Abstract: Accurate description of rainfall infiltration is essential for understanding the slope instability mechanism and for preventing and controlling rainfall-induced landslides. Currently, numerical solutions of the Richards equation and the Green-Ampt model are widely used to analyze rainfall infiltration in slopes. Although the Richards equation yields high accuracy, it can suffer from low computational efficiency and convergence issues. Moreover, the classic Green-Ampt model neglects soil stratification and unsaturated-transition layers, and thus cannot accurately represent rainfall infiltration in heterogeneous, multi-layered slopes. To address these limitations, we introduce the concepts of equivalent hydraulic conductivity and elliptical transition layer theory and dynamically simulate rainfall infiltration in heterogeneous, multi-layered slopes. Based on this framework, an improved Green-Ampt model is proposed. The model addresses two key challenges: (1) modifying the calculation formula for the equivalent hydraulic conductivity to describe water migration as the wetting front crosses interfaces between soil layers; (2) deriving a parametric analytical equation for the elliptical transition layer to efficiently compute the spatial distribution of slope volumetric water content for different rainfall durations. Results show that the proposed model yields seepage, stability, and reliability analyses that are highly consistent with Richards equation solutions under both homogeneous and heterogeneous conditions, particularly in the early rainfall stage. Moreover, the model offers high computational efficiency and does not suffer from convergence issues, thereby providing strong theoretical support for reliability analysis of complex slopes and for the prevention and control of rainfall-induced landslides.

Key words: multi-layered soil slope, rainfall infiltration analysis, reliability analysis, Green-Ampt model, equivalent hydraulic conductivity, elliptical transition layer