Numerical Modelling of Water Flow Through Granular Material for Isolated and Simultaneous Extractions in Block Caving

摘要

In this work, we numerically solve the Brinkman-Darcy equation coupled to the granular kinematic model using the finite elements method in 2D, to describe the entry of water into draw points in Block Caving mining. We perform a total of 990 numerical simulations incorporating the relative change of local rock density (/p), particle size (Dp), extraction area (S) and the separation between draw points (L). We propose two mathematical models using scale arguments for estimating the velocity of the water in the draw point as a function of two and three dimensionless numbers (for isolated and simultaneous extractions, respectively). The relative error in the estimation of the results using the mathematical model for the set of numerical experiments ranges from 0.83 to 6.09%, where the greatest deviations correspond to Dp=6mm. The proposed models allow estimating the water velocity at the draw point, which in turn helps to predict the time and place where there is a greater probability of a mud rush occurrence. The results can be applied in the design and optimisation of extraction sequences when the water present in the subsoil of a mine is a relevant factor to consider.