Modeling of runout length of high-speed granular masses

The power balance of a high speed granular mass sliding along planar surfaces is written by taking into account its volume, the slopes of the surfaces (runout and runup), an assigned basal fluid pressure and different possibilities for the energy dissipation. In particular, collisions acting within a thin layer (“shear zone”) at the base of the mass and shear resistance due to friction along the basal surface induce the dissipation of energy. The solution of the ODE describing the mass displacements vs time is numerically obtained. The runout length and the speed evolution of the sliding mass depend on the involved geometrical, physical and mechanical parameters as well as on the rheological laws assumed to express the energy dissipation effects. The well known solutions referred to the Mohr-Coulomb or Voellmy resistance laws are recovered as particular cases. The runout length of a case is finally back analysed, as well as a review of some relationships expressing the runout length as a function of the volume V of the sliding mass.