Vertical soil-structure interaction of nuclear power plants subjected to seismic excitation

The vertical soil-structure interaction problem is investigated by coupling an N-mass lumped mass structure to a two-dimensional elastic half space. This problem is formulated as an integral equation of the Volterra type. Numerical results are obtained by iteration for an idealized threemass two-mode model of a nuclear power plant containment structure. The effects of interaction are evaluated by comparing free-field acceleration spectrum response curves with similar curves determined from foundation motion.     

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.     

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.     

Equivalent modal response method for seismic design of structures

A new method is proposed in which the response in several modes of vibration under the three components of earthquake is replaced by the response in a small number of equivalent modes.     

Stochastic prediction of maximum seismic response of light secondary systems

A stochastic model is presented for predicting the elastic response of light multi-degree-of-freedom secondary systems to strong motion earthquakes. Secondary systems may include light mechanical or electrical equipment, piping, or other light systems attached at one or several points to walls or floors of the supporting or primary structures. The critical functions of these secondary systems in nuclear power plants make the accurate prediction of their maximum responses important. The response of such secondary structures may be obtained by a direct time-history analysis, or more approximately, by the response spectrum method. The time-history solution is, of course, expensive; moreover, there is no single representative earthquake and thus a number of possible earthquake ground motions have to be considered. On the other hand, the response spectrum method applied to secondary systems can lead to unreliable results.Within the framework of the normal mode method, a decoupled stationary random vibration model is developed based on the assumption of Gaussian response process and Poisson barrier crossings. The accuracy of the proposed model is verified by comparing the calculated responses, at the 10 and 50% probability of exceedance level, with the second highest and average of the time-history responses from eight normalized accelerograms. The influence of decoupling, i.e. ignoring the dynamic interaction between the primary and the secondary systems, on the response is examined.The influence of nonstationarity is also evaluated. It is observed that nonstationarity is unimportant for earthquakes of relatively long duration, and that for a given damping most of the error can be accounted for by a simple scaling. It is also shown that one aspect of the proposed method constitutes the basis for some of the approximations in the response spectrum method; however, the proposed method yields results that are consistently more reliable than the response spectrum method. Moreover, results obtained with the proposed method represent maximum response statistics from an ensemble of earthquakes rather than a single earthquake.     

Preliminary evaluation of the seismic response of the ELSY LFR

The main goal of the present study is the preliminary evaluation of the seismic demand of a LFR with reference to European Lead System project (ELSY) considered one of the most promising innovative Generation IV reactor. The safety aspects of the ELSY reactor in the event of a Safe Shutdown Earthquake, taking into account also the effects of the possible fluid–structure interaction, have been analyzed.To the purpose to determine the seismic demand, in according with the international rules, a non-linear dynamic analysis method was used with rather refined 3-D model of LFR for the foreseen structural analyses and simulations of the plant and of the reactor internals behaviour. In this report numerical results are presented and discussed highlighting the relevance of the fluid–structure interaction in terms of structural integrity as well as the isolation technique effectiveness, which is expected to increase the safety margin of the reactor structures during a seismic event, if the isolators frequency is far from that of the reactor.The present work has been performed within the 6th European Framework Project.     

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.     

Significance of seismic response spectrum normalization in nuclear power plant design

Peak ground acceleration has been used most commonly to normalize seismic response spectra. Apparently, there is a general consensus that this is not the best parameter for spectrum normalization. Several other parameters have been proposed, such as, peak acceleration-velocity-displacement triad, peak velocity and spectrum intensity. This paper presents statistical studies of response spectra from a number of recorded earthquake motions normalized by several different parameters. The parameters used are peak acceleration, peak velocity, spectrum intensity, spectrum ordinate, etc. Spectrum shapes are generated corresponding to 84 percentile probability level for different normalization parameters. These shapes are compared with the other standrad spectrum shapes used in the nuclear power plant design to investigate significance of different normalization techniques.     

Analysis for seismic response of dry storage facility for spent fuel

Most of the dry storage systems for spent fuel are freestanding, which leads to stability concerns in an earthquake. In this study, as a safety check, the ABAQUS/Explicit code is adopted to analyse the seismic response of the dry storage facility planned to be installed at Nuclear Power Plant #1 (NPP1) in Taiwan. A 3D coupled finite element (FE) model was established, which consisted of a freestanding cask, a concrete pad, and underneath soils interacting with frictional contact interfaces. The scenario earthquake used in the model included an artificial earthquake compatible to the design spectrum of NPP1, and a strong ground motion modified from the time history recorded during the Chi-Chi earthquake. The results show that the freestanding cask will slide, but not tip over, during strong earthquakes. The scale of the sliding is very small and a collision between casks will not occur. In addition, the differential settlement of the foundation pad that takes place due to the weight of the casks increases the sliding potential of the casks during earthquakes.     

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.     

Lead extrusion dampers for reducing seismic response of coolant channel assembly

In Indian type pressurized heavy water reactors (PHWRs), two fuelling machines (F/Ms) are located on either side of the reactor. The behavior of the coolant channel and tie rod when fuelling machines are engaged on both the ends of the channel for refueling under earthquake is studied. It is observed that the loads acting on the coolant tube were high. In order to reduce the earthquake load acting on coolant channel the fuelling machines are restrained by energy absorbers called lead extrusion dampers (LED). The design of an LED is performed based on the extrusion principle. The aim of the paper is to study the effectiveness of such a device in reducing the response. It was observed that the stresses in the coolant channel due to earthquake are reduced significantly when LEDs are used. Response spectrum analysis is also carried out for the system with LED. In this analysis the LED is replaced with an equivalent viscous damper and stiffness obtained using Caughy’s linearisation techniques. Response spectrum analysis results and the nonlinear time history analysis results show good agreement.     

A note on the seismic response of rigid cantilever retaining walls

The elasticity based dynamic response of retaining walls, attached to a semi-infinite elastic backfill stratum, has yet to be solved exactly. There are three analytical approximation approaches in the literature to simplify the equations of motion. The solutions based on these approaches can be numerically implemented. However, the frequency range for which these solutions may provide accurate results has not yet been established. In this paper, the exact frequency equation and frequency spectra for the problem under free vibration are presented first, and the three simplified equations of motion are then reviewed. Next, the exact frequency spectra are then used to assess the frequency range of applicability of the three approximation approaches. It is concluded that for all practical values of Poisson's ratio, all three approaches provide a reasonable approximation to the exact solution in the low frequency range of the first mode. The first mode response of the horizontal and rocking impedance functions, for the rigid retaining wall are then derived, based on the simplified equations of motion, and the numerical data are presented for the low frequency range identified.     

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.     

Distribution of ground rigidity and ground model for seismic response analysis in Hualian project of large scale seismic test

An international joint research program called HLSST is proceeding. HLSST is large-scale seismic test (LSST) to investigate soil-structure interaction (SSI) during large earthquake in the field in Hualien, a high seismic region in Taiwan. A model building was constructed on the gravelly soil in this site, and the backfill material of crushed stone was placed around the model plant after excavation for the construction. Also the model building and the foundation ground were extensively instrumental to monitor structure and ground response. To accurately evaluate SSI during earthquakes, geotechnical investigation and forced vibration test were performed during construction process namely before/after base excavation, after structure construction and after backfilling. And the distribution of the mechanical properties of the gravelly soil and the backfill are measured after the completion of the construction by penetration test and PS-logging etc. This paper describes the distribution and the change of the shear wave velocity V_s measured by the field test. Discussion is made on the effect of overburden pressure during the construction process on V_s in the neighbouring soil and, further on the numerical soil model for SSI analysis.     

Status and research needs for prediction of seismic response in liquid containers

Current methods for seismic design of liquid storage tanks and steam suppression pools are reviewed to establish requirements for future research. The use of a transfer function and response spectrum method is emphasized for prediction of slosh response and impulsive loading. The method is also applicable to operating transient loads that occur in nuclear power plants. Direct applicability is noted for much of the available design data that had previously been developed for aerospace launch vehicles.     

Approximate formulas to calculate the seismic response of light attachments to buildings

Simple approximate formulas are proposed to compute the maximum response of equipment or any other light secondary system attached to buildings subjected to earthquake ground motions. The formulas are derived on the basis of a modified version of the conventional response spectrum method and the consideration of building and attachment as one unit. Notwithstanding, they are expressed in terms of the independent dynamic properties of the two components and ordinates from the response spectrum of a specified ground motion. Secondary systems with multiple degrees of freedom attached to one or two arbitrary points of a supporting multistory structure may be considered. As presented, however, the formulas are restricted to cases in which the independent primary and secondary systems are linear elastic with classical modes of vibration, and the masses of the secondary system are small in comparison with those of the primary one. Their accuracy is verified by means of a comparative study with time-history solutions. In this comparative study, the approximate formulas yield an average error of about 4% and a maximum of about 22%.     

New discrete models and their application to seismic response analysis of structures

New discrete models and their application to seismic response analysis of structures is proposed in this paper. These models consist of finite number of small rigid bodies connected with springs distributed over the contact area of two neighbouring bodies. In general size of stiffness matrices of these elements are at most (6 × 6) which are equal to or even smaller than of those of conventional finite elements so that considerable reduction of computing time can be expected. Effectiveness of these elements in nonlinear structural analysis, especially dynamic response analysis of structures will be demonstrated by several numerical examples.     

Active seismic response control systems for nuclear power plant equipment facilities

To sustain severe earthquake ground motion, a new type of anti-seismic structure is proposed, called a Dynamic Intelligent Building (DIB) system, which is positioned as an active seismic response controlled the structure. The structural concept starts from a new recognition of earthquake ground motion, and the structural natural frequency is actively adjusted to avoid resonant vibration, and similarly the external counter-force cancels the resonant force which comes from the dynamic structural motion energy. These concepts are verified using an analytical simulator program. The advanced application of the DIB system, is the Active Supporting system and the Active Stabilizer system for nuclear power plant equipment facilities.     

Evaluation of response factors for seismic probabilistic safety assessment of nuclear power plants

This paper presents a method for evaluating “response factors” of components in nuclear power plants for use in a seismic probabilistic safety assessment (PSA). The response factor here is a measure of conservatism included in response calculations in seismic design analysis of components and is defined as a ratio of conservative design response to actual response. This method has the following characteristic features: (1) the components are classified into several groups based on the differences in their location and in the vibration models used in design response analyses; (2) the response factors are decomposed into subfactors corresponding to the stages of the seismic response analyses in the design practices; (3) the response factors for components are calculated as products of subfactors; (4) the subfactors are expressed either as a single value or as a function of parameters that influence the response of components.This paper describes the outline of this method and results from an application to a sample problem in which response factors were quantified for examples of components selected from the groups.