DEM modelling of unsaturated seepage flows through porous media

A new hybrid discrete–continuum numerical approach that explores the key advantages of both discrete and continuum approaches is proposed to model unsaturated seepage flows through porous media. In contrast to existing approaches where a porous medium is often represented by a continuum medium or required a background mesh, the proposed approach explicitly exploits the discrete contact network formed by an assembly of discrete solid particles. Each solid particle is assumed to occupy an equivalent-continuum space, over which the governing equations for unsaturated seepage flow are derived. These governing equations are then discretised and solved on the discrete contact network through a new numerical procedure that links micro-diffusivity to the macro-one. Thanks to this concept, the proposed approach is capable of describing the nature of flow in unsaturated porous media at the microscale level. This unique feature also enables the proposed approach to naturally simulate the water flow through the heterogeneous porous media without any ad hoc treatments. In this paper, the mathematical concept of the proposed approach together with its implementation features and performances for a rigid porous media is presented and discussed. The focus is placed on its application to the discrete element method (DEM), although the proposed concept, in general, can be applied to any other methods possessing similar features.