Modelling snow failure with a fibre bundle model

Abstract

Dry-snow slab avalanches initiate from a failure in a weak snow layer below a cohesive slab. Snow is considered as a porous ice structure, and the strength distribution of the single elements of this structure, i.e. grains and bonds between grains, shows a high degree of disorder. On the bond or microstructural level, the failure process is believed to start if the fracturing of bonds between snow grains is not balanced by the formation of new bonds. We use a statistical fracture model - a fibre bundle model - to study the failure process in a weak snow layer. The model consists of fibres of various strengths representing single snow grains between two rigid plates which represent the slab above and the substratum below the weak layer. The fibres deform in a linear elastic manner and break instantly at their rupture strength. Broken fibres may sinter (re-bond) and regain strength after a finite sintering time. We show that the different characteristic times for breaking and sintering lead to the rate dependence of snow strength. This is, to our knowledge, the first statistical model to reproduce the ductile-to-brittle transition which snow exhibits with increasing strain rate. When the model is applied to simulate experimental stress-strain curves for different strain rates, the model and experimental results are in fair agreement.