Development of an unsteady non-linear model for flow through coarse porous media
A numerical model has been developed to analyse unsteady, non-linear flow through coarse porous media. The model takes factors such as the spatial variability of material properties and the variability of the cross-sectional geometry into account. It was intended to be particularly applicable to flow through valley fills and rock drains resulting from waste dumps from mining operations. The modified Saint-Venant equations together with the Forchheimer equation constitute the mathematical formulation of the flow system. A four-point finite difference method was employed and a Newton-Raphson iterative scheme was used to solve the resulting non-linear equations. With regard to the vertical heterogeneity of the materials, a superposition method was developed and used in the model. Laboratory studies on three, 1.5 m long, rockfills made of different homogeneous materials and one layered rockfill were used to verify the model under different initial and boundary conditions. Attempts to use hydraulic parameters determined for the materials in a permeameter were unsuccessful due to changes in material characteristics when placed in the physical model. As such, the material hydraulic parameters were determined using steady-state runs in the model. The resulting hydraulic parameters were then used to model unsteady conditions. It was found that the model is able to reproduce the experimental results well in terms of both water surface profiles and depth variation with time curves in the physical model. There is a need to minimise the environmental impacts of mining activities. The model resulting from this research has the potential to be applied to field conditions to test various designs and to thereby assess their potential impact on the environment (e.g., modified flow regime in the downstream channel).