Finite element model updating for structures with parametric constraints

This paper presents a finite element (FE) model updating procedure applied to complex structures using an eigenvalue sensitivity‐based updating approach. The objective of the model updating is to reduce the difference between the calculated and the measured frequencies. The method is based on the first‐order Taylor‐series expansion of the eigenvalues with respect to some structural parameters selected to be adjusted. These parameters are assumed to be bounded by some prescribed regions which are determined according to the degrees of uncertainty that exist in the parameters. The changes of these parameters are found iteratively by solving a constrained optimization problem. The improvement of the current study is in the use of an objective function that is the sum of a weighted frequency error norm and a weighted perturbation norm of the parameters. Two weighting matrices are introduced to provide flexibility for individual tuning of frequency errors and parameters' perturbations. The proposed method is applied to a 1/150 scaled suspension bridge model. Using 11 measured frequencies as reference, the FE model is updated by adjusting ten selected structural parameters. The final updated FE model for the suspension bridge model is able to produce natural frequencies in close agreement with the measured ones. Copyright © 2000 John Wiley & Sons, Ltd.     

结构参数对高低墩刚构连续梁桥体系地震响应的影响

地震作用下,相邻主梁间的碰撞会改变桥台-引桥-刚构连续梁桥结构体系的动力响应。为了探究主桥结构形式、墩高、引桥跨数和伸缩缝间距等结构参数对伸缩缝处碰撞效应和桥梁结构地震响应的影响,以某实际桥梁为背景,考虑碰撞能量耗散、桩土相互作用、桥台与台后填土相互作用以及支座和桥墩的非线性行为,采用CSIBridge建立桥台-引桥-刚构连续梁桥结构体系的有限元模型进行碰撞弹塑性动力分析。研究结果表明：不同主桥结构形式的主桥墩受力区别较大,相邻主桥墩高差较大时,选择连续梁桥结构体系更加合理。墩高增加使主引桥间动力差异增大,碰撞效应更加显著,仅对刚构墩受力影响较大。引桥跨数增多和伸缩缝间距增大分别使伸缩缝处碰撞效应增大和减小,碰撞抑制作用的增强和减弱也使得刚构墩内力和变形分别减小和增大,但对于其他桥墩基本无影响。     

伸缩缝刚度对大跨度悬索桥动力特性的影响

伸缩缝作为大跨度桥梁与引桥之间的重要连接构件,其抗推刚度及可能存在的变异性对主桥及引桥动力特性的影响不可忽略。本文建立了大跨度悬索桥及引桥的有限元模型,采用弹簧单元模拟加劲梁与引桥箱梁之间的伸缩缝,分析伸缩缝刚度对悬索桥及引桥自振特性及其地震响应的影响规律。分析结果表明:伸缩缝刚度对加劲梁的横弯振型、竖弯与纵飘耦合振型的频率有明显的影响;伸缩缝刚度的变化会导致加劲梁与引桥的振型相互耦合,同时这些振型的频率发生相应的突变,当伸缩缝刚度较大时,加劲梁两个竖弯与纵飘的耦合振型解耦成为独立的竖弯和纵飘振型;当引桥与悬索桥加劲梁的纵飘振型发生耦合时,在纵向和竖向地震作用下的悬索桥及引桥的地震响应达到最小。伸缩缝刚度对悬索桥动力特性影响的分析可为悬索桥的模态参数确认、损伤识别、抗震性能分析提供有价值的借鉴。     

曲线桥地震响应分析

曲线桥是现代交通中的一种重要桥型。与直线桥相比,曲线桥的自由振动与地震响应有着其自身的特点。文中运用有限元法,对曲线桥与直线桥的自振特性与地震响应作了对比分析。分析结果表明,曲线桥的以扭转为主的自振频率比直线桥高。在地震作用下,曲线桥上部结构的内力与直线桥相差不大;曲线桥竖向支座反力比直线桥小;曲线桥水平支座剪力比直线桥大。因此,在对曲线桥进行抗震设计时,上部结构可按直线桥进行设计,但应该准确计算其水平支座反力,并采取适当的支座抗剪措施。     

Dynamic characterization of a long span bridge: A finite element based approach

Aging bridges coupled with increasing traffic loads are producing a severe toll on the nation's infrastructure. This has made it necessary to take a closer look at the health of existing bridges and develop automated damage identification methods if possible. Recent works in the field of structural dynamics have shown that damage detection techniques utilizing parameters like mode shapes, modal frequencies and damping ratios can be used to identify damage in structural systems. It is, however, important to be able to establish a baseline model for the structure first, and then a model updating technique can be utilized to evaluate the condition of the structure from time to time. It is with this goal in mind that the authors have decided to establish the process for obtaining a baseline model for a long span bridge. Based on the actual design drawings of a bridge, finite element (FE) models of the bridge in question are developed using SDRC-IDEAS. Three models of the bridge are simulated using Normal Mode Dynamics solver in SDRC-IDEAS to obtain the modal parameters of interest, in this case the modal frequencies and the mode shapes. A modal assurance criteria (MAC) is utilized to compare the different simulated mode shapes and, finally, the modal frequencies that have been obtained from the FE analysis are compared to frequencies that have been obtained from some preliminary field tests.     

A Bayesian methodology to update the probabilistic seismic hazard assessment

This paper presents a Bayesian methodology for updating the seismic hazard curves. The methodology is based on the comparison of predictive exceedance rates of a fixed acceleration level (given by the seismic hazard curves) and the observed exceedance rates in some selected sites. The application of the methodology needs, firstly, the definition of a prior probabilistic seismic hazard assessment based in a logic tree. Each main branch corresponds to a probabilistic model of calculus of seismic hazard. The method considers that, initially (or a priori), the weights of all branches of the logic tree are equivalent. Secondly, the method needs to compile the observations in the region. They are introduced in a database containing the recorded acceleration data (during the instrumental period). Nevertheless, the instrumental period in stable zones (as France) shows only very low acceleration levels recorded during a short observation period. Then, a method to enlarge the REX (number of observations) is presented taking into account the historical data and defining “synthetic” accelerations in the sites of observation. The synthetic REX allows to expand the period of observation and to increase the acceleration thresholds used in the Bayesian updating process. The application of the Bayesian approach leads to a new and more objective definition of the weights of each branch of the logic tree and, therefore, to new seismic hazard curves (mean and centiles). The Bayesian approach doesn’t change the probabilistic models (seismic hazard curves). It only modifies the weights of each branch of the logic tree.     

汶川地震庙子坪特大桥主桥箱梁开裂震害分析

2008年汶川地震中庙子坪特大桥主桥箱梁开裂严重,并在两个端部（过渡墩处）有较大的横向残余位移。为深入了解主梁开裂震害原因,选取桥址附近台站实测的八条强震动记录及常用El Centro等波作为输入,考虑箱梁施工过程及初始应力影响,通过时程分析进行数值模拟并与实际震害比较。结果表明:不同地震波输入下得到的箱梁高应力区与实际开裂区吻合较好,预示箱梁开裂震害不属于偶然现象。箱梁在主墩处、边跨和中跨合龙段区域处的顶板,边跨1/6~1/2及中跨1/4~3/4区域处的腹板,边跨和中跨合龙段及其相邻2~3个节段处的底板,在地震中易出现高拉或压应力区。地震过程中估计纵向预应力筋应力增加接近100MPa,横桥向挡块破坏降低了跨中箱梁的拉和压应力,对箱梁开裂震害有一定减轻作用。     

在役公路梁式桥综合震害等级预测研究

为客观预测在役公路梁式桥综合震害状况,考虑在役桥梁在运营期存在的病害问题,从压力和承压两方面建立在役公路梁式桥综合震害预测评价指标体系.以桥梁作为承灾体,建立在役公路梁式桥综合震害物元可拓模型,运用熵权法进行赋权,确定桥梁的综合震害状况.以一座在役梁式桥为例,运用上述模型确定算例的综合震害状况.研究结果表明,该桥的综合...     

基于损伤分析的旧曲线梁桥抗震性能评估

曲线桥梁在役期间可能面临地震灾害,导致结构损坏甚至坍塌,为了评估在役桥梁的抗震性能,提出基于损伤分析的曲线梁桥抗震性能评估方法.建立旧曲线梁桥有限元模型,基于损伤分析的原理,提出适合曲线梁桥地震响应特性的构件损伤模型,在全桥有限元模型中输入不同类型地震动,计算各构件的损伤指数,并结合旧桥检算系数,由各构件损伤指数综合得...     

Cluster computing-aided model updating for a high-fidelity finite element model of a long-span cable-stayed bridge

Accurate and high-fidelity finite element (FE) models are in great demand in the design, performance assessment, and life-cycle maintenance of long-span cable-stayed bridges. The structural system of a long-span cable-stayed bridge is often huge in size and complex with many components connected and various materials constituted. Therefore, the FE model of a long-span cable-stayed bridge involves a large number of elements and nodes with many uncertainties. The model updating of the FE model to best represent a real bridge is necessary but very challenging. One of the challenging issues is that the numerical computation needed for searching the global optimum of a large set of structural parameters is so extensive that the existing FE (not surrogate) model-based updating methods cannot fulfill this task. In this study, a cluster computing-aided FE model updating framework is proposed for the high-performance FE model updating of large and complex structures. In the framework, several computer software packages, including MSC.Marc, Python, and MATLAB, are interconnected for making use of their respective functions of strength. The shake table test of a scaled physical structure of the Sutong cable-stayed bridge in China is used to validate the accuracy and efficiency of the proposed framework. The simulated bridge responses based on the updated FE model are in good agreement with the measured ones from the shake table test. The successful application of the proposed framework provides a reference for the model updating of other types of large and complex structures.     

海底地震动作用下近海桥梁地震响应研究

以某近海大桥引桥段连续梁桥为工程背景,建立考虑海底地震动特性和腐蚀效应的近海桥梁地震反应分析模型。采用增量动力分析方法分析腐蚀效应以及海底地震动作用对近海桥梁地震响应的影响。研究结果表明:腐蚀效应与海底地震动作用都会不同程度影响近海桥梁结构的抗震性能。其中:腐蚀效应会增大近海桥梁的破坏指标,降低最大墩底剪力和弯矩值,从而降低桥梁的抗震性能;海底地震动作用会增大近海桥梁的破坏指标及最大墩底剪力、弯矩值;在2种因素耦合作用下,桥梁的抗震性能将会进一步降低。     

Linear vertical vibrations of suspension bridges: A review of continuum models and some new results

The classical continuum model for the linear vertical vibrations of a suspension bridge (Bleich et al., 1950 [1]) is re-examined. The primary objective of the study is to extend the definitive analytical and numerical results of Irvine and Caughey (1974) [2], Irvine and Griffin (1976) [3] and Irvine (1980, 1981) [4], [5] for the natural frequencies, mode shapes, and modal participation factors for an extensible suspension cable, which depend on one dimensionless parameter related to the elasticity of the cable, to the case of a stiffened suspension bridge in which the response depends also on a second dimensionless parameter related to the stiffness of the girder. The continuum suspension bridge model is also used to understand the pattern of variation of mode shapes as a function of cable elasticity and girder stiffness, which has been shown by West et al. (1984) [6] to be considerably more complex than that for a suspension cable. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

爬移状态对服役曲线梁桥抗震性能影响分析

服役曲线梁桥常存在爬移病害。为探讨爬移病害程度对曲线梁桥抗震性能的影响规律,通过总结服役曲线梁桥爬移病害,确定以不同梁端爬移位移量作为描述服役曲线梁桥爬移状态的对比分析工况,并以一座三跨预应力混凝土曲线梁桥为例,采用MIDAS Civil建立有限元模型,考虑桩-土相互作用、双向碰撞效应及材料非线性,分析曲线梁桥支座及桥墩等主要受力构件地震响应规律,探讨爬移状态对服役曲线梁桥抗震性能影响。研究结果表明：主梁的爬移病害对桥梁的抗震性能会产生不利影响,会导致支座位移的增长,增加支座破坏的风险,从而增加桥梁上部结构碰撞效应及落梁风险;随着爬移位移的增加,桥墩的损伤状态可能由爬移前的无损伤转变为考虑爬移后的严重损伤状态。因此,在进行服役曲线梁桥抗震性能评估时应量化其爬移状态,并采用合理的措施对主梁的爬移进行限制。     

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.     

钢桁梁桥基于模型修正方法的损伤程度识别研究

在钢桁梁桥模型损伤定位的基础上,采用模型修正方法对其损伤程度进行识别,对其中几个关键问题进行了研究分析,得出了一些有用的结论,可作为实际桥梁健康监测的参考依据。     

Performance-based seismic design of integral abutment bridges

Integral abutment bridges (IAB) are experiencing increasing diffusion in the short to mid-range lengths, where they offer some advantages over traditional girder bridges with non-monolithic connection at the abutments. One challenging problem with their analysis and design is that consideration of the interaction between foundation soil, structure and backfill is unavoidable, also for the deck design. Further, the end of the construction is only one of the conditions that need to be verified during design. Cyclic deformations, such as those occurring during ground shaking, typically lead to an increase in stresses in the abutments and connections, due to progressive compaction (ratcheting) of the backfill soil. This problem is magnified when the bridge is comprised between two embankments, whose response may amplify the input motion and drive the deformation of the bridge. Performance-based design aims at superseding current design procedures by explicitly checking that the target performances set out are achieved, and not overly exceeded. Such a design paradigm naturally calls, on the one hand, for improved accuracy in response determination and more refined analyses, and, on the other, for taking into account the uncertainties entering into the problem by means of an explicitly probabilistic approach. With this objective in mind, the paper presents an inelastic dynamic model for the seismic analysis and design of IABs. The model, that features a balanced compromise between the setup and evaluation effort on one hand, and accuracy on the other, has been developed for implementation in typical commercial analysis packages. It builds on 1D site-response analysis and on inelastic Winkler-like modeling, to reproduce the main physical aspects of the seismic response of IABs. One example application to a highway overpass in Italy illustrates the model and the relevance of a fully probabilistic approach to performance-based design. The application offers also important insight into the choice of an efficient intensity measure for this type of structure.     

Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge

Observation of human-induced large-amplitude lateral vibration of an actual pedestrian bridge in an extremely congested condition is reported. Walking motions of pedestrians recorded by a video camera are analysed. It is found that walking among 20 per cent or more of the pedestrians on the bridge was synchronized to the girder lateral vibration. With this synchronization, the total lateral force from the pedestrians to the girder is evidently increased and it acts as a resonant force on the girder lateral vibration.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

双向地震作用下高铁FPS隔震简支梁桥纵向地震碰撞反应研究

为了准确分析FPS隔震桥梁的纵向地震碰撞反应,针对一典型3跨FPS隔震简支梁桥,建立了考虑FPS双向耦合效应和梁缝处三维碰撞效应的非线性动力计算模型,分析双向地震作用下FPS隔震简支梁桥纵向地震碰撞反应;研究支座半径和摩擦系数对简支梁桥纵向地震碰撞反应的影响规律。研究结果表明:横向地震作用会增大简支梁邻梁间纵向地震碰撞次数和碰撞力,降低墩底纵向剪力;为减小地震碰撞反应,设计时可适当增大支座半径和支座摩擦系数。     

Transient responses of girder bridges with vertical poundings under near‐fault vertical earthquake

Previous studies on pounding responses of bridge structures mainly focus on the horizontal pounding between adjacent structures. However, the vertical pounding responses of bridge are rarely studied. The aim of this paper is develop a theoretical approach to investigate the transient behavior of continuous bridge under near‐fault vertical ground motions. The transient behavior of bridge manifests as the earthquake‐induced response wave and pounding‐induced response wave travel throughout bridge. Based on a new continuous model of beam–spring–rod, the theoretical solution of bridge responses involving multiple vertical poundings is derived by the expansion of transient wave functions in a series of eigenfunctions. A new theoretical solving approach of the multiple vertical pounding forces is presented based on the transient internal force on the contact surface of the girder and bearing. The numerical results show that the present method can reasonably capture the propagations of the earthquake‐induced response wave and pounding‐induced response wave. The calculations of pounding force by the present method are convergence of the time‐step size and truncation number of wave modes. As the effect of transient wave is taken into account, the numerical results show several transient phenomena involving the vertical pounding, the high pounding force, the multiple‐pounding phenomenon, the vertical separation of girder from the bearing, the dependence of poundings on earthquake period and the narrow period window of poundings. Copyright © 2015 John Wiley & Sons, Ltd.