Modeling of unsaturated water flow in double-porosity soils by the homogenization approach

Double-porosity media are composed of two distinct regions with contrasted hydraulic parameters. Due to this type of structure, transient water flow is characterized by local non-equilibrium conditions. This paper will present a macroscopic model of water flow in such media that was obtained by the method of homogenization. This method enables us to derive the macroscopic model and its effective parameters from a description of the phenomena at the local scale, without any a priori hypothesis for the form of the model. The macroscopic non-equilibrium water flow is described by a single macroscopic equation with a highly non-linear exchange term, leading to a tailing effect. The effective properties, namely the hydraulic conductivity tensor and the specific water capacity, are defined as depending on the hydraulic characteristics of the more conductive (and connected) domain and the local geometry of the medium. A numerical implementation (Fortran program) of the proposed model was developed. Numerical simulations were performed for two different types of geometry. For each problem the results obtained from homogenization are compared with a fine scale numerical simulation where heterogeneous structure of the medium is explicitly represented (SWMS_3D commercial software). Comparisons with the phenomenological approach of Gerke and van Genuchten [Water Resour. Res. 29 (1993) 305] are also presented.