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.     

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.     

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。     

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.     

安全壳外挂水箱结构强度分析

我国自主设计的第3代核电站安全壳外挂水箱用于超设计基准事故下内层安全壳的长期排热,这是确保安全壳完整、核电厂安全的重要设施。因此,有必要对外挂水箱在极限安全地震动与温度异常工况组合作用下的结构强度进行分析。建立带有外挂水箱的外层安全壳有限元模型,开展网格敏感性分析,并通过模态分析研究结构的振动特性。采用时程分析法,对结构同时施加温度和地震动载荷,基于流固耦合方法分析水体与结构的相互作用,研究外挂水箱结构的地震动响应以及水箱内水体振荡特性。研究表明,水体在水箱凹沉处水面振荡幅度较大,在EL Centro地震动、人工合成地震动和长周期地震动工况下外挂水箱的最大拉应变和最大压应变绝对值均小于C60混凝土许用应变值。     

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。     

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.     

Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained by the Newmark's step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period of isolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further, there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value. Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displacements but it may increase the base shear.     

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.     

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.     

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.     

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。     

Parametric study of relay seismic capacity

An evaluation of the existing relay test data base at Brookhaven National Laboratory (BNL) has indicated that the seismic capacity of a relay may depend on various parameters related to the design or the input motion. In order to investigate the effect of these parameters on the seismic fragility level, BNL has conducted a relay test program. Establishing the correlation between the single frequency fragility test input and the corresponding multifrequency response spectrum (TRS) is also an objective of this test program. The testing has been performed at Wyle Laboratories. This paper discusses the methodology used for testing and presents a brief summary of important test results.     

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.     

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。     

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。     

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.     

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.     

考虑地基岩土参数不确定性的核电厂结构随机地震反应分析

在考虑土-结构相互作用(SSI)效应的情况下,引入随机地震反应分析方法,探讨地基岩土参数的不确定性对核电厂地震响应的影响.基于ANSYS程序,采用常数阻抗法,通过设置边界弹簧和阻尼来考虑地基土的作用,并通过设置弹簧和阻尼参数的不确定性,来模拟岩土动态参数的不确定性.针对某1000MW级压水堆核电站反应堆厂房结构,进行随机地震反应的数值仿真分析,并将随机反应结果与确定论分析结果进行了对比.结果表明,随机分析方法是确定论分析方法的有益补充,二者结合能更合理地反映参数的不确定性对结构地震响应的影响.     

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。