Effect of vehicle bridge interaction on seismic response and fragility of bridges

This study focuses on understanding and evaluating the effect of vehicle bridge interaction (VBI) on the response and fragility of bridges subjected to earthquakes. A comprehensive study on the effect of VBI on bridge seismic performance is conducted, providing metamodels for seismic response and fragility estimates for bridges in the presence of various types of vehicles. For this purpose, the performance of multispan simply supported concrete girder bridges with varying design and geometric parameters is assessed with 3 different types of stationary trucks placed atop them. To delineate the effects of VBI and additional truck mass, the trucks are modeled in 2 different ways—with additional masses and suspension springs (ie, with VBI) and using additional masses only (without VBI). The results provide insight on VBI effects, such as the fact that when bridge and vehicle mode shapes are in‐phase, the component responses increase and vice versa; additionally, the presence of a heavy axle near a bent increases component responses. Sensitivity analyses are also performed to determine the bridge parameters that significantly alter the component responses in the presence of vehicles. Furthermore, differences in component responses and fragilities highlight that modeling vehicles with additional masses alone is not sufficient to model the effect of truck presence on the seismic response of bridges. Finally, this study concludes that depending on the characteristics of the bridge and the vehicle, presence of a vehicle atop the bridge during an earthquake may be either beneficial or detrimental to bridge performance.     

Seismic fragility analysis of bridges by relevance vector machine based demand prediction model

A relevance vector machine(RVM) based demand prediction model is explored for efficient seismic fragility analysis(SFA) of a bridge structure. The proposed RVM model integrates both record-to-record variations of ground motions and uncertainties of parameters characterizing the bridge model. For efficient fragility computation, ground motion intensity is included as an added dimension to the demand prediction model. To incorporate different sources of uncertainty, random realizations of differen...     

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.     

Multi‐angle,multi‐damage fragility curves for seismic assessment of bridges

The scope of this study is to investigate the effect of the direction of seismic excitation on the fragility of an already constructed, 99‐m‐long, three‐span highway overpass. First, the investigation is performed at a component level, quantifying the sensitivity of local damage modes of individual bridge components (namely, piers, bearings, abutments, and footings) to the direction of earthquake excitation. The global vulnerability at the system level is then assessed for a given angle of incidence of the earthquake ground motion to provide a single‐angle, multi‐damage probabilistic estimate of the bridge overall performance. A multi‐angle, multi‐damage, vulnerability assessment methodology is then followed, assuming uniform distribution for the angle of incidence of seismic waves with respect to the bridge axis. The above three levels of investigation highlight that the directivity of ground motion excitation may have a significant impact on the fragility of the individual bridge components, which shall not be a priori neglected. Most importantly, depending on the assumptions made for the component to the system level transition, this local sensitivity is often suppressed. It may be therefore necessary, based on the ultimate purpose of the vulnerability or the life cycle analysis, to obtain a comprehensive insight on the multiple damage potential of all individual structural and foundation components under multi‐angle excitation, to quantify the statistical correlation among the distinct damage modes and to identify the components that are both most critical and sensitive to the direction of ground motion and carefully define their limit states which control the predicted bridge fragility. Copyright © 2015 John Wiley & Sons, Ltd.     

Fractional order intensity measures for probabilistic seismic demand modeling applied to highway bridges

Probabilistic seismic analysis of structures involves the construction of seismic demand models, often stated as probabilistic models of structural response conditioned on a seismic intensity measure. The uncertainty introduced by the model is often a result of the chosen intensity measure. This paper introduces the concept of using fractional order intensity measures (IMs) in probabilistic seismic demand analysis and uses a single frame integral concrete box‐girder bridge class and a seismically designed multispan continuous steel girder bridge class as case studies. The fractional order IMs considered include peak ground response and spectral accelerations at 0.2 and 1.0 s considering a single degree of freedom system with fractional damping, , as well as a linear single degree of freedom system with fractional response, . The study reveals the advantage of fractional order IMs relative to conventional IMs such as peak ground acceleration, peak ground velocity, or spectral acceleration at 0.2 and 1.0 s. Metrics such as efficiency, sufficiency, practicality, and proficiency are measured to assess the optimal nature of fractional order IMs. The results indicate that the proposed fractional order IMs produce significant improvements in efficiency and proficiency, whereas maintaining practicality and sufficiency, and thus providing superior demand models that can be used in probabilistic seismic demand analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of seismic excitation direction on the fragility analysis of horizontally curved concrete bridges

The focus of this study is the impact of the seismic excitation direction on the fragility of horizontally curved bridges. Nonlinear time history analyses are performed on a typical, curved concrete bridge in China using a set of real ground motions with different incident angles. To build reliable probabilistic seismic demand models, ten commonly used intensity measures (IMs) are assessed in terms of various metrics to determine the optimal IMs, which account for the influence of the seismic excitation directions. Subsequently, fragility surfaces with respect to both the optimal IM and incident angles are generated to qualify the fragility sensitivity for various components and the bridge system to the seismic excitation directions. Moreover, the rationality and applicability of the methods recommended by the Caltrans, Eurocode 8 and Chinese codes for determining the seismic excitation direction of curved bridges are evaluated. The results indicate that the excitation direction imposes a minor impact on the optimal IM rankings. Compared to structure-independent IMs, structure-dependent IMs are more appropriate for predicting the demands of horizontally curved concrete bridges. However, the seismic excitation direction significantly affects the component fragilities, and the level of the effect intensifies with increasing limit states. If the incident angle occurrence probability is not provided, the Chinese code method for the seismic excitation direction is more suitable for the horizontally curved concrete bridge fragility assessment, which has the advantages of computational efficiency when compared to the Caltrans code and relatively conservative results when compared to Eurocode 8.     

Effects of structural characterizations on fragility functions of bridges subject to seismic shaking and lateral spreading

This paper evaluates the seismic vulnerability of different classes of typical bridges in California when subjected to seismic shaking or liquefaction-induced lateral spreading. The detailed structural configurations in terms of superstructure type, connection, continuity at support and foundation type, etc. render different damage resistant capability. Six classes of bridges are established based on their anticipated failure mechanisms under earthquake shaking. The numerical models that are capable of simulating the complex soil-structure interaction effects, nonlinear behavior of columns and connections are developed for each bridge class. The dynamic responses are obtained using nonlinear time history analyses for a suite of 250 earthquake motions with increasing intensity. An equivalent static analysis procedure is also implemented to evaluate the vulnerability of the bridges when subjected to liquefaction-induced lateral spreading. Fragility functions for each bridge class are derived and compared for both seismic shaking （based on nonlinear dynamic analyses） and lateral spreading （based on equivalent static analyses） for different performance states. The study finds that the fragility functions due to either ground shaking or lateral spreading show significant correlation with the structural characterizations, but differences emerge for ground shaking and lateral spreading conditions. Structural properties that will mostly affect the bridges＇ damage resistant capacity are also identified.     

铁路桥梁抗震规范与新版公路桥梁抗震规范的比较

2020年6月交通运输部发布了新版《公路桥梁抗震设计规范》（JTG/T 2231-01-2020）（简称"《公规》"）。本文比较了现行《铁路工程抗震设计规范》（GB 50111-2006）（2009年版）（以下简称"《铁规》"）与《公规》的抗震设计相关内容,并分别采用两本规范对25m墩高（D类）、35m墩高（C类）和40m墩高（B类）简支梁进行抗震设计,比较二者地震力和配筋设计结果差异。结果表明:《公规》和《铁规》的抗震设计框架和内容基本一致,在具体规定上如E2或罕遇地震设计最大加速度响应值以及桥墩强度和延性验算方法等方面不同;D类桥梁《铁规》地震力明显大于《公规》,C类和B类桥梁《铁规》和《公规》地震力相当;地震力相同时,《铁规》配筋率计算值大于《公规》,因《铁规》配筋设计基于容许应力法,而《公规》基于极限状态法。     

Vector-valued fragility functions for seismic risk evaluation

This article presents a method for the development of vector-valued fragility functions, which are a function of more than one intensity measure (IM, also known as ground-motion parameters) for use within seismic risk evaluation of buildings. As an example, a simple unreinforced masonry structure is modelled using state-of-the-art software and hundreds of nonlinear time-history analyses are conducted to compute the response of this structure to earthquake loading. Dozens of different IMs (e.g. peak ground acceleration and velocity, response spectral accelerations at various periods, Arias intensity and various duration and number of cycle measures) are considered to characterize the earthquake shaking. It is demonstrated through various statistical techniques (including Receiver Operating Characteristic analysis) that the use of more than one IM leads to a better prediction of the damage state of the building than just a single IM, which is the current practice. In addition, it is shown that the assumption of the lognormal distribution for the derivation of fragility functions leads to more robust functions than logistic, log-logistic or kernel regression. Finally, actual fragility surfaces using two pairs of IMs (one pair are uncorrelated while the other are correlated) are derived and compared to scalar-based fragility curves using only a single IM and a significant reduction in the uncertainty of the predicted damage level is observed. This type of fragility surface would be a key component of future risk evaluations that take account of recent developments in seismic hazard assessment, such as vector-valued probabilistic seismic hazard assessments.     

An earthquake-source-based metric for seismic fragility analysis

The seismic fragility of a system is the probability that the system enters a damage state under seismic ground motions with specified characteristics. Plots of the seismic fragilities with respect to scalar ground motion intensity measures are called fragility curves. Recent studies show that fragility curves may not be satisfactory measures for structural seismic performance, since scalar intensity measures cannot comprehensively characterize site seismicity. The limitations of traditional seismic intensity measures, e.g., peak ground acceleration or pseudo-spectral acceleration, are shown and discussed in detail. A bivariate vector with coordinates moment magnitude m and source-to-site distance r is proposed as an alternative seismic intensity measure. Implicitly, fragility surfaces in the (m, r)-space could be used as graphical representations of seismic fragility. Unlike fragility curves, which are functions of scalar intensity measures, fragility surfaces are characterized by two earthquake-hazard parameters, (m, r). The calculation of fragility surfaces may be computationally expensive for complex systems. Thus, as solutions to this issue, a bi-variate log-normal parametric model and an efficient calculation method, based on stochastic-reduced-order models, for fragility surfaces are proposed.     

Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground

Seismic intensity measures (IMs) perform a pivotal role in probabilistic seismic demand modeling. Many studies investigated appropriate IMs for structures without considering soil liquefaction potential. In particular, optimal IMs for probabilistic seismic demand modeling of bridges in liquefied and laterally spreading ground are not comprehensively studied. In this paper, a coupled-bridge-soil-foundation model is adopted to perform an in-depth investigation of optimal IMs among 26 IMs found in the literature. Uncertainties in structural and geotechnical material properties and geometric parameters of bridges are considered in the model to produce comprehensive scenarios. Metrics such as efficiency, practicality, proficiency, sufficiency and hazard computability are assessed for different demand parameters. Moreover, an information theory based approach is adopted to evaluate the relative sufficiency among the studied IMs. Results indicate the superiority of velocity-related IMs compared to acceleration, displacement and time-related ones. In particular, Housner spectrum intensity (HI), spectral acceleration at 2.0 s (S _a-20), peak ground velocity (PGV), cumulative absolute velocity (CAV) and its modified version (CAV ₅) are the optimal IMs. Conversely, Arias intensity (I _a ) and shaking intensity rate (SIR) which are measures often used in liquefaction evaluation or related structural demand assessment demonstrate very low correlations with the demand parameters. Besides, the geometric parameters do not evidently affect the choice of optimal IMs. In addition, the information theory based sufficiency ranking of IMs shows an identical result to that with the correlation measure based on coefficient of determination (R ²). This means that R ² can be used to preliminarily assess the relative sufficiency of IMs.     

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.     

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.     

Inelastic seismic response of stiffening systems and development of demand spectrum: Application to MSSS bridges

A stiffening system is a system that increases its stiffness as it goes under large displacements. Such behavioural characteristic can result from constitutive behaviour or at the structural level often from closure of gaps between various components (sub‐systems) of the structure. An example of the latter situation is multi‐span simply supported (MSSS) bridges under horizontal earthquake ground motion. Unlike softening systems, stiffening systems have not been studied. In addition to the need for more understanding of the seismic response of stiffening systems, there is a need to develop response spectrum that can be used in design. Several parameters including gap size and ratios of sub‐systems stiffness, strength, and mass control the behaviour of a stiffening system. In this study, a simplified stiffening model is developed and over 367 000 cases are analysed to investigate the nonlinear stiffening behaviour and pounding. Parameters considered also include ground motion characteristic. Results are evaluated and compared in terms of displacement and dissipated hysteretic energy. Parameter study results show that, on average, the displacement response is lower for stiffening systems, however, they dissipates higher hysteretic energy, due to higher yield cycles and yield excursions, and can possibly sustain more damage than a bilinear, elastic–plastic system. Using parameter study database, design response spectrum for stiffening systems is also proposed and its practical application is demonstrated through its application to an MSSS bridge. Results of this study goes beyond MSSS bridges and will have application for many structural systems where response is characterized by a stiffening behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

油浸式高压变压器地震易损性分析

油浸式变压器是由多种材料组成的复杂结构。本文对油浸式高压变压器建立了较为精确的有限元模型，考虑了各组件之间相互作用的影响。对该设备进行了动力性能和地震响应分析以及易损性分析。分析结果表明，大型高压变压器在地震中的首要破坏模式为瓷套破坏，其地震响应的离散度较高。易损性分析得到设备的地震易损性曲线，可直接应用于电力系统的抗震分析。     

Comparison of seismic fragility analysis methods for arch dams

This study focuses on the seismic fragility analysis of arch dams. The multiple stripe analysis(MSA), cloud analysis(CLA), and incremental dynamic analysis(IDA) methods are compared. A comprehensive dam-reservoir-foundation rock system, which considers the opening of contraction joints, the nonlinearity of dam concrete and foundation rock, the radiation damping effect of semi-unbounded foundation, and the compressibility of reservoir water, is used as a numerical example. 225, 80, and 15 earthqu...     

地震易损性分析方法研究综述

结构的地震易损性分析对于预测结构的抗震性能、进行结构的抗震设计、加固和维修决策具有重要的应用价值。本文将对近几十年来地震易损性评估方法领域内的重大发展做全面综述,并对易损性分析方法的类别和优缺点及其应用作了总结和讨论。     

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.     

Analytical seismic fragility functions for highway and railway embankments and cuts

A fundamental tool in seismic risk assessment of transportation systems is the fragility curve, which describes the probability that a structure will reach or exceed a certain damage state for a given ground motion intensity. Fragility curves are usually represented by two‐parameter (median and log‐standard deviation) cumulative lognormal distributions. In this paper, a numerical approach, in the spirit of the IDA, is applied for the development of fragility curves for highways and railways on embankments and in cuts due to seismic shaking. The response of the geo‐construction to increasing levels of seismic intensity is evaluated using a 2D nonlinear finite element 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 to the soil strain level. The effect of soil conditions and ground motion characteristics on the response of the embankment and cut is taken into account considering different typical soil profiles and seismic input motions. This study will provide input for the assessment of the vulnerability of the road/railway network regarding the performance of the embankments and cuts; therefore, the level of damage is described in terms of the permanent ground displacement in these structures. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity, which is described by PGA. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the element's geometry, the input motion, and the soil properties as well as the associated uncertainties. A relationship between the computed permanent ground displacement on the surface of the embankment and the PGA in the free field is also suggested based on the results of the numerical analyses. Finally, the proposed fragility curves are compared with existing empirical data and the limitations of their applicability are outlined. Copyright © 2015 John Wiley & Sons, Ltd.