基于Copula函数的主余震地震动强度参数相关性分析
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摘要
该文从PEER NGA-West2地震动数据库挑中选出662条主余震地震动,对主震和余震地震动强度参数之间的相关性进行了分析。计算了主震和余震地震动强度参数之间的相关系数,并结合K-S检验以及AIC准则和BIC准则确定了它们的最优概率模型。同时,利用AIC准则和BIC准则确定了主震和余震地震动强度参数之间的最优Copula函数,并基于Copula函数建立了它们之间的联合分布函数。在此基础之上,给出了给定主震地震动参数条件下,余震地震动强度参数的条件分布和条件均值。研究结果表明:在34个所选强度参数中,卓越持时之间的相关性最高;利用Copula函数可以较为精确地建立主震和余震地震动强度参数间的联合分布;给定主震地震动强度参数条件下,Copula条件均值可以用来预测余震地震动强度参数的取值。
This study selects 662 mainshock-aftershock(MS-AS) ground motions from PEER NGA-West2 ground motion database, to analyze the correlation of the intensity measures(IMs) among the MS-AS ground motions. The correlation coefficients of these IMs among the MS-AS ground motions are calculated, and their optimal probability models are determined according to the K-S test, the AIC criterion and the BIC criterion. Meanwhile, the AIC criterion and the BIC criterion are used to determine the optimal copula functions among the MS-AS ground motion IMs, and their joint distributions are built based on the copula functions. On this basis, the conditional distribution and the conditional mean of the aftershock ground motion IMs are obtained, given those of the mainshock. The results show that: the significant duration has the highest correlation amongst the 34 selected IMs, the joint distributions can be built using the Copula function with reasonable accuracy, and the Copula conditional mean can be used to predict the IMs of the aftershock ground motions, given the IMs of the mainshock ground motions.
This study selects 662 mainshock-aftershock(MS-AS) ground motions from PEER NGA-West2 ground motion database, to analyze the correlation of the intensity measures(IMs) among the MS-AS ground motions. The correlation coefficients of these IMs among the MS-AS ground motions are calculated, and their optimal probability models are determined according to the K-S test, the AIC criterion and the BIC criterion. Meanwhile, the AIC criterion and the BIC criterion are used to determine the optimal copula functions among the MS-AS ground motion IMs, and their joint distributions are built based on the copula functions. On this basis, the conditional distribution and the conditional mean of the aftershock ground motion IMs are obtained, given those of the mainshock. The results show that: the significant duration has the highest correlation amongst the 34 selected IMs, the joint distributions can be built using the Copula function with reasonable accuracy, and the Copula conditional mean can be used to predict the IMs of the aftershock ground motions, given the IMs of the mainshock ground motions.
引文
[1]Zhang Y,Chen J,Sun C.Damage-based strength reduction factor for nonlinear structures subjected to sequence-type ground motions[J].Soil Dynamics and Earthquake Engineering,2017,92(Supplement C):298-311.
[2]Wen W,Zhai C,Ji D,et al.Framework for the vulnerability assessment of structure under mainshockaftershock sequences[J].Soil Dynamics and Earthquake Engineering,2017,101(Supplement C):41-52.
[3]Shokrabadi M,Burton H V,Stewart J P.Impact of sequential ground motion pairing on mainshockaftershock structural response and collapse performance assessment[J].Journal of Structural Engineering,2018,144(10):04018177(1―13).
[4]Ruiz-García J,Aguilar J D.Influence of modeling assumptions and aftershock hazard level in the seismic response of post-mainshock steel framed buildings[J].Engineering Structures,2017,140(Supplement C):437-446.
[5]Shin M,Kim B.Effects of frequency contents of aftershock ground motions on reinforced concrete(RC)bridge columns[J].Soil Dynamics and Earthquake Engineering,2017,97:48-59.
[6]丁国,陈隽.序列型地震动物理随机模型研究[J].工程力学,2017,34(9):125-138.Ding Guo,Chen Jun.Study on physical random model of seismic sequences[J].Engineering Mechanics,2017,34(9):125-138.(in Chinese)
[7]Helmstetter A,Sornette D.B?th's law derived from the Gutenberg-Richter law and from aftershock properties[J].Geophysical research letters,2003,30(20):SDE11.1-SDE11.4.
[8]B?th M.Lateral inhomogeneities of the upper mantle[J].Tectonophysics,1965,2(6):483-514.
[9]Goda K,Taylor C A.Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes[J].Earthquake Engineering&Structural Dynamics,2012,41(15):2311-2330.
[10]Goda K.Nonlinear response potential of mainshockaftershock sequences from Japanese earthquakes[J].Bulletin of the seismological Society of America,2012,102(5):2139-2156.
[11]杨成,陈文龙,徐腾飞.余震地区桥梁施工过程易损性分析[J].工程力学,2016,33(增刊1):251-256.Yang Cheng,Chen Wenlong,Xu Tengfei.The vulnerability analysis of bridge construction in aftershock area[J].Engineering Mechanics,2016,33(Suppl 1):251-256.(in Chinese)
[12]Han R,Li Y,Van De Lindt J.Assessment of seismic performance of buildings with incorporation of aftershocks[J].Journal of Performance of Constructed Facilities,2015,29(3):04014088(1―17).
[13]赵银刚,刘庆杰,王晨,等.基于线性回归分析的主余震相关关系[J].地震地磁观测与研究,2017,38(2):71-76.Zhao Yingang,Liu Qingjie,Wang Chen,et al.Correlation of the minshock-aftershock based on the linear regression[J].Seismological and Geomagnetic Observation and Research,2017,38(2):71-76.(in Chinese)
[14]Yeo G L,Cornell C A.A probabilistic framework for quantification of aftershock ground‐motion hazard in California:Methodology and parametric study[J].Earthquake Engineering&Structural Dynamics,2009,38(1):45-60.
[15]Kumitani S,Takada T.Probabilistic assessment of buildings damage considering aftershocks of earthquakes[J].Journal of Structural&Construction Engineering,2009,74(74):459-465.
[16]易桂喜,龙锋,张致伟.汶川M_S8.0地震余震震源机制时空分布特征[J].地球物理学报,2012,55(4):1213-1227.Yi Guixi,Long Feng,Zhang Zhiwei.Spatial and temporal variation of focal mechanisms for aftershocks of the 2008 MS8.0 Wenchuan earthquake[J].Chinese Journal of Geophysics,2012,55(4):1213-1227.(in Chinese)
[17]Li Y,Song R,Van De Lindt J W.Collapse fragility of steel structures subjected to earthquake mainshockaftershock sequences[J].Journal of Structural Engineering,2014,140(12):04014095(1-10).
[18]Tothong P,Luco N.Probabilistic seismic demand analysis using advanced ground motion intensity measures[J].Earthquake Engineering&Structural Dynamics,2007,36(13):1837-1860.
[19]Baker J W,Allin Cornell C.A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon[J].Earthquake Engineering&Structural Dynamics,2005,34(10):1193-1217.
[20]Baker J W,Allin Cornell C.Spectral shape,epsilon and record selection[J].Earthquake Engineering&Structural Dynamics,2006,35(9):1077-1095.
[21]Bommer J J,Martnez-Pereira A.The effective duration of earthquake strong motion[J].Journal of Earthquake Engineering,1999,03(02):127-172.
[22]Iervolino I,Manfredi G,Cosenza E.Ground motion duration effects on nonlinear seismic response[J].Earthquake Engineering&Structural Dynamics,2006,35(1):21-38.
[23]Raghunandan M,Liel A B.Effect of ground motion duration on earthquake-induced structural collapse[J].Structural Safety,2013,41:119-133.
[24]Kumar M,Castro J,Stafford P,et al.Influence of the mean period of ground motion on the inelastic dynamic response of single and multi degree of freedom systems[J].Earthquake Engineering&Structural Dynamics,2011,40(3):237-256.
[25]于晓辉,吕大刚,肖寒.主余震序列型地震动的增量损伤谱研究[J].工程力学,2017,34(3):47-53,114.Yu Xiaohui,LüDagang,Xiao Han.Incremental damage spectra of mainshock-aftershock sequence-type ground motion[J].Engineering Mechanics,2017,34(3):47-53,114.
[26]Kim B,Shin M.A model for estimating horizontal aftershock ground motions for active crustal regions[J].Soil Dynamics and Earthquake Engineering,2017,92:165-175.
[27]Ruiz-García J,Negrete-Manriquez J C.Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences[J].Engineering Structures,2011,33(2):621-634.
[28]Ruiz-García J.Issues on the response of existing buildings under mainshock-aftershock seismic sequences[C]//Proceedings of the 15th World conference on earthquake engineering,Lisboa,2012.
[29]Ruiz-García J.Mainshock-aftershock ground motion features and their influence in building's seismic response[J].Journal of Earthquake Engineering,2012,16(5):719-737.
[30]Song R,Li Y,Van De Lindt J W.Impact of earthquake ground motion characteristics on collapse risk of post-mainshock buildings considering aftershocks[J].Engineering Structures,2014,81:349-361.
[31]Rathje E M,Faraj F,Russell S,et al.Empirical relationships for frequency content parameters of earthquake ground motions[J].Earthquake Spectra,2004,20(1):119-144.
[32]Xu Y,Tang X S,Wang J,et al.Copula-based joint probability function for PGA and CAV:a case study from Taiwan[J].Earthquake Engineering&Structural Dynamics,2016,45(13):2123-2136.
[33]Tesfamariam S,Goda K.Seismic performance evaluation framework considering maximum and residual inter-story drift ratios:application to non-code conforming reinforced concrete buildings in Victoria,British Columbia,Canada[J].Frontiers in Built Environment,2015,1-18.
[34]宋帅,钱永久,吴刚.桥梁系统地震易损性分析的混合Copula函数方法[J].工程力学,2017,34(1):219-227.Song Shuai,Qian Yongjiu,Wu Gang.Mixed copula function method for seismic fragility analysis of bridge system[J].Engineering Mechanics,2017,34(1):219-227.
[35]李典庆,唐小松,周创兵.基于Copula理论的岩土体参数不确定性表征与可靠度分析[M].北京:科学出版社,2015:28-48.Li Dianqing,Tang Xiaosong,Zhou Chuangbing.Uncertainty uncertainty and reliability analysis of the parameters of rock and soil materials based on the copula theory[M].Beijing:Science Press,2015:28-48.(in Chinese)
[36]刘亭亭,于晓辉,吕大刚.地震动多元强度参数主成分与结构损伤的相关性分析[J].工程力学,2018,35(8):122-129,137.Liu Tingting,Yu Xiaohui,LüDagang.Analysis of correlation between principal components of multivariate earthquake intensity measures and structural damage[J].Engineering Mechanics,2018,35(8):122-129,137.(in Chinese)
[37]Abrahamson N,Silva W,Kamai R.Update of the AS08ground-motion prediction equations based on the NGA-West2 data set,PEER report 2013/04,pacific earthquake engineering research center[R].Berkeley:University of California,Berkeley,2013:3―9
[38]Zhu R G,Lu D G,Yu X H,et al.Conditional Mean Spectrum of Aftershocks[J].Bulletin of the seismological Society of America,2017,107(4):1940-1953.
[39]Riddell R.On ground motion intensity indices[J].Earthquake Spectra,2007,23(1):147-173.
[40]Riddell R,Garcia J E.Hysteretic energy spectrum and damage control[J].Earthquake Engineering&Structural Dynamics,2001,30(12):1791-1816.
[41]Von Thun J L,Roehm L H,Scott G A,et al.Earthquake ground motions for design and analysis of dams[J].Earthquake Engineering and Soil Dynamics II-Recent Advances in Ground-Motion Evaluation,Geotechnical Special Publication,1988,20:463-481.
[42]Mackie K R.Fragility-based seismic decision making for highway overpass bridges[D].Berkeley:University of California,Berkeley,2004.
[43]Fajfar P,Vidic T,Fischinger M.A measure of earthquake motion capacity to damage medium-period structures[J].Soil Dynamics and Earthquake Engineering,1990,9(5):236-242.
[44]Trifunac M D,Brady A G.A study on the duration of strong earthquake ground motion[J].Bulletin of the Seismological Society of America,1975,65(3):581-626.
[45]褚延涵.地震地面运动加速度记录与强度参数选择的统计方法研究[D].哈尔滨:哈尔滨工业大学,2010.Chu Yanhan.Study on statistical methods for selection of accerelation records and intensity measures of earthquake ground motions[D].Harbin:Harbin Institute of Technology,2010.(in Chinese)
[2]Wen W,Zhai C,Ji D,et al.Framework for the vulnerability assessment of structure under mainshockaftershock sequences[J].Soil Dynamics and Earthquake Engineering,2017,101(Supplement C):41-52.
[3]Shokrabadi M,Burton H V,Stewart J P.Impact of sequential ground motion pairing on mainshockaftershock structural response and collapse performance assessment[J].Journal of Structural Engineering,2018,144(10):04018177(1―13).
[4]Ruiz-García J,Aguilar J D.Influence of modeling assumptions and aftershock hazard level in the seismic response of post-mainshock steel framed buildings[J].Engineering Structures,2017,140(Supplement C):437-446.
[5]Shin M,Kim B.Effects of frequency contents of aftershock ground motions on reinforced concrete(RC)bridge columns[J].Soil Dynamics and Earthquake Engineering,2017,97:48-59.
[6]丁国,陈隽.序列型地震动物理随机模型研究[J].工程力学,2017,34(9):125-138.Ding Guo,Chen Jun.Study on physical random model of seismic sequences[J].Engineering Mechanics,2017,34(9):125-138.(in Chinese)
[7]Helmstetter A,Sornette D.B?th's law derived from the Gutenberg-Richter law and from aftershock properties[J].Geophysical research letters,2003,30(20):SDE11.1-SDE11.4.
[8]B?th M.Lateral inhomogeneities of the upper mantle[J].Tectonophysics,1965,2(6):483-514.
[9]Goda K,Taylor C A.Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes[J].Earthquake Engineering&Structural Dynamics,2012,41(15):2311-2330.
[10]Goda K.Nonlinear response potential of mainshockaftershock sequences from Japanese earthquakes[J].Bulletin of the seismological Society of America,2012,102(5):2139-2156.
[11]杨成,陈文龙,徐腾飞.余震地区桥梁施工过程易损性分析[J].工程力学,2016,33(增刊1):251-256.Yang Cheng,Chen Wenlong,Xu Tengfei.The vulnerability analysis of bridge construction in aftershock area[J].Engineering Mechanics,2016,33(Suppl 1):251-256.(in Chinese)
[12]Han R,Li Y,Van De Lindt J.Assessment of seismic performance of buildings with incorporation of aftershocks[J].Journal of Performance of Constructed Facilities,2015,29(3):04014088(1―17).
[13]赵银刚,刘庆杰,王晨,等.基于线性回归分析的主余震相关关系[J].地震地磁观测与研究,2017,38(2):71-76.Zhao Yingang,Liu Qingjie,Wang Chen,et al.Correlation of the minshock-aftershock based on the linear regression[J].Seismological and Geomagnetic Observation and Research,2017,38(2):71-76.(in Chinese)
[14]Yeo G L,Cornell C A.A probabilistic framework for quantification of aftershock ground‐motion hazard in California:Methodology and parametric study[J].Earthquake Engineering&Structural Dynamics,2009,38(1):45-60.
[15]Kumitani S,Takada T.Probabilistic assessment of buildings damage considering aftershocks of earthquakes[J].Journal of Structural&Construction Engineering,2009,74(74):459-465.
[16]易桂喜,龙锋,张致伟.汶川M_S8.0地震余震震源机制时空分布特征[J].地球物理学报,2012,55(4):1213-1227.Yi Guixi,Long Feng,Zhang Zhiwei.Spatial and temporal variation of focal mechanisms for aftershocks of the 2008 MS8.0 Wenchuan earthquake[J].Chinese Journal of Geophysics,2012,55(4):1213-1227.(in Chinese)
[17]Li Y,Song R,Van De Lindt J W.Collapse fragility of steel structures subjected to earthquake mainshockaftershock sequences[J].Journal of Structural Engineering,2014,140(12):04014095(1-10).
[18]Tothong P,Luco N.Probabilistic seismic demand analysis using advanced ground motion intensity measures[J].Earthquake Engineering&Structural Dynamics,2007,36(13):1837-1860.
[19]Baker J W,Allin Cornell C.A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon[J].Earthquake Engineering&Structural Dynamics,2005,34(10):1193-1217.
[20]Baker J W,Allin Cornell C.Spectral shape,epsilon and record selection[J].Earthquake Engineering&Structural Dynamics,2006,35(9):1077-1095.
[21]Bommer J J,Martnez-Pereira A.The effective duration of earthquake strong motion[J].Journal of Earthquake Engineering,1999,03(02):127-172.
[22]Iervolino I,Manfredi G,Cosenza E.Ground motion duration effects on nonlinear seismic response[J].Earthquake Engineering&Structural Dynamics,2006,35(1):21-38.
[23]Raghunandan M,Liel A B.Effect of ground motion duration on earthquake-induced structural collapse[J].Structural Safety,2013,41:119-133.
[24]Kumar M,Castro J,Stafford P,et al.Influence of the mean period of ground motion on the inelastic dynamic response of single and multi degree of freedom systems[J].Earthquake Engineering&Structural Dynamics,2011,40(3):237-256.
[25]于晓辉,吕大刚,肖寒.主余震序列型地震动的增量损伤谱研究[J].工程力学,2017,34(3):47-53,114.Yu Xiaohui,LüDagang,Xiao Han.Incremental damage spectra of mainshock-aftershock sequence-type ground motion[J].Engineering Mechanics,2017,34(3):47-53,114.
[26]Kim B,Shin M.A model for estimating horizontal aftershock ground motions for active crustal regions[J].Soil Dynamics and Earthquake Engineering,2017,92:165-175.
[27]Ruiz-García J,Negrete-Manriquez J C.Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences[J].Engineering Structures,2011,33(2):621-634.
[28]Ruiz-García J.Issues on the response of existing buildings under mainshock-aftershock seismic sequences[C]//Proceedings of the 15th World conference on earthquake engineering,Lisboa,2012.
[29]Ruiz-García J.Mainshock-aftershock ground motion features and their influence in building's seismic response[J].Journal of Earthquake Engineering,2012,16(5):719-737.
[30]Song R,Li Y,Van De Lindt J W.Impact of earthquake ground motion characteristics on collapse risk of post-mainshock buildings considering aftershocks[J].Engineering Structures,2014,81:349-361.
[31]Rathje E M,Faraj F,Russell S,et al.Empirical relationships for frequency content parameters of earthquake ground motions[J].Earthquake Spectra,2004,20(1):119-144.
[32]Xu Y,Tang X S,Wang J,et al.Copula-based joint probability function for PGA and CAV:a case study from Taiwan[J].Earthquake Engineering&Structural Dynamics,2016,45(13):2123-2136.
[33]Tesfamariam S,Goda K.Seismic performance evaluation framework considering maximum and residual inter-story drift ratios:application to non-code conforming reinforced concrete buildings in Victoria,British Columbia,Canada[J].Frontiers in Built Environment,2015,1-18.
[34]宋帅,钱永久,吴刚.桥梁系统地震易损性分析的混合Copula函数方法[J].工程力学,2017,34(1):219-227.Song Shuai,Qian Yongjiu,Wu Gang.Mixed copula function method for seismic fragility analysis of bridge system[J].Engineering Mechanics,2017,34(1):219-227.
[35]李典庆,唐小松,周创兵.基于Copula理论的岩土体参数不确定性表征与可靠度分析[M].北京:科学出版社,2015:28-48.Li Dianqing,Tang Xiaosong,Zhou Chuangbing.Uncertainty uncertainty and reliability analysis of the parameters of rock and soil materials based on the copula theory[M].Beijing:Science Press,2015:28-48.(in Chinese)
[36]刘亭亭,于晓辉,吕大刚.地震动多元强度参数主成分与结构损伤的相关性分析[J].工程力学,2018,35(8):122-129,137.Liu Tingting,Yu Xiaohui,LüDagang.Analysis of correlation between principal components of multivariate earthquake intensity measures and structural damage[J].Engineering Mechanics,2018,35(8):122-129,137.(in Chinese)
[37]Abrahamson N,Silva W,Kamai R.Update of the AS08ground-motion prediction equations based on the NGA-West2 data set,PEER report 2013/04,pacific earthquake engineering research center[R].Berkeley:University of California,Berkeley,2013:3―9
[38]Zhu R G,Lu D G,Yu X H,et al.Conditional Mean Spectrum of Aftershocks[J].Bulletin of the seismological Society of America,2017,107(4):1940-1953.
[39]Riddell R.On ground motion intensity indices[J].Earthquake Spectra,2007,23(1):147-173.
[40]Riddell R,Garcia J E.Hysteretic energy spectrum and damage control[J].Earthquake Engineering&Structural Dynamics,2001,30(12):1791-1816.
[41]Von Thun J L,Roehm L H,Scott G A,et al.Earthquake ground motions for design and analysis of dams[J].Earthquake Engineering and Soil Dynamics II-Recent Advances in Ground-Motion Evaluation,Geotechnical Special Publication,1988,20:463-481.
[42]Mackie K R.Fragility-based seismic decision making for highway overpass bridges[D].Berkeley:University of California,Berkeley,2004.
[43]Fajfar P,Vidic T,Fischinger M.A measure of earthquake motion capacity to damage medium-period structures[J].Soil Dynamics and Earthquake Engineering,1990,9(5):236-242.
[44]Trifunac M D,Brady A G.A study on the duration of strong earthquake ground motion[J].Bulletin of the Seismological Society of America,1975,65(3):581-626.
[45]褚延涵.地震地面运动加速度记录与强度参数选择的统计方法研究[D].哈尔滨:哈尔滨工业大学,2010.Chu Yanhan.Study on statistical methods for selection of accerelation records and intensity measures of earthquake ground motions[D].Harbin:Harbin Institute of Technology,2010.(in Chinese)
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