基于MVFOSM有限元可靠度方法的结构整体概率抗震能力分析
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摘要
结构整体概率抗震能力分析既属于结构体系抗力统计分析研究内容,也属于地震易损性分析研究范畴,多采用数值模拟方法。作为一种不确定性传递的近似解析分析工具,平均值一次二阶矩方法(MVFOSM)广泛地应用于结构构件抗力的统计分析,但是很难应用于结构整体抗力的统计分析,主要困难在于结构反应是基本随机变量的隐式函数,梯度信息很难得到。将结构体系抗力的统计分析和地震易损性分析结合起来,通过基于MVFOSM的有限元可靠度方法,以新一代的地震工程模拟仿真软件OpenSees为计算平台,以最大层间位移角作为结构整体抗震能力参数,对钢筋混凝土框架结构的整体概率抗震能力进行分析,并用Monte Carlo模拟法结果进行验证,从而建立了钢筋混凝土框架结构的整体概率抗震能力模型。算例分析表明,MVFOSM有限元可靠度方法的精度和效率都很高,只需要进行一次有限元分析即可较为准确地获得结构整体概率抗震能力的前二阶矩信息。
The analysis of global seismic capacity of structures belongs to the category of resistance analysis of structural systems,meanwhile,it is also a kind of seismic fragility analysis of the structures in nature,in which numerical simulation methods are generally applied.As an approximate probability analysis method and an efficient uncertainty propagation tool,mean value first order second moment(MVFOSM) has been successfully applied in statistical analysis of structural member resistance,however,it is difficult to apply in statistical analysis of structural system resistance,the main reason is that structural responses are implicit functions of basic random variables,and the gradient information in MVFOSM is hardly obtained.In this paper,the statistical analysis of the structural system resistance and the seismic fragility analysis are combined in a unified framework.The new generation of earthquake engineering simulation software OpenSees is taken as the computation platform.The global probabilistic seismic capacity of reinforced concrete frame structures is analyzed by using MVFOSM-based the finite element reliability method,and compared to its accuracy and efficiency with Monte Carlo simulation method.The first two statistical information(i.e.,mean value and standard deviation) of the maximum inter-storey displacement angle which is taken as the parameter of global seismic capacity is gained,and its probability model is built up.It is shown by a numerical example that both accuracy and efficiency of MVFOSM-based finite element reliability method are high,in fact,only once of finite element analysis is needed to get the statistical information and probability model of the global seismic capacity of the structures.
The analysis of global seismic capacity of structures belongs to the category of resistance analysis of structural systems,meanwhile,it is also a kind of seismic fragility analysis of the structures in nature,in which numerical simulation methods are generally applied.As an approximate probability analysis method and an efficient uncertainty propagation tool,mean value first order second moment(MVFOSM) has been successfully applied in statistical analysis of structural member resistance,however,it is difficult to apply in statistical analysis of structural system resistance,the main reason is that structural responses are implicit functions of basic random variables,and the gradient information in MVFOSM is hardly obtained.In this paper,the statistical analysis of the structural system resistance and the seismic fragility analysis are combined in a unified framework.The new generation of earthquake engineering simulation software OpenSees is taken as the computation platform.The global probabilistic seismic capacity of reinforced concrete frame structures is analyzed by using MVFOSM-based the finite element reliability method,and compared to its accuracy and efficiency with Monte Carlo simulation method.The first two statistical information(i.e.,mean value and standard deviation) of the maximum inter-storey displacement angle which is taken as the parameter of global seismic capacity is gained,and its probability model is built up.It is shown by a numerical example that both accuracy and efficiency of MVFOSM-based finite element reliability method are high,in fact,only once of finite element analysis is needed to get the statistical information and probability model of the global seismic capacity of the structures.
引文
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[6]Vamvatsikos D,Cornell C A.Direct estimation of the seismic demand and capacity of oscillators with multi-linear static pushovers through IDA[J].Earthquake Engineering and Structural Dynamics,2006,35(9):1097-1117.
[7]Zareian F,Krawinkler H.Assessment of probability of collapse and design for collapse safety[J].Earthquake Engineering and Structural Dy-namics,2007,36(13):1901-1914.
[8]Ellingwood B R,Celik O C,Kinali K.Fragility assessment of building structural systems in Mid-America[J].Earthquake Engineering andStructural Dynamics,2007,36(13):1935-1952.
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[17]吕大刚,李晓鹏,胡晓琦,等.钢框架结构的非线性静力抗震可靠性分析II.可靠度指标及其灵敏度[J].地震工程与工程振动,2008,28(1):71-78.
[18]吕大刚,李晓鹏,王光远.基于可靠度和性能的结构整体地震易损性分析[J].自然灾害学报,2006,15(2):107-114.
[19]吕大刚,李晓鹏,张鹏,等.土木工程结构地震易损性分析的有限元可靠度方法[J].应用基础与工程科学学报,2006,14(suppl.):264-272.
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[21]Federal Emergency Management Agency(FEMA).NEHRP Guideline for the seismic rehabilitation of buildings[R].FEMAReport273,1997.
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[23]Federal Emergency Management Agency(FEMA).Next-generation performance-based seismic design guidelines[R].FEMA Report 445,2006.
[24]Applied Technology Council(ATC).Seismic evaluation and retrofit of existing concrete buildings[R].ATC 40,1996.
[25]Structural Engineering Association of California(SEAOC).Performance based seismic engineering of buildings[R].April,1995.
[26]GB 50011-2001,建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[27]JGJ 3-2002,高层建筑混凝土结构技术规程[S].北京:中国建筑工业出版社,2002
[2]李国强,刘玉妹,赵欣.钢结构框架体系高等分析与系统可靠度设计[M].北京:中国建筑工业出版社,2006.
[3]Vamvatsikos D,Cornell C A.Incremental dynamic analysis[J].Earthquake Engineering and Structural Dynamics,2002,31(3):491-514.
[4]Vamvatsikos D,Cornell C A.Direct estimation of seismic demand and capacity of multi degree-of-freedomsystems through incremental dynamic a-nalysis of single degree of freedom approximation[J].ASCE Journal of Structural Engineering,2005,131(4):589-599.
[5]Vamvatsikos D,Cornell C A.Developing efficient scalar and vector intensity measures for IDAcapacity estimation by incorporating elastic spectralshape information[J].Earthquake Engineering and Structural Dynamics,2005,34(13):1573-1600.
[6]Vamvatsikos D,Cornell C A.Direct estimation of the seismic demand and capacity of oscillators with multi-linear static pushovers through IDA[J].Earthquake Engineering and Structural Dynamics,2006,35(9):1097-1117.
[7]Zareian F,Krawinkler H.Assessment of probability of collapse and design for collapse safety[J].Earthquake Engineering and Structural Dy-namics,2007,36(13):1901-1914.
[8]Ellingwood B R,Celik O C,Kinali K.Fragility assessment of building structural systems in Mid-America[J].Earthquake Engineering andStructural Dynamics,2007,36(13):1935-1952.
[9]Wen Y K,Ellingwood B R,Veneziano D,et al.Uncertainty modeling in earthquake engineering[R].MAE Center Project FD-2 Report,2003.
[10]Wen Y K,Ellingwood B R,Bracci J.Vulnerability function framework for consequence-based engineering[R].MAE Center Project DS-4 Re-port,2004.
[11]Koduru S D,Haukaas T,Elwood K J.Probabilistic evaluation of global seismic capacity of degrading structures[J].Earthquake Engineeringand Structural Dynamics,2007,36(13):2043-2058.
[12]Montiel MA,Ruiz S E.Influence of structural capacity uncertainty on seismic reliability of buildings under narrow-band motions[J].Earth-quake Engineering and Structural Dynamics,2007,36(13):1915-1934.
[13]Melchers R E.Structural reliability:analysis and prediction[M].2nd Edition.New York:John Wiley,1999.
[14]Der Kiureghian A,Haukaas T,Fujimura K.Structural reliability software at the University of California,Berkeley[J].Structural Safety,2006,28(1/2):44-67.
[15]Haukaas T,Der Kiureghian A.Methods and object-oriented software for FE reliability and sensitivity analysis with application to a bridge structure[J].ASCE Journal of Computing in Civil Engineering,2007,21(3):151-163.
[16]吕大刚,李晓鹏,胡晓琦,等.钢框架结构的非线性静力抗震可靠性分析I.有限元反应及其灵敏度[J].地震工程与工程振动,2007,27(5):55-60.
[17]吕大刚,李晓鹏,胡晓琦,等.钢框架结构的非线性静力抗震可靠性分析II.可靠度指标及其灵敏度[J].地震工程与工程振动,2008,28(1):71-78.
[18]吕大刚,李晓鹏,王光远.基于可靠度和性能的结构整体地震易损性分析[J].自然灾害学报,2006,15(2):107-114.
[19]吕大刚,李晓鹏,张鹏,等.土木工程结构地震易损性分析的有限元可靠度方法[J].应用基础与工程科学学报,2006,14(suppl.):264-272.
[20]McKenna F,Fenves G L,Scott MH.Open systemfor earthquake engineering simulation[R].Pacific Earthquake Engineering Research Center,Univ.of California,Berkeley,Calif.2008.
[21]Federal Emergency Management Agency(FEMA).NEHRP Guideline for the seismic rehabilitation of buildings[R].FEMAReport273,1997.
[22]Federal Emergency Management Agency(FEMA).Prestandard and commentary for the rehabilitation of buildings[R].FEMA Report 356,2000.
[23]Federal Emergency Management Agency(FEMA).Next-generation performance-based seismic design guidelines[R].FEMA Report 445,2006.
[24]Applied Technology Council(ATC).Seismic evaluation and retrofit of existing concrete buildings[R].ATC 40,1996.
[25]Structural Engineering Association of California(SEAOC).Performance based seismic engineering of buildings[R].April,1995.
[26]GB 50011-2001,建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[27]JGJ 3-2002,高层建筑混凝土结构技术规程[S].北京:中国建筑工业出版社,2002
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