Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Implications of seismic pounding on the longitudinal response of multi-span bridges - an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach. Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is cssential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding

Major earthquakes in the past indicated that pounding between bridge decks may result in significant structural damage or even girder unseating. With conventional expansion joints, it is impossible to completely avoid seismic pounding between bridge decks, because the gap size at expansion joints is usually not big enough in order to ensure smooth traffic flow. With a new development of modular expansion joint (MEJ), which allows a large joint movement and at the same time without impeding the smoothness of traffic flow, completely precluding pounding between adjacent bridge decks becomes possible. This paper investigates the minimum total gap that a MEJ must have to avoid pounding at the abutments and between bridge decks. The considered spatial ground excitations are modelled by a filtered Tajimi‐Kanai power spectral density function and an empirical coherency loss function. Site amplification effect is included by a transfer function derived from the one‐dimensional wave propagation theory. Stochastic response equations of the adjacent bridge decks are formulated. The effects of ground motion spatial variations, dynamic characteristics of the bridge and the depth and stiffness of local soil on the required separation distance are analysed. Soil–structure interaction effect is not included in this study. The bridge response behaviour is assumed to be linear elastic. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of ground motion spatial variation,site condition and SSI on the required separation distances of bridge structures to avoid seismic pounding

It is commonly understood that earthquake ground excitations at multiple supports of large dimensional structures are not the same. These ground motion spatial variations may significantly influence the structural responses. Similarly, the interaction between the foundation and the surrounding soil during earthquake shaking also affects the dynamic response of the structure. Most previous studies on ground motion spatial variation effects on structural responses neglected soil–structure interaction (SSI) effect. This paper studies the combined effects of ground motion spatial variation, local site amplification and SSI on bridge responses, and estimates the required separation distances that modular expansion joints must provide to avoid seismic pounding. It is an extension of a previous study (Earthquake Engng Struct. Dyn. 2010; 39 (3):303–323), in which combined ground motion spatial variation and local site amplification effects on bridge responses were investigated. The present paper focuses on the simultaneous effect of SSI and ground motion spatial variation on structural responses. The soil surrounding the pile foundation is modelled by frequency‐dependent springs and dashpots in the horizontal and rotational directions. The peak structural responses are estimated by using the standard random vibration method. The minimum total gap between two adjacent bridge decks or between bridge deck and adjacent abutment to prevent seismic pounding is estimated. Numerical results show that SSI significantly affects the structural responses, and cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

Response of indeterminate two-span beam to spatially varying seismic excitation

In order to examine the effect of the spatial variation of ground motion on the response of an indeterminate structure, the stochastic responses of a two-span beam to spatially varying support excitations are analysed. A space-time earthquake ground motion model that accounts for both coherency decay and seismic wave propagation is used to specify the support motions, and the results are compared with those for various simplified excitations that are commonly used in practice. The response is computed through a linear random vibration approach with the structure being modelled by finite elements. The results of the study indicate that, even for moderate lengths, the effect of the spatial variation of ground motion can be significant. The assumption of fully coherent support motions (same excitations at all supports or delayed excitations allowing only for wave propagation) may be overconservative for some beams and unconservative for others.     

Dynamic soil–structure interaction effects on the seismic response of suspension bridges

A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 John Wiley & Sons Ltd.     

Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

基于随机振动理论确定桥梁地震碰撞的临界间隙

确定梁桥邻跨间避免地震碰撞的最小间隙,对于梁桥地震碰撞危险性预测及防地震碰撞措施的设计有着显著意义。本文基于随机振动理论建立梁桥地震碰撞邻跨临界间隙的计算方法,分析模型采用跨径不等的两跨简支梁桥,且考虑隔震支座非线性恢复力的影响。文中首先建立了系统的非线性运动方程;随后运用随机等效线性化理论将其线性化;最后在复模态空间推导了临界碰撞间隙的均值与方差的计算方法。人工地震动的非线性时程分析结果验证了本文算法的正确性。参数分析表明,临界间隙随邻跨长度比增大而增大,随支座屈服力与上部结构重量比值减小而增大,随隔震支座屈服位移增大而增大,随桥墩振动周期增大而增大。隔震支座屈服前后刚度比值对临界间隙大小影响很小。     

Response analysis of flexible MDF systems for multiple-support seismic excitations

Two practical approaches, response spectrum and time-history methods, are developed to evaluate the response of flexible multi-degree-of-freedom (MDF) systems, notably long-span bridges, to multiple-support seismic excitations. For practical convenience, ground motions within a group of adjacent supports on continuous soil or rock are assumed to be uniform and synchronized, while those of different groups are treated as non-uniform and uncorrelated. The response spectrum analysis is extended to include the cross-correlation of modal responses, which prove important when closely spaced modal frequencies exist. An example of the significance of multiple-support excitations is illustrated by application to a suspension bridge. Qualitatively comparable effects can be expected for other bridges of similar type or dimensions.     

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.     

Lifeline response to spatially variable ground motions

Lifeline systems have been heavily damaged during past earthquakes; this has often been attributed to the effect of differential ground motion at the supports of these long structures. Based on a stochastic model for the ground excitation the responses of pipelines and bridges of various span lengths subjected to either perfectly or partially correlated random input motions in the axial, lateral (i.e. transverse horizontal) and vertical directions are investigated and the significance of the spatial variation of ground motion is examined.     

双向地震作用下互通式斜交桥梁地震响应及碰撞效应分析

斜交桥梁由于其不规则的结构形式使其受力规律与规则桥梁相比具有特殊性和复杂性,在地震作用下梁体的平动与转动存在弯扭耦合效应,导致结构动力响应分析复杂。针对斜交桥梁的结构特点,建立包含桩土相互作用的三维有限元模型,在考虑水平双向地震作用下,采用反应谱法及时程分析法对京包高速公路某互通式斜交桥梁进行地震反应分析。结果表明:互通式简支斜交桥梁的地震响应受地震动输入方向的影响较大,在考虑碰撞效应后,碰撞涉及结构部位的地震位移显著增加,地震内力也出现较大差异,即说明在斜交桥梁抗震设计时有必要适当考虑地震动输入方向和梁端与墩台及相邻梁端的碰撞效应。     

A comparative study between China and U.S. on seismic design philosophy and practice of a long span arch bridge

This paper presents the first of a series of case studies on the seismic design of long span bridges （cable-stayed bridges, suspension bridges and arch bridges） under a cooperative research project on seismic behavior and design of highway bridges between the State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University and the Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo. The objective of this series of case studies is to examine the differences and similarities on the seismic design practice of long span bridges in China and the U.S., to identify research needs and to develop design guidelines beneficial to bridge engineers in both countries. Unlike short to medium span bridges, long span bridges are not included in most seismic design specifications, mainly because they are location dependent and structurally unique. In this paper, an available model of a steel tied half through arch bridge with a main span of 550m in China is discussed. Analysis is focused on comparisons of the seismic responses due to different ground motions. Seismic design criteria and seismic performance requirements for long span bridges in both countries were first introduced and compared, and then three near field earthquake records with large vertical components were selected as the excitations to examine the seismic behavior and seismic vulnerability of the bridge. Results show that （1） the selected near field ground motions cause larger responses to key components （critical sections） of the bridge （such as arch rib ends） with a maximum increase of more than twice those caused by the site specific ground motions; （2） piers, longitudinal girders and arch crowns are more vulnerable to vertical motions, especially their axial forces; and （3） large vertical components of near field ground motions may not significantly affect the bridge＇s internal forces provided that their peak acceleration spectra ordinates only appear at periods of less than 0.2s. However, they may have more influence on the longitudinal displacements of sliding bearings due to their large displacement spectra ordinates at the fundamental period of the bridge.     

断层走向对刚构桥地震反应的影响

我国西部部分连续刚构桥临近地震断层建设,在抗震分析时通常会忽略断层走向与桥梁纵桥向夹角对其地震反应的影响。利用Midas Civil软件建立4座墩高不同的大跨度连续刚构桥模型,选取10组近断层强震记录进行时程分析,研究断层走向对刚构桥地震反应(位移和弯矩反应)的影响。结果显示：在水平双向近断层地震动输入下,桥梁主墩及主梁纵桥向地震反应在断层走向与纵桥向夹角为75°～135°范围内最大,而横桥向最大地震反应则发生在夹角为0°～30°或120°～180°范围;在三向近断层地震动输入下,与仅考虑水平双向地震动输入下的桥梁地震反应相比,竖向地震动对主梁竖向弯矩响应的影响较大,特别是主墩和主梁的交界处,增大比例可达2倍及以上。就文章选取的4座桥梁算例,不考虑断层走向和桥梁纵桥向的夹角则存在低估桥梁地震反应的可能,低估误差在15%～40%左右。     

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.     

Seismic responses of deck-type arch bridges

The dynamic responses of three deck-type arch bridges, with main spans of 59,213 and 518m, are presented. The ratios of natural period to arch span were found to be quite close for all three bridges. Artificial ground motions were applied separately in three directions to finite-element models of each bridge. Three acceleration levels were considered—0.09g, 0.22g and 0.50g—corresponding to the AASHTO Seismic Risk Zones I, II and III, respectively. Responses to uniform lateral motion were generally the largest, while the responses to vertical motion were generally lower than those due to lateral or longitudinal motion. In all cases considered, none of the total stresses in the main members exceeded the yield stress. Connection and secondary member responses were also calculated and are presented. In addition, the effects of unequal motions at the supports were sampled by various deterministic inputs. While the effects of such motions in the vertical and lateral directions were less than the responses to uniform motion, the effects of unequal longitudinal motions at the supports were substantial.     

The effect of spatially varying earthquake ground motions on the stochastic response of bridges isolated with friction pendulum systems

In this paper, a comprehensive investigation of the effect of spatially varying earthquake ground motions on the stochastic response of bridges isolated with friction pendulum systems is performed. The spatially varying earthquake ground motions are considered with incoherence, wave-passage and site-response effects. The importance of the site-response effect, which arises from the difference in the local soil conditions at different support points of the isolated bridge, is investigated particularly. Mean of maximum and variance response values obtained from the spatially varying earthquake ground motions are compared with those of the specialised cases of the ground motion model. It is shown that site-response component of the spatially varying earthquake ground motion model has important effects on the stochastic response of the isolated bridges. Therefore, to be more realistic in calculating the isolated bridge responses, the spatially varying earthquake ground motions should be incorporated in the analysis.     

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges using Probabilistic Risk Analysis (PRA) procedure is presented for determining their failure probability under random ground motion. Seismic input to the bridge support is considered to be a risk consistent response spectrum which is obtained from a separate analysis. For the response analysis, the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysis provides a coupled stiffness matrix for the spring system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges .The response of the bridge deck is obtained by the response spectrum method of analysis as applied to multidegree of freedom system which duly takes into account the quasi - static component of bridge deck vibration. The fragility analysis includes uncertainties arising due to the variation in ground motion, material property, modeling, method of analysis, ductility factor and damage concentration effect. Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM) method of reliability. A three span double plane symmetrical fan type cable stayed bridge of total span 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations. Some of the important conclusions of the study indicate that (i) not only vertical component but also the horizontal component of ground motion has considerable effect on the probability of failure; (ii) ground motion with no time lag between support excitations provides a smaller probability of failure as compared to ground motion with very large time lag between support excitation; and (iii) probability of failure may considerably increase for soft soil condition.     

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...