非一致地震激励下大跨度桥梁随机振动时域显式法
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摘要
对于大跨度桥梁结构,地震激励的空间效应不应忽略。考虑到随机地震激励的非平稳特性,为提高计算效率,有必要在时域内直接开展非一致地震激励下大跨度桥梁的随机振动分析。基于相对运动法,推导非一致地震激励下结构动力响应的时域显式表达式,提出可考虑非一致地震激励的时域显式直接法,可快速获取结构响应的统计矩;同时提出高效的时域显式随机模拟法,可进一步获取非一致地震激励下结构响应的平均峰值等更全面的统计信息,并可有效实现结构的动力可靠度分析。以某主跨1200m悬索桥为工程实例,开展顺桥向非一致地震激励下的随机振动分析,分别研究地震激励的行波效应、失相干效应和局部场地效应对桥梁关键响应标准差、平均峰值和结构抗震动力可靠度的影响。研究结果表明,对于该桥主梁跨中和主塔塔顶顺桥向位移,非一致地震激励下的响应标准差和平均峰值均小于一致地震激励下的结果;而对于该桥主塔塔底内力,非一致地震激励下的响应标准差和平均峰值有可能大于一致地震激励下的结果,其中弯矩和剪力的平均峰值增幅分别可达21.6%和19.5%;此外,地震激励的空间效应对该桥的体系失效概率也有较大影响。
For long-span bridges, the spatial variability effects of seismic excitations should be taken into account. In view of the non-stationarity of seismic excitations, to improve the computational efficiency, it is necessary to carry out the random vibration analysis of long-span bridges in the time domain with non-uniform ground motion. Based on the relative motion method, the explicit time-domain expression of the dynamic response of a structure under non-uniform seismic excitation was first deduced, and an explicit time-domain method was then proposed for fast calculation of the statistical moments of structural responses under non-uniform seismic excitations. Meanwhile, using the explicit time-domain expressions of dynamic responses,an efficient Monte-Carlo simulation method was further proposed for obtaining the mean peak values of structural responses and for analyzing the dynamic reliability of the structure with non-uniform ground motion.Taking a long-span suspension bridge with a main span of 1200 m as a practical example, the random vibration analysis of the bridge under longitudinal non-uniform seismic excitations was conducted in the present study. The traveling-wave effect, the incoherence effect and the local site effect on the standard deviations and mean peak values of critical responses and structural seismic dynamic reliability were studied, respectively. The results show that, for the longitudinal displacements at the mid-span section of the bridge girder and at the top sections of the main towers, the standard deviations and mean peak values of the responses under non-uniform seismic excitations are smaller than those under uniform seismic excitation. However, for the internal forces at the bottom sections of the main towers, the standard deviations and mean peak values of the responses under non-uniform seismic excitations may be larger than those under uniform seismic excitation, and the mean peak value of the bending moment and the shear force may be 21.6% and 19.5% larger, respectively. In addition, it can be observed that the spatial variability effects of seismic excitations have great influences on the failure probability of the bridge system.
For long-span bridges, the spatial variability effects of seismic excitations should be taken into account. In view of the non-stationarity of seismic excitations, to improve the computational efficiency, it is necessary to carry out the random vibration analysis of long-span bridges in the time domain with non-uniform ground motion. Based on the relative motion method, the explicit time-domain expression of the dynamic response of a structure under non-uniform seismic excitation was first deduced, and an explicit time-domain method was then proposed for fast calculation of the statistical moments of structural responses under non-uniform seismic excitations. Meanwhile, using the explicit time-domain expressions of dynamic responses,an efficient Monte-Carlo simulation method was further proposed for obtaining the mean peak values of structural responses and for analyzing the dynamic reliability of the structure with non-uniform ground motion.Taking a long-span suspension bridge with a main span of 1200 m as a practical example, the random vibration analysis of the bridge under longitudinal non-uniform seismic excitations was conducted in the present study. The traveling-wave effect, the incoherence effect and the local site effect on the standard deviations and mean peak values of critical responses and structural seismic dynamic reliability were studied, respectively. The results show that, for the longitudinal displacements at the mid-span section of the bridge girder and at the top sections of the main towers, the standard deviations and mean peak values of the responses under non-uniform seismic excitations are smaller than those under uniform seismic excitation. However, for the internal forces at the bottom sections of the main towers, the standard deviations and mean peak values of the responses under non-uniform seismic excitations may be larger than those under uniform seismic excitation, and the mean peak value of the bending moment and the shear force may be 21.6% and 19.5% larger, respectively. In addition, it can be observed that the spatial variability effects of seismic excitations have great influences on the failure probability of the bridge system.
引文
[1]Kiureghian A D,Neuenhofer A.Response spectrum method for multi-support seismic excitations[J].Earthquake Engineering and Structural Dynamics,1992,21(8):713-740
[2]朱位秋.随机振动[M].北京:科学出版社,1992(Zhu Weiqiu.Random vibration[M].Beijing:Science Press,1992(in Chinese))
[3]Harichandran R S,Hawwari A,Sweidan B N.Response of long-span bridges to spatially varying ground motion[J].Journal of Structural Engineering,1996,122(5):476-484
[4]Allam S M,Datta T K.Seismic behaviour of cable-stayed bridges under multi-component random ground motion[J].Engineering Structures,1999,21(1):62-74
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[6]焦常科,李爱群.大跨度斜拉桥多点激励随机地震响应研究[J].振动工程学报,2013,26(5):707-714(Jiao Changke,Li Aiqun.Research on random seismic response of long-span cable-stayed bridge under multi-excitation[J].Journal of Vibration Engineering,2013,26(5):707-714(in Chinese))
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[8]赵雷,刘宁国.大跨度叠合梁斜拉桥多维多点非平稳随机地震响应分析[J].应用数学和力学,2017,38(1):118-125(Zhao Lei,Liu Ningguo.Non-stationary random seismic analysis of large-span composite beam cable-stayed bridges under multi-support and multi-dimensional earthquake excitations[J].Applied Mathematics and Mechanics,2017,38(1):118-125(in Chinese))
[9]苏成,徐瑞.非平稳随机激励下结构体系动力可靠度时域解法[J].力学学报,2010,42(32):512-520(Su Cheng,Xu Rui.Time-domain method for dynamic reliability of structural systems subjected to non-stationary random excitations[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(3):512-520(in Chinese))
[10]Su C,Huang H,Ma H T.Fast equivalent linearization method for nonlinear structures under non-stationary random excitations[J].Journal of Engineering Mechanics,ASCE,2016,142(8):04016049
[11]苏成,徐瑞,刘小璐.大跨度空间结构抗震分析的非平稳随机振动时域显式法[J].建筑结构学报,2011,32(11):169-176(Su Cheng,Xu Rui,Liu Xiaolu.Non-stationary seismic analysis of large-span spatial structures by time-domain explicit method[J].Journal of Building Structures,2011,32(11):169-176(in Chinese))
[12]苏成,黄志坚,刘小璐.高层建筑地震作用计算的时域显式随机模拟法[J].建筑结构学报,2015,36(1):13-22(Su Cheng,Huang Zhijian,Liu Xiaolu.Time-domain explicit random simulation method for seismic analysis of tall buildings[J].Journal of Building Structures,2015,36(1):13-22(in Chinese))
[13]Clough R W,Penzien J.Dynamic of structure[M].New York:Mcgraw-Hill,1975
[14]Harichandran R S,Vanmarcke E H.Stochastic variation of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,1986,112(2):154-175
[15]周国良,李小军,刘必灯,等.大质量法在多点激励分析中的应用、误差分析与改进[J].工程力学,2011,28(1):48-54(Zhou Guoliang,Li Xiaojun,Liu Bideng,et al.Error analysis and improvement of large mass method used in multi-support seismic excitation analysis[J].Engineering Mechanics,2011,28(1):48-54(in Chinese))
[16]周国良,李小军,刘必灯,等.大刚度法在结构动力分析中的应用、误差分析与改进[J].工程力学,2011,28(8):30-44(Zhou Guoliang,Li Xiaojun,Liu Bideng,et al.Error analysis and improvements of large spring/stiffness method for structural dynamic response analysis[J].Engineering Mechanics,2011,28(8):30-44(in Chinese))
[17]代希华,李保木,苏成,等.大跨度悬索桥地震响应的几何非线性影响研究[J].桥梁建设,2017,47(3):19-23(Dai Xihua,Li Baomu,Su Cheng.Study of geometric nonlinearity influences of seismic responses of long span suspension bridge[J].Bridge Construction,2017,47(3):19-23(in Chinese))
[18]范立础,王君杰,陈玮.非一致地震激励下大跨度斜拉桥的响应特征[J].计算力学学报,2001,18(3):358-363(Fan Lichu,Wang Junjie,Chen Wei.Response characteristics of long-span cable-stayed bridges under non-uniform seismic action[J].Chinese Journal of Computational Mechanics,2001,18(3):358-363(in Chinese))
[19]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10(Xue Suduo,Wang Xuesheng,Cao Zi.Parameters study on seismic random model based on the new seismic code[J].China Civil Engineering Journal,2003,36(5):5-10(in Chinese))
[20]JTG/TB 02-01-2008公路桥梁抗震细则[S].北京:人民交通出版社,2008(JTG/TB 02-01-2008Guidelines for seismic design of highway bridges[S].Beijing:China Communications Press,2008(in Chinese))
[2]朱位秋.随机振动[M].北京:科学出版社,1992(Zhu Weiqiu.Random vibration[M].Beijing:Science Press,1992(in Chinese))
[3]Harichandran R S,Hawwari A,Sweidan B N.Response of long-span bridges to spatially varying ground motion[J].Journal of Structural Engineering,1996,122(5):476-484
[4]Allam S M,Datta T K.Seismic behaviour of cable-stayed bridges under multi-component random ground motion[J].Engineering Structures,1999,21(1):62-74
[5]Lin J H,Zhang Y H,Li Q S,et al.Seismic spatial effects for long-span bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207-1216
[6]焦常科,李爱群.大跨度斜拉桥多点激励随机地震响应研究[J].振动工程学报,2013,26(5):707-714(Jiao Changke,Li Aiqun.Research on random seismic response of long-span cable-stayed bridge under multi-excitation[J].Journal of Vibration Engineering,2013,26(5):707-714(in Chinese))
[7]宋刚,汪飞澜.多点演变随机激励下连续刚构桥地震响应[J].土木工程学报,2013,46(增2):249-254(Song Gang,Wang Feilan.Seismic responses of a continuous rigid-framed bridge subjected to multi-support evolutionary random excitations[J].China Civil Engineering Journal,2013,46(S2):249-254(in Chinese))
[8]赵雷,刘宁国.大跨度叠合梁斜拉桥多维多点非平稳随机地震响应分析[J].应用数学和力学,2017,38(1):118-125(Zhao Lei,Liu Ningguo.Non-stationary random seismic analysis of large-span composite beam cable-stayed bridges under multi-support and multi-dimensional earthquake excitations[J].Applied Mathematics and Mechanics,2017,38(1):118-125(in Chinese))
[9]苏成,徐瑞.非平稳随机激励下结构体系动力可靠度时域解法[J].力学学报,2010,42(32):512-520(Su Cheng,Xu Rui.Time-domain method for dynamic reliability of structural systems subjected to non-stationary random excitations[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(3):512-520(in Chinese))
[10]Su C,Huang H,Ma H T.Fast equivalent linearization method for nonlinear structures under non-stationary random excitations[J].Journal of Engineering Mechanics,ASCE,2016,142(8):04016049
[11]苏成,徐瑞,刘小璐.大跨度空间结构抗震分析的非平稳随机振动时域显式法[J].建筑结构学报,2011,32(11):169-176(Su Cheng,Xu Rui,Liu Xiaolu.Non-stationary seismic analysis of large-span spatial structures by time-domain explicit method[J].Journal of Building Structures,2011,32(11):169-176(in Chinese))
[12]苏成,黄志坚,刘小璐.高层建筑地震作用计算的时域显式随机模拟法[J].建筑结构学报,2015,36(1):13-22(Su Cheng,Huang Zhijian,Liu Xiaolu.Time-domain explicit random simulation method for seismic analysis of tall buildings[J].Journal of Building Structures,2015,36(1):13-22(in Chinese))
[13]Clough R W,Penzien J.Dynamic of structure[M].New York:Mcgraw-Hill,1975
[14]Harichandran R S,Vanmarcke E H.Stochastic variation of earthquake ground motion in space and time[J].Journal of Engineering Mechanics,1986,112(2):154-175
[15]周国良,李小军,刘必灯,等.大质量法在多点激励分析中的应用、误差分析与改进[J].工程力学,2011,28(1):48-54(Zhou Guoliang,Li Xiaojun,Liu Bideng,et al.Error analysis and improvement of large mass method used in multi-support seismic excitation analysis[J].Engineering Mechanics,2011,28(1):48-54(in Chinese))
[16]周国良,李小军,刘必灯,等.大刚度法在结构动力分析中的应用、误差分析与改进[J].工程力学,2011,28(8):30-44(Zhou Guoliang,Li Xiaojun,Liu Bideng,et al.Error analysis and improvements of large spring/stiffness method for structural dynamic response analysis[J].Engineering Mechanics,2011,28(8):30-44(in Chinese))
[17]代希华,李保木,苏成,等.大跨度悬索桥地震响应的几何非线性影响研究[J].桥梁建设,2017,47(3):19-23(Dai Xihua,Li Baomu,Su Cheng.Study of geometric nonlinearity influences of seismic responses of long span suspension bridge[J].Bridge Construction,2017,47(3):19-23(in Chinese))
[18]范立础,王君杰,陈玮.非一致地震激励下大跨度斜拉桥的响应特征[J].计算力学学报,2001,18(3):358-363(Fan Lichu,Wang Junjie,Chen Wei.Response characteristics of long-span cable-stayed bridges under non-uniform seismic action[J].Chinese Journal of Computational Mechanics,2001,18(3):358-363(in Chinese))
[19]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5-10(Xue Suduo,Wang Xuesheng,Cao Zi.Parameters study on seismic random model based on the new seismic code[J].China Civil Engineering Journal,2003,36(5):5-10(in Chinese))
[20]JTG/TB 02-01-2008公路桥梁抗震细则[S].北京:人民交通出版社,2008(JTG/TB 02-01-2008Guidelines for seismic design of highway bridges[S].Beijing:China Communications Press,2008(in Chinese))