Two-dimensional simulation of debris flows in erodible channels

Debris flows are massive sediment transports of poorly sorted material that occur in small steep mountain catchments. The paper addresses the problem of the propagation of cohesionless debris flows, in which the erosion and sedimentation processes are important and the fixed bed assumption is not acceptable. The depth-averaged motion equations are integrated numerically in a two-dimensional domain. The model is based on a two-phase description of the flow with immediate adaptation of the transport to local flow conditions and with rheological closure valid in the grain-inertia regime. The set of partial differential equations is simplified in order to end up with a hyperbolic system that is solved numerically by means of a second order Godunov-type, finite volume scheme that is accurate in space and time. The scheme uses an approximated Riemann solver of LHLL type, which takes into account the non-conservative terms, and an implicit discretization of the bed shear-stress source terms. The model parameters are determined by means of laboratory flume tests on the site material. Two real-case applications show the effectiveness of the code and how it can be used in predictive situations as in the case of defensive work assessment and verification or hazard mapping.