One-dimensional Mathematical Modelling of Debris Flow Impact on Open-check Dams

The impact of debris flows on open-check dams is modeled as a Riemann problem in a rectangular cross-section channel with downstream dry state. Under the assumption that the energy is conserved through the structure, this special Riemann problem exhibits four different solution configurations. It is shown that the solution always exists, but there are ranges of the initial conditions and of the geometric characteristics for which the solution is not unique. Two different criteria for the disambiguation of the solution are proposed, and it is shown that these criteria are in agreement. The exact solutions presented can be used as internal boundary conditions in one-dimensional numerical models for the propagation of the debris-flow in river channels and narrow valleys, or as a numeric benchmark.