Seismic fragility curves for greek bridges: methodology and case studies

This study focusses on the estimation of seismic fragility curves for all common bridge types found in modern greek motorways. At first a classification scheme is developed in order to classify the existing bridges into a sufficient number of classes. A total of 11 representative bridge classes resulted, based on the type of piers, deck, and pier-to-deck connection. Then an analytical methodology for deriving fragility curves is proposed and applied to the representative bridge models. This procedure is based on pushover analysis of the entire bridge and definition of damage states in terms of parameters of the bridge pushover curves. The procedure differentiates the way of defining damage according to the seismic energy dissipation mechanism in each bridge, i.e. bridges with yielding piers of the column type and bridges with bearings (with or without seismic links) and non-yielding piers of the wall type. The activation of the abutment-backfill system due to closure of the gap between the deck and the abutments is also taken into account. The derived fragility curves are subjected to a first calibration against empirical curves based on damage data from the US and Japan.     

限制位移桥墩的连续刚构桥抗震性能研究

沿着摇摆桥墩的概念提出一种限制位移桥墩连续刚构桥体系。该体系通过对连续刚构桥墩底和承台之间采取一定措施,使桥梁在地震发生时能够在限制的位移量内活动,减小输入到桥梁结构中的能量,达到减震的目的。通过对一座铁路连续刚构桥的分析,发现这种限制位移桥墩连续刚构桥体系能大幅减小桥墩的延性和强度地震需求,减震效果明显,在选择合适的限制位移量的情况下,可保证桥墩在高烈度罕遇地震作用下几乎保持弹性工作状态,震后经简单处理即可保证使用功能,为震后救援工作带来极大便利,也大大减少了修复成本。     

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.     

Seismic fragilities of single-column highway bridges with rocking column-footing

Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures has been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single-column concrete box-girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi-class responses (eg, full contacted or uplifting foundation) and multi-mode damage (eg, overturning, uplift impact, and column nonlinearity). A multi-step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as-built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time.     

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.     

MPA方法在不同高度桥墩地震响应分析中的适用性研究

桥梁通常是线路中的控制工程,其抗震性能显得尤为重要。作为梁桥重要组成部分的桥墩,往往是地震作用下容易受到损伤的构件。结合西部山区梁桥的典型桥墩结构形式,基于纤维模型的有限元方法建立桥墩的非线性数值分析模型。采用MPA方法对不同高度桥墩的地震响应进行分析,以非线性时程分析方法的计算结果为基准研究MPA方法的适用性。计算表明MPA方法在分析高阶模态参与程度较高的高墩构件时适用性较差。     

Seismic behavior of a post-tensioned integral bridge including soil–structure interaction (SSI)

Current practice usually pays little attention to the effect of soil–structure interaction (SSI) on seismic analysis and design of bridges. The objective of this research study is to assess the significance of SSI on the modal with geometric stiffness and seismic response of a bridge with integral abutments that has been constructed using a new bridge system technology. Emphasis is placed on integral abutment behavior, since abutments together with piers are the most critical elements in securing the integrity of bridge superstructures during earthquakes. Comparison is made between analytical results and field measurements in order to establish the accuracy of the superstructure–abutment model. Sensitivity studies are conducted to investigate the effects of foundation stiffness on the overall dynamic and seismic response of the new bridge system.     

Seismic response of rocking frames with top support eccentricity

The seismic response of rocking frames that consist of a rigid beam freely supported on rigid freestanding rectangular piers has received recent attention in the literature. Past studies have investigated the special case where, upon planar rocking motion, the beam maintains contact with the piers at their extreme edges. However, in many real scenarios, the beam‐to‐pier contact lies closer to the center of the pier, affecting the overall stability of the system. This paper investigates the seismic response of rocking frames under the more general case which allows the contact edge to reside anywhere in‐between the center of the pier and its extreme edge. The study introduces a rocking block model that is dynamically equivalent to a rocking frame with vertically symmetric piers of any geometry. The impact of top eccentricity (ie, the distance of the contact edge from the pier's vertical axis of symmetry) on the seismic response of rocking frames is investigated under pulse excitations and earthquake records. It is concluded that the stability of a top‐heavy rocking frame is highly influenced by the top eccentricity. For instance, a rocking frame with contacts at the extreme edges of the piers can be more seismically stable than a solitary block that is identical to one of the frame's piers, while a rocking frame with contacts closer to the centers of the piers can be less stable. The concept of critical eccentricity is introduced, beyond which the coefficient of restitution contributes to a greater reduction in the response of a frame than of a solitary pier.     

Evaluation of code criteria for bridges with unequal pier heights

One of the challenges associated with Eurocode 8 and AASHTO-LRFD is predicting the failure of irregular bridges supported by piers of unequal heights. EC8 currently uses “moment demand-to-moment capacity” ratios to somewhat guarantee simultaneous failure of piers on bridges, while AASHTO-LRFD relies on the relative effective stiffness of the piers. These conditions are not entirely valid, in particular for piers with a relative height of 0.5 or less, where a possible combination of flexure and shear failure mode may occur. In this case, the shorter piers often result in brittle shear failure, while the longer piers are most likely to fail due to flexure, creating a combination of different failure modes experienced by the bridge. To evaluate the adequacy of EC8 design procedures for regular seismic behavior, various irregular bridges are simulated through a non-linear pushover analysis using shear-critical fiber-based beam-column elements. The paper investigates the behavior of irregular monolithic and bearing-type bridges experiencing different failure modes, and proposes different methods for regularizing the bridge performance to balance damage. The ultimate aim is to obtain a simultaneous or near-simultaneous failure of all piers irrespective of the different heights and failure mode experienced.     

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.     

地震作用下双薄壁高墩刚构桥桥台处的碰撞效应及减碰措施

针对双薄臂高墩连续刚构桥两侧桥台处主梁与背墙的碰撞现象,基于桥台-背土作用简化模型和Kelvin碰撞模型,采用非线性时程法研究碰撞对双薄臂墩地震剪力、弯矩、曲率和位移,以及支座纵向变形的影响。提出可牺牲背墙、阻尼器、加强型横系梁等三种减碰措施,并对比分析其减碰效果。研究表明:碰撞会显著增大高墩的地震内力和曲率响应,降低墩顶位移和支座的纵向变形;碰撞刚度的变化对碰撞效应的影响在20%以内;可牺牲背墙和阻尼器两种减碰措施均可大幅降低桥墩的地震内力和曲率,使其接近不考虑碰撞时的状态,阻尼器同时还可以保护支座不超过容许变形,而可牺牲背墙则会导致支座的地震破坏;加强型横系梁不能发挥减碰作用,反而会增大桥墩的地震响应。     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Planar rocking response and stability analysis of an array of free‐standing columns capped with a freely supported rigid beam

This paper investigates the planar rocking response of an array of free‐standing columns capped with a freely supported rigid beam in an effort to explain the appreciable seismic stability of ancient free‐standing columns that support heavy epistyles together with the even heavier frieze atop. Following a variational formulation, the paper concludes to the remarkable result that the dynamic rocking response of an array of free‐standing columns capped with a rigid beam is identical to the rocking response of a single free‐standing column with the same slenderness yet with larger size, that is a more stable configuration. Most importantly, the study shows that the heavier the freely supported cap beam is (epistyles with frieze atop), the more stable is the rocking frame regardless of the rise of the center of gravity of the cap beam, concluding that top‐heavy rocking frames are more stable than when they are top light. This ‘counter intuitive’ finding renders rocking isolation a most attractive alternative for the seismic protection of bridges with tall piers, whereas its potential implementation shall remove several of the concerns associated with the seismic connections of prefabricated bridges. Copyright © 2012 John Wiley & Sons, Ltd.     

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。     

Seismic responses of bridges with rocking column-foundation: A dimensionless regression analysis

Rocking column-foundation system is a new design concept for bridges that can reduce overall seismic damage, minimize construction and repair time, and achieve lower cost in general. However, such system involves complex dynamic responses due to impacts and highly nonlinear rocking behavior. This study presents a dimensionless regression analysis to estimate the rocking and shaking responses of the flexible column-foundation system under near-fault ground motions. First, the transient drift and rocking responses of the system are solved numerically using previously established analytical models. Subsequently, the peak column drifts and uplift angles are derived as functions of ground motion characteristics and the geometric and dynamic parameters of column-foundation system in regressed dimensionless forms. The proposed response models are further examined by validating against the numerical simulations for several as-built bridge cases. It is shown that the proposed model not only physically quantifies the influences of prominent parameters, but also consistently reflects the complex dynamics of the system. The seismic demands of rocking column-foundation system can be realistically predicted directly from structural and ground motion characteristics. This can significantly benefit the design of bridges incorporating this new design concept.     

Dynamic behaviour of R/C highway bridges under the combined effect of vertical and horizontal earthquake motions

Measurements of ground motions during past earthquakes indicate that the vertical acceleration can reach values comparable to horizontal accelerations or may even exceed these accelerations. Furthermore, measurements of structural response show the possibility of significant amplification in the response of bridges in the vertical direction that can be attributed to the vertical component of ground motion. In this study, the relative importance of the vertical component of ground motion on the inelastic response of R/C highway bridges is investigated. Particular emphasis is placed on modelling of the deck and piers to account for complex loading histories under combined vertical and horizontal earthquake motions. Analyses of actual bridges indicate that, in general, the vertical motion will increase the level of response and the amount of damage sustained by a highway bridge. Vertical motion generates fluctuating axial forces in the columns, which cause unstability of the hysteresis loops and increase the ductility demand. Furthermore, vertical motion can generate forces of high magnitude in the abutments and foundations that are not accounted for by the current seismic design guidelines. Thus, it is important to consider this component of the ground motion in the design of highway bridges, especially for those located in regions near seismic faults.     

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。     

Shake-table tests and numerical simulation of an innovative isolation system for highway bridges

Damage investigation of small to medium-span highway bridges in Wenchuan earthquake revealed that typical damage of these bridges included: sliding between laminated-rubber bearings and bridge girders, concrete shear keys failure, excessive girder displacements and even span collapse. However, the bearing sliding could actually act as a seismic isolation for piers, and hence, damage to piers for these bridges was minor during the earthquake. Based on this concept, an innovative solation system for highway bridges with laminated-rubber bearings is developed. The system is comprised of typical laminated-rubber bearings and steel dampers. Bearing sliding is allowed during an earthquake to limit the seismic forces transmitting to piers, and steel dampers are applied to restrict the bearing displacements through hysteretic energy dissipation. As a major part of this research, a quarter-scale, two-span bridge model was constructed and tested on the shake tables to evaluate the performance of this isolation system. The bridge model was subjected to a Northridge and an artificial ground motion in transverse direction. Moreover, numerical analyses were conducted to investigate the seismic performance of the bridge model. Besides the test bridge model, a benchmark model with the superstructure fixed to the substructure in transverse direction was also included in the numerical analyses. Both the experimental and the numerical results showed high effectiveness of this proposed isolation system in the bridge model. The system was found to effectively control the pier-girder relative displacements, and simultaneously, protect the piers from severe damage. Numerical analyses also validated that the existing finite element methods are adequate to estimate the seismic response of bridges with this isolation system.