Dynamic impact of a debris flow front against a vertical wall

Abstract

Recent experimental results obtained at the University of Trento show that a liquid-granular wave can impact against a vertical obstacle producing two different mechanisms of reflection, depending on the Froude number: if the front is sufficiently fast, the flow is completely deviated in the vertical direction, producing a vertical jet-like bulge, while if it is relatively slow it can be totally reflected in direction normal to the obstacle. The standard theoretical approaches for the analysis of the dynamic impact of a granular front against an obstacle take into account only the second mechanism described above and are obtained from the mass and momentum balances applied to the reflected bore under the hypothesis of homogeneous fluid. We extend this approach to the case of a two-phase granular-liquid mixture, taking into account the presence of a deposit of granular material near the wall, as observed in the experiments. Furthermore we propose a theoretical analysis of the formation of the vertical bulge, that is usually observed for Froude numbers larger than one, and propose an original analytical expression to estimate the dynamic impact forces also in this situation.The theoretical approaches we propose are suitable to describe the experimental results with a reasonable agreement.