Survey of seismic fragilities used in PRA studies of nuclear power plants

In recent years, seismic PRA studies have been performed on a large number of nuclear power plants in the USA. This paper presents a summary of a survey on fragility databases and the range of evaluated fragility values of various equipment categories based on past PRAs. The survey includes the use of experience data, the interpretations of available test data, and the quantification of uncertainties. The surveyed fragility databases are limited to data available in the public domain such as NUREG reports, conference proceedings and other publicly available reports. The extent of the availability of data as well as limitations are studied and tabulated for various equipment categories. The survey of the fragility values in past PRA studies includes not only the best estimate values, but also the dominant failure modes and the estimated uncertainty levels for each equipment category. The engineering judgments employed in estimating the uncertainty in the fragility values are also studied.This paper provides a perspective on the seismic fragility evaluation procedures for equipment in order to clearly identify the engineering analysis and judgment used in past seismic PRA studies.     

Quantitative risk analysis of oil storage facilities in seismic areas

Quantitative risk analysis (QRA) of industrial facilities has to take into account multiple hazards threatening critical equipment. Nevertheless, engineering procedures able to evaluate quantitatively the effect of seismic action are not well established. Indeed, relevant industrial accidents may be triggered by loss of containment following ground shaking or other relevant natural hazards, either directly or through cascade effects ('domino effects'). The issue of integrating structural seismic risk into quantitative probabilistic seismic risk analysis (QpsRA) is addressed in this paper by a representative study case regarding an oil storage plant with a number of atmospheric steel tanks containing flammable substances. Empirical seismic fragility curves and probit functions, properly defined both for building-like and non building-like industrial components, have been crossed with outcomes of probabilistic seismic hazard analysis (PSHA) for a test site located in south Italy. Once the seismic failure probabilities have been quantified, consequence analysis has been performed for those events which may be triggered by the loss of containment following seismic action. Results are combined by means of a specific developed code in terms of local risk contour plots, i.e. the contour line for the probability of fatal injures at any point (x, y) in the analysed area. Finally, a comparison with QRA obtained by considering only process-related top events is reported for reference.     

A methodology for the quantitative risk assessment of major accidents triggered by seismic events

A procedure for the quantitative risk assessment of accidents triggered by seismic events in industrial facilities was developed. The starting point of the procedure was the use of available historical data to assess the expected frequencies and the severity of seismic events. Available equipment-dependant failure probability models (vulnerability or fragility curves) were used to assess the damage probability of equipment items due to a seismic event. An analytic procedure was subsequently developed to identify, evaluate the credibility and finally assess the expected consequences of all the possible scenarios that may follow the seismic events. The procedure was implemented in a GIS-based software tool in order to manage the high number of event sequences that are likely to be generated in large industrial facilities. The developed methodology requires a limited amount of additional data with respect to those used in a conventional QRA, and yields with a limited effort a preliminary quantitative assessment of the contribution of the scenarios triggered by earthquakes to the individual and societal risk indexes. The application of the methodology to several case-studies evidenced that the scenarios initiated by seismic events may have a relevant influence on industrial risk, both raising the overall expected frequency of single scenarios and causing specific severe scenarios simultaneously involving several plant units.     

Seismic fragility analysis of electric substation equipment and structures

This paper presents a seismic fragility analysis of equipment and structures in an electric substation in the eastern United States, using Substation 21 in Memphis as an example. The fragility data of substation equipment and structures can be generated using actual earthquake damage data, experimental data, or analytical approaches. Seismic damage to electric facilities in the eastern United States is rare and information on dynamic testing of electric equipment similar to those installed in the substation is not available; thus, an analytical approach is used to perform the fragility analysis in this study. The fragility analysis results can reveal the expected performance of equipment and structures in the substation in the event of an earthquake. The fragility analysis results also provide the necessary data for the seismic performance evaluation of an entire electric substation and for a system reliability analysis of an electric system.     

Risk assessment and early warning systems for industrial facilities in seismic zones

Industrial equipments and systems can suffer structural damage when hit by earthquakes, so that accidental scenarios as fire, explosion and dispersion of toxic substances can take place. As a result, overall damage to people, environment and properties increases. The present paper deals with seismic risk analysis of industrial facilities where atmospheric storage tanks (anchored or unanchored to ground), horizontal pressurised tanks, reactors and pumps are installed. Simplified procedures and methodologies based on historical database and literature data on natural-technological (Na-Tech) accidents for seismic risk assessment are discussed.Equipment-specific fragility curves have been thus derived depending on a single earthquake measure, peak ground acceleration (PGA). Fragility parameters have been then transformed to linear probit coefficients in order to obtain reliable threshold values for earthquake intensity measure, both for structural damage and loss of containment. These threshold values are of great interest when development of active and passive mitigation actions and systems, safety management, and the implementation of early warning system are concerned.The approach is general and can be implemented in any available code or procedure for risk assessment. Some results of seismic analysis of atmospheric storage tanks are also presented for validation.     

钢筋混凝土剪力墙和连梁易损性曲线研究

构件易损性曲线表征了构件的指标参量(如位移角、转角等)与达到某个指定损伤等级的概率之间的函数关系,可用于评价构件的损伤程度和确定修复方法,是结构抗震性能和韧性评价的重要依据。该文对满足中国GB 50011―2010《建筑抗震设计规范》要求的74个钢筋混凝土(RC)剪力墙试件和32个RC连梁试件的试验数据进行了统计分析,确定了构件的各损伤等级对应的损伤状态现象及相应的修复方法;并分别采用位移角和连梁转角为指标参量,建立了RC剪力墙和连梁的易损性曲线。分析讨论了设计轴压比对RC剪力墙易损性曲线的影响,以及跨高比对RC连梁易损性曲线的影响。比较了该文建立的易损性曲线和美国FEMA P-58规定的易损性曲线,并分析了两者差异原因。     

Seismic probabilistic risk assessment and seismic margins studies for nuclear power plants

This paper reviews the seismic probabilistic risk assessment and seismic margins studies for nuclear power plants in the United States. The techniques employed in these studies are briefly described. A few comments on the evaluation of the fragility of structures and equipment are discussed. Seismic PRA is a systematic process to evaluate the safety of nuclear power plants. In the process, it integrates all the elements such as seismic hazard, component fragility and plant system. Thus, it provides the overall view of the safety of an entire plant under a seismic event.

The major tasks of a seismic PRA such as the evaluation of hazard curves, component fragility and plant system are also present in probabilistic analyses of nonnuclear facilities. The concept and technique embodied in seismic PRA for nuclear power plants can be applied to other types of engineering facilities.     

Uncertainty quantification and seismic fragility of base-isolated liquid storage tanks using response surface models

Seismic response of base-isolated liquid storage tank is represented using response surface model (RSM) to consider the uncertainty in the isolator parameters. The effectiveness of RSM to represent the probability distributions of the peak seismic response quantities of the base-isolated liquid storage tank is studied in the framework of Monte Carlo (MC) simulation. Broad and slender configurations of the tanks isolated by lead–rubber bearing (New Zealand – NZ system) characterized with non-linear force-deformation behavior is considered in the present study. The influence of the uncertain isolator parameters on the seismic response of the base-isolated liquid storage tanks is investigated. Subsequently, seismic fragility of the base-isolated liquid storage tanks is evaluated using the RSM based MC simulation. The RSM estimates the non-linear seismic response of the base-isolated liquid storage tanks with sufficient accuracy. It is observed that the uncertainties in the isolator parameters significantly influence the peak response quantities of the base-isolated liquid storage tanks. The effectiveness of the base isolation technique, in terms of the reduced probability of failure, is observed by comparing the fragility curves for the fixed-base and base-isolated liquid storage tanks. It is also observed that increase in the isolation time period decreases the probability of failure for the base-isolated liquid storage tanks. It is concluded that the peak ground acceleration (PGA) of the earthquake ground motion can be included in the RSM to reduce the computational efforts for seismic fragility analysis.     

Failure modes of a seismically isolated continuous girder bridge

Reliable estimates of the failure modes of basic facilities, especially the seismically isolated bridge, are required for almost any form of analysis used for the seismic design and retrofit of bridge. The Hong Kong-Zhuhai-Macau (HZM) Bridge (HZMB), a seismically isolated continuous girder bridge with six spans, is a sea-crossing bridge, which is now under construction and will connect the Mainland China, Hong Kong, and Macau. Because the bridge is located in a highly active seismic zone, it is essential to evaluate the seismic performance of this bridge, in particular of its failure modes. Based on this practical engineering, this paper investigated the failure modes of isolated continuous girder bridge subjected to strong ground motions by developed weighted rank sum ratio method, in combination with developed 3D finite element bridge models. Firstly, three-dimensional finite element bridge models are developed and assessed using the incremental dynamic analysis method. Due to the flexibility of seismic isolation, both bending and rotational stiffness of isolation bearings are taken into account in the analysis. In addition, the rotational angle of bearings is found to be sensitive to seismic analytical results of isolated continuous girder bridges. Then, it conducted the nonlinear dynamic analysis on the HZM Bridge under sixteen strong earthquake records. Further, statistically significant failure modes and the weakest failure mode of this bridge are identified through the weighted rank sum ratio method. It resulted that, the final failure modes of this isolated continuous girder bridge are presented at the isolation bearings on a part of middle piers, at the isolation bearings on the abutments, at the isolation bearings at a side pier, and at the bottoms of side piers, respectively. The results of the failure mode analysis would greatly assist engineers to establish effective strategies for performance enhancement and seismic retrofit of bridge in the future.     

基于BP神经网络的RC框架结构地震易损性曲面分析:考虑地震动强度和持时的影响

与短持时地震动相比,长持时地震动会加剧结构的损伤,增加结构的失效概率,因此有必要更充分地研究地震动持时特性对结构地震易损性分析结果的影响。该文提出了一种基于BP神经网络的地震易损性曲面分析方法,使用神经网络模型,综合考虑地震动强度和持时特性对结构地震需求的影响,并进行地震易损性分析,得到不同损伤水平下考虑地震动持时特性的结构易损性曲面。选用3个不同高度的钢筋混凝土框架结构为研究对象,分别选择具有长、短持时特性的2组地震动记录为输入,采用BP神经网络模型建立地震动强度指标与结构响应间的关系,在此基础上得到目标地震易损性曲面,并对该方法的有效性进行讨论。分析结果表明,研究建立的BP神经网络模型精度较高,依据该方法可得到可信的损伤概率分析结果。相比于传统方法,神经网络可以更为有效和准确地建立持时与结构损伤的相关关系,得到考虑持时特性的易损性分析结果。该文的方法亦可进一步拓展,将更多地震动特性纳入地震易损性分析过程,具有明确的应用前景。     

第二代基于性能地震工程中的地震易损性模型及正逆概率风险分析

第二代基于性能地震工程理论中的地震易损性主要是指结构构件以及非结构构件的抗震能力,与传统地震风险理论中的地震易损性定义和内涵并不相同。为了澄清二者的不一致性,首先介绍传统地震风险理论中地震易损性的定义和概率模型,然后指出第二代基于性能地震工程理论存在五个层次的地震易损性模型:地震需求易损性模型、抗震能力易损性模型、地震损伤易损性模型、地震损失易损性模型和抗震决策易损性模型,指出了这五种模型的区别及其相互关系,推导得到了地震需求易损性模型和地震损伤易损性模型分布参数的解析表达式。在此基础上,根据不同的不确定性传递路径,提出了正向PBEE和逆向PBEE的概念,以通过不同方式求解第二代基于性能地震工程理论的风险积分公式。基于地震危险性函数的近似表达式以及地震易损性模型及其分布参数的解析表达式,通过正向PBEE和逆向PBEE方法,分别得到了具有相同表达形式的工程需求参数EDP、地震损伤DM和决策变量DV三个层次的概率地震风险表达式。通过该文的研究,将传统地震风险分析理论与第二代基于性能地震工程理论统一在一致的理论框架之中。     

基于云图-条带法的概率地震需求分析与地震易损性分析

提出一种概率地震需求分析的云图-条带法。该方法通过引入经验地震易损性分析中的数据处理方法,解决传统云图法无法处理海量非线性时程分析结果的局限。为说明该文提出方法,选取100条地震动作为输入,针对23个钢筋混凝土框架结构进行了云图法分析。基于所有结构的云图结果,采用云图-条带法建立了群体结构的概率地震需求模型,并计算得到了群体结构的地震易损性。研究表明:云图-条带法可以有效地处理海量非线性时程分析结果,建立较为合理的概率地震需求模型。在输入地震动的强度范围内,群体结构整体发生严重破坏和完全破坏的概率很低,而主要以发生轻微破坏和中等破坏为主。     

基于概率性地震需求模型的桥梁易损性分析

采用概率性地震需求分析方法,建立了汶川地区典型简支梁桥的分析型地震易损性模型。基于汶川地震桥梁震后调查资料,评估了桥梁结构参数的不确定性,抽样并生成一系列桥梁的有限元模型样本。利用汶川地震实测地震波对所建立的桥梁有限元模型进行非线性动力时程分析,并记录每一组分析中桥梁构件的地震峰值响应,通过回归分析建立地震动强度和桥梁构件地震需求之间的关系。在确定桥梁不同损伤状态对应的构件极限状态后,基于对数正态分布假设生成不同损伤状态对应的地震易损性曲线,最后基于可靠度理论计算得到桥梁系统易损性的上下确界。生成的地震易损性曲线可以进一步用于地震风险评估和震后加固优先级决策。     

地震动持时对考虑梁柱节点区不同破坏模式RC框架的地震易损性影响

地震动持时对非弹性结构的累积损伤和破坏有较大影响,但目前抗震分析设计中对地震动持时的规定是不明确的。从美国太平洋地震工程研究中心地震动数据库中选择具有不同持时和加速度峰值的60条地震动记录（PEER）中选取具有不同持时和加速度峰值的60条地震动记录,并划分为长、短持时两组各30条。利用OpenSees分析软件建立了一钢筋混凝土框架-填充墙结构教学楼的三维空间模型。分别以梁柱节点区不考虑非弹性变形、梁柱节点区考虑钢筋黏结滑移、梁柱节点区考虑钢筋黏结滑移和剪切变形三种工况来依次模拟节点区的破坏模式。以此60条地震动记录为输入进行结构的地震易损性分析,得到在五种损伤水平下,对应于不同工况两组持时记录的结构地震易损性曲线,进而评估地震动持时对考虑节点区不同破坏模式结构抗震性能的影响。分析结果表明,相对于短持时地震动记录,长持时地震动记录使结构在相应损伤水平和工况下的超越概率明显提高;同一损伤水平下,按照梁柱节点区不考虑非弹性变形,考虑钢筋黏结滑移,同时考虑钢筋黏结滑移和剪切变形的顺序,长、短持时地震动记录作用下其超越概率均显著提高,且长持时地震动记录对节点区考虑钢筋黏结滑移和剪切变形结构的影响更为明显。     

Risk assessment of LPG automotive refuelling facilities

Quantified risk analysis (QRA) was used for the revision of regulatory separation distances associated with medium size liquefied petroleum gas (LPG) refuelling facilities used in automotive service (gas) stations. Typically these facilities consist of a 7.5 kl pressure vessel, pump, pipework, dispensing equipment and safety equipment. Multi-tank installations are relatively uncommon.This paper describes the hazard scenarios considered, the risk analysis procedure and the selection and application of data for initiating events and for rates of failure of mechanical components and of the pressure vessel. Human errors and intervention possibilities were also considered. Because of the inapplicability of established consequence models and the relatively small scale of the facilities, a number of tests were performed to estimate flame length, flame impingement effects, ignition probabilities and the effectiveness of screening devices.     

基于多个响应量的拱坝地震易损性分析

以白鹤滩拱坝为研究对象,选取成组强震记录,同时考虑地震动和材料的不确定性,采用增量法对白鹤滩拱坝进行了地震易损性分析。统计连续调幅地震动作用下拱坝损伤破坏过程,直观的划分了拱坝地震破坏等级,确定了拱冠位移、横缝开度和损伤体积比这三个响应量在各破坏等级间的界限值,从而可通过这三个响应量定量描述拱坝的破坏等级。通过拟合增量动力分析结果,分别建立了三个响应量的概率地震需求模型,进而求得地震易损性曲线,并综合比较了不同破坏等级下基于三个响应量的易损性曲线,全面反映了拱坝易损性。利用易损性曲线可以预测不同强度地震作用下拱坝达到各级破坏的概率,为基于性能的拱坝抗震安全评价提供了理论依据。     

桥梁系统地震多维易损性分析

综合考虑地震地面运动以及性能极限状态的不确定性,提出了基于多地震需求参数分析的桥梁系统易损性评估方法,将易损性概念从一维扩展到多维。该方法首次提出服从多元对数正态分布的概率地震需求模型探讨桥梁体系各构件响应相关性,同时考虑各构件性能极限状态的相关性建立多维性能极限状态方程,确定结构失效域,通过MonteCarlo模拟计算系统多维地震易损性。以某一钢筋混凝土多跨连续梁高速公路桥为算例,通过非线性动力分析法获得最大响应样本,利用最大似然估计求得概率地震需求模型未知参数,计算体系多维易损性,并与构件易损性相比较。结果表明:桥梁体系多维易损性较构件易损性偏大,可避免用单一构件易损性代替系统易损性产生的非保守估计,预测结果更利于工程安全,为桥梁修复加固和交通系统可靠性分析提供理论依据。     

An expert system for finding fragility curves of building structural systems at the preliminary design stage

This research developed an expert system for determining seismic fragility curves of structural systems in a nuclear power plant or conventional building at the preliminary design stage. The resulting system simulates the performance of human experts in identifying the potential failure modes and their likelihood for a structure of interest. Induction technique is used for knowledge acquisition. The characteristics of structural systems are described by their attributes and their values.     

HAZUS相容的钢筋混凝土框架结构地震易损性分析

HAZUS作为一款多灾害损失评估软件,在世界范围内得到了广泛应用。确定结构的地震易损性函数是HAZUS软件进行地震损失评估的关键。然而,现有的传统地震易损性分析结果无法满足HAZUS的格式要求。为此,该文提出一种与HAZUS相容的地震易损性分析的简化方法,该方法直接利用传统的地震易损性分析结果,通过能力谱方法确定地震动记录的谱位移作为其参数,转化得到满足HAZUS格式要求的地震易损性结果。为说明该文提出的方法,选择4个不同高度的钢筋混凝土框架结构作为算例,并将该文方法的分析结果与HAZUS软件提供的地震易损性曲线进行对比。结果表明:由于分析方法和分析对象的不同,HAZUS相容的地震易损性结果与HAZUS软件所提供的地震易损性结果之间存在较为明显的差异。     

变电站复合材料绝缘子的动力特性与地震易损性研究

复合材料在变电站绝缘子上的应用,有望提高电气设备的抗震性能。测试了复合材料绝缘子的动力特性、弯曲刚度和承载能力;运用测试结果,建立了该复合材料绝缘子构成的电气设备的有限元模型;基于概率地震易损性分析理论,研究了电气设备的地震易损性。结果表明,复合材料绝缘子中套管与金属法兰的胶装连接段是抗弯承载力的薄弱部位,该段抗弯刚度明显小于套管刚度;该绝缘子组成的电气设备在0.4g等级地震下发生中度和重度失效的概率较小,但轻度失效的概率达38%,提高胶装段抗弯能力是提高抗震性能的关键;以失效概率为指标的易损性分析实现了电气设备抗震性能的概率化评价。