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.     

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.     

核电厂电气厂房地震响应敏感性分析

利用人工地震波生成算法,探讨考虑土壤-结构相互作用的核电厂电气厂房地震响应动力分析模型和计算方法。通过比较楼层反应谱,研究岩土材料参数和载荷的不确定性对结构响应的影响。结果表明:岩土材料参数对核电厂电气厂房地震响应的影响更大,单一岩土材料参数下计算得到的拓宽后的楼层反应谱不能完全包络参数变化带来的地震响应差别。即使最终的反应谱大于或等于各种不同岩土参数下的楼层反应谱,仍有必要对不同岩土参数下的楼层反应谱做包络。     

Effective seismic input through rigid foundation filtering

This paper develops a simple yet realistic approach to account for a class of important soil-structure interaction phenomenon, namely wave scattering. The foundation is considered to act as a filter, partitioning the impinging excitation into lowpass filtered translational motion together with torsional motion (for horizontally polarized shear and Love waves) and rocking motion (for compressional, vertically polarized shear, and Rayleigh waves). These effects are evaluated for arbitrarily incident, horizontally polarized shear waves. The results are expressed in terms of filtering functions for various foundation geometries and embedment conditions and compared with ‘exact’ and other approximate solutions. Numerical results for a time history are presented in the form of translational and torsional acceleration response spectra. The formulae for these filters in the frequency domain show an interesting general relationship between the ‘effective’ translational and torsional motions of the foundation: the two motions are 90° out of phase for a given free-field harmonic wave, suggesting the possibility of computing the responses of structures to the two foundation motion components independently and combining the results by SRSS method. The future research need for adaptation of filtering concept to seismic excitations is discussed.     

Seismic proof tests using explosives to produce strong ground motion

When performing seismic tests of large structures or equipment, it is often desirable to produce responses in the range of 0.5−5 g in the frequency range 1 – 30 Hz. For massive structures this cannot be done with mechanical vibrators. For equipment weighing 100 t or less, high level tests can be performed using vibrators or large shake tables. However, such laboratory tests often to simulate realistically the soil effects, soil-foundation interaction, and the effects of supports, appurtenances and adjacent equipment. For these reasons it is useful to have a convenient economical method for in situ testing of large structures. Recent research indicates that blast tests using explosive charges buried in the soil can be employed to produce response spectra with a predetermined amplitude and frequency content.Semi-empirical methods are utilized to formulate ground motion spectra which produce the desired response in the structure. The spectral input is a function of charge distance, depth, soil characteristics, multiple charge time sequencing, and charge size. These parameters can be combined to control the spectrum and amplitude input to the structure, resulting in a controlled ‘earthquake’. The duration of ground motion can be made arbitrarily long using multiple delayed blasts. In our procedure we attempt to simulate the 5–10 sec of intense shaking present in typical strong motion earthquake time histories. Our research indicates that responses of up to 30 sec can be achieved if the damping is not too high.The procedure for performing a test is first to compute response spectra for a site as a function of the charge size, distance, depth, etc. To do this we measure soil parameters such as shear wave velocity and the depth of soil layers. These data along with information concerning the types and placement of explosives are used as inputs for a computer program developed by us. This program, called ANBLAST, computes peak soil responses, frequencies, and determines response spectra for various values of damping. Several types of instruments were used in the measurement of ground, foundation and instrument motion. These include unbonded strain gage accelerometers, a strong motion seismograph, a passive mechanical peak shock recording device, triaxial borehole seismometers, and geophones to measure seismic velocities in the soil. All the instrument outputs were recorded with a wide band FM tape recorder. Subsequent Fourier transform spectra and time response data were obtained from the original tape recordings. The resulting instrument responses agree satisfactorily, showing excellent correlation in measurements made at similar locations using different instruments. In addition, the reduced data and resulting response spectra agree with the expected values obtained from analytical studies.In conclusion, we feel that tests using strong ground motions produced by explosives allow seismic studies to be made at peak amplitudes and durations approaching those of strong motion earthquakes and open a new dimension in in situ testing of massive devices and structures.     

Analysis of seismic testing motions with instantaneous response spectra

Synthetic multiple-frequency and single-frequency motions are analyzed for their adequacy to simulate a calculated seismic motion for seismic testing of nuclear power plant equipment. The analysis is performed by first comparing their time-independent response spectra and then comparing response spectra derived at an instant of time, that is, instantaneous response spectra. The results show that even though the time-independent response spectrum of the calculated motion is fully enveloped by that of a synthetic test motion, full enveloping is never obtained with the actual responses at any given time. Recommendations are given on practical test methods and type of test motions.     

乏燃料贮存格架流固耦合参数的数值模拟

乏燃料贮存格架是储存乏燃料组件的重要设备。在地震载荷下,其响应是非线性的,可能产生滑移、颠覆等。发生地震时,存在于格架间隙内的流体耗散了结构的能量,保证了格架的完整性。本文使用3/10缩比模型,利用CFD软件Fluent进行了乏燃料贮存格架2D瞬态分析。计算过程中利用动网格方法模拟格架强迫振动,并进行了参数不确定性分析。利用CFD瞬态流体力分别获得了双Ⅱ区、双Ⅰ区格架附加质量矩阵。利用同轴圆柱体附加质量的计算解与解析解进行对比验证,证明了本文计算方法的准确性。本文计算所得的附加质量矩阵可为乏燃料贮存格架结构动态软件提供流固耦合参数。     

Lateral-torsional structural response from free-field ground motion

Lateral-torsional responses of structures subjected to the action of both the free-field ground inputs and external forces and moments are investigated. By expanding the work of Scanlan [1], both lateral and torsional foundation inputs due to a travelling shear wave are derived from the free-field point motions. The free-field torsional motions are used as the basis of numerical studies. Responses for different soil stiffness and structural characteristics are studied, as well as different dynamic models. In one dynamic model, the effects of interaction between lateral inertial force and lateral foundation motion are considered. And in the second model, the structure is excited by the external torque and torsional inputs. Both models are coupled to an elastic half-space. Finally, torsional structural response caused by torsional inputs is compared with lateral response caused by lateral inputs to determine the significance of torsional excitation on the seismic response of building structures. Numerical results show that these torsional seismic loads may be as large or larger than those from lateral excitations.     

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.     

三向地震载荷下HTR-10厂房土壤-结构相互作用分析

土壤-结构相互作用（SSI）会影响核电厂厂房的地震响应。本文充分考虑SSI效应的影响,对10 MW高温气冷堆（HTR-10）厂房在三向地震载荷下的响应进行了分析。建立了土壤-结构耦合有限元模型,通过构造人工边界实现对地震波在无限域内传播过程的模拟,并对模型的准确性进行了验证。利用该模型计算了HTR-10厂房的地震响应,并对不同楼层的反应谱计算结果进行了分析。对于水平向反应谱,各楼层的反应谱谱型类似,SSI影响规律基本一致。在竖直方向上,结构的响应特点与楼板自身的竖向频率特性有明显关系,不同楼板的响应差别较大。一般情况下,SSI效应对竖向响应有抑制作用,且随着楼层增加更为明显。当楼板与土壤的固有频率接近时,竖向响应与其他楼层相比会有显著放大。     

Improved method to demonstrate the structural integrity of high density fuel storage racks

Reracking of existing fuel pools to the maximum extent is desirable from an economical point of view. This goal can be achieved by minimizing the gaps between the spent fuel storage racks. Since the rack design is aimed at enabling consolidated fuel rod storage, additional requirements arise with respect to the design and the structural analysis. The loads resulting from seismic events are decisive for the structural analysis and require a specially detailed and in-depth analysis for high seismic loads. The verification of structural integrity and functionality is performed in two phases. In the first phase the motional behavior of single racks, rows of racks and, where required, of all racks in the pool is simulated by excitation with displacement time histories under consideration of the fluid–structure interaction (FSI). The displacements from these simulations are evaluated, while the loads are utilized as input data for the structural analysis of the racks and the pool floor. The structural analyses for the racks comprise substantially stress analyses for base material and welds as well as stability analyses for the support channels and the rack outside walls. The analyses are performed in accordance with the specified codes and standards.     

利用HHT产生与多阻尼楼板谱匹配的地震波

美国原子能管理委员会（USNRC）规范规定了用于核电厂抗震分析和设计的地震波要求。在抗震分析和设计中，采用的地震波可与多阻尼目标反应谱匹配，也可与单阻尼目标反应谱匹配。然而，在对核电设备和部件进行动力时程分析时，则需要与多阻尼目标楼板谱匹配的地震波。基于此问题，提出利用希尔伯特-黄变换（HHT）方法，通过修改种子地震波的频率和振幅信息，使之与多阻尼目标楼板谱匹配，且完全符合USNRC规范的匹配标准，从而为核电设备和部件的地震安全评估提供合适的地震激励。      

Soil-structure interaction — an engineering evaluation

The two methods of analysis for soil-structure interaction, the impedance and the finite element methods, are reviewed with regard to their present capabilities to address the significant factors of the problem. The objective of the paper is to evaluate if an adequate engineering solution to the problem is provided by either approach. Questions related to the reduction of seismic motions with depth, scattering of incident waves, the three-dimensionality of the real problem, soil damping, strain dependency of soil properties and the uncertainties associated with all of the above are discussed in sufficient detail. All conclusions made are based on referenced material. It appears that, although both methods as presently practised have not yet completely solved the problem, the impedance approach has come closer to addressing the more significant issues. Because of this finding, in addition to its simplicity and low cost, the impedance approach is the preferred engineering method for soil-structure interaction.     

Criteria for seismic analysis of nuclear plant structures and substructures

This paper encompasses criteria used for seismic analysis of nuclear power plant structures such as supporting structures founded on ground, as well as substructures. Nuclear power plant equipment and systems can be treated as substructures. Modeling of structures and substructures is described. Since instructure response spectra play an important role in the design and analysis of nuclear power plant equipment, systems and components, methods for development of instructure response spectra as well as variations of input parameters considered in determining these spectra are described.When the principal contribution to the equipment response is due to flexibility of the supporting substructures, an analytical approach to the problem for obtaining reduced stiffness and associated mass matrices of supporting substructures with finite element representation for use in the dynamic analysis of equipment and supporting structures is presented. When supporting structures and equipment, that have inherently different damping properties, are included as intergral parts of the dynamic models, the approximate evaluation of the modal damping based on the weighted damping according to the modal energy stored in each component is outlined. Use of time history and response spectrum analyses is presented. The effects of relative displacements due to different motion of the support points of substructures in each significant mode of the supporting structures as well as procedures of combining modal responses are detailed.     

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.     

乏燃料组件抓具混合双摆模型及地震响应分析

核动力厂对乏燃料组件抓具提出了抗安全停堆地震(SSE)的要求,而抓取过程的地震响应是评价其安全性的重要依据。为精确分析抓取过程的地震响应,根据乏燃料组件抓具的结构和工作方式,建立乏燃料组件抓具工作状态的混合双摆模型,推导其运动微分方程,采用Runge-Kutta法求解其在地震载荷作用下的响应,根据动力学理论进一步求得钢丝绳和抓具上的动态载荷,并对结果进行分析。此方法为类似结构的精确抗震设计、综合评定提供参考。     

Effects of foundation rotation on seismic inertia forces of nuclear power plant structures

Effects of foundation rotation on seismic inertia forces are studied in two different plane strain finite element investigations. A three-mass model is used to approximate the dynamic characteristics of a containment vessel of a nuclear power plant and its internal structure. In the first study a large finite element mesh is specified in order to eliminate unwanted reflections from the boundary. Motion input to the structure is limited to 2 sec duration. A quiet boundary technique is employed in the second investigation. As a result, earthquake motion inputs of any duration could be specified. Most results are based on portions of two recorded earthquake motions of 4 sec in length. Effects of foundation rotation and lateral soil-structure interaction are evaluted with program output. Results are presented in graphs and tables.     

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。     

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.