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).