Stochastic modelling of rock fragment flow in caving mines

The movement pattern of rock fragments under gravity was simulated with a stochastic model which was developed based on Litwiniszyn’s stochastic theory. The downward rock fragment flow is represented in terms of an equivalent upward-biased random flight of voids originating at the draw point. In a steady state, the upward-biased random flight of voids is described with a differential equation which is formally identical to the diffusion equation. By introducing a density change from no-flow zone to flow zone, the model delineates the nonsteady state where the flow zone is being developed during the drawing process. A linear function was introduced in the model to compensate draw shape discrepancy. The parameters in the linear function are material specific. The model was implemented in a computer program employing the finite difference method. The agreement between the stochastic model and a large scale physical model was excellent.