Multiscale interactions of elastic anisotropy in unsaturated clayey rocks using a homogenization model

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

“…This will henceforth; help compare the model with classic elasto-plastic approaches such as the Barcelona Basic Model (Alonso et al, 1990). Third, to consider most clayey rocks, another prospect would be to add a transverse isotropic framework (Eghbalian et al, 2022a(Eghbalian et al, , 2019Giraud et al, 2007;Ip and Borja, 2023). Fourth, one can add another homogenization scale to account for clay aggregates while tackling soils and other clay geomaterials such as bentonite.…”

“…Moreover, this has been widely used to formulate multiscale models at different scales and considering not only the isotropic framework as detailed in Abou-Chakra Guéry et al (2007) but also transverse isotropy (Ip and Borja, 2023;Zhao et al, 2022). Besides, the Self-Consistent approach, despite its preciseness and effectiveness, presents a percolation threshold making it incomplete to reproduce the whole behavior for a wide range of interparticular porosities (Gross and Seelig, 2011).…”

“…For more considerations, the electrostatic repulsion and the attractive component of van der Waals were assembled in terms of net energy in the frame of the highly acknowledged Derjaguin-Landau-Verwey-Overbeek DLVO theory (Derjaguin and Landau, 1993;Derjaguin et al, 1987b;Verwey and Overbeek, 1947). It is worth noting that these aspects were commonly used to describe clay electro-chemohydromechanical behavior (Ogata and Komine, 1996;Komine and Ogata, 2003;Ogata and Komine, 1996;Liu, 2013;and more recently Eghbalian et al, 2019;Kyokawa, 2020;Kyokawa et al, 2020;Eghbalian et al, 2022aEghbalian et al, , 2022bIp and Borja, 2023). Each term of the formulations of Eqs.…”

“…With respect to what has been detailed herein, the mathematical formulation corresponding to the interparticular equivalent pore pressure figuring in Eq. ( 2) reads as follows (Cariou et al, 2013;Ip and Borja, 2023):…”

“…Other models exist and are consistent with the precedent models developed by Cariou et al (2013) and Dormieux et al (2006b) which are more general and more elaborate, adding new physics of the swelling pressure and homogenization not only for the pores but also at the level of the cracks. We can cite among others (Eghbalian et al, 2019;Ip and Borja, 2023;Wan and Eghbalian, 2017). More recently, Zhao et al (2022) developed a multiscale constitutive model using a general approach incorporating the anisotropy of clayey rock and taking further modeling aspects with a viscoplastic approach.…”