A solid–fluid mixture theory of porous media

The theories of mixtures in the framework of continuum mechanics have been developed throughout the sixties and seventies. In this paper, we shall focus on one of the typical constitutive theories obtained by Bowen (1976) for mixture of elastic materials. We employ a different procedure in the exploitation of the entropy principle, by the use of Lagrange multipliers for a solid–fluid mixture. It is interesting to note that these two theories are completely equivalent concerning the constitutive restrictions.The general results are then applied to the studies of porous media by introducing the concept of porosity. The resulting theory is consistent with Darcy’s law and the concepts of pore fluid pressure and effective stress principle in soil mechanics.