Seismic fragility analysis of subway station structures considering statistical uncertainty of seismic demands
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摘要: 为避免非完备地震需求样本集所导致的地铁车站结构地震易损性分析认知不确定性，提出了一种可考虑地震需求统计不确定性的地铁车站结构地震易损性分析方法。首先，基于Bootstrap法将有限地震需求样本问题转换为大样本问题；其次，结合最大熵原理和Copula理论构建统计不确定性变量的联合概率分布模型；在此基础上，进一步量化由地震需求统计不确定性所导致的地震易损性水平变异性，并求解得出均值地震易损性曲线以及对应一定置信度的包络地震易损性曲线；最后，以大开地铁车站为具体对象，系统分析了地震需求统计不确定性的影响规律。研究表明：在有限地震需求样本条件下地铁车站结构地震易损性水平具有显著的变异性，且该变异性会随着地震动强度的增加呈现出先增大后减小的变化趋势；均值与包络易损性曲线可有效考虑基于有限地震需求样本的地铁车站结构地震易损性不确定性程度，且具有良好可信度。所提出的相关分析方法和结论可为地铁车站结构抗震性能和地震风险评估提供参考和指导作用。
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关键词:
- 地铁车站结构 /
- 地震易损性 /
- 认知不确定性 /
- Bootstrap法 /
- 最大熵原理
Abstract: To avoid the epistemic uncertainty for seismic fragility of subway station structures caused by the incomplete seismic demand sample set, a novel procedure of seismic fragility analysis of subway station structures considering the statistical uncertainty of seismic demands is proposed. The limited set of seismic demand samples is firstly converted into a large sample problem based on the Bootstrap method. Then, the joint probability distribution model of statistical uncertainty variables is further established by combining the maximum entropy principle with the copula theory. On this basis, the variability of seismic fragility of subway station structures caused by the statistical uncertainty of seismic demands is further quantified, and the mean fragility curves and envelope fragility curves with certain confidence level are obtained. Finally, the Daikai subway station is taken as the prototype to investigate the influences of the statistical uncertainty. The results show that the seismic fragility of subway station structures derived from the limited seismic demand samples has significant variability which shows a tendency of increase and then decrease with the increase of the ground motion intensity. Moreover, the mean fragility curves and envelope fragility curves can effectively reflect the uncertainty of seismic fragility derived from the limited seismic demand samples, and have higher reliability. It may provide reference and guidance for the seismic performance and seismic risk assessment of subway station structures. -
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图 7 统计不确定性变量概率密度函数曲线
Figure 7. Marginal probability density curves of statistical uncertainty variables
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图 10 地铁车站均值与包络地震易损性曲线
Figure 10. Mean and envelope seismic fragility curves of subway station
表 1 地铁车站抗震能力均值及对数标准差
Table 1 Mean values and logarithmic standard deviations of seismic capacity
极限状态 轻微破坏 中等破坏 严重破坏 完全破坏 mc/% 0.1453 0.2983 0.3795 0.5308 βc 0.1763 0.1681 0.1508 0.2222 
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表 2 边缘概率密度函数待定参数拟合结果
Table 2 Fitting results of parameters for marginal probability density functions
待定参数 统计不确定性变量 α1 α2 βd b0 -22.6662 -207.6298 -38.8341 b1 1.9867 -4.3506 186.5833 b2 72.4687 3.1861 -126.8387 b3 2.1695 -5.6748 62.6025 b4 -59.7779 -0.9661 -733.9239 ζ 7.96×10-9 3.08×10-13 1.91×10-9
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表 3 统计不确定性变量间相关性系数
Table 3 Correlation coefficients between statistical uncertainty variables
变量 Pearson相关系数 Kendall秩相关系数 Gaussian Copula相关系数 α1和α2 0.9523 0.8066 0.9542 α1和βd -0.0071 -0.0070 -0.0109 α2和βd -0.0046 -0.0064 -0.0101
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表 4 标准差峰值对应的地震动强度
Table 4 Ground motion intensities corresponding to peak standard deviation
极限状态 考虑相关性 未考虑相关性 轻微破坏 0.095g/0.0769 0.111g/0.0443 中等破坏 0.340g/0.0523 0.274g/0.0404 严重破坏 0.435g/0.0618 0.371g/0.0556 完全破坏 0.630g/0.0821 0.560g/0.0736
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表 5 不同地震动强度下各极限状态的包络地震易损性
Table 5 Envelope seismic fragilities of limit states under different ground motion intensities
PGA/g 轻微破坏 中等破坏 严重破坏 完全破坏 上界 下界 上界 下界 上界 下界 上界 下界 0.1 0.5787 0.3367 0.0095 0.0279 0.0009 0.0057 0.0001 0.0008 0.2 0.9806 0.7638 0.3257 0.2225 0.1251 0.0864 0.0341 0.0205 0.3 0.9992 0.9171 0.7438 0.4636# 0.4941* 0.2481 0.2099 0.0793 0.4 0.9999 0.9685 0.9251 0.6501# 0.7854* 0.4224# 0.4661* 0.1687 0.5 1.000 0.9870 0.9798 0.7751# 0.9215* 0.5715# 0.6825* 0.2710 0.6 1.000 0.9942# 0.9945* 0.8550# 0.9732* 0.6880# 0.8244* 0.3728 0.7 1.000 0.9973# 0.9985* 0.9055# 0.9908* 0.7725# 0.9064* 0.4669 注：符号#和*所对应数值分别代表相邻极限状态的包络地震易损性交叉区间下限和上限。
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