Earthquake Risk Assessment of Bridge Based on Failure Probability Method
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摘要: 为了研究地震破坏下高速铁路连续梁桥发生破坏的可能性，根据地震风险性（risk）为地震危险性（hazard）与易损性（fragility）乘积的定义，基于失效概率法，对高速铁路连续梁桥地震风险评估方法进行了分析.通过条带法建立桥梁地震需求模型，基于可靠度函数获得桥梁地震易损性曲线，拟合得到桥梁易损性概率密度函数；根据桥址处地震危险性资料，推导桥址处地震加速度概率密度函数；通过地震加速度概率密度函数与桥梁结构易损性概率密度函数的数值积分，实现桥梁地震风险概率评估.以一座（32+48+32）m高速铁路连续梁桥为例系统演绎了失效概率法桥梁风险评估的实现过程.研究结果表明：当地震危险性资料缺乏或不足时可以通过地震烈度分布函数及其与地震峰值加速度之间的换算关系，推导和完善地震危险性分析资料；对于高速铁路（32+48+32）m连续梁桥100年设计期间内发生轻微损伤的概率为5.16%，发生中等损伤的概率为4.46%，桥梁受到轻微损伤和中等损伤风险概率接近，几乎不可能发生严重损伤和完全破坏.Abstract: To study the possibility of destruction of a high-speed railway continuous girder bridge under the influence of seismic damage, a seismic risk assessment of the bridge was conducted. The failure probability method was used, in which seismic risk is defined as the product of seismic hazard and fragility (i.e., seismic risk=seismic hazard×fragility). The bridge seismic demand model was established using the strip coating method. The bridge seismic fragility curve was obtained based on the reliability function, and the probability density function of the bridge fragility was fitted. According to seismic risk data of the bridge site, the probability density function of seismic acceleration of the bridge site was derived. The probability density function of seismic acceleration was numerically integrated with that of the bridge structural vulnerability to accomplish the probability evaluation of the bridge earthquake risk. Taking a (32+48+32) m high-speed railway continuous girder bridge as an example, the system conducted the bridge risk assessment using the failure probability method. The results show that when earthquake risk data are lacking or insufficient, it is possible to deduce and improve seismic risk analysis data using the conversion relation between the earthquake intensity distribution function and the seismic peak acceleration. For the high-speed railway (32+48+32) m continuous girder bridge, within 100 years of use, the occurrence probability of slight damage is 5.16% and that of secondary damage is 4.46%. The probabilities of slight damage and secondary damage risk of the bridge are similar, whereas the probabilities of serious damage and complete destruction are very small, indicating that serious damage and complete destruction are almost impossible.
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表 1 支座刚度
Table 1. Bearing stiffness
支座位置 支反力/MN 支座刚度/(MN·m-1) 1号墩 5.4 54 2号墩 39.0 390 3号墩 39.0 390 4号墩 5.4 54 
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表 2 桥墩破坏状态定义
Table 2. Definition of pier damage states
损伤状态 损伤准则 基本完好 ϕ≤ϕ1 轻微损伤 ϕ1＜ϕ≤ϕ2 中等损伤 ϕ2＜ϕ≤ϕ3 严重损伤 ϕ3＜ϕ≤ϕ4 结构破坏 ϕ＞ϕ4
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表 3 桥墩不同状态破坏指标
Table 3. Different piers damage criteria
方向 墩号 ϕ1/×10-4 ϕ2/×10-4 ϕ3/×10-3 ϕ4/×10-3 顺向 3号 7.44 8.52 16.80 29.10 1号 4.82 6.24 8.87 11.90 横向 2号 3.63 4.44 6.21 7.76 3号 3.64 4.45 6.12 7.64 4号 4.84 6.24 8.73 11.70
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表 4 支座破坏状态定义
Table 4. Definition of bearing damage states
损伤状态 损伤准则 基本完好 D≤150 mm 轻微损伤 150 mm＜D≤200 mm 中等损伤 200 mm＜D≤250 mm 严重损伤 250 mm＜D≤300 mm 完全破坏 D＞300 mm
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表 5 桥梁整体易损性概率密度函数拟合参数
Table 5. Fitting parameters of overall fragility probability density function
拟合参数 轻微损伤 中等损伤 严重损伤 破坏 α 1.004 7 1.005 6 1.014 0 1.016 5 λ -1.008 9 -1.009 9 -1.015 9 -1.017 3 δ 1.670 7 1.778 8 6.581 4 8.121 9 u 10.408 3 10.414 1 9.143 9 8.542 6
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表 6 地震危险性资料
Table 6. Seismic hazard information
对应峰值加速度/(×g) 发生概率 0.001 95 0.999 9 0.003 91 0.999 9 0.007 82 0.999 9 0.015 64 0.999 9 0.031 27 0.969 2 0.062 54 0.618 2 0.125 01 0.189 9 0.250 17 0.032 3 0.500 30 0.003 0 1.000 30 0.000 1
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表 7 桥梁风险概率
Table 7. Bridge risk probability
破坏程度 轻微损伤 中等损伤 严重损伤 完全破坏 风险概率 0.051 64 0.044 57 4.711×10-4 2.634×10-4
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