surface and bulk mechanisms. In any case, mass is depleted from relatively high-energy sites such as convex surfaces and added to relatively low-energy sites such as concave ice surfaces. The net effect of this transfer is to increase the neck thickness between individual grains (Fig. 1), and thus strengthen the ice-pore structure. This strengthening process, called sintering, begins as soon as ice grains are brought into contact. Since new snow grains have rather high curvatures, sintering proceeds very rapidly at first; snow strength increases dramatically 24 hours after a snowfall. Sintering diminishes gradually as curvatures are equalized.
Fig. 1. As snow densifies, grains lose their original texture, become rounded,
and sinter together. Left photo by E.R. LaChapelle: newly fallen snow,
density about 150 kg/m3; center photo by Daisuke Kuroiwa: thin section
of medium-density snow, about 350 kg/m3; right photo by E.R. LaChapelle:
thin ice crust from mountain snowpack.
Sintering is in competition with a mass redistribution process known as temperature-gradient metamorphism (TG- metamorphism). During TG-metamorphism, H20 vapor is transported from relatively warm to relatively cold stratigraphic levels so as to reduce the temperature gradient. At those levels where TG-metamorphism dominates, vapor is deposited on crystal faces, and not necessarily on the necks between grains. This causes the grains to enlarge and become more angular. Grain enlargement without corresponding neck increase tends to weaken the ice- pore structure. TG-grains may enlarge to several millimeters; the larger, more angular grains are called depth hoar (Fig. 2). Generally, the growth period of the depth hoar is on the order of weeks.
Because the snow surface temperature can fluctuate well below 0 degrees C, whereas the ground surface temperature remains rather steady at about 0 degrees C, temperature gradients are always present in the mountain snowpack. Gradients are highest early in the winter when the snowpack is relatively thin and air temperature is relatively cold. Gradients diminish in the spring, and the snowpack approaches an isothermal state of about 0 degrees C. As a general rule, gradients in excess of 10 degrees C/m are sufficient to drive TG-metamorphism. Since the TG-process depends on vapor transport, the rate of grain enlargement is also strongly controlled by density.
Fig. 2. In the presence of strong temperature gradients
(about 10 degrees C/m or greater), grains re-crystallize from rounded texture
(left photo) to coarse enlarged grains (center photo). If recrystallization continues,
grains may enlarge to about 8 mm (right photo). Photos by E.R. LaChapelle.
Thick layers of TG-grains, O 1(10 cm) thickness, are found just above the ground surface. Thinner TG-layers, O(1 cm) thickness, are found at midstratigraphic levels, sometimes just above or beneath a crust. Under certain temperature and humidity conditions, TG-crystals may grow directly on the snow surface from atmospheric moisture. These so-called surface hoar crystals form as a very weak, thin layer,O(1 mm) thickness. TG-layers at all stratigraphic levels are known to play an important role in snow slope failure.
Sintering and TG-metamorphism are characteristic of the dry snowpack. Snow properties change most drastically when free water is introduced by rain or melting. Free water may percolate down to a barrier level, such as a crust or the ground, and promote stratigraphic weakness by dissolving bonds at that level. When the free water freezes, it cements grains together, forming a hard, strong crust. Repeated melt and freeze cycles produce large, polycrystalline aggregates.
As the result of the above processes, the mountain snowpack evolves toward a complex assortment of layers. In the broadest sense, slope failure occurs because the stress in some layer exceeds the strength in that layer. The next section provides a closer look at the mechanical properties of snow, with special emphasis on those properties that relate to a stress and failure analysis of the snowpack.
STRESS AND FAILURE ANALYSIS OF SNOW
If a snow layer is loaded at a sufficiently high rate, then the dissipative processes described in the previous section cannot keep pace with the energy input to the layer. The layer eventually fractures. Slab fracture may propagate near the speed of sound O(100 m/s), or relatively slowly, O(1 m/day). Rapid fracture is observed at all snow temperatures; slow fractures are usually restricted to wet slabs (Figs. 3 and 4).
Fracture of snow can be viewed in terms of a Griffith-like energy balance. Elastic strain energy builds up in the ice skeleton until some limit is reached, whereupon fracturing dissipates part of the energy and converts part into the surface energy of new fracture faces. Very little is known about the details of the energy balance either at the continuum or microscopic level, and the theoretical and experimental work needed to compute the balance has begun only recently (Salm, 1971; Brown et al., 1973).
*O is abbreviation for "order of magnitude of".
Fig. 3. Fast, brittle fracture of snow slab triggered by skier. Photos by R. Ludwig.
Fig. 4. Slow fracture of a warm snowpack (snow retaining
structures in background) Photo by H. Frutiger.
The constitutive complexity of snow is a major obstacle to formulating a fracture criterion. How is snow to be classified as a material? The answer seems to be that an investigator can find within snow almost any constitutive response he looks for: elastic, viscous, plastic, etc. In a recent study, Brown et al. (1973) modeled snow as a nonlinear viscoelastic material. They used a multiple integral representation to the third order, and were able to predict material response for arbitrary loading and unloading paths on the basis of nine material coefficients. However, their study did not completely model the response of snow since the experiments were restricted to nearly infinitesimal deformation at approximately constant density (290 +/- 10 kg/m3) and constant temperature (-10 degrees C).
Considering the constitutive complexity of snow, it is natural to search for precursor failure signals which supplement stress-strain and stress-strainrate data. In this connection, acoustic emission studies are in progress at Montana State University (MSU) (St. Lawrence et al., 1973; St. Lawrence and Bradley, 1973). The MSU group loaded snow samples at various rates and identified sonic and ultrasonic burst patterns prior to failure. They found that snow which is loaded, unloaded, and reloaded exhibits a Kaiser effect. Most recently, St. Lawrence and Bradley (1974) have explained acoustic phenomena in terms of dislocations and microscopic mechanisms.
The strength of any material, and snow is no exception, is controlled by inhomogeneities or flaws. Dislocations are examples of small-scale flaws. Snow layers contain many types of larger-scale flaws. As an example, density inhomogeneity caused by wind action was mentioned earlier. Other examples of large flaws are non-snow protrusions such as rocks and trees. Locally weak regions of TG-grains can also be regarded as flaws.
In essence, as the volume of a material increases, the probability of finding a flaw increases, and hence the strength decreases. This statistical effect has been studied in detail for engineering materials. The dependency of snow strength on volume has been investigated recently by Sommerfeld (1971), who compared the tensile strength of two volumes in a centrifugal spin test; the mean strength of the larger volume (2.3 * 10-3 m3) was approximately one-half the mean strength of the smaller volume (5 * 10-1 m3). The variance was much greater in the smaller samples.
Numerous measurements have been made of strength indices for small snow samples (Butkovich, 1956; Keeler and Weeks, 1967; Keeler, 1969; Martinelli, 1971). Despite large scatter, the strength indices for medium- and high- density snow seem to fit the trend predicted by Ballard and Felt (1966):
where o is the strength index, k is a material constant, and n is the bulk porosity of the sample.
For tensile tests, k is approximately 2.5 * 106 N/m2, and varies depending on the type of test, sample size, and geographical location of snowpack. The values of k for shear tests are usually less, sometimes an order of magnitude less. This difference is rather hard to explain since standard theory predicts that tensile strength cannot exceed twice the shear strength. Indeed, most materials have relatively small fracture resistance in tension.
The large scatter around Ballard and Felt's equation  is to be expected since any strength index, especially at low snow densities, should be a function of snow texture as well as porosity. For example, the strengths of porous materials are often expressed as functions of grain size and porosity. In the studies of Keeler and Weeks (1967), Keeler (1969), and Martinelli (1971), a qualitative distinction among samples on the basis of snow texture improved the fit of strength predictions. Unfortunately, snow texture parameters such as grain size are not readily identified, and therefore no one has successfully related snow strength to quantitative measures of texture.
Alpine snow samples are not easily transported from starting zones to laboratory; it is often advantageous to test starting zone snow in situ. Keeler and Weeks (1967) describe and compare several types of in-situ tests, including the shear frame, shear vane, centrifugal spin test, and several types of penetrometers. For the purpose of slope instability evaluation, the shear frame developed by Roch (1966a, b) has a decided advantage because it is the only in-situ test known at present that measures the strength index of a thin layer. However, field tests show that the shear frame index is sensitive to the frame area, rate of loading, and operator variability. For example, a frame with 100 cm2 area gives an index which is 10-20% higher than a 500 cm2 frame; this may be additional confirmation of a statistical size effect. In any case, the 100-cm2 stability indices, which will be presented in the next section, have too high a variance for confident slope stability evaluation. The general problem of how to measure an index of snow slope stability is today largely unsolved
SLAB AVALANCHE OBSERVATIONS
On the basis of starting zone appearance, snow avalanches are classified into two categories: point avalanches and slab avalanches. The point avalanche initiates within a cohesionless layer located immediately below the surface. The failure is similar to the rotational failure of a cohesionless soil slope, except the initial snow failure is quite localized and may involve little more than a small lump of snow. As soon as it breaks loose, the unstable lump rolls down the slope, bulldozing out a widening pattern which, when observed from a distance, gives the distinct impression that failure originated at a well-defined point (Fig. 5). During storms, point avalanches occur frequently where the slope angle is steeper than about 45 degrees. This gradual snow transfer minimizes the load on high-angle slopes, In the late spring, when the snowpack is wet and cohesionless, point avalanches may reach hazardous proportions. Otherwise, they are rarely a threat unless in descent they trigger a slab avalanche, which is the main concern of this section.
Fig. 5. Point avalanche. Photo by E.R. LaChapelle.
Slab release is characterized by an initial spectacular propagation of cracks followed by the crumbling of a slab-like region of the slope into numerous blocks with dimensions on the order of about 1 m (see Fig. 3). Unless the track is relatively short, slab blocks are pulverized as they slide and topple downslope. Occasionally, the blocks of a relatively hard slab may survive a lengthy trip.
Whereas the initial failure location of a point avalanche is easily identified, it is not immediately clear, and is in fact a controversial subject, where slab failure initiates: deep in the slab, or at the snow surface. However, it is clear that the stability of a slab depends on the stress state and fracture toughness of a large, cohesive mass. For this reason, slab failure more nearly resembles the block glide failure of cohesive rocks than the rotational failure of cohesionless soils.
Fig. 6. Slab avalanche at Alta, Utah, January 1970. Nomenclature
of slab fracture surfaces shown below.
After slab failure, sharply defined fracture surfaces which outline the slab boundaries remain at the starting zone. These fracture surfaces (Fig. 6) are designated as follows:
bed surface: main sliding surface of slab (shear type of failure)
crown surface: upslope fracture surface (tension fracture)
stauchwall: downslope boundary (shear fracture)
flank surfaces: two side boundaries of the slab (combination of tension and shear fractures)
Fig. 7. Bed surface inclination
of 100 slab avalanches; samples
from Switzerland, Japan, and U.S.A.
Several investigators have toured the starting zones after slab release to study geometry of fracture surfaces and to measure properties of snow remaining on the slope above the crown; they include Haefeli (1939), Roch (1966b), Shoda (1967), Perla (1971), and Wakabayashi (1971). From these published observations and from many unpublished observations emerges the following description of slab geometry and snow properties:
(1) Observed bed surfaces are essentially flat; the minimum radius of curvature of the bed surface is rarely less than O(102 m), and is most often O(103 m). The number of concave bed surfaces tends to exceed the number of convex bed surfaces. (Concave means that the bed surface inclination steepens the closer one climbs up to the crown.)
(2) With rare exception, the inclination of the bed surface to the horizontal ranges between 30 and 50 degrees. For medium to large slabs, the bed surface inclination has a strong peak between 35 and 40 degrees (Fig. 7). There is evidence that the peak shifts to between 40degrees and 45 degrees if small slabs are included in the sample.
(3) The angle between the bed surface and the crown surface (a in Fig. 12) is on the average 90 +/-10 degrees. The angle varies along the crown with an overall tendency to slightly exceed 90 degrees. The fact that a is approximately 90 degrees suggests again that snow slab failure is more analogous to block glide failure of rock (or cohesive soil) rather than to rotational failure of cohesionless soil, since for rotational failure, the average of a is greater than 90 degrees, and often approaches 135 degrees.
(4) There is an observed tendency for crown fracture to propagate as a relatively smooth arc between the flanks; however, the fracture trajectory is strongly determined by natural stress concentrations or pinpoints such as rocks and trees (Fig. 8).
(5) Maximum height of the crown surface is O(1 m). Usually, but not always, the crown height tapers off toward the flanks.
(6) The thickness of the slab layer tends to taper off above the crown; in some cases, the crown is immediately below a cliff band.
(7) In some cases, the crown fracture arcs around as a semicircle and a separate flank section is not observed. If a flank section exists, it often has a peculiar sawtooth pattern which consists of intersecting tension and shear fractures (Fig. 9).
(8) Stauchwalls are not always observed, possibly because the moving slab blocks obliterate this downslope feature. In a large number of cases it is also possible that the bed surface tapers up gradually to intersect the snow surface, and therefore the stauchwall surface degenerates to a line (toeline).
(9) The flank-to-flank dimension tends to exceed the crown-to-stauchwall dimension. Notable exceptions are slabs squeezed by gully walls (Fig. 10).
(10) The observed ratio of the flank-to-flank dimension to slab thickness varies between O(10) and O(103), and is typically O(102).
Little information is available concerning density, temperature, strength, grain texture, and other slab properties. Table I summarizes twenty-three slab measurements made by Perla (1971) at Alta, Utah, during the winter season 1969-1970. As an example of these measurements, slab no. 7 from Table I is diagrammed in Fig. 11.
Fig. 8. Example of extensive crown fracture linking several natural
pinpoints; Alpine Meadows, California, February 1972.
Photo by N. Wilson.
Fig. 9. Flank of slab avalanche; Alta, Utah, January 1973.
Fig. 10. Slab confined by gully walls; Rocky Mountain
National Park, Colorado, July 1973. In this example,
flank length exceeds crown length; however, in the
absence of confinement, crown length tends to exceed
flank length as shown in Figs. 6 and 8.
Fig. 11. Example of profile study of slab crown: slab no. 7, Table I.
Note that the shear frame index shows a definite weakness at the observed bed surface. However, it is difficult to explain for this case and for many other cases why failure did not occur at an alternative stratigraphic level (for example, the graupel layer in Fig. 11) where the strength-to-load ratio is lower.
The columns in Table I are explained as follows: column 4 is the "trigger" mechanism of the slab. Many avalanche paths in developed areas are tested and controlled by high-explosive charges equivalent to about 1 kg TNT per target. The explosives are either hand-thrown onto the targets, or launched by artillery. Some of the smaller avalanche paths in ski areas are ski-released by professional control teams who take necessary precautions. Slab no. 15 may have released naturally, although there is a possibility that it released sympathetically during artillery control of neighboring slopes.
Column 6 summarizes the grain texture observed in the slab substratum at the approximate bed surface center. Grain textures can be divided into two main categories: TG-grains and ET-grains. The former are relatively coarse grains associated with temperature-gradient metamorphism (as discussed earlier) and the latter are small, well- sintered grains that have metamorphosed in the absence of strong temperature gradients (equitemperature metamorphism). TG-grains were found in the majority of the substrata investigated.
Column 7 gives the maximum thickness of the slab layer as measured at the crown. The mean of column 7 is 0(1 m); this thickness is typical of slabs which pose a threat to life and property. Small slabs, about 10 cm thick, are quite numerous and usually harmless. The thickest slabs observed anywhere are about 5 m thick. These giants usually occur in deep wind-drift pockets. Slab no. 17 is a thick slab by all standards.
Columns 8, 9, and 10 summarize snow density measurements taken at the crown, about halfway between the flanks. Column 8 gives the average density of the slab. Column 9 gives the density of the heaviest layer in the slab profile; column 10 gives the density of the lightest layer. The respective means of columns 8, 9, and 10 are 228, 285, and 155 kg/m3.
The shear frame index at the bed surface is given in column 11. Reported values are the average of three measurements. For comparison, the shear frame index measured 5 cm above the bed surface is given in column 12. Note that the mean shear index above the bed surface is 50% higher than the mean index at the bed surface. Thus, a simple qualitative model of a snow slab is a stack of relatively strong layers resting on a relatively weak layer.
The snow temperature at the bed surface is given in column 13. It is not known if there is any special significance to the fact that observed temperatures seem to fall in the narrow band -15 degrees C < T < 0 degrees C. This band may only reflect the climatological peculiarities of Alta, Utah. On the other hand, it would be interesting to obtain temperature data on avalanches that have released in the colder mountain ranges of the world.
The texture of the snow observed at the extension of the bed surface into the crown varied considerably for the twenty-three cases. In many cases, the bed surface was in the TG-layer nearest to the snow surface. However, there were several cases where the bed surface was in an ET-layer. For almost all of the ET-cases, no definite plane of weak texture could be observed visually (although the shear frame index generally indicated a weakness). In some cases, special crystal forms such as graupel and surface hoar were observed. In a few cases, the slab failed immediately above a hard crust.
Column 14 gives the ratio of the shear frame index at the bed surface to the shear stress on the bed surface. The shear indices were corrected for the Coulomb-Mohr effect (Roch, 1966a); the shear stress and normal stress were computed from the density profile and the bed surface inclination. As discussed earlier, the variance is too high for comfortable stability evaluation. Much of the variance can perhaps be explained by the inadequacy of the shear frame; some of this variance might be removed by employing a larger frame. However, a significant portion of the variance is caused by the variation of snow properties around the crown. In a series of measurements made on the crown of a ski-triggered avalanche at Alta, Utah (Sunspot avalanche, January 20, 1973), the strength-to-load ratio around the 0.75 m thick crown was found to vary between 1.4 5 and 2.46. This suggests that failure originated where the strength-to-load ratio was low, and propagated into a stronger section of the crown. This further implies that a single strength-to-load test at an arbitrary location is unlikely to measure the "weakest link" in the slab structure.
The sequence of events preceding slab release is apt to vary considerably depending on meteorological conditions, and also on the immediate trigger,
which may be an artificial explosive blast of enormous energy or a subtle internal disturbance. The following are a few of the wide variety of avalanche triggers:
(1) New snow load. There is an observed high probability of avalanche occurrence during or immediately after a severe storm. Snow strength due to sintering cannot keep pace with the increasing stress caused by the load of new or windblown snow.
(2) Wet snow instability. Avalanches tend to occur during thaw caused by rain or heat energy. Wet slabs are triggered by the combined effects of water weight and bed surface lubrication.
(3) Ski loads. A ski traverse across an unstable slab is often an effective way to trigger instability. The technique employed by professional control teams is to cut quickly across the crown and cause crown fracture. A strong downhill push is applied to the slab by the back of the skis to reinforce fracturing.
(4) Shock. Examples of natural and artificial shock energy which cause avalanche release are: earthquakes, cornice falls, artillery bursts, and sonic booms.
Recent theoretical studies of release mechanisms have been made by Haefeli (1967), Sommerfeld (1969), Perla and LaChapelle (1970), Brown et al. (1972), and Lang et al. (1973). As pointed out by Sommerfeld, there is probably no single mechanism that applies to all slab release; one must invoke many mechanisms to explain the wide variety of natural and artificially induced avalanches. Surely, this problem is not unique to snow avalanches, and other geophysical hazards such as earthquakes and landslides cannot be explained by a single unifying mechanism.
Despite the diversity of slab phenomena, it is possible to make a broad distinction between stable and unstable trends in snow slab evolution. If all other factors remain the same, slab densification is a stable trend. The basic explanation is that snow strength increases exponentially with density (refer to equation [11 ), whereas stress can only increase linearly with density. For this reason, slab avalanches are not observed where the density exceeds about 500 kg/m3. Also, as discussed by Mellor (1968), ice avalanches usually initiate as the slow creep of glaciers which overhang cliffs; this bears little resemblance to the mechanism of snow slab failure.
What is the sequence of events for an unstable trend? The most important initial factor seems to be a substratum weakness relative to the slab load. Although details are only speculative at this time, the sequence could follow the basic model outlined by Perla and LaChapelle (1970):
(1) Due to increasing stress, or decreasing strength as a result of metamorphism, there is an increasing strain and/or strain-rate at the bed surface. The physical processes that occur during this bed surface softening are unknown, but could possibly involve a rate process whereby the rate of bond breakage increases beyond the rate of sintering.
(2) Since the shear support begins to fall to below what is required by the equilibrium conditions, the maximum principal stress t1 (Fig. 12) must increase in the crown region, and elastic strain energy must begin to accumulate in the slab. As the elastic energy builds up, the slab becomes primed for fracture.
(3) Any sudden disturbance of equilibrium may trigger catastrophic fracturing. The extensive fracturing needed to cut out the slab around the periphery and at the bed surface is probably a cooperative phenomenon; tension fractures reinforce shear fractures, and vice versa.
(4) The crux of the model is that the elastic energy stored in the slab is converted through tension fractures into the dynamic jolt needed to overcome the residual strength of the bed surface. Initiation of bed surface fracture removes shear support, increasest1, alines t1 in the slope parallel direction, and thus sets the stage for further tension fracturing. In this way, the two types of fractures cooperate to cut loose the entire slab.
(5) If catastrophic failure does not occur, the shear strength of the substratum will eventually begin to recover through sintering, t1 will relax, and the slab will revert to a stable trend.
Fig. 12. Principal stress convention used in this chapter. Algebraic
maximum principal stress is t1 and forms an angle 6 with the x-direction.
Angle a formed by crown and bed surface is nearly perpendicular
(+/-10 degrees). It is hypothesized that prior to failure, 5 shifts to
Fig. 13. Envisioned mechanism of cooperation between shear and tensile fractures.
The alining of t1 with the slope parallel direction deserves more discussion. It is generally accepted from laboratory studies of solid-earth materials that tensile fractures tend to aline perpendicular to L. Since the crown surface is invariably perpendicular to the bed surface, t1 must somehow reorient to the slope-parallel direction. The reorientation may initiate slowly with strain softening of the bed surface, but a sudden alinement probably occurs at the moment of fracture. This seems possible if the tensile fracture moves with or lags slightly behind the shear fracture as depicted in Fig. 13. It is rather difficult to explain the alinement of t1 over the entire crown length solely on the basis of the pre-fracture stress.
The above model of bed surface disturbance is not all inclusive. For example, it is believed that instability does not always originate at the observed bed surface, but instead begins by either slow or instantaneous collapse of a thick, weak layer that may be located somewhat below the observed bed surface (Bradley, 1970). Due to bridging effects, collapse generates a high bending stress and hence a large amount of elastic energy within the slab. Tensile fracture will release the energy, and jar the slab loose on a bed surface which is not necessarily contained within the layer that collapsed initially. In the events leading up to failure, strain softening of the bed surface may have played a minor role, and it is only after receiving a dynamic shock that the observed bed surface is activated as a failure plane.
With regard to how natural stress concentrations and pinpoints influence the failure process, there is a striking analogy to current laboratory experiments on rock fracture. Accumulating evidence indicates that the introduction of small holes of arbitrary geometry into rock specimens does not weaken the specimen by an appreciable amount, providing the artificial holes are small compared to the specimen size; that is, a rock specimen with an artificial circular hole will not fall at one-third of the tensile stress of an unflawed specimen. However, once failure initiates, fracture trajectories usually intersect the artificial flaw. The same thing probably happens on a large scale within snow slabs. Stress concentrations are always present, but it is not until the nominal stress t1 reaches a high enough level that the stress concentrations influence failure and determine fracture trajectories.
Is it possible to monitor avalanche slopes for precursor signals of slab failure? Presently, the favored candidates for precursor data are acoustic emission signals. On the basis of the above mechanisms it seems very likely that many slab releases are preceded by gradual increase of tensile stress. In principle, it should be possible to monitor acoustic signals for tension buildup within the slab profile. The other possibility would be to monitor either the yield along a potential bed surface or the gradual collapse of a weak layer. Search for precursor signals on actual avalanche slopes is part of the active research program now underway at Montana State University, where laboratory studies of acoustic emission have provided the fundamental groundwork.
Hopefully, the search for precursor signals will pay off with more under standing of slope failure mechanisms. Meanwhile, several other experimental tasks lie ahead. The need for a better measure of shear strength was mentioned earlier. With the aid of the strength measure it may be possible to systematically catalog unstable stratigraphies and possibly discriminate between stable and unstable trends. Related experiments include a systematic study of slab geometry, collection of data on the variation of properties throughout the slab, and photography of slabs in the process of fracturing. Finally, a practical problem tied closely to the theory of release mechanisms is how to optimize avalanche hazard control by artificial release of slabs. Important questions are: What type of explosive is most effective for activating instability? How much explosive is needed for given conditions? Which is the most effective target: crown, stauchwall, or flank regions? The answers will no doubt suggest an improved model of slab release. In return the improved model will lead to better methods of avalanche hazard prediction and control.
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