A Model for Saturated-Unsaturated Flow with Fractures Acting as Capillary Barriers

Abstract

In this paper, we present a model for saturated-unsaturated flow in fractured soils using an explicit representation of the fractures. The model is based on Richards' equation in the matrix and hydrostatic equilibrium in the fractures. While the first modeling choice is standard, the latter is motivated by the difference in flow regimes between matrix and fractures, i.e., the water velocity inside the fractures is considerably larger than in the soil even under saturated conditions. On matrix/fracture interfaces, the model permits water exchange between matrix and fractures only when the capillary barrier offered by the presence of air inside the fractures is overcome. Thus, depending on the wetting conditions, fractures can either act as impervious barriers or as paths for rapid water flow. Since in numerical simulations each fracture face in the computational grid is a potential seepage face, solving the resulting system of non-linear equations is a non-trivial task. Here, we propose a general framework based on a discretefracture matrix approach, a finite volume discretization of the equations, and a practical iterative technique to solve the conditional flow at the interfaces. Numerical examples support the mathematical validity and the physical applicability of the model.