Mechanics of rigid disc inclusions in fluid saturated poroelastic media.

摘要

echanics of inclusions are classical mixed boundary value problems in mathematical physics and applied mechanics which have important applications to various branches of engineering and science. However, due to the intrinsic difficulties associated with the mathematical formulations and the ensuing numerical evaluations, the majority of the investigations have concentrated on the study of the static responses of inclusions embedded in linear elastic media. A study of the literature on inclusion problems reveals that only limited results have been obtained with regard to the time-dependent behaviour of inclusions embedded in saturated poroelastic media, visco-elastic media, or thermoelastic media. This thesis presents a rigorous mathematical and analytical investigation of the mechanics of rigid disc inclusions embedded in poroelastic media saturated with compressible pore fluids. Using the classical integral transform technique for the solution of linear partial differential equations, a simple and direct matrix based approach is developed to systematically and rigorously solve the (mixed) boundary value and initial value problems associated with saturated poroelastic layered media. Based on the results, a general Fourier and Laplace transform based approach is further proposed for analytical solution of mixed boundary value and initial value problems in saturated poroelastic layered media. Systems of Fredholm integral equations of the second kind in the Laplace transform domain are systematically formulated for the fundamental problem of a rigid disc inclusion embedded in bonded contact with a poroelastic medium of infinite extent saturated with a compressible fluid. Special techniques are presented for numerical solution in the temporal domain of the systems of Fredholm integral equations of the second kind in the Laplace transform domain. The adopted numerical scheme has high stability and accuracy for the very long time interval associated with the process of soil consolidation. The results of three limiting conditions are rigorously examined in all the above equations, formulations and solutions. These limiting conditions are the initial response as