Analytical solution for infiltration into single-layer cover under heavy rainfall events and its application for slope stability analysis
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摘要: 近年来中国极端降雨事件频发,研究强降雨条件下单层土质覆盖层的入渗规律及斜坡稳定性具有重要意义。基于二维非饱和土渗流控制方程,采用指数函数模型描述土体的土水特征曲线和渗透系数曲线,针对强降雨过程中表层土体达到饱和状态前后分别采用恒定流量和恒定压力水头作为覆盖层表面边界条件,推导了强降雨条件下单层土质覆盖层的入渗解析解。通过与有限元软件Geostudio-Seep/W的计算结果进行对比,证明了该解析解的有效性。在解析解的基础上,根据非饱和土抗剪强度理论,分析了单层土质覆盖层的斜坡稳定安全系数在强降雨条件下的发展情况,结果表明潜在滑动面的埋深越大,覆盖层稳定安全系数对降雨的响应速度越慢。强降雨期间以覆盖层底面作为滑动面的稳定安全系数始终保持最小,说明覆盖层最易沿着该滑动面发生失稳。得到的解析解为单层土质覆盖层的防渗性能评价及斜坡稳定性分析提供了简单实用的工具。Abstract: In recent years, the extreme rainfall events have occurred frequently in China, and so investigating the infiltration law and slope stability of single-layer soil covers under heavy rainfall events is of great significance. An analytical solution for rainwater infiltration into single-layer soil covers is derived based on the two-dimensional governing equation for unsaturated flows. This analytical solution is obtained by employing the constant flow rate and constant pore water pressure head as the top boundary conditions of the cover before and after the surface soil reaches saturation during a heavy rainfall event. The analytical solution is validated by comparing with the results of the finite element software Geostudio-Seep/W. Based on the analytical solution and the theory of shear strength of unsaturated soils, the variation of the factor of safety of a single-layer soil cover under a heavy rainfall event is analyzed. The results indicate that the greater depth the potential sliding surface, the slower the response of the factor of safety to rainfall. During the whole rainfall period, the factor of safety with the bottom surface of the cover as the sliding surface remains the smallest, indicating that the cover is most prone to sliding along this sliding surface. The analytical solution obtained in this study provides a simple and practical tool for evaluating the anti-seepage performance and stability analysis of single-layer soil covers.
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图 4 不同解析解下覆盖层孔隙水压力水头剖面随降雨时间的变化(曲线为本文解析解结果,符号为文献[11]解析解结果)
Figure 4. Changes of pore water pressure head profile over rainfall duration for different analytical solutions (splines present results of analytical solutions in this study and symbols present results of analytical solutions in reference [11])
表 1 解析法和数值法中使用的参数
Table 1 Parameters used in analytical and numerical methods
饱和体积含水量θs/% 残余体积含水量θr/% 减饱和系数α/m-1 饱和渗透系数ks/(m·s-1) 初始体积含水量θ0/% 降雨强度q/(m·s-1) 降雨历时/h 47.13 10.44 0.05 1.29×10-7 34.0 2.85×10-6 24 覆盖层厚度/m 坡度δ/(°) 干土重度γd/(kN·m-3) 水重度γw/(kN·m-3) 有效黏聚力c′/kPa 有效内摩擦角φ′/(°) 基质吸力角φb/(°) 1.0 arctan(1/3) 14.2 9.81 5.74 26.6 14.1 -
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