基于地震易损性解析函数的概率地震风险理论研究
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摘要
基于不确定性传递,推导了考虑本质不确定性的地震易损性函数和考虑知识不确定性的地震易损性函数的解析表达式,并给出了其参数确定方法。证明了基于位移的函数与基于地震动强度的函数之间存在一致性。推导了考虑知识不确定性的地震易损性点估计函数的置信度水平。利用地震风险等于地震危险性与地震易损性的卷积,采用幂指数形式的地震危险性函数,进一步将已获得的地震易损性解析函数拓展得到概率地震风险函数的解析形式。利用得到的地震易损性与风险的解析函数,可简化地震易损性和风险评估的过程,方便对不同结构体系进行概率地震安全评估。
From the viewpoint of uncertainty propagation,both the seismic fragility function considering aleatory uncertainty and the seismic fragility function considering epistemic uncertainty are derived in analytical forms,and the corresponding parameters are determined. The consistency between the displacement-based function and the earthquake-intensity-based function,which are two categories of commonly used seismic fragility functions considering aleatory uncertainty, is proved. The confidence level of the point estimate function of seismic fragility with consideration of epistemic uncertainty is developed. Based on the equation of seismic risk that is equal to the convolution of seismic fragility and seismic hazard,the derived analytical seismic fragility functions are further extended to the corresponding probabilistic seismic risk functions by adopting a power-law seismic hazard function.Using the derived analytical functions of seismic fragility and seismic risk,the process of seismic fragility and risk evaluations can be simplified,and it is convenient to conduct probabilistic seismic safety assessment for various types of structural systems.
From the viewpoint of uncertainty propagation,both the seismic fragility function considering aleatory uncertainty and the seismic fragility function considering epistemic uncertainty are derived in analytical forms,and the corresponding parameters are determined. The consistency between the displacement-based function and the earthquake-intensity-based function,which are two categories of commonly used seismic fragility functions considering aleatory uncertainty, is proved. The confidence level of the point estimate function of seismic fragility with consideration of epistemic uncertainty is developed. Based on the equation of seismic risk that is equal to the convolution of seismic fragility and seismic hazard,the derived analytical seismic fragility functions are further extended to the corresponding probabilistic seismic risk functions by adopting a power-law seismic hazard function.Using the derived analytical functions of seismic fragility and seismic risk,the process of seismic fragility and risk evaluations can be simplified,and it is convenient to conduct probabilistic seismic safety assessment for various types of structural systems.
引文
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[17]Bazzurro P,Cornell C A,Shome N,et al.Three proposals for characterizing MDOF nonlinear seismic response[J].Journal of Structural Engineering,ASCE,1998,124(11):1281-1289.
[2]GB 50011—2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.(GB 50011—2010 Code for seismic design of buildings[S].Beijing:China Architecture&Building Press,2010.(in Chinese))
[3]Cornell C A,Jalayer F,Hamburger R O,et al.The probabilistic basis for the 2000 SAC/FEMA steel moment frame guidelines[J].Journal of Structural Engineering,ASCE,2002,128(4):526-533.
[4]Der Kiureghian A,Ditlevsen O.Aleatory or epistemic does it matter[J].Structural Safety,2009,31(2):105-112.
[5]吕大刚,于晓辉,宋鹏彦,等.抗震结构最优设防水平决策与全寿命优化设计的简化易损性分析方法[J].地震工程与工程振动,2009,29(4):150-159.(LDagang,YU Xiaohui,SONG Pengyan,et al.Simplified fragility analysis methods for the optimal protection level decision-making and minimum life-cycle cost design of aseismic structures[J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(4):150-159.(in Chinese))
[6]Cornell C A.Risk-based structural design[C]//Nowak A.Proceedings of Symposium on Risk Analysis.Michigan,USA:University of Michigan,1994:37-48.
[7]吕大刚,于晓辉,陈志恒.钢筋混凝土框架结构侧向倒塌的地震易损性分析[J].哈尔滨工业大学学报,2011,43(6):1-5.(LDa-gang,YU Xiao-hui,CHEN Zhi-heng.Lateral seismic collapse fragilityInstitute of Technology,2011,43(6):1-5.(in Chinese))
[8]于晓辉,吕大刚.考虑结构不确定性的地震倒塌易损性分析[J].建筑结构学报,2012,33(10):8-14.(YU Xiaohui,LDagang.Seismic collapse fragility analysis considering structural uncertainties[J].Journal of Building Structures,2012,33(10):8-14.(in Chinese))
[9]施炜,叶列平,陆新征,等.不同抗震设防RC框架结构抗倒塌能力的研究[J].工程力学,2011,28(3):41-48.(SHI Wei,YE Lie-ping,LU Xin-zheng,et al.Study on the collapse-resistant capacity of RC frames with different seismic fortification levels[J].Engineering Mechanics,2011,28(3):41-48.(in Chinese))
[10]FEMA 273 NEHRP guidelines for the seismic rehabilitation of buildings[S].Washinton DC:Federal Emergency Management Agency,1997.
[11]吕大刚.结构抗震可靠度的二种简化解析表达式及其一致性证明[J].地震工程与工程振动,2009,29(10):59-65.(LDagang.Verification of consistency of two simplified analytical formulations for structural seismic reliability[J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(10):59-65.(in Chinese))
[12]Hwang H,刘晶波.地震作用下钢筋混凝土桥梁结构易损性分析[J].土木工程学报,2004,37(6):47-51.(Hwang H,Liu Jingbo.Seismic fragility analysis of reinforced concrete bridges[J].China CivilEngineering Journal,2004,37(6):47-51.(in Chinese))
[13]刘晶波,刘阳冰,闫秋实,韩强.基于性能的方钢管混凝土框架结构的地震易损性分析[J].土木工程学报,2010,43(2):39-47.(Liu Jingbo,Liu Yangbing,Yan Qiushi,Han Qiang.Performance-based seismic fragility analysis of CFST frame structures[J].China Civil Engineering Journal,2010,43(2):39-47.(in Chinese))
[14]周靖,罗高杰,方小丹.强震作用下竖向不规则RC框架结构抗震易损性分析[J].建筑结构学报,2011,32(11):134-142.(ZHOU Jing,LUO Gaojie,FANG Xiaodan.Fragility analysis of vertical irregular reinforced concrete frame structures subjected to pulselike ground motion[J].Journal of Building Structures,2011,32(11):134-142.(in Chinese))
[15]Wen Y K,Ellingwood B R,Veneziano D,et al.Uncertainty modeling in earthquake engineering[R].Project FD-2 Report.Memphis,USA:MAE Center,2003:10-11.
[16]Bradley B A,Dhakal R P,Cubrinovski M,et al.Improved seismic hazard model with application to probabilistic seismic demand analysis[J].Earthquake Engineering and Structural Dynamics,2007,36(14):2211-2225.
[17]Bazzurro P,Cornell C A,Shome N,et al.Three proposals for characterizing MDOF nonlinear seismic response[J].Journal of Structural Engineering,ASCE,1998,124(11):1281-1289.
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