Dynamics and wave dispersion of strongly heterogeneous fluid-saturated porous media

Abstract

The paper deals with the homogenization approach to the modelling dynamics and wave dispersion of fluid-saturated periodic media. At the mesoscopic scale, the medium is described by the Biot model which is characterized by large contrasts in material properties of two mesoscopic constituents periodically distributed in the two porosities, called the matrix and the channels. By virtue of the homogenization, this contrast is related to the scale parameter which is subject of the asymptotic analysis. In the matrix, the material is much less permeable than in the channels, while the channels are much more compliant than the matrix. We analyze numerically properties of such a material using the homogenized double porosity model developed recently in [1]. The wave dispersion responses obtained using the double porosity model are compared with the analogous responses of a more standard homogenized model without the large contrast assumption (the single porosity model). The double porosity model exhibits much more important dispersion than the single porosity model.