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

Philip's two-term infiltration equation has been widely used to infer soil saturated hydraulic conductivity (K_s), 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 K_s estimations under specific soil conditions (e.g., soil isotropy and/or uniform initial water content). This study aimed to provide a comprehensive analysis by systematically considering eight heterogeneous and anisotropic soils with nonuniform initial water contents. Specifically, we examined the validity of Philip's infiltration equation as well as the recently proposed two forms (i.e., infiltration and time forms) of Parlange's infiltration equation both theoretically and in practical applications of double-ring infiltration. Then the time form of Parlange's equation was applied to infer K_s using double-ring infiltrometer measurements with different combinations of six inner ring diameters (10, 20, 40, 80, 120, and 200 cm) and three buffer index (defined as the ratio of the difference between inner and outer ring diameters to the outer ring diameter) values (0.20, 0.33, and 0.50). For each infiltrometer set, 20 stochastic K_s fields were randomly generated by adopting five standard deviation values (0.1, 0.3, 0.5, 0.7, and 0.9). Furthermore, we investigated the effects of five horizontal correlation lengths (30, 60, 150, 300, and 600 cm) on K_s estimations. The results demonstrated that Parlange's equation, compared to Philip's equation, was more universal in describing the cumulative infiltration relationship for the test soils. The combination of inner ring diameter and buffer index of 40 cm and 0.2, respectively, which satisfied most of the practical requirements for determining K_s in the Soil Water Infiltration Global (SWIG) database was optimal. When the horizontal correlation length exceeded a threshold (i.e., 150 cm in our study), the inner ring diameter was required to increase to 80 cm. Our findings contribute to accurate K_s estimations of different soils using double-ring infiltrometers.