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斜拉桥系统地震易损性评估的Pair Copula技术

宋帅 吴元昊 徐佰顺 吴刚 张金

宋帅, 吴元昊, 徐佰顺, 吴刚, 张金. 斜拉桥系统地震易损性评估的Pair Copula技术[J]. 工程力学, 2021, 38(9): 110-123. doi: 10.6052/j.issn.1000-4750.2020.09.0629
引用本文: 宋帅, 吴元昊, 徐佰顺, 吴刚, 张金. 斜拉桥系统地震易损性评估的Pair Copula技术[J]. 工程力学, 2021, 38(9): 110-123. doi: 10.6052/j.issn.1000-4750.2020.09.0629
SONG Shuai, WU Yuan-hao, XU Bai-shun, WU Gang, ZHANG Jin. PAIR COPULA TECHNIQUE OF SEISMIC VULNERABILITY ASSESSMENT OF CABLE-STAYED BRIDGE SYSTEM[J]. Engineering Mechanics, 2021, 38(9): 110-123. doi: 10.6052/j.issn.1000-4750.2020.09.0629
Citation: SONG Shuai, WU Yuan-hao, XU Bai-shun, WU Gang, ZHANG Jin. PAIR COPULA TECHNIQUE OF SEISMIC VULNERABILITY ASSESSMENT OF CABLE-STAYED BRIDGE SYSTEM[J]. Engineering Mechanics, 2021, 38(9): 110-123. doi: 10.6052/j.issn.1000-4750.2020.09.0629

斜拉桥系统地震易损性评估的Pair Copula技术

doi: 10.6052/j.issn.1000-4750.2020.09.0629
基金项目: 国家自然科学基金项目(51808376);中国博士后科学基金项目(2019M651076);山西省高等学校科技创新资助项目(20192L0276);江西省教育厅科技项目(GJJ190338);国家自然科学基金项目(52008047)
详细信息
    作者简介:

    宋 帅(1987−),男,河南人,副教授,博士后,主要从事桥梁抗震及可靠性研究(E-mail: shuaissw@126.com)

    吴元昊(1996−),男,河南人,硕士生,主要从事桥梁抗震及可靠性研究(E-mail: 18790383658@163.com)

    徐佰顺(1986−),男,黑龙江人,讲师,博士,主要从事桥梁检测及抗震加固研究(E-mail: xu_baishun@sina.com)

    吴 刚(1988−),男,江西人,讲师,博士,主要从事桥梁抗震研究(E-mail: wugang523@126.com)

    通讯作者:

    张 金(1988−),男,甘肃人,讲师,博士后,主要从事桥梁抗震及可靠性研究(E-mail: zhangjin18@cdut.edu.cn)

  • 中图分类号: U442.5+5

PAIR COPULA TECHNIQUE OF SEISMIC VULNERABILITY ASSESSMENT OF CABLE-STAYED BRIDGE SYSTEM

  • 摘要: 大跨度斜拉桥作为高次超静定结构,通常包含主塔、斜拉索、主梁、辅助墩及连接墩等较多构件,由于地震作用下各构件相互影响,准确模拟构件地震响应之间的相关性对斜拉桥整体系统的易损性评估十分关键。因Pair Copula能较好地模拟构件两两之间的相关性,理论上可将Pair Copula分层迭代模拟斜拉桥整体系统,进而提出基于Pair Copula迭代模型的斜拉桥系统地震易损性评估方法。基于结构不确定性参数及地震动不确定性,采用拉丁超立方抽样技术建立桥梁-地震动概率地震响应分析样本;通过非线性动力时程及相关性分析,量化构件地震响应之间的相关性;采用极大似然估计拟合Pair Copula模型,基于AIC及BIC准则对其进行优选;通过Pair Copula分层迭代,建立斜拉桥整体模型并对其进行地震易损性评估。工程实例表明,基于Pair Copula分层迭代技术能准确模拟多构件之间的相关性,假定构件地震响应完全不相关,会显著高估斜拉桥整体系统的地震易损性。
  • 图  1  Pair Copula迭代示意图

    Figure  1.  Schematic diagram of Pair Copula iteration

    图  2  平面6杆桁架结构示意图

    Figure  2.  Schematic diagram of planar 6-bar truss structure

    图  3  算例结果对比验证

    Figure  3.  Comparative verification of example results

    图  4  斜拉桥示意图 /m

    Figure  4.  Schematic diagram of the cable-stayed bridge

    图  5  斜拉桥全桥数值模型

    Figure  5.  Analytical model of the cable-stayed bridge

    图  6  所选148条地震动记录

    Figure  6.  Selected 148 ground motion records

    图  7  构件概率需求模型

    Figure  7.  Probabilistic demand models of components

    图  8  构件地震需求之间相关性

    Figure  8.  Correlation between component seismic demands

    图  9  整体系统的Pair Copula模型

    Figure  9.  Pair Copula model of the overall system

    图  10  构件地震需求残差处理

    Figure  10.  Residual processing of component seismic demands

    图  11  构件响应概率变换

    Figure  11.  Probabilistic transformations of component demands

    图  12  构件地震易损性曲线

    Figure  12.  Seismic vulnerability curves of components

    图  13  斜拉桥系统地震易损性曲线

    Figure  13.  Seismic vulnerability curves of bridge system

    图  14  相关性对系统易损性影响

    Figure  14.  Influence of correlations on system vulnerability

    表  1  常规Copula 函数汇总

    Table  1.   Summary of general Copula functions

    类别名称参数量可转角度/(°)
    椭圆CopulaGaussian1
    t2
    阿基米德CopulaClayton10,90,180,270
    Gumbel10,90,180,270
    Frank1
    Joe10,90,180,270
    BB120,90,180,270
    BB620,90,180,270
    BB720,90,180,270
    BB820,90,180,270
    下载: 导出CSV

    表  2  算例结构中不确定性参数

    Table  2.   Uncertainty parameters of the example structure

    不确定参数概率分布均值变异系数
    杆件长度/mm正态1×1030.2
    截面积1、3、5杆/mm2正态2×1040.2
    截面积2、4、6杆/mm2正态1×1040.2
    弹性模量/MPa正态2×1050.2
    集中荷载/N正态1×1050.2
    下载: 导出CSV

    表  3  斜拉桥结构中不确定性参数

    Table  3.   Uncertainty parameters of cable-stayed bridge

    构件描述分布均值变异系数
    主塔桥墩混凝土弹模/GPa正态32.500.08
    混凝土抗压强度/MPa正态28.600.14
    钢筋屈服强度/MPa正态4000.04
    主梁混凝土弹模/GPa正态35.500.08
    混凝土抗压强度/MPa正态39.300.14
    拉索拉索极限强度/GPa正态1.860.04
    拉索弹性模量/GPa正态1950.10
    支座摩擦系数对数正态0.020.10
    塔墩梁混凝土容重/(kN/m3)正态26.500.07
    过渡墩截面纵向尺寸/m正态4.660.05
    截面横向尺寸/m正态8.660.05
    辅助墩截面纵向尺寸/m正态4.720.05
    截面横向尺寸/m正态8.720.05
    主塔塔底截面纵向尺寸/m正态7.680.05
    塔底截面横向尺寸/m正态4.200.05
    塔顶截面纵向尺寸/m正态6.500.05
    塔顶截面横向尺寸/m正态3.500.05
    总体阻尼比 对数正态 0.05 0.10
    下载: 导出CSV

    表  4  构件概率地震响应模型

    Table  4.   Probabilistic seismic demand models of components

    构件lnabβD|IMR2p
    1#支座1.47/2.141.01/1.190.42/0.840.57/0.851.79×10-28/4.93×10-63
    2#支座1.47/1.591.01/1.050.43/0.650.61/0.861.51×10-31/9.21×10-64
    3#支座1.14/1.631.01/1.320.38/0.870.83/0.878.74×10-58/8.83×10-68
    4#支座1.13/1.671.01/1.320.39/0.860.76/0.881.25×10-47/3.05×10-68
    5#支座1.45/1.611.02/1.070.40/0.640.90/0.861.32×10-74/9.71×10-65
    6#支座1.46/2.161.02/1.200.41/0.790.90/0.871.54×10-74/1.30×10-65
    1#墩−7.96/−8.541.15/0.511.98/1.150.57/0.441.79×10-28/2.65×10-20
    2#墩−7.26/−8.281.18/0.551.65/1.310.61/0.451.51×10-31/1.14×10-20
    5#墩−7.80/−8.441.12/0.561.54/1.470.83/0.498.74×10-58/8.46×10-23
    6#墩−8.30/−8.311.14/0.571.86/1.490.76/0.491.25×10-47/4.17×10-23
    3-1塔−3.38/−3.811.45/1.192.23/1.230.77/0.804.12×10-48/2.03×10-53
    3-2塔−3.35/−3.741.46/1.212.16/1.240.77/0.814.95×10-49/9.15×10-54
    4-1塔−3.40/−3.801.45/1.202.23/1.230.77/0.804.67×10-48/1.74×10-53
    4-2塔−3.33/−3.731.46/1.212.15/1.240.78/0.812.52×10-49/9.41×10-54
    注:数据间的/为纵向与横向数据的分隔符。
    下载: 导出CSV

    表  5  Pair Copula的参数估计及优选

    Table  5.   Parameter estimation and selection of Pair Copulas

    方向构件组合类别参数1参数2AICBICp
    纵桥向1P+1BGumbel1.97−91.27−88.280.57
    2P+2BGumbel2.07−100.99−98.000.38
    3T1+3T2t0.983−478.70−472.710.10
    4T1+4T2t0.982−467.38−461.380.11
    5P+5BBB83.601−134.09−128.090.55
    6P+6BJoe3.90−172.81−169.810.31
    1PB+2PBGumbel10.87−634.60−631.600.91
    5PB+6 PBt0.982−519.09−513.100.11
    3T+3BGumbel1.73−63.07−60.070.92
    4T+4BGumbel1.72−62.09−59.090.66
    12PB+56PBGaussian0.96−399.32−396.320.88
    3TB+4TBGaussian1.00−1062.63−1059.630.72
    PB+TBGumbel3.59−257.73−254.730.28
    横桥向1P+1BGumbel1.44−30.85−27.850.69
    2P+2BGumbel1.60−48.63−45.630.66
    3T1+3T2Gumbel13.60−618.00−615.000.55
    4T1+4T2Gumbel13.74−618.93−615.930.22
    5P+5BJoe1.73−37.62−34.620.27
    6P+6BGumbel1.41−28.22−25.220.38
    1PB+2PBGaussian0.97−464.59−461.590.42
    5PB+6 PBt0.975−467.97−461.980.37
    3T+3BGaussian0.63−60.79−57.790.79
    4T+4BGaussian0.63−61.18−58.180.88
    12PB+56PBGumbel10.29−559.54−556.550.91
    3TB+4TBGaussian1.00−1069.01−1066.010.56
    PB+TBGumbel2.34−149.76−146.760.90
    下载: 导出CSV

    表  6  构件极限状态定义

    Table  6.   Definition of component limit states

    构件类型方向轻微损伤中等损伤严重损伤完全破坏
    橡胶支座纵向0.03 m0.10 m0.15 m0.25 m
    横向0.03 m0.10 m0.15 m0.25 m
    过渡墩纵向3.60×10−45.30×10−41.00×10−31.80×10−3
    横向2.00×10−43.07×10−45.80×10−41.05×10−3
    辅助墩纵向3.80×10−45.40×10−41.06×10−31.91×10−3
    横向2.10×10−43.07×10−46.00×10−41.09×10−3
    主塔纵向2.20×10−43.44×10−46.78×10−41.26×10−3
    横向5.49×10−47.00×10−49.19×10−41.58×10−3
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-09-03
  • 修回日期:  2020-12-21
  • 网络出版日期:  2021-03-11
  • 刊出日期:  2021-09-13

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