Numerical computation of fragility curves for NPP equipment

The seismic probabilistic risk assessment (PRA) methodology is a popular approach for evaluating the risk of failure of engineering structures due to earthquake. In this framework, fragility curves express the conditional probability of failure of a structure or component for a given seismic input motion parameter A, such as peak ground acceleration (PGA) or spectral acceleration. The failure probability due to a seismic event is obtained by convolution of fragility curves with seismic hazard curves. In general, a log-normal model is used in order to estimate fragilities. In nuclear engineering practice, these fragilities are determined using safety factors with respect to design earthquake. This approach allows to determine fragility curves based on design study but largely draws on expert judgement and simplifying assumptions. When a more realistic assessment of seismic fragility is needed, simulation-based statistical estimation of fragility curves is more appropriate. In this paper, we will discuss statistical estimation of parameters of fragility curves and present results obtained for a reactor coolant system of nuclear power plant. We have performed non-linear dynamic response analyses using artificially generated strong motion time histories. Uncertainties due to seismic loads as well as model uncertainties are taken into account and propagated using Monte Carlo simulation.     

A numerical procedure for computing the fragility of NPP components under random seismic excitation

A numerical procedure is proposed in the paper for computing seismic fragility functions for equipment components in Nuclear Power Plants. The procedure is based on the hypothesis, which is typical when seismic excitation of components is addressed, of linear behaviour of the building. Given the large size of the FE element models adopted for the building, which makes direct Monte Carlo simulation impossible, the response surface methodology is used to model the influence of the random variables on the dynamic response. To account for stochastic loading the latter is estimated by means of a simulation procedure. Once the response surfaces defining the statistical properties of the response are available, the Monte Carlo method is used to compute the failure probability. A procedure for refining the RS estimation is also proposed, based on the evaluation of risk for a prototype site.A validation example is given, regarding the simplified modelling of a reactor building resting on a base-isolation system; results obtained by plain Monte Carlo analysis are compared to those computed via the proposed procedure The latter is finally applied to a real life case, taken from the preliminary design of the auxiliary building within the IRIS international project.     

Seismic probabilistic risk analysis based on stochastic simulation of accelerograms for nuclear power plants in the UK

This article presents an approach to probabilistically assess the seismic risk of nuclear power plants (NPPs) in the UK. The approach proposed is based on direct stochastic simulation of the seismic input to conduct nonlinear dynamic analysis of a structural model of the NPP analysed. Therefore, it does not require the use of ground motion prediction equations and scaling/matching procedures to define suitable accelerograms as is done in conventional approaches. Additionally, as the structural response is directly calculated, it does not require the use of Monte Carlo-type algorithms to simulate the damage state of the NPP analysed. However, it demands longer use of computer resources as a relatively large number of nonlinear dynamic analyses are needed to perform. The approach is illustrated using an example of a 1000 MW Pressurised Water Reactor building located in a representative UK nuclear site. A comparison of risk assessment is made between the conventional and proposed approaches. Results obtained are reasonable and well constrained by conventional procedures; hence, it can confidently be used by the UK New Build Programme in the next two decades to generate 16 GWe of new nuclear capacity.     

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。     

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。     

Seismic reliability of electrical power transmission systems

The reliability of electric power transmission systems is important for the probabilistic safety assessment of nuclear power plants under a given earthquake loading as it relates to the loss of off site power to the nuclear power plants. Here, a comprehensive model to evaluate the seismic reliability of electric power transmission systems is presented. The model provides probabilistic assessments of structural damage and abnormal power flow that can lead to power interruption in a transmission system under a given earthquake. With the proposed methodology seismic capacities of electrical. equipment are determined on the basis of available test data and simple modeling from which fragility functions of specific substations are developed. Earthquake ground motions are defined as stochastic processes. Probabilities of network disconnectivity and abnormal power flow are assessed through Monte Carlo simulations. The proposed model is applied to the electric power network in San Francisco and vicinity under the 1989 Loma Prieta earthquake, and the probabilities of power interruption are contrasted with the actual power failures observed during that earthquake.     

百万千瓦级核电厂地震风险评价和见解

针对特定百万千瓦级压水堆核电厂开展地震概率风险评价,开发了电厂特定的地震危险性曲线和设备的地震易损度曲线,建立地震概率风险评价模型并完成定量化,给出地震风险结果和见解。结果表明,该特定电厂地震风险水平较低,在0.3g～0.6g地震动水平区间内地震风险贡献最为突出。     

考虑竖向地震动影响的某核电安全壳地震易损性研究

核电厂等重要基础设施的抗震设计和评估需要考虑竖向地震动影响,目前竖向地震动对核电安全壳地震易损性影响研究还较少。本文进行了考虑竖向地震动影响的核电安全壳地震易损性研究,分析了以水平向场地相关谱为目标谱选取的地震动记录的不足,提出了同时匹配水平和竖向场地相关谱的地震动选取方法,选取了指定场址的水平和竖向地震动记录。采用增量动力分析方法,基于选取的水平和竖向地震动,分别进行核电安全壳水平向地震动作用下与水平和竖向地震动联合作用下的易损性分析。采用基于混合易损性数据的易损性分析方法,得到了具有置信度的易损性曲线和高置信度低失效概率。分析结果表明：竖向地震动对安全壳抗震能力和地震易损性有较大影响。     

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。     

Methodology and results of the seismic probabilistic safety assessment of Krško Nuclear Power Plant

A seismic IPEEE (Individual Plant Examination for External Events) was performed for the Kr

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ko plant. The methodology adopted is the seismic PSA (probabilistic safety assessment). The Kr

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ko NPP is located on a medium to high seismicity site. The PSA study described here includes all the steps in the PSA sequence, i.e. reassessment of site hazard, calculation of plant structures response including soil–structure interaction, seismic plant walkdowns, probabilistic seismic fragility analysis of plant structures and components, and quantification of seismic core damage frequency (CDF). Relay chatter analysis and soil stability studies were also performed. The seismic PSA described here is limited to the analysis of CDF (level 1 PSA). The subsequent determination and quantification of plant damage states, containment behaviour and radioactive releases to the outside (level 2 PSA) have been performed for the Kr

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ko NPP but are not further described in this paper. The results of the seismic PSA study indicates that, with some upgrades suggested by the PSA team, the seismic induced CDF is comparable with most US and Western Europe NPPs located in high seismic areas.     

Uncertainty analysis of system fragility for seismic safety evaluation of NPP

In this study, a Seismic Probabilistic Safety Assessment (SPSA) methodology considering the uncertainty of fragilities was studied. A system fragility curve is estimated by combining component fragilities expressed by two variance sources, inherent randomness and modeling uncertainty. The sampling based methods, Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS), were used to quantify the uncertainties of the system fragility. The SPSA of an existing nuclear power plant (NPP) was performed to compare the two uncertainty analysis methods. Convergence of the uncertainty analysis for the system fragility was estimated by calculating High Confidence Low Probability of Failure (HCLPF) capacity. Alternate HCLPF capacity by composite standard deviation was also verified. The annual failure frequency of the NPP was estimated and the result was discussed with that from the other researches. As a result, the criteria of the uncertainty analysis and its effect was investigated.     

Preliminary seismic analysis of an innovative near term reactor: Methodology and application

Nuclear power plant (NPP) design is strictly dependent on seismic hazard and safety aspects concerned with the external events of the site. Earthquake resistant structures design requires realistic and accurate physical and theoretical models to describe the response of the nuclear power plants (NPPs) that depend on both the ground motion characteristics and the dynamic properties of the structures themselves. In order to improve the design of new NPPs and, at the same time, to retrofit existing ones the dynamic behaviour of structures subjected to critical seismic excitations that may occur during their expected service life must be evaluated.The aim of this work is to select new effective methods to assess NPPs vulnerability by properly capturing the effects of a safe shutdown earthquake (SSE) event on nuclear structures, like the near term deployment IRIS reactor, and to evaluate the seismic resistance capability of as-built structures systems and components. To attain the purpose a validated deterministic methodology based on an accurate finite element modelling coupled to substructure and time history approaches was employed for studying the overall dynamic behaviour of the NPP relevant components. Moreover the set up three-dimensional model was also validated to evaluate the performance and reliability of the adopted FEM code (mesh refinements and type element influence). This detailed numerical assessment, involving the most widely used finite element numerical codes (MSC.Marc^® and Ansys^®), allowed to solve, perform and simulate as accurately as possible the dynamic behaviour of structures which may withstand a lot of more or less complicate structural problems.To evaluate the accuracy and the reliability as well as to determine the related error of the set-up procedure, the obtained seismic analyses results in term of accelerations, propagated from the ground to the auxiliary building systems and components, and displacements were compared highlighting a very good agreement.     

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.     

Improved response factor methods for seismic fragility of reactor building

A seismic probabilistic risk assessment (PRA) method has been applied to evaluate the safety of nuclear reactor buildings during earthquakes. Improvement was made to two methods (based on linear response and based on non-linear response) of fragility analysis in seismic PRA. The conventional method, which is based on linear response, considers increases of seismic capacity implicitly, using the non-linear behaviour of the structure. We described how to evaluate the capacity increase factor for the linear response method. Secondly, we proposed a method based on the non-linear response and a stratified two-point estimation method which can efficiently evaluate the variability of non-linear responses. We applied the two method to a PWR-type nuclear reactor building and ascertained that these method are useful and effective.     

基于经验-解析数据的某核电安全壳地震易损性分析

本文基于混合数据的地震易损性分析方法,对我国已运行核电厂地震易损性分析进行研究。首先基于地震危险性分析和分解结果,生成了我国华南地区某核电厂厂址条件谱;然后采用贪心优化算法,选取符合厂址危险性的地震动记录;基于增量动力分析方法,生成我国某核电厂安全壳地震易损性安全系数FS和FSA的解析数据;地震易损性其他参数采用经验数据,基于经验-解析数据,生成了我国某核电厂安全壳地震易损性曲线。建议将基于经验-解析数据的地震易损性分析方法应用于我国核电厂安全壳初步地震易损性分析中。     

Seismic individual plant examination of external events of US nuclear power plants: insights and implications

As part of the implementation of the severe accident policy, nuclear power plants in the US are conducting the individual plant examination of external events (IPEEE). Seismic events are treated in these IPEEEs by either a seismic probabilistic risk assessment (PRA) or a seismic margin assessment. The major elements of a seismic PRA are the seismic hazard analysis, seismic fragility evaluation of structures and equipment and systems analysis using event tree and fault tree analysis techniques to develop accident sequences and calculate their frequencies of occurrence. The seismic margin assessment is a deterministic evaluation of the seismic margin of the plant beyond the design basis earthquake. A review level earthquake is selected and some of the components that are on the success paths are screened out as exceeding the review level earthquake; the remaining ones are evaluated for their seismic capacity using information from the original plant design criteria, test data and plant walkdown. The IPEEEs of over 100 operating nuclear power plants are nearing completion. This paper summarizes the lessons learned in conducting the IPEEEs and their applicability to nuclear power plants outside of the United States.     

The LBB project for the new generation of WWER plants and lessons learned from the WWER 440 model 230 LBB project

As part of the safety enhancement of WWER-type nuclear power plants (NPPs) with model 213 and 320 reactors operated or constructed in the Czech and Slovak Republics, the leak-before-break (LBB) methodology is applied to main circulating pipe and pressuriser surge lines. The typical feature of all these NPPs is the horizontal type steam generator. The resultant effect is that the lengths of all safety significant piping are longer in comparison with standard western PWRs. For this reason the complex dynamical model is used for seismic response assessment performed as part of LBB methodology. In this paper the results of decoupling studies and the new set of experiments concerning both leak rates and accomplished diagnostics measurements are described.     

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.     

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。