Earthquake response of nuclear reactor building deeply embedded in soil

This paper is concerned with experimental and analytical studies to investigate dynamic behavior of deeply embedded structures such as nuclear reactor buildings. The principal points studied are as follows: (1) Examination of stiffness and radiation damping effects according to embedded depth, (2) verification for distributions of earth pressure according to embedded depth, (3) differences of response characteristics during oscillation according to embedded depth, and (4) proposal of an analytical method for seismic design. Experimental studies were performed by two ways: forced vibration test, and earthquake observation against a rigid body model embedded in soil. Three analytical procedures were performed to compare experimental results and to examine the relation between each procedure. Finally, the dynamic behavior for nuclear reactor buildings with different embedded depths were evaluated by an analytical method.     

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.     

Effects of slip and separation on seismic SSI response of nuclear reactor building

The seismic soil-structure interaction response of a nuclear reactor building requires modeling of the soil-structure interface. It allows slip and separation at the interface that affects the behavior and response of the reactor. The joint elements used to model the soil-structure interface, require incorporation of appropriate joint stiffness so that slip and separation phenomena take place under the warranted conditions. This slip and separation causes change in the response of the structure. This paper duly addresses the related aspects through comparative study of responses and draws important conclusions useful for design of nuclear reactor building.     

Assessment of the seismic resistance of a ventilation stack on a reactor building

The paper analyzes the seismic resistance of a ventilation stack on a reactor building, including the possible reserves of increasing the resistance. Structures of this type are highly sensitive to seismic loads, as the tuning of the stack (the spectrum of its lowest natural frequencies) corresponds with the frequency spectrum of excitation due to seismic effects. The purpose of the paper is to present an example of an actual structure to show the character of the response of the structure, and the participation of the individual frequency components of the response in the overall stress and strain state of a structure of this type. The methodology for a numerical analysis of the structure is also given. The load of the stack proper is modified by the transfer characteristics of the building. In engineering practice, the system is usually divided into two subsystems: the building with the sub-base, and the stack proper. The level of justification for the application of this simplification depends on the distance of the natural frequencies of the stack from the natural frequencies of the building. Finally, the paper deals with possible errors in determining the actual seismic resistance of the stack structure.     

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 response analysis of deeply embedded nuclear reactor buildings considering frequency-dependent soil impedance in time domain

In order to estimate the seismic behavior of deeply embedded nuclear power buildings, it is important to accurately transform the soil impedance in the frequency domain to the impulse response in the time domain. Although the transform is important for some nuclear buildings because they are deeply embedded in the soil, there are few practical and accurate methods at present. The author has proposed practical transform methods. In this paper, seismic response analyses considering frequency-dependent soil impedance in the time domain are shown. First, the formulation of the proposed transform methods is described. Then, the response analysis of a nuclear reactor building deeply embedded in inhomogeneous soil was performed considering the full matrix soil impedance as the example of practical problems. Through these analyses, the validity and efficiency of the methods were confirmed.     

Earthquake response analysis of reactor structures

The general nature of the principles upon which earthquake resistant design is based is described with particular reference to components and elements of nuclear reactor facilities. Special attention is paid to the response and design criteria of items of equipment or of components that are mounted on or attached to responding elements, and basic procedures are developed to bound the dynamic response of such items.

Consideration is given to vertical as well as horizontal excitation, and the combination of the effects of the various exciations. Suitable approximations are developed for inelastic response estimates.

One section of the paper is devoted to relative motions of points some distance apart, and to bounds for such relative motions.

Recommendations are made for the general criteria governing the design of nuclear facilities, including the basic parameters governing response characteristics and energy absorption.     

大亚湾核电站反应堆厂房楼层反应谱分析评估

大亚湾核电站核岛厂房的抗震分析遵循技术输出国-法国M310型机组的土建技术规范RCC-G,采用简化的阻抗函数法计算地基岩土的作用.根据大亚湾厂址的地基岩土特点,拟采用更为精确的三维连续半空间边界子结构法来考虑地基岩土的作用,并与原设计进行对比.另外,在原设计中采用多组时程作为地震输入,取各组计算结果的平均值作为设计值的基础(称为"平均"法).在研究中基于相同的时程,拟分别采用"平均"法和更为常用的"包络"法,处理多组时程的响应.基于上述两方面,通过反应堆厂房的地震响应计算,得到核电站系统设备重要的设计基础数据-楼层反应谱(FRS),并将计算的楼层反应谱同设计谱进行比较,从而对设计方法及其结果进行评估,为电站的抗震设计裕量评估和安全管理提供可资参考的结论.     

Response of a NPP reactor building under seismic action with regard to different soil properties

The object of this investigation is the response of a reactor building on seismic action with systematic variation of the soil stiffness. A thin-walled orthotropic containment shell on varying heavy and rigid foundations is regarded as calculation model. The soil stiffness is simulated by means of spring elements for horizontal translation and for rocking motions of the building. By the response spectra method the loads of the containment shell are calculated for a horizontal seismic excitation. The investigation is aimed at determining the influence of differentiated soil stiffnesses on the containment action effects and at recognizing the causes for the occurring effects.The results are thoroughly represented by selected quantities of the building's response, the effects from the soil-structure interaction are discussed and the causes of the effects clearly explained. A possibility is provided for determining critical soil stiffnesses which cause a significant intensification effect.The results of the investigations show that both the soil stiffness and structural configuration of the reactor building, particularly in case of the substructure being heavy and rigid, exert a decisive influence on the loading of the superstructure.     

An application of systems analysis techniques to the study of reactor seismic safety

Systems analysis is being used in conjunction with structural analysis to study the conservatisms and to provide insights into aspects of reactor seismic safety. An event-tree/fault-tree model of a commercial nuclear power plant is being constructed to determine the probability of release and probabilities of system and component failures caused by possible seismic events. The event-tree/fault-tree model is evaluated using failure data generated by applying the response a component sees to the component's fragility function. The responses are calculated by a structural analysis code using earthquake time histories as forcing functions. The quantification of the event-tree/fault-tree model is done conditional on a given seismic event and the conditional probabilities thus calculated unconditioned by integrating the results over the seismic hazard curve. In this way, most of the dependencies between event failures resulting from the seismic event itself are removed making known fault-tree analysis quentification techniques applicable. The outputs from the computations will be used in sensitivity studies to determine the key calculations and variables involved in seismic analyses of nuclear power plants.     

Application of seismic analysis methodology to small modular integral reactor internals

The fluid–structure interaction (FSI) effect should be carefully considered in a seismic analysis of nuclear reactor internals to obtain the appropriate seismic responses because the dynamic characteristics of reactor internals change when they are submerged in the reactor coolant. This study suggests that a seismic analysis methodology considered the FSI effect in an integral reactor, and applies the methodology to the System-Integrated Modular Advanced Reactor (SMART) developed in Korea. In this methodology, we especially focus on constructing a numerical analysis model that can represent the dynamic behaviors considered in the FSI effect. The effect is included in the simplified seismic analysis model by adopting the fluid elements at the gap between the structures. The overall procedures of the seismic analysis model construction are verified by using dynamic characteristics extracted from a scaled-down model, and then the time history analysis is carried out using the constructed seismic analysis model, applying the El Centro earthquake input in order to obtain the major seismic responses. The results show that the seismic analysis model can clearly provide the seismic responses of the reactor internals. Moreover, the results emphasize the importance of the consideration of the FSI effect in the seismic analysis of the integral reactor.     

Estimates on seismic amplification factors of reactor components

Employing an averaging technique we obtain estimates on seismic amplification factors for different components in nuclear reactors.     

Seismic analysis of the pile foundation of the reactor building of the NPP Angra 2

A pile foundation subjected to dynamic loads interacts with the surrounding soil. Frequency-dependent stiffness and radiation damping must be properly taken into account in pile-soil-pile interaction. Assuming that the soil consists of horizontal layers of elastic material with hysteretic damping, the dynamic stiffness of a group of (even battered) piles can be determined, accounting rigorously for the cavities where the soil is subsequently replaced by the piles. By way of illustration, this substructure procedure, which works in the frequency domain, is applied to the final design of the pile foundation of the Reactor Building of Angra 2 in Brazil. Below the basemat, a strongly horizontally-layered compressive soil of 36 m thickness rests on bedrock. The reactor building is founded on 202 endbearing piles and 88 floating piles of 15 m length. Every pile is modelled. Along each pile, compatibility between the pile and the soil in all three directions is formulated in seven nodes. The basemat is assumed to be rigid. On the level of bedrock a broad-banded response spectrum specifies the excitation (outcropping). The specified acceleration time-history at the outcropping of bedrock is first transformed to the motion at the same location, but within, using the free-field soil profile. With this motion the kinematic-interaction part of the seismic analysis is performed. Substantial amplification results up to the level of the basemat, but is smaller than that arising for the same level in the free field. The pile forces due to kinematic interaction are one order of magnitude smaller than those due to inertial interaction.As expected, the inertial-interaction part of the analysis leads to larger pile forces on the boundary than in the centre of the pile group, this tendency being more pronounced for the shear forces than for the axial forces, while the bending moments exhibit quite an even distribution. The distribution of the horizontal displacement of the transverse shear and of the bending moment along the pile is hardly affected by the position of the pile within the group. However, the vertical displacement and the axial force for the boundary piles decay more rapidly than the corresponding values for the piles in the centre. This results, for the boundary piles, in a larger part of the vertical load being supported by friction along the pile than for the others. When determining the maximum total forces, it is in many cases unconservative to combine the results of inertial and kinematic interactions by the square root of the sum of the squares. If compatibility were formulated at only the pile heads by equating the pile forces and by enforcing the deformations at this point, this method would lead to a much stronger diminution of the pile forces along the pile.     

Experimental study on dynamic response of reactor vessel to an HCDA

This paper presents a discussion on the model experiments results for reactor structure dynamic response on FBR hypothetical core disruptive accident (HCDA) and the results of analysis using the dynamic response analysis code under experimental conditions. The purpose of this study is to clarify experimentally the dynamic response by use of scale models, as well as to attempt to confirm and improve the dynamic response analysis code on the basis of experimental data. The experimental results have clarified the inner barrel effects on reactor vessel deformation and its behavior due to a impact load. On the other hand, dynamic analysis was made of the 1/7.5 scale complex model by a dynamic response analysis code “PISCES-2DL”, using the explosive combustion characteristics as inputs. Obtained values were compared with experimental values. Results showed that this method was fairly capable of evaluating radial deformation behavior in lower cylindrical parts of the vessel.     

Stochastic seismic response analysis of soft soil sites

A well-known equivalent linearization technique is proposed for the stochastic response analysis in the time-domain of horizontally layered soil deposits under vertically propagating random shear waves. The Bouc-Wen smooth hysteretic model is used and properly extended to better represent the nonlinear-hysteretic shearing stress-strain relation of soils observed under cyclic loading with fixed and variable limits. The earthquake ground motions are modeled as nonstationary Gaussian processes and the soil response is obtained in terms of its response statistics from which the statistics of the surface ground accelerations and site-specific response spectra can be obtained.     

Consideration of uncertainties in seismic analysis of coupled building piping systems

In this paper, we present an analytical study for incorporating the effect of uncertainties in modal properties of uncoupled primary and secondary systems in the seismic analysis of non-classically damped coupled systems such as building piping by response spectrum method. Monte Carlo simulation is used to illustrate that the secondary system design response when defined at a non-exceedence probability of 0.84 over the individual responses obtained from multiple response spectrum analyses by considering uncertainties in modal parameters is excessively higher than the design response specified at the same non-exceedence probability over the responses obtained from multiple time history analyses. This is so because the earthquake input in a response spectrum method is characterized by a design spectrum which by itself is specified at a non-exceedence probability of 0.84 over the multiple time histories with normalized peak ground acceleration. Accurate evaluation of design response at a non-exceedence probability of 0.84 in the response spectrum method requires that the individual modal responses be defined at appropriate probability levels that may be different than the conventionally used non-exceedence probability value of 0.84. The required probability values are evaluated by using first order reliability method. It is shown that the modal responses, when defined at a non-exceedence probability of 0.84, would give relatively accurate values of design response only if the individual modes are perfectly correlated or a single mode contributes to the particular response quantity of interest. For all other cases, the design response would be excessively high. The accurate probability values needed to specify each modal response evaluated using the first order reliability method cannot be incorporated directly in a response spectrum analysis due to computational inefficiency. Two simplified methods, based on total probability theorem, are developed in this paper to overcome this limitation. It is shown that these methods give design response values that are very close to the true values obtained from multiple time history analyses.     

Trip setpoint analysis for the reactor protection system of an advanced integral reactor

The trip setpoints for the reactor protection system of a 65-MWt advanced integral reactor have been analyzed through sensitivity evaluations by using the Transients and Setpoint Simulation/System-integrated Modular Reactor code. In the analysis, an inadvertent control rod withdrawal event has been considered as an initiating event because this event results in the worst consequences from the viewpoint of the minimum critical heat flux ratio and its consequences are considerably affected by the trip setpoints. Sensitivity evaluations have been performed by changing the trip setpoints for the ceiling of a variable overpower trip (VOPT) function and the pressure of a high pressurizer pressure trip function. Analysis results show that a VOPT function is an effective means to satisfy the acceptance criteria as the control rod rapidly withdraws: on the other hand, a high pressurizer pressure trip function is an essential measure to preserve the safety margin in the case of a slow withdrawal of the control rod because a reactor trip by a VOPT function does not occur in this case. It is also shown that the adoptions of 122.2% of the rated core power and 16.25 MPa as the trip setpoint for the ceiling of a VOPT function and the pressure of a high pressurizer pressure trip function are good selections to satisfy the acceptance criteria.     

Nonlinear dynamic analysis of prismatic elements for high-temperature gas-cooled reactor cores

The high-temperature gas-cooled reactor (HTGR) core consists of several thousand prismatic graphite fuel elements arranged in columns within a prestressed concrete vessel. A major research and development effort was initiated in 1970 at General Atomic Company to study the dynamic response of the HTGR core arrangement to seismic excitation.This paper presents a discussion of the history and some of the results of this effort, with respect to advances made in the development of analytical methods. The computer programs developed to perform the analysis are described, along with certain techniques and the modeling required to utilize them. The purpose is to describe the nonlinear dynamic analysis techniques employed to analyze the HTGR core. Correlation of the codes is beyond the scope of the paper and will be discussed in subsequent publications.Each fuel column in the HTGR core is composed of stacked elements doweled together to ensure alignment of the coolant channels. Gaps exist between columns, allowing the elements to impact during a seismic disturbance. Analysis of this type of structure by standard structural dynamics techniques is not possible since both nonlinearities and discontinuities exist. One- and two-dimensional models of the three-dimensional core have been developed with explicit time integration methods. Various methods to treat the impact between elements are discussed.Three computer codes were developed. CRUNCH-1D models a one-dimensional horizontal strip through the core; CRUNCH-2D, a two-dimensional horizontal planar section; and MCOCO, a two-dimensional vertical planar section. The dynamic characteristics of these three representations of the full core structure are compared and the methods evaluated in the text. Plans for additional development and work to improve the techniques are also discussed.