Hydraulic Properties of Swelling Clay-Sand Mixtures: Microscale Modeling and Measurements

Abstract

Changes in volume and pore space induced by the shrink-swell behavior of clay minerals present a challenge to predictive modeling of hydraulic properties of clayey soils. We present a pore-scale framework that combines physico-chemical processes with pore-geometrical, hydrostatic, and hydrodynamic considerations toward prediction of constitutive hydraulic relationships for swelling porous media. Variations in pore space are modeled by considering the soil clay fabric as an assembly of colloidal-size tactoids with lamellar structure. The arrangement of clay tactoids and the spacing between individual lamellae are functions of primarily clay hydration state quantifiable via the disjoining pressure that is dominated by a large electrostatic repulsive component. Solution chemistry and clay type are also considered. Silt and sand textural constituents are represented as rigid spheres interspaced by clay fabric in two basic configurations of expansive and reductive unit cells. Bulk soil properties such as clay content, porosity and surface area serve as constraints for modeling pore-space geometry. Liquid saturation within the idealized pore space is calculated as a function of chemical potential considering volume changes due to clay shrink-swell behavior. Closed-form expressions for prediction of unsaturated hydraulic conductivity are derived from calculations of average flow velocities in ducts, parallel plates, and in corners bounded by liquid-vapor interfaces, and invoking proportionality between flux density and hydraulic gradient. Measurements of saturated hydraulic properties are used to evaluate model predictions and lay the foundation for upscaling considerations to sample and profile scales. Advanced flexible-wall permeametry is employed to measure permeability of clay-sand mixtures with mono- and divalent ionic solutions. Preliminary pore-scale model calculations show favorable agreement with measured permeability values for a wide range of clay contents and varying ionic solutions.