Poroelastodynamic potential method for transversely isotropic fluid-saturated poroelastic media

Abstract

• A potential method is introduced for transversely isotropic fluid-saturated media. • A pair of scalar potentials is employed to uncouple the Biot's equations of motion. • Solutions are given for a half-space under an arbitrary surface time-harmonic loading. • The free surface is considered either completely permeable or impermeable boundary. • Half-space Green's functions for uniform circular surface patch loads are derived. By introduction of two scalar potentials, an analytical method is developed for the solution of poroelastodynamic boundary value problems in transversely isotropic fluid-saturated poroelastic media. The governing equations of motion are considered in the framework of Biot's complete model without any assumption or simplification. As a case of application, solutions in three dimensions for a transversely isotropic fluid saturated porous half space loaded by an arbitrary distribution of time harmonic tractions at the free surface is derived. The free surface of the half space may be considered either permeable or impermeable. As a particular solution, Green's functions for uniform vertical and horizontal circular patch loads are presented as semi-infinite integrals which may be evaluated by means of an appropriate numerical method proposed. The accuracy of the solutions is verified both analytically and numerically against the preceding solutions. Some numerical results are also presented to clarify the influence of different degrees of anisotropy and frequency of excitation on the response of the medium.