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.     

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。     

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。     

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.     

电气机柜的地震概率易损度分析

为开展电气机柜的地震概率安全分析（PSA）,利用抗震能力与条件失效概率之间的关系和抗震鉴定试验数据,通过地震易损度的对数正态分布特性开展了电气机柜的概率易损度评价,得到某电气机柜的抗震能力中值为0.75g、随机性对数标准差为0.21、不确定性对数标准差为0.50及高置信度低失效概率（HCLPF）值为0.23g。该评价方法对电气设备的地震易损度分析具有借鉴作用。      

Seismic damage hazard analysis for requalification of nuclear power plant structures: methodology and application

A methodology for the evaluation of the annual probability of occurrence of post-elastic seismic damage in realistic structures is presented. The seismic damage hazard analysis (SDHA) is carried out here by coupling conventional seismic hazard analysis (SHA) for the site and the structural response to earthquakes of different intensities. The structural performance is statistically investigated by conducting appropriate non-linear dynamic analyses for a limited set of real ground-motion records that might potentially pose a threat to the structure at the site. The merging of these two approaches permits calculation of the seismic hazard faced by the structure in direct damage terms. The methodology is presented in this paper with the aid of a simple illustrative case study where the annual probability of damage and, eventually, failure of a power house steel structure is computed. This methodology can find practical applications in seismic retrofit of nuclear power plant structures and in the evaluation of seismic damage hazards in new structure designs.     

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。     

Concept for comprehensive Hazards PSA and Fire PSA application

This contribution presents results of recent research and development activities in the field of Hazards PSA (HPSA). The reactor accidents at Fukushima Dai-ichi in March 2011 gave reason and indications for checking the risk assessment approach for internal and external hazards as currently described in the German PSA Guideline and its supplementary technical documents. A standardized approach for performing a comprehensive HPSA has been developed emphasizing the complete consideration of all potential failure dependencies induced by hazards. The systematic extension of the given plant model of Level 1 PSA is the real crux of the new HPSA approach. The extension is carried out for each hazard H using the corresponding hazard equipment list (H-EL) and the corresponding hazard dependency list (H-DL). Parts of the approach have already been tested.In the paper a successful application for the plant internal hazard fire is presented. A German licensee plans a system modification of the spent fuel pool cooling, therefore a Level 1 PSA has been carried out to compare the fuel damage frequencies for the existing and the modified version. It is outlined how the systematic (and partly automatic) extension of the fault trees is performed using a so-called Fire Equipment List (F-EL). The F-EL contains a compartment assignment for all relevant components and cables. The probability of a compartment failure by fire must be determined for any compartment mapped. This is the conditional probability that the components and cables within the compartment are inoperable due to the fire.     

核电厂安全壳近场地震动下易损性分析

安全壳结构作为核电厂最重要的结构之一,其地震易损性是核电厂结构概率地震安全评价工作中关注的重点。结合非线性有限元分析技术和增量动力分析方法,对核电厂安全壳在近场地震动作用下的易损性展开分析。此外,为克服传统基于顶点位移的安全壳结构整体损伤指标的局限性,本文提出了基于能量的整体损伤指标,并验证其有效性。最后提出了考虑地震易损性参数统计不确定性的易损性曲线构造方法。研究结果表明:本文提出的安全壳结构整体损伤指标能很好地反映安全壳结构整体变形特性,并且其变异性小于基于顶点位移整体损伤指标的变异性。统计不确定性对安全壳结构不同损伤性能水准下对应的易损性曲线的整体影响可以忽略,但对易损性曲线下尾部分有一定影响。      

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。     

Probabilistic seismic risk analysis of CANDU containment structure for near-fault earthquakes

In this study, the seismic risk of a CANDU (CANada Deuterium Uranium) containment structure is estimated by performing the nonlinear seismic analysis for the near-fault earthquakes. Nonlinear seismic analysis is more effective to consider the distinct nonlinear behavior of concrete structures subjected to the near-fault ground motion which has high input energy. In Korea, the seismic fragility analysis has been performed by using the design analysis results which were obtained from a linear elastic analysis.The lumped mass model of the containment structure was used for a nonlinear dynamic time history analysis. The tri-linear skeleton curve was used for the nonlinear behavior of the prestressed concrete containment structure. In order to estimate the inelastic nonlinear response of the containment, the maximum point-oriented model was used for the hysteretic rule of the shear deformation.For the nonlinear seismic analyses, 30 set of real near-fault earthquake records were used as the input motion. The seismic fragility and risk of the containment for the near-fault ground motions are compared with those from the results based on the conventional method.     

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。     

Serviceability design load factors and reliability assessments for reinforced concrete containment structures

A reinforced concrete nuclear power plant containment structure is subjected to various random static and stochastic loads during its lifetime. Since these loads involve inherent randomness and other uncertainties, an appropriate probabilistic model for each load must be established in order to perform reliability analysis. The current ASME code for reinforced concrete containment structures are not based on probability concepts. The stochastic nature of natural hazard or accidental loads and the variations of material properties require a probabilistic approach for a rational assessment of structural safety and performance. The paper develops probability-based load factors for the limit state design of reinforced concrete containment structures. The purpose of constructing reinforced concrete containment structure is to protect against radioactive release, and so the use of a serviceability limit state against crack failure that can cause the emission of radioactive materials is suggested as a critical limit state for reinforced concrete containment structures. Load factors for the design of reinforced concrete containment structures are proposed and carried out the reliability assessments.     

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。     

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。     

核电厂地震PSA中的风险定量化研究

论述了核电厂地震概率安全评价（PSA）定量化方法和工具的现状,指出了定量化工具面临的挑战和存在的问题。根据定量化的概率论本质,提出了计算方法。以我国某核电厂厂址多方案概率地震危险性分析（PSHA）结果和核电厂地震响应分析给出的最小割集为例,展示了计算方法的应用过程,分析了地震动参数和置信度参数对定量化计算结果的影响。结果表明,针对置信度参数进行拉丁超立方采样,采样次数较小时即可给出地震导致的核电厂堆芯损坏频率（SCDF）的稳定估计值;通常情况下,设备失效对SCDF的贡献最大,厂房失效的影响相对较小;地震动年发生率对SCDF的贡献需要根据工程场地的位置进行具体分析。      

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。     

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.     

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.     

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.