Numerical modeling of double-ring infiltrometers for determining saturated hydraulic conductivity in heterogeneous and anisotropic soils

Abstract

Philip’s two-term infiltration equation has been widely used to infer soil saturated hydraulic conductivity (Ks), the accuracy of which is usually influenced by the size of infiltration rings and soil conditions. Previous studies have primarily focused on exploring the ring-size dependence of Ks estimations under specific soil conditions (e.g., soil isotropy and/or uniform initial water content). This study aims to provide a comprehensive analysis by systematically considering eight heterogeneous and anisotropic soils with non-uniform initial water contents. Specifically, we first examined the validity of Philip’s equation as well as the recently proposed two forms (i.e., infiltration- and time-form) of Parlange’s infiltration equations both theoretically and in practical applications of double-ring infiltration. Then the time form of Parlange’s infiltration equation was applied to infer Ks using double-ring infiltrometer measurements with different combinations of six inner ring diameters (di = 10, 20, 40, 80, 120, and 200 cm) and three buffer indices (i.e., defined as the ratio of the difference between inner and outer ring diameters to the outer ring diameter, here b = 0.2, 0.33, and 0.5). For each infiltrometer set, 20 stochastic Ks fields were randomly generated by adopting five standard deviation values (i.e., σlnKs = 0.1, 0.3, 0.5, 0.7, and 0.9). Furthermore, we investigated the influence of the horizontal correlation length (i.e., λx = 30, 60, 150, 300, and 600 cm) on Ks estimations. The results demonstrate that Parlange’s equation, compared to Philip’s equation, is more universal in describing the cumulative infiltration relationship for the test soils; the optimal combination of inner ring diameter and buffer index was 40 cm and 0.2, respectively, which satisfied most of the practical requirements for determining Ks in the Soil Water Infiltration Global (SWIG) database; when the horizontal correlation length exceeds a threshold (i.e., 150 cm in our study), the inner ring diameter is required to increase to 80 cm. Our findings contribute to accurate Ks estimations of different soils using double-ring infiltrometers.