考虑变量相关性的桥梁时变地震易损性研究
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摘要
为研究变量相关性对桥梁时变地震易损性的影响,引入Nataf变换和均匀设计,提出了一种考虑变量相关性的桥梁时变地震易损性分析方法。以一多跨连续梁桥为研究对象,基于OpenSees建立其非线性分析模型,考虑氯离子侵蚀引起的钢筋直径及面积的退化,基于OpenSees截面非线性分析及单条地震波的非线性地震响应分析,探讨了氯离子侵蚀对桥梁抗震能力和地震需求的影响。然后,考虑桥墩、铅芯橡胶支座(LRB)、板式橡胶支座(PETB)和桥台等构件的地震损伤,建立了桥梁时变地震易损性曲线;最后,针对结构参数变量相关性对桥梁抗震能力、地震需求和时变地震易损性曲线的影响进行了定性分析。研究结果表明:①氯离子侵蚀会导致桥墩截面极限抗弯承载能力下降,而截面极限曲率、延性能力却略有提升;②考虑由氯离子侵蚀引起的纵筋锈蚀后,桥梁墩底截面弯矩需求有一定程度的下降,而墩顶位移和墩底截面曲率延性需求却有所增大,桥梁在不同损伤状态下的损伤超越概率会随服役时间的增加而增大;③该方法可较好处理结构参数变量相关性,并且考虑变量相关性后,在全寿命设计基准期内,桥墩截面极限抗弯承载能力有所提升,而墩顶位移、墩底截面弯矩和曲率延性需求则有一定程度的下降;④忽略变量相关性条件的影响,可能会高估桥梁结构的时变地震易损性。
In order to study effects of variables' correlation on bridge time-varying seismic fragility, introducing Nataf transformation and uniform design(UD), an approach for bridge time-varying seismic fragility analysis considering variables' correlation was proposed. A multi-span continuous highway bridge was taken as the study object, and its nonlinear finite element analysis model was built with the software OpenSees. Considering degradation of diameter and cross-section area of longitudinal reinforcement due to chlorine ion induced corrosion(CIIC), the cross-section nonlinear analysis based on OpenSees and the nonlinear seismic response analysis under excitation of a single earthquake wave were conducted for the bridge to study effects of CIIC on the bridge's seismic capacity and seismic demand. Then, considering seismic damages of bridge pier, lead rubber bearing(LRB), platy elastomeric type bearing(PETB) and bridge abutment, the bridge time-varying seismic fragility curves were drawn. Finally, effects of structural parameter variables' correlation on the bridge's seismic capacity, seismic demand and time-varying seismic fragility curves were qualitatively analyzed. The results showed that 1) CIIC may cause pier cross-section's ultimate anti-bending ability to drop and its cross-section ultimate curvature and ductility ability to slightly rise; 2) corrosion of longitudinal reinforcement due to CIIC may reduce pier bottom cross-section bending moment demand to a certain extent and increase pier top displacement and pier bottom cross-section curvature ductility demands; the bridge's damage exceedance probabilities under different damage states increase with its service time; 3) the proposed approach can effectively deal with structural parameter variables' correlation; after considering variables' correlation, pier's cross-section ultimate anti-bending ability increases, while pier top displacement, pier bottom bending moment and curvature ductility demands drop to a certain extent; 4) neglecting effects of variables' correlation may overestimate the bridge's time-varying seismic fragility.
In order to study effects of variables' correlation on bridge time-varying seismic fragility, introducing Nataf transformation and uniform design(UD), an approach for bridge time-varying seismic fragility analysis considering variables' correlation was proposed. A multi-span continuous highway bridge was taken as the study object, and its nonlinear finite element analysis model was built with the software OpenSees. Considering degradation of diameter and cross-section area of longitudinal reinforcement due to chlorine ion induced corrosion(CIIC), the cross-section nonlinear analysis based on OpenSees and the nonlinear seismic response analysis under excitation of a single earthquake wave were conducted for the bridge to study effects of CIIC on the bridge's seismic capacity and seismic demand. Then, considering seismic damages of bridge pier, lead rubber bearing(LRB), platy elastomeric type bearing(PETB) and bridge abutment, the bridge time-varying seismic fragility curves were drawn. Finally, effects of structural parameter variables' correlation on the bridge's seismic capacity, seismic demand and time-varying seismic fragility curves were qualitatively analyzed. The results showed that 1) CIIC may cause pier cross-section's ultimate anti-bending ability to drop and its cross-section ultimate curvature and ductility ability to slightly rise; 2) corrosion of longitudinal reinforcement due to CIIC may reduce pier bottom cross-section bending moment demand to a certain extent and increase pier top displacement and pier bottom cross-section curvature ductility demands; the bridge's damage exceedance probabilities under different damage states increase with its service time; 3) the proposed approach can effectively deal with structural parameter variables' correlation; after considering variables' correlation, pier's cross-section ultimate anti-bending ability increases, while pier top displacement, pier bottom bending moment and curvature ductility demands drop to a certain extent; 4) neglecting effects of variables' correlation may overestimate the bridge's time-varying seismic fragility.
引文
[1] 吴文朋,李立峰,王连华,等.基于IDA的高墩大跨桥梁地震易损性分析[J].地震工程与工程振动,2012,32(3):117-123.WU Wenpeng,LI Lifeng,WANG Lianhua,et al.Evaluation of seismic vulnerability of high-pier long-span bridge using incremental dynamic analysis[J].Journal of Earthquake Engineering and Engineering Vibration,2012,32(3):117-123.
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[3] GHOSH J,PADGETT J E.Aging considerations in the development of time-dependent seismic fragility curves[J].Structural Engineering,2011,136(12):1497-1512
[4] 彭建新,胡守旺,张建仁.考虑温室效应的氯盐环境下RC桥梁锈胀开裂性能预测[J].工程力学,2013,30(8):103-110.PENG Jianxin,HU Shouwang,ZHANG Jianren.Corrosion-induced crack performance prediction of RC bridge under chloride attack consideration effect of global warming[J].Engineering Mechanics,2013,30(8):103-110.
[5] 李立峰,吴文朋,胡思聪,等.考虑氯离子侵蚀的高墩桥梁时变地震易损性分析[J].工程力学,2016,33(1):163-170.LI Lifeng,WU Wenpeng,HU Sicong,et al.Time-dependent seismic fragility analysis of high pier bridge based on chloride ion induced corrosion[J].Engineering Mechanics,2016,33(1):163-170.
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[8] BIONDINI F,CAMNASIO E,PALERMO A.Lifetime seismic performance of concrete bridges exposed to corrosion[J].Structure and Infrastructure Engineering,2014,10(7):880-900.
[9] DONG Y,FRANGOPOL D M,SAYDAM D.Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards[J].Earthquake Engineering & Structural Dynamics,2013,42(10):1451-1467.
[10] 李超,李宏男.考虑氯离子腐蚀作用的近海桥梁结构全寿命抗震性能评价[J].振动与冲击,2014,33(11):70-77.LI Chao,LI Hongnan.Life-cycle seismic performance evaluation of offshore bridge structures considering chlorides ions corrosion effects[J].Journal of Vibration and Shock,2014,33(11):70-77.
[11] 赵桂峰,何双,马玉宏,等.基于钢筋坑蚀效应的近海隔震桥梁易损性分析[J].中国公路学报,2016,29(8):67-76.ZHAO Guifeng,HE Shuang,MA Yuhong,et al.Fragility analysis of offshore isolated bridge based on steel pitting corrosion effect[J].China Journal of Highway and Transport,2016,29(8):67-76.
[12] LIU P L,DER KIUREGHIAN A.Multivariate of distribution models with prescribed marginal and covariance[J].Probabilistic Engineering Mechanics,1986(2):105-112.
[13] 吴帅兵,张坤,李典庆.相关非正态变量变换时相关性变化对可靠度的影响[J].武汉大学学报(自然科学版),2011,44(2):151-155 WU Shuaibing,ZHANG Kun,LI Dianqing.Effects of correlation change from transformation of correlated abnormal variables on structural reliability[J].Engineering Journal of Wuhan University(Natural Sciences),2011,44(2):151-155.
[14] 吴帅兵,李典庆,周创兵.结构可靠度分析中变量相关时三种变换方法的比较[J].工程力学,2011,28(5):41-49.WU Shuaibing,LI Dianqing,ZHOU Chuangbing.Comparisons among three transformation methods for structural reliability analysis with correlated variables[J].Engineering Mechanics,2011,28(5):41-49.
[15] NIELSON B.Analytical fragility curves for highway bridges in moderate seismic zones[D].Atlanta:Georgia Institute of Technology,2005.
[16] MAZZONI S,MCKENNA F,SCOTT M H,et al.OpenSees command language manual[M].Pacific Earthquake Engineering Research (PEER) Centre,2011.
[17] 公路桥梁抗震设计细则:JTG/TB02-01—2008[S].北京:人民交通出版社,2008.
[18] AVIRAM A,MACKIE K,STOJADINOVIC B.Guidelines for nonlinear analysis of bridge structures in California[R].Pacific Earthquake Engineering Research Center,University of California,Berkeley,2008.
[19] BARBATO M,GU Q,CONTE J P.Probabilistic push-over analysis of structural and soil-structure systems[J].Journal of Structural Engineering,2010,136(11):1330-1341.
[20] 李立峰,吴文朋,黄佳梅,等.地震作用下中等跨径RC连续梁桥系统易损性研究[J].土木工程学报,2012,45(10):152-160.LI Lifeng,WU Wenpeng,HUANG Jiamei,et al.Study on system vulnerability of medium span reinforced concrete continuous girder bridge under earthquake excitation[J].China Civil Engineering Journal,2012,45(10):152-160.
[21] COLLEPARDI M,MARCIAS A,TURRIZIAN R.Penetration of chloride ions into cement pastes and concretes[J].Journal of the American Ceramic Society,1972,55(10):534-535.
[22] MA Yafei,ZHANG Jianren,WANG Lei,et al.Probabilistic prediction with bayesian updating for strength degradation of RC bridge beams[J].Structural Safety,2013,44:102-109.
[23] THOFT-CHRISTENSEN P,JENSEN F M,MIDDLETON C R,et al.Revised rules for concrete bridges[S].Thomas Telford:London,UK,1997.
[2] 谷音,黄怡君,卓卫东.高墩大跨连续刚构桥梁地震易损性分析[J].地震工程与工程振动,2011,31(2):91-97.GU Yin,HUANG Yijun,ZHUO Weidong.Study on seismic vulnerability of long-span continuous rigid frame bridge with high piers[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(2):91-97.
[3] GHOSH J,PADGETT J E.Aging considerations in the development of time-dependent seismic fragility curves[J].Structural Engineering,2011,136(12):1497-1512
[4] 彭建新,胡守旺,张建仁.考虑温室效应的氯盐环境下RC桥梁锈胀开裂性能预测[J].工程力学,2013,30(8):103-110.PENG Jianxin,HU Shouwang,ZHANG Jianren.Corrosion-induced crack performance prediction of RC bridge under chloride attack consideration effect of global warming[J].Engineering Mechanics,2013,30(8):103-110.
[5] 李立峰,吴文朋,胡思聪,等.考虑氯离子侵蚀的高墩桥梁时变地震易损性分析[J].工程力学,2016,33(1):163-170.LI Lifeng,WU Wenpeng,HU Sicong,et al.Time-dependent seismic fragility analysis of high pier bridge based on chloride ion induced corrosion[J].Engineering Mechanics,2016,33(1):163-170.
[6] ASCE.Report card for America's infrastructure[R].American Society of Civil Engineers,Reston,VA,2009.
[7] SIMON J,BRACCI J M,GARDONI P.Seismic response and fragility of deteriorated reinforced concrete bridges[J].Journal of Structural Engineering,2010,136(10):1273-1281.
[8] BIONDINI F,CAMNASIO E,PALERMO A.Lifetime seismic performance of concrete bridges exposed to corrosion[J].Structure and Infrastructure Engineering,2014,10(7):880-900.
[9] DONG Y,FRANGOPOL D M,SAYDAM D.Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards[J].Earthquake Engineering & Structural Dynamics,2013,42(10):1451-1467.
[10] 李超,李宏男.考虑氯离子腐蚀作用的近海桥梁结构全寿命抗震性能评价[J].振动与冲击,2014,33(11):70-77.LI Chao,LI Hongnan.Life-cycle seismic performance evaluation of offshore bridge structures considering chlorides ions corrosion effects[J].Journal of Vibration and Shock,2014,33(11):70-77.
[11] 赵桂峰,何双,马玉宏,等.基于钢筋坑蚀效应的近海隔震桥梁易损性分析[J].中国公路学报,2016,29(8):67-76.ZHAO Guifeng,HE Shuang,MA Yuhong,et al.Fragility analysis of offshore isolated bridge based on steel pitting corrosion effect[J].China Journal of Highway and Transport,2016,29(8):67-76.
[12] LIU P L,DER KIUREGHIAN A.Multivariate of distribution models with prescribed marginal and covariance[J].Probabilistic Engineering Mechanics,1986(2):105-112.
[13] 吴帅兵,张坤,李典庆.相关非正态变量变换时相关性变化对可靠度的影响[J].武汉大学学报(自然科学版),2011,44(2):151-155 WU Shuaibing,ZHANG Kun,LI Dianqing.Effects of correlation change from transformation of correlated abnormal variables on structural reliability[J].Engineering Journal of Wuhan University(Natural Sciences),2011,44(2):151-155.
[14] 吴帅兵,李典庆,周创兵.结构可靠度分析中变量相关时三种变换方法的比较[J].工程力学,2011,28(5):41-49.WU Shuaibing,LI Dianqing,ZHOU Chuangbing.Comparisons among three transformation methods for structural reliability analysis with correlated variables[J].Engineering Mechanics,2011,28(5):41-49.
[15] NIELSON B.Analytical fragility curves for highway bridges in moderate seismic zones[D].Atlanta:Georgia Institute of Technology,2005.
[16] MAZZONI S,MCKENNA F,SCOTT M H,et al.OpenSees command language manual[M].Pacific Earthquake Engineering Research (PEER) Centre,2011.
[17] 公路桥梁抗震设计细则:JTG/TB02-01—2008[S].北京:人民交通出版社,2008.
[18] AVIRAM A,MACKIE K,STOJADINOVIC B.Guidelines for nonlinear analysis of bridge structures in California[R].Pacific Earthquake Engineering Research Center,University of California,Berkeley,2008.
[19] BARBATO M,GU Q,CONTE J P.Probabilistic push-over analysis of structural and soil-structure systems[J].Journal of Structural Engineering,2010,136(11):1330-1341.
[20] 李立峰,吴文朋,黄佳梅,等.地震作用下中等跨径RC连续梁桥系统易损性研究[J].土木工程学报,2012,45(10):152-160.LI Lifeng,WU Wenpeng,HUANG Jiamei,et al.Study on system vulnerability of medium span reinforced concrete continuous girder bridge under earthquake excitation[J].China Civil Engineering Journal,2012,45(10):152-160.
[21] COLLEPARDI M,MARCIAS A,TURRIZIAN R.Penetration of chloride ions into cement pastes and concretes[J].Journal of the American Ceramic Society,1972,55(10):534-535.
[22] MA Yafei,ZHANG Jianren,WANG Lei,et al.Probabilistic prediction with bayesian updating for strength degradation of RC bridge beams[J].Structural Safety,2013,44:102-109.
[23] THOFT-CHRISTENSEN P,JENSEN F M,MIDDLETON C R,et al.Revised rules for concrete bridges[S].Thomas Telford:London,UK,1997.