Modelling of unsaturated water flow in soils with highly permeable inclusions

Abstract

In this paper the mathematical macroscopic modeling of unsaturated water flow in a porous medium (soil) with highly permeable porous inclusions is presented. It is supposed that water flow in each sub domain can be described by the strongly non-linear Richards' equation. Gravity effects are considered. The upscaling process of this stiff problem is performed using the homogenization method of periodic structures with asymptotic expansions. The resulting non-linear macroscopic description is a one equation model, revealing the local equilibrium of the capillary pressure head. The effective water retention capacity was found to be the volume average of the water retention capacities of the two porous sub-domains. The effective conductivity tensor is obtained from a linear and non-stiff boundary value problem at the heterogeneity scale. To cite this article: J. Lewandowska, J.-L. Auriault, C. R. Mecanique 332 (2004).