Uncertainty in Determination of the Soil-Water Characteristic Curve Based on the van Genuchten Model

Abstract

The van Genuchten (1980) (VG) model is one of the most popular and widely used equations to achieve the best fitting of experimental data of the soil-water characteristic curve (SWCC) test. As the best-fitted SWCC is determined from regression analysis, there are various possible solutions for the best-fitted curve (or the determined fitting parameters). The residual error, which is obtained from regression analyses, can be considered as an index indicating the incapability of the SWCC equation in representing the measured SWCC experimental data. As a result, there is always uncertainty associated with determined SWCC from the regression analysis. The residual error from the regression analysis can be used for the quantification of the uncertainty of determined SWCC. In this paper, Taylor’s expansion is adopted, and only the first-order term is considered for the VG model. Subsequently, the variances of the fitting parameters in the VG model are estimated from the residual error. Consequently, the uncertainty of SWCC using the VG model is quantified by using the upper and lower bounds with a 95% confidence level. The artificial soil, composed of mixed sand and kaolin, was prepared for the SWCC measurement. This paper shows that the proposed method can be used to quantify the uncertainty of SWCC from different specimens (a total of 12 specimens).