Dry-snow Slab Research Articles

Using video detection of snow surface movements to estimate weak layer crack propagation speeds

Abstract Dry-snow slab avalanches release due to crack propagation in a weak snow layer under a cohesive snow slab. Crack propagation speeds can provide insights into the potential size of avalanches and inform fracture and avalanche release models. Despite their importance, slope-scale crack speed measurements from real avalanches are limited. Further, most existing slope-scale measurements utilize the appearance of slab fractures on the snow surface. However, we have no evidence that the appearance of surface cracking is a good indicator of the weak layer crack propagation tip. Here we present a novel method to estimate crack propagation speed from snow surface movements in avalanche videos. Our technique uses changes in frame pixel intensity, allowing us to detect the location of weak layer cracks well before slab fractures appear on the snow surface. We use field experiments and numerical simulations to validate our method before applying it to five avalanches. Our estimates show that cracks propagate faster up and down the slope than in the cross-slope direction; this suggests that different propagation regimes likely govern crack propagation up/down the slope, cross-slope and in flat terrain.

A closed-form model for layered snow slabs

Abstract. We propose a closed-form analytical model for the mechanical behavior of stratified snow covers for the purpose of investigating and predicting the physical processes that lead to the formation of dry-snow slab avalanches. We represent the system of a stratified snow slab covering a collapsible weak layer by a beam composed of an arbitrary number of layers supported by an anisotropic elastic foundation in a two-dimensional plane-strain model. The model makes use of laminate mechanics and provides slab deformations, stresses in the weak layer, and energy release rates of weak-layer anticracks in real time. The quantities can be used in failure models of avalanche release. The closed-form solution accounts for the layering-induced coupling of bending and extension in the slab and of shear and normal stresses in the weak layer. It is validated against experimentally recorded displacement fields and a comprehensive finite-element model indicating very good agreement. We show that layered slabs cannot be homogenized into equivalent isotropic bodies and reveal the impact of layering on bridging with respect to weak-layer stresses and energy release rates. It is demonstrated that inclined propagation saw tests allow for the determination of mixed-mode weak-layer fracture toughnesses. Our results suggest that such tests are dominated by mode I when cut upslope and comprise significant mode II contributions when cut downslope. A Python implementation of the presented model is publicly available as part of the Weak Layer Anticrack Nucleation Model (WEAC) software package under https://github.com/2phi/weac (last access: 28 March 2023) and https://pypi.org/project/weac (last access: 28 March 2023, Rosendahl and Weißgraeber, 2022).

Laboratory set-up for surface hoar layer growth over rounded grain snow

Growth of surface hoar (SH) crystals by deposition of water vapour onto the snow surface and their subsequent burial by snowfall leads to the formation of a persistent weak SH layer in mountain snowpack of Greater Himalayas. The mechanical properties and failure behaviour of SH layers are critical for avalanche hazard assessment as failure of buried SH layers is frequently the primary cause for the release of dry snow slab avalanches. However, extraction of snow samples containing sandwiched SH layer and their transportation to cold laboratory for experimentation is extremely difficult due to the fragile nature of SH layer. To overcome this limitation, we developed a setup that mimics the natural environmental conditions under which the SH crystals grow. The setup consists of a hot (Th = 1oC) and a cold (Tc = − 25oC) environmental chambers which are connected via an air-duct. The warm air from hot chamber is driven over a water bath through the air-duct towards the cold chamber. A sieved snow sample of desired dimension, which act as the base snow layer, is placed just below the air-duct outlet inside the cold chamber. Difference between the temperature and water vapour pressure of the air at duct outlet, and the surface of base snow layer, resulted in the deposition of water vapour and growth of SH crystals on the exposed snow surface. The growth of SH crystals was primarily observed in the direction normal to the snow surface while their typical shapes were predominantly plates, sector plates and dendrite. With the present setup, an SH layer of ∼10 mm thickness over a base snow layer of surface area 0.07 m2 could be grown within a time interval of ∼13 hr. The average growth rate of SH layer is found to be in the range of ∼0.5 − 0.9 mm hr−1 and the accommodation coefficient of water vapour derived from the analysis of growth measurements varied between α = 0.54 − 0.94 under different experimental conditions. Comparison of cumulative mass of deposited water vapour with measured SH layer thickness also yielded an apparent SH density of 42.5 kg m−3. The strength values (0.6 − 2.2 kPa) of snow samples with artificially grown sandwiched SH layer prepared in this study matches closely with weak layer strength reported in literature thereby indicating the usefulness of present experimental setup for investigating the multi-axial failure behaviour of surface hoar under controlled conditions.

Micro-mechanical insights into the dynamics of crack propagation in snow fracture experiments

Dry-snow slab avalanches result from crack propagation in a highly porous weak layer buried within a stratified and metastable snowpack. While our understanding of slab avalanche mechanisms improved with recent experimental and numerical advances, fundamental micro-mechanical processes remain poorly understood due to a lack of non-invasive monitoring techniques. Using a novel discrete micro-mechanical model, we reproduced crack propagation dynamics observed in field experiments, which employ the propagation saw test. The detailed microscopic analysis of weak layer stresses and bond breaking allowed us to define the crack tip location of closing crack faces, analyze its spatio-temporal characteristics and monitor the evolution of stress concentrations and the fracture process zone both in transient and steady-state regimes. Results highlight the occurrence of a steady state in crack speed and stress conditions for sufficiently long crack propagation distances (> 4 m). Crack propagation without external driving force except gravity is possible due to the local mixed-mode shear-compression stress nature at the crack tip induced by slab bending and weak layer volumetric collapse. Our result shed light into the microscopic origin of dynamic crack propagation in snow slab avalanche release that eventually will improve the evaluation of avalanche release sizes and thus hazard management and forecasting in mountainous regions.

Application of dynamic fracture mechanics to dry snow slab avalanche release

Field observations and measurements show that dry snow slab avalanches initiate by propagating shear fractures within a relatively thin weak layer sandwiched between a planar, stronger, thicker slab above and stronger material below. After initiation, the weak layer fracture can propagate up and down slope for distances which range from about 10 to 100′s of meters to cause tensile fracture through the body of the slab which results in avalanche release. In this paper, dynamic fracture mechanics is applied to slab tensile fracture after which avalanche release is imminent. Two mechanisms for production of tensile stress are explored employing field measurements of slab properties and lab measurements. The first considers inertial effects related to quasi-brittle fracture near the tip of a propagating weak layer shear fracture. The second is concerned with the tensile stress generation from the stress drop behind the crack front as the fracture propagates in the weak layer. Analysis suggest that both mechanisms can contribute to produce the tensile fracture line which precedes avalanche release. Even though both mechanisms may operate together, they are analyzed separately in this paper.

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).

Micromechanical modeling of snow failure

Abstract. Dry-snow slab avalanches start with the formation of a local failure in a highly porous weak layer underlying a cohesive snow slab. If followed by rapid crack propagation within the weak layer and finally a tensile fracture through the slab, a slab avalanche releases. While the basic concepts of avalanche release are relatively well understood, performing fracture experiments in the laboratory or in the field can be difficult due to the fragile nature of weak snow layers. Numerical simulations are a valuable tool for the study of micromechanical processes that lead to failure in snow. We used a three-dimensional discrete element method (3-D DEM) to simulate and analyze failure processes in snow. Cohesive and cohesionless ballistic deposition allowed us to reproduce porous weak layers and dense cohesive snow slabs, respectively. To analyze the micromechanical behavior at the scale of the snowpack (∼1 m), the particle size was chosen as a compromise between low computational costs and detailed representation of important micromechanical processes. The 3-D-DEM snow model allowed reproduction of the macroscopic behavior observed during compression and mixed-mode loading of dry-snow slab and the weak snow layer. To be able to reproduce the range of snow behavior (elastic modulus, strength), relations between DEM particle and contact parameters and macroscopic behavior were established. Numerical load-controlled failure experiments were performed on small samples and compared to results from load-controlled laboratory tests. Overall, our results show that the discrete element method allows us to realistically simulate snow failure processes. Furthermore, the presented snow model seems appropriate for comprehensively studying how the mechanical properties of the slab and weak layer influence crack propagation preceding avalanche release.

Numerical investigation of the mixed-mode failure of snow

The failure of a weak snow layer underlying a cohesive slab is the primary step in the release process of a dry snow slab avalanche. The complex and heterogeneous microstructure of snow limits our understanding of failure initiation inside the weak layer, especially under mixed-mode shear–compression loading. Further complication arises from the dependence of snow strength on the loading rate induced by the balance between bond breaking and bond formation (sintering) during the failure process. Here, we use the discrete element method to investigate the influence of mixed-mode loading and fast sintering on the failure of a weak layer generated using cohesive ballistic deposition. Both fast and slow loading simulations resulted in a mixed-mode failure envelope in good agreement with laboratory experiments. We show that the number of broken bonds at failure and the weak layer strength significantly decreases with increasing loading angle, regardless of the loading rate. While the influence of loading rate appears negligible in shear-dominant loading (for loading angles above 30^{circ }), simulations suggest a significant increase in the weak layer strength at low loading angles and low loading rates, characteristic of natural avalanches, due to the presence of an active sintering mechanism.

Probabilistic size effect law for mode II fracture from critical lengths in snow slab avalanche weak layers

ABSTRACTFrom field observations, dry snow slab avalanche initiation is associated with fracture within relatively thin weak layers under stronger, cohesive slabs. For risk-based avalanche prediction, it is important to understand the fracture properties of alpine snow. Alpine snow is a quasi-brittle material with a fracture mechanical size effect on nominal shear strength meaning that strength decreases with increasing specimen size. A related size effect is the critical length required for rapid propagation of a shear fracture. In that case, the probability of fracture increases with increasing crack length. In this paper, 45 sets of field-measured critical lengths are presented based on 591 individual tests. From analysis, a probabilistic size effect law based on critical lengths is derived analogous to the deterministic size effect law for nominal shear strength related to fracture mechanics. The new size effect law may be useful in applications, particularly since the critical length is easily measured in the field and it is a principal component of weak layer fracture toughness.

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).

Assessing snow instability in skier-triggered snow slab avalanches by combining failure initiation and crack propagation

Dry-snow slab avalanches start with a local failure in a weak snowpack layer buried below cohesive snow slab layers. If the size of the failed zone exceeds a critical size, rapid crack propagation occurs possibly followed by slab release if the slope is steep enough. The probability of skier-triggering a slab avalanche is generally characterized by classical stability indices that do not account for crack propagation. In this study, we propose a new model to evaluate the conditions for the onset of crack propagation in skier-triggered slab avalanches. For a given weak layer, the critical crack length characterizing crack propagation propensity was compared to the size of the area where the skier-induced stress exceeds the shear strength of the weak layer. The ratio between both length scales yields a stability criterion combining the processes of failure initiation and crack propagation. The critical crack length was calculated from a recently developed model based on numerical simulations. The skier-induced stress was computed from analytical solutions and finite element simulations to account for slab layering. A detailed sensitivity analysis was performed for simplified snow profiles to characterize the influence of snowpack properties and slab layering on crack propagation propensity. Finally, we applied our approach to manually observed snow profiles and compared our new criterion to Rutschblock scores.

Snow fracture in relation to slab avalanche release: critical state for the onset of crack propagation

Abstract. The failure of a weak snow layer buried below cohesive slab layers is a necessary, but insufficient, condition for the release of a dry-snow slab avalanche. The size of the crack in the weak layer must also exceed a critical length to propagate across a slope. In contrast to pioneering shear-based approaches, recent developments account for weak layer collapse and allow for better explaining typical observations of remote triggering from low-angle terrain. However, these new models predict a critical length for crack propagation that is almost independent of slope angle, a rather surprising and counterintuitive result. Based on discrete element simulations we propose a new analytical expression for the critical crack length. This new model reconciles past approaches by considering for the first time the complex interplay between slab elasticity and the mechanical behavior of the weak layer including its structural collapse. The crack begins to propagate when the stress induced by slab loading and deformation at the crack tip exceeds the limit given by the failure envelope of the weak layer. The model can reproduce crack propagation on low-angle terrain and the decrease in critical length with increasing slope angle as modeled in numerical experiments. The good agreement of our new model with extensive field data and the ease of implementation in the snow cover model SNOWPACK opens a promising prospect for improving avalanche forecasting.

Snow instability evaluation: calculating the skier-induced stress in a multi-layered snowpack

Abstract. The process of dry-snow slab avalanche formation can be divided into two phases: failure initiation and crack propagation. Several approaches tried to quantify slab avalanche release probability in terms of failure initiation based on shear stress and strength. Though it is known that both the properties of the weak layer and the slab play a major role in avalanche release, most previous approaches only considered slab properties in terms of slab depth, average density and skier penetration. For example, for the skier stability index, the additional stress (e.g. due to a skier) at the depth of the weak layer is calculated by assuming that the snow cover can be considered a semi-infinite, elastic, half-space. We suggest a new approach based on a simplification of the multi-layered elasticity theory in order to easily compute the additional stress due to a skier at the depth of the weak layer, taking into account the layering of the snow slab and the substratum. We first tested the proposed approach on simplified snow profiles, then on manually observed snow profiles including a stability test and, finally, on simulated snow profiles. Our simple approach reproduced the additional stress obtained by finite element simulations for the simplified profiles well – except that the sequence of layering in the slab cannot be replicated. Once implemented into the classical skier stability index and applied to manually observed snow profiles classified into different stability classes, the classification accuracy improved with the new approach. Finally, we implemented the refined skier stability index into the 1–D snow cover model SNOWPACK. The two study cases presented in this paper showed promising results even though further verification is still needed. In the future, we intend to implement the proposed approach for describing skier-induced stress within a multi-layered snowpack into more complex models which take into account not only failure initiation but also crack propagation.

Modeling of crack propagation in weak snowpack layers using the discrete element method

Abstract. Dry-snow slab avalanches are generally caused by a sequence of fracture processes including (1) failure initiation in a weak snow layer underlying a cohesive slab, (2) crack propagation within the weak layer and (3) tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e., to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited. To shed more light on this issue, we performed numerical propagation saw test (PST) experiments applying the discrete element (DE) method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, in order to compare the numerical and experimental results, the slab mechanical properties (Young's modulus and strength) which are not measured in the field were derived from density. The simulations nicely reproduced the process of crack propagation observed in field PSTs. Finally, the mechanical processes at play were analyzed in depth which led to suggestions for minimum column length in field PSTs.

Mode II fracture parameters of dry snow slab avalanche weak layers calculated from the cohesive crack model

Release of dry snow slab avalanches starts with shear failure within a thin weak layer beneath a stronger, cohesive slab. The propagating fracture is within the weak layer as mode II. The fundamental fracture properties include the weak layer critical mode II fracture energy and stress intensity factors. In this paper, mode II fracture energy was calculated from the cohesive crack model from dry slab avalanche fracture line data and in-situ shear fracture tests. One advantage of the cohesive crack model is that it does not require the effective elastic modulus which is highly rate dependent and largely unknown in avalanche release. The results gave weak layer mode II fracture toughness less than mode I fracture toughness for the cohesive slab and fracture energy about one order of magnitude less than for solid ice. From the fracture energy and the mode II stress intensity factor, Irwin’s relation enables calculation of the effective elastic modulus. Calculations of the effective modulus for mode II initiation were compared with other estimates and they were shown to be consistent.

Influence of weak layer heterogeneity and slab properties on slab tensile failure propensity and avalanche release area

Abstract. Dry-snow slab avalanches are generally caused by a sequence of fracture processes, including failure initiation in a weak snow layer underlying a cohesive slab followed by crack propagation within the weak layer (WL) and tensile fracture through the slab. During past decades, theoretical and experimental work has gradually increased our knowledge of the fracture process in snow. However, our limited understanding of crack propagation and fracture arrest propensity prevents the evaluation of avalanche release sizes and thus impedes hazard assessment. To address this issue, slab tensile failure propensity is examined using a mechanically based statistical model of the slab–WL system based on the finite element method. This model accounts for WL heterogeneity, stress redistribution by slab elasticity and possible tensile failure of the slab. Two types of avalanche release are distinguished in the simulations: (1) full-slope release if the heterogeneity is not sufficient to stop crack propagation and trigger a tensile failure within the slab; (2) partial-slope release if fracture arrest and slab tensile failure occur due to the WL heterogeneity. The probability of these two release types is presented as a function of the characteristics of WL heterogeneity and the slab. One of the main outcomes is that, for realistic values of the parameters, the tensile failure propensity is mainly influenced by slab properties. Hard and thick snow slabs are more prone to wide-scale crack propagation and thus lead to larger avalanches (full-slope release). In this case, the avalanche size is mainly influenced by topographical and morphological features such as rocks, trees, slope curvature and the spatial variability of the snow depth as often claimed in the literature.

Risk analyses for dry snow slab avalanches released by skier triggering

Since human triggering is responsible for about 90 % of deaths from slab avalanches in Europe and North America, risk analysis is very important for skier triggering of avalanches. The depth to the weak layer and the slope angle are two key measureable quantities prior to dry slab avalanche release. Both are important in risk analysis. The probability of avalanche release dramatically increases as the slope angle increases above 25°. As the slab depth increases, the consequences increase rapidly if an avalanche releases. Simple risk analyses for skier triggering were done for both slope angle and slab depth. The slab depth analysis showed there is a range of about 0.6–1.0 m for which the risk of death is highest. For slope angles, the range with highest risk was shown to be 33°–45° within the known range (25°–55°) for skier-triggered avalanches.

Three-dimensional microstructure and numerical calculation of elastic properties of alpine snow with a focus on weak layers

AbstractThe microstructure and stratigraphy of a snowpack determine its physical behaviour. Weak layers or weak interfaces buried under a slab are prerequisites for the formation of dry-snow slab avalanches, and a precise characterization of weak layers or interfaces is essential to assess stability. Yet their exact geometry and micromechanical properties are poorly known. We cast weak layers and their adjacent layers in the field during two winters and reconstructed their three-dimensional microstructure using X-ray microcomputer tomography. The high resolution of 10–20 μm allowed us to study snow stratigraphy at the microstructural scale. We quantified the microstructural variability for 32 centimetre-sized layered samples and we calculated Young’s modulus and Poisson’s ratio by tomography-based finite-element simulations. Layers in a sample could therefore be differentiated not only by a change in morphology or microstructure, but also by a change in mechanical properties. We found a logarithmic correlation of Young’s modulus with density for two different density ranges, consistent with previous studies. By calculating the relative microstructural changes within our samples, we showed that a large change could indicate a potential weak layer, but only when the weak layer and both adjacent layers, i.e. the sandwich, were considered.

Weak layer fracture: facets and depth hoar

Abstract. Understanding failure initiation within weak snow layers is essential for modeling and predicting dry-snow slab avalanches. We therefore performed laboratory experiments with snow samples containing a weak layer consisting of either faceted crystals or depth hoar. During these experiments the samples were loaded with different loading rates and at various tilt angles until fracture. The strength of the samples decreased with increasing loading rate and increasing tilt angle. Additionally, we took pictures of the side of four samples with a high-speed video camera and calculated the displacement using a particle image velocimetry (PIV) algorithm. The fracture process within the weak layer could thus be observed in detail. Catastrophic failure started due to a shear fracture just above the interface between the depth hoar layer and the underlying crust.