Probabilistic seismic safety study of an existing nuclear power plant

This study was conducted as part of an overall safety study of the Oyster Creek nuclear power plant. The earthquake hazard was considered as an initiating event that could result in radioactive release from the site as a result of core melt. The probability of earthquake initiated releases were compared with the probability of releases due to other initiating events.Three steps are necessary to evaluate the probability of earthquake initiated core melt.

1. (1) estimate the ground motion (peak ground acceleration) and uncertainty in this estimate as functions of annual probability of occurrence;

2. (2) estimate the conditional probability of failure and its uncertainty for structures, equipment, piping, controls, etc., as functions of ground acceleration; and

3. (3) combine these estimates to obtain probabilities of earthquake induced failure and uncertainties in such estimates to be used in event trees, system models, and fault trees for evaluating the probability of earthquake induced core melt.

This paper concentrates on the first two steps with emphasis on step 2. The major difference between the work presented and previous papers is the development and use of uncertainty estimates for both the ground motion probability estimates and the conditional probability of failure estimates.The ground motion capacity of a structure, component, etc., is treated for simplicity and clarity as a product random variable A given by , where is the best estimate of the median ground acceleration capacity, _R and _U are lognormal random variables with unit median and logarithmic standard deviation β_R and β_U, respectively. β_R expresses the dispersion in the ground acceleration capacity due to underlying randomness from such sources as (1) the variability of an earthquake time-history and thus of structural response when the earthquake is only defined in terms of the peak ground acceleration; and (2) the variability of structural material properties associated with strength, inelastic energy absorption and damping. Essentially, β_R represents those sources of dispersion which cannot be reduced by more detailed evaluation or more data. Uncertainty concerning the ground motion capacity is expressed by β_U which results from such things as (1) lack of complete knowledge of structural material properties; and (2) errors in calculating response due to approximate modelling. This paper presents a methodology (with examples) for estimating , β_R, and β_U for structures and components. These estimates are then used to estimate conditional probabilities of failure with confidence bounds on these estimates.The conclusion is that a rational approach exists for estimating earthquake induced probabilities of failure. Confidence bounds on such estimates can be developed to express uncertainty in the parameters used. Such an approach is preferable over one in which dispersion due to underlying randomness, and due to uncertainty in the data are combined into a single probability of failure estimate with no estimate of the uncertainty in this probability.     

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。     

Probabilistic cost-benefit seismic design criterion for a dedicated shutdown heat removal system

A probabilistic methodology is developed for assessing the risk reduction potential and cost-benefit tradeoff of a Dedicated Shutdown Heat Removal System (DSHRS) for a PWR as a function of its seismic design capability. The option of coping with a very small LOCA is included. The annual seismic risk of a plant and a similar hypothetical plant having a proposed DSHRS with various seismic strengths are computed. The difference in the annual seismic risks is the annual seismic risk reduction benefit for having the system. The present value of the future risk reduction benefit is then compared to the cost of building a DSHRS and the incremental seismic cost associated with building the system to withstand a stronger earthquake.A reactor like Zion was used for application of the method due to the availability of data. Studies were performed to investigate the sensitivity of the results to the assumed seismic hazard, probability of occurrence of seismic-induced accident initiating events, equipment seismic fragility, accident costs, and discount rate. The incremental seismic risk reduction benefit computed in these studies ranges from $207 million for a DSHRS with a median seismic capacity of 1.70g (i.e. 10 × SSE) in a new plant built at the site. The total cost of a DSHRS is crudely estimated to be $25 million or more, if it were built to withstand the current SSE of the plant (for which the system probably would have a median seismic capacity of 0.85g or more due to various design and construction conservatisms). The cost associated with the seismic design aspect of such a system is estimated to be approximately $2.5 million and it may be doubled if the seismic design capability of the system is tripled. The cost/benefit results and their inherent large uncertainties are not definitive but indicate that probabilistic seismic design of a DSHRS should be examined in further detail.     

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。     

Seismic loads for crack stability assessment, in a review of leak-before-break (LBB) applicability

This study was performed to define the seismic loading conditions for use in the crack stability assessment of a BWR for the applicability of the leak-before-break (LBB) criterion. The LBB has been applied to the design of Class 1 piping in Japanese light-water reactors. Crack penetrated condition with detectable leak in the LBB applicability review is classified into the Level C service condition. Here an S₁-earthquake (maximum design earthquake) is currently assumed, rather than an S₂-earthquake (extreme design earthquake). In order to justify this assumption, the frequency of an S₁-earthquake occurring during coolant leakage due to crack propagation was determined. The frequency of coolant leakage from Class 1 piping must be less than that of the Level C service condition (2.5 × 10⁻² to 1 × 10⁻⁴ per year) in order to assume that an S₁-earthquake is appropriate. Accordingly, the frequency of coolant leakage from Class 1 piping was calculated using a probabilistic fracture mechanics (PFM). The results of this analysis indicate that the frequency of coolant leakage from Class 1 piping is less than the expected occurrence of an S₁-earthquake. As the results, it is concluded that the assumption of the seismic loading employed in an LBB applicability review should be appropriate.     

Monte Carlo uncertainty quantification of the effective delayed neutron fraction

The applicability of Monte Carlo techniques, namely the Monte Carlo sensitivity method and the random-sampling method, for uncertainty quantification of the effective delayed neutron fraction β_eff is investigated using the continuous-energy Monte Carlo transport code, MCNP, from the perspective of statistical convergence issues. This study focuses on the nuclear data as one of the major sources of β_eff uncertainty. For validation of the calculated β_eff, a critical configuration of the VENUS-F zero-power reactor was used. It is demonstrated that Chiba's modified k-ratio method is superior to Bretscher's prompt k-ratio method in terms of reducing the statistical uncertainty in calculating not only β_eff but also its sensitivities and the uncertainty due to nuclear data. From this result and a comparison of uncertainties obtained by the Monte Carlo sensitivity method and the random-sampling method, it is shown that the Monte Carlo sensitivity method using Chiba's modified k-ratio method is the most practical for uncertainty quantification of β_eff. Finally, total β_eff uncertainty due to nuclear data for the VENUS-F critical configuration is determined to be approximately 2.7% with JENDL-4.0u, which is dominated by the delayed neutron yield of ²³⁵U.     

Probabilistic assessment of seismic risk for nuclear power plants

Probabilistic approaches to the design, siting, and safety analysis of nuclear power plants have been proposed by Farmer, Wall, and Garrick. Farmer and Wall established a limit line which delineates between acceptable and unacceptable risks. To implement the method, all accidental chains are systematically analyzed to determine their probability and associated fission product release magnitude; the combination is compared to the limit line. For proper implementation, the seismic risk should be evaluated in a quantified manner. Conceptually, this evaluation is made in two stages: the probability of an earthquake occurrence as a function of its intensity and, given a seismic intensity, the conditional probability of damage. This paper reports on an initial study into the latter aspect.The effect of uncertainty in several parameters which determine the response of a nuclear reactor building to earthquake forces is assessed. Probability distributions for material properties were determined from site measurements and these distributions were utilized for determining the building response and the damage criterion. A subjective probability density function for damping was assigned from the available information and the judgment of experienced engineers. Four accelerograms, El Centro N---S 1940, and three artificial earthquakes were used to represent the variability in the forcing functions. The uncertainty in the model idealization was assessed by evaluating three alternate models. A versatile computer program was developed to compute the response of the mathematical model to the forcing functions using matrix formulation and modal method of analysis. An exact solution, rather than numerical integration, was used to obtain the dynamic response of the system in generalized coordinates.The stresses within the reactor building are similar for different earthquakes considered in this study when they are normalized to ground acceleration, indicating that the shape of the accelerogram and its frequency content are less significant than the magnitude of the maximum ground acceleration for the reactor building. The variation in modulus of elasticity for concrete had a significant effect on the building response. Damping, in general, reduced the response, but in cases where the duration of an earthquake is short the effect was not very significant.A simple failure criteria for ultimate shear stress in shear walls, τ_ult = 4.75 √ƒ′_c, where ƒ′_c is the ultimate compressive strength of concrete, is used to estimate the initiation of cracking in the walls. The normal design of the reactor building is deterministic and is based on a 0.2 g design basis earthquake. Using the results obtained by the parametric study on the variation of response, the probability of damage was estimated by a Monte Carlo analysis. It was estimated that, given the occurrence of a design basis earthquake, there is less than approximately 10⁻³ probability of cracking in the shear walls of the reactor building. The initiation of cracking in the concrete should not lead to a significant release of contained fission products.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.     

Sleeve-type expansion anchor behavior in cracked and uncracked concrete

A test was performed to investigate the effect of concrete cracks on the static behavior of sleeve-type expansion anchors, and to confirm the seismic and fatigue resistance capability in cracked concrete. The tensile and shear test was conducted on single anchors with three different anchor diameters. Concrete test specimens are sufficiently large to prevent the effect of the concrete edges on the anchor behavior. The types of failure, the static strength and displacement behavior of the anchors in uncracked and cracked concrete were compared to evaluate the effect of the cracks. The strength reduction rate of the anchors due to the cracks was exhibited almost less than the corresponding value specified in ACI 349-01, APP. B. Through the residual strength tests, the seismic and fatigue resistance capability of the anchors was confirmed in cracked concrete. The characteristics of the anchor shear capacity significantly vary with how the displacement failure criteria are determined.     

Fragmentation of continuous molten copper droplets penetrating into sodium pool

The progression of hypothetical core disruptive accidents (CDAs) in metal fuel cores is strongly affected by exclusion of molten metal fuel from the core region due to molten fuel–coolant interaction (FCI). As a basic study of FCI, the present paper focuses on the fragmentation characteristics of continuous molten copper droplets with a total mass from 20 to 50 g penetrating into a sodium pool. The results show that the fragmentation of the continuous molten copper droplets is sensitive to the change of the hydrodynamic and thermal conditions when the instantaneous contact interface temperature (T_i) is lower than the turning point (T_tp) and insensitive at T_i > T_tp. Compared with the fragmentation of a single droplet, the fragmentation of continuous droplets is accelerated and enhanced due to the collision between the droplets and the upward microjets. The present mass median diameter (D_m) or dimensionless mass median diameter (D_m/D₀) of continuous copper droplets shows a distribution with smaller values than those of single copper droplet, and larger values than those of copper jets under similar thermal and hydrodynamic conditions. These results are promising to assure the termination of accidents in CDAs and useful to the core design with enhanced safety in FBRs.     

Damping characteristic identification for a nonlinear seismic isolation system

The steady-state response of structures to harmonic excitation is of both direct and indirect importance. Such a response is of obvious direct importance in problems which involve excitation from rotating machinery or other sources of steady harmonic excitation. It is also of indirect importance in problems involving transient excitation where knowledge of the harmonic response may be used in estimating and interpreting the transient structural response. For example, the “effective” natural frequencies, damping ratios and mode shapes identified from full-scale harmonic tests of structures are often used to interpret the transient non-linear response of these structures to earthquakes. The non-linearity is confined to the connection between the structure and the moving base. This system might be a highly idealized model for a reactor structure including non-linear seismic isolation effects.In this paper a phase resonance method is given for damping characteristic identification of the nonlinear device seismic isolation in the harmonic excitation case. The method allows the shape of the symmetric function of the system to be determined, when is not known. If F_d(x) is asymmetric then the elasticity characteristic should be known.The identification algorithm has been derived assuming that F_d(x) is given in an analytic form. The validity of the method was checked for some systems with strongly nonlinear damping characteristics.     

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。     

Uncertainty analysis in Monte Carlo criticality computations

Uncertainty analysis is imperative for nuclear criticality risk assessments when using Monte Carlo neutron transport methods to predict the effective neutron multiplication factor (k_eff) for fissionable material systems. For the validation of Monte Carlo codes for criticality computations against benchmark experiments, code accuracy and precision are measured by both the computational bias and uncertainty in the bias. The uncertainty in the bias accounts for known or quantified experimental, computational and model uncertainties. For the application of Monte Carlo codes for criticality analysis of fissionable material systems, an administrative margin of subcriticality must be imposed to provide additional assurance of subcriticality for any unknown or unquantified uncertainties. Because of a substantial impact of the administrative margin of subcriticality on economics and safety of nuclear fuel cycle operations, recently increasing interests in reducing the administrative margin of subcriticality make the uncertainty analysis in criticality safety computations more risk-significant. This paper provides an overview of two most popular k_eff uncertainty analysis methods for Monte Carlo criticality computations: (1) sampling-based methods, and (2) analytical methods. Examples are given to demonstrate their usage in the k_eff uncertainty analysis due to uncertainties in both neutronic and non-neutronic parameters of fissionable material systems.     

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 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.     

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.     

Seismic probabilistic risk assessment and its impact on margin studies

In recent years a number of seismic probabilistic risk assessments of nuclear power plants have been conducted. These studies have highlighted the significance of seismic events to the overall plant risk and have identified several dominant contributors to the seismic risk. It has been learnt from the seismic PRAs that the uncertainty in the seismic hazard results contribute to the large uncertainty in the core damage and severe release frequencies. A procedure is needed to assess the seismic safety of a plant which is somewhat removed from the influence of the uncertainties in seismic hazard estimates. In the last two years, seismic margin review methodologies have been developed based on the results and insights from the seismic probabilistic risk assessments. They focus on the question of how much larger an earthquake should be beyond the plant design basis before it compromises the safety of the plant. An indicator of the plant seismic capacity called the High Confidence Low Probability of Failure (HCLPF) capacity, is defined as the level of earthquake for which one could state with high confidence that the plant will have a low probability of severe core damage. The seismic margin review methodologies draw from the seismic PRAs, experience in seismic analyses, testing and actual earthquakes in order to minimize the review effort. The salient steps in the review consists of preliminary screening of components and systems, performance of detailed seismic walkdowns and evaluation of seismic margins for components, systems and plant.     

EBaLM-THP - A neural network thermohydraulic prediction model of advanced nuclear system components

In lieu of the worldwide energy demand, economics and consensus concern regarding climate change, nuclear power - specifically near-term nuclear power plant designs are receiving increased engineering attention. However, as the nuclear industry is emerging from a lull in component modeling and analyses, optimization for example using ANN has received little research attention. This paper presents a neural network approach, EBaLM, based on a specific combination of two training algorithms, error-back propagation (EBP), and Levenberg-Marquardt (LM), applied to a problem of thermohydraulics predictions (THPs) of advanced nuclear heat exchangers (HXs).The suitability of the EBaLM-THP algorithm was tested on two different reference problems in thermohydraulic design analysis; that is, convective heat transfer of supercritical CO₂ through a single tube, and convective heat transfer through a printed circuit heat exchanger (PCHE) using CO₂. Further, comparison of EBaLM-THP and a polynomial fitting approach was considered. Within the defined reference problems, the neural network approach generated good results in both cases, in spite of highly fluctuating trends in the dataset used. In fact, the neural network approach demonstrated cumulative measure of the error one to three orders of magnitude smaller than that produce via polynomial fitting of 10th order.     

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.     

地震载荷下反应堆系统的不确定性量化

反应堆结构力学分析中,由于设计变更、制造安装、计算偏差等因素的影响,会导致力学分析关键输入参数存在一定的不确定性,这种不确定性将直接影响到动力响应、载荷分配与最终的力学评价结果。为量化参数不确定性对载荷计算的影响,本文采用不确定性量化的方法,以反应堆系统为研究对象,开展了地震载荷下系统关键结构参数对系统动力响应与载荷分配的不确定性量化研究。首先依据关键参数的基本特性,利用最大熵原理,建立了描述反应堆系统部件间接触刚度和间隙的概率密度函数。随后,应用马尔科夫链蒙特卡罗采样技术对系统关键参数进行采样,并通过有限元瞬态计算获得了输入输出数据池。最后,以样本数据为基础,考察了不确定性参数对部件动力响应统计分布的影响,开展了名义模型的可靠性与不确定性量化分析。研究发现,结构参数不确定性对系统响应的影响在不同部位、不同频域内呈现不同的分布。在考察名义模型的可靠性时应根据响应具体形式有针对性地进行量化。本文所提出的不确定性量化方法对核动力装置其他系统和设备的动力分析具有推广价值。