Abstract

A three-scale model is proposed to describe electro-chemo-mechanical couplings in unsaturated swelling clays characterized by two porosity levels and three separate length scales. The nanoscale portrait consists of charged clay particles separated by a nanoporous network saturated by a binary monovalent aqueous electrolyte solution. Local ion distribution and electric potential are governed by the Poisson–Boltzmann problem. At the microscale, the system is represented by swollen clay clusters separated from each other by a network of micropores filled with a mixture of bulk water and air. Under mechanical equilibrium characterized by the competition between disjoining forces of electrochemical nature and capillary attraction effects, we derived a novel form of the effective stress principle in the asymptotic limit of scale separation. Such form includes a new macroscopic equivalent pore pressure weighted by a two-scale effective Bishop coefficient that incorporates the effects of the adsorbed water at the secondary nanopore level in addition to the contributions of the water–air interfaces at the micropore level. Within the thermodynamic context for constructing macroscopic constitutive laws based on stress–strain variables, the three-scale model leads to a set of three work-conjugated state variables. In addition to the contact stress between particles and the new effective Bishop-type component, the novel form includes salinity as an additional stress-conjugated variable and a three-scale version of the electrochemical swelling stress. The potential of the multiscale approach in capturing the complex features of unsaturated expansive clays is illustrated by numerical reconstruction of the effective coefficients in a simplified isotropic microstructure.

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