An accurate modeling of the sorption-induced deformation of porous materials is essential for a variety of applications related to energy applications (e.g., natural gas production from and CO2 sequestration into coalbed and shale formations) or civil engineering applications (e.g., drying shrinkage of concrete or soils). Many materials for those applications share the fact that their pore size distribution is wide, ranging from nanopores to macropores. This PhD study is dedicated to modeling the deformation of such porous materials with a wide pore size distribution in partially saturated conditions when submitted to variations of fluid chemical potential.

A first theoretical work extends a poromechanical model derived from thermodynamic considerations by El Tabbal et al. (2020)1 for mesoporous and macroporous materials. The model considers that fluid-induced deformations originate from capillary effects, surface energy effects, and adsorption effects. One improvement to the model lies in modeling the strain that occurs during the adsorbate cavitation. We validate the model by applying it to data from the literature, namely strain measurements of a variety of adsorbents (e.g., coals, cement, Vycor glass, etc.) upon sorption/desorption with a variety of adsorbates (water, CO2, nitrogen, etc.). In this validation, we consider that fluid adsorption is non-site-specific and that the elastic behavior is linear. The model is capable of predicting the shape of strain isotherms with no fitting parameter.

We then study the impact of several choices or experimental uncertainties on the shape of the strain isotherm, namely the choice of the method used to back-calculate the pore size distribution from the sorption isotherms, the value of the cavitation pressure, the experimentally defined “dry state”, and the calculated specific surface area.

Other improvements to the model include the ability to consider 1) the nonlinearity of the elastic behavior and 2) the site specificity of fluid adsorption on the pore surface. Assuming a logarithmic relation between the equivalent pore pressure and the strain, the model is able to predict reversible humidity-induced deformations of soils. When considering the site specificity of fluid adsorption on the pore surface, the poromechanical model makes it possible to model an initial contraction of the material at very low partial pressures (w.r.t. the dry state) – a feature observed experimentally. This contraction originates from the fact that surface stress and surface tension are two different thermodynamic entities whose evolutions with adsorption generally differ, except when adsorption is non-site-specific.

This last result points out the need for a more detailed understanding of the difference between surface tension and surface stress. Given the difficulty of measuring this latter experimentally, we investigate surface stress with molecular simulations. First, we perform Grand Canonical Monte Carlo (GCMC) simulations of water in two C-S-H slit mesopores that differ by their C/S ratio (i.e., 1.1 and 1.7) and obtain water adsorption isotherms at 6 various temperatures ranging from 300 K to 525K. Second, at a constant amount of water in micropores, we simulate closed and open mesopores: the pressure difference between the two configurations provides a value for the surface stress at various water contents (or relative humidities). The results show that the surface stress of the C-S-H surface is on the order of several hundred mN/m. Comparing this surface stress and the surface tension calculated with the Gibbs adsorption isotherm shows that the magnitudes of the variations of the surface stress and surface tension do indeed differ from each other significantly.