Analytical Solution for Delayed-Peak Heavy Rainfall Infiltration and Slope Stability Assessment

This study mechanistically investigats slope stability under delayed-peak heavy rainfall infiltration. We develop a theoretical framework for unsaturated soil seepage using the two-dimensional Richards equation, with exponential function models characterizing both soil-water characteristic curves and hydraulic conductivity functions. During intense rainfall events, flux boundary and constant pressure head boundary conditions were applied to simulate the complete infiltration and surface runoff phases, respectively. Through rigorous mathematical derivation, we obtained a spatiotemporal analytical solution for delayed-peak heavy rainfall infiltration that accounts for surface runoff dynamics. The proposed analytical solution was verified through finite element simulations using Geostudio-Seep/W software. Subsequently, the temporal-spatial evolution characteristics of slope stability under five distinct rainfall scenarios were systematically investigated employing Fredlund's dual-stress variable strength theory. The principal findings include: (1) the initial rainfall phase significantly influences slope stability degradation; (2) the runoff-to-total rainfall ratio positively correlates with rainfall intensity; and (3) the safety factor shows strong spatiotemporal coupling with pore water pressure distribution patterns.