  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.
