Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.     

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.     

Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios

Probabilistic seismic demand models are a common and often essential step in generating analytical fragility curves for highway bridges. With these probabilistic models being traditionally conditioned on a single seismic intensity measure (IM), the degree of uncertainty in the models is dependent on the IM used. Selection of an optimal IM for conditioning these demand models is not a trivial matter and has been the focus of numerous studies. Unlike previous studies that consider a single structure for IM selection, this study evaluates optimal IMs for use when generating probabilistic seismic demand models for bridge portfolios such as would be found in HAZUS‐MH. Selection criteria such as efficiency, practicality, sufficiency, and hazard computability are considered in the selection process. A case study is performed considering the multi‐span simply supported steel girder bridge class. Probabilistic seismic demand models are generated considering variability in the geometric configurations and material properties, using two suites of ground motions—one synthetic and one recorded motion suite. Results show that of the 10 IMs considered, peak ground acceleration (PGA) and spectral acceleration at the fundamental period are the most optimal for the synthetic motions, and that cumulative absolute velocity is also a close contender when using recorded motions. However, when hazard computability is considered, PGA is selected as the IM of choice. Previous studies have shown that spectrally based quantities perform better than PGA for a given structure, but the findings of this study indicate that when a portfolio of bridges is considered, PGA should be used. Copyright © 2007 John Wiley & Sons, Ltd.     

基于改进云图法的结构概率地震需求分析

概率地震需求分析是美国太平洋地震工程研究中心(Pacific Earthquake Engineering ResearchCenter,PEER)提出的新一代"性能化地震工程(Performance-Based Earthquake Engineering,PBEE)"理论框架的重要一环。传统的概率地震需求分析方法称为"云图法",这种方法针对确定性结构进行一系列地震动作用下的非线性动力分析,从而得到地震动强度参数与结构地震需求的"云图"。然而,传统的云图法只能考虑地震动的不确定性,而无法考虑结构的不确定性。为此,结合拉丁超立方体抽样技术,提出一种能综合考虑地震动不确定性和结构不确定性的改进云图法,并将传统的概率地震需求分析内容拓展为概率地震需求模型、概率地震需求易损性分析、概率地震需求危险性分析三个层次。以一榀五层三跨钢筋混凝土框架结构为例,分别采用传统云图法和改进云图法对其进行概率地震需求分析,得到了该结构的概率地震需求模型、地震需求易损性曲线和地震需求危险性曲线。分析结果表明:提出的方法可以有效地考虑地震动与结构的不确定性,避免不考虑结构的不确定性而低估结构的地震风险性。     

Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.     

Enhancing resilience of highway bridges through seismic retrofit

The present study evaluates seismic resilience of highway bridges that are important components of highway transportation systems. To mitigate losses incurred from bridge damage during seismic events, bridge retrofit strategies are selected such that the retrofit not only enhances bridge seismic performance but also improves resilience of the system consisting of these bridges. To obtain results specific to a bridge, a reinforced concrete bridge in the Los Angeles region is analyzed. This bridge was severely damaged during the Northridge earthquake because of shear failure of one bridge pier. Seismic vulnerability model of the bridge is developed through finite element analysis under a suite of time histories that represent regional seismic hazard. Obtained bridge vulnerability model is combined with appropriate loss and recovery models to calculate seismic resilience of the bridge. Impact of retrofit on seismic resilience is observed by applying suitable retrofit strategy to the bridge assuming its undamaged condition prior to the Northridge event. Difference in resilience observed before and after bridge retrofit signified the effectiveness of seismic retrofit. The applied retrofit technique is also found to be cost‐effective through a cost‐benefit analysis. First order second moment reliability analysis is performed, and a tornado diagram is developed to identify major uncertain input parameters to which seismic resilience is most sensitive. Statistical analysis of resilience obtained through random sampling of major uncertain input parameters revealed that the uncertain nature of seismic resilience can be characterized with a normal distribution, the standard deviation of which represents the uncertainty in seismic resilience. Copyright © 2013 John Wiley & Sons, Ltd.     

A probabilistic approach for the prediction of seismic resilience of bridges

This paper proposes a probabilistic approach for the pre‐event assessment of seismic resilience of bridges, including uncertainties associated with expected damage, restoration process, and rebuilding/rehabilitation costs. A fragility analysis performs the probabilistic evaluation of the level of damage (none, slight, moderate, extensive, and complete) induced on bridges by a seismic event. Then, a probabilistic six‐parameter sinusoidal‐based function describes the bridge functionality over time. Depending on the level of regional seismic hazard, the level of performance that decision makers plan to achieve, the allowable economic impact, and the available budget for post‐event rehabilitation activities, a wide spectrum of scenarios are provided. Possible restoration strategies accounting for the desired level of resilience and direct and indirect costs are investigated by performing a Monte Carlo simulation based on Latin hypercube sampling. Sensitivity analyses show how the recovery parameters affect the resilience assessment and seismic impact. Finally, the proposed approach is applied to an existing highway bridge located along a segment of I‐15, between the cities of Corona and Murrieta, in California. Copyright © 2013 John Wiley & Sons, Ltd.     

Functionality‐fragility surfaces

The evaluation of functionality and its evolution in the aftermath of extreme events and during the restoration phase is a critical step in disaster resilience assessment. To this respect, this paper presents the ‘Functionality‐Fragility Surface’ (FFS), which is a tool for probabilistic functionality and resilience evaluation of damaged structures, infrastructure systems, and communities. FFS integrates two well‐known tools, namely Fragility Curves and Restoration Functions, to present the probability of loss of functionality of a system as a function of the extreme‐event intensity, as well as the elapsed time from the initiation of the restoration process. Because of their versatility, FFSs can be applied to components and systems belonging to different infrastructure sectors (e.g., transportation, power distribution, and telecommunication), so they provide a common rigorous paradigm for integrated resilience analyses of multiple sectors, as well as for studies on interdependencies within and across sectors. While it is shown that FFSs can be developed using available data and simple computations for different types of structures and infrastructure systems, this paper proposes also a sophisticated simulation‐based methodology to develop FFSs for individual bridges, taking into account the uncertainties involved in the response, damage, and restoration scheduling of bridges. A Multi‐Span Simply Supported Steel Girder bridge is used to showcase the application of the proposed methodology. Copyright © 2017 John Wiley & Sons, Ltd.     

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。     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

Seismic demand models for probabilistic risk analysis of near fault vertical ground motion effects on ordinary highway bridges

The influence of vertical ground motions on the seismic response of highway bridges is not very well understood. Recent studies suggest that vertical ground motions can substantially increase force and moment demands on bridge columns and girders and cannot be overlooked in seismic design of bridge structures. For an evaluation of vertical ground motion effects on the response of single‐bent two‐span highway bridges, a systematic study combining the critical engineering demand parameters (EDPs) and ground motion intensity measures (IMs) is required. Results of a parametric study examining a range of highway bridge configurations subjected to selected sets of horizontal and vertical ground motions are used to determine the structural parameters that are significantly amplified by the vertical excitations. The amplification in these parameters is modeled using simple equations that are functions of horizontal and vertical spectral accelerations at the corresponding horizontal and vertical fundamental periods of the bridge. This paper describes the derivation of seismic demand models developed for typical highway overcrossings by incorporating critical EDPs and combined effects of horizontal and vertical ground motion IMs depending on the type of the parameter and the period of the structure. These models may be used individually as risk‐based design tools to determine the probability of exceeding the critical levels of EDP for pre‐determined levels of ground shaking or may be included explicitly in probabilistic seismic risk assessments. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling level selection for seismic analysis of concrete‐filled steel tube/moment‐resisting frames by using fragility curves

The seismic behavior of plane moment‐resisting frames (MRFs) consisting of I steel beams and concrete‐filled steel tube (CFT) columns is investigated in this study. More specifically, the effect of modeling details of each individual component of CFT‐MRFs, such as the composite CFT columns, the beam‐column connections, the panel zones, and the steel I beams on their seismic behavior, is studied through comparisons against available experimental results. Then, fragility curves are constructed for three typical CFT‐MRFs, designed according to European codes, for various levels of modeling sophistication through nonlinear time‐history analyses. On the basis of these fragility curves, one can select the appropriate modeling level of sophistication that can lead to the desired seismic behavior for a given seismic intensity. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of cumulative seismic damage and corrosion on the life‐cycle cost of reinforced concrete bridges

Bridge design should take into account not only safety and functionality, but also the cost effectiveness of investments throughout a bridge life‐cycle. This paper presents a probabilistic approach to compute the life‐cycle cost (LCC) of corroding reinforced concrete (RC) bridges in earthquake‐prone regions. The approach is developed by combining cumulative seismic damage and damage associated with corrosion due to environmental conditions. Cumulative seismic damage is obtained from a low‐cycle fatigue analysis. Chloride‐induced corrosion of steel reinforcement is computed based on Fick's second law of diffusion. The proposed methodology accounts for the uncertainties in the ground motion parameters, the distance from the source, the seismic demand on the bridge, and the corrosion initiation time. The statistics of the accumulated damage and the cost of repairs throughout the bridge life‐cycle are obtained by Monte‐Carlo simulation. As an illustration of the proposed approach, the effects of design parameters on the LCC of an example RC bridge are studied. The results are valuable in better estimating the condition of existing bridges and, therefore, can help to schedule inspection and maintenance programs. In addition, by taking into consideration the two deterioration processes over a bridge life‐cycle, it is possible to estimate the optimal design parameters by minimizing, for example, the expected cost throughout the life of the structure. A comparison between the effects of the two deterioration processes shows that, in seismic regions, the cumulative seismic damage affects the reliability of bridges over time more than the corrosion even for corrosive environments. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of vertical seismic response for a large‐scale beam‐supported aqueduct

By the theories of potential flow and structural vibration, the formulae for evaluating the ‘wet’ (with water) frequencies and mode shapes of the beam‐supported aqueduct are derived through a simplified fluid‐structure interaction analysis. The time‐history formulae of structural responses to the vertical seismic excitation are obtained. Applying the response‐spectrum principle, the equivalent vertical earthquake load exerted on the beam and the corresponding effects are also derived. Several illustrative examples are conducted. The analytical results show that: (i) The ‘wet’ frequencies of the structure are lower than the corresponding ‘dry’ (without water) frequencies due to the participating water mass, but the ‘wet’ mode shapes are identical to the corresponding ‘dry’ ones. (ii) The water mass plays an important role in the vertical seismic response, which varies with the different geological sites. For the different seismic inputs, the deeper the water is, the greater are the structural responses. (iii) The vertical seismic effects on the beam are generally not too small to be neglected and should be considered in the structural designs of a beam‐supported aqueduct. Copyright © 2002 John Wiley & Sons, Ltd.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

Uniform fragility spectra for the performance‐based seismic design of structures considering variabilities in structural properties

This paper presents a new methodology based on structural performance to determine uniform fragility design spectra, i.e., spectra with the same probability of exceedance of a performance level for a given seismic intensity. The design spectra calculated with this methodology provide directly the lateral strength, in terms of yield‐ pseudo‐accelerations, associated with the rate of exceedance of a specific ductility characterizing the performance level for which the structures will be designed. This procedure involves the assessment of the seismic hazard using a large enough number of seismic records of several magnitudes; these records are simulated with an improved empirical Green function method. The statistics of the performance of a single degree of freedom system are obtained using Monte Carlo simulation considering the seismic demand, the fundamental period, and the strength of the structure as uncertain variables. With these results, the conditional probability that a structure exceeds a specific performance level is obtained. The authors consider that the proposed procedure is a significant improvement to others considered in the literature and a useful research tool for the further development of uniform fragility spectra that can be used for the performance‐based seismic design and retrofit of structures.     

Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time‐history analysis

Fragility curves are generally developed using a single parameter to relate the level of shaking to the expected structural damage. The main goal of this work is to use several parameters to characterize the earthquake ground motion. The fragility curves will, therefore, become surfaces when the ground motion is represented by two parameters. To this end, the roles of various strong‐motion parameters on the induced damage in the structure are compared through nonlinear time‐history numerical calculations. A robust structural model that can be used to perform numerous nonlinear dynamic calculations, with an acceptable cost, is adopted. The developed model is based on the use of structural elements with concentrated nonlinear damage mechanics and plasticity‐type behavior. The relations between numerous ground‐motion parameters, characterizing different aspects of the shaking, and the computed damage are analyzed and discussed. Natural and synthetic accelerograms were chosen/computed based on a consideration of the magnitude‐distance ranges of design earthquakes. A complete methodology for building fragility surfaces based on the damage calculation through nonlinear numerical analysis of multi‐degree‐of‐freedom systems is proposed. The fragility surfaces are built to represent the probability that a given damage level is reached (or exceeded) for any given level of ground motion characterized by the two chosen parameters. The results show that an increase from one to two ground‐motion parameters leads to a significant reduction in the scatter in the fragility analysis and allows the uncertainties related to the effect of the second ground‐motion parameter to be accounted for within risk assessments. Copyright © 2009 John Wiley & Sons, Ltd.     

Methodology for preliminary seismic design of extended pile‐shafts for bridge structures

Seismic design of extended pile‐shafts requires a careful consideration of the influence of the surrounding soil on the overall response of the soil–pile system. In this paper, a procedure that incorporates soil properties into the process is developed for preliminary seismic design of extended pile‐shafts. The method follows the well‐accepted approach of using a force reduction factor to determine the lateral strength of the structure. The procedure involves an iterative process to arrive at the required amount of longitudinal reinforcement. Other outcomes of the procedure include the appropriate lateral stiffness and strength, as well as an estimation of the local curvature demand and ultimate drift ratio that can be used to ensure a satisfactory lateral response. The design procedure is capable of providing reliable results for a practical range of structural and soil properties. The versatility of the procedure is illustrated using two numerical examples of extended pile‐shafts constructed in different soil sites. Copyright © 2006 John Wiley & Sons, Ltd.     

Towards probabilistic seismic performance of vehicle-bridge interaction systems: From stochastic dynamic model to fragility analysis

This paper aims to assess the seismic fragility of vehicle-bridge-interaction (VBI) systems considering the effects of vehicle types, traffic conditions, and road surface qualities. A stochastic nonlinear mechanical model for the earthquake-VBI system is developed, and the fragility functions for the proposed VBI model are derived by considering the relevant probabilistic seismic demand parameters. On the basis of a typical four-span continuous prestressed concrete highway bridge in China, a complete numerical model for the VBI system is built considering multiple uncertainties from bridge and vehicle parameters, as well as the road surface qualities. A total of 120 real ground motion records with different combinations of magnitude-source-to-site distance (M-R) and earthquake intensity characteristics are selected. Meanwhile, 80 scenarios in terms of different combinations of vehicle types, vehicle speeds, and road surface irregularities are defined. In this context, 96,000 nonlinear time-history analyses are performed, and the developed fragility models are applied to the VBI system at both component and system levels. Results indicate that the fragilities of pier drift, bearing shear strain, and the overall VBI system increase with the increase of the vehicle weight or the decrease of the vehicle speed, while the vertical deck displacement is dominated by the vehicle weight. It is also found that the road surface quality has a negligible effect on both component and system fragilities.