A thermodynamic framework for constitutive modeling of coupled moisture-mechanical induced damage in partially saturated viscous porous media

A general thermodynamic-based framework is proposed to derive coupled moisture-mechanical induced damage constitutive relationships for multi-phase viscoelastic porous media. The well-known (Kachanov, 1958) effective (undamaged) configuration and the concept of effective stress space are extended to moisture-susceptible materials to couple the detrimental effects of moisture to the mechanical response of materials. A physically-based moisture-induced damage internal state variable is introduced within the proposed framework to account for the moisture aggravation effect, and to couple moisture-induced damage with mechanical responses. The principle of virtual power, Clausius-Duhem inequality and maximum rate of energy dissipation are constructed for multi-phase porous media. These principles are used to obtain the main macroscopic and microscopic balance laws, the general framework, and the constitutive relationships. The thermodynamic conjugate forces are decomposed into energetic and dissipative components, obtained from Helmholtz free energy and the rate of energy dissipation, to accurately estimate the rate of energy dissipation. The proposed thermodynamic framework is used to develop a comprehensive viscoelastic model, which takes into account the effect of pore water pressure, a constitutive relationship to model the detrimental effect of moisture diffusion inside the solid phase, Darcy's law, Fick's second law and, the Fourier heat conduction equation. The resulting constitutive relationships describe the coupled effects of mechanical loading and moisture-induced damage and accurately predict the response of partially saturated viscous porous media under various mechanical loading and environmental conditions.