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

Abstract

International audienceIn 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

The Linear Hygroscopic Expansion Coefficient of Cement-Based Materials and Its Determination

“…Equation 14is very similar to Equation (9), which was firstly derived and proposed by us. The differences are that the influence of the aggregate volume fraction (V a /V c ) and the saturation factor (S) are considered in Equation 9, while the area fraction of the wetted solid skeleton (χ ws ) is considered in Equation (14). Equation 14describes the linear shrinkage strain of cement-based materials at a constant temperature.…”

“…It is very important to investigate the hygro-thermo-mechanical deformation cracking performance and mechanisms of concrete. A number of studies have been published on the coupled hygro-thermo mechanical deformation of concrete, with hygro-thermal transference and induced deformation being investigated at high temperatures to analyze the behavior of concrete in fire [12][13][14]. Some studies based on thermodynamics of partially-saturated porous media will benefit the future research on the hygro-thermal-mechanical performance of structural concrete [12,15,16].…”

Plasto-damage modelling for semi-brittle geomaterials

“…Nonlinear elastic, elastoplastic and elasto-damage constitutive laws as well as soilatmosphere interaction model have already been incorporated in the code [21][22][23][24][25].…”

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

“…For unsaturated soils, Gatmiri and Jabbari [6,7,9,10] have derived the first fundamental solutions for the nonlinear governing differential equations for static and quasi-static 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 (for both two and threedimensional problems) [11] and Gatmiri et al (for two-dimensional problems) [12].According to the authors' knowledge, the three-dimensional fundamental solutions of the governing partial differential equations for unsaturated porous media by considering the thermohydro-mechanical behaviour have not been developed so far, hence the development of a BEM model for unsaturated phenomena is not yet possible.In this paper first, the set of fully coupled governing differential equations of thermo-hydromechanical behaviour of unsaturated porous media subjected to quasi-static loadings is presented based on the suction-based mathematical model presented by Gatmiri [13] and Gatmiri et al [14]. In this approach, heat and moisture transfer equations are given in an alternative form based on THERMO-HYDRO-MECHANICAL FUNDAMENTAL SOLUTIONS 299 water and air pressures.…”

“…For unsaturated soils, Gatmiri and Jabbari [6,7,9,10] have derived the first fundamental solutions for the nonlinear governing differential equations for static and quasi-static 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 (for both two and threedimensional problems) [11] and Gatmiri et al (for two-dimensional problems) [12].…”