Seismic fragilities for nuclear power plant risk studies

Seismic fragilities of critical structures and equipment are developed as families of conditional failure frequency curves plotted against peak ground acceleration. The procedure is based on available data combined with judicious extrapolation of design information on plant structures and equipment. Representative values of fragility parameters for typical modern nuclear power plants are provided. Based on the fragility evaluation for about a dozen nuclear power plants, it is proposed that unnecessary conservatism existing in current seismic design practice could be removed by properly accounting for inelastic energy absorption capabilities of structures. The paper discusses the key contributors to seismic risk and the significance of possible correlation between component failures and potential design and construction errors.     

Seismic fragility analyses of nuclear power plant structures based on the recorded earthquake data in Korea

By nature, the seismic fragility analysis results will be considerably affected by the statistical data of design information and site-dependent ground motions. The engineering characteristics of small magnitude earthquake spectra recorded in the Korean peninsula during the last several years are analyzed in this paper. An improved method of seismic fragility analysis is evaluated by comparative analyses to verify its efficiency for practical application to nuclear power plant structures. The effects of the recorded earthquake on the seismic fragilities of Korean nuclear power plant structures are also evaluated from the comparative studies. Observing the obtained results, the proposed method is more efficient for the multi-modes structures. The case study results show that seismic fragility analysis based on the Newmark's spectra in Korea might over-estimate the seismic capacities of Korean facilities.     

基于蒙特卡罗抽样和最大-最小法的地震易损度算法研究

本文探索并研究了一种新的地震易损度算法,基于蒙特卡罗（MC）抽样和最大-最小法计算了单个设备和多个设备组合的最小割集的易损度。最小割集包括3种类型：纯地震失效最小割集、包含非事件的最小割集、地震失效和随机失效混合割集。对于仅包含地震失效的事故序列,可直接采用基于蒙特卡罗抽样和最大 最小法的易损度算法进行计算。涉及地震失效和随机失效混合的事故序列,可采用极限近似方法（MCUB）或其他割集定量化算法进行计算。经对比,基于蒙特卡罗抽样和最大 最小法的地震易损度算法计算结果与理论值一致,为工程应用中的地震易损度计算提供了另一种可行的算法。     

Fragility estimation for seismically isolated nuclear structures by high confidence low probability of failure values and bi-linear regression

A method for the fragility estimation of seismically isolated nuclear power plant structure is proposed. The relationship between the ground motion intensity parameter (e.g. peak ground velocity or peak ground acceleration) and the response of isolated structures is expressed in terms of a bi-linear regression line, whose coefficients are estimated by the least-square method in terms of available data on seismic input and structural response. The notion of high confidence low probability of failure (HCLPF) value is also used for deriving compound fragility curves for coupled subsystems.     

Development of the site-specific uniform hazard spectra for Korean nuclear power plant sites

A seismic risk analysis has been performed to evaluate the seismic safety of a nuclear power plant for strong earthquakes beyond a design earthquake level. A site-specific median spectrum has generally been used for a seismic fragility analysis of structures and equipment in Korean nuclear power plants as a part of a probabilistic seismic risk assessment. The site-specific response spectrum, however, does not represent the same probability of an exceedance over entire frequency range of interest. The site-specific uniform hazard spectrum (UHS) is more appropriate for use in a seismic probabilistic risk assessment (SPRA) than the site-specific spectrum, since there are only a few strong motion data and seismological information for the nuclear plant sites in Korea. In this study, the uniform hazard spectra were developed using the available seismic hazard data for four Korean NPP sites.     

A probabilistic seismic risk assessment procedure for nuclear power plants: (I) Methodology

A new procedure for probabilistic seismic risk assessment of nuclear power plants (NPPs) is proposed. This procedure modifies the current procedures using tools developed recently for performance-based earthquake engineering of buildings. The proposed procedure uses (a) response-based fragility curves to represent the capacity of structural and nonstructural components of NPPs, (b) nonlinear response-history analysis to characterize the demands on those components, and (c) Monte Carlo simulations to determine the damage state of the components. The use of response-rather than ground-motion-based fragility curves enables the curves to be independent of seismic hazard and closely related to component capacity. The use of Monte Carlo procedure enables the correlation in the responses of components to be directly included in the risk assessment. An example of the methodology is presented in a companion paper to demonstrate its use and provide the technical basis for aspects of the methodology.     

高温气冷堆蓄电池组地震易损性研究

为验证核电厂发生地震外部事件时的电力安全，需要对蓄电池组进行抗震鉴定试验。本文以高温气冷堆（HTR）核电厂安全级蓄电池组为研究对象、以安全级蓄电池组抗震鉴定试验数据和工程经验为基础，通过识别、量化蓄电池组的地震易损性变量，并应用基于试验的易损性分析法推导出地震易损性曲线和高置信度低失效概率（HCLPF）抗震能力。研究结果表明，安全级蓄电池组的抗震能力远高于核电厂设计基准地震动需求。      

考虑知识不确定性的核电厂地震易损性概率模型研究

考虑知识不确定性的地震易损性模型公式是核电厂地震易损性分析的理论基础,包括具有置信度的易损性公式和平均值易损性公式。本文分别对两类公式进行了推导,分析了公式中参数的相互关系,研究了基于两类易损性公式分别得到的高置信度低失效概率值的关系。分析结果表明:基于易损性的不确定性角度的公式推导丰富了具有置信度易损性公式的内涵;对于具有置信度的易损性模型公式,失效概率与置信度服从某种分布,且两类不确定性对失效概率具有不同影响;两类不确定性的对数标准差取值相近时,两类高置信度低失效概率能力值近似相等。     

重要厂用水系统地震情况下可靠性分析

重要厂用水系统是核电厂重要的安全系统之一,其失效概率通常由系统可靠性分析获得。而地震情况下设备的失效概率是地震动峰值加速度的函数,且地震的发生又具有随机性,目前概率安全评价中传统的故障树分析方法对此种情况缺乏足够的处理能力。本文采用蒙特卡罗模拟方法解决条件概率的问题,针对地震情况系统可靠性分析,提出了评价模型,并对核电厂重要厂用水系统进行了分析计算,得到地震情况下重要厂用水系统的年失效概率为1.46×10^-4。计算结果与设备抗震性能数据符合,验证了分析模型的合理性。     

核电厂地震易损性分析模型研究

福岛核事故发生后,我国要求开展外部事件对核电厂影响的评价,“十二五”核安全规划要求2015年之前开展外部事件概率安全分析工作。地震是需要重点评价的外部事件之一,而地震易损性分析是地震概率安全评价（SPSA）的一项重要内容,易损性分析模型是地震易损性分析的基础。本文介绍了地震易损性的概念,研究了美国核管会（NRC）和电力研究院（EPRI）推荐的地震易损性模型,并从数学上对该模型进行推导。给出易损性模型的应用实例,讨论随机性和不确定性对易损度的影响。结果表明,进行易损性分析时,需拥有丰富的知识和经验,以减少不确定性,使得到的分析结果更接近实际。     

Study of ultimate seismic response and fragility evaluation of nuclear power building using nonlinear three-dimensional finite element model

The probabilistic safety assessment (PSA) is important for nuclear power buildings in Japan because the risk of the occurrence of seismic ground motions beyond the design assumption cannot be denied. In this paper, the building fragility of the seismic PSA was evaluated using a high accuracy analysis model (three-dimensional nonlinear FEM building model considering soil-structure interaction and basemat uplift behavior). First, the response analyses were conducted increasing the input acceleration up to 3500 Gal, until the damage of the building reached the ultimate condition. The damage of the building was estimated from the shear strain, the axial stress, and the consumed strain energy of the shear walls. Then, the influence on the response given by the vertical ground motion and the basemat uplift was evaluated. In addition, considering the shear destruction of the web wall and compressive crash of the flange wall as the fracture modes, the building fragility was evaluated. As a result, it was shown that the investigated method is efficient for more accurate seismic PSA estimation.     

多种影响因素下的设备易损性计算

抗震裕度评估是核电厂地震安全评估的方法之一，通过地震易损性分析计算高置信度低失效概率的抗震能力值是抗震裕度评估中很重要的一步。本文对于同时受到多种失效模式影响的设备易损性计算进行了研究，讨论了蒙特卡罗抽样方法和拉丁超立方分布抽样方法在设备易损性计算中的应用，对两种抽样方法的计算效率和准确度进行了评价。结果表明，在小样本抽样计算时拉丁超立方抽样方法有更好的计算效率和收敛速度，在1 000次样本数量时，两种抽样方法计算结果均可达到收敛。     

堆芯补水箱地震易损性分析

本文采用有限元软件ANSYS建立AP1000核电站堆芯补水箱（CMT）三维有限元模型，通过模态分析获得其结构特征，采用时程分析法较为真实地模拟CMT地震下响应。通过地震易损性数学模型，对CMT的各项易损性参数进行分析，获得了其抗震能力中值A_m、随机性标准差β_R以及不确定性标准差β_U，计算出其高置信度低失效概率（HCLPF）值。结果表明：CMT的HCLPF值明显高于设计安全停堆地震强度0.3g，说明其具有较高的抗震能力，且HCLPF值略高于采用确定论方法得到的值。对易损性参量误差敏感性分析发现β_R取值变化对CMT的条件失效概率和HCLPF值影响较小，可简化部分随机性误差的考虑，使得易损性分析更简洁。     

How to eliminate non-damaging earthquakes from the results of a probabilistic seismic hazard analysis (PSHA)—A comprehensive procedure with site-specific application

The results of probabilistic seismic hazard analyses are frequently presented in terms of uniform hazard spectra or hazard curves with spectral accelerations as the output parameter. The calculation process is based on the evaluation of the probability of exceedance of specified acceleration levels without consideration of the damaging effects of the causative earthquakes. The same applies to the empirical attenuation equations for spectral accelerations used in PSHA models. This makes interpreting and using the results in engineering or risk applications difficult. Uniform hazard spectra and the associated hazard curves may contain a significant amount of contributions of weak, low-energy earthquakes not able to damage the seismically designed structures of nuclear power plants. For the development of realistic engineering designs and for realistic seismic probabilistic risk assessments (seismic PRA) it is necessary to remove the contribution of non-damaging earthquakes from the results of a PSHA. A detailed procedure for the elimination of non-damaging earthquakes based on the CAV (Cumulative Absolute Velocity)-filtering approach was developed and applied to the results of the large-scale PEGASOS probabilistic seismic hazard study for the site of the Goesgen nuclear power plant. The procedure considers the full scope of epistemic uncertainty and aleatory variability present in the PEGASOS study. It involves the development of a set of empirical correlations for CAV and the subsequent development of a composite distribution for the probability of exceedance of the damaging threshold of 0.16 gs. Additionally, a method was developed to measure the difference in the damaging effects of earthquakes of different strengths by the ratio of a power function of ARIAS-intensity or, in the ideal case, by the ratio of the square roots of the associated strong motion durations. The procedure was applied for the update of the Goesgen seismic PRA and for the confirmation of a revised safe shutdown earthquake for the Goesgen nuclear power plant. The application of the procedure leads to results which are in reasonable compliance with evaluations based on the macroseismic method using European macroseismic intensities and associated vulnerabilities. The paper is an extended version of the paper #1142 presented at the 19th SMIRT conference in Toronto, 2007.     

储液容器地震易损性参数计算

本文介绍了核电厂设备的易损性分析方法以及易损性模型的参数化计算方法。对核电厂中的典型储液容器应急补水箱（ASG水箱）使用Housner质量-弹簧简化模型进行了分析。对ASG水箱的各项易损性参数进行了计算，绘制出其易损性曲线，并得出高置信度低失效概率（HCLPF）值。结果表明：ASG水箱的HCLPF值低于安全停堆地震（SSE）水平，属于抗震能力较低的设备，需在结构上进行加强。     

地震概率安全分析中地震易损度不确定性分布的研究

核电厂地震概率安全分析(PSA)中,构筑物和设备的地震易损度是在给定地面运动强度条件下的条件失效概率。地震易损度的不确定性分布较为复杂,在地震PSA定量化过程中难于处理。本文针对地震易损度的数学模型进行研究,采用数值方法求解地震易损度的均值和方差。在均值和方差相等的条件下,以几种常见的不确定性分布类型近似地震易损度的不确定性分布。通过比较可以看出,Beta分布可以较为准确地描述地震易损度的不确定性分布。     

The use of the uniform risk spectra in the seismic PSA for a PWR power station

This paper describes a simple method for incorporating the effects of the uniform risk spectra (URS) in the seismic probabilistic safety assessment (PSA) for a pressurized water reactor (PWR) power station. The “traditional” fragility parameters for a range of critical equipment items in a PWR power station on two typical UK sites are modified to incorporate the URS using this simple method and the effect on the high confidence low probability of failure (HCLPF) acceleration levels and seismic-induced failure probabilities of the equipment items is examined. The results illustrate the potential benefit of using the URS in the seismic PSA for a PWR power station.     

Lower bound earthquake magnitude for probabilistic seismic hazard evaluation

This paper presents the results of a study that develops an engineering and seismological basis for selecting a lower-bound magnitude (LBM) for use in seismic hazard assessment. As part of a seismic hazard analysis the range of earthquake magnitudes that are included in the assessment of the probability of exceedance of ground motion must be defined. The upper-bound magnitude is established by earth science experts based on their interpretation of the maximum size of earthquakes that can be generated by a seismic source. The lower-bound or smallest earthquake that is considered in the analysis must also be specified.The LBM limits the earthquakes that are considered in assessing the probability that specified ground motion levels are exceeded. In the past there has not been a direct consideration of the appropriate LBM value that should be used in a seismic hazard assessment. This study specifically looks at the selection of a LBM for use in seismic hazard analyses that are input to the evaluation/design of nuclear power plants (NPPs). Topics addressed in the evaluation of a LBM are earthquake experience data at heavy industrial facilities, engineering characteristics of ground motions associated with small-magnitude earthquakes, probabilistic seismic risk assessments (seismic PRAs), and seismic margin evaluations. The results of this study and the recommendations concerning a LBM for use in seismic hazard assessments are discussed.     

Methods to derive seismic fragility of NPP components: A summary

Seismic fragility of structure, system or component (SSC) is the probability of its reaching a limit state, for a given seismic demand. It is evaluated in terms of ground motion parameters, which is generally peak ground acceleration. Seismic fragility of a nuclear power plant (NPP) is derived from the fragility of its SSC. Seismic qualification, prerequisite for determination of seismic fragility of the SSC of a NPP, is conducted by either direct method involving analysis and testing; or indirect one involving experience based method. The paper surveys and summarizes the methods available to derive the seismic fragility of SSC(s) of an NPP, which are qualified by direct as well as indirect methods.     

基于分离变量的地震PSA相关性分析方法研究

为解决现有地震概率安全评价（PSA）相关性分析简化假设存在的问题,建立更准确反映核电厂构筑物、系统和部件（SSC）地震相关性的分析方法,对基于分离变量的易损度相关性分析开展了研究。结合易损度模型对分析方法进行了理论推导,并对方法的实施过程进行了介绍。利用该方法对不同条件下SSC的联合失效开展案例分析,得到了联合失效的易损度曲线和失效频率分析结果,并与现有相关性简化假设得到的结果进行了对比。研究结果表明,基于分离变量的地震PSA相关性分析方法能弥补现有方法的不足,支持核电厂地震PSA开发和应用。