An Eshelbian Micromechanics Approach to Non-saturated Porous Media

Abstract

The main goal of the present paper is to develop a mathematical framework for modeling the field equations arising in the problem of an elastic, isotropic, non-saturated porous media (pores filled with air and water) within the context of Eshelbian mechanics. The global balance of pseudomomentum is performed in a fully material manifold to account for the configurational forces due to material inhomogeneities, involving the Maxwell stress tensor. Biot’s momentum conservation equations in a dilute scheme for a micromechanical environment, combined with the Mori–Tanaka homogenization theory, are employed for the geomechanical solution. In the mathematical description, pores are treated as Eshelby inhomogeneous inclusions within a solid skeleton, making them the source of configurational forces. The resulting field equations show that these configurational forces evolve in a strongly nonlinear manner due to their dependence on the nature of the pores as well as the soil's mechanical properties. This behavior was numerically observed through the implementation of the boundary value problem using the Finite Element Method.