Development and numerical implementation of a multiscale constitutive law for double-porosity swelling clayey rocks

The swelling of clayey rocks originates at different scales of the material. Clay mineral swelling is governed by two different phenomena: crystalline and osmotic swellings. In this paper, we adapt a multiscale numerical model that considers both crystalline swelling and interlayer osmotic swelling (four water layers and more) to efficiently implement it in a finite element method code. To this end, we itemize the different interactions arising in the interlayer space with respect to the disjoining pressure, and in the interparticular space considering the capillary effects. The overall model is based on the upscaling of the constitutive law from the nanoscopic scale to the macroscopic scale by adding all the different interactions that appear while upscaling. Additionally, the general model adapted in this paper can be considered as a new definition of the effective stress governing the chemo-hydromechanical behavior of clayey rocks. The numerical model is then implemented in Code_Aster software. The validation of our model is conducted by reproducing constant-volume swelling test. Simulation results for different pore size distributions demonstrate fair agreement between the experimental results and the numerical modeling in comparison with linear elasticity that overestimate the final swelling pressure compared to the model developed herein.