A Two-Threshold Model for Scaling Laws of Non-Interacting Snow Avalanches
Jerome Faillettaz, Francois Louchet, Jean-Robert Grasso
Abstract
The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock- or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.
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