Wave Propagation in Unsaturated Poroelastic Media: Boundary Integral Formulation and Three-dimensional Fundamental Solution

Pooneh Maghoul (1) , Behrouz Gatmiri (2) , Denis Duhamel (3)

1 navier umr 8205 - Laboratoire Navier
2 cermes - Géotechnique
3 Dynamique des structures et identification

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 Hörmander. 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.

Mots clés: Boundary element method; Boundary integral equations; Fundamental solution; Singular behavior; Unsaturated soil; Multiphase porous media; Dynamic behavior

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Pooneh Maghoul, Behrouz Gatmiri, Denis Duhamel. Wave Propagation in Unsaturated Poroelastic Media: Boundary Integral Formulation and Three-dimensional Fundamental Solution. Computer Modeling in Engineering and Sciences, 2011, 78 (1), pp.51-76. ⟨10.3970/cmes.2011.078.051⟩. ⟨hal-00669004⟩