Time-varying reliability analysis of unsaturated reservoir bank slopes under water level drop considering multi-parameter spatial variability
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摘要: 库水降落及土体参数空间变异性是影响边坡稳定性的重要因素，对这两种因素作用下库岸边坡进行可靠度评价具有重要意义。但现有可靠度分析大多仅考虑单一抗剪强度参数或水力参数的空间变异性，且仅分析某一时刻的静态可靠度，忽略了多参数空间变异性及时变因素的影响。为此，提出了同时考虑这两种因素的库岸边坡时变可靠度分析方法。采用Karhunen-Loève展开方法对土体参数随机场进行离散，利用分片逆回归（SIR）方法对随机变量进行降维预处理，基于降维后的变量构建高斯过程回归（GPR）代理模型，进而采用蒙特卡洛模拟（MCS）方法评估边坡失效概率。最后，以某一非饱和库岸边坡为例验证了所提方法的有效性，探讨了边坡在不同水位降落工况下的可靠度变化规律，并对关键土体参数进行了敏感性分析。结果表明：所提方法能准确、高效地描绘边坡失效概率（Pf）的时变规律，为考虑多参数空间变异性的非饱和边坡时变可靠度问题提供了一条有效的途径；库水降落越快时边坡安全系数（FS）下降和失效概率上升的速率越快；多个土体参数的空间变异性和相关性均对边坡可靠度计算结果有影响。Abstract: The reservoir water level drop and the spatial variability of soil parameters are the important factors affecting slope stability, and it is important to evaluate the reliability of reservoir slopes under the action of these two factors. However, most of the existing reliability analyses only consider the spatial variability of a single shear strength parameter or hydraulic parameter, and only the static reliability at a certain moment is analyzed, ignoring the influences of multi-parameter spatial variability and time-varying factors. For this reason, a time-varying reliability analysis method for reservoir slopes that considers both factors is proposed. The Karhunen-Loève expansion method is used to discretize the random field of soil parameters, and the slice inverse regression (SIR) method is used to reduce the dimension of random variables. Based on the reduced variables, the Gaussian process regression (GPR) surrogate model is constructed, and then the Monte Carlo simulation (MCS) method is used to evaluate the slope failure probability. Finally, the effectiveness of the proposed method is verified by taking an unsaturated reservoir bank slope as an example, and the reliability variation law of the slope under different water level plunge conditions is explored, and the sensitivity analysis of key soil parameters is conducted. The proposed method can accurately and efficiently describe the time-varying law of slope failure probability (Pf), which provides an effective way for the time-varying reliability problem of unsaturated slopes considering multi-parameter spatial variability. The faster the reservoir water plummets, the faster the slope safety factor (FS) decreases and the failure probability increases. The spatial variability and correlation of multiple soil parameters have an impact on the calculated results of slope reliability.
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Keywords:
- slope /
- reliability /
- spatial variability /
- surrogate model /
- time-varying water level /
- parameter sensitivity
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利益冲突声明/Conflict of Interests：所有作者声明不存在利益冲突。All authors disclose no relevant conflict of interest.作者贡献/Authors' Contributions：邓志平完成方法的提出和论文的写作与修改；邹艺完成程序的编写和论文的写作与修改；潘敏完成指导和论文的修改；蒋水华参与指导和论文的修改；郑克红参与论文的修改和数据分析。所有作者均阅读并同意最终稿件的提交。DENG Zhiping: Conceptualization, Methodology, Writing – Original Draft, Writing – Review & Editing. ZOU Yi: Software (Code Implementation), Writing – Original Draft, Writing – Review & Editing. PAN Min: Supervision, Writing – Review & Editing. JIANG Shuihua: Supervision, Writing – Review & Editing. ZHENG Kehong: Writing – Review & Editing, Data Analysis. All authors have read and approved the final manuscript for submission.
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图 1 考虑参数空间变异性的非饱和边坡可靠度分析流程图
Figure 1. Flow chart of reliability analysis of unsaturated spatially variable reservoir bank slopes
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图 2 库岸边坡尺寸和确定性模型
Figure 2. Dimensions and deterministic model for reservoir bank slope
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图 3 不同计算工况下库水位变化
Figure 3. Variation of reservoir water level under different working conditions
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图 4 土-水特征曲线和渗透系数曲线
Figure 4. Soil-water characteristic curve and permeability coefficient curve
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图 5 孔隙水压力分布和最危险滑动面
Figure 5. Distribution of pore water pressure and most dangerous sliding surface
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图 7 不同水位降落工况下库岸边坡安全系数和失效概率随时间变化
Figure 7. Safety factors and probability failure of reservoir bank slope with time for different water level plunge conditions
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图 10 土体参数空间变异性对库岸边坡Pf的影响
Figure 10. Influences of spatial variability of soil parameters on Pf
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图 11 土体参数空间变异性对FS概率密度函数的影响
Figure 11. Influences of spatial variability of soil parameters on probability density function of FS
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图 12 土体参数相关性对库岸边坡Pf的影响
Figure 12. Influences of correlation among soil parameters on reservoir bank slope Pf
表 1 土体物理力学参数
Table 1 Physical and mechanical parameters of soil
确定性分析 渗流 稳定 参数 ks/(10-6 m·s-1) a/kPa n c'/kPa φ'/(°) 均值 1.160 28.44 1.720 5 30 标准差 0.696 11.376 0.344 1.5 6 变异系数 0.6 0.4 0.2 0.3 0.2 互相关系数 -0.25 -0.5 
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表 2 不同时刻库岸边坡安全系数
Table 2 Safety factor of reservoir bank slope at different moments
时间步序号 时间/d FS 1 0 1.846 2 1 1.544 3 2 1.358 4 3 1.258 5 5 1.256 6 8 1.316 7 11 1.355 8 15 1.393 9 22 1.441 10 30 1.479
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