Multi-scale description of hydro-mechanical coupling in swelling clays. Part I: Nonlinear poroelasticity

Abstract

This paper presents a micromechanical description of the swelling behavior of partially saturated clays following a two-stage homogenization procedure on a three-dimensional Representative Elementary Volume (REV) of clay. At the nano-scale, the REV of clay particles includes idealized parallel clay platelets and oblate spheroidal pores in between them that are saturated with an electrolyte solution. Swelling forces at all spacing ranges, including the crystalline and osmotic regimes, are considered. At the micro-scale, the REV of clay is comprised of dispersed clay aggregates and partially saturated (variably-sized) spherical pores in between them. At issue, is reconstructing the couplings of mechanical, hydraulic and electrochemical forces at the macroscopic level and their effect on the overall behavior of clay. In Part I, we focus on reversible deformation mechanisms in clay. A generalized nonlinear form of the classical Biot’s poroelasticity relation is obtained with additional terms accounting for capillary and swelling stresses. Capillary stress emerges from interaction of fluid phases at different scales, and takes into account the surface tension effects. The swelling part on the other hand, correlates with the net disjoining hydration and electrochemical forces at the nano-scale. As a result, the stress description of clays is embedded with microstructural information. In addition, a robust localization procedure is utilized to track the microstructural changes associated to micro-porosity and clay platelet spacing. The nonlinearity of the stress–strain description is shown to originate from the dependency of the particles’ elasticity on spacing with electrochemical origins. Finally, base-line features of the model are investigated through material point simulations of a clay swelling test. The discrepancies between the model predictions and experimental measurements are resolved in Part II of this paper by considering also the plastic deformations within the framework developed in Part I.