Dynamic Deformations in the Theory of Fluid-Saturated Porous Solid Materials

Abstract

In the present article, the dynamics of a fluid-saturated porous solid material is described by the general theory of porous media, which is defined as the classical theory of mixtures extended by the concept of volume fractions. The reader, who is interested in the various details of this approach is referred, e. g., to Bowen [1, 2], Ehlers [3] or de Boer et al. [4]. For simplicity and convenience, thermal effects as well as mass exchanges between the constituents are excluded from the following treatment. Based on this approach, the objective of the paper is to re-formulate and to solve the mechanical balance equations of a binary model, especially, of a binary model of incompressible constituents (elastic solid skeleton and viscous pore fluid). In particular, initial boundary-value problems of one-dimensional and two-dimensional dynamic consolidation problems are solved within the finite element method (FEM), thus delivering a successful alternative to the different numerical studies based on the well-known Biot approach; concerning the Biot approach, compare [5, 6, 7].