A graphical approach to solving the van Genuchten soil-water retention equation

Abstract

Accurate prediction of unsaturated soil behaviour depends on the reliable estimation of the soil-water retention curve (SWRC) and the corresponding hydraulic conductivity function (HCF). Although the van Genuchten-Mualem (VG-M) model is widely accepted for this purpose, its parameter estimation typically relies on nonlinear optimisation methods, which may produce values with limited physical meaning. This research presents a graphical method for directly identifying model parameters from essential characteristics of the SWRC, including the saturated and residual water contents, the inflection point, and the residual suction. The proposed approach removes the requirement for repetitive numerical fitting, improves the clarity and physical understanding of the parameters. The method was applied to measured SWRC datasets representing different soil textures. The graphical fits produced R ² values of 0.9619–0.9926 and RMSE values of 0.0065–0.0172. For comparison, nonlinear least-squares fitting produced R ² of 0.9909–0.9989 and RMSE values of 0.0020–0.0118. Although optimisation yielded lower errors, the graphical method retained a direct physical interpretation of the parameters. The graphically derived parameters for the VG-M HCF model captured the general hydraulic conductivity trend ( R ² of 0.8540). Deviations at high suction were mainly associated with known limitations of the VG-M model at the dry end, rather than the graphical procedure itself.