Fabric dependence of poroelastic wave propagation.

Abstract

The governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric. Fabric is a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. With the addition of the second order symmetric tensor fabric variable, the formulation of wave motions in the poroelastic theory is consistent with the presentations of Biot and later authors. The dependence of all the material tensors in the Biot theory on the fabric tensor aligns the material tensors, so when a single direction that is a plane of material symmetry is selected, the equations simplify considerably. The customary polynomial of the sixth deg for the wave speeds of the anisotropic Biot theory in a selected direction reduces to three quadratic equations to solve for the wave speeds and attenuation. While the theory is applicable to any saturated porous material, the two longitudinal waves predicted by this model are measured in cancellous bone and used to derive the corresponding anisotropic elastic constants. Representative examples of bone loss are analyzed as a function of the porosity, tissue density, and fabric.