Pore-Scale Model for Estimating Saturated and Unsaturated Hydraulic Conductivity from Grain Size Distribution

An approach is presented for predicting saturated hydraulic conductivity ($k_{\text{sat}}$) and the unsaturated hydraulic conductivity function (HCF) of coarse-grained soils using pore-scale modeling of liquid configurations in idealized unit pores. Procedures are described for estimating $k_{\text{sat}}$ and the HCF from simple measurements of grain size distribution (GSD) obtained using mechanical sieve analysis. Measured GSD is converted into an equivalent population of spherical particles arranged to form subassemblies representing relatively loose and relatively dense particle configurations. Capillary theory and the geometry of unit pores formed within the particle subassemblies are used to quantify pore-scale liquid configurations as a function of matric suction. Corresponding hydraulic conductivity is calculated from pore-scale hydrodynamic considerations. Comparison between measured and predicted $k_{\text{sat}}$ for a suite of sand-sized soils demonstrates that the approach is an improvement over existing approaches, based solely on empirical correlation between hydraulic conductivity and GSD, porosity, or fractional grain size (e.g., $d_{10}$). The unsaturated HCF is effectively predicted to degrees of saturation as low as 20%. Assumptions and constraints in the framework restrict the applicability of the model to materials with a rigid matrix, with particles predominantly in the sand- to silt-sized range.