A second gradient theory for deformable fluid-saturated porous media

Local dilatancy and solid-fluid surface tension are two of the driving micro-phenomena which characterize the behaviour of fluid saturated porous media. The first one is essentially due to micro-filtration occurrence and pore opening, the second one to wetting phenomena at the solid-fluid interface at the micro-level. In order to describe these phenomena at the macro-scalewe propose in this paper an extension of the classical Biot model of porous media, which includes so called second gradient effects. Starting from a mixture theory model involving two second gradient constituents, so as to describe local dilatancies in the solid as well as capillarity effects, we derive a poromechanical model, which describes not only the effects of porosity but also those of the porosity gradient. It is proven how starting from the first and the second principle of thermodynamics a suitable macro-scale potential for the skeleton can be defined in order to state a consistent formulation of constitutive relations. Moreover an extended formulation of the Darcy law is derived. © 2005 Taylor & Francis Group, London