强地震作用下大跨度桥梁空间动力效应及列车运行安全研究
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摘要
本文是国家自然科学基金项目“强地震/强风作用下长大桥梁空间动力效应及行车安全控制研究”的研究成果之一。
高速铁路对解决大城市之间的交通问题以及促进经济、社会发展起到越发重要的作用。为了减少对铁路沿线对既有环境的影响,高架桥梁在高速铁路线中的比重不断增加。随着列车速度的提高,列车运营班次亦随之增加,呈现出“公交化”趋势。相对于过去,在地震多发区域列车行驶在桥梁上遭遇突发地震的概率大大提高。因此,车桥耦合动力分析考虑地震作用成为了一项重要课题。在借鉴国内外已有研究成果的基础上,针对长大桥梁特点,视地震、桥梁和车辆为一个统一的大系统,建立了多层次的地震-车-桥分析模型；并编制了相应的分析程序；研究了不同地震动输入模式、地震动空间变异因素、行车速度等对桥梁上运行列车安全性的影响。主要研究工作和成果如下：
11考虑空间变异性的多点地震动模拟
针对长大桥梁,在仅已知场地特征条件下,采用基于谱方法的无条件模拟技术产生多点地震波；若给定单点地震波,则采用基于多变量线性预测理论的条件模拟技术产生多点地震波。桥梁一般远离震源,结束时刻的速度、位移均为零值；采用一致化方法能够从地震加速度时程得到满足该要求的地震记录。
21地震动输入模式
在回顾桥梁抗震中地震激励输入的基础上,结合车桥耦合振动特点,对比分析了不同地震激励输入模式的特点、实现方法以及适用性,得到如下结论：
与桥梁抗震关注相对运动不同,地震-车-桥分析需要研究系统的绝对运动。
位移输入模式对于所有轮轨关系均能适用；而加速度输入模式仅适用于轮轨关系为线性的情况,并且需要考虑拟静力分量对车桥耦合系统的影响。
》当桥梁结构采用振型叠加法时,若采用地震位移输入模式,则必须考虑尽可能多的结构模态。
31多层次的地震-车-桥分析模型
视简支梁桥为连续体,运动由微分方程描述,而列车简化为一系列的簧上质量；从而建立了多点地震激励作用下车桥耦合简化分析模型。应用该模型可以研究地震多点激励、轨道不平顺等对车桥系统耦合振动的影响。
基于有限元法与轮轨分离模型,建立了强地震作用下高速列车通过长大桥时动力相互作用分析模型。该分析模型既考虑了长大桥梁的多点地震激励,又模拟了可能出现的车轮悬浮。
4)地震-车-桥分析的数值求解
在考虑层、联结度判据基础上,通过新增列高和判据进行节点正序排列,从而解决了有限元带宽优化RCM算法的不稳定性问题；然后,应用于地震-车-桥分析。采用Newmark-β方法结合同步迭代求解车桥动力相互作用；迭代初始时刻的车桥系统运动状态由前两步的系统运动状态应用显式积分公式预测得到。在采用极小时间步长的情况下,上述策略使得数值求解成为可能。
将桥梁、车辆分别简化为竖向振动的弹簧振子、簧上质量系统,应用谱半径理论研究不同轮轨关系、不同迭代格式下车桥动力相互作用的数值求解稳定性问题,针对可能引起迭代计算发散的原因,提出了基于虚拟质量法的改进措施。
5)地震作用下高速列车过桥时动力响应及轮轨分离规律研究
选取8节IEC3列车通过3跨钢桁拱桥遭遇地震作用为研究对象进行分析,从数值结果中得出如下结论：
地震地面运动的空间变异性对对车-桥系统的动力响应影响很大。
采用地震地面运动加速度作为地震输入由于忽略了拟静力项的影响,可能低估车-桥系统的地震响应。
非均匀的地面运动显著加大了单位时间内轮轨分离的次数和持续时间。另外,车速越快,轮轨分离的可能性越大。
High-speed railways play a growing important role in solving traffic problem between major cities and promoting further economic and social development. In high-speed railway lines, more and more elevated bridges are adopted to reduce the influence of railway lines on the existing built environment. The number of trains running on a railway line is also increasing because of high speed. As a result, the probability that an earthquake occurs when a train is running over a bridge in earthquake-prone regions is much higher than before. Therefore, dynamic interaction analysis of train-bridge system under seismic ground motion becomes an important subject. Based on the existing research results in China and abroad, multilevel frameworks with the consideration of the characteristic of large-span and long extension bridges are established to analyze dynamic interaction of train-bridge system during earthquakes from the point of view of a large system. Corresponding computer simulation programs are worked out. The influences of input pattern, spatial variation of seismic ground motion and train speed on the train running safety are investigated.
This research is sponsored by the National Natural Scientific Foundation of China (grant No.51078029). The main contents and research results are as follows:
1) Seismic ground motion simulation with full consideration of the spatial variation.
For long-extension and long-span bridges, the unconditional simulation approach based on the spectral representation is used to generate seismic acceleration time histories of bridge supports where only site characteristics is known. The conditional simulation approach on the basis of multivariate linear prediction theory is employed when the seismic acceleration time history of one support is provided. Generally, the bridge site is far from the epicenter, which means that the displacements, velocities and accelerations of the end of the record should be zero. Corresponding consistent earthquake record can be obtained from the accelerogram by using several methods.
2) Input pattern of Seismic ground motion
Based on the seismic excitation input in bridge aseismatic analysis and combined with coupled vibration characteristics of train-bridge system, the acceleration and displacement input patterns are compared in their characteristics, implementation methods and applicability. And the following conclusions can be drawn:
Dynamic interaction analysis of train-bridge system during earthquakes focuses on the absolute motion, which is different from common bridge aseismatic analysis paying more attention to the relative motion.
The displacement input pattern is applicable for all wheel-rail relations whereas the acceleration input pattern is only suited for linear case in consideration of the influence of the pseudo-static components.
More modes of bridge vibration in mode superposition method should be taken into accout for the displacement input pattern.
3) Multilevel frameworks for analyzing dynamic interaction of train-bridge system during earthquakes
A simply-supported beam bridge is taken as a continuum which motion can be expressed by the differential equation. The vehicles are simplified into a series of sprung mass. Thus, a simplified framework with the consideration of multipoint seismic excitation and rail irregularities is established.
On the basis of FE method and wheel-rail separation relationship, the framework for analyzing dynamic interaction between long-span bridges and high-speed train is presented, in which multi-support seismic excitation and the possible separation between wheels and rails are considered.
4) Numerical solution
The instability of RCM algorithm optimizing bandwidth in finite element analysis is solved by increasing the column height sum as a new criterion for node sequential arrange, on the base of considering layer and number of neighbor nodes as two old criterions. And the modified algorithm is applied in this research. The Newmark-βmethod with a simultaneous iteration approach is used to find the best solution for the nonlinear dynamic interaction, in which the initial iteration value can be acquired from known motions of the foregoing two interaction steps with the aid of the explicit integration expression. The above-mentioned schemes make the solution manageable under the condition of tiny time interval used in the analysis.
The bridge and vehicle subsystems are simplified into spring-damping, sprung mass oscillators in vertical direction, respectively. The numerical stabilities of iterative schemes in solving dynamic interaction of train-bridge system are studied for different wheel-rail relations on the basis of the spectral radius theory. The virtual mass approach is proposed to avoid potential divergence
5) Investigation of dynamic interaction of train-bridge system and possible separation between rails and wheels during earthquake
The IEC3 high-speed train with eight cars running over a 3-span steel truss-arch bridge subject to earthquakes are taken as a case study. The following conclusions can be drawn from numerical results:
The influence of spatial variation of seismic ground motion on dynamic response of coupled train-bridge system is great.
The seismic response of train-bridge system may be seriously underestimated when using the acceleration input pattern due to the ignorance of the pseudo-static item.
The separation number and duration time between rails and wheels are enlarged by non-uniform seismic ground motion. Moreover, the separation probability greatly increases with train speed.
高速铁路对解决大城市之间的交通问题以及促进经济、社会发展起到越发重要的作用。为了减少对铁路沿线对既有环境的影响,高架桥梁在高速铁路线中的比重不断增加。随着列车速度的提高,列车运营班次亦随之增加,呈现出“公交化”趋势。相对于过去,在地震多发区域列车行驶在桥梁上遭遇突发地震的概率大大提高。因此,车桥耦合动力分析考虑地震作用成为了一项重要课题。在借鉴国内外已有研究成果的基础上,针对长大桥梁特点,视地震、桥梁和车辆为一个统一的大系统,建立了多层次的地震-车-桥分析模型；并编制了相应的分析程序；研究了不同地震动输入模式、地震动空间变异因素、行车速度等对桥梁上运行列车安全性的影响。主要研究工作和成果如下：
11考虑空间变异性的多点地震动模拟
针对长大桥梁,在仅已知场地特征条件下,采用基于谱方法的无条件模拟技术产生多点地震波；若给定单点地震波,则采用基于多变量线性预测理论的条件模拟技术产生多点地震波。桥梁一般远离震源,结束时刻的速度、位移均为零值；采用一致化方法能够从地震加速度时程得到满足该要求的地震记录。
21地震动输入模式
在回顾桥梁抗震中地震激励输入的基础上,结合车桥耦合振动特点,对比分析了不同地震激励输入模式的特点、实现方法以及适用性,得到如下结论：
与桥梁抗震关注相对运动不同,地震-车-桥分析需要研究系统的绝对运动。
位移输入模式对于所有轮轨关系均能适用；而加速度输入模式仅适用于轮轨关系为线性的情况,并且需要考虑拟静力分量对车桥耦合系统的影响。
》当桥梁结构采用振型叠加法时,若采用地震位移输入模式,则必须考虑尽可能多的结构模态。
31多层次的地震-车-桥分析模型
视简支梁桥为连续体,运动由微分方程描述,而列车简化为一系列的簧上质量；从而建立了多点地震激励作用下车桥耦合简化分析模型。应用该模型可以研究地震多点激励、轨道不平顺等对车桥系统耦合振动的影响。
基于有限元法与轮轨分离模型,建立了强地震作用下高速列车通过长大桥时动力相互作用分析模型。该分析模型既考虑了长大桥梁的多点地震激励,又模拟了可能出现的车轮悬浮。
4)地震-车-桥分析的数值求解
在考虑层、联结度判据基础上,通过新增列高和判据进行节点正序排列,从而解决了有限元带宽优化RCM算法的不稳定性问题；然后,应用于地震-车-桥分析。采用Newmark-β方法结合同步迭代求解车桥动力相互作用；迭代初始时刻的车桥系统运动状态由前两步的系统运动状态应用显式积分公式预测得到。在采用极小时间步长的情况下,上述策略使得数值求解成为可能。
将桥梁、车辆分别简化为竖向振动的弹簧振子、簧上质量系统,应用谱半径理论研究不同轮轨关系、不同迭代格式下车桥动力相互作用的数值求解稳定性问题,针对可能引起迭代计算发散的原因,提出了基于虚拟质量法的改进措施。
5)地震作用下高速列车过桥时动力响应及轮轨分离规律研究
选取8节IEC3列车通过3跨钢桁拱桥遭遇地震作用为研究对象进行分析,从数值结果中得出如下结论：
地震地面运动的空间变异性对对车-桥系统的动力响应影响很大。
采用地震地面运动加速度作为地震输入由于忽略了拟静力项的影响,可能低估车-桥系统的地震响应。
非均匀的地面运动显著加大了单位时间内轮轨分离的次数和持续时间。另外,车速越快,轮轨分离的可能性越大。
High-speed railways play a growing important role in solving traffic problem between major cities and promoting further economic and social development. In high-speed railway lines, more and more elevated bridges are adopted to reduce the influence of railway lines on the existing built environment. The number of trains running on a railway line is also increasing because of high speed. As a result, the probability that an earthquake occurs when a train is running over a bridge in earthquake-prone regions is much higher than before. Therefore, dynamic interaction analysis of train-bridge system under seismic ground motion becomes an important subject. Based on the existing research results in China and abroad, multilevel frameworks with the consideration of the characteristic of large-span and long extension bridges are established to analyze dynamic interaction of train-bridge system during earthquakes from the point of view of a large system. Corresponding computer simulation programs are worked out. The influences of input pattern, spatial variation of seismic ground motion and train speed on the train running safety are investigated.
This research is sponsored by the National Natural Scientific Foundation of China (grant No.51078029). The main contents and research results are as follows:
1) Seismic ground motion simulation with full consideration of the spatial variation.
For long-extension and long-span bridges, the unconditional simulation approach based on the spectral representation is used to generate seismic acceleration time histories of bridge supports where only site characteristics is known. The conditional simulation approach on the basis of multivariate linear prediction theory is employed when the seismic acceleration time history of one support is provided. Generally, the bridge site is far from the epicenter, which means that the displacements, velocities and accelerations of the end of the record should be zero. Corresponding consistent earthquake record can be obtained from the accelerogram by using several methods.
2) Input pattern of Seismic ground motion
Based on the seismic excitation input in bridge aseismatic analysis and combined with coupled vibration characteristics of train-bridge system, the acceleration and displacement input patterns are compared in their characteristics, implementation methods and applicability. And the following conclusions can be drawn:
Dynamic interaction analysis of train-bridge system during earthquakes focuses on the absolute motion, which is different from common bridge aseismatic analysis paying more attention to the relative motion.
The displacement input pattern is applicable for all wheel-rail relations whereas the acceleration input pattern is only suited for linear case in consideration of the influence of the pseudo-static components.
More modes of bridge vibration in mode superposition method should be taken into accout for the displacement input pattern.
3) Multilevel frameworks for analyzing dynamic interaction of train-bridge system during earthquakes
A simply-supported beam bridge is taken as a continuum which motion can be expressed by the differential equation. The vehicles are simplified into a series of sprung mass. Thus, a simplified framework with the consideration of multipoint seismic excitation and rail irregularities is established.
On the basis of FE method and wheel-rail separation relationship, the framework for analyzing dynamic interaction between long-span bridges and high-speed train is presented, in which multi-support seismic excitation and the possible separation between wheels and rails are considered.
4) Numerical solution
The instability of RCM algorithm optimizing bandwidth in finite element analysis is solved by increasing the column height sum as a new criterion for node sequential arrange, on the base of considering layer and number of neighbor nodes as two old criterions. And the modified algorithm is applied in this research. The Newmark-βmethod with a simultaneous iteration approach is used to find the best solution for the nonlinear dynamic interaction, in which the initial iteration value can be acquired from known motions of the foregoing two interaction steps with the aid of the explicit integration expression. The above-mentioned schemes make the solution manageable under the condition of tiny time interval used in the analysis.
The bridge and vehicle subsystems are simplified into spring-damping, sprung mass oscillators in vertical direction, respectively. The numerical stabilities of iterative schemes in solving dynamic interaction of train-bridge system are studied for different wheel-rail relations on the basis of the spectral radius theory. The virtual mass approach is proposed to avoid potential divergence
5) Investigation of dynamic interaction of train-bridge system and possible separation between rails and wheels during earthquake
The IEC3 high-speed train with eight cars running over a 3-span steel truss-arch bridge subject to earthquakes are taken as a case study. The following conclusions can be drawn from numerical results:
The influence of spatial variation of seismic ground motion on dynamic response of coupled train-bridge system is great.
The seismic response of train-bridge system may be seriously underestimated when using the acceleration input pattern due to the ignorance of the pseudo-static item.
The separation number and duration time between rails and wheels are enlarged by non-uniform seismic ground motion. Moreover, the separation probability greatly increases with train speed.
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