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.

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.

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.

[1] The evaluation of extreme snowfalls is an important challenge for hazard management in mountainous regions. In this paper, the extreme snowfall data acquired from 40 meteorological stations in the French Alps since 1966 are analyzed using spatial extreme statistics. They are then modeled within the formal framework of max-stable processes (MSPs) which are the generalization of the univariate extreme value theory to the spatial multivariate case. The three main MSPs now available are compared using composite likelihood maximization, and the most flexible Brown-Resnick one is retained on the basis of the Takeuchi information criterion, taking into account anisotropy by space transformation. Furthermore, different models with smooth trends (linear and splines) for the spatial evolution of the generalized extreme value (GEV) parameters are tested to allow snowfall maps for different return periods to be produced. After altitudinal correction that separates spatial and orographic effects, the different spatial models are fitted to the data within the max-stable framework, allowing inference of the GEV margins and the extremal dependence simultaneously. Finally, a nested model selection procedure is employed to select the best linear and spline models. Results show that the best linear model produces reasonable quantile maps (assessed by cross-validation using other stations), but it is outperformed by the best spline model which better captures the complex evolution of GEV parameters with space. For a given return period and at fixed elevation of 2000 m, extreme 3 day snowfalls are higher in the NE and SE of the French Alps. Maxima of the location parameter of the GEV margins are located in the north and south, while maxima of the scale parameter are located in the SE which corresponds to the Mediterranean influence that tends to bring more variability. Besides, the dependence of extreme snowfalls is shown to be stronger on the local orientation of the Alps, an important result for meteorological variables confirming previous studies. Computations are performed for different accumulation durations which enable obtaining magnitude-frequency curves and show that the intensity of the extremal directional dependence effect is all the more important when the duration is short. Finally, we show how the fitted model can be used to evaluate joint exceedence probabilities and conditional return level maps, which can be useful for operational risk management.

ABSTRACT. The evaluation of avalanche release depths constitutes a great challenge for risk assessment in mountainous areas. This study focuses on slab avalanches, which generally result from the rupture of a weak layer underlying a cohesive slab. We use the finite-element code Cast3M to build a mechanical model of the slab/weak-layer system, taking into account two key ingredients for the description of avalanche release: weak-layer heterogeneity and stress redistribution via slab elasticity. The system is loaded by increasing the slope angle until rupture. We first examine the cases of one single and two interacting weak spots in the weak layer, in order to validate the model. We then study the case of heterogeneous weak layers represented through Gaussian distributions of the cohesion with a spherical spatial covariance. Several simulations for different realizations of weak-layer heterogeneity are carried out and the influence of slab depth and heterogeneity correlation length on avalanche release angle distributions is analyzed. We show, in particular, a heterogeneity smoothing effect caused by slab elasticity. Finally, this mechanically based probabilistic model is coupled with extreme snowfall distributions. A sensitivity analysis of the predicted distributions enables us to determine the values of mechanical parameters that provide the best fit to field data.