Application of a Multi-Scale form of Terzaghi’s Effective Stress Principle for Unsaturated Expansive Clays to Simulate Hydro-Mechanical Behavior During Hydration

Abstract

Abstract.Our recently developed multi-scale form of Terzaghi's effective stress principle for unsaturated swelling clays that was rigorously derived by periodic homogenization starting from micro-and nano-mechanical analyses is applied to numerically simulate one-dimensional swelling pressure tests of compacted bentonites during hydration. The total macroscopic stress captures the coupling between disjoining forces at the nanoscopic scale of clay platelets and capillary effects at the microscopic scale of clay aggregates over the entire water content range. The numerical results allow to draw conclusions on the water transfer mechanism between inter-and intra-aggregate pores during hydration and consequently on the evolution of the external swelling pressure resulting from the competition between capillary and disjoining forces. In addition, such application highlights the abilities and the limits of the electrical double-layer theory to compute the disjoining pressure in the nano-pores. For large platelet distances, in the range of osmotic swelling, the nature of the disjoining pressure is electro-chemical and can be computed from PoissonBoltzmann theory. Conversely, at small distances, in the crystalline swelling, a solvation component has to be added to account for the molecular nature of the solvent. As a first improvement of the nano-scale description the solvent is treated as a hard sphere fluid using Density Functional Theory.

Effective stresses and estimations of the apparent Biot coefficient in stacked clay layers

“…Other molecular-scale informed studies (Le et al 2013) (Mainka et al 2016) resort to Density Functional Theory (DFT) and Mean Spherical Approximations (MSA) to compute the disjoining pressure in clays. Contrary to molecular simulations, analyses based on DFT/MSA and Poisson-Boltzmann distribution cannot capture the non-monotonous character of counterions distribution within clay micropores (Tinnacher et al 2016).…”

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

“…This model can be considered as a new multiscale effective stress approach governing the macroscopic behavior of clayey soils and rocks with a general conceptualization of the major interactions that occur in clay materials. The implemented model can be compared to existing previous approaches that consider solely osmotic pressure along with other microstructural parameters (Zhang et al, 2020b;Alonso et al, 2010;Pereira et al, 2010) or to those considering only the effective disjoining pressure (Mainka et al, 2016;Likos and Lu, 2006). Considering the formulation given in Eq.…”