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.     

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.     

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.     

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 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.     

Seismic steel jacketing of rectangular RC bridge columns for the mitigation of lap‐splice failures

This paper investigated the use of external steel jacketing for seismic retrofit of non‐ductile reinforced concrete (RC) bridge columns to prevent lap‐splice failure. Three 1/2.5‐scale specimens were tested under cyclic loads. The effectiveness of two types of steel jackets for improving the ductility and strength of specimens using inadequate transverse reinforcing and lap‐splice details were examined. An octagonal steel jacketing scheme for the seismic retrofitting of rectangular RC bridge columns was proposed. In addition, the methods for seismic retrofitting rectangular columns using elliptical steel jacketing were also critically tested. The test results indicated that the octagonal steel jackets can effectively provide confinement thereby mitigating failures as a result of inadequate transverse reinforcing and inadequate lap‐splices. Tests also confirmed that the ductility performance and the energy dissipation capacity of the specimens can be significantly improved by the octagonal steel jacket. Copyright © 2010 John Wiley & Sons, Ltd.     

Fragility curves for reinforced concrete structures in Skopje (Macedonia) region

A method for the development of earthquake intensity–damage relations, given as fragility curves and damage probability matrices is proposed in this paper. The proposed method is applied on reinforced-concrete frame-wall structures. Two sets of fragility curves and damage probability matrices are developed. The first one is for reinforced-concrete frame structures lower than 10 stories. For this purpose, a six-story frame structure is used. The other set is defined for reinforced-concrete frame-wall structures higher than 10 stories. A 16-story frame-wall structure was chosen as a sample. The sample structures were designed according to Macedonian design code. The conditions of the local seismic hazard were the subject of special concern for the development of earthquake intensity–damage relations. Because of the limited number of real time histories from the Skopje region, a set of 240 synthetic time histories were generated. Geological dates from the Skopje region were used. Response of the sample structures under earthquake excitation was defined performing nonlinear dynamic analysis. Modeling of the nonlinear behavior of the structural elements was completed according to state-of-the-art methods in this field. A modified Park and Ang damage model was chosen as a measure of the structure's response to earthquake excitation. Five damage states were defined to express the condition of damage. As a result of the analytical research, the values of the global damage index corresponding to each damage state were determined. Using the dates from the nonlinear dynamic analysis of the sample structures under all 240 synthetic time histories, the two sets of fragility curves and damage probability matrices were defined.     

Parametric study on performance of bridge retrofitted by unseating prevention devices

1 Introduction Structural retro?t techniques (Roberts, 2005), such as restrainers, concrete shear keys, steel jackets, CFRPshells, base isolators, or dampers have been widely studied and implemented in actual structures based on the experiences learned from past earthquakes. In the Chi-Chi earthquake (EERI, 2001), the damage to simply-supported PCI girder bridges provided a different view from which to examine the function of a rubber bearing system for simply- supported bridges (NCREE,…     

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.     

Strengthening and rehabilitation of RC beam–column joints using carbon‐FRP jacketing and epoxy resin injection

The scope of this study is to present results of an experimental investigation on the behaviour of critical external beam–column joints repaired or/and strengthened with a combination of epoxy resin injections and carbon‐fibre‐reinforced plastics (C‐FRP) sheets and to extract useful and practical conclusions. The experimental program comprises 12 external beam–column joint connection subassemblages tested in cyclic loading. From the observed responses of the examined specimens it can be deduced that the technique of epoxy resin injections is appropriate for the total rehabilitation of the joints seismic capacity, since no damages have been observed at the joint area of the specimens after the repair. The combination of this technique with the use of C‐FRP sheets leads to a significant improvement of the loading capacity, the energy absorption and the ductility and finally it leads to improved type of damages compared with the damage modes of the specimens during the initial loading. Shortcomings of the application of C‐FRP sheets for practical use are also pointed out. Copyright © 2008 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.     

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.     

基于随机森林的中小跨径公路梁桥双柱墩地震易损性模型

为准确建立线路中小跨径梁桥桥墩的地震易损性模型,采用统计工具得到某山区高速公路桥梁双柱墩的结构、几何和材料特性的概率分布,由拉丁超立方体抽样生成桥墩属性数据集,建立了参数化的有限元模型.通过Pushover分析和基于非弹性需求谱的能力谱方法获取双柱墩的地震需求和抗震性能数据点,提出由随机森林(RF)模型建立桥墩地震易损...     

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.     

Local retrofit of exterior RC beam–column joints using thin RC jackets—An experimental study

The use of a new type of reinforced concrete (RC) jacket for RC exterior beam–column connections damaged by seismic excitations is addressed and experimentally investigated. The proposed jacket has very small thickness and includes small diameter steel reinforcement. This jacketing applies at the joint region and at a small part of the columns and the beam. The main advantage of the proposed thin and locally applied jacket compared with the commonly used concrete jacket is the fact that its application is not restrained by space limitations, and since it slightly changes the initial size of the elements, the building's dynamics and seismic behaviour remain practically unaffected. For the needs of this study, 10 exterior beam–column joint subassemblages were constructed and subjected to increasing cyclic loading. Later, the damaged specimens were locally retrofitted using the proposed thin RC jackets and they were retested with the same load sequence. Three different specimen configurations with various amounts of shear reinforcement in the joint area were examined and two types of jackets (a) with light and (b) with dense reinforcement were applied. Test results indicated that the seismic performance of the retrofitted specimens was fully restored and in some cases substantially improved with respect to the performance of the same specimens in the initial loading, since they exhibited higher values of load capacity and hysteretic energy dissipation. Discussion for the conditions of the use of the examined jacketing technique either as a repair or as a strengthening method is also included. Copyright © 2007 John Wiley & Sons, Ltd.     

Pushover分析方法的发展及其在桥梁结构中的应用

非线性静力分析方法（Pushover分析方法）可以较好地检验结构的变形能力,找到结构的薄弱环节,控制强烈地震作用下结构破坏程度,对工程设计有很强的指导意义。但目前Pushover分析方法的种类很多,各自有着不同的优缺点和适用范围,针对桥梁结构,阐述静力非线性分析方法（Pushover）的原理及其研究发展概况,评述了各种Pushover方法的优缺点,并分析了Pushover方法用于桥梁结构的基本原理和评价方法,指出Pushover方法用于桥梁结构存在的问题。     

Mainshock-aftershock state-dependent fragility curves: A case of wood-frame houses in British Columbia,Canada

During a mainshock-aftershock (MSAS) sequence, there is no time to retrofit structures that are damaged by a mainshock; therefore, aftershocks could cause additional damage. This study proposes a new approach to develop state-dependent fragility curves using real MSAS records. Specifically, structural responses before and after each event of MSAS sequences are used to obtain statistical relationships among the engineering demand parameter prior to the seismic event (pre-EDP), the intensity measure of the seismic event (IM), and the engineering demand parameter after the seismic event (post-EDP). The developed fragility curves account for damage accumulation, providing the exceeding probability of damage state (DS) given the IM of the event and the DS of the structure prior to the seismic excitation. The UBC-SAWS model, which was developed for wood-frame houses in British Columbia, Canada, is considered as a case study application. Results indicate that for the examined structural typology, state-dependent fragility curves based on residual interstorey drift ratio (pre-EDP), peak ground velocity (IM), and maximum inter-storey drift ratio (post-EDP) are the best choice to characterise the cumulative damage effect. An illustration of the developed fragility curves is provided by considering a hypothetical MSAS scenario of a M_w 9.0 Cascadia mainshock triggering a M_w 6.0 crustal event in the Leech River fault, affecting wooden houses in Victoria, Canada. The MSAS scenario increases Yellow tags (restricted access) by 12.3% and Red tags (no access) by 4.8%.     

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

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

Generation of hazard-consistent fragility curves

This paper presents an analytical method for generating fragility curves of structures. In the proposed method, seismic sources, path attenuation, local soil conditions, and nonlinear building behavior are systematically considered. The uncertainties in the earthquake-site-structure system are quantified by considering the uncertainties in the seismic, site, and structural parameters that define the system. For an illustration, the proposed method is used to generate fragility curves and a damge probability matrix for Smith Hall on the main campus of The University of Memphis, Memphis, Tennessee.