Johan Gaume

Relative influence of mechanical and meteorological factors on avalanche release depth distributions: An application to French Alps

The evaluation of avalanche release depth distributions represents a challenging issue for the mapping, zoning and long-term hazard management in mountainous regions. To that aim, both the distribution of snowfalls and the occurrence probability of an avalanche release for a given snow height need to be assessed. In this study, a rigorous formalism allowing coupling of these two ingredients into a mechanical-statistical model is presented. The stability criterion of a layered snowpack is investigated using a finite-element analysis accounting for the spatial heterogeneity of weak-layer mechanical properties, while the available snow depth is evaluated by studying the distribution of 3-day extreme snowfalls. The release depth distributions predicted by this coupled model are then compared to a well- documented database encompassing 369 natural slab avalanches recorded in La Plagne, France. It appears that with only one adjustable parameter, an excellent agreement can be obtained both for the power-law tail of the distribution, corresponding to large slab depths, and for its core corresponding to shallow slab depths. Two important conclusions can be drawn: (1) Small to medium-sized avalanches are controlled mainly by mechanics, whereas large avalanches are influenced by a strong mechanical- meteorological coupling. (2) The release depth distributions, including the value of the power-law exponent obtained for large slab depths, are highly variable in space and cannot be regarded as universal. Finally, the model is extended using a robust interpolation procedure in order to produce maps of expected release depths for different return periods.

Evaluation of slope stability with respect to snowpack spatial variability

The evaluation of avalanche release conditions constitutes a great challenge for risk assessment in mountainous areas. The spatial variability of snowpack properties has an important impact on snow slope stability and thus on avalanche formation, since it strongly influences failure initiation and crack propagation in weak snow layers. Hence, the determination of the link between these spatial variations and slope stability is very important, in particular, for avalanche public forecasting. In this study, a statistical-mechanical model of the slab-weak layer (WL) system relying on stochastic finite element simulations is used to investigate snowpack stability and avalanche release probability for spontaneously releasing avalanches. This model accounts, in particular, for the spatial variations of WL shear strength and stress redistribution by elasticity of the slab. We show how avalanche release probability can be computed from release depth distributions, which allows us to study the influence of WL spatial variations and slab properties on slope stability. The importance of smoothing effects by slab elasticity is verified and the crucial impact of spatial variation characteristics on the so-called knock-down effect on slope stability is revisited using this model. Finally, critical length values are computed from the simulations as a function of the various model parameters and are compared to field data obtained with propagation saw tests.

Granulation of snow: From tumbler experiments to discrete element simulations

It is well known that snow avalanches exhibit granulation phenomena, i.e., the formation of large and apparently stable snow granules during the flow. The size distribution of the granules has an influence on flow behavior which, in turn, affects runout distances and avalanche velocities. The underlying mechanisms of granule formation are notoriously difficult to investigate within large-scale field experiments, due to limitations in the scope for measuring temperatures, velocities, and size distributions. To address this issue we present experiments with a concrete tumbler, which provide an appropriate means to investigate granule formation of snow. In a set of experiments at constant rotation velocity with varying temperatures and water content, we demonstrate that temperature has a major impact on the formation of granules. The experiments showed that granules only formed when the snow temperature exceeded -1(degrees)C. No evolution in the granule size was observed at colder temperatures. Depending on the conditions, different granulation regimes are obtained, which are qualitatively classified according to their persistence and size distribution. The potential of granulation of snow in a tumbler is further demonstrated by showing that generic features of the experiments can be reproduced by cohesive discrete element simulations. The proposed discrete element model mimics the competition between cohesive forces, which promote aggregation, and impact forces, which induce fragmentation, and supports the interpretation of the granule regime classification obtained from the tumbler experiments. Generalizations, implications for flow dynamics, and experimental and model limitations as well as suggestions for future work are discussed.

A new mixed-mode failure criterion for weak snowpack layers

The failure of a weak snow layer is the first in a series of processes involved in dry-snow slab avalanche release. The nature of the initial failure within the weak layer is not yet fully understood but widely debated. The knowledge of the failure criterion is essential for developing avalanche release models and hence for avalanche hazard assessment. Yet different release models assume contradictory criteria as input parameters. We analyzed loading experiments on snow failure performed in a cold laboratory with samples containing a persistent weak snow layer of either faceted crystal, depth hoar, or buried surface hoar. The failure behavior of these layers can be described well with a modified Mohr-Coulomb model accounting for the possible compressive failure of snow. We consequently propose a new mixed-mode shear-compression failure criterion that can be used in avalanche release models.

Fragmentation of wind‐blown snow crystals

Understanding the dynamics driving the transformation of snowfall crystals into blowing snow particles is critical to correctly account for the energy and mass balances in polar and alpine regions. Here we propose a fragmentation theory of fractal snow crystals that explicitly links the size distribution of blowing snow particles to that of falling snow crystals. We use discrete element modeling of the fragmentation process to support the assumptions made in our theory. By combining this fragmentation model with a statistical mechanics model of blowing snow, we are able to reproduce the characteristic features of blowing snow size distributions measured in the field and in a wind tunnel. In particular, both model and measurements show the emergence of a self-similar scaling for large particle sizes and a systematic deviation from this scaling for small particle sizes.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxters sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Dynamic anticrack propagation in snow

Continuum numerical modeling of dynamic crack propagation has been a great challenge over the past decade. This is particularly the case for anticracks in porous materials, as reported in sedimentary rocks, deep earthquakes, landslides, and snow avalanches, as material inter-penetration further complicates the problem. Here, on the basis of a new elastoplasticity model for porous cohesive materials and a large strain hybrid Eulerian–Lagrangian numerical method, we accurately reproduced the onset and propagation dynamics of anticracks observed in snow fracture experiments. The key ingredient consists of a modified strain-softening plastic flow rule that captures the complexity of porous materials under mixed-mode loading accounting for the interplay between cohesion loss and volumetric collapse. Our unified model represents a significant step forward as it simulates solid-fluid phase transitions in geomaterials which is of paramount importance to mitigate and forecast gravitational hazards.Anticrack propagation in snow results from the mixed-mode failure and collapse of a buried weak layer and can lead to slab avalanches. Here, authors reproduce the complex dynamics of anticrack propagation observed in field experiments using a Material Point Method with large strain elastoplasticity.

Stress Concentrations in Weak Snowpack Layers and Conditions for Slab Avalanche Release: STRESS CONCENTRATION IN SNOW

Dry-snow slab avalanches release due to the formation of a crack in a weak layer buried below cohesive snow slabs, followed by rapid crack propagation. The onset of rapid crack propagation occurs if stresses at the crack tip in the weak layer overcome its strength. In this study, we use the finite element method to evaluate the maximum shear stress τmax induced by a preexisting crack in a weak snow layer allowing for the bending of the overlaying slab. It is shown that τmax increases with increasing crack length, slab thickness, slab density, weak layer elastic modulus, and slope angle. In contrast, τmax decreases with increasing elastic modulus of the slab. Assuming a realistic failure envelope, we computed the critical crack length ac for the onset of crack propagation. The model allows for remote triggering from flat (or low angle) terrain. Yet it shows that the critical crack length decreases with increasing slope angle. Plain Language Summary Dry-snow slab avalanches release due to the formation of a crack in a weak layer buried below cohesive snow slabs, followed by rapid crack propagation. Characterizing conditions for the onset of crack propagation in snow is a great challenge and has been the subject of several investigations. Yet there is still no consensus about the nature of the initial failure in the weak layer, whether it occurs in shear only or if the collapse of the weak layer helps to drive crack propagation. Here, to investigate this question, we employed a numerical model to study stress concentrations in the weak layer in the presence of a preexisting crack, allowing the bending of the overlaying slab. We computed the maximum shear stress close to the crack tip for different system configurations and mechanical properties. We showed that steeper slopes promote crack propagation as predicted by classical shear models. However, the collapse of the weak layer is essential for crack propagation from flat terrain and thus remote avalanche triggering.