Two-dimensional mathematical and numerical model for the dynamics of granular avalanches

This paper considers a model that reproduces the dynamics of snow avalanches from initiation to runout for a given terrain topography and given the volume, shape and position of the initial mass. According to the Savage-Hutter theory, the granular avalanche is treated as an incompressible cohesionless continuum, which satisfies a Mohr-Coulomb yield criterion and with a Coulomb-type friction law at the bottom. The internal and bottom friction angles, ϕ and δ, are the only rheological parameters to be set. The balance laws of mass and momentum are simplified imposing the “shallow water” assumption and then averaged along the vertical direction. The momentum balance along the direction normal to the bottom reduces to a hydrostatic distribution of pressure in a form which includes the centrifugal forces due to the curvature. The stress tensor is written in a coordinate system independent of the topography and related to the velocity vector. The numerical model is validated by laboratory experiments, performed at the Hydraulic Laboratory of the University of Trento, and by comparing the simulation results with data collected from the literature. The applicability of the model to natural snow avalanches is discussed with reference to observations on granular avalanches reported in the literature and to the surveys carried out at the Lavina Granda and Spini Valley avalanche sites in Trentino Province (Italy).