Pore-Scale Model for Water Retention and Fluid Partitioning of Partially Saturated Granular Soil

Abstract

A model for the water retention behavior of unsaturated granular soil is developed by extending the classic bundled cylindrical capillary representation of pore space to a geometry more closely approximating that of granular porous media. Expressions for pore-scale saturation are derived as functions of matric suction for a three-dimensional unit pore comprising angular pore space bounded by spheres in simple cubic packing order. Water retention curves are modeled by assigning a statistical distribution of pore sizes optimized to best match experimentally determined retention curves. A key model attribute is its capability to capture evolution of fluid partitioning along drainage or wetting paths by differentiating pore water retained as thin films adsorbed to particle surfaces, liquid bridges retained in wedge-shaped pores, and saturated pockets in relatively small pores. Interfacial surface tension, solid-liquid contact angle, wetting direction, and mineralogy (Hamaker constant) are treated as model variables to examine their influences on water retention. Modeled retention curves compare well with measured curves obtained for glass beads, natural sands, and soils from the literature. The model effectively estimates hysteretic wetting-drying response, surfactant-induced surface tension lowering, and air-water interface area as a function of saturation. Capability to model evolution of fluid distribution has potentially important implications toward more robust understanding of macroscopic hydraulic, electrical, thermal, and mechanical behavior of unsaturated soil.