Improved Green–Ampt Model for Evaluating Rainfall Infiltration and Slope Stability

Rainfall infiltration is one of the critical external triggers for landslide disasters. However, uncertainties remain regarding the underlying mechanisms through which rainfall infiltration induces such geological hazards. Therefore, conducting in-depth research on the patterns of rainfall infiltration in slopes and its impact on slope stability holds significant engineering value for revealing the instability mechanisms of rainfall-induced landslides. In this paper, the Green-Ampt (GA) model is improved by considering the exponential distribution characteristics of soil initial moisture content (θi), the time boundary conditions of rainfall infiltration, and the dynamic development features of the depth of saturated and unsaturated zones. This improved model is then applied to analyze seepage and stability in a homogeneous soil slope. The improved GA model is systematically compared with an existing improved GA model and the numerical solution of the Richards equation, and the results demonstrate good convergence. Notably, the wetting front depth (zf) curve derived in this study can more effectively reflect the dynamic changes in the rainfall infiltration process and further reveal the intrinsic mechanism of rainfall infiltration in slopes. The θi distribution pattern exerts a significant impact on the infiltration time boundary conditions of slope soil. The slope stability factor (Fs) is found to decrease rapidly with increasing rainfall duration (t) in the early stage, followed by a stabilization trend. Specifically, for the stage of t ≤ tp1, slope stability is dominated by the wetting front; for the stage of t > tp1, intersection points emerge between the zf curve and the saturated–unsaturated interface curve. The comparison analysis of parameters shows that the order of influence on the time boundary (from strongest to weakest) is rainfall intensity (q), slope angle (`), soil saturated hydraulic conductivity (ks), and fitting parameter of initial moisture content (α). Regarding the influence on zf, q has the most significant effect, followed by ks, while β and a have the least significant effects. Moreover, compared with a and ks, q and β have more significant impact on zf, Fs and t corresponding to the intersection point of curves of Fs at both the wetting front interface (WFI) and the saturated–unsaturated interface (SUI). The improved GA model more accurately captures the dynamic relationship between rainfall infiltration and slope stability, thereby providing a theoretical basis for analyzing landslide mechanisms and developing early warning systems.