Upscaling of Richards’ equation for soils containing highly conductive inclusions

The paper concerns macroscopic modeling of water flow in an unsaturated double-porosity soil consisting of highly conductive inclusions embedded in a less conductive matrix. The flow at the local scale in both sub-domains is assumed to be governed by the Richards equation. Application of the asymptotic homogenization method leads to a macroscopic flow model in the form of a single equation with two effective parameters. The effective water capacity depends on the local capacities of both sub-domains and their volumetric fractions, while the effective conductivity depends on the conductivity of the porous matrix and the local geometry of the medium. The conductivity of the inclusions does not influence the calculation of the effective conductivity. The domain of validity of the model is defined. An example of numerical simulation is presented for 1D infiltration into initially dry soil. The local geometry of the considered medium is 2D. The results obtained from homogenization are close to the fine scale solution (SWMS_2D program), where the local heterogeneous structure of the medium is explicitly represented.