Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

Abstract

International audienceThe governing differential equations of unsaturated soils considering the thermo-poro-mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three-dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed-form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed-form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution

Boundary integral formulation and two-dimensional fundamental solutions for dynamic behavior analysis of unsaturated soils

“…The idea of this method is to reduce the highly complicated operator given in (63) to simple well known operators. An overview of this method is found in the original work by Hörmander [29] and more exemplary in References [38,24,16,17,18,19,20,30,32].…”

“…For unsaturated soils, Jabbari (2004a, b, 2005a, b) [17,18,19,20] have derived the first fundamental solution for the nonlinear governing differential equations for static and quasistatic poroelastic media for both two and three-dimensional problems. The corresponding thermo-poro-mechanic fundamental solutions for static and quasi-static problems are, respectively, derived by Jabbari and Gatmiri (2007) [30] (for both two and three dimensional problems) and [24] (for two-dimensional problems) and Maghoul et al (2009) [38] (for three-dimensional problems).…”

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

“…Jabbari and Gatmiri (2007) have derived the thermo-poro-elastic fundamental solution for the nonlinear governing differential equations for static and for both two and three-dimensional problems. Also in 0020-7683/$ -see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.ijsolstr.2009.10.022 the case of quasi-static thermo-poro-elastic problems, the corresponding 3D fundamental solutions are obtained by Maghoul et al (2009).…”

Isotropic damage phenomena in saturated porous media: a bem formulation

“…As for works that address poroplasticity, Wutzow (2008) can be cited, which incorporated stiffeners into the solid matrix. Kamalian et al (2008) and Maghoul et al (2010) present fundamental solutions in time domain for media under saturated and unsaturated conditions.…”