Elastic wave propagation in fluid-saturated porous media

Abstract

A new identification of the coefficients in the strain energy functional for Biot’s theory is presented. Two types of porous media are distinguished: (1) With the granular constituents fully consolidated so the porous frame acts as a cohesive unit, and (2) with the granular constituents only partially consolidated so a fraction of the solid particles compose the porous frame 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 [Trans. AIME 210, 331 (1957)] and of Biot and Willis [J. Appl. Mech. 24, 594 (1957)] 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. A method from the theory of composites is used to estimate the frame moduli and a theoretical model of the frame inertia in a fluid environment is developed. The predictions of the resulting model are compared to Plona’s [Appl. Phys. Lett. 36, 259 (1980)] recent measurements on a water-saturated porous structure of sintered glass beads. Good agreement between the theory for a fully consolidated frame and the experiment is found. Measured fast and slow compressional wave speeds agree with the theoretical predictions within experimental error (3%) in all cases.