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     

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.     

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.     

Methodology for the development of bridge‐specific fragility curves

A new methodology for the development of bridge‐specific fragility curves is proposed with a view to improving the reliability of loss assessment in road networks and prioritising retrofit of the bridge stock. The key features of the proposed methodology are the explicit definition of critical limit state thresholds for individual bridge components, with consideration of the effect of varying geometry, material properties, reinforcement and loading patterns on the component capacity; the methodology also includes the quantification of uncertainty in capacity, demand and damage state definition. Advanced analysis methods and tools (nonlinear static analysis and incremental dynamic response history analysis) are used for bridge component capacity and demand estimation, while reduced sampling techniques are used for uncertainty treatment. Whereas uncertainty in both capacity and demand is estimated from nonlinear analysis of detailed inelastic models, in practical application to bridge stocks, the demand is estimated through a standard response spectrum analysis of a simplified elastic model of the bridge. The simplified methodology can be efficiently applied to a large number of bridges (with different characteristics) within a road network, by means of an ad hoc developed software involving the use of a generic (elastic) bridge model, which derives bridge‐specific fragility curves. Copyright © 2016 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.     

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.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of seismic retrofit of bridges on transportation networks

The objective of this research is to determine the effect earthquakes have on the performance of transportation network systems. To do this, bridge fragility curves, expressed as a function of peak ground acceleration (PGA) and peak ground velocity (PGV), were developed. Network damage was evaluated under the 1994 Northridge earthquake and scenario earthquakes. A probabilistic model was developed to determine the effect of repair of bridge damage on the improvement of the network performance as days passed after the event. As an example, the system performance degradation measured in terms of an index, “Drivers Delay,“ is calculated for the Los Angeles area transportation system, and losses due to Drivers Delay with and without retrofit were estimated.     

Developing collapse fragility curves for base-isolated buildings

Seismic isolation technique is increasingly used both for the design of new buildings and for the seismic retrofit of existing buildings. Nevertheless, so far, little attention has been paid on the collapse capacity of these structures, mainly because it requires refined nonlinear models and careful consideration of different sources of uncertainties. To fill this gap, a set of collapse fragility functions for existing reinforced concrete-frame buildings, designed for gravity loads only and then retrofitted with different isolation systems (including rubber-based and friction-based isolation systems), are derived in this study. For completeness, buildings with low and high seismic resistance are also considered. Collapse fragility functions are derived through incremental dynamic analysis, considering different collapse conditions both for isolation system and superstructure. For each case study building, mean and dispersion values are obtained considering both aleatory and epistemic uncertainties, due to record-to record and model variability, respectively. Finally, some comments on the possible use of the results of this study for practical applications are made.     

Spectral and fragility evaluations of retrofitted structures through strength reduction and enhanced damping

A retrofit procedure for existing buildings called the "weakening and damping technique" (WED) is presented in this paper. Weakening of structures can limit the maximum response accelerations during severe ground motions, but leads to an increase in the displacements or inter-story drifts. Added damping by using viscous dampers, on the other hand, reduces the inter-story drifts and has no significant effect on total accelerations, when structures behave inelastically. The weakening and damping technique addresses the two main causes for both structural and nonstructural damage in structures. The weakening retrofit is particularly suitable for structures that have overstressed components and weak brittle components. In this paper, the advantages of the WeD are verified by nonlinear dynamic analysis and simplified spectral approach that has been modified to fit structures with additional damping devices. A hospital structure located in the San Femando Valley in California is selected as a case study. The results from both analyses show that the retrofit solution is feasible to reduce both structural acceleration and displacement. A sensitivity analysis is also carried out to evaluate the effectiveness of the retrofitting method using different combinations of performance thresholds in accelerations and displacements through fragility analysis.     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method

This study presents a seismic fragility analysis and ultimate spectral displacement assessment of regular low-rise masonry infilled (MI) reinforced concrete (RC) buildings using a coefficient-based method. The coefficient-based method does not require a complicated finite element analysis; instead, it is a simplified procedure for assessing the spectral acceleration and displacement of buildings subjected to earthquakes. A regression analysis was first performed to obtain the best-fitting equations for the inter-story drift ratio (IDR) and period shift factor of low-rise MI RC buildings in response to the peak ground acceleration of earthquakes using published results obtained from shaking table tests. Both spectral acceleration-and spectral displacement-based fragility curves under various damage states (in terms of IDR) were then constructed using the coefficient-based method. Finally, the spectral displacements of low-rise MI RC buildings at the ultimate (or near-collapse) state obtained from this paper and the literature were compared. The simulation results indicate that the fragility curves obtained from this study and other previous work correspond well. Furthermore, most of the spectral displacements of low-rise MI RC buildings at the ultimate state from the literature fall within the bounded spectral displacements predicted by the coefficient-based method.     

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.     

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。     

Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression

Recent efforts of regional risk assessment of structures often pose a challenge in dealing with the potentially variable uncertain input parameters. The source of uncertainties can be either epistemic or aleatoric. This article identifies uncertain variables exhibiting strongest influences on the seismic demand of bridge components through various regression techniques such as linear, stepwise, Ridge, Lasso, and elastic net regressions. The statistical results indicate that Lasso regression is the most effective one in predicting the demand model as it has the lowest mean square error and absolute error. As the sensitivity study identifies more than 1 significant variable, a multiparameter fragility model using Lasso regression is suggested in this paper. The proposed fragility methodology is able to identify the relative impact of each uncertain input variable and level of treatment needed for these variables in the estimation of seismic demand models and fragility curves. Thus, the proposed approach helps bridge owners to spend their resources judiciously (e.g., data collection, field investigations, and censoring) in the generation of a more reliable database for regional risk assessment. This proposed approach can be applicable to other structures.     

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.     

Further development of a multimodal pushover analysis procedure for seismic assessment of bridges

An improvement is first suggested to the modal pushover analysis (MPA) procedure for bridges initially proposed by the writers (Earthquake Engng Struct. Dyn. 2006; 35 (11):1269–1293), the key idea being that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The proposed MPA procedure is then verified by applying it to two actual bridges. The first structure is the Krystallopigi bridge, a 638 m‐long multi‐span bridge, with significant curvature in plan, unequal pier heights, and different types of pier‐to‐deck connections. The second structure is a 100 m‐long three‐span overpass bridge, typical in modern motorway construction in Europe, which, although ostensibly a regular structure, is found to exhibit a rather unsymmetric response in the transverse direction, mainly due to torsional irregularity. The bridges are assessed using response spectrum, ‘standard’ pushover (SPA), and MPA, and finally using non‐linear response history analysis (NL‐RHA) for a number of spectrum‐compatible motions. The MPA provided a good estimate of the maximum inelastic deck displacement for several earthquake intensities. The SPA on the other hand could not predict well the inelastic deck displacements of bridges wherever the contribution of the first mode to the response of the bridge was relatively low. Copyright © 2009 John Wiley & Sons, Ltd.     

结构抗震可靠度二种简化解析表达式的一致性证明

结构抗震可靠度分析的解析求解一直是结构可靠度领域和地震工程领域研究者们的追求目标.解析表达式不仅有利于简化结构抗震可靠度分析这个极端困难的工作,而且也有利于进行基于可靠度的结构概率抗震性能设计与评定.从全概率定理的两种不同表达式出发,介绍了国际上流行的两种结构抗震可靠度解析表达式,过去一直认为这是两种理论基础不同的表达式.本文通过对地震易损性函数关系的解析推导,揭示了若干重要关系,证明了两种表达式的一致性.