Dry-snow Slab Avalanche Release Research Articles

Modeling snow slab avalanches caused by weak-layer failure – Part 1: Slabs on compliant and collapsible weak layers

Abstract. Dry-snow slab avalanche release is preceded by a fracture process within the snowpack. Recognizing weak-layer collapse as an integral part of the fracture process is crucial and explains phenomena such as whumpf sounds and remote triggering of avalanches from low-angle terrain. In this two-part work we propose a novel closed-form analytical model for a snowpack under skier loading and a mixed-mode failure criterion for the nucleation of weak-layer failure. In the first part of this two-part series we introduce a closed-form analytical model of a snowpack accounting for the deformable layer. Despite the importance of persistent weak layers for slab avalanche release, no simple analytical model considering weak-layer deformations is available. The proposed model provides deformations of the snow slab, weak-layer stresses and energy release rates of cracks within the weak layer. It generally applies to skier-loaded slopes as well as stability tests such as the propagation saw test. A validation with a numerical reference model shows very good agreement of the stress and energy release rate results in several parametric studies including analyses of the bridging effect and slope angle dependence. The proposed model is used to analyze 93 propagation saw tests. Computed weak-layer fracture toughness values are physically meaningful and in excellent agreement with finite element analyses. In the second part of the series (Rosendahl and Weißgraeber, 2020) we make use of the present mechanical model to establish a novel failure criterion crack nucleation in weak layers. The code used for the analyses in both parts is publicly available under https://github.com/2phi/weac (last access: 6 January 2020) (2phi, 2020).

Comparing measurements of snow mechanical properties relevant for slab avalanche release

ABSTRACTSnow properties relevant to the fracture processes involved in dry-snow slab avalanche release include weak layer specific fracture energy, slab elastic modulus and density. Various techniques exist to determine these snow mechanical properties, but it is presently unclear how values determined with different methods compare. In the laboratory, the 3-D microstructure of cm-sized snow samples is reconstructed by micro-computed tomography (μCT) so that density and elastic modulus can be computed. In the field, fracture energy and modulus are estimated based on particle tracking velocimetry (PTV) of the displacement field observed during propagation saw tests. Snow stratigraphy is measured with the snow micro-penetrometer (SMP) in either, field or laboratory. We compared SMP-derived properties to correspondingμCT- and PTV-derived values. Values of snow density related well toμCT results and so were SMP-derived elastic moduli related to PTV-derived values. By taking into account snow anisotropy a good relation between SMP- andμCT-derived moduli resulted suggesting the SMP-derived modulus characterizes the components of the modulus perpendicular to the axis of penetration. SMP- and PTV-derived values of fracture energy were correlated. The SMP can provide a bridge between scales and techniques, yet further improvements in signal interpretation are still needed.

A mechanically-based model of snow slab and weak layer fracture in the Propagation Saw Test

Dry-snow slab avalanche release is the result of failure initiation in a weak snowpack layer buried below a cohesive snow slab, which is then followed by rapid crack propagation. The Propagation Saw Test (PST) is a field experiment which allows to evaluate the critical crack length for the onset of crack propagation and the propagation distance. Although a widely used method, the results from this field test are difficult to interpret in practice because (i) the fracture process in multilayer systems is very complex and only partially explored and (ii) field data is typically insufficient to establish direct causal links between test results and snowpack characteristics. Furthermore, although several studies have focused on the critical crack length assuming linear elasticity for the slab, it still remains unclear how the complex interplay between the weak layer failure and slab fracture impacts the outcome of the PST.To address this knowledge gap, an analytical model of the PST was developed, based on the Euler–Bernoulli beam theory, in order to compute both the critical crack length and the propagation distance as a function of snowpack properties and beam geometry (e.g. beam length and slab height). This work aims to create a link between the two main outcomes of the PST, namely full propagation (END) and slab fracture (SF), and the quantitative results of critical crack length and propagation distance.Moreover, introducing empirical relationships based on laboratory experiments (Scapozza, 2004; Sigrist, 2006) between the elastic modulus, the tensile strength and slab density, it is possible to describe the onset of slab fracture for a given geometry of the PST using only the slab density. As a result, the model allows to reproduce the increasing trend of the propagation distance with increasing slab density, as observed in field experiments. For slabs characterized by low density, slab fracture occurs before reaching the critical crack length (SFb); for intermediate density values, slab fracture occurs after the onset of crack propagation in the weak layer (SFa); then, large densities lead to full propagation in the weak layer without slab fracture (END).

Seismic sensor array for monitoring an avalanche start zone: design, deployment and preliminary results

AbstractIn snow, acoustic emissions originate from the breaking of bonds between snow crystals and the formation of cracks. Previous research has shown that acoustic signals emanate from a natural snowpack. The relation between these signals and the stability of the snowpack has thus far remained elusive. Studies on other hazardous gravitational processes suggest that damage accumulation precedes major failure. If increased cracking activity could be detected in snow this might be used for avalanche prediction. We report on the development of a seismic sensor array to continuously monitor acoustic emissions in an avalanche start zone. During three winters, over 1400 sensor days of continuous acoustic data were collected. With the aid of automatic cameras and a microphone the main types of background noise were identified. Seismic signals generated by avalanches were also identified. Spectrograms from seismic signals generated by avalanches exhibit a unique triangular shape unlike any source of background noise, suggesting that automatic detection and classification of events is possible. Furthermore, discriminating between loose-snow and snow-slab avalanches is possible. Thus far we have not identified precursor events for natural dry-snow slab avalanche release. Detailed investigation of one dry-snow slab avalanche showed that signals observed prior to the release originated from background noise or small loose-snow avalanches.

Triggering of dry snow slab avalanches: stress versus fracture mechanical approach

Abstract This paper analyses the conditions for triggering of dry snow slab avalanches. As suggested by several Authors, we assume as a basic mechanism for avalanche triggering the mode II fracture of the weak layer lying beneath the stiff snow slab, i.e. we assume the presence of super-weak zones in the basal layer. By means of a linear elastic analysis, the shear stresses in the weak layer as well as the strain energy release rate caused by an increment of the super-weak zone are evaluated. Hence we introduce a stress failure criterion as well as an energy one. It is shown that the latter criterion can be seen as an extension of the criterion firstly proposed by McClung [McClung, D.M., 1979. Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release. Journal of Geophysical Research, 84(B7), 3519-3526.] for dry snow slab avalanche release. Finally we couple the two criteria, showing that the weak layer can fail only in a min–max band of thickness.

Snowpack observations and fracture concepts for skier-triggering of dry-snow slab avalanches

Abstract Dry-snow slab avalanche release is generally believed to proceed in three stages: 1) initiation of a local failure (crack), 2) widespread fast propagation of that fracture beneath the slab, and 3) detachment of the slab from its margins. To date, most field stability tests primarily assess the strength of the weak layer and thus relate to the first stage of avalanche release — failure initiation. Field methods that comprehensively evaluate the second stage – fracture propagation – have remained elusive. In this paper, we explore evidence that field estimates of stability can be improved by integrating three elements: stability test score, fracture character or release type, and a simple index of structural stability (the stratigraphical threshold sum across the fracture interface). Using field data collected from skier-triggered avalanches and skier-tested slopes that did not release, we show that when these three elements fall into their respective critical ranges the accuracy of predicting the probability of a skier triggered avalanche is higher than when any one element is used alone. Further, we show through a qualitative analysis that these three elements fulfill, at least partially, the criteria for fracture initiation and propagation. As with any field stability method that relies on local snowpack data, the approach presented here is not intended to be used in isolation, but in conjunction with other measurements and observations that relate to the probability and consequences of avalanche release.

Fracture energy applicable to dry snow slab avalanche release

Dry slab avalanches release by a sequence of propagating fractures: first by shear fracture (mode II and mode III) in a weak layer at the base of the slab and second by tensile fracture through the crown after which release of the slab is imminent. The fracture energy is the energy which must be provided to produce a unit area of fracture surface. It is a key parameter in determining how and when fractures will propagate and important slab characteristics such as length and width that are necessary in order to estimate slab mass and volume in relation to destructive potential. In this paper, approximate estimates of fracture energy are calculated from field measurements of slab properties, laboratory measurements and in‐situ strength tests in alpine snow. Estimates of fracture energy are given for both tensile fracture (mode I) through the crown as well as for shear fracture (mode II) in fragile weak layers of slab avalanches. The results, when compared with other values from ice, rock and engineering materials, suggest that snow has the lowest values.

On size and shape effects in snow fracture toughness measurements

Dry snow slab avalanche release is preceded by two fracture mechanical processes: shear failure of a weak layer or an interface within the snowpack, followed by tensile failure of the overlaying slab. For a slope stability analysis based on fracture mechanics, the fracture toughness of snow has to be known. The purpose of this work was to evaluate snow fracture toughness in mode I, to determine to what extent it is affected by the specimen size and shape and to search for adequate correction methods. Edge-cracked beam-shaped snow specimens cut from homogeneous layers of naturally deposited snow were subjected to three-point bending and cantilever beam tests. To describe the size dependence an empirical size effect law and the FAD (failure assessment diagram) approach were explored. By comparing the three-point bending with the cantilever beam tests a shape dependence of the toughness was found. The fracture process zone was estimated to be in the order of at least one centimetre. Due to the large size of the fracture process zone a dependence of the toughness on the specimen size has to be expected, as it is typical for non-linear, quasi-brittle materials. Experiments with four different specimen sizes clearly confirmed that toughness is size dependent, possibly up to the scale of a slab avalanche. Preliminary results suggest that the actual fracture toughness might be twice as large as the one determined experimentally. Therefore, size correction functions will be essential to transform toughness data of laboratory-scaled experiments to the scale relevant for snow slope stability models.

On the fracture toughness of snow

AbstractThe release of a dry-snow slab avalanche involves brittle fracture. It is therefore essentially a non-linear fracture mechanics problem. Traditional snow-stability evaluation has mainly focused on snow strength measurements. Fracture toughness describes how well a material can withstand failure. The fracture toughness of snow is therefore a key parameter to assess fracture propagation propensity, and hence snows lope stability. Fracture toughness in tension KIc and shear KIIc was determined with notched cantilever-beam experiments in a cold laboratory. Measurements were performed at different temperatures and with different snow types of density ρ = 100–300 kgm–3, corresponding to typical dry-snow slab properties. The fracture toughness in tension KIc was found to be larger (by about a factor of 1.4) than in shear KIIc. Typical values of the fracture toughness were 500–1000 Pam1/2 for the snow types tested. This suggests that snow is one of the most brittle materials known to man. A power-law relation of toughness KIc on relative density was found with an exponent of about 2. The fracture toughness in tension KIc decreased with increasing temperature following an Arrhenius relation below about –8°C with an apparent activation energy of about 0.16 eV. Above –6°C the fracture toughness increased with increasing temperature towards the melting point, i.e. the Arrhenius relation broke down. The key property in dry-snow slab avalanche release, the critical crack size under shear at failure, was estimated to be about 1 m.

The skier’s zone of influence in triggering slab avalanches

AbstractIn recent years, most avalanche fatalities have been due to dry-snow slab avalanches triggered by the victims themselves during recreational activities, at least in countries where recreational skiing takes place, as in Western Europe and North America. Simple analysis suggests, and previous measurements have shown, that the skier’s dynamic impact is relevant for triggering, decreasing with increasing depth within the snow cover and depending on the layering of the snow cover. The stress distribution below a skier in the snow cover is not known, but is important in view of the critical area required for fracture propagation preceding dry-snow slab avalanche release. The skier’s zone of influence was measured with load cells buried within the snow cover in a level study plot for different depths. The size of the area of influence is of the order of a few 0.1 m2, but also depends on the weak-layer strength. Stresses in the snow cover below skiers who walk behind each other are not cumulative. The effect on the influence size is in accordance with the independent estimate for the critical size (0.1–1 m) for fracture propagation in the case of rapid loading. It supports the hypothesis that skiers induce a brittle fracture within the weak layer or at a weak interface between layers, leading under certain conditions to slab release, without necessarily hitting a pre-existing flaw.

Texture and strength changes of buried surface-hoar layers with implications for dry snow-slab avalanche release

AbstractBuried layers of surface hoar are the failure plane for many slab avalanches, including fatal human-triggered avalanches in various mountain regions. These layers may persist as weak layers in the snow cover for weeks or months. It is therefore essential for operational avalanche forecasters to monitor the evolution of persistent weak layers, such as buried surface hoar. Traditional grain-shape observations of isolated grains with a magnifier and crystal screen do not show bonding that is decisive for strength. In this study we used in situ microphotography and observations of texture to complement strength measurements from shear frame tests. Buried layers of surface hoar consist of crystals most of which extend from the layer below to the layer above, and may exhibit a columnar or truss-like structure. Observations and measurements show that texture and crystal size change little over periods of up to several months during which the snowpack remains dry. Under these conditions, layer thickness decreases while density and strength increase. Based on field measurements, we argue that the increase in strength is primarily due to penetration of the surface-hoar crystals into the adjacent layers, especially at the bottom of the buried surface-hoar layer, where bonding is critical. The weak bonding at the bottom implies that shear failure occurs at the lower interface rather than within the weak layer. On slopes, we find that surface-hoar crystals that were initially surface-normal are tilted downslope faster than predicted by published shear strain rates for settled snow, indicating that shear strain is concentrated in these layers. The characteristic texture of buried surface hoar (columnar or truss-like) permits collapsing at the time of fracture. The gravitational energy released by the displacement of the slab may contribute to the extensive fracture propagation associated with buried surface-hoar layers.

Review of dry snow slab avalanche release

Dry snow slab avalanche release starts with failure in the weak layer underlying the slab. The stress in the weak layer has to locally exceed the strength that strongly depends on the strain rate. Models for dry snow slab avalanche release are reviewed, with emphasis on the role of deficit zones. Most models assume a priori existing deficit or superweak zones. Providing the damaged area is large enough so that sufficient deformation energy is released, a shear fracture may propagate and release a slab avalanche. Model calculations give a wide range of values on the size of these zones, typically between 0.1 to 10 m. However, field studies have not proven the existence of shear deficit zones. Skiers may definitely trigger slab avalanche without incidentally hitting a deficit zone. Deficit zones are supposed to be a transient phenomenon, in particular due to the sintering process. A comprehensive link between snow failure, described as the result of the two competing main processes: fracturing and sintering, and slab release is still missing. As field studies show spatial variability in stability, future operational models of avalanche formation should probably include this variation by using a statistical approach. Doing so a simple stress criterion might be sufficient, in particular to describe skier triggered and direct-action avalanches.