Multi-dimensional seismic fragility analysis method of bridge system based on Nataf transformation
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摘要: 在多维性能极限状态理论框架下,考虑桥梁各构件地震响应参数相关性,引入Nataf变换,提出了改进的桥梁系统多维地震易损性分析方法; 以一座三跨V撑连续梁桥为例,利用OpenSees软件建立桥梁系统非线性动力分析模型,从美国太平洋地震研究中心强震数据库中选取20条地震波进行增量动力分析,并获得桥梁结构在地震作用下的最大响应样本; 利用最大似然估计法获得桥梁构件地震需求概率模型统计参数,结合定义的桥梁构件损伤指标,应用提出的方法,分析了算例桥梁多维系统地震易损性。分析结果表明:提出的方法在考虑构件地震响应参数与性能极限状态相关性的基础上,可以不依赖构件地震响应参数间的联合概率密度函数,计算得到桥梁系统易损性; 在构建多维极限状态方程时,桥梁构件失效模式排序对桥梁系统地震多维易损性影响偏差在3%以内,构件失效模式排序对易损性分析结果影响不大; 在任一损伤状态下,随着地面峰值加速度与极限状态相关系数的增加,桥梁系统与过渡墩在地震作用下的失效概率比值逐渐减小,并接近于1,不同桥梁构件间的性能极限状态相关性变弱,系统失效域面积变小,导致桥梁系统失效概率降低,系统多维易损性越接近性能指标相互独立时的评估结果,当采用多维性能指标时,性能指标间的相关性不可忽略,否则将导致过高估计桥梁结构的抗震性能。
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关键词:
- 桥梁工程 /
- 结构安全 /
- 地震易损性 /
- Nataf变换 /
- 多维性能极限状态函数
Abstract: In the framework of multi-dimensional performance limit state theory, the correlation of seismic response parameters of bridge components was considered, and an improved multi-dimensional seismic fragility analysis method of bridge system was proposed by introducing Nataf transformation. Taking a three-span V-shaped continuous girder bridge as an example, the nonlinear dynamic analysis model of the bridge system was established by using OpenSees software, 20 seismic waves were selected from the strong earthquake database of Pacific Seismic Research Center for the incremental dynamic analysis, and the maximum response samples of the bridge structure under earthquake were obtained. The maximum likelihood estimation method was used to obtain the statistical parameters of the bridge component's seismic demand probability model. Combined with the defined bridge component damage index, the seismic fragility of the example bridge multi-dimensional system was analyzed by using the proposed method. Analysis results show that on the basis of considering the correlation between the seismic response parameters of the components and the performance limit states, the proposed method can calculate the fragility of the bridge system without relying on the joint probability density function between the seismic response parameters of the components. When constructing the multi-dimensional limit state equation, the influence deviation of the bridge component failure mode ranking on the multi-dimensional seismic fragility of the bridge system is less than 3%, so the component failure mode ranking has little influence on the fragility analysis result. In any damage state, with the increase of the correlation coefficient between the ground peak acceleration and the limit state, the ratios of the failure probability of the bridge system and the transition pier under the action of earthquake gradually decrease and approach 1, the correlation between the performance limit states of different bridge components becomes weaker, and the area of the system failure domain becomes smaller, resulting in that the failure probability of the bridge system reduces, and the multi-dimensional fragility of the bridge system is closer to the evaluation result when the performance indexes are independent of each other. When the multi-dimensional performance indicators are used, their correlation cannot be ignored, otherwise it will lead to the overestimation of the seismic performance of the bridge structure. 4 tabs, 6 figs, 30 refs. -
表 1 二十条地震记录
Table 1. Twenty seismic records
序号 地震名称 时间 测站名称 震级 1 Kern County 1952 Santa Barbara Courthouse 7.4 2 Kern County 1952 Taft Lincoln School 7.4 3 Northern Calif-03 1954 Ferndale City Hall 5.7 4 Borrego Mtn 1968 El Centro Array 6.5 5 San Fernando 1971 LA-Hollywood Stor FF 6.6 6 San Fernando 1971 Lake Hughes #1 6.6 7 San Fernando 1971 Palmdale Fire Station 6.6 8 San Fernando 1971 Pasadena-CIT Athenaeum 6.6 9 San Fernando 1971 Santa Felita Dam (Outlet) 6.6 10 San Fernando 1971 Whittier Narrows Dam 6.6 11 Tabas Iran 1978 Boshrooyeh 7.4 12 Imperial Valley-06 1979 Calipatria Fire Station 6.5 13 Imperial Valley-06 1979 Delta 6.5 14 Imperial Valley-06 1979 El Centro Array #13 6.5 15 Imperial Valley-06 1979 Niland Fire Station 6.5 16 Livermore-01 1980 Del Valle Dam (Toe) 5.8 17 Trinidad 1980 Rio Dell Overpass E Ground 5.5 18 Trinidad 1980 Rio Dell Overpass W Ground 5.5 19 Irpinia Italy-01 1980 Brienza 6.9 20 Irpinia Italy-02 1980 Rioneroin Vulture 6.2 表 2 桥梁构件在不同损伤状态下的损伤指标
Table 2. Damage indexes of bridge components under different damage states
构件 损伤指标 损伤状态 轻微损伤 中等损伤 中等损伤 完全破坏 过渡墩 曲率延性比 1 2 4 7 支座 位移/m 0.2 0.4 0.6 0.8 表 3 桥梁各构件地震响应均值与标准差
Table 3. Means and standard deviations of seismic responses of bridge components
峰值地面加速度/g 过渡墩 主桥支座 过渡墩支座 均值 标准差 均值/m 标准差/m 均值/m 标准差/m 0.1 0.209 0.095 0.054 0.015 0.037 0.010 0.2 0.498 0.201 0.094 0.034 0.065 0.024 0.3 0.842 0.347 0.138 0.055 0.096 0.039 0.4 1.233 0.471 0.182 0.076 0.126 0.054 0.5 1.622 0.643 0.225 0.097 0.155 0.069 0.6 2.081 0.933 0.267 0.117 0.186 0.083 0.7 2.606 1.350 0.309 0.137 0.214 0.099 0.8 3.148 1.740 0.353 0.157 0.244 0.114 0.9 3.814 2.233 0.399 0.177 0.275 0.129 1.0 4.474 2.772 0.444 0.198 0.308 0.143 表 4 桥梁各构件地震响应间的相关系数
Table 4. Correlation coefficients of seismic responses of bridge components
相关系数 过渡墩 主墩支座 过渡墩支座 过渡墩 1.000 0.768 0.750 主墩支座 0.768 1.000 0.996 过渡墩支座 0.750 0.996 1.000 -
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