Avalanche mechanics: LEFM vs. Gradient model

Document Type

Conference Proceeding

Publication Date

1-1-2006

Department

Department of Materials Science and Engineering

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.

Publication Title

Fracture of Nano and Engineering Materials and Structures - Proceedings of the 16th European Conference of Fracture

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