Prediction of saturated hydraulic conductivity of sandy soil using Sauter mean diameter of soil particles

Saturated hydraulic conductivity of soil, Ksat, is a critical parameter for mathematical modelling of groundwater and soil water flow. Current empirical Ksat models, such as Kozeny–Carman model, Hazen models, or empirical approaches based on soil pedotranfer functions (PTFs) rely on the specific surface area, certain characteristic particle size(s), for example, d5, d10, d15, d50, etc., or the fractionation of sand, silt and clay. In this study, we proposed an alternative modelling framework to estimate Ksat from void ratio and arithmetic mean diameter of soil particles. We suggested to describe the particle size distribution (PSD) using a continuous mathematical distribution function, for example, the lognormal distribution function, and to obtain the Sauter mean diameter (dS) by calculating the moments of the PSD function. The proposed empirical equations were tested against the measured Ksat values for 54 sand samples with available measured PSD and void ratio as reported in Toumpanou et al. and validated using 49 sandy soil samples obtained from the Unsaturated Soil Database (UNSODA). We found that the dS was more relevant to Ksat than the number mean diameter (dN) and mass mean diameter (dM) (the RMSE was 0.486 for Ksat ‐ dN; 0.187 for Ksat ‐ dS; and 0.212 for Ksat ‐ dM, respectively). We also found that the proposed equation with dS had superior performance over the Hazen equation and PTF‐based models. Our results indicated that the Ksat calculated using dS, which was either estimated from discrete experimental data or calculated from a continuous lognormal PSD function, best matched with the measured values for coarse‐textured soils. Future studies should focus on developing empirical relationships for soil water retention curves and other soil properties based on continuous PSD functions. Highlights A modelling framework to estimate Ksat from the void ratio and arithmetic mean diameter is proposed. Sauter mean diameter, dS, can be obtained by calculating the moments of the PSD function. Ksat model using dS performs better than that using dN, dM, d5, d10, or d50 or PTF‐based models.