A Dimension-Reduced Line-Element Method to Model Unsaturated Seepage Flow in Porous Media

Contrary to the continuum hypothesis, which averages water flow across the entire domain, including both grains and pores, the line-element model concentrates unsaturated flow in the pore space in the intermediate region of horizontal and vertical channels. The flux equivalent principle is used to deduce the equivalent unsaturated hydraulic conductivity, the flow velocity and the continuity equations. It is found that the relative hydraulic conductivities derived from the line-element model and the continuum model are identical. The continuity equations in the two models are also similar, except that the coefficient in the water content term is half that in the line-element model. Thus, the unsaturated flow problem in porous media is transformed into a one-dimensional problem. A dimension-reduced finite line-element method is proposed that includes a complementary algorithm for Signorini's-type boundary conditions involving the seepage-face boundary and the infiltration boundary. The validity of the proposed model is then proved by good agreement with analytical, experimental and simulated results for one-dimensional infiltration in a vertical soil column, unsaturated flow in a sand flume with drainage tunnels, and transient unsaturated flow water-table recharge in a soil slab, respectively. In general, the proposed method has good computational efficiency, especially for smaller mesh sizes and short time intervals.