The relation between dilatancy, effective stress and dispersive pressure in granular avalanches

Abstract

Here we investigate three long-standing principles of granular mechanics and avalanche science: dilatancy, effective stress and dispersive pressure. We first show how the three principles are mechanically interrelated: Shearing of a particle ensemble creates a mechanical energy flux associated with random particle movements (scattering). Because the particle scattering is inhibited at the basal boundary, there is a spontaneous rise in the center of mass of the particle ensemble (dilatancy). This rise is connected to a change in potential energy. When the center of mass rises, there is a corresponding reaction at the base of the flow that is coupled to the vertical acceleration of the ensemble. This inertial stress is the dispersive pressure. Dilatancy is therefore not well connected to effective-stress-type relations, rather the energy fluxes describing the configurational changes of the particle ensemble. The strict application of energy principles has far-reaching implications for the modeling of avalanches and debris flows and other dangerous geophysical hazards.