A depth average SPH model including μ(I) rheology and crushing for rock avalanches

Classical depth-integrated smoothed particle hydrodynamics (SPH) models for avalanches are extended in the present work to include a (I)- rheological model enriched with a fragmentation law. With this improvement, the basal friction becomes grain distribution dependent. Rock avalanches, where grain distribution tends to change with time while propagating, are the appropriate type of landslide to apply the new numerical proposal. The (I)-< rheological models considered in the present work are those of Hatano and Gray, combined with two different fragmentation laws, a hyperbolic and a fractal-based law. As an application, Frank avalanche, which took place in Canada in 1903, is analyzed under the scope of the present approach, focusing in the influence of the rheological and fragmentation laws in the evolution of the avalanche.