多维多点激励下大跨度刚构桥的线性与非线性分析
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摘要
随着桥梁工程技术的飞速发展,桥梁的跨径越来越大,桥墩越来越高,导致体系也越来越柔,这对大跨度桥梁的抗震设计提出了新的挑战。刚构桥作为桥梁工程中广泛使用的桥型,也在向高墩大跨发展。由于目前对于桥梁的抗震设计均是基于一致激励的,而对于大跨度桥梁,由于地震波的行波效应、不相干效应以及局部场地效应的影响,桥梁各墩处的地面运动并不一致,因此,研究多点激励下大跨度桥梁的地震响应规律具有很重要的意义。
本文首先对既有的分析模型与原理进行了归纳总结,为之后的计算分析奠定了理论基础。然后以一五跨连续刚构桥为例,采用有限元软件ANSYS对其进行了功率谱分析,分析中分别考虑了地震动行波效应、不相干效应以及局部场地效应单独与联合作用下刚构桥的地震响应规律。其次合成了基于功率谱模型与相关函数模型的多维多点人工地震波,并采用该人工地震波对刚构桥进行了多维多点激励的线性与非线性时程分析。最后对直线刚构桥与曲线刚构桥在多维多点激励下的地震响应进行了对比研究。论文主要结论包括以下几点：
1、局部场地效应对刚构桥地震响应的影响是很明显的,在实际工程中采用不随空变化的场地土特性进行抗震验算有可能使刚构桥趋于不利；不相干效应的影响较小；单独考虑行波效应时,刚构桥墩底弯矩的地震响应往往较一致激励时的小；相对而言,行波效应对刚构桥墩顶弯矩的影响要大于对墩底弯矩的影响；考虑行波效应以后,刚构桥的高阶振型有可能被激起；
2、综合考虑了局部场地效应、不相干效应与行波效应以后,刚构桥桥墩的地震响应有可能比一致激励的大,也有可能比一致激励的小,而主梁的响应通常高于一致激励的结果；
3、合成了多维多点人工地震动时程,并在同时考虑了材料非线性与几何非线性以后对刚构桥进行了多维多点激励非线性时程分析,结果证明多维多点激励下各方向地震动会有耦合的现象,刚构桥的地震响应并不等于单向地震响应的简单叠加；考虑了非线性以后刚构桥墩顶部位比墩底部位形成了更为饱满的塑性铰滞回环,建议在实际工程中重视刚构桥墩顶截面的延性设计；
4、获得了水平地震波一维多点输入与二维多点输入时,针对曲线刚构桥某个地震响应的最不利输入角度公式,依据该公式可以方便的找到地震波平面一维多点输入与二维多点输入时针对曲线刚构桥某个地震响应量的最不利输入角度精确值；
5、三维多点激励下曲线刚构桥桥墩与主梁的横向弯矩通常比直线桥梁的小,而桥墩的纵向弯矩与主梁的竖向弯矩往往比直线桥的大。
With the rapid development of bridge engineering, the spans of bridges become larger and larger, and piers become higher and higher, Therefore, systems are often more flexible than ever. Which bring new challenges to seismic design of long span bridges. As a widely used project type, rigid frame bridges are also developing towards large spans and high piers.Currently, seismic design of bridges is all based on uniform excitation method,but ground motion of different pier of large-span bridges are usually not consistent because of influences of traveling wave effect, partially coherent effect and partial site effect. Therefore, study on earthquake responses of large-span bridges under multi-support excitations is of great importance.
In this paper, analysis model and principle is summarized firstly, which laid the foundation for the following calculation and analysis. Secondly, as a example, a5-span prestressed concrete rigid frame bridge is analyzed with finite element software-ANSYS using power spectrum method, in which earthquake responses of rigid frame bridge is studied in the condition that traveling wave effect, partially coherent effect and partial site effect is considered both separately and together. Thirdly, multi-dimensional and multi-support artificial seismic waves are generated based on target power spectrum model and target correlation function model, and the rigid frame bridge is analyzed with time history method using the generated artificial seismic waves. Finally, earthquake response of both curved rigid frame bridge and straight rigid frame bridge is studied comparatively. The main conclusions in this paper include the following:
1. The influence of partial site effect is obvious,adopting site soil of which characteristic doesn't vary with spatial location may make rigid frame bridge unfavorable; The influence of partially coherent effect is little; In the condition only seismic wave effect is considered, the moments on the top of piers of rigid frame bridge is usually less compared with results of uniform excitation; The influence of traveling wave effect on the top of piers is relatively large than that at the bottom; After traveling wave effect is taken account, higher modes of rigid frame bridge may be aroused.
2. In the condition that traveling wave effect, partially coherent effect and partial site effect is considered comprehensively, the earthquake responses of piers may increase or decrease while the earthquake responses of main girders usually increase compared with the case of uniform seismic excitation.
3.Multi-dimensional and multi-support seismic waves are generated, and multi-dimensional and multi-support time history is implemented after both material nonlinearity and geometric nonlinearity is taken into account, results show that earthquake responses of different direction are coupled with each other in the case of multi-dimensional and multi-support excitations, earthquake responses of rigid frame bridge don't equal to the simply superimposed results of one-dimensional; Full plastic hinge loops appear on the top of piers in the case of multi-dimensional and multi-support excitations after taking nonlinear property, so ductile design on the top of piers of rigid frame bridges should be paid attention in practical engineering.
5. The formula of the most unfavorable input angel of seismic waves of determined response variable of curved rigid frame bridge, under one-dimensional and multi-support excitations and two-dimensional and multi-support excitations, is obtained. According to the formula, exact value of input angel of the one and two-dimensional and multi-support seismic waves, against a determined response variable, can be easily obtained.
6. Under three-dimensional and multi-support excitations, transverse moments of piers and main girders of curved rigid frame bridge are usually less than that of straight rigid frame bridge while longitudinal moments of piers and vertical moments of main girders are usually more.
本文首先对既有的分析模型与原理进行了归纳总结,为之后的计算分析奠定了理论基础。然后以一五跨连续刚构桥为例,采用有限元软件ANSYS对其进行了功率谱分析,分析中分别考虑了地震动行波效应、不相干效应以及局部场地效应单独与联合作用下刚构桥的地震响应规律。其次合成了基于功率谱模型与相关函数模型的多维多点人工地震波,并采用该人工地震波对刚构桥进行了多维多点激励的线性与非线性时程分析。最后对直线刚构桥与曲线刚构桥在多维多点激励下的地震响应进行了对比研究。论文主要结论包括以下几点：
1、局部场地效应对刚构桥地震响应的影响是很明显的,在实际工程中采用不随空变化的场地土特性进行抗震验算有可能使刚构桥趋于不利；不相干效应的影响较小；单独考虑行波效应时,刚构桥墩底弯矩的地震响应往往较一致激励时的小；相对而言,行波效应对刚构桥墩顶弯矩的影响要大于对墩底弯矩的影响；考虑行波效应以后,刚构桥的高阶振型有可能被激起；
2、综合考虑了局部场地效应、不相干效应与行波效应以后,刚构桥桥墩的地震响应有可能比一致激励的大,也有可能比一致激励的小,而主梁的响应通常高于一致激励的结果；
3、合成了多维多点人工地震动时程,并在同时考虑了材料非线性与几何非线性以后对刚构桥进行了多维多点激励非线性时程分析,结果证明多维多点激励下各方向地震动会有耦合的现象,刚构桥的地震响应并不等于单向地震响应的简单叠加；考虑了非线性以后刚构桥墩顶部位比墩底部位形成了更为饱满的塑性铰滞回环,建议在实际工程中重视刚构桥墩顶截面的延性设计；
4、获得了水平地震波一维多点输入与二维多点输入时,针对曲线刚构桥某个地震响应的最不利输入角度公式,依据该公式可以方便的找到地震波平面一维多点输入与二维多点输入时针对曲线刚构桥某个地震响应量的最不利输入角度精确值；
5、三维多点激励下曲线刚构桥桥墩与主梁的横向弯矩通常比直线桥梁的小,而桥墩的纵向弯矩与主梁的竖向弯矩往往比直线桥的大。
With the rapid development of bridge engineering, the spans of bridges become larger and larger, and piers become higher and higher, Therefore, systems are often more flexible than ever. Which bring new challenges to seismic design of long span bridges. As a widely used project type, rigid frame bridges are also developing towards large spans and high piers.Currently, seismic design of bridges is all based on uniform excitation method,but ground motion of different pier of large-span bridges are usually not consistent because of influences of traveling wave effect, partially coherent effect and partial site effect. Therefore, study on earthquake responses of large-span bridges under multi-support excitations is of great importance.
In this paper, analysis model and principle is summarized firstly, which laid the foundation for the following calculation and analysis. Secondly, as a example, a5-span prestressed concrete rigid frame bridge is analyzed with finite element software-ANSYS using power spectrum method, in which earthquake responses of rigid frame bridge is studied in the condition that traveling wave effect, partially coherent effect and partial site effect is considered both separately and together. Thirdly, multi-dimensional and multi-support artificial seismic waves are generated based on target power spectrum model and target correlation function model, and the rigid frame bridge is analyzed with time history method using the generated artificial seismic waves. Finally, earthquake response of both curved rigid frame bridge and straight rigid frame bridge is studied comparatively. The main conclusions in this paper include the following:
1. The influence of partial site effect is obvious,adopting site soil of which characteristic doesn't vary with spatial location may make rigid frame bridge unfavorable; The influence of partially coherent effect is little; In the condition only seismic wave effect is considered, the moments on the top of piers of rigid frame bridge is usually less compared with results of uniform excitation; The influence of traveling wave effect on the top of piers is relatively large than that at the bottom; After traveling wave effect is taken account, higher modes of rigid frame bridge may be aroused.
2. In the condition that traveling wave effect, partially coherent effect and partial site effect is considered comprehensively, the earthquake responses of piers may increase or decrease while the earthquake responses of main girders usually increase compared with the case of uniform seismic excitation.
3.Multi-dimensional and multi-support seismic waves are generated, and multi-dimensional and multi-support time history is implemented after both material nonlinearity and geometric nonlinearity is taken into account, results show that earthquake responses of different direction are coupled with each other in the case of multi-dimensional and multi-support excitations, earthquake responses of rigid frame bridge don't equal to the simply superimposed results of one-dimensional; Full plastic hinge loops appear on the top of piers in the case of multi-dimensional and multi-support excitations after taking nonlinear property, so ductile design on the top of piers of rigid frame bridges should be paid attention in practical engineering.
5. The formula of the most unfavorable input angel of seismic waves of determined response variable of curved rigid frame bridge, under one-dimensional and multi-support excitations and two-dimensional and multi-support excitations, is obtained. According to the formula, exact value of input angel of the one and two-dimensional and multi-support seismic waves, against a determined response variable, can be easily obtained.
6. Under three-dimensional and multi-support excitations, transverse moments of piers and main girders of curved rigid frame bridge are usually less than that of straight rigid frame bridge while longitudinal moments of piers and vertical moments of main girders are usually more.
引文
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[3]王君杰,王前信,江近仁.大跨拱桥在空间变化地震动下的响应[J].振动工程学报,vo1.8,No2.1995：119-126
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[5]陈幼平,周宏业.斜拉桥地震反应的行波效应[J].土木工程学报,1996,29(6)：61-68
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[7]罗尧治,王荣.索弯顶结构动力特性及多维多点抗震性能研究[J].浙江大学学报江学版).2005,39(1)：394
[8]杨志,韩庆华,周全智等.多维多点激励下老山自行车馆屋盖结构的地震反应分析.天津大学学报,2007,40(11)：1277-1283
[9]张永亮,陈兴冲,夏修身,行波效应对铁路大跨连续刚构桥地震反应的影响[J],西北地震学报,2010,32(3)：268-272
[10]黄小国,胡大琳,张后举,行波效应对大跨度连续刚构桥地震反应的影响,长安大学学报,2008,28(1)：72-76
[11]屈铁军,王前信.空间相关的多点地震动合成(Ⅰ)基本公式[J].地震工程与工程振动.1998,18(1)：8-15
[12]屈铁军,王前信.空间相关的多点地震动合成(Ⅱ)合成实例[J].地震工程与工程振动.1998,18(2)：25-32
[13]杨庆山,姜海鹏.基于相位差谱的人造地震动的反应谱拟合[J].地震工程与工程振动.2002,22(1)：32-38
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