On the inclusion of a velocity-dependent basal drag in avalanche models

The Savage-Hutter model is generalized by including a velocity-dependent drag in addition to the usual Coulomb dry friction at the base of the avalanche. Both linear and quadratic velocity dependencies are considered, with either constant or asymptotically constant drag coefficients for large thickness h. The singular nature of the constant coefficient model for small h is demonstrated and it is shown that the asymptotic model allows the tail of the avalanche to move at a finite velocity. The inclusion of velocity drag changes the stress state in the avalanche and new earth-pressure relations are derived and investigated.