Mathematical formulation of thermo-hygro-mechanical coupling problem in non-saturated porous media Original Research Article

Mathematical formulation of thermo-hygro-mechanical coupling problem in non-saturated porous media Original Research Article Pages 5105-5122 Wafa Obeid, Ghassan Mounajed, Abdenour Alliche Close preview | Related articles | Related reference work articles Abstract | Figures/Tables | References Abstract A coupling model is developed to simulate the response of porous materials when subjected to combined thermal, hydrous and mechanical stresses. This modelling is based on the theory of the Mechanics of Non-Saturated Porous Media taking into account some of the simplifying assumptions, which can be justified as far as buildings are concerned. The model constitutes a basis for a numerical formulation comprising space discretisation using Galerkinʹs method, time discretisation using the finite-difference method with an implicit scheme, and non-linear computation using Newton–Raphsonʹs method. This mathematical model was integrated in a finite-element code SYMPHONIE. To illustrate the model, this study covers two cases of simulation on building structure walls. These simulations concern the drying and the condensation of moisture on a thin wall. Article Outline Nomenclature 1. Introduction 2. Thermo-hygro-mechanical coupling model 2.1. Basic assumptions of the model 2.2. Constituent equations of the model 2.2.1. Conservation laws 2.2.2. Behaviour laws 2.3. Field equations of the model 2.3.1. The Navier equation 2.3.2. The equation of heat diffusion 2.3.3. The equation of moisture diffusion 2.4. Boundary conditions 2.4.1. Mechanical boundary conditions 2.4.2. Thermal boundary conditions 2.4.3. Hydrous boundary conditions 2.5. Initial conditions 2.6. Model parameters 3. Numerical formulation of the model 4. Numerical simulations 4.1. Drying a thin wall 4.1.1. Evaluating of the drying time 4.1.2. Influence of the drying phenomenon on mechanical behaviour 4.2. Thermo-hydrous exchange on a building wall 4.2.1. Temperature variation curves 4.2.2. Calculating the risk of condensation 5. Conclusions Acknowledgements Appendix A Appendix B Appendix C.