An equation for spreading length, center of mass and maximum run-out shortenings of dense avalanche flows by vertical obstacles

In this paper, we consider dense snow avalanches interacting with a defense structure. The maximum run-out distance of dense snow avalanches is the sum of the center of mass run-out and the spreading length. We make the simplifying assumptions that the center of mass run-out is mainly dependent on the velocity of the avalanche flow and the spreading length is mainly linked to the volume of the deposit. The obstacle reduces momentum of the avalanche by (i) velocity reduction and (ii) mass reduction by deposition upstream of the obstacle. The first effect leads to the shortening of the center of mass run-out and the second one explains the spreading length decrease. Therefore, the maximum run-out reduction is a function of both velocity and volume reductions. An equation is proposed to predict the maximum run-out reduction. This equation is tested on small-scale granular avalanches. For laboratory experiments with confined granular avalanches interacting with a thin vertical dam, velocity and volume reductions are expressed as simple functions of the vertical dam height. The equation for the maximum run-out shortening is then calibrated on experimental data and used to predict the velocity reduction and the critical height for which the granular avalanche is entirely stopped by the vertical dam.