Comptes Rendus
Modelling of unsaturated water flow in soils with highly permeable inclusions
Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 91-96.

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.

Nous étudions dans cette Note le modèle mathématique macroscopique de l'écoulement non-saturé d'eau dans un milieu poreux contenant des inclusions poreuses très conductrices. L'écoulement est décrit dans chaque milieu par l'équation fortement non-linéaire de Richards. La gravité est prise en considération. La macroscopisation de ce problème raide est conduite au moyen de la méthode d'homogénéisation de structures périodiques. Le modèle résultant à l'échelle macroscopique est un modèle non-linéaire à une équation qui traduit l'équilibre local de la pression capillaire. La rétention d'eau effective est la moyenne de volume des rétentions locales. Le tenseur effectif de conductivité est obtenu à partir de la solution d'un problème local linéaire non raide.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2003.10.012
Keywords: Granular media, Soils, Porous media
Mot clés : Milieux granulaires, Sols, Milieux poreux

Jolanta Lewandowska 1; Jean-Louis Auriault 2

1 Laboratoire LTHE, UJF, INPG, CNRS, IRD, UMR 5524, BP 53X, 38041 Grenoble cedex, France
2 Laboratoire 3S, UJF, INPG, CNRS UMR 5521, BP 53X, 38041 Grenoble cedex, France
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Jolanta Lewandowska; Jean-Louis Auriault. Modelling of unsaturated water flow in soils with highly permeable inclusions. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 91-96. doi : 10.1016/j.crme.2003.10.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.012/

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