U. G. A. Puswewala

Axisymmetric fundamental solutions for a completely saturated porous elastic solid

Abstract This paper is concerned with the derivation of axisymmetric fundamental solutions that are required in the application of boundary integral equation method to solve complicated boundaryvalue problems involving poroelastic semi-infinite and infinite domains. General solutions for a fully saturated poroelastic solid derived through the application of Laplace and Hankel integral transforms with respect to time and radial coordinates are utilized in the analysis. The derivation of complete fundamental solutions requires the consideration of three boundary-value problems involving unit buried ring loads acting in the vertical and radial directions and a unit buried ring flow source. These boundary-value problems are solved for both half space and full space regions. Explicit solutions for Laplace transform of displacements, tractions, pore fluid pressure and fluid flow are presented. Solutions corresponding to a buried vertical point load and a point source in a poroelastic half space are also deduced from ring load and source solutions. Thereafter, solutions are presented for buried distributed normal load, radial shear load and a flow source with intensity specified by a polynomial of arbitrary degree. Selected numerical results corresponding to buried uniform and non-uniform distributed vertical loads are presented to illustrate computational procedure.