Avalanche Mechanics: Lefm vs. Gradient Model

Abstract

In this study the initiation of avalanches by failure of the interface between the show slab and the underlying bedrock is considered. A pre-existing shear crack is assumed at the interface, in analogy with the classical work of Palmer and Rice [1] on shear bands in over-consolidated clay. A criterion for failure by shear band propagation was obtained and it was applied to snow slab avalanches by McClung [2]. According to this criterion, for a given load due to the weight of the slope above the plane of shear, the slope starts to slide when the length of the shear band exceeds a critical value. Analogous criteria have been obtained in the work of Fyffe et al. [3] and Zaiser et al. [4], where, in addition, variations in interface toughness due to the presence of small-scale heterogeneities were considered. Similar expressions are also derived in the present study. A Linear Elastic Fracture Mechanics (LEFM) approach (Pugno and Carpinteri [5]; Chiaia et al. [6]) is first used in order for a critical value of the energy release rate G for avalanche initiation to be calculated; this provides a critical value for the height of the fallen snow. A gradient model, similar to the ones that have been used successfully in the past for problems of shear banding in metal plasticity (Aifantis [7], Zbib and Aifantis [8]), is then utilized providing expressions for the energy release rate and the height of the fallen snow. The results of both models are compared. Although these simple one-dimensional models have a completely different origin, it is shown that their predictions in terms of the critical height for the fallen snow and the critical slope angle are very similar.

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