Slope Reliability Analysis Incorporating Observation of Stability Performance under A Past Rainfall Event
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摘要: 降雨诱发斜坡失稳机理及可靠度分析通常忽略了现场观测信息的影响，包括斜坡在天然条件下保持稳定或经历历史降雨后保持稳定等观测信息.以无限长斜坡模型为例，采用贝叶斯更新方法基于“斜坡经历某次历史降雨后仍保持稳定”这一现场观测信息概率反分析空间变异水力和抗剪强度参数，基于蒙特卡洛模拟方法计算不同降雨历时下斜坡失效概率，对比分析忽略观测信息对斜坡失效概率估计所造成的影响.结果表明：概率反分析通过融合历史降雨下斜坡稳定性观测信息，可有效排除因抗剪强度参数空间变异性导致斜坡沿软弱层发生失稳的可能性，为客观评价降雨诱发的空间变异斜坡失效概率奠定了基础.如果忽略“斜坡经历某次历史降雨后仍保持稳定”这一观测信息会明显高估斜坡失效概率，尤其在降雨初期.本研究成果为揭示降雨诱发斜坡失稳机制提供新的视角.Abstract: Failure mechanism and reliability analysis of rainfall-induced slopes generally ignore the effects of field observation information, such as the observation that the slope keeps stable in natural conditions or after a historical rainfall event. In this paper, with an infinite slope model as an example, the BUS (Bayesian Updating with Subset simulation) method is adopted for the probabilistic back analysis of spatially variable hydraulic and shear strength parameters based on the field observation that the slope survived from a previous extreme rainfall event. The probabilities of slope failure under different rainfall durations are evaluated within the framework of Monte-Carlo simulation. The influence of ignoring/incorporating the field observation on the estimate of probability of slope failure is also investigated. The results indicate that the possibility of slope failing along the weak zones caused by the spatial variability of soil parameters can be effectively excluded through the probabilistic back analysis incorporating the field observation. Based on this, more realistic probability of slope failure induced by the rainfall can be produced. If the field observation that the slope survived from a previous extreme rainfall event is ignored, the probability of slope failure will be significantly overestimated, especially in the early stage of rainfall. The research outcomes provide a new perspective for interpreting the rainfall-induced slope failure mechanisms in the spatially variable soils.
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Key words:
- slope /
- landslide /
- rainfall infiltration /
- spatial variability /
- probabilistic back analysis /
- reliability analysis /
- hazard geology
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图 4 历史降雨事件下斜坡孔隙水压力沿埋深分布
Fig. 4. Comparison of the pore pressure distributions of the depth under the past rainfall event
图 5 确定性斜坡安全系数随时间变化曲线
Fig. 5. Variation of the factor of safety with rainfall durations
图 6 历史降雨事件下斜坡失效概率随降雨历时变化曲线
Fig. 6. Variation of the probability of slope failure with the rainfall durations under the past rainfall event
图 7 沿垂直方向土体参数先验与后验均值比较
Fig. 7. Comparison of the prior and posterior mean values of soil parameters along the depth
图 8 沿垂直方向土体参数先验与后验变异系数比较
Fig. 8. Comparison of the prior and posterior COVs of soil parameters along the depth
图 9 参数先验与后验PDF和CDF曲线的比较（z=1.975 m）
Fig. 9. Comparison of the prior and posterior probability density functions and cumulative distribution functions of soil parameters at z = 1.975 m
图 11 目标降雨事件下孔隙水压力沿埋深分布
Fig. 11. Comparison of the pore pressure distributions of the depth under the target rainfall event
图 12 目标降雨事件下斜坡失效概率随时间的变化曲线
Fig. 12. Variation of the probability of slope failure with the time under the target rainfall event
表 1 土体参数取值
Table 1. Values of soil parameters
计算参数 取值 计算参数 取值 饱和渗透系数ks 7.2 mm/h 初始基质吸力 10 kPa 饱和含水率$ {\theta }_{s} $ 46.9% 残余含水率$ {\theta }_{r} $ 10.6% 水力参数a 0.943 m 水力参数n 1.395 有效内摩擦角$ {\varphi }^{{'}} $ 32° 有效黏聚力$ {c}^{{'}} $ 5 kPa 土体干重度$ {\gamma }_{d} $ 16 kN/m3 水的重度$ {\gamma }_{w} $ 9.8 kN/m3 
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