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.     

高架桥地震反应半主动控制分析

本文探讨了高架桥结构地震反应LQR(Linear Quadratic Regulator)半主动控制算法以及考虑刚度退化的桥墩非线性计算模型，并利用Matlab语言编制的程序对其进行了数值仿真计算。结果表明，将隔震技术与利用MR阻尼器的半主动控制技术相结合，能够有效地减小高架桥的地震反应；MR阻尼器的设置位置以及结构的参数对控制效果有较大影响。考虑桥墩非线性影响将能得到更为接近实际的计算结果。     

Modelling of shear keys in bridge structures under seismic loads

Shear keys are used in the bridge abutments and piers to provide transverse restraints for bridge superstructures. Owing to the relatively small dimensions compared to the main bridge components (girders, piers, abutments, piles), shear keys are normally regarded as secondary component of a bridge structure, and their influences on bridge seismic responses are normally neglected. In reality, shear keys are designed to restrain the lateral displacements of bridge girders, which will affect the transverse response of the bridge deck, thus influence the overall structural responses. To study the influences of shear keys on bridge responses to seismic ground excitations, this paper performs numerical simulations of the seismic responses of a two-span simply-supported bridge model without or with shear keys in the abutments and the central pier. A detailed 3D finite element (FE) model is developed by using the explicit FE code LS-DYNA. The bridge components including bridge girders, piers, abutments, bearings, shear keys and reinforcement bars are included in the model. The non-linear material behaviour including the strain rate effects of concrete and steel rebar are considered. The seismic responses of bridge structures without and with shear keys subjected to bi-axial spatially varying horizontal ground motions are calculated and compared. The failure mode and damage mechanism of shear keys are discussed in detail. Numerical results show that shear keys restrain transverse movements of bridge decks, which influence the torsional–lateral responses of the decks under bi-axial spatially varying ground excitations; neglecting shear keys in bridge response analysis may lead to inaccurate predictions of seismic responses of bridge structures.     

Dynamic behaviour of a cable-stayed bridge

The dynamic response of a cable-stayed bridge to seismic, wind and simulated traffic loads is discussed. The analysis procedure which is used considers non-linear behaviour of the cables, caused by the variation in sag with tensile force, and non-linear behaviour of the bending members, caused by the interaction of axial and bending deformations. It is concluded that the non-linearity of the structure must be considered in determining the stiffness of the structure in the dead load deformed state. A linear dynamic analysis, however, starting from the dead load deformed state will give results within normally required design accuracy.     

基于黏滞液体阻尼器的铁路钢桁梁桥减震研究

以某高墩大跨度铁路简支钢桁梁桥为实际工程背景,研究了黏滞液体阻尼器对结构纵向抗震性能的影响.采用非线性时程分析方法,对黏滞液体阻尼器的相关参数及布置位置进行了优化分析.分析结果表明:合理选择黏滞液体阻尼器的布置位置、个数及阻尼参数,高墩大跨铁路简支钢桁梁桥具有明显的减震效果.     

大跨铁路钢桁连续梁桥减隔震方案比较研究

为研究适用于大跨铁路钢桁连续梁桥的减隔震方案及合理优化参数,以一座全长504 m的三跨铁路钢桁连续梁特大桥为工程背景,使用非线性结构分析软件SAP2000建立有限元模型,采用快速非线性分析方法分析对比摩擦摆、阻尼器、速度锁定器等减隔震方案在各种装置参数下的减震效率。研究表明:由于大跨铁路钢桁连续梁桥墩身自振导致的地震力较大,摩擦摆方案内力减震效率一般,同时墩底内力对滑动面半径变化并不敏感,在选取滑动半径时应更多地考虑行车平顺性和梁端位移值的限制。速度锁定器会极大地增加此类桥梁地震输入能量,不适用于此类桥型。阻尼器方案对活动墩内力减震效果明显,但不能有效降低固定墩内力。摩擦摆支座附加阻尼器组合减震方案能有效控制此类桥梁的内力和位移响应。研究结论可为大跨度钢桁连续梁桥减隔震设计提供参考。     

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。     

Optimization of the stochastic response of a bridge isolation system with hysteretic dampers

A bridge structure with a seismic isolation system consisting of rubber bearings and hysteretic dissipators is considered. The non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise or a filtered white noise ground acceleration is determined by using the method of equivalent linearization. The sensitivity of the stochastic response to principal pàrameters for the bridge is investigated. Results of optimum design of the isolation system are presented.     

Effect of torsional stiffness of prestressed concrete box girders and uplift of abutment bearings on seismic performance of bridges

Uplift of certain abutment bearings during earthquake may be utilized as a safety mechanism for the protection of the bridge against excessive stress. For this reason design codes such as Eurocode 8 permit the uplift of such bearings under certain conditions. Uplift of an abutment bearing occurs when the torque at the deck end exceeds a critical value. Therefore the torsional stiffness of the deck, before or after concrete cracking, is an important factor. In this work realistic values for the cracked torsional stiffness of the bridge deck are estimated from a parametric study of typical thin-walled prestressed box girders, based on non-linear analysis of softened space truss models proposed in the literature. Moreover the interaction between bearing uplift and pier flexural response is investigated and recommendations for the seismic design of bridges are proposed, taking into account the possibility of uplift of abutment bearings before or after yielding of the piers.     

SV波入射下地形条件对大跨刚构桥地震响应的影响

计算了SV波在3种角度入射下两座山峰及其间自由场地的时程响应, 并以此作为两座山峰之间大跨桥的桥台及桥墩基础处的多点地震输入.这种地震输入考虑了行波传播效应和地形效应的综合影响. 然后基于多点激励下桥梁地震响应分析方法, 计算了地形条件下总长440 m的高墩连续刚构桥的墩顶位移及墩底内力, 并与忽略地形条件仅考虑行波效应时结构的响应进行了对比分析. 该结果可为建于复杂地形条件下结构的抗震设计提供参考.      

基于性态的液化场地多跨桥梁桩基地震响应分析

针对液化场地多跨简支桩基桥梁体系,考虑地震随机性的不确定性和认知的不确定性,结合地震危险性曲线自身的不确定性,推导性态指标危险性曲线的解析表达式.利用地震动强度指标PGV/PGA,输入不同幅值的地震动,进行液化场地多跨桩基桥梁体系地震反应有限元分析.基于有限元数值分析结果,选取地震过程中关键位置位移和弯矩的最大值作为性...     

Dynamic interaction of bridge–train system under non‐uniform seismic ground motion

The probability that an earthquake occurs when a train is running over a bridge in earthquake‐prone regions is much higher than before, for high‐speed railway lines are rapidly developed to connect major cities worldwide. This paper presents a finite element method‐based framework for dynamic analysis of coupled bridge–train systems under non‐uniform seismic ground motion, in which rail–wheel interactions and possible separations between wheels and rails are taken into consideration. The governing equations of motion of the coupled bridge–train system are established in an absolute coordinate system. Without considering the decomposition of seismic responses into pseudo‐static and inertia‐dynamic components, the equations of motion of the coupled system are formed in terms of displacement seismic ground motions. The mode superposition method is applied to the bridge structure to make the problem manageable while the Newmark‐β method with an iterative computation scheme is used to find the best solution for the problem concerned. Eight high‐speed trains running over a multi‐span steel truss‐arch bridge subject to earthquakes are taken as a case study. The results from the case study demonstrate that the spatial variation of seismic ground motion affects dynamic responses of the bridge–train system. The ignorance of pseudo‐static component when using acceleration seismic ground motions as input may underestimate seismic responses of the bridge–train system. The probability of separation between wheels and rails becomes higher with increasing train speed. Copyright © 2011 John Wiley & Sons, Ltd.     

大跨度斜拉桥地震响应非线性时程分析

以有限元分析理论为基础,结合某大跨度斜拉桥工程实例,利用ANSYS软件建立有限元模型,通过修正后的El Centro波分别考虑横向、竖向及纵向输入,采用时程分析方法对其进行地震反应分析.计算分析表明:考虑几何非线性后,结构的内力和位移响应明显增大,且对主梁和索塔内力与位移的影响程度及规律也不尽相同,须区别对待分析.同时表明该桥抗震性能良好,地震荷载不控制设计.由此得出结论,对于斜拉桥这类柔性体系, 不可忽视结构几何非线性的影响.     

多维地震输入下曲线匝道桥梁伸缩缝碰撞响应

针对曲线匝道桥梁伸缩缝地震碰撞破坏现象,依托某市多层互通式立交体系中一座独立、单支、多联、曲线、箱梁匝道桥,用Kelvin接触单元模拟了伸缩缝处地震和碰撞效应,建立了全桥空间动力分析模型。利用非线性时程分析法,分别输入单维(X方向、Y方向)和多维共8种地震动工况,分析了曲线匝道桥梁伸缩缝的地震碰撞响应差异。结果表明:曲线匝道桥梁由于曲率的影响,不同方向地震动响应存在耦合效应,其伸缩缝碰撞响应的最不利值应考虑多维地震输入工况,并用碰撞力和碰撞位移双指标控制伸缩缝的地震碰撞响应。     

5跨连续中承式钢管混凝土拱桥抗震性能分析

钢管混凝土拱桥由于桥型优美在城市桥梁中得到广泛应用,对某正在设计的5跨连续巾承式钢管混凝土拱桥进行了动力特性和抗震性能分析,根据该桥的结构特点,建立了’该桥的空间有限元分析模型,计算桥梁的自振特性,基于反应谱方法计算了该桥在横向、纵向水平地震反应,计算结果表明：该桥拱肋的面外刚度相对较小,在桥梁振动中首先出现拱肋的面外振动;桥梁的竖向振动表现为拱肋与桥面的整体竖向振动,其基频明显比拱肋面外振动大;主拱肋的轴力由横桥向地震动控制,其他内力由纵桥向地震动控制;地震作用对弯矩的影响较大,故主拱的内力计算应考虑地震力的影响;在设计计算中除常规关键点应作为控制点外,内外拱连接处也应作为控制点。计算结果已为该桥的抗震设计提供了参考。     

城市轨道桥梁桩基抗震简化模型的比较研究

以郑州城郊铁路工程中独柱高架车站为例,将土体化为一系列弹簧,描述土体的变形性质。通过比较《城市轨道交通结构抗震设计规范》中的非线性土弹簧、《铁路桥涵地基和基础设计规范》中的m系数法弹簧及Mindlin解弹簧进行建模计算得到的车站结构的地震响应,由结果可知结构地震响应对承台处弹簧刚度最为敏感。另外,将分布弹簧模型等代为六弹簧模型进行地震反应计算,结果表明桩体质量的影响与承台质量相比很小。     

Seismic fragility assessment of integral precast multi-span bridges in areas of moderate seismicity

In lack of seismic provisions in the pre-Eurocode ages, most of the existing Hungarian bridges were not designed for seismic actions, therefore their seismic performance is questionable. The most commonly used structural type in highway construction is the integral precast multi-girder bridge. These bridges are typically constructed as continuous multi-support systems with monolithic joints at each support, thus their behavior may be significantly different from those applying simply supported beams and conventional bearings. A parametric fragility analysis of a wide range of different layouts is carried out using detailed and advanced non-linear numerical models. The results indicate that the abutment joints are highly vulnerable and piers are also critical for longer bridges. The study implies that without seismic design, integral precast multi-girder bridges are highly susceptible to pier shear failure, the probability of collapse is relatively high. The results also provide a solid basis for retrofit planning as well as for development of design concepts of newly built structures in moderate seismic zones.     

Analysis on influence of seismic travelling wave effect on semi-active control for long-span rigid-continuous bridge

Introduction The methods of enhancing ability of bridge to resist earthquake disaster can be divided into two aspects. One is enhancing the resisting earthquake ability from the designing ways; the other is adding control devices on the existing structures to effectively control the seismic responses of bridge from the vibration control ways. The great progress has been made in structure control technique in the last years. It has the advantages of security, validity, economical and wide appli…     

行波效应对大跨刚构连续桥梁半主动控制影响分析

给出了地震动行波输入下大跨刚构连续桥梁的半主动控制分析方法,在桥梁支座部位设置磁流变阻尼器,对一座五跨刚构连续桥梁进行了不同视波速行波输入下的半主动控制计算分析. 结果表明,行波效应对该大跨刚构连续桥梁的无控制地震反应、半主动控制地震反应和减震效果均有显著影响,对主梁和桥墩均会在较低视波速地震行波输入时表现出不利影响,并且使半主动控制减震效果明显降低. 因此,在确定半主动控制系统的参数时应考虑地震行波效应的影响以确保控震效果.      

高烈度区大跨刚构-连续梁桥地震响应分析

为研究大跨刚构-连续梁桥在高烈度地区的地震响应,选取羊记沟左线大桥为工程背景,利用Midas软件建立多个有限元模型,考虑纵、横桥向的水平地震波输入,比较反应谱与时程分析结果,获得结构动力响应特点,为大跨刚构-连续梁桥的抗震设计提供参考依据。结果表明:刚构-连续体系仅单墩刚构时不宜采用反应谱分析,高烈度地区桥梁进行地震响应时程分析时,选用与场地适应的地震波的同时,应考虑采用本地地震参数转化人工波作为地震激励源。桥墩不等高时,可通过改变墩截面形状及其与主梁连接方式调节内力分布,避免矮墩刚度大导致的内力集中。