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后峰型强降雨入渗解析解及斜坡稳定性分析

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

  • 摘要: 针对后峰型强降雨入渗机理对斜坡稳定性的影响,基于Richards二维非饱和土渗流控制方程,采用指数函数模型描述土水特征曲线和渗透系数曲线,在强降雨过程中使用流量边界与恒定压力水头边界来分别模拟完全入渗阶段与地表径流阶段,推导了考虑地表径流的后峰型强降雨入渗时空动态解析解。通过有限元软件Geostudio-Seep/W验证了该解析解的准确性,并利用Fredlund双应力变量强度理论探讨了5种不同降雨条件下边坡稳定性的时空演变特征。结果表明:(1)降雨的前期阶段对边坡稳定性的影响较大;(2)随降雨强度的增加,径流量与总降雨量的比值增大;(3)稳定安全系数与孔隙水压力的时空变化密切相关。

     

    Abstract: 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.

     

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