Reliability analysis based on joint uncertainty: A case study of a rock slope in Tibet
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摘要:
边坡稳定性一直是边坡安全的重点研究对象，针对边坡评价中常见的不确定性因素，可靠度分析是值得利用的方法。为评价某节理发育的岩质岸坡稳定性，通过有限元计算软件，结合现场勘探测绘数据，建立以边坡节理强度参数c、φ为输入变量，安全系数为输出变量的点估计（PEM）计算概率模型，计算结果表明：节理发育对该边坡变形具有明显控制作用；边坡整体可靠性较好，破坏概率极低。最后，通过蒙托卡罗法对可靠度结果进行验证，结果表明两种方法的计算结果不存在显著性差异。研究结果表明节理对岩质边坡稳定具有良好的敏感性，基于节理不确定性的点估计法分析边坡可靠度是一种有效的方法。
Abstract:Slope stability has always been the key research object of slope safety. In view of the common uncertain factors in slope evaluation, reliability analysis is a valuable method. To evaluate the stability of a jointed rock slope, a point estimation (PEM) calculation probability model is established by using the finite element analysis software and the field survey data, The PEM method takes the joint strength parameters c, φ and the safety factor as input and output variables. The results suggest that, the joints have a significant control effect on the deformation of the slope; The overall reliability of slope is great, and the failure probability is extremely low. Finally, the reliability results are verified by Monte Carlo method, and the results show that there is no significant difference between the two methods. The results indicate that the joints have good sensitivity to the stability of rock slope, and the point estimation method based on joint uncertainty is an effective method to analyze the slope reliability.
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Key words:
- Jointed rock slope /
- reliability /
- baecher model /
- point estimate /
- Monte carlo
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表 1 岩体参数取值
Table 1. Parameter values of rock mass
材料 弹性模量/MPa 泊松比 φ/(°) c/MPa 容重/(kN·m−3) 均值 标准差 均值 标准差 强风化花岗岩 10000 0.28 38 2 0.12 0.01 23.5 弱风化花岗岩 13000 0.26 42 2 0.15 0.02 25.0 微新花岗岩 20000 0.25 49 3 0.50 0.04 27.0 
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表 2 结构面几何特征值
Table 2. Geometric characteristc values of structural plane
边坡分层 节理组 产状 迹长 密度/（条·m−2） 平均倾向/(°) 平均倾角/(°) 分布类型 Fisher常数 均值/m 分布类型 强风化层 J1 235 67 Fisher 95 8 负指数分布 0.20 J2 125 45 45 5.5 0.25 J1 245 74 50 15 负指数分布 0.06 弱风化层 J2 125 58 Fisher 40 5 0.03 J3 105 30 90 5 0.05 微新基岩 J1 236 78 Fisher 30 6 负指数分布 0.02 J2 135 55 110 4 0.01
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表 3 结构面强度特征值
Table 3. Strength characteristic values of structural plane
节理组号 φ/(°) c/MPa 法向刚度/（MPa·m−1） 切向刚度/（MPa·m−1） 抗拉强度/MPa 均值 标准差 均值 标准差 J1 30 2 0.04 0.002 8000 2500 0 J2 33 2 0.08 0.003 10000 3000 0 J3 38 3 0.10 0.005 13000 3800 0
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表 4 敏感性计算结果
Table 4. Sensitivity calculation results
节理强度参数 岩体强度参数 稳定性系数 c/MP φ/(°) c/MPa φ/(°) 0.04 30 0.15 42 1.35 0.034 30 0.15 42 1.33 0.046 30 0.15 42 1.38 0.04 24 0.15 42 1.23 0.04 36 0.15 42 1.45 0.04 30 0.144 42 1.34 0.04 30 0.156 42 1.37 0.04 30 0.150 36 1.27 0.04 30 0.150 48 1.44
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表 5 敏感性指标计算结果
Table 5. Sensitivity index calculation results
节理强度参数 岩体强度参数 c/MP φ/(°) c/MP φ/(°) 0.0370 0.1630 0.0222 0.1259
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表 6 可靠度对比分析结果
Table 6. Results of reliability comparison analysis
稳定性参数 JEF-PEM点估计 MCS蒙托卡罗 平均值 1.344 1.590 标准差 0.0573 0.0854 可靠性指数 6.007 6.907 破坏概率 0.001 <0.001
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