Dynamic Wave Propagation in Porous Media Semi-Infinite Domains

• Published in: Proceedings in applied mathematics and mechanics Vol. 10; no. 1; pp. 499 - 500
• Main Authors: Heider, Yousef, Markert, Bernd, Ehlers, Wolfgang
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.12.2010; WILEY‐VCH Verlag
• DOI: 10.1002/pamm.201010242
• ISSN: 1617-7061

The problem of dynamic wave propagation in semi‐infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half‐space and soil‐structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary‐value problems (IBVP). Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid‐fluid aggregates. Based on the continuum‐mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi‐static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time‐integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two‐dimensional IBVP. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)