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.     

Double variable frequency pendulum isolator for seismic isolation of liquid storage tanks

The paper describes the behaviour of liquid storage slender and broad tanks isolated by the double variable frequency pendulum isolator (DVFPI). The DVFPI is a double sliding isolation system having elliptical sliding surfaces. The geometry and coefficient of friction of top and bottom sliding surfaces can be unequal. The governing equations of motion and energy balance equation of the tank-isolation system subjected to bilateral ground excitation are derived and solved in the incremental form. In order to investigate the behaviour of the DVFPI, the response is obtained under different parametric variations for a set of 20 far-field earthquake ground motions. Four different combinations of the DVFPI design cases having different isolator geometry and coefficient friction at top and bottom sliding surfaces are studied and the criterion to optimize its performance is proposed based on minimum responses and energy quantities. Further, influences of the initial time period, coefficient of friction and frequency variation factors at the two sliding surfaces and the tank aspect ratio are investigated. It is found that the performance of the DVFPI can be optimized by designing the top sliding surface with high initial stiffness relative to the bottom one and the coefficient of friction of both sliding surfaces to be equal for a slender tank whereas both surfaces should be designed with equal initial stiffness and coefficient of friction for a broad tank.     

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.     

Effect of near-fault earthquakes on North American nuclear design spectra

Ground motion records from recent earthquakes show that near-fault ground motions are different from far-field ground motions in that they often contain strong coherent dynamic long period pulses and permanent ground displacements. The objective of the current study is to assess the safety implications of near-fault earthquakes (NFE) on nuclear power plant structures designed according to North American codes. Fifty-four fault-normal near-fault records in the forward directivity were selected for this investigation. Spectral comparison of the selected earthquake records with the US and Canadian design spectra was conducted. From the investigation it was concluded that the current nuclear design spectra may need to be adjusted to better reflect the effect of near-fault earthquake ground motions.     

Seismic response of annular cylindrical tanks

A study is made of the dynamic response of liquid containing, upright annular cylindrical tanks subjected to the horizontal component of a seismic excitation at its base. The tank is assumed to be rigid. Critical response quantities for rigid annular tanks are evaluated over wide ranges of parameters involved and the results presented in a form convenient for use in practical applications. The effect of tank flexibility on the response is then assessed by the procedure proposed by Veletsos and Yang (1977). Simple approximation equations for estimating the fundamental frequency of the outer tank wall-liquid and inner tank wall-liquid systems are proposed.     

质量-弹簧模型在储液容器抗震分析中的应用

核电厂有很多储液容器,对这些储液容器进行抗震分析时,液体的晃动可明显改变容器的质心和转动惯量等一些力学参数,因此,液体晃动对设备造成的载荷是不可忽略的。质量-弹簧模型是Housner理论和ASCE-4-98规范中对储液容器在地震作用下承受的液动压力给出的简化计算模型。本工作依据Housner理论和ASCE-4-98规范,对储液容器和容器内液体建立了三维质量 弹簧有限元模型,并据此计算了核电厂的储液容器在承受水平地震载荷时液体的作用力。将计算得到的液体频率结果及对流液体对容器的作用结果与应用公式计算的结果进行比较表明,三维有限元模型的计算结果是合理、可靠的。与ASCE-4-98规范相比,将质量 弹簧模型应用到三维有限元模型中,可直接从地震输入的模型中得到板壳元或三维实体有限元上位移和应力分布结果,这样更为直观方便。     

Cost-effectiveness analysis of seismically isolated pool structures for the storage of nuclear spent-fuel assemblies

This study introduces a method for evaluating cost-effectiveness of seismically isolated pool structures, taking account of fluid–structure interaction effects. As a measure of cost-effectiveness, the procedure estimates minimum life-cycle cost, sum of initial construction cost and excepted damage cist over life-cycle of the structure. The expected damage cost is the function of failure probabilities, which are computed by frequency domain analysis for convenience. Input ground motions are represented by a power spectral density function compatible with site-dependent response spectrums. The interaction effects between flexible walls and contained fluid are considered in the form of the added mass matrix. The thickness of wall and the stiffness of isolator are considered two key design variables in achieving a design with minimum life-cycle cost. The numerical examples show that seismically isolated pool tanks are highly cost-effective in low-to-moderate seismic regions.     

Modeling of slabs in seismic analysis of nuclear power plant buildings

Safety related nuclear power plant buildings are commonly represented as lumped mass weightless elastic beam stick models to determine their dynamic behavior under seismic ground motions. Implicit in this analysis procedure is the assumption that the floor slabs are rigid. This paper critically evaluates the slab flexibilities in typical power plant buildings and presents a practical approach to include these in the seismic analysis. Vertical as well as horizontal earthquake components are considered. Results presented include amplified floor response spectra for equipment qualification and design forces in floor slabs and the supporting walls. A satisfactory analysis procedure would consist of traditional stick model analysis to obtain overall seismic responses, force distribution by static analysis using suitable methods such as the finite element method and subsystem analysis to evaluate local amplifications, if necessary.     

采用组合质量-弹簧模型的快堆卧式贮钠罐晃动分析

在核电工程中广泛使用各类形式的储液容器,储液容器的抗震分析必须考虑液体晃动的影响。针对矩形储液容器,不同于传统的单向质量-弹簧模型将液体晃动对容器侧壁、底部的作用都等效为对侧壁的作用,本文提出一种组合质量-弹簧模型及计算公式,模拟了液体晃动分别对容器的侧壁、底部的作用。组合质量-弹簧模型在三维有限元模型上的加载位置更加合理,容器底部的应力结果更加真实。利用组合质量-弹簧模型对中国实验快堆的卧式贮钠罐进行横向晃动有限元计算,算例表明了计算结果的可靠性。组合质量-弹簧模型为储液容器的有限元抗震分析提供了一种有效的方法。     

Development and use of seismic instructure response spectra in nuclear plants

This paper encompasses methods for the development of instructure response spectra as well as the use of these spectra in the seismic design and analysis of nuclear plant components. The time history modal analysis method to generate instructure response spectra is described. This includes the effects of rigid body transformation associated with angular accelerations of the lumped mass nodal points due to eccentric locations of the equipment or system support points. A general method of generating and using the instructure response spectra associated with both translational and angular input motions is presented. An approximate way of treating light equipment mounted on relatively flexible floors or shear walls is considered.Various numerical techniques for the integration of differential equations of motion are outlined. The time interval to be used is chosen so as to avoid mathematical instability and inaccuracy. Comparison of the results using different techniques for the numerical integration of a sample problem, for the purpose of verifying solution accuracy, is provided. Consideration is given to determining how small the period interval should be in generating instructure response spectra to avoid truncation of resonance peaks. The use of three-dimensional instructure response spectra developed for each of the three orthogonal translational directions of ground motion is presented. Methods of developing instructure response spectra other than the time history method are discussed.     

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.     

Coupling effect between liquid sloshing and flexible fluid-filled systems

Current practice in seismic design of flexible liquid-filled systems is reviewed. A coupled fluid-structure finite element method which considers the sloshing effect is developed for the seismic analysis of liquid-filled systems of various geometries with and without internal components. An analysis of the dynamic interaction between the structural vibration and liquid sloshing is also presented. Both rigid and flexible fluid-tank systems of different configurations are considered. Results demonstrate that tank flexibility can affect the amplitude of the free surface wave and hence the sloshing pressure and structural response. This result is consistent with the perturbation analysis. The dynamic interaction depends on (1) the ratio of natural frequency between fluid sloshing and the fluid-tank system and (2) the ratio of the effective areas of the fluid-structure interface and free surface of the fluid. Hence it is expected that in analyzing tanks with flexible internal components, this coupling effect can be more pronounced.     

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。     

Analyses of reactor building by 3D nonlinear FEM models considering basemat uplift for simultaneous horizontal and vertical ground motions

The nonlinear behavior of basemat uplift, which is an important point in seismic designs of nuclear power plants in Japan, has been investigated by arranging joint elements between the reactor building basemat and the soil on a three-dimensional (hereafter referred to as 3D) FEM model of the soil. However, the nonlinearity of the basemat uplift has been investigated separately from the nonlinearity of reactor buildings. These nonlinearities have yet to be taken into account simultaneously in past studies. In this paper, models of the building and the soil using 3D FEM elements with consideration to the nonlinearity of building materials as well as the nonlinearity of the basemat uplift were subjected. The behavior of the building's elements were investigated by carrying out seismic response analyses for horizontal ground motions only, as well as for simultaneous horizontal and vertical ground motions using these models. As a result, it was found that there was little difference in the horizontal response of the building between the horizontal input motions only and the simultaneous horizontal and vertical input motions. The effects of the vertical ground motions on the basemat uplift behavior which is represented by the ground contact ratio were also slight.     

Seismic response analysis of full-scale boiling water reactor using three-dimensional finite element method

This paper presents the three-dimensional finite element seismic response analysis of full-scale boiling water reactor BWR5 at Kashiwazaki-Kariwa Nuclear Power Station subjected to the Niigata-ken Chuetsu-Oki earthquake that occurred on 16 July 2007. During the earthquake, the automatic shutdown system of the reactors was activated successfully. Although the monitored seismic acceleration significantly exceeded the design level, it was found that there were no significant damages of the reactor cores or other important systems, structures and components through in-depth investigation. In the seismic design commonly used in Japan, a lumped mass model is employed to evaluate the seismic response of structures and components. Although the lumped mass model has worked well so far for a seismic proof design, it is still needed to develop more precise methods for the visual understanding of response behaviors. In the present study, we propose the three-dimensional finite element seismic response analysis of the full-scale and precise BWR model in order to directly visualize its dynamic behaviors. Through the comparison between both analysis results, we discuss the characteristics of both models. The stress values were also found to be generally under the design value.     

Seismic considerations in siting and design of power plants

A methodology which provides guidelines for the preliminary evaluation of the safety of nuclear power stations subjected to strong vibratory ground motions from earthquakes is outlined. The methodology includes a procedure for estimating a spectral envelope of ground motion at the reactor site. On the basis of this ground motion the seismic response of structural systems and equipment of the power plant can be estimated. A comparison of the expected seismic response of these systems with their strength and functional capabilities yields an evaluation of the safety of the power plant systems studied.     

Response of piping system on friction support to bi-directional excitation

Installation of friction devices between a piping system and its supporting medium is an effective way of energy dissipation in the piping systems. In this paper, seismic effectiveness of friction type support for a piping system subjected to two horizontal components of earthquake motion is investigated. The interaction between the mobilized restoring forces of the friction support is duly considered. The non-linear behavior of the restoring forces of the support is modeled as an elastic-perfectly plastic system with a very high value of initial stiffness. Such an idealization avoids keeping track of transitional rules (as required in conventional modeling of friction systems) under arbitrary dynamic loading. The frictional forces mobilized at the friction support are assumed to be dependent on the sliding velocity and instantaneous normal force acting on the support. A detailed systematic procedure for analysis of piping systems supported on friction support considering the effects of bi-directional interaction of the frictional forces is presented. The proposed procedure is validated by comparing the analytical seismic responses of a spatial piping system supported on a friction support with the corresponding experimental results. The responses of the piping system and the frictional forces of the support are observed to be in close agreement with the experimental results validating the proposed analysis procedure. It was also observed that the friction supports are very effective in reducing the seismic response of piping systems. In order to investigate the effects of bi-directional interaction of the frictional forces, the seismic responses of the piping system are compared by considering and ignoring the interaction under few narrow-band and broad-band (real earthquake) ground motions. The bi-directional interaction of the frictional forces has significant effects on the response of piping system and should be included in the analysis of piping systems supported on friction supports. Further, it was also observed that the velocity dependence of the friction coefficient does not have noticeable effects on the peak responses of the piping system.     

Earthquake simulator studies of cylindrical tanks

An experimental investigation on the seismic response of ground-supported, cylindrical metal tanks is described. Experimental and analytical research by other investigators over the past forty years has provided a firm basis for the computation of free- and forced-vibration behavior in ideal liquid-filled circular cylindrical shells with a variety of elementary support conditions. However, the actual seismic behavior of ground-supported tanks has not been known, and practical design methods necessarily have been based on simplifying assumptions. The present results provide the first opportunity for rational evaluation of seismic design assumptions, and suggest theoretical developments which would enhance the realism of refined seismic analyses.The aluminum scale model discussed here, 12 ft in diameter and 6 ft high, represents a 36-ft diameter steel prototype. It was tested, in anchored and unanchored base configurations, under action of a time-scaled El Centro, 1940, earthquake with peak acceleration of 0.5 g, using the Earthquake Simulator Facility of the University of California, Berkeley. Stresses and displacements of the model, in both anchored and unanchored conditions, were dominated by effects of “out-of-round” response in higher-order circumferential modes, a result which is not predicted by current seismic analysis theory, and which contradicts basic assumptions of current design practice. The experimental observations are discussed in relation to dynamic analysis theory, practical design methods, and the history of tank performance in past earthquakes.     

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。     

Seismic resistant design of safety class structures and equipment

Some commonly encountered problems in the seismic resistant design of nuclear power plant facilities are discussed. The topics included here are ground input motions, local geology versus source mechanism and travel path, three components inputs, torsional responses, floor response spectra, seismic resistant design of heavy equipment, the application of component mode synthesis technique, seismic resistant design of piping systems, equipment qualification by testing, the effects of close modes, underground pipe design, and soil structure interaction.