A fracture-entrainment model for snow avalanches

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Abstract
We use the invariant Γ integral of fracture mechanics to calculate the frontal pressure and resistance to the downward motion a of snow avalanche. A basic characteristic property of the snowpack, termed the entrainment toughness, is introduced. From an analysis of the non-entrainment frictional mechanisms of avalanches, we find the necessary condition for a fracture-entrainment regime, and from an analysis of limiting equilibrium of gravitational force and frontal resistance, the necessary condition equation for the start of avalanches. We then derive the governing equations for the dynamics of avalanches, using a point-mass approach with entrainment taken into account. The governing equations are used to numerically simulate the Vallée de la Sionne (Switzerland) avalanche of 7 February 2003.