Hydraulic functions for swelling soils: pore scale considerations

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. Despite well-developed theory for crystalline and osmotic swelling of clay minerals at the scale of individual clay lamellae, their translation to prediction of hydraulic properties of swelling soils is limited. In this study we propose a framework that combines physico-chemical processes with pore scale 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 the 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 saturated hydraulic conductivity are derived from calculations of average flow velocities in ducts and between parallel plates, and invoking proportionality between water flux density and unit hydraulic gradient. Preliminary model calculations compare favorably with published data, and show great potential for upscaling considerations.