On the mechanics of a rigid disc inclusion embedded in a fluid saturated poroelastic medium

The paper utilizes the classical integral transform techniques to develop the systems of Fredholm integral equations of the second kind, in the Laplace transform domain, governing the generalized displacement or loading of a rigid disc inclusion embedded in either permeable or impermeable bonded contact with a fluid saturated poroelastic infinite space. The generalized displacements correspond to an axial displacement, a rotation about the axial axis, a rotation about a diametral axis and an in-plane translation. The coupled integral equations in the Laplace transform domain are solved in a numerical fashion to generate results of technological interest. The numerical procedures focus on quadrature schemes for the solution of the integral equations and a procedure used for the inversion of Laplace transforms. The closed-form solutions of the integral equations as either t → 0⁺ or t → +∞ and as v → v_u are also obtained. The numerical results are presented for the time-dependent displacements and rotations of the inclusion subjected to Heaviside-step function type loads and moments, and for the time-dependent relaxation of the force and moment resultants in an inclusion subjected to Heaviside-step function type displacements and rotations. In particular, the influence of the compressibility of the pore fluid on the time dependent responses of the inclusion is documented.