Coupled Problems of Dynamics in Materially Incompressible Saturated Porous Media

Abstract

AbstractThe mechanical behavior of saturated porous materials is largely governed by the interaction between the solid skeleton and the pore fluid. This interaction is particularly strong in dynamic problems and leads to numerical challenges especially in the case of incompressible constituents. In fact, the permeability plays a significant role in this coupling and influences the choice of a proper time integration scheme. Proceeding from the macroscopic Theory of Porous Media (TPM) within the isothermal and geometrical linear regime, the governing balance equations of the dynamic binary solid–fluid model are the solid and fluid momentum balances, and the overall volume balance of the biphasic mixture. This set of coupled partial differential equations (PDEs) is solved within the framework of the mixed Finite Element Method (FEM) applying two different time solution methods, viz., a monolithic implicit and a splitted implicit–explicit scheme. The time stepping algorithms are implemented into the FE program PANDAS and a Scilab FE routine and compared on a one–dimensional wave propagation example. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)