Scram and nonlinear reactor system seismic analysis for a liquid metal fast reactor

Earthquake vibrations cause large forces and stresses that can significantly increase the scram time required for safe shutdown of a nuclear reactor. The horizontal deflections of the reactor system components cause impact between the control rods and their guide tubes and ducts. The resulting frictional forces, in addition to other operational forces, delay the travel time of the control rods. To obtain seismic responses of the various reactor system components (for which a linear response spectrum analysis is considered inadequate) and to predict the control rod drop time, a non-linear seismic time history analysis is required. Nonlinearities occur due to the clearances or gaps between various components. When the relative motion of adjacent components is large enough to close the gaps, impact takes place with large impact accelerations and forces.This paper presents the analysis and results for a liquid metal fast rector system which was analyzed for both scram times and seismic responses such as bending moments, accelerations and forces. The reactor system was represented with a one-dimensional nonlinear mathematical model with two degrees of freedom per node (translational and rotational). The model was developed to incorporate as many reactor components as possible without exceeding computer limitations. It consists of 12 reactor components with a total of 71 nodes, 69 beam and pin-jointed elements and 27 gap elements. The gap elements were defined by their clearances, impact spring constants and impact damping constants based on a 50% co-efficient of restitution.The horizontal excitation input to the model was the response of the containment building at the location of the reactor vessel supports. It consists of a 10 sec safe shutdown eathquake (SSE) acceleration-time history at 0.005 sec intervals and with a maximum acceleration of 0.408 g. The analysis was performed with two Westinghouse special purpose computer programs. The first program calculated the reactor system seismic responses and stored the impact forces on tape. The impact forces on the control rod driveline were converted into vertical frictional forces by multiplying them by a coefficient of friction, and then these were used by the second program for the scram time determination.The results give time history plots of various seismic responses, and plots of scram times as a function of control rod travel distance for the most critical scram initiation times. The total scram time considering the effects of the earthquake was still acceptable but about four times longer than that calculated without the eathquake. The bending moment and shear force responses were used as input for the structural analysis (stresses, deflections, fatigue) of the various components, in combination with the other applicable loading conditions.     

Simplified seismic analysis methods in Belgium

Seismic design and analysis of nuclear plant systems, structures and components have requested huge effort and tremendous costs in the past two decades. The extended use of sophisticated, linear response type methods (modal analysis, spectral response) and the associated conservatism are responsible for the significant stiffening of the piping systems and the multiplication of supports and snubbers. The remedy used against the seismic risk seems worse than the pain itself, and safety might be impaired rather than improved. Indeed, system stiffening increases the average load level in normal operation (stresses, fatigue, nozzle loads, etc.); supports do not behave ideally as assumed (friction, rust, etc.) and snubbers are remarkably unreliable. On the other hand, experience with actual earthquakes shows that industrial facilities designed using very simplistic seismic techniques, or even no seismic requirement at all, suffer essentially no damage, even in the case of a large earthquake. This paradox challenges the traditional seismic design techniques, and appeals for revised seismic qualification methods of piping systems. When the assumption of the occurrence of an earthquake event is made in a plant in operation, which has not been designed against seismic criteria, the use of the standard seismic qualification techniques is still more questionable; simplified (quasi-static) techniques offer in this case a valuable and economically justified alternative. The paper describes the application of the quasi-static “modified load coefficient method” to the seismic assessment of the piping in a nuclear plant in operation, designed during the pre-seismic era.     

Seismic analysis and design of electrical cable trays and support systems

Most cable trays in nuclear power plants are classified as seismic category I components. Current safety requirements dictate that all such components be adequately designed in order to remain functional during and after the most severe possible earthquake, so that a safe and orderly plant shut-down can be ensured. The design aspects of electrical cable trays and support systems are discussed from the seismic and structural standpoint. The effects of the inherent flexibility of commonly used cable trays is considered. A procedure for the selection of trays and the design of their support structure is recommended. The dynamic characteristics of typical trays are determined analytically and also from test results. The advantages of a rigid support system are discussed. Two procedures are presented for the design of the support systems, namely, static loading and spectral analysis. The interaction between trays and supports is discussed.     

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.     

Analysis and test correlation of flexible and stiff piping systems

An in situ pipe test program was conducted to provide a basis for evaluating piping analysis methodologies and design philosophies. In this program, a 20.3-cm boiler feedwater line with two fundamentally different support systems was tested and analyzed. One system employed hanger supports and was very flexible. The second system employed strut and snubber supports and was relatively stiff. Snapback and forced vibration tests were performed on the piping systems. The test results were used to determine piping damping values and to correlate with analyses. These analyses were used to evaluate current piping analysis methodologies and their analytical models. Also, parametric studies were performed with the analytical models to evaluate the effect of different support systems on the pipe behavior for thermal and seismic loads. In addition, the seismic analysis results were compared to quantify the differences between direct time integration and response spectra analysis methods.     

Analysis of piping with hysteretic supports using response spectra

This paper introduces a response spectra-based method for analyzing piping with hysteretic nonlinear supports. The method is developed to be as simple and versatile as possible, yet accurate enough to model the essential nonlinear behavior of the supports. The required data is the hysteresis loops of the supports, the linear properties of the piping, and the linear acceleration response spectra. The supports are modeled by equivalent linear stiffness and damping, and the combined piping/support system is analyzed using complex modal properties that account for high-damping effects. The final peak response is obtained by a mode combination rule which is a new generalization of Complete Quadrature Combination (CQC) that accounts for nonlinear properties and complex modes. Sensitivities that indicate the degree of nonlinear behavior and support interaction are also determined. The method is used to analyze two three-dimensional piping systems with multiple nonlinear supports, which have been tested on a shaking table. Comparisons between experimental and analytical results show good agreement.     

Friction modelling of preloaded tube contact dynamics

Many loosely supported components are subjected to flow-induced vibration leading to localized wear. Life prediction depends on robust and accurate modelling of the nonlinear dynamics as the components interact with their supports. The output of such analysis is the component dynamic response and impact forces, including friction forces during stick–slip motions. Such results are used to determine the normal work rates, which are utilized to predict fretting wear damage. Accurate estimates of these parameters are essential. This paper presents simulations of a loosely supported fuel-channel tube subject to turbulence excitation. The effects of tube/support clearance and preload are investigated. Several friction models, including velocity-limited, spring-damper and force-balance are utilized. A comparison of these models is carried out to investigate their accuracy. The results show good agreement with experimental work rates when a simple iterative procedure to update the friction forces is used.     

Dynamic load effects on gate valve operability and snubber performance

The Idaho National Engineering Laboratory (INEL) participated in an internationally sponsored seismic research program conducted at the decommissioned Heissdampfreaktor (HDR) located in the Federal Republic of Germany. An existing piping system was modified by installation of 200-mm, naturally aged, motor-operated gate valve from a U.S. nuclear power plant and a piping support system of U.S. design. Using various combinations of snubbers and other supports, six other piping support systems of varying flexibility from stiff to flexible were also installed and tested. Additional valve loadings included internal hydraulic loads and, during one block of tests, elevated temperature. The operability and integrity of the aged gate valve and the dynamic response of the various piping support systems were measured during 25 representative simulations of seismic events.     

Enhanced seismic criteria for piping

In situ or laboratory experiments have shown that piping systems exhibit satisfactory seismic behavior. Seismic motion is not severe enough to significantly damage piping systems unless large differential motions of anchorage are imposed. Nevertheless, present design criteria for piping are very severe and require a large number of supports, which creates overly rigid piping systems. CEA, in collaboration with EDF, FRAMATOME and IRSN, has launched a large R&D program on enhanced design methods which will be less severe, but still conservative, and compatible with defect justification during operation. This paper presents the background of the R&D work on this matter, and CEA proposed equations.Our approach is based on the difference between the real behavior (or the best estimated computed one) with the one supposed by codified methods. Codified criteria are applied on an elastically calculated behavior that can be significantly different from the real one: the effect of plasticity may be very meaningful, even with low incursion in the plastic domain. Moreover, and particularly in piping systems, the elastic follow-up effect affects stress distribution for both seismic and thermal loads.For seismic load, we have proposed to modify the elastic moment limitation, based on the interpretation of experimental results on piping systems. The methods have been validated on more industrial cases, and some of the consequences of the changes have been studied: modification of the drawings and of the number of supports, global displacements, forces in the supports, stability of potential defects, etc.The basic aim of the studies undertaken is to make a decision on the stress classification problem, one that is not limited to seismic induced stresses, and to propose simplified methods for its solution.     

Impact of structural steel flexibility and restraints gaps on the dynamic behaviour of piping

The effect of gaps present in the seismic supports of nuclear piping systems and of the flexibility of the steel structure to which intermediate supports are attached, is studied in this paper. An actual piping system is used to investigate the impact of structural steel and mechanical snubber gaps on the dynamic behaviour of piping. An evaluation is thus performed of the finite element modeling techniques employed by the designers in the dynamic analysis of piping systems.     

Seismic analysis of ZPR-6 Reactor Facility

A safe shutdown earthquake analysis of ZPR 6 Reactor Facility was conducted through seismic risk analysis, soil-structure interaction analysis, reactor building dynamic time history analysis and equipment response spectrum analysis due to an assumed El Centro earthquake. Several ASME, AISC and ANSI design codes were used to demonstrate the adequacy of this facility and to design several equipment and piping supports.     

Effects of ductility on seismic response of piping systems and their implication on design and qualification

This study is concerned with the inelastic seismic response of nuclear power plant piping systems. Two systems are examined. The first one is an idealized four-equal-span pipe run and the second one consists of two configurations modified from an existing pipe run. Detailed finite element seismic time history analyses are performed using the computer program. By varying the various geometrical and physical parameters, calculations are made for a total of 76 cases. The results show that ductility generally contributes to reducing the response of piping systems. An empirical relation between the support load reduction factor and support ductility demand is given and a chart and simple procedures are suggested for the design and qualification of piping supports taking ductility into consideration.     

Soil-structure interaction of nuclear reactor structures considering through-soil coupling between adjacent structures

The theoretical problem concerning the influence of through-soil coupling between adjacent structures on the seismic loading of nuclear reactors has been investigated by considering a soil-structure interaction model in which several three-dimensional flexible structures are bonded to an elastic half-space. These structures, which are allowed to be either similar or dissimilar, are modeled as conventional discrete systems mounted on separate base slabs of close proximity. For the purpose of this study, it is assumed that the stiffness of any structure such as piping connecting the adjacent buildings is negligible.For purposes of comparison, the seismic responses of structural masses are determined both with and without the influence of nearby structures. Both transient and steady-state results are presented and discussed for some typical simplified two- and three-structure complexes. Emphasis is placed on the effects of through-soil coupling on the dynamic response of the system rather than actual magnitudes of response which have previously been treated for plants erected on a single base slab. The significant findings are that nuclear power plants can be designed to achieve a reduction in seismic loads due to interaction with neighboring structures. Conversely, improper plant design and layout may result in mutual reinforcement of resonances with increased loads.     

塑性变形对管系地震动力响应的影响

在评述线弹性分析方法的基础上,阐明了在管系特别是核管系动力响应分析中考虑塑性变形影响的重要性,介绍了现有考虑塑性影响的方法及其存在的问题.指出要降低现行规范的保守性,提出合理的管系抗震设计方法,     

Seismic stops vs. snubbers, a reliable alternative

The Seismic Stops methodology has been developed to provide a reliable alternative for providing seismic support to nuclear power plant piping. The concept is based on using rigid passive supports with large clearances. These gaps permit unrestrained thermal expansion while limiting excessive seismic displacements. This type of restraint has performed successfully in fossil fueled power plants.A simplified production analysis tool has been developed which evaluates the nonlinear piping response including the effect of the gapped supports. The methodology utilizes the response spectrum approach and has been incorporated into a piping analysis computer program RLCA-GAP.Full scale shake table tests of piping specimens were performed to provide test correlation with the developed methodology. Analyses using RLCA-GAP were in good agreement with test results. A sample piping system was evaluated using the Seismic Stops methodology to replace the existing snubbers with passive gapped supports. To provide further correlation data, the sample system was also evaluated using nonlinear time history analysis. The correlation comparisons showed RLCA-GAP to be a viable methodology and a reliable alternative for snubber optimization and elimination.     

Seismic response analysis of structural system subjected to multiple support excitation

In the seismic analysis of a multiply supported structural system subjected to nonuniform excitations at each support point, the single response spectrum, the time history, and the multiple response spectrum are the three commonly employed methods. In the present paper the three methods are developed, evaluated, and the limitations and advantages of each method assessed. A numerical example has been carried out for a typical piping system. Considerably smaller responses have been predicted by the time history method than that by the single response spectrum method. This is mainly due to the fact that the phase and amplitude relations between the support excitations are faithfully retained in the time history method. The multiple response spectrum prediction has been observed to compare favorably with the time history method prediction. Based on the present evaluation, the multiple response spectrum method is the most efficient method for seismic response analysis of structural systems subjected to multiple support excitation.     

Nuclear piping system damping data studies

A program has been conducted at the Idaho National Engineering Laboratory to study structural damping data for nuclear piping systems and to evaluate if changes in allowable damping values for structural seismic analyses are justified. The existing pipe damping data base was examined, from which a conclusion was made that there were several sets of data to support higher allowable values. The parameters which most influence pipe damping were identified and an analytical investigation demonstrated that increased damping would reduce the required number of seismic supports. A series of tests on several laboratory piping systems was used to determine the effect of various parameters such as types of supports, amplitude of vibration, frequency, insulation, and pressure on damping. A multiple regression analysis was used to statistically assess the influence of the various parameters on damping, and an international pipe damping data bank has been formed.     

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.     

Response spectrum analysis of piping systems with elastic-plastic gap supports

A new seismic support device and its application in piping systems is described. The device, E-BAR (patented), can be cost effectively used for snubber replacement programs, mitigation of hydraulic transients, pipe whip and as a thermal stop. The device has pre-set gaps to allow free thermal movement. During a seismic or other dynamic load event, if the pipe movement exceeds the gap dimension, the device acts as an elastic or elastic-plastic restraint. The device also has a unique design feature for not exceeding the restraint force beyond a specified limit design value. To analyze piping systems with gap supports having elastic-plastic characteristics, modal analysis procedures for both response spectrum and time history methods are developed. The comparison of responses obtained from the procedures with nonlinear time history analysis and test results available in the literature shows excellent correlation. A pilot program conducted for snubber replacement with E-BARs demonstrates that the limit force feature of E-BAR makes them very attractive for snubber replacement. This is because a particular E-BAR with a specified limit design force can be selected, such that, the E-BAR replacing the snubber does not require any modifications be made to the existing support steel and hardware.     

Positive use of damping devices for piping systems — Some experiences and new proposals

An increase of the damping ratio is known to be very effective for the seismic design of a piping system. It is reported that the energy dissipation in piping supports contributes to increase the damping ratio of the piping system. In this paper, with regard to increasing the damping and reducing the seismic response of the piping system, three application methods of damping devices used in other engineering fields are reviewed: (1) direct damper, (2) dynamic vibration absorber, and (3) connecting damper. Based on the results of this review, the following three types of damping devices for piping systems are introduced: (1) visco-elastic dampler (direct damper), (2) elasto-plastic damper (direct damper), and (3) compact dynamic absorber (dynamic vibration absorber). The dynamic characteristics of these damping devices are investigated by a component test and the applicability of them to the piping system was confirmed by the vibration test using a three-dimensional piping model. These damping devices are more effective than mechanical snubbers to suppress the vibration of the piping system.