A theoretical framework for dynamic anticrack and supershear propagation in snow slab avalanches

Abstract

Snow slab avalanches release after the failure and collapse of a weak layer buried below a cohesive snow slab. The initial failure is induced by local overloading of the slab, such that the passage of a skier. This results in the propagation of a subsidence, known as a collapse wave or anticrack. The slab may eventually break and detach from the rest of the snowpack and start to slide down, provided that the slope is steep enough to enable gravity to overcome the friction at the interface between the slab and the failed weak layer.The approach to anticracks so far has mostly focused on (i) static configurations for the bending slab while the weak layer collapses, thereby leading to analytical conditions for the onset of an anticrack because of the metastability of the snowpack, and (ii) the observation of anticrack propagation as a result of numerical simulation methods (DEM, FEM, MPM) and field experiments (PST). The only theoretical framework to date, based on a simple modelling of the bending of the slab during the weak layer collapse, led to the well-known Heierli (2005) model which suggested an explicit solution for the propagation speed in steady state. It, however, could not account for the weak layer properties, was not mathematically bounded for certain values of the physical constants involved, and could not explain the newly uncovered “supershear” transition for steep slopes.In this paper, a new model for the stationary propagation of anticracks is set up, so as to account for the anticrack speed regime on the one hand, and the supershear regime on the other hand, the existence of which has been recently revealed and ascertained by numerical simulations. The results presented here seem consistent with most of the available data, and highlight the role that the compaction of the weak layer can play in reducing the anticrack speed. On the contrary, by storing energy upon failure and suddenly releasing it at the crack tip, the weak layer elasticity could help justify the higher speeds sometimes observed in both regimes. Finally, a more accurate model is proposed, based on the modelling of both the slab and the weak layer as Timoshenko beams; although its complexity prevents us from solving it analytically, it provides enlightening insights into the mechanical processes at work at the interface between both layers, from a strength-of-materials perspective.This analysis is a first step towards a better understanding of the underlying mechanisms of propagation of cracks in slab avalanches, and towards more accurate avalanche size and occurrence predictions.