Fluid point source and point forces in linear elastic diffusive half-spaces

Abstract

Abstract This paper derives the fundamental solutions for the interior fluid point source and point forces embedded in a linear elastic fluid-saturated porous half-space. McNamee-Gibson and Schiffman-Fungaroli displacement functions are employed to uncouple the equilibrium equations of linear poroelasticity. Laplace-Hankel transform technique is used to solve the resulting partial differential equations for the displacement functions with appropriate boundary conditions. Analytic solutions in terms of inverse transforms are obtained. Numerical results show that the immediate radial displacement can be larger than the long terns movement under vertical point force; conversely, the immediate vertical displacement can be larger than the long term settlement under horizontal point force. As expected, Mindlin's solution is recovered as the steady state solution as the time factor ct/h2 approaches infinity (where c is the coefficient of consolidation, t the time variable and h the depth at which the point force or fluid point source is applied). The solutions for fluid point source compare well with the finite element predictions.