Biot's theory of elastic waves in fluid-saturated porous media

Abstract

A new method of identifying the coefficients of the strain energy functional in Biot's theory is presented. Two types of porous media are distinguished: (1) with the granular constituents fully consolidated so the porous frame acts at a cohesive unit and (2) with the granular constituents only partially consolidated so the porous frame consists of a fraction of the solid particles while the remaining particles are (essentially) suspended in the saturating fluid. For complete consolidation, an exact identification of the coefficients is found. This identification differs from the standard identification of Geertsma and of Biot and Willis for frames whose effective elastic moduli are not related to the grain moduli by the Voigt average. For partial consolidation, an exact identification of the coefficients is not known but the standard identification is a good approximation. The predictions of the theory for a fully consolidated frame are compared to Plona's recent measurements on a water-saturated porous structure of sintered glass beads. Measured fast and slow compressional wave speeds and shear wave speeds agree with the theoretical predictions within experimental error (3%) in all cases.