Deriving the equations of motion for porous isotropic media

Abstract

The equations of motion and stress/strain relations for the linear dynamics of a two-phase, fluid/solid, isotropic, porous material have been derived by a direct volume averaging of the equations of motion and stress/strain relations known to apply in each phase. The equations thus obtained are shown to be consistent with Biot’s equations of motion and stress/strain relations; however, the effective fluid density in the equation of relative flow has an unambiguous definition in terms of the tractions acting on the pore walls. The stress/strain relations of the theory correspond to ‘‘quasistatic’’ stressing (i.e., inertial effects are ignored). It is demonstrated that using such quasistatic stress/strain relations in the equations of motion is justified whenever the wavelengths are greater than a length characteristic of the averaging volume size.