Time-harmonic response of saturated porous transversely isotropic half-space under surface tractions

- A saturated porous half space under surface tractions is modeled analytically.
- The medium behaves transversely isotropic in both mechanical and hydraulic fields.
- Two scalar potential functions are introduced to uncouple the Biot's equations.
- The response of the medium including displacements and fluid pressure are studied.

SummaryAn analytical investigation is here presented for dynamic analysis of a half-space containing saturated porous transversely isotropic material under surface tractions. The solid displacement-pore fluid pressure formulation of Biot's theory known as u-p formulation is accepted as the governing equations for the whole half-space, which is the domain of the problem. The free surface of the half-space is considered completely permeable. Two scalar potential functions are for the first time introduced to uncouple the governing system of partial differential equations. The potential functions are introduced in such a way that the governing operators for the potential functions to be physically meaningful. By applying Fourier and Hankel integral transforms, the potential functions are determined by solving two ordinary differential equations. Then, the displacements, stresses and pore fluid pressure are presented as the solutions for the boundary value problem involved in this paper in terms of some line integrals that are evaluated numerically. These responses are derived for general patch load, and presented for horizontal and vertical circular loads, vertical ring load and vertical point load as well as special cases. In addition, the degeneration of the proposed solution to thermoelastodynamics is shown. Selected numerical results for a half-space subjected to uniform horizontal load applied on a circular disc are illustrated.