Abstract

A generalized purely kinematic model is proposed for the description of the displacement field in a granular material slowly discharging from a hopper. In addition to the diffusion constant of the well-known kinematic model, our generalized version includes a new parameter accounting for the dilatancy effect that takes place at early stages of the flow. Experimental measurements of particle tracers displacements were made in a "quasi two-dimensional" hopper and a promising agreement with the model was found. Applications to quasi static flows occurring in underground mining are discussed. It is shown that the effect of a small dilation on drawbody shapes can be introduced by taking a slightly larger diffusion constant DP in the kinematic model. As a consequence, the drawbody width W links to the drawbody height H as W2 ∝ DP H, with DP being a linear function of granulate size. This result that is valid in two and three dimensions, captures the main features of independent laboratory measurements as well as observations performed in operating mines. © 2007.