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.     

Effect of the angle of seismic incidence on the fragility curves of bridges

This study examines the effect of the angle of seismic incidence θ on the fragility curves of bridges. Although currently, fragility curves of bridges are usually expressed only as a function of intensity measure of ground motion (IM) such as peak ground acceleration, peak ground velocity, or S_a(ω₁), in this study they are expressed as a function of IM with θ as a parameter. Lognormal distribution function is used for this purpose with fragility parameters, median c_m and standard deviation ζ to be estimated for each value of θ chosen from 0 < θ < 360°. A nonlinear 3D finite element dynamic analysis is performed, and key response values are calculated as demand on the bridge under a set of acceleration time histories with different IM values representing the seismic hazard in Los Angeles area. This method is applied to typical straight reinforced concrete bridges located in California. The results are validated with existing empirical damage data from the 1994 Northridge earthquake. Even though the sample bridges are regular and symmetric with respect to the longitudinal axis, the results indicate that the weakest direction is neither longitudinal nor transverse. Therefore, if the angle of seismic incidence is not considered, the damageability of a bridge can be underestimated depending on the incidence angle of seismic wave. Because a regional highway transportation network is composed of hundreds or even thousands of bridges, its vulnerability can also be underestimated. Hence, it is prudent to use fragility curves taking the incident angle of seismic waves into consideration as developed here when the seismic performance of a highway network is to be analyzed. Copyright © 2012 John Wiley & Sons, Ltd.     

横桥向地面运动作用下独塔部分斜拉桥易损性分析

桥梁作为交通生命线系统中的重要工程,屡次在中等强度地震的作用下,遭受严重破坏甚至整体损毁,因此桥梁结构地震易损性研究在世界各国得到重视和发展。部分斜拉桥作为一种新桥型,由于兼有经济性和美学特性,近十年来在国内外发展迅速,但这种新桥型尚未经受地震的考验,在可能的地震灾害下,部分斜拉桥的地震破坏损伤概率还不明确,有必要开展有关的易损性研究。本文在桥梁地震易损性研究的基础上,分析在横桥向地面运动作用下独塔部分斜拉桥的易损性,定义五级损伤极限状态,建立桥墩、桥塔、限位器和全桥的易损性曲线,研究结果表明在横桥向地面运动作用下,独塔部分斜拉桥全桥易损性主要受到限位器和中墩的控制。     

Seismic fragility methodology for highway bridges using a component level approach

Bridge fragility curves, which express the probability of a bridge reaching a certain damage state for a given ground motion parameter, play an important role in the overall seismic risk assessment of a transportation network. Current analytical methodologies for generating bridge fragility curves do not adequately account for all major contributing bridge components. Studies have shown that for some bridge types, neglecting to account for all of these components can lead to a misrepresentation of the bridges' overall fragilities. In this study, an expanded methodology for the generation of analytical fragility curves for highway bridges is presented. This methodology considers the contribution of the major components of the bridge, such as the columns, bearings and abutments, to its overall bridge system fragility. In particular, this methodology utilizes probability tools to directly estimate the bridge system fragility from the individual component fragilities. This is illustrated using a bridge whose construction and configuration are typical to the Central and Southeastern United States and the results are presented and discussed herein. This study shows that the bridge as a system is more fragile than any one of the individual components. Assuming that the columns represent the entire bridge system can result in errors as large as 50% at higher damage states. This provides support to the assertion that multiple bridge components should be considered in the development of bridge fragility curves. The findings also show that estimation of the bridge fragilities by their first‐order bounds could result in errors of up to 40%. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

A performance-based adaptive methodology for the seismic evaluation of multi-span simply supported deck bridges

A performance-based adaptive methodology for the seismic assessment of highway bridges is proposed. The proposed methodology is based on an Inverse (I), Adaptive (A) application of the Capacity Spectrum Method (CSM), with the capacity curve of the bridge derived through a Displacement-based Adaptive Pushover (DAP) analysis. For this reason, the acronym IACSM is used to identify the proposed methodology. A number of Performance Levels (PLs), for which the seismic vulnerability and seismic risk of the bridge shall be evaluated, are identified. Each PL is associated to a number of Damage States (DSs) of the critical members of the bridge (piers, abutments, joints and bearing devices). The IACSM provides the earthquake intensity level (PGA) corresponding to the attainment of the selected DSs, using over-damped elastic response spectra as demand curves. The seismic vulnerability of the bridge is described by means of fragility curves, derived based on the PGA values associated to each DS. The seismic risk of the bridge is evaluated as convolution integral of the product between the fragility curves and the seismic hazard curve of the bridge site. In this paper, the key aspects and basic assumptions of the proposed methodology are presented first. The IACSM is then applied to nine existing simply supported deck bridges, characterized by different types of piers and bearing devices. Finally, the IACSM predictions are compared with the results of nonlinear response time-history analysis, carried out using a set of seven ground motions scaled to the expected PGA values.     

Seismic risk assessments and GIS technology: applications to infrastructures in the Friuli–Venezia Giulia region (NE Italy)

This paper illustrates the seismic risk preliminary estimates of two different groups of structures located on the territory of the Friuli–Venezia Giulia region (NE Italy) : the first group includes some special industrial plants, and the second group includes bridges and tunnels belonging to the regional highway network. The part of the study on special industrial plants tries to evaluate the degree of expected damage, taking into account their structural typology and ground shaking expressed in terms of macroseismic intensity. The second part of the study is an application of the HAZUS methodology to the tunnels and bridges of a highway network: the combination of expected ground shaking and the construction characteristics lead to very different risk levels, especially when considering the bridges. The resulting damage levels to bridges and tunnels are still only indicative because of the fragility curves used in the evaluations: they were developed for existing bridge and tunnel structural typologies in the U.S.A. Moreover, both examples show the power of GIS technology in storing, elaborating, and mapping spatial data. Copyright © 2003 John Wiley & Sons, Ltd.     

Analytical fragility analysis of southern Illinois wall pier supported highway bridges

An analytical fragility analysis was conducted in order to characterize the seismic vulnerability of existing southern Illinois wall pier supported highway bridges to potential earthquakes. To perform this fragility analysis, a detailed inventory survey was first taken of the wall pier bridges identified in an earlier random sampling of southern Illinois priority emergency route bridges. From the survey three types of wall pier bridges were identified. Of those identified, hammerhead and regular wall pier supported bridges represented nearly 90% of the population. Incorporating structural variations determined from the random sample survey, nearly 100 three‐dimensional nonlinear finite element models were constructed. Each model was subjected to a randomly assigned synthetic earthquake representative of those that could potentially occur within the region. From these analyses, a series of wall pier supported bridge fragility curves were produced. In addition, a liquefaction fragility analysis was conducted in order to characterize the seismic vulnerability of southern Illinois wall pier supported highway bridge sites to liquefaction in potential earthquakes. To perform this second fragility analysis, wall pier bridges within the southern Illinois random sample that may be susceptible to liquefaction were identified. A soil profile from each of these susceptible bridge sites was then subjected to randomly assigned bedrock motions, and an Arias intensity liquefaction analysis was carried out. From these analyses, a fragility curve for the potentially liquefiable wall pier supported bridge sites was produced. Overall results of this study indicate that southern Illinois wall pier supported bridges are moderately vulnerable to structural damage in a 2% probability of exceedance in 50 year earthquake, and in some cases they could also be highly vulnerable to on‐site liquefaction events. Copyright © 2009 John Wiley & Sons, Ltd.     

Development of fragility functions for geotechnical constructions: Application to cantilever retaining walls

Fragility curves constitute an emerging tool for the seismic risk assessment of all constructions at risk. They describe the probability of a structure being damaged beyond a specific damage state for various levels of ground shaking. They are usually represented as two-parameter (median and log-standard deviation) cumulative lognormal distributions. In this paper a numerical approach is proposed for the construction of fragility curves for geotechnical constructions. The methodology is applied to cantilever bridge abutments on surface foundation often used in road and railway networks. The response of the abutment to increasing levels of seismic intensity is evaluated using a 2D nonlinear FE model, with an elasto-plastic criterion to simulate the soil behavior. A calibration procedure is followed in order to account for the dependency of both the stiffness and the damping on the soil strain level. The effect of soil conditions and ground motion characteristics on the global soil and structural response is taken into account considering different typical soil profiles and seismic input motions. The objective is to assess the vulnerability of the road network as regards the performance of the bridge abutments; therefore, the level of damage, is described in terms of the range of settlement that is observed on the backfill. The effect of backfill material to the overall response of the abutment wall is also examined. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the structure geometry, the input motion and the soil properties as well as the associated uncertainties. The proposed fragility curves are verified based on observed damage during the 2007 Niigata-Chuetsu Oki earthquake.     

Fragility curves of concrete bridges retrofitted by column jacketing

The Northridge earthquake inflicted various levels of damage upon a large number of Caltrans’ bridges not retrofitted by column jacketing. In this respect, this study represents results of fragility curve development for two (2) sample bridges typical in southern California, strengthened for seismic retrofit by means of steel jacketing of bridge columns. Monte Carlo simulation is performed to study nonlinear dynamic responses of the bridges before and after column retrofit. Fragility curves in this study are represented by lognormal distribution functions with two parameters and developed as a function of PGA. The sixty (60) ground acceleration time histories for the Los Angeles area developed for the Federal Emergency Management Agcncy (FEMA) SAC (SEAOC-ATC-CUREe) steel project are used for the dynamic analysis of the bridges. The improvement in the fragility with steel jacketing is quantified by comparing fragility curves of the bridge before and after column retrofit. In this first attempt to formulate the problem of fragility enhancement, the quantification is made by comparing the median values of the fragility curves before and after the retrofit. Under the hypothesis that this quantification also applies to empirical fragility curves developed on the basis of Northridge earthquake damage, the enhanced version of the empirical curves is developed for the ensuing analysis to determine the enhancement of transportation network performance due to the retrofit. Supported by: MCEER/FHWA under Contract No.DTFH 61-98-C-00094 and Caltrans under Contract No.59A0304     

Statistical determination of significant curved I-girder bridge seismic response parameters

Curved steel bridges are commonly used at interchanges in transportation networks and more of these structures continue to be designed and built in the United States. Though the use of these bridges continues to increase in locations that experience high seismicity, the effects of curvature and other parameters on their seismic behaviors have been neglected in current risk assessment tools. These tools can evaluate the seismic vulnerability of a transportation network using fragility curves. One critical component of fragility curve development for curved steel bridges is the completion of sensitivity analyses that help identify influential parameters related to their seismic response. In this study, an accessible inventory of existing curved steel girder bridges located primarily in the Mid-Atlantic United States (MAUS) was used to establish statistical characteristics used as inputs for a seismic sensitivity study. Critical seismic response quantities were captured using 3D nonlinear finite element models. Influential parameters from these quantities were identified using statistical tools that incorporate experimental Plackett-Burman Design (PBD), which included Pareto optimal plots and prediction profiler techniques. The findings revealed that the potential variation in the influential parameters included number of spans, radius of curvature, maximum span length, girder spacing, and cross-frame spacing. These parameters showed varying levels of influence on the critical bridge response.     

Seismic fragility curves of as-built single-span masonry arch bridges

Masonry arch bridges are crucial elements in the railway transportation network throughout Europe. Although significant advances in seismic risk assessment of various bridge types have been made by developing fragility curves of generalized classes of structures, there are no comparable tools for masonry arch structures. In this context, this paper presents the construction of seismic fragility curves of single-span masonry bridges according to the limit analysis method. An iterative procedure is implemented to define the capacity curve of the equivalent single degree of freedom system through non-linear kinematic analysis. The process involves determination of the collapse mechanism, calculation of the limit load multiplier, and definition of the thrust line. The intrinsic variability of the seismic action is incorporated with the use of different sets of elastic spectra compatible with EC 8 Type-1 spectrum for various types of soil, with peak ground acceleration varying over the range 0.05–1.5 g. The fragility curves of the generalized classes of single-span masonry bridges are finally obtained from the effective ranges of the main geometric and material parameters affecting arch bridge capacity.     

斜交连续刚构桥桥墩地震易损性分析

以美国西部地区某斜交公路连续刚构桥为研究对象，研究其不等高墩易损性差异以及斜交角的改变对桥墩地震易损性的影响。考虑桥梁结构参数和地震动的不确定性，选取100条地震动，沿纵桥向输入，生成"结构-地震动"样本库，以地震动峰值加速度（PGA）为强度指标（IM），利用OpenSees软件对结构进行非线性时程分析得到桥墩动力响应，而后以桥墩曲率延性比衡量桥梁破坏状态，在确定桥墩损伤指标的基础上，采用可靠度理论得到各桥墩的地震易损性曲线，判断桥墩的损伤模式、损伤特点。在此基础上，改变桥梁斜交角度进行易损性分析，得到斜交角变化对桥墩地震易损性的影响。研究表明：该桥最矮墩发生损伤的概率大于其他桥墩，桥墩最先进入塑性的是墩顶和墩底区域；不同斜交角对桥墩的地震响应影响显著，各墩损伤破坏排序与斜交桥结构构造特点有关，同一排架墩的两侧墩柱易损性呈现与角度变化趋势相反的排列，损伤越严重，趋势越明显；对于此不等高的斜交刚构桥，最矮墩为其抗震薄弱环节，斜交角越大，越应该关注钝角处矮墩的损伤情况，并提高其设计标准，在进行斜交刚构桥抗震设计中应予以重视。     

基于高斯过程模型的桥梁时变系统地震易损性分析

桥梁在长期服役过程中面临的氯离子侵蚀作用会导致材料性能退化,进而影响桥梁结构的抗震性能。准确评估服役桥梁的抗震性能可以有效保障和提高桥梁结构的安全性,因此开展考虑时变效应的桥梁地震易损性分析非常必要。考虑到地震易损性分析涉及大量的动力时程分析,计算效率很低,故采用高斯过程模型取代耗时的动力时程分析,旨在提高地震易损性分析效率。以一座三跨连续梁桥为例,探究氯离子侵蚀作用下桥墩材料性能的退化规律,建立纵筋、箍筋以及保护层和核心混凝土材料性能退化时变曲线;基于高斯过程模型和联合概率地震需求模型,建立桥梁系统在不同服役年限下的易损性曲线和曲面。结果表明：(1)氯离子侵蚀作用明显降低了桥墩钢筋混凝土材料的强度;(2)氯离子侵蚀作用明显提高了高等级损伤的桥梁地震易损性,结构更容易发生高等级损伤。     

Vector-intensity measure based seismic vulnerability analysis of bridge structures

This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure(v IM), which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa(T1) and Sa(T2) are chosen as v IM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on v IM is studied with DunnettSobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to v IM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.     

考虑主余震作用的近海桥墩时变地震易损性分析

基于OpenSEES平台,以某近海刚构桥桥墩为例,选取符合场地类型的地震波,并根据地震记录构造主余震序列。运用"能力需求比"分析方法建立不同服役时间节点桥墩控制截面在不同损伤状态条件下的地震易损性曲线,研究氯离子侵蚀和主余震序列对桥墩抗震性能的影响。结果表明:同一损伤状态的超越概率随着服役时间延长和PGA增大而不断变大,且随着损伤状态等级提高,超越概率逐渐降低。轻微损伤状态下,主余震序列对桥墩易损性影响较小;中等损伤、严重破坏和完全倒塌状态下,同一服役期,考虑主余震序列作用下桥墩的超越概率相比于仅考虑主震作用明显增大。     

隔震与非隔震支座对混凝土箱梁桥地震易损性的影响

为评估隔震和非隔震支座对桥梁地震易损性的影响,以一座3跨连续混凝土箱梁桥为分析对象,首先建立采用铅芯橡胶隔震支座与非隔震型盆式橡胶支座下桥梁的数值模型,求得不同程度地震作用下墩顶与支座的最大位移响应;再定义转角延性比损伤指标,结合支座剪应变,分析桥墩和支座的地震易损性情况;最后通过宽界限法建立全桥地震易损性曲线。研究结果表明,支座是较容易发生损坏的构件,而桥梁系统比桥墩或支座更易发生破坏,同时铅芯橡胶支座的破坏概率明显低于非隔震型盆式支座,可见采用隔震支座能有效减小桥墩墩顶在地震作用下的最大位移,此时桥墩地震易损性优于采用非隔震支座的情况。     

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.     

The seismic performance of braced timber pile bents

The seismic performance of timber bridge substructures is not well established, particularly when compared to concrete highway bridges. This paper presents a dual experimental‐computational modelling program to investigate the seismic behaviour of typical braced timber bridge pile bents. For this purpose, a prototype timber bridge was used to develop a near‐full‐size physical model that was used for shaking table experiments and quasi‐static reversed cyclic loading tests on the laboratory strong‐floor. A non‐linear force‐displacement computational modelling study was also undertaken as a companion effort to the experimental investigation. On the basis of the experimental study, seismic vulnerability analysis was conducted for this kind of timber bridge principally with shaking in the transverse direction. In this analysis, a simplified fundamental mechanics‐based approach was employed from which fragility curves were derived. The study showed that braced timber pile bents have considerable strength and deformability capability. Nevertheless, they are not immune from earthquake damage. Copyright © 2003 John Wiley & Sons, Ltd.     

RC jacketing parameters to retrofit highway bridges

Highway bridges are essential structures in the transportation system of any country in the world. Many highway bridges are reinforced concrete (RC) bridges that were constructed before the 1980s, prior to current seismic regulation codes. The continuous modification of regulation codes makes it necessary to evaluate structures, and in many cases, existing bridges require interventions to increase their seismic capacity. Among the different techniques used to improve bridge capacity, encasing the columns with RC jackets increases the strength and stiffness of the substructure. RC jacketing increases the column cross sections, improves the seismic capacity and reduces the seismic vulnerability of the bridge substructures. This work presents a parametric study to assess the expected demands of seismically deficient medium length highway bridges retrofitted with RC jacketing aimed at determining the best jacket parameters. A suite of twenty strong ground motions, recorded from a subduction seismic source close to the Pacific Coast in Mexico, was selected to characterize the seismic demand. The bridge superstructures are simply supported with five 30 m long spans for a total length of 150 m. The bridge models have five possible pier heights of 5, 10, 15 20 and 25 m and three different jacket thicknesses and steel ratios. Pushover analyses and capacity spectra of the family of accelerograms allow for the determination of the pier demands by obtaining the performance point as the intersection of the capacity and demand curves. The results allow for the determination of the influence of each parameter on the expected seismic behavior of the bridge models, with the aim of selecting the most suitable jacket characteristics to improve the seismic bridge performance.