Thermodynamic approach to governing differential equations of unsaturated poroelastodynamic media

The mechanics of unsaturated porous media is expressed as the superposition of different continua intime and space. In this approach, all constituents are considered continuous that overlap in amacroscopic volume known as the representative elementary volume. In the present work, theunsaturated porous media comprises a porous skeleton and two immiscible and chemically inert fluidsthat saturate the pore space. The skeleton is defined by a solid matrix and the pore space and the fluidsare called liquid and gas , as are water and air in soil mechanics. A macro-mechanical approach isused to achieve governing differential equations and constitutive relations of the media at infinitesimaland isothermal evolution. The incremental constitutive relations are adapted to nonlinear elasticbehavior and the capillary pressure constitutive relation is deduced from the second thermodynamic lawafter applying the complementary assumptions of material isotropy and incompressibility of the solid

Keywords:

poromechanics , unsaturated media , governing equations