Soil moisture migration model based on flux-concentration relation under steady rainfall

Moisture content distribution in soil is of great importance for understanding rainfall-induced slope failure and roadbed settlement. This study aims to develop a moisture migration model that improves the quantification of moisture content at an arbitrary point of the soil at any time for the whole process of infiltration under steady rainfall. The model was derived from the Richards equation using the flux-concentration relation, which was validated by numerical solutions calculated by Hydrus-1D software to evaluate the performance of the model. Results showed good accuracy and high adaptability for the moisture migration simulation of a wide range of soil types, and is applicable for short-duration and long-duration steady rainfall. Moreover, it can also reflect the stratification phenomenon for soil profile wetting by infiltration. Our analysis indicates that the flux and surface volumetric moisture content together can bound the boundary conditions of rainfall infiltration, which presents a shift from constant-flux to constant-concentration during long-duration steady rainfall. The migration rate of the wetting front in the later stage of infiltration positively correlates with rainfall intensity under the constant-flux condition, while it finally stabilizes at Ks/(θs − θi) under the constant-concentration condition (i.e., Ks – saturated hydraulic conductivity, θs – saturated volumetric moisture content, θi – initial volumetric moisture content).