Inertial Effects in Poroelasticity

Abstract

The dynamic behavior of a chemically inert, isothermal mixture of an isotropic elastic solid and an elastic fluid is studied. Geometrically, this mixture is assumed to comprise a layer of fixed depth, bounded below by a rigid, impervious surface, and above by a free surface to which loads are applied. The resulting boundary-initial value problem is solved by use of a Green’s function. Two different loading conditions are used to demonstrate the effect of including inertia terms in the equations of motion. In the first example of a constant compressive load, our result is found to agree with the inertia-free solution only for a certain long-time approximation. The second example shows that for a harmonically varying compression, resonance displacements occur at certain loading frequencies, whereas the solution obtained by neglecting inertia does not predict this behavior.