Fluid mass sources and point forces in linear elastic diffusive solids

Abstract

Solutions for the point force and line load suddenly applied in a linear elstic fluid-infiltrated porous solid are rederived in a manner that emphasizes the relation to solutions for the homogeneous diffusion equation. Specifically, the stress, displacement, and pore pressure due to instantaneous and continuous injection of fluid mass are obtained. These are differentiated to yield solutions for fluid mass dipoles. Finally, the desired solutions are obtained by adding a constant multiple of the continuous dipole solution to the pure elasticity solution based on the undrained (short-time) moduli.