Wave Propagation in Unsaturated Poroelastic Media: Boundary Integral Formulation and Three-dimensional Fundamental Solution
P. Maghoul; B. Gatmiri; D. Duhamel

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 78, No. 1, pp. 51-76, 2011
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Keywords Boundary element method, Boundary integral equations, Fundamental solution, Singular behavior, Unsaturated soil, Multiphase porous media, Dynamic behavior
Abstract This paper aims at obtaining boundary integral formulations as well as three dimensional(3D) fundamental solutions for unsaturated soils under dynamic loadings for the first time. The boundary integral equations are derived via the use of the weighted residuals method in a way that permits an easy discretization and implementation in a Boundary Element code. Also, the associated 3D fundamental solutions for such deformable porous medium are derived in Laplace transform domain using the method of Hérmander. The derived results are verified analytically by comparison with the previously introduced corresponding fundamental solutions in elastodynamic limiting case. These solutions can be used, afterwards, in a convolution quadrature method (CQM)-based boundary element formulations in order to model the wave propagation phenomena in such media in time domain.
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