Special Issue on Boundary Element Method; Editor-in-Chief: M. H. AliabadiNo Access

Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media

Pooneh Maghoul

http://orcid.org/0000-0003-0457-3968

Department of Civil Engineering, University of Manitoba, 15 Gillson St., Winnipeg, MB, R3T 5V6, Canada

E-mail Address: pooneh.maghoul@umanitoba.ca

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and

Behrouz Gatmiri

Department of Civil Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

Ministre de l’environnement et de développement durable et de l’énergie, Paris, France

E-mail Address: gatmiri@aviation-civile.gouv.fr

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https://doi.org/10.1142/S175697371750007XCited by:4 (Source: Crossref)

Abstract

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements $u_{i}$ , water pressure $p_{w}$ and air pressure $p_{a}$ are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic $u - p_{w} - p_{a}$ theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.

Keywords:

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