Dynamic behaviour of an infinite saturated transversely isotropic porous media under fluid-phase excitation

One of the required fundamental solutions of a poroelastodynamic problem is the solution of the saturated porous medium under a fluid flux or pressure. In the framework of coupled formulations of the displacement and pore-fluid pressure proposed by Biot, the fundamental solutions for a transversely isotropic fluid-saturated porous full-space are analytically presented when the domain of interest is affected by a time-harmonic fluid either ring flux or ring pressure. To this end, a solely scalar potential function is used to uncouple the Biot's coupled partial differential equations, where a sixth order partial differential equation achieved, from which the potential function is determined with the aid of Hankel integral transform and Fourier expansion series. The analytical fundamental displacements, stresses and pore-fluid pressure are presented in the form of one-dimensional semi-infinite integrals, which are due to inverse Hankel integral transforms. The integrals are also degenerated for the isotropic material in mechanical point of view. Because of the complexity of the integrands, the integrals are evaluated numerically. To this end, an adaptive numerical quadrature is adopted and coded in MATHEMATICA software. Some numerical results have been provided to illustrate the displacements, stresses and pore-fluid pressure.