Analytical derivation of water retention for random monodisperse granular media

The mechanics of water retention in unsaturated granular media is of critical importance to a broad range of disciplines including soil science, geotechnical engineering, hydrology and agriculture. Fundamental to water retention is the relationship between degree of saturation and suction, referred to as the water retention curve (WRC). The majority of WRC models are empirically based and seldom incorporate physically meaningful parameters. This study presents an analytical model for the WRC that considers separate contributions from fully filled pores and partially filled pores containing liquid bridges. A recently established unique k-gamma pore volume distribution function for randomly assembled monodisperse granular materials is adopted to determine the contributions of fully filled pores. Calculation of the contribution of residual pore water retained in partially filled pores is undertaken by representing pores as individual cells shaped as platonic shapes of various sizes and determining the volume of all liquid bridges suspended between particles within the pore cells. Weighting factors for the various cell types are obtained from the pore volume distribution to determine the relative contribution of different pore cell geometries to the total residual pore water. The combined model accurately describes experimental data for monodisperse spherical glass beads for both wetting and drying, even though the underlying assumptions do not reflect exactly the complex, interconnected and highly irregular geometry of the pore space. A single parameter provides the lateral shift between the wetting and drying curves. The results of this study provide a geometric understanding of the mechanisms of water retention in granular media.