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

Saturated hydraulic conductivity of soil, K-sat, is a critical parameter for mathematical modelling of groundwater and soil water flow. Current empirical K-sat 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, d(5), d(10), d(15), d(50), etc., or the fractionation of sand, silt and clay. In this study, we proposed an alternative modelling framework to estimate K-sat 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 (d(S)) by calculating the moments of the PSD function. The proposed empirical equations were tested against the measured K-sat 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 d(S) was more relevant to K-sat than the number mean diameter (d(N)) and mass mean diameter (d(M)) (the RMSE was 0.486 for K-sat - d(N); 0.187 for K-sat - d(S); and 0.212 for K-sat - d(M), respectively). We also found that the proposed equation with d(S) had superior performance over the Hazen equation and PTF-based models. Our results indicated that the K-sat calculated using d(S), 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 K-sat from the void ratio and arithmetic mean diameter is proposed. Sauter mean diameter, d(S), can be obtained by calculating the moments of the PSD function. Ksat model using d(S) performs better than that using d(N), d(M), d(5), d(10), or d(50) or PTF-based models.

Automated summary

In this study, an alternative modelling framework to estimate the saturated hydraulic conductivity (K-sat) of soil was proposed. The framework uses the void ratio and arithmetic mean diameter to estimate K-sat. The results showed that the Sauter mean diameter performed better than other diameter indicators and PTF-based models. This study provides guidance for future empirical relationships between soil water retention curves, other soil properties, and continuous particle size distribution functions.