Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains

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

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

In this paper, the closed form two-dimensional fundamental solutions for a non-isothermal unsaturated deformable porous medium have been derived for a symmetric polar domain in both Laplace transform and time domains. The governing differential equations of the non-isothermal unsaturated soil consist of equilibrium, moisture, air and heat transfer equations including the suction effect, temperature effect and dissolved air in water. The derived fundamental solution has been verified mathematically by comparison with the previously presented corresponding fundamental solutions in three limiting cases including the steady-state thermo-hydro-mechanical, steady-state hydro-mechanical and elastostatic fundamental solutions. Also these 2D kernel functions are tested in comparison with a finite element method (FEM)

Mots clés: Boundary element method; Fundamental solution; Unsaturated soil; Multiphase porous medium; Thermo-hydro-mechanical behaviour; Linear elastic behaviour

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Behrouz Gatmiri, Pooneh Maghoul, Denis Duhamel. Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains. International Journal of Solids and Structures, 2010, 47 (5), pp.595-610. ⟨10.1016/j.ijsolstr.2009.10.022⟩. ⟨hal-00520412⟩