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.     

Seismic fragility assessment of low-rise stone masonry buildings

Many historic buildings in old urban centers in Eastern Canada are made of stone masonry reputed to be highly vulnerable to seismic loads.Seismic risk assessment of stone masonry buildings is therefore the first step in the risk mitigation process to provide adequate planning for retrofit and preservation of historical urban centers.This paper focuses on development of analytical displacement-based fragility curves reflecting the characteristics of existing stone masonry buildings in Eastern Canada.The old historic center of Quebec City has been selected as a typical study area.The standard fragility analysis combines the inelastic spectral displacement,a structure-dependent earthquake intensity measure,and the building damage state correlated to the induced building displacement.The proposed procedure consists of a three-step development process:(1) mechanics-based capacity model,(2) displacement-based damage model and(3) seismic demand model.The damage estimation for a uniform hazard scenario of 2% in 50 years probability of exceedance indicates that slight to moderate damage is the most probable damage experienced by these stone masonry buildings.Comparison is also made with fragility curves implicit in the seismic risk assessment tools Hazus and ELER.Hazus shows the highest probability of the occurrence of no to slight damage,whereas the highest probability of extensive and complete damage is predicted with ELER.This comparison shows the importance of the development of fragility curves specific to the generic construction characteristics in the study area and emphasizes the need for critical use of regional risk assessment tools and generated results.     

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.     

A simplified method of constructing fragility curves for highway bridges

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic fragility of lightly reinforced concrete frames with masonry infills

Seismic fragility of lightly reinforced concrete frames with masonry infills is assessed through numerical simulations considering uncertainty in ground motion and building materials. To achieve this aim, a numerical model of the components is developed, a rational approach to proportion and locate individual struts in the equivalent three‐strut model is proposed, and an explicit nonlinear column shear response model accounting for the infill–column interaction and soft‐story mechanism is employed. The proposed numerical model is used to (1) generate probabilistic seismic demand models accounting for a wide range of ground motion intensities with different frequency content and (2) determine limit state models obtained from nonlinear pushover analysis and incremental dynamic analysis. Using the demand and limit state model, fragility curves for the masonry‐infilled frames are developed to investigate the impact of various infill properties on the frame vulnerability. It is observed that the beneficial effect of the masonry infill diminishes at more severe limit states because of the interaction with the boundary frame. In some cases, this effect almost vanishes or switches to an adverse effect beyond a threshold of ground motion intensities. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic fragility curves of shallow tunnels in alluvial deposits

In this paper a numerical approach is proposed for the construction of fragility curves for shallow metro tunnels in alluvial deposits, when subjected to transversal seismic loading. The response of the tunnel is calculated under quasi static conditions applying the induced seismic ground deformations which are calculated through 1D equivalent linear analysis for an increasing level of seismic intensity. The results of the present numerical analyses are compared with selected closed form solutions, highlighting the limitations of the latter, while indicative full dynamic analysis are performed in order to validate the results of the quasi-static method. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the tunnel geometries and strength characteristics, the input motion and the soil properties as well as the associated uncertainties. The comparison between the new fragility curves and the existing empirical ones highlights the important role of the local soil conditions, which is not adequately taken into account in the empirical curves.     

Seismic fragility assessment of highway bridges using support vector machines

Seismic fragility curves provide a powerful tool to assess the reliability of structures. However, conventional fragility analysis of structures comprising a large number of components requires enormous computational efforts. In this paper, the application of probabilistic support vector machines (PSVM) for the system fragility analysis of existing structures is proposed. It is demonstrated that support vector machine based fragility curves provide accurate predictions compared to rigorous methodologies such as component based fragilities developed by Monte Carlo simulations. The proposed method is applied to an existing bridge structure in order to develop fragility curves for serviceability and collapse limit states. In addition, the efficiency of using the PSVM method in the application of vector-valued ground motion intensity measures (IM) as well as traditional single-valued IM are investigated. The results obtained from an incremental dynamic analysis of the structure are used to train PSVMs. The application of PSVM in binary and multi-class classifications is used for the fragility analysis and reliability assessment of the bridge structure.     

Methodology for the development of analytical fragility curves for retrofitted bridges

Fragility curves for retrofitted bridges indicate the influence of various retrofit measures on the probability of achieving specified levels of damage. This paper presents an analytical methodology for developing fragility curves for classes of retrofitted bridge systems. The approach captures the impact of retrofit on the vulnerability of multiple components, which to date has not been adequately addressed, and results in a comparison of the system fragility before and after the application of different retrofit measures. Details presented include analytical modeling, uncertainty treatment, impact of retrofit on demand models, capacity estimates, and component and system fragility curves. The findings indicate the importance of evaluating the impact of retrofit not only on the targeted response quantity and component vulnerability but also on the overall bridge fragility. As illustrated by the case study of a retrofitted multi‐span continuous (MSC) concrete girder bridge class, a given retrofit measure may have a positive impact on some components, yet no impact or a negative impact on other critical components. Consideration of the fragility based only on individual retrofitted components, without regard for the system, may lead to over‐estimation or under‐estimation of the impact on the bridge fragility. The proposed methodology provides an opportunity to effectively compare the fragility of the MSC concrete bridge retrofit with a range of different retrofit measures. The most effective retrofit in reducing probable damage for a given intensity is a function of the damage state of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

基于增量动力分析方法的砌体结构地震易损性分析

砌体结构是一种脆性结构,变形能力和承载力均较低,因取材方便、施工简单和造价低等优势在中国被广泛应用。为了评估砌体结构的抗震性能,本文基于增量动力分析（Incremental Dynamic Analysis,IDA）方法研究了多层砌体结构的地震易损性,分析了影响砌体结构地震易损性的主要因素以及群体多层砌体结构地震易损性。研究结果表明:在相同场地条件情况下,砌体结构的房屋层数、砌筑砂浆强度、设防烈度和墙体面积率对结构的地震易损性影响较明显;当结构层高在2.8~3.3 m之间时,层高对结构地震易损性的影响不大。抗震设防砌体结构抗震能力比不设防结构有明显提高,说明构造柱和圈梁等构造措施能显著提高砌体结构的抗倒塌能力,这与目前的基本认识相同,也证明了增量动力分析方法的有效性。     

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.     

Seismic fragility of reinforced concrete girder bridges using Bayesian belief network

Infrastructure owners and operators, or governmental agencies, need rapid screening tools to prioritize detailed risk assessment and retrofit resources allocation. This paper provides one such tool, for use by highway administrations, based on Bayesian belief network (BBN) and aimed at replacing so‐called generic or typological seismic fragility functions for reinforced concrete girder bridges. Resources for detailed assessments should be allocated to bridges with highest consequence of damage, for which site hazard, bridge fragility, and traffic data are needed. The proposed BBN based model is used to quantify seismic fragility of bridges based on data that can be obtained by visual inspection and engineering drawings. Results show that the predicted fragilities are of sufficient accuracy for establishing relative ranking and prioritizing. While the actual data and seismic hazard employed to train the network (establishing conditional probability tables) refer to the Italian bridge stock, the network structure and engineering judgment can easily be adopted for bridges in different geographical locations. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic vulnerability assessment and fragility analysis of pre-code masonry buildings in Portugal

Bulletin of Earthquake Engineering - Despite the fact that in recent years Portugal has not seen the occurrence of high-magnitude earthquakes, it remains threatened by these events due to its...     

Seismic fragility assessment of nonstructural components in unreinforced clay brick masonry buildings

The results of an investigation of the probability of earthquake damage to nonstructural unreinforced masonry (URM) components are presented. The components include parapets, chimneys, and out-of-plane loaded facades typical of low-rise pre-1940 construction in Australia and New Zealand. The study is based on a street survey of component geometry, in situ data on material strength, and simplified mechanical models. Uncertainties in capacity and demand were quantified based on, respectively, stochastic and deterministic approaches. The damage probabilities were compared with relevant guidelines and empirical damage data from three earthquakes. The study established a link between the qualitative damage states reported in existing guidelines and the quantitative URM component damage states. While some median damage state thresholds correlated well with the data from the guidelines, a larger dispersion value was found in the current study due to the large variations in component properties. Comparisons with empirical data suggest that the developed fragility data provide a realistic estimate of nonstructural component damage that occurred in similar buildings, with a reasonable level of conservatism. The outcome is useful in rapid assessment of the seismic risks due to nonstructural component collapse in URM precincts.     

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.     

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.     

Effect of isolation on fragility curves of highway bridges based on simplified approach

The trend of isolating highway bridges is on the rise after the recent large earthquakes in Japan, the United States, and other countries. Recent investigation shows that isolated systems perform well against seismic forces as the substructures of such systems experience less lateral forces due to energy dissipation of the isolation device. Hence, it is anticipated that there might be an effect on fragility curves of highway bridges due to isolation. In this study, 30 isolated bridge models were considered (and they were designed according to the seismic design code of highway bridges in Japan) to have a wider range of the variation of structural parameters, e.g. pier heights, weights, and over-strength ratio of structures. Then, fragility curves were developed by following a simplified procedure using 250 strong motion records, which were selected from 5 earthquake events that occurred in Japan, the USA, and Taiwan. It is observed that the level of damage probability for the isolated system is less than that of the non-isolated one for a lower level of pier height. However, having the same over-strength ratio of the structures, the level of damage probability for the isolated system is found to be higher for a higher level of pier height compared to the one of the non-isolated system. The proposed simple approach may conveniently be used in constructing fragility curves for a class of isolated bridge structures in Japan that have similar characteristics.     

Seismic fragility assessment of integral precast multi-span bridges in areas of moderate seismicity

In lack of seismic provisions in the pre-Eurocode ages, most of the existing Hungarian bridges were not designed for seismic actions, therefore their seismic performance is questionable. The most commonly used structural type in highway construction is the integral precast multi-girder bridge. These bridges are typically constructed as continuous multi-support systems with monolithic joints at each support, thus their behavior may be significantly different from those applying simply supported beams and conventional bearings. A parametric fragility analysis of a wide range of different layouts is carried out using detailed and advanced non-linear numerical models. The results indicate that the abutment joints are highly vulnerable and piers are also critical for longer bridges. The study implies that without seismic design, integral precast multi-girder bridges are highly susceptible to pier shear failure, the probability of collapse is relatively high. The results also provide a solid basis for retrofit planning as well as for development of design concepts of newly built structures in moderate seismic zones.     

大跨度钢管混凝土拱桥抗震性能指标研究

高轴压比钢管混凝土墩柱的试验结果对钢管混凝土拱肋具有较大的借鉴意义。为明确大跨度钢管混凝土拱桥的抗震性能指标,研究了高轴比钢管混凝土构件的破坏过程及延性性能。以弯矩作为性能指标将高轴压比钢管混凝土构件的试验破坏过程分为轻微损伤、有限损伤与严重损伤3个阶段,结合钢管混凝土截面性能状态的数值分析,探讨了高轴压比钢管混凝土构件的破坏机理。结果表明:高轴压比钢管混凝土构件具有一定的可用延性;提出了以计算等效屈服弯矩作为抗震性能指标,适当利用延性和实现钢管混凝土拱桥的有限损伤抗震设计,并给出了与有限损伤相关的截面性能状态及参数。研究成果弥补了规范在此方面的不足,可供高烈度地震区大跨度钢管混凝土拱桥抗震设计时参考。