Dynamic analysis of storage racks for spent fuel assemblies

Nuclear Engineering and Design 54 (1979) 379-383 © North-Holland Publishing Company

DYNAMIC ANALYSIS OF STORAGE RACKS FOR SPENT FUEL ASSEMBLIES * G. HABEDANK, L.M. HABIP and H. SWELIM Kraftwerk Union A G, Reaktortechnik, Postfach 70 06 49, 6000 Frankfurt 70, Fed. Rep. Germany Received 8 June 1979

The dynamic response of storage racks for spent fuel assemblies subjected to base excitation is calculated. While classical methods of linear structural dynamics may be adequate at low levels of excitation, nonlinear effects due to uplift, for example, can no longer be neglected at high excitation levels. Several nonlinear dynamic analyses have been performed for different types of storage racks with uplift capability. With the help of the numerical results, the rocking behavior of storage racks and their structural integrity has been examined.

1. Introduction

2. Description of a storage rack structure

Storage racks for spent fuel assemblies in nuclear power plants must be designed to withstand dynamic loads caused by an earthquake, an airplane crash, or an explosion. The corresponding task o f structural analysis usually consists of the following steps: (a) compilation o f a specification covering design guidelines, load cases, component characteristics, and acceptance criteria, (b) preliminary analysis with the help of simple models and former experience, (c) calculations based on suitable methods of dynamic analysis, and (d) structural evaluation and design review. Depending on the severity of base excitation, different theoretical methods can be used to predict the structural response of storage racks. While classical methods of linear structural dynamics may be ,adequate at low levels of excitation, nonlinear effects due to uplift, for example, can no longer be neglected at the high excitation levels currently being considered. Accordingly, several nonlinear dynamic analyses have been performed for different types of storage racks with uplift capability. The present work summarizes some o f their major aspects.

A 3 × 4 arrangement of the main storage racks resting on the floor of the fuel storage pool of a pressurized water reactor (PWR) plant is shown in fig. 1(a). Dimensions are in mm. The storage pool is filled with water. A similar 6 × 5 configuration for a boiling water reactor (BWR) plant is shown in fig. l(b). Many different types o f storage racks are presently in use, including compact models which can accom-

* Presented at the 5th International Conference on Structural Mechanics in Reactor Technology, Berlin, August 1979.

Fig. 1. Arrangement of main storage racks for spent fuel assemblies in the fuel storage pool: (a) PWR plant, (b) BWR plant.

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modate a larger number of spent fuel assemblies per unit available space. The load-carrying structure of a storage rack of the latter category is shown schematically in fig. 2, where the location of the fuel assemblies is indicated by means of short vertical lines. Dimensions are in mm. Related information on spent fuel assemblies and associated absorber shafts is available elsewhere [1 ]. The structure is made of stainless steel, and consists of the horizontal upper and lower supports, parts 1 and 3, respectively, and of the vertical center support, part 2. The center support shafts with a thin-walled, square cross section are slender and flexible, while the upper and lower support structures provide considerable axial and bending rigidity, respectively. The upper support consists of longitudinal and transverse struts hinged to the center support shafts. The lower support is a perforated plate, reinforced with ribs; the center support shafts are bolted to it. The rack is free at the top and rests on feet (part 4), a typical one of which is shown in fig. 2. It can be seen that, while the structure is prevented from sliding in the horizontal plane by means of guide pins (part 5) anchored at the pool floor, it can lift up vertically when subjected to base excitation via the building structure. The rack executes then an overall rocking motion combined with the bending motions of the shafts. At the feet, parts 4a and 4b can slide vertically relative to each other, so that part 4b stays down on the guide pin as long as a certain level of uplift is not exceeded.

The case of earthquake excitation will be considered here. Most of the present discussion, however, applies also for other types of base excitation, such as due to an airplane crash or an explosion, except when noted otherwise. At low excitation levels the acceleration response spectrum of the reactor building at the point of support of the storage racks is used in order to perform a linear dynamic analysis. At moderate to high excitation levels, acceleration time histories are needed in order to perform nonlinear dynamic analyses in which an uplift of the storage rack is allowed. The response spectrum associated with such an acceleration time history is shown qualitatively in fig. 3(a) for a given damping ratio. Often, the nonlinear computational methods that are available require the absolute displacement time history as base excitation. This is obtained from the acceleration time history by means of double integration including a zero baseline correction. The method used here for the latter is that of Berg and Housner [2]. An absolute displacement time history corresponding to the acceleration function whose response spectrum is shown in fig. 3(a) is exhibited in fig. 3(b). Nonlinear dynamic analyses are performed by applying horizontal and vertical excitations simultaneously. In the case of dynamic loads caused by an airplane crash or an explosion, a zero base line correction is usually not necessary because the absolute displacement time histories are readily available. However, if

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acceleration time histories are artificially generated from "envelope" floor response spectra which cover all the many variations in the assumed airplane crash points and/or in soil and reactor building properties, then such a correction may become desirable.

4. Computational models and methods Provided racks of a given type are filled equally with fuel assemblies, their individual dynamic response to base excitation will be comparable, assuming the influence of neighboring structures to be the same for all. Model tests with several racks vibrating in water in close proximity to each other and in the vicinity of solid boundaries have shown this assumption to be approximately valid. Accordingly, only single storage racks have been considered in dynamic analyses performed to date. As a first approximation the structure is assumed to be held at the base in all directions. A linear dynamic analysis is then performed. If considerable tensile forces develop at the feet of the structure in the vertical direction, a nonlinear dynamic analysis with uplift becomes necessary. At moderate to high excitation levels this is usually the case. Nonlinear dynamic analyses of simplified mathematical models of storage racks, both two-dimensional

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(2D) and three-dimensional (3D), have been performed by means of the general purpose computer program ANSYS [3] which utilizes the matrix displacement method of analysis based on a finite element discretization of the structure. Since the nonlinearity is caused only by the support conditions of the rack, the entire structure could be considered as a linear elastic "superelement". For similar nonlinear systems a recent discussion of such methods based on the use of substructures is due to Clough and Wilson [4]. The corresponding computational models consisting of beam elements are shown in fig. 4. The structural stiffness and mass properties of these models simulate particular designs of storage racks. Various height-towidth (H/W) ratios, and symmetrical as well as asymmetrical configurations have been considered, with dashed vertical lines denoting fuel assemblies modeled as a separate structure. The support conditions are typically represented by means of frictionless gap elements, shown in fig. 4, which cannot transmit tensile forces and are suitably connected to the superelement along common nodes. The spring constants of the gap elements simulate the rigid sut~port conditions at the pool floor and the local + xibility of the rack feet. In the calculations, the specified horizontal and vertical base excitations in the form of preprocessed digital data for displacements are applied to the structure over these gap elements, as indicated in fig. 4. Whereas the vertical excitation ceases following uplift, the horizontal excitation remains. As mentioned earlier, this holds for the particular design chosen for the rack feet and guide pins, shown in fig. 2, provided a certain level of uplift is not exceeded. The results of the calculations show this to be the case. Because storage racks are submerged in water, the structural mass must be increased by the amount of added mass due to the water in calculating the natural modes and frequencies of the structure assumed held at the base. The corresponding fundamental frequency, due to the first bending mode of the center support structure, is indicated in fig. 3(a) by means of a vertical line. It is seen that, with the amount of added mass considered here, a structural frequency is obtained which lies just above that of the peak of the acceleration spectrum. Noting that the "frequency" of a system which uplifts lies always somewhat lower than that of the system held down,

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it can be stated that a conservative method has been used here to account for added mass effects. This approach was chosen because the actual added mass of a complicated deformable structure such as a storage rack is very difficult to evaluate. The results of the calculations have confirmed that the response of the structure with uplift lies in the frequency range of maximum earthquake acceleration. The counterpart of this conservative method for structures without uplift, for which a linear analysis applies, has been proposed by Dong [5]. In that case the fundamental frequency with added mass ought to lie just at the peak of the acceleration spectrum. Finally, another conservative effect in standard dynamic analyses of submerged structures results from the increased total mass, necessary for the natural frequency calculation, being multiplied by the acceleration due to base excitation during the forced vibration calculation. Actually, a mass which is even less than that of the structure alone, as shown, for example, by Fritz [6], should be used for this purpose. Based on the governing frequencies of the structure, a typical damping curve shown qualitatively in fig. 5 was utilized in the calculations. Points A and B on this curve correspond to damping levels associated respectively with the bending frequencies of structural parts that are bolted and welded. An implicit finite difference time integration procedure was adopted with acceleration varying linearly across the time step. The smallest integration step is governed by the rocking behavior of the structure and, in particular, by its impact and rebound characteristics following uplift. Use was made of restart procedures, and the results of the calculations were post-processed for plotting and evaluation.

5. Results and conclusion The primary objective of the nonlinear dynamic analyses was to determine the maximum uplift, the global structural forces and moments, and the forces transmitted to the pool floor from the time history of the response to base excitation. Additionally, an estimate of global dynamic loads transmitted to the fuel assemblies was of interest. The computational models presented here proved to be fully adequate for these purposes. The horizontal, relative displacement time history of the upper support structure of a storage rack subjected to earthquake excitation is shown qualitatively in fig. 6(a). The corresponding uplift of a point at the base of the rack is also shown in fig. 6(a). Similar information for the center of gravity and the base of a storage rack of asymmetrical construction is given in fig. 6(b). The amplitudes of displacement and uplift in fig. 6 have different scales. The time history of the bending moment at the foot of a center support shaft is shown qualitatively in fig. 7(a). The corresponding axial compressive force transmitted to the pool floor is shown in fig. 7(b). With the help of such numerical results obtained from nonlinear dynamic analyses, the rocking behavior of storage racks was examined in order to ascertain their stability against overturning. Furthermore, since the

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highest stresses in the storage rack, and the largest forces and acceleration~ transmitted respectively to the pool floor and fuel assemblies occur, as expected, during the impact and rebound phase following uplift, these analyses were essential in checking the structural integrity and function of the racks. Thus, the feasibility of compact storage racks with uplift capability could be demonstrated conclusively.

Acknowledgments The authors are indebted to their co-workers, Ms. Y. Ernst and Messrs. H. Ungoreit and H. Eggers, for computational model development and implementation of the nonlinear dynamic analysis method;

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to Messrs. L. Widuch and H. Behechti for preprocessing the dynamic loads data, performing natural frequency analyses, and postprocessing various results; to their colleagues at KWU, Berlin, Messrs. H. Wellen and W. Punger for defining equivalent properties based on particular designs for some of the models considered here and their help in technical report preparation for the three-dimensional models, and W. Beuchel for some additional numerical results. Finally, the consulting services of Dr. G.J. DeSalvo, Dr. E.G. Kost, Mr. S. Shankar, Dr. J.A. Swanson, and Dr. K. Zilch are gratefully acknowledged.

References [ 1] KWU Publication 445-101a, Dept. GA 19, Kraftwerk Union AG, Erlangen (Sept. 1978). [2] G.V. Berg and G.W. Housner, Bull. Seismol. Soc. Amer. 51 (1961) 175. [3] G.J. DeSalvo and J.A. Swanson, ANSYS User's Manual, Swanson Analysis Systems, Inc., Houston, Pennsylvania (Aug. 1978); P.C. Kohnke, ANSYS Theoretical Manual, Swanson Analysis Systems, Inc., Elizabeth, Pennsylvania (Nov. 1977). [4] R.W. Clough and E.L. Wilson, Comput. Methods Appl. Mech. Eng. 17/18 (1979) 107. [5] R.G. Dong, UCRL-52342, Lawrence Livermore Laboratory, University of California, Livermore, California (Apr. 1978), p. 62. [6] R.J. Fritz, J. Eng. Ind.,Trans. ASME, Ser. B 94 (1972) 167.