The eigenvalues of isolated bridges with transverse restraints at the end abutments

This paper examines the eigenvalues of multi‐span seismically isolated bridges in which the transverse displacement of the deck at the end abutments is restricted. With this constraint the deck is fully isolated along the longitudinal direction, whereas along the transverse direction the deck is a simple‐supported beam at the end abutments which enjoys concentrated restoring forces from the isolation bearings at the center piers. For moderate long bridges, the first natural period of the bridge is the first longitudinal period, while the first transverse period is the second period, given that the flexural rigidity of the deck along the transverse direction shortens the isolation period offered by the bearings in that direction. This paper shows that for isolated bridges longer than a certain critical length, the first transverse period becomes longer than the first longitudinal period despite the presence of the flexural rigidity of the deck. This critical length depends on whether the bridge is isolated on elastomeric bearings or on spherical sliding bearings. This result is also predicted with established commercially available numerical codes only when several additional nodes are added along the beam elements which are modeling the deck in‐between the bridge piers. On the other hand, this result cannot be captured with the limiting idealization of a beam on continuous distributed springs (beam on Wrinkler foundation)—a finding that has practical significance in design and system identification studies. Finally, the paper shows that the normalized transverse eigenperiods of any finite‐span deck are self‐similar solutions that can be represented by a single master curve and are independent of the longitudinal isolation period or on whether the deck is supported on elastomeric or spherical sliding bearings. Copyright © 2009 John Wiley & Sons, Ltd.     

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。     

Behavior of a seismically isolated bridge crossing a fault rupture zone

The effect of the fault rupture zone traversing a seismically isolated bridge is investigated utilizing a finite element model of a section of the Bolu Viaduct and a set of synthetic broadband strong ground motions simulated for the Bolu Viaduct site due to the 1999 Duzce earthquake. Both the original and a potential retrofit seismic isolation system designs are considered in the analyses. The results show double isolation system demands when fault crossing is considered, as compared to the case where fault crossing is ignored. The pier drift demands, however, remain comparable in both cases. Furthermore, the location of fault crossing along the bridge length, as well as the fault orientation with respect to the bridge longitudinal direction are shown to influence substantially the response of the seismically isolated bridge. Isolation system permanent displacements are greatly influenced by the restoring force capability of the isolation system when fault crossing effects in the excitations are ignored. In the case of fault crossing, the permanent displacements of the isolation system are dominated by the substantial permanent tectonic displacement along the fault trace which is imposed upon the structure. The results of this study contribute to developing a better understanding of how seismically isolated bridges respond when traversed by fault rupture zones. The lack of analyses and design guidelines for bridges crossing faults in international standards renders this study a useful reference for the profession.     

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,该桥的综合震害等级为Ⅲ级,破坏等级中等,且根据结果分析影响桥梁震害程度的主要影响因素;该模型通过对多个指标关联系数的综合分析来评价在役梁式桥的综合震害等级,极大地提高了该模型评估的准确率及可靠性,为桥梁震害等级的预测提供一定的参考,对提升桥梁综合抗震能力具有积极意义。     

Seismic response of isolated bridges with soil–structure interaction

The modern transportation facilities demand that the bridges are to be constructed across the gorges that are located in seismically active areas and at the same time the site conditions compel the engineers to rest the pier foundation on soil. The purpose of this study is to assess the effects of soil–structure interaction (SSI) on the peak responses of three-span continuous deck bridge seismically isolated by the elastomeric bearings. The emphasis has been placed on gauging the significance of physical parameters that affect the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. The soil surrounding the foundation of pier is modelled by frequency independent coefficients and the complete dynamic analysis is carried out in time domain using complex modal analysis method. In order to quantify the effects of SSI, the peak responses of isolated and non-isolated bridge (i.e. bridge without isolation device) are compared with the corresponding bridge ignoring these effects. A parametric study is also conducted to investigate the effects of soil flexibility and bearing parameters (such as stiffness and damping) on the response of isolated bridge system. It is observed that the soil surrounding the pier has significant effects on the response of the isolated bridges and under certain circumstances the bearing displacements at abutment locations may be underestimated if the SSI effects are not considered in the response analysis of the system.     

Simplified method for real‐time seismic damage assessment of motorway bridges: Transverse direction—Accounting for abutment stoppers

In the context of developing a real‐time seismic damage assessment technique, this paper proposes a simplified model that accounts for abutment stoppers, focusing on the transverse direction. Detailed 3D finite element models of 4 bridges of the Attiki Odos motorway are developed and used as benchmarks to assess its efficiency. The selected bridges vary in length, pier typologies, clearances, and pier‐deck connections. The simplified model entails a SDOF system of a pier, with assemblies of gap elements, lateral and rotational springs, and dashpots (top and bottom), representing the deck, the bearings, the abutment stoppers, and the foundation. The effect of stoppers is initially studied, focusing on the response of the abutment‐embankment system. To shed more light on the role of abutment stoppers, a parametric study is conducted, considering a wide range of clearances. Subsequently, the effect of variabilities in span length and pier height is examined. The simplified method is extended to nonideally symmetric systems and verified against the 3D benchmarks. Finally, the model is modified to account for multicolumn piers. The extended simplified model offers a reasonable prediction of the seismic damage state, reducing significantly the computational cost, and allowing detailed parametric studies. The latter are used to develop nonlinear regression model equations correlating a selected damage index with statistically significant intensity measures. Such equations offer a viable alternative for network‐wide seismic damage assessment as part of a real‐time emergency response framework. A pilot implementation is presented, illustrating the applicability of the proposed methodology.     

Double deck bridge behavior and failure mechanism under seismic motions using nonlinear analyzes

This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis.A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions,and to detect the effect of bidirectional loading on the seismic response of this type of bridge.The results showed that some characteristics,such as the variable lateral stiffness,the foundation modelling,and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions.It was found that the soft story failure mechanism is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure.The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading was severely increased compared to the bridge response under unidirectional transverse loading,and out-of-phase movements were triggered between adjacent girders.     

减隔震桥梁设计方法及抗震性能研究综述

桥梁作为交通系统中的生命线工程,其抗震性能问题尤为重要。桥梁减隔震技术主要通过减隔震装置来降低结构的地震损伤,目前已发展成为提高强震区桥梁抗震能力的重要措施。为促进减隔震技术在中国桥梁工程领域的进一步发展,首先总结减隔震桥梁的设计方法,归纳其地震反应和震害情况,对采用不同减隔震装置桥梁的非线性动力性能、减隔震效果、地震随机响应、易损性及性能优化方法等研究情况进行梳理;其次,概述减隔震技术在斜交桥、曲线桥及铁路桥梁中的应用情况与研究进展,并介绍新型韧性抗震设计理念在桥梁工程领域中的应用情况和发展前景;最后,总结减隔震桥梁的试验研究情况,指出目前减隔震桥梁研究中的不足和发展趋势。     

Dynamic performance analysis of a seismically isolated bridge under braking force

In order to study the dynamic performance of seismically isolated bridges under the most unfavorable loads in the longitudinal direction,a dynamic equation for vehicle braking in the longitudinal direction is established.A four or fiveorder Runge-Kutta method is adopted to obtain the time-history response of a wheel set under braking force.The quadratic discretization method is then used to transform this time-history into a braking and bending force time-history of a structural fixed node,and a dynamic response analysis of the seismically isolated bridge under the vehicle’s braking force is carried out using ANSYS,a universal finite element analysis software.According to the results,seismic isolation design results in a more rational distribution of braking force among piers;the influence of the initial braking velocity on the vehicle braking force is negligible;the location where the first wheel set leaves the bridge is the most unfavorable parking location;a seismic isolation bridge bearing constructed according to typical design methods enters into a yield stage under the braking force, while the shearing force at the bottom of the pier declines as the isolation period is extended;the design requirements can be met when the yield displacement of the seismic isolation bearing is less than 5 mm and the yield strength is greater than the braking force.     

无缝桥抗震性能的对比研究

本文以一座三跨总长60 m的整体桥为案例桥,分别试设计了同跨径的半整体桥、延伸桥面板桥和常规连续梁桥。通过Midas/Civil软件建立四种桥型的有限元模型,并对其进行了E1和E2反应谱分析和时程分析,对比了四种桥型的结构反应峰值（墩顶位移、桥墩及桩基剪力与弯矩、台底位移、桥台桩基剪力与弯矩）。计算结果表明:当桥梁存在15°的斜交角,整体桥、半整体桥在地震动沿平行于桥台长边方向及其垂直方向输入时更不利,而延伸桥面板桥和常规连续梁桥在地震动沿顺桥向和横桥向输入时更不利。四种桥型在地震作用下:整体桥抗震性能最优异,但其台底位移、桥台桩基的剪力和弯矩最大;半整体桥台底位移、桥台桩基的剪力和弯矩最小,其墩顶位移、桥墩及桩基的剪力和弯矩仅比整体桥大;延伸桥面板桥和常规连续梁桥的墩-梁相对位移远大于整体桥和半整体桥,不适用于地震基本烈度高的区域。     

A simplified design method for metallic dampers used in the transverse direction of cable-stayed bridges

The aseismic design of cable-stayed bridges in the transverse direction with newly proposed metallic dampers that can accommodate both longitudinal and transverse movement of the deck has recently been considered. This work focuses on developing a simplified method to design an appropriate metallic damper. The seismic performance of cablestayed bridges with different damper stiffness, main span lengths, tower shapes and types of deck in the transverse direction are investigated. The transverse displacement of the deck of a cable-stayed bridge increases significantly with the increment of the damper stiffness, which proves that the design of the damper stiffness is crucial. A simplified model considering the damper stiffness, cable system and tower in the transverse direction is developed to evaluate the period and lateral displacement of a complicated cable-stayed bridge. Based on the simplified model, a design method is proposed and assessed using two cable-stayed bridges as examples. The results show that metallic dampers can be designed with high efficiency, and the optimal ductility of the damper can be selected.     

Passive seismic control of cable-stayed bridges with damped resonant appendages

A study is conducted to investigate the effectiveness of attaching to cable-stayed bridges resonant appendages with a relatively small mass and a high damping ratio as a means to reduce their response to earthquake excitations. The study is based on a previously developed formulation that shows that the use of these appendages may increase the inherent damping of building structures and, as a result, may reduce their response to seismic disturbances. It includes numerical and experimental tests that are conducted to assess the validity of such a formulation for the case of cable-stayed bridges and the extent to which such appendages can reduce their seismic response. In the numerical study, an actual cable-stayed bridge is modelled with finite elements and analysed with and without the proposed appendages under different earthquake ground motions. Appendages with damping ratios of 10, 15, 20 and 30 per cent and masses that, respectively, represent 0.67, 1.5, 2.7 and 6.0 per cent of the total mass of the bridge are considered. In the experimental test, a 3.7 m long cable-stayed bridge and an appendage consisting of a small mass, a small spring and a small viscous damper are built and the bridge tested, without and with the appendage, on a pair of shaking tables which are set to reproduce ground acceleration records from past earthquakes. The damping ratio of the appendage in this test is 32 per cent and its mass represents about 8 per cent of the total mass of the bridge model. In the numerical test, it is found that the appendages reduce the longitudinal response of the bridge deck up to 88 per cent. Similarly, in the experimental test it is found that the appendage reduces the longitudinal bridge deck response by about 41 per cent. From these studies, it is concluded that the suggested appendages may indeed be effective in reducing the seismic response of cable-stayed bridges as they are for building structures.     

Seismic performance evaluation of steel arch bridges against major earthquakes. Part 1: dynamic analysis approach

In this study the inelastic behavior of steel arch bridges subjected to strong ground motions from major earthquakes is investigated by dynamic analyses of a typical steel arch bridge using a three‐dimensional (3D) analytical model, since checking seismic performance against severe earthquakes is not usually performed when designing such kinds of bridge. The bridge considered is an upper‐deck steel arch bridge having a reinforced concrete (RC) deck, steel I‐section girders and steel arch ribs. The input ground motions are accelerograms which are modified ground motions based on the records from the 1995 Hyogoken‐Nanbu earthquake. Both the longitudinal and transverse dynamic characteristics of the bridge are studied by investigation of time‐history responses of the main parameters. It is found that seismic responses are small when subjected to the longitudinal excitation, but significantly large under the transverse ground motion due to plasticization formed in some segments such as arch rib ends and side pier bases where axial force levels are very high. Finally, a seismic performance evaluation method based on the response strain index is proposed for such steel bridge structures. Copyright © 2004 John Wiley & Sons, Ltd.     

EXPERIMENTAL STUDY OF FPS SYSTEM IN BRIDGE SEISMIC ISOLATION

An experimental study of a seismically isolated and a comparable non-isolated bridge is presented. The bridge model featured flexible piers, weighed 158kN and was tested on a shake table with an array of real and simulated seismic motions with peak acceleration in the range 0⋅1–1⋅1g. When isolated, the bridge deck was supported by four spherically shaped sliding bearings (known as Friction Pendulum System or FPS bearings) with friction coefficient under dynamic conditions in the range 0⋅07–0⋅12. The experimental results demonstrated a substantial improvement in the ability of the isolated bridge to sustain all levels of seismic excitation under elastic conditions.     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

Effect of variation of normal force on seismic performance of resilient sliding isolation systems in highway bridges

In this study, a series of shaking table tests are carried out on scaled models of two seismically isolated highway bridges to investigate the effect of rocking motion and vertical acceleration on seismic performance of resilient sliding isolators. In addition, performance of RSI is compared with system having solely natural rubber bearings. Test results show that variation of normal force on sliders due to rocking effect and vertical acceleration makes no significant difference in response of RSI systems. In addition, analytical response of prototype isolated bridge and the model used in experiments is obtained analytically by using non‐linear model for isolation systems. It is observed that for seismically isolated bridges, dynamic response of full‐scale complex structures can be predicted with acceptable accuracy by experiments using a simple model of the structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Reduction of pounding effects in elevated bridges during earthquakes

Pounding of adjacent superstructure segments in elevated bridges during severe earthquakes can result in significant structural damage. The aim of this paper is to analyse several methods of reduction of the negative effects of collisions induced by the seismic wave propagation effect. The analysis is conducted on a detailed three‐dimensional structural component model of an isolated highway bridge. The results show that the influence of pounding on the structural response is significant in the longitudinal direction of the bridge and significantly depends on the gap size between superstructure segments. The smallest response can be obtained for very small gap sizes and for gap sizes large enough to prevent pounding. Further analysis indicates that the bridge behaviour can be effectively improved by placing hard rubber bumpers between segments and by stiff linking the segments one with another. The experimental results show that, for the practical application of such connectors, shock transmission units can be used. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of bridge structures crossing strike-slip fault rupture zones: A simple method for generating across-fault seismic ground motions

This article presents a simple and effective method for generating across-fault seismic ground motions for the analysis of ordinary and seismically isolated bridges crossing strike-slip faults. Based on pulse models available in the literature, two simple loading functions are first proposed to represent the coherent (long-period) components of ground motion across strike-slip faults. The loading functions are then calibrated using actual near-fault ground-motion records with a forward-directivity velocity pulse in the fault-normal direction and a fling-step displacement in the fault-parallel direction. The effectiveness of the proposed method is demonstrated by comparing time history responses and seismic demands of ordinary and seismically isolated bridges obtained from nonlinear response history analyses using the actual ground-motion records and the calibrated loading functions. A comprehensive methodology is also presented for selecting the input parameters of the loading functions based on empirical equations and practical guidelines. Finally, an analysis procedure for bridge structures crossing strike-slip faults is introduced based on the proposed method for generating across-fault ground motions and the parameter selection methodology for the loading functions.     

Seismic response of multi-frame bridges

Long cast-in-place concrete bridges are often constructed in multiple frames separated by in-span hinges. The multi-frame system offers lower construction and maintenance costs, fewer adverse effects due to creep, post-tensioning, and thermal deformations as a few of its advantages. However, the seismic response of multi-frame bridges has been uncertain owing to the complexities of their discrete system. This study intends to improve the understanding of the seismic response of multi-frame bridge systems and evaluate the applicability of current design assumptions. Responses of multi-frame bridges and comparable single-frame bridges of the same length are compared. Seismic demands on multi-frame bridge columns, abutments, and in-span hinges were investigated through high-fidelity analytical simulations. Approximately 3400 nonlinear time history analyses of prototype bridges with realistic designs were performed using the OpenSees platform. Analysis of variance was implemented along with a factorial design to study the effect of several independent factors, including the number of frames, substructure system, unequal column heights, soil type, ground motion intensity, and capacity-to-demand ratio. It was observed for elastic dynamic analysis that a 90 % modal mass participation ratio is not adequate to accurately estimate dynamic responses. Seismic demands on columns in multi-frame bridges are typically smaller than those in comparable single-frame bridges. The multi-frame system is seismically more robust than the single-frame system, specifically for bridges spanning non-uniform valleys that include unequal column heights. To prevent longitudinal unseating at in-span hinges, it is critical to consider the interaction of transverse and longitudinal responses. The seismic damage to abutment backwalls and backfills in multi-frame bridges is expected to be extensive owing to small expansion joints.     

Fuzzy logic control of bridge structures using intelligent semi-active seismic isolation systems

Passive supplemental damping in a seismically isolated structure provides the necessary energy dissipation to limit the isolation system displacement. However, damper forces can become quite large as the passive damping level is increased, resulting in the requirement to transfer large forces at the damper connections to the structure which may be particularly difficult to accommodate in retrofit applications. One method to limit the level of damping force while simultaneously controlling the isolation system displacement is to utilize an intelligent hybrid isolation system containing semi-active dampers in which the damping coeffic ient can be modulated. The effectiveness of such a hybrid seismic isolation system for earthquake hazard mitigation is investigated in this paper. The system is examined through an analytical and computational study of the seismic response of a bridge structure containing a hybrid isolation system consisting of elastomeric bearings and semi-active dampers. Control algorithms for operation of the semi-active dampers are developed based on fuzzy logic control theory. Practical limits on the response of the isolation system are considered and utilized in the evaluation of the control algorithms. The results of the study show that both passive and semi-active hybrid seismic isolation systems consisting of combined base isolation bearings and supplemental energy dissipation devices can be beneficial in reducing the seismic response of structures. These hybrid systems may prevent or significantly reduce structural damage during a seismic event. Furthermore, it is shown that intelligent semi-active seismic isolation systems are capable of controlling the peak deck displacement of bridges, and thus reducing the required length of expansion joints, while simultaneously limiting peak damper forces. Copyright © 1999 John Wiley & Sons, Ltd.