Rainfall-Induced Landslide Stability for Variably Shaped Slopes: A Multi-Model Integration Approach Through Green-Ampt Theory and Numerical Validation

As one of the most catastrophic geological hazards globally, landslides exhibit heightened risks due to their increasing frequency, destructive potential, and extensive spatial distribution. The primary objective of this study is to develop an integrated analytical framework to quantitatively evaluate the stability of variably shaped slopes under rainfall infiltration. The core hypothesis is that slope curvature significantly alters infiltration behavior and stress distribution, leading to morphology-dependent failure mechanisms. Employing Green-Ampt infiltration theory coupled with limit equilibrium analysis, we establish stability prediction models for three fundamental slope geometries (linear, concave, convex) under contrasting rainfall regimes (high-intensity vs. low-intensity precipitation). The derived analytical solutions reveal two critical phenomena: (1) progressive downward migration of the saturation front maintaining parallelism with slope surfaces during infiltration and (2) time-dependent stability deterioration following hyperbolic decay patterns. The proposed models are rigorously validated through numerical simulations employing finite element methods, which demonstrate remarkable congruence with theoretical predictions, showing safety factor discrepancies below 5% (ΔFs < 0.05). Particularly, concave slopes exhibit 18–22% faster destabilization rates compared to convex counterparts under equivalent rainfall conditions. The validated models elucidate the spatiotemporal evolution of matric suction and pore pressure distributions, providing quantitative insights into morphology-dependent failure thresholds. These findings advance predictive capabilities for rainfall-induced landslides through physics-based stability criteria, offering critical guidance for terrain-specific early warning systems and mitigation strategies in geohazard-prone regions.