Scaling Relationships between van Genuchten Model Parameters and Hydraulic Conductivity

Abstract

The soil-water characteristic curve (SWCC) is indispensable for predicting the behaviour of groundwater flow in vadose zones. It remains difficult to determine SWCC, particularly for fractured rocks, under field conditions when little or no test data is available. It is generally believed that the van Genuchten model (VG) parameters α and n are related to pore size distribution (PSD) of soil and can be estimated from PSD data. In this study, correlations are proposed for predicting the VG parameters α and n from hydraulic conductivity K. The VG parameters were obtained by curve-fitting the experimental data of 993 soil samples collected from UNSODA database and published papers. The hydraulic conductivity K of the soil samples varies in six orders of magnitude from 1.30 × 10 −9 m/s to 1.22 × 10 −3 m/s. The statistical distribution of the VG parameters α and n is, respectively, examined using hypothesis test and Anderson-Darling test, showing that α follows a normal distribution after a Box-Cox transformation, and n follows a three-parameter lognormal distribution. The mean and standard deviation of α can be best estimated from K by and σ α = 1.4K 0.13, and the parameter n can be similarly estimated by and σ n = 6.6K 0.18. These correlations are also validated against site-scale test data at Yucca Mountain and published data on fractured rocks and applied to estimate the VG parameters of fractured rocks in the left bank slope at the site of Changbo Hydropower Project. The compiled data and the proposed equations are useful for estimating a narrower range of VG parameters from the more easily-obtained K values at site scale or in case of unavailable test data, and these estimates can be used as input for inverse modelling and simulation of unsaturated flow in porous or fractured media.