On a micro‐macro transition for a poroelastic three‐component model

Abstract

AbstractIn this paper a macroscopic linear model is constructed which is intended to describe wave propagation processes in partially saturated soils under isothermal conditions. A porous medium consisting of a deformable skeleton and compressible pore fluids is investigated. The form of the partial stresses is an extension to the two‐component model of Biot. Additionally to the classical coupling between solid and fluid there appear coupling parameters between solid and gas and fluid and gas. Macroscopic material parameters have to be determined from their measurable microscopic counterparts either by a micro‐macro‐transition or using relations for the three‐component body by Santos, Douglas, and Corberó which are analogous to the Gassmann relations for saturated porous media. The transition is illustrated using the examples of oil‐water and air‐water‐mixtures in sandstone. Finally, a glance on the results of the application of the model to wave propagation is given.