随机地震动场多点激励下大跨度桥梁地震反应分析方法

地震输入问题一直是工程结构抗震研究关注的焦点。对大跨度桥梁结构，考虑随机地震动场的多点激励而进行地震反应分析较为合理。本文结合大跨度桥梁抗震设计，系统地介绍了随机地震动场的模型以及随机地震动场多点激励下大跨度桥梁地震反应分析的方法。     

Random vibration analysis of long-span structures subjected to spatially varying ground motions

On the basis of the pseudo-excitation method (PEM), a random vibration methodology is formulated for the seismic analysis of multi-supported structures subjected to spatially varying ground motions. The ground motion spatial variability consists of the wave passage, incoherence and site–response effects. Advantages of this method are that less computation effort is required and that the cross-correlations both between normal modes and between excitations are automatically included. Random seismic responses of a realistic long-span bridge due to the wave passage, incoherence and site–response effects are extensively investigated. It is shown that all these effects have significant influence on the seismic response of the structure.     

大跨斜拉桥的近断层地震响应及减震控制

近断层地震长周期成分丰富,存在速度大脉冲效应;而大跨度斜拉桥一般采用半漂浮体系或漂浮体系,所以固有频率较低。为了研究大跨度斜拉桥在近断层地震作用下的反应规律及减震措施,利用ANSYS软件分析了某半漂浮体系的大跨斜拉桥在近断层地震作用下的时程响应,并对其减震控制方法进行了探讨。研究表明,大跨度斜拉桥的近断层地震响应随着PGV/PGA值的增大而增大,且增大幅度较大,近场脉冲效应较为显著;对于近断层地震作用,不建议采用塔梁弹性连接装置作为主梁纵漂的减震措施,而采用参数适宜的铅挤压阻尼器和粘滞阻尼器则均能获得很好的减震效果;由于大跨度斜拉桥的近断层地震反应较大,应提高其支座的设计允许位移。     

Local site effects on a high-pier railway bridge under tridirectional spatial excitations: Nonstationary stochastic analysis

This paper presents a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute-response-oriented scheme of PEM in nonstationary stochastic analysis of structure under tridirectional spatial seismic motions, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions, is proposed to resolve the drawbacks of conventional indirect approach. To apply the proposed theoretical approach readily in stochastic seismic analysis of complex and significant structures, this scheme is implemented and verified in a general finite element platform, and is then applied to a high-pier railway bridge under spatially varying ground motions considering the local site effect and the effect of ground motion nonstationarity. Conclusions are drawn and can be applied in the actual seismic design and analysis of high-pier railway bridges under tridirectional nonstationary multiple excitations.     

大跨度拱桥地震动输入模式研究

地震动输入是大跨度桥梁地震反应分析的重要一环。从明确大跨度拱桥的临界跨度入手,探讨了大跨度拱桥地震动输入模式中的行波效应、三向输入及其地震动选取问题。基于某大跨度钢管混凝土拱桥,建立了有限元分析模型,考查了行波效应及三向地震动输入对拱关键截面内力、减隔震支座位移及粘滞阻尼器冲程的影响。结果表明:给出的大跨度拱桥临界跨度确定方法合理,行波效应对拱顶轴力有重要影响,不考虑三向地震动同时作用会明显低估大跨度拱桥的地震反应。确定大跨度拱桥地震动输入模式时需考虑行波效应与三向地震动同时输入。     

行波效应对大跨度空间结构随机地震响应的影响

深入研究了行波效应对大跨度空间结构随机地震响应的影响,进一步完善了大跨度空间结构随机地震响应分析理论。推导了双支座、单自由度体系地震响应功率谱密度函数的解析表达式,研究了不同频率体系的响应峰值随地面视波速的变化规律,分析了多支撑点、多自由度体系的地震响应功率谱矩阵的特点,发现多自由度体系地震响应随地面视波速的变化规律与单自由度体系相似。数值模拟了某体育馆网壳结构在不同地面视波速情况下的随机地震响应,结果表明,考虑地震动行波效应后,结构地震响应随地面视波速的变化而显著变化,当视波速较低时其变化规律很复杂;且支撑点附近、受拟静力位移影响较大的部分杆件的地震响应明显增大,远离支撑点处、受拟静力位移影响较小的部分杆件的地震响应稍有减小。由此得出结论,对于大跨度空间结构的随机地震响应分析,必须考虑地震动的行波效应,尤其当受拟静力位移影响较大的部分杆件对结构抗震设计起控制作用时;且应对可能出现的地面视波速进行全面分析,作为结构抗震设计依据。     

随机地震动场多点激励下大跨度连续刚构桥的地震反应分析

本文基于随机地震动场的功率谱模型和多点地震激励，建立了大跨度桥梁在随机地震动场多点激励的地震反应分析方法，并数值模拟了某四跨预应力混凝土连续刚构桥的地震反应，考虑了行波效应、部分相干效应和局部场地效应等因素的影响，并与确定性地震一致激励下的计算结果进行了比较。对工程建设具有参考意义。     

行波效应对铁路大跨连续刚构桥地震反应的影响

介绍了模拟地震地面运动的大质量法,推导了大跨度桥梁考虑行波效应的分析模型及解析方法。以大准黄河特大桥为工程背景,选取墩身刚度、地震波视波波速及不同的地震记录为主要参数,进行了考虑行波效应下铁路大跨连续刚构桥的时程反应分析,并与一致激励下的结果进行了对比。系统总结了此类桥梁在行波效应激励下的地震反应特点。本文分析方法和结果对同类桥梁的设计与研究具有一定的参考价值。     

地震作用下大跨度悬索桥几何非线性影响分析

大跨度悬索桥几何非线性主要来自3个方面：缆索垂度效应、梁柱效应、大位移引起的几何形状变化。鉴于地震波高频成分振幅大,低频成分振幅小的特点,很难对地震作用下大跨度悬索桥几何非线性的影响做出定性判断。目前大跨度桥梁的几何非线性研究主要集中在斜拉桥,且不同的学者得出了不同的结论。本文以逐级加大振幅的Ⅳ类场地多条地震波为激励,通过对称与非对称的2座典型大跨度悬索桥的几何非线性影响对比分析,探讨了几何非线性对大跨度悬索桥重要地震响应量的影响程度及其原因,并提出了相应的抗震设计参考建议。     

基于小波变换的长周期桥梁选波方法研究

时程分析输入地震波的选取对长周期大跨度桥梁影响显著。本文基于规范目标谱,以MATLAB为依托,通过选取最优小波基并利用小波系数迭代法实现频域调整,使地震波反应谱不断逼近给定目标谱,最后结合相对误差和长周期拟合参数两个指标进行综合评价,选取适用于长周期大跨度桥梁的时程分析地震波,提出长周期桥梁全过程批量选波方法。将该方法应用于奉节长江大桥,与基于时域调整方法的Seismo Match选波软件对比选波效果,并将选波结果应用于背景桥梁的时程分析。结果表明,利用本文选波方法所得结构关键截面响应与软件选波所得响应在横桥向和竖桥向存在一定差异。本文方法可为长周期大跨度桥梁时程分析选波提供参考。     

Seismic spatial effects on long-span bridge response in nonstationary inhomogeneous random fields

The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-θ schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.     

行波效应对桥梁不同振动控制方法减震效果的影响分析

给出了地震行波输入下大跨度桥梁的主动、半主动和被动控制分析方法,并对1座4跨连续刚构桥梁进行了行波输入下地震反应计算,分析了8种振动控制情况下纵桥向和横桥向地震反应的减震效果。结果表明,行波效应会明显降低该连续刚构桥梁8种振动控制方法的纵桥向地震反应减震效果,最大开关控制算法对纵桥向的减震效果相对最好;最大阻尼力被动控制和最大开关控制算法对横桥向的减震效果相对最好,采用该2种控制方法时行波效应对横桥向总体减震效果影响不大。     

Effects of ground motion spatial variability on the response of cable-stayed bridges

In order to extend our knowledge of the performance of long-span bridges under earthquake loading the effects of spatial variability of ground motion on the structural response of cable-stayed bridges are studied; the result can be useful to practising bridge engineers. The multiple-support excitation analysis is described, and two three-dimensional models representing the modern and future trends in cable-stayed bridge design are utilized to shed some light on salient features of the seismic response characteristics of these modern bridges. In addition, models of steel- and concrete-design alternates of an existing bridge are considered. Differential ground motion records (obtained from dense instrument arrays) are used as synchronous and non-synchronous support motions; in addition, non-dispersive seismic waves travelling along the bridge are considered. The bridge response to non-uniform ground motion is compared to its response to uniform input. An overview of the unique dynamic characteristics of these cable-supported bridges is also presented. Finally, the study, which was used in the seismic design of several existing cable-stayed bridges in U.S. and Canada, indicates that the response quantities may increase substantially from the non-uniform input ground motion, especially for more rigid bridges and for bridges having different dynamic properties of the local soils at the supporting points, but the degree of increase depends upon the specific problem, in particular upon the aspects of span length, rigidity and structural redundancy. Thus, the response to non-uniform input ground motion should be examined for these bridges.     

基于响应面法的连续刚构地震可靠度分析

地震可靠度是桥梁抗震研究中的重要问题。基于随机分析的响应面理论和规范反应谱法,提出了一种分析具有随机结构参数的桥梁地震可靠度的方法,研究了结构的破坏准则及其极限状态方程,计算了高墩大跨连续刚构桥在地震激励下设计基准期内的动力可靠度。分析时考虑了结构参数和场地土的随机性,分别计算了连续刚构在多遇地震、设防地震和罕遇地震作用下的失效概率,得到了结构在设计基准期内,"三水准设防标准"条件下的地震可靠度。结果表明,该桥设计满足抗震规范要求。     

抗震约束下大跨度空间钢结构设计中支吊架的合理选取

大跨度空间钢结构设计中,合理选取支吊架对建筑的抗震性有着重要的影响,当前设计过程中未考虑支吊架组合后的抗震性能。综合选取适用于大跨度空间钢结构的支吊架结构,使其具有更优的抗震性能。首先给出目前应用较多的三种结构,其次给出一定的抗震约束条件,如承载力、应力应变与拉伸变形等。在条件约束下,给出具有抗震能力的支吊架选取模型并给出具体计算示例,选取和组合具有一定抗震能力的大跨度空间钢结构支吊架。结果表明,相较于传统的随机支吊架选取方式,具有抗震能力的模型下支吊架核心钢结构抗震水平明显提升。     

A parametric study of the required seating length for bridge decks during earthquake

During the recent major earthquakes, some bridges suffered severe damage due to the pull-off-and-drop collapse of their decks. This is due to the large differential movements of the adjacent spans of bridges during strong shaking compared to the seating lengths provided. The differential movements are primarily due to the different vibration properties of adjacent spans and non-uniform ground excitations at the bridge supports. This paper analyses the effects of various bridge and ground motion parameters on the required seating lengths for bridge decks to prevent the pull-off-and-drop collapse. The random vibration method is used in the analysis. A two-span bridge model with different span lengths and vibration frequencies and subjected to various spatially varying ground excitations is analysed. Non-uniform spatial ground motions are modelled by the filtered Tajimi–Kanai power spectral density function and an empirical coherency function. Ground motions with different intensities, different cross-correlations and different site conditions are considered in the study. The required seating lengths for bridge decks are calculated. Numerical results are presented and discussed with respect to different bridge vibration and ground motion properties. © 1998 John Wiley & Sons, Ltd.     

地震动空间效应对大跨度桥梁非线性地震响应的影响

由于大跨度桥梁的桥墩间距离较大,其地震响应分析应考虑地震动输入的空间效应。本文建立了多点激励下大跨度桥梁地震响应分析方法,采用损伤塑性本构模型模拟混凝土材料特性,考虑地震动空间效应对大跨度连续刚构桥进行非线性地震响应分析,从而分析地震动空间效应对大跨度桥梁地震响应的影响。研究表明:考虑行波激励或多点激励时桥梁地震响应较一致激励而言有所差异,考虑地震动空间效应时可能会夸大或减小桥梁结构的动力响应;多点激励时桥梁地震响应会随视波速的改变而变化。由此得出结论,对于大跨度桥梁地震响应分析应合理的考虑地震动空间效应。     

Non-linear earthquake-response analysis of long-span cable-stayed bridges: Applications

The dynamic non-linear behaviour of three-dimensional long-span cable-stayed bridges under seismic loadings is studied. The cases of multiple-support as well as uniform seismic excitations of these long and flexible structures are considered. Different sources of non-linearity for such bridges are included in the analysis, as outlined in the companion paper. In this accompanying analysis a tangent stiffness iterative procedure is utilized to estimate the non-linear seismic response. Numerical examples are presented in which a comparison between a linear earthquake-response analysis (based on the utilization of the tangent stiffness matrix of the bridge at the dead-load deformed state which is obtained from the geometry of the bridge under gravity load conditions) and a non-linear earthquake response analysis using the step-by-integration procedure is made. In these examples two three-dimensional bridge models representing recent and future trends in cable-stayed bridge design are utilized. The study sheds some light on the salient features of the seismic analysis and design of these long contemporary bridges. In addition, parameters affecting the seismic response of these bridges are discussed: other factors considered are non-linearity, uniformity and spatial variation of ground motion inputs and structural configuration.     

空间网格结构多维多点随机地震响应分析的高效算法

将林家浩教授提出的“虚拟激励法”进一步推广应用于空间网格结构多维多点非平稳随机地震响应分析,推导了多维虚拟激励随机振动分析方法的理论公式,给出了峰值响应估计方法,并讨论了多维地震动的随机模型及参数选取,通过编制的专用计算机程序分析了网壳结构的随机地震响应。本方法自动包含了参振振型间及各输人地震分量间的相关项,计算精确、快速,非常适合分析频率密集型空间网格结构的随机地震响应,是一种高效的随机振动分析算法。     

Seismic response of a cable‐stayed bridge deck under multi‐component non‐stationary random ground motion

A Markov method of analysis is presented for obtaining the seismic response of cable‐stayed bridges to non‐stationary random ground motion. A uniformly modulated non‐stationary model of the random ground motion is assumed which is specified by the evolutionary r.m.s. ground acceleration. Both vertical and horizontal components of the motion are considered to act simultaneously at the bridge supports. The analysis duly takes into account the angle of incidence of the earthquake, the spatial correlation of ground motion and the quasi‐static excitation. A cable‐stayed bridge is analysed under a set of parametric variations in order to study the non‐stationary response of the bridge. The results of the numerical study indicate that (i) frequency domain spectral analysis with peak r.m.s. acceleration as input could provide more r.m.s. response than the peak r.m.s. response obtained by the non‐stationary analysis; (ii) the longitudinal component of the ground motion significantly influences the vertical vibration of the bridge; and (iii) the angle of incidence of the earthquake has considerable influence on the deck response. Copyright © 2003 John Wiley & Sons, Ltd.