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.     

Evaluation of seismic fragility of structures—a case study

The present paper attempts to evaluate the seismic fragility for a typical elevated water-retaining structure. The structure is analysed for two cases: (i) empty tank; and (ii) tank filled with water. The various parameters that could affect the seismic structural response include material strength of concrete and reinforcing steel, effective prestress available in the tank, ductility ratio and structural damping available within the structure, normalised ground motion response spectral shape, foundation and surrounding soil parameters and the total height of water available in the tank. Based on this case study, the seismic fragility of the structure is developed. The results are presented as families of conditional probability curves plotted against peak ground acceleration (PGA) at two critical locations. The procedure adopted, incorporates the various randomness and uncertainty associated with the parameters under consideration.     

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。     

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.     

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.     

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。     

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。     

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.     

拟合核电厂设计反应谱及峰值位移的地震动调整方法

提出一种以核电厂设计用伪速度反应谱及峰值位移为拟合目标的地震动调整方法。该方法基于样条小波的快速分解与回复算法,将实际地震加速度记录应用2阶基数B-样条小波进行分解,以识别对峰值位移、峰值加速度影响最大的小波分量;并在此基础上,通过改进地震动调整的小波分析法与时域叠加小波函数法,实现对目标反应谱及峰值位移、峰值加速度的同时拟合。算例分析结果表明,该方法具有较高的拟合精度。     

Seismic response and fragility analysis of a water storage structure

Stress analysis of a water storage structure has been carried out for static and seismic loading. Based on the stress analyses results, assessment of most likely failure modes for the structure caused by seismic event has been carried out. An attempt has been made to quantify the initial leakage rate and average emptying time for the structure during seismic event after evaluating the various crack parameters, viz., crack-width and crack-spacing at the locations of interest. Finally, the seismic fragility of the structure is developed as families of conditional probability curves plotted against peak ground acceleration (PGA) parameter at the location of interest considering the randomness and uncertainty associated with various parameters that could affect the seismic structural response.     

The seismic reliability of VVER-1000 NPP prestressed containment building

The failure probability assessment of the containment building is an essential feature of the Level 2 PSA studies of nuclear power plants. The primary purpose of this paper is to demonstrate the methodology of evaluating containment seismic induced probability of failure without containment pressurization. The Loviisa, Finland site is one of the most seismically stable in the world and the numerically evaluated seismic induced failure probabilities are not representative for other sites. In addition, the containment concept described in this paper is not the typical Russian design which uses helical tendons in the cylindrical part of the structure and has a ring girder at the spring line of the structure. So the conclusions reached are applicable only to the containment configuration described in the paper. The geometry of the containment was determined by its preliminary design. The seismic hazard of the plant site was assessed during Level 1 PSA of the Loviisa plant. The initial information for seismic fragility analysis of the containment is the seismic response of the structure. The structural model for response analysis was the stick model. The stress analysis of the containment was carried out using the shell element model. The fragility evaluation of the containment was performed with the PROSAN-program. The structure was modeled as a parallel system consisting of the most heavily stressed elements. The resulting fragility curve gives the conditional probability of failure as a function of peak ground acceleration. The seismic hazard and the fragility were convolved to obtain the annual nonexceedance probability distribution for the collapse frequency of the structure.     

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.     

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。     

Fragility estimation of an isolated FBR structure considering the ultimate state of rubber bearings

This paper presents a methodology and the results on the fragility estimation of an isolated reactor building for the FBR (Fast Breeder Reactor). The methodology is based on a regression analysis between the intensity of the input earthquake motion and the response obtained from non-linear response analyses in which the effect of non-linear restoring characteristics regarding isolators and superstructure are taken into account. And also the result of a probabilistic estimation on the ultimate capacity of the isolation layer is incorporated in the fragility estimation.     

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.     

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。     

Variable friction pendulum system for seismic isolation of liquid storage tanks

Earthquake response of liquid storage steel tanks isolated with variable friction pendulum system (VFPS) is investigated under normal component of six recorded near-fault ground motions. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The corresponding stiffness constants associated with these lumped masses are worked out depending upon the properties of the tank wall and liquid mass. The governing equations of motion of the tanks isolated with variable friction pendulum system are derived and solved by Newmark's step-by-step method assuming linear variation of acceleration over small time interval. In order to verify the effectiveness of the VFPS in tanks, the seismic response of tanks isolated with VFPS is compared with that of the same tanks isolated using the conventional friction pendulum system (FPS). Furthermore, a parametric study is also carried out to critically examine the behaviour of tanks isolated with VFPS. The various important parameters considered are the tank aspect ratio, the isolation period and initial time period of the VFPS. In addition, the seismic response of tanks isolated with VFPS under trigonometric cycloidal pulses is also investigated. From these investigations, it is concluded that with the installation of VFPS in tanks, the seismic response of tanks during near-fault ground motions can be controlled within a desirable range. Finally, it is also observed that the response of tanks isolated with VFPS under the near-fault ground motions and trigonometric cycloidal pulses matches well only when the isolation period reaches high values.     

考虑SSI效应的核电站泵房结构楼层反应谱分析

采用Super SAP和CLASSI程序对某在建核电站泵房结构进行了极限安全地震震动和运行安全地震震动情况下的土壤-结构相互作用(SSI)的地震分析,揭示了结构在时域内的特性;通过傅立叶变换(FFT)分析了结构在频域内的特性,求得建筑结构中各楼层反应谱,结合核电厂设计规范分别给出了在较硬地基岩土条件下,结构考虑和不考虑SSI时各楼层反应谱,并对其进行了比较分析.结果表明,SSI效应对结构楼层反应谱的谱形、谱值以及零周期平台高度有一定的影响.     

Artificial ground motion compatible with specified peak ground displacement and target multi-damping response spectra

With respect to the design ground motion of nuclear power plant (NPP), the Regular Guide 1.60 of the US not only defined the standard multi-damping response spectra, i.e. the RG1.60 spectra, but also definitely prescribed the peak ground displacement (PGD) value corresponding to the standard spectra. However, in the engineering practice of generating multi-damping-spectra-compatible artificial ground motion for the seismic design of NPP, the PGD value had been neglected. Addressing this issue, this paper proposed a synthesizing method which generates the artificial ground motion compatible with not only the target multi-damping response spectra but also the specified PGD value. Firstly, by the transfer formula between the power spectrum and the response spectrum, an initial uniformly modulated acceleration time history is synthesized by multiplying the stationary Gaussian process with the prescribed intensity envelope to simulate the amplitude-non-stationarity of earthquake ground motion. And then by superimposing a series of narrow-band time histories in the time domain, the initial time history is modified in the iterative manner to match the target PGD as well as the target multi-damping spectra with the pre-specified matching precisions. Numerical examples are provided to demonstrate the matching precisions of the proposed method to the target values.     

An improved spectrum superposition method for structures with rigid modes

Based on a precise probabilistic formulation, a spectrum superposition method has been proposed to obtain very accurate estimate of the seismic response of structures with significant contribution from high-frequency rigid modes. The proposed approach computes the exact statistics of the ordered-peaks of response, which is defined in terms of the first few moments of the power spectral density function (PSDF) of the response. Like many other studies, the PSDFs for various response quantities have been defined in terms of the PSDF of input ground acceleration, the modal properties of a few lowest frequency modes and the pseudostatic response of the structure to an acceleration of unit magnitude. However, the other methods express the final results directly in terms of the response spectrum amplitudes under several simplifying assumptions, which results in unacceptable error in many cases. Due to its exactness, the proposed method has been found to give consistently good agreement with the exact solution for a wide variety of input excitations and structural systems. Furthermore, the present method also has the response spectrum as its basis by defining the PSDF of input excitation which is compatible with a given design spectrum.