Dynamic analysis of VVER type nuclear power plants using different procedures for consideration of soil-structure interaction effects

The dynamic response of structures due to seismic loadings is conventionally analyzed in the time domain using substructure methods (decoupled system models). This procedure uses frequency-independent impedances to represent capabilities of the soil underneath the structure. The soil parameters are tuned to the fundamental frequencies of the soil-structure system. This is a common procedure widely used in the preliminary design of power plant structures which provides conservative results. However, parallel to the rapid progress being made in upgrading the capability of data processing systems, methods and software tools have become available which work also in the frequency domain using complex models (for the soil and the structure) or models in which the soil is represented by frequency-dependent impedances. This procedure (coupled system models) also allows realistic treatment of kinematic interaction effects and especially consideration of the embedment parameters of the building structure. The main goal of the study presented here was to demonstrate the effects of different procedures for consideration of soil-structure interaction on the dynamic response of the structures mentioned above. The analyses were based on appropriate mathematical models of the coupled vibrating structures (reactor building, turbine hall, intermediate building structures of a VVER 440/213 as well as the main building of the VVER 1000) and the layered soil. On the basis of this study, it can be concluded that substructure methods using frequency-independent impedances (equivalent dashpots) and cut-off of modal damping usually provide conservative results. Coupled system models which allow the soil-structure interaction effects to be realistically represented (by coupled models of the soil and the structure or by frequency-dependent impedances) provide more accurate results. The advantage of the analysis using coupled system models will be demonstrated and discussed, based on results obtained for the VVER 440/213 PAKS and VVER 1000 Kozloduy.     

The use of frequency-independent soil-structure interaction parameters

The validity of approximating frequency-independent foundation impedance functions by constant parameters was evaluated for nuclear power plant structures. The soil-structure interaction system with the frequency-dependent impedances was analyzed using the Foss method to uncouple the equations of motion; this closely follows the method developed by Jennings and Bielak. The interaction system with the constant impedances was approximately analyzed by the normal mode method using equivalent modal damping values computed according to a procedure developed by Tsai. The above two methods were applied to simplified containment structural models founded on an idealized elastic half-space, the shear wave velocities being taken to be 600, 1150, 2000 and 10 000 ft/sec. The results such as frequencies, damping, and in-structure response spectra were then compared. It was concluded that frequency-independent foundation impedances can be adequately used for plant sites having relatively deep and uniform overburdens.     

Reanalysis and evaluation of the seismic capacity of the CANDU 700 MW NPP CERNAVODA

The dynamic response of structures of the CANDU 700 MW NPP due to seismic loadings was conventionally analyzed in the time domain using modal substructure procedures. The frequency-independent parameters were tuned to the main frequencies of the soil-structure system. This is a common procedure widely used in the preliminary design of power plant structures and provides conservative results. However, parallel to the rapid progress being made in upgrading the capability of data processing systems, methods and software tools have become available which work in the frequency domain using complex (soil-structure) mathematical models or models in which the soil is represented by frequency-dependent impedances. In order to demonstrate the reserves existing in the design of the CANDU 700 reactor building, frequency-domain calculations were additionally prepared. The analyses were based on appropriate mathematical 3D-models of the coupled vibrating structures of the reactor building and as the soil represented by frequency-dependent impedances. The results obtained by using the time and frequency domain methods were compared and the safety margins of the CANDU design discussed.     

Dynamic stiffness and seismic input motion of a group of battered piles

The dynamic stiffness (impedance function) and the corresponding seismic input motion of a group of battered piles, which can be end-bearing and floating, situated in any desired configuration in horizontally stratified soil, are determined. The soil and the piles consist of (frequency-dependent) visco-elastic material with hysteretic damping. The base mat can be rigid or flexible. Any seismic excitation, for which the free-field motion can be calculated, can be specified (body waves, propagating at an arbitrary angle, generalized surface waves). The soil is discretized by toroidal finite elements in conjunction with a Fourier expansion in the circumferential direction. Radiation and hysteretic damping are accounted for. The dynamic-flexibility matrix of the soil is generated, superimposing the basic dynamic-flexibility coefficients calculated by applying sequentially a horizontal and a vertical force at all nodes located on the axis of symmetry. The influence of the soil which is subsequently replaced by piles is taken into consideration. Pile-soil-pile interaction is accounted for in this method. The formulation can also be applied to embedded foundations and buried structures such as tunnels and pipe systems.     

Experimental and numerical determination of the dynamic properties of the reactor building of Atucha II NPP

Determination of the dynamic properties of the reactor building of Atucha II NPP is carried out in order to: (i) obtain valuable information for seismic qualification of the plant and (ii) access some procedures for testing and analysis that are used in the process of seismic evaluation of existing nuclear facilities founded on Quaternary soil deposits. Both steady state and impulsive dynamic tests were performed but attention is centered here in the techniques used to determine natural frequencies and modal damping ratios with impulsive tests. Numerical analyses were performed by means of a 3-D model of the superstructure together with foundation stiffness coefficients derived in a separate paper from steady state vibration tests, and also from analysis with a 2-D FE model of the soil layers capable of approximating the 3-D features of the problem. The computed foundation stiffness coefficients are compared both with those obtained from the tests and from an axisymmetric FE model: results indicate that foundation stiffness coefficients calculated with FE models with soil parameters given by laboratory tests performed on cored samples are significantly lower than those given by the steady state vibration tests.     

Full scale dynamic tests of Atucha II NPP

This paper summarizes the main results of a series of dynamic tests of the reactor building of Atucha II NPP performed to determine the dynamic properties of its massive structure deeply embedded in quaternary soil deposits. Tests were performed under two different types of loading conditions: steady state harmonic loads imposed by mechanical exciters and impulsive loads induced by dropping a weight on the ground surface in the vicinity. Natural frequencies and mode shapes were identified and the associated modal damping ratios were experimentally determined. Numerical analyses of the reactor building-foundation system by two different F.E. models were performed. One of them, based on an axisymmetric representation of the soil-structure system, was used to simulate the steady state vibration tests and to calculate the dynamic stiffness of the foundation slab and soil layers for comparison with those experimentally obtained. The other, a 3-D F.E. model of the superstructure, was used to assess the natural frequencies and mode shapes obtained from the tests, representing dynamic stiffness of the foundation with stiffness coefficients derived both from the tests and from the axisymmetric F.E. model. Good agreement of the natural frequencies given by two types of tests were generally found, with the largest difference between them in the fundamental frequency of the building. Estimates of modal damping derived from the tests showed significant differences depending on the technique used to calculate them. For the fundamental mode, damping was found to be 23–42%, gradually decreasing with frequency to 2–4% for 10 Hz.     

In situ dynamic tests and seismic records on the RHR system building enel IV nuclear plant/caorso (Italy)

The tests on the RHR Building of the Caorso Nuclear Plant are part of a program of dynamic tests on large structures sponsored by ENEL, which ISMES is presently carrying out.The main purposes of this program are:

• - to collect information on the effectiveness of different excitation methods;

• - to set up the most suitable recording and processing technique;

• - to compare the experimental results with the computed ones, in view of the validation of the adopted computing schemes.

The structure has been excited by a mechanical vibrator delivering sinusoidal forces in a frequency range 2 to 20 cps, in conditions of empty, , and completely full pools. The response, recorded by 36 velocity transducers was digitally processed by means of a Fourier Analyzer. Moreover, a number of Friuli earthquake aftershocks could be picked up, and the building response recorded in many points.More than ten natural frequencies could be detected, and the related damping and mode shapes determined, in a frequency range from 3 to 16 cps.The structure frequencies determined by tests are lower than the computed ones.The energy content of the seismic excitation, due to the large distance from the epicentral area, is confined within very low frequencies. Some data on the behaviour of the RHR and Reactor buildings could however be obtained.The testing technique adopted, which does not require long testing time and high costs, supplies a large amount of reliable data in case of excitation within the linear range. To account for non-linearities, different testing methods should be used, such as blasting or strong forced vibrations of the foundation. Moreover, the adopted method can fully describe the higher vibration modes, which are of noticeable importance as to the behaviour of mechanical and electric equipment installed in the structure.     

Soil-structure interaction with separation of base mat from soil (lifting-off)

In reactor buildings having a separate base mat and a shield-building (outer concrete shell) of large mass, large overturning moments are developed for severe earthquake loading. The standard linear elastic half-space theory is used in the soil-structure interaction model. For a circular base mat, if the overturning moment exceeds the product of the normal force (dead weight minus the effect of the vertical earthquake) and one-third of the radius, then tension will occur in part of the area of contact, assuming distribution of stress as in the static case. For a strip foundation the same arises if the eccentricity of the normal force exceeds a quarter of the total width. As tension is incompatible with the constitutive law of soils, the base mat will become partially separated from the underlying soil.Assuming that only normal stresses in compression and corresponding shear stresses (friction) can occur in the area of contact, a method of analyzing soil-structure interaction including partial lifting-off is derived, which otherwise is based on the elastic behaviour of the soil. A rigorous procedure to determine the nonlinear impedance function of a rigid plate of arbitrary shape, only in partial contact with the elastic half-space, is developed. Complex dynamic influence coefficients for displacements are used which can either be determined with the finite-element method or based on solutions of displacements on the surface of an elastic half-space at a certain distance from a rigid subdisk. Constant and variable stiffness methods of solving the non-linear equations of motion are explained which also determine the area of contact. Slipping of the entire mat or of a part thereof can also be taken into consideration.A simpler approximate method is discussed. For a given force and moment acting on the rigid plate, the area of contact is determined by iteration or based on quadratic programming techniques using the static influence coefficients for displacements. The complex-valued impedance function is estimated by substituting an equivalent circular plate for the actual area of contact. Transforming the equivalent lumped system to the centre of the plate, the non-linear stiffness and damping matrices of the soil are derived. Formulae are given for the partial lifting-off of a disk and a strip. The results of the numerical method are compared to rigorous solutions for full contact. As an example, the dynamic response of the reactor building of a 1000 Mw plant to earthquake motion is calculated using the rigorous and approximate methods. Parametric studies are carried out. The influence of the frequency on the impedance function and on the distribution of stress in the area of contact, which determines the beginning of lift-off, is discussed.     

Analysis of equations of motion with complex stiffness mode superposition method applied to systems with many degrees of freedom

According to past experimental studies, the damping effects of a structure may be considered to be structural damping mechanics in the elastic range, the damping factors or logarithmic damping ratios of which are independent of the frequencies of the disturbing force or the eigenvalues of the structure. In this paper, the authors propose a simple method of expressing the above-mentioned damping effects using complex numbers, although viscous damping mechanics is generally used as the conventional mathematical method. Thus, the spring constant can be expressed as k = k₀ exp(i sgn ωø), where sgn ω = 1 for ω > 0; sgn ω = 0 for ω = 0; sgn ω = −1 for ω < 0.The concept of complex damping is described comparing it with the most common ‘Voigt model’ for a system with a single degree of freedom and it is concluded that both solutions are exactly identical under the conditions of free and forced vibration when both systems have equivalent natural periods and damping ratios. Furthermore, the authors attempt to apply the above complex stiffness to multi systems with many degrees of freedom and investigate their mathematical and dynamical characteristics. The fundamental mathematical characteristics can be described as follows:

1. (1) Any n degrees of freedom system that has 2n distinct eigenvalues occurring as n complex conjugate pairs and n complex conjugate pairs of corresponding eigenvectors according to the definition of ‘sgn ω’.

2. (2) The eigenvectors establish the orthogonality of the frequency domain when either ω > 0 or ω < 0, but they do not establish this property over the domains for both ω > 0 and ω <.

3. (3) By using the above properties, the equations of motion can be reduced to n conjugate pairs of first order differential equations and the solution is obtained by the superposition of n complex conjugate pairs.

The fundamental dynamic characteristics can also be described as follows:

1. (1) When the same damping values are assigned to all structural elements making up a vibrational system, the reduced equations form an estimate of the constant damping ratio over all of the modes from the lowest to the highest.

2. (2) Furthermore, when the different damping values are assigned to each individual structural element, the damping values of the reduced equations denote the value which is equivalent to that of any structure of which the mode shapes are predominant.

Finally, the authors present the computed results of a system with 18 degrees of freedom consisting of four individual structural elements with different damping values. Through the above studies, it is concluded that the authors' method is reasonable for estimating the damping effects of the structure.     

Vibrations of a rigid disc on a layered viscoelastic medium

A method of obtaining the dynamic impedance functions for a rigid circular foundation placed on a layered viscoelastic half-space is presented. Both hysteretic and Voigt models of internal damping are considered. The results obtained indicate that the presence of internal damping introduces important changes in the dynamic response of the foundation for vertical, rocking and horizontal steady-state excitation.     

Seismic response analysis of deeply embedded nuclear reactor buildings considering frequency-dependent soil impedance in time domain

In order to estimate the seismic behavior of deeply embedded nuclear power buildings, it is important to accurately transform the soil impedance in the frequency domain to the impulse response in the time domain. Although the transform is important for some nuclear buildings because they are deeply embedded in the soil, there are few practical and accurate methods at present. The author has proposed practical transform methods. In this paper, seismic response analyses considering frequency-dependent soil impedance in the time domain are shown. First, the formulation of the proposed transform methods is described. Then, the response analysis of a nuclear reactor building deeply embedded in inhomogeneous soil was performed considering the full matrix soil impedance as the example of practical problems. Through these analyses, the validity and efficiency of the methods were confirmed.     

Soil-structure-interaction analysis in time domain

The procedures to perform nonlinear soil-structure-interaction analysis in the time domain are summarized. The nonlinearity is restricted to the structure and possibly an adjacent irregular soil region. The unbounded soil (far field) must remain linear in this formulation.Besides the direct method where local frequency-independent boundary conditions are enforced on the artificial boundary, various formulations based on the substructure method are addressed, ranging from a discrete model with springs, dashpots and masses to boundary-element methods with convolution integrals involving either the dynamic-stiffness coefficients or the Green's functions in the time domain via the iterative hybrid-frequency-time-domain analysis procedure with the nonlinearities affecting only the right-hand side of the equations of motion.     

Structural analysis and design of a nuclear power plant building for aircraft crash effects

The object of this investigation is to assess the effect of a large commercial airplane crashing perpendicularly on to the surface of a spherical reactor building dome. This investigation is related to a project currently in execution. Practical solutions of the postulated case, which vary in the degree of engineering effort used, are shown. Based on safety consideration the various solutions are discussed from the viewpoint of penetration, cracking and collapse modes of failure, where, primarily, the carrying capacity of the structure under an equivalent statical load is considered. The performed investigations include:

1. (a) Calculation of the failure load following the yield line theory;

2. (b) Calculation of the sectional forces using the linear-elastic shell theory and subsequent design by the ultimate strength method;

3. (c) Calculation of the failure load, establishing of the failure mechanism and distribution of sectional forces using the plastic shell theory;

4. (d) Calculation using a three-dimensional FEM program with plastic capabilities; this includes the collapse load, the failure mechanism and the distribution of sectional forces.

A discussion of the resultant forces and the configutation of the critical section is given for the various methods used. The evaluation of the carrying capacity of the structure with respect to load is based on energy considerations. It is attempted to compare such results, to evaluate possible simplifications in the used solutions, and to give some recommendations for the practical design and for the development of structural details.     

Models test on dynamic structure–structure interaction of nuclear power plant buildings

A reactor building of an NPP (nuclear power plant) is generally constructed closely adjacent to a turbine building and other buildings such as the auxiliary building, and in increasing numbers of NPPs, multiple plants are being planned and constructed closely on a single site. In these situations, adjacent buildings are considered to influence each other through the soil during earthquakes and to exhibit dynamic behaviour different from that of separate buildings, because those buildings in NPP are generally heavy and massive. The dynamic interaction between buildings during earthquake through the soil is termed here as ‘dynamic cross interaction (DCI)’. In order to comprehend DCI appropriately, forced vibration tests and earthquake observation are needed using closely constructed building models. Standing on this background, Nuclear Power Engineering Corporation (NUPEC) had planned the project to investigate the DCI effect in 1993 after the preceding SSI (soil–structure interaction) investigation project, ‘Model Tests on Embedment Effect of Reactor Building’. The project consists of field and laboratory tests. The field test is being carried out using three different building construction conditions, e.g. a single reactor building to be used for the comparison purposes as for a reference, two same reactor buildings used to evaluate pure DCI effects, and two different buildings, reactor and turbine building models to evaluate DCI effects under the actual plant conditions. Forced vibration tests and earthquake observations are planned in the field test. The laboratory test is planned to evaluate basic characteristics of the DCI effects using simple soil model made of silicon rubber and structure models made of aluminum. In this test, forced vibration tests and shaking table tests are planned. The project was started in April 1994 and will be completed in March 2002. This paper describes an outline and the summary of the current status of this project.     

Soil-structure interaction parameters from finite element analysis

A series of two-dimensional finite element computer runs were made to compute the frequency dependent soil-structure interaction coefficients. Variations in the element size, mesh dimensions, boundary conditions, and soil hysteretic damping ratio to determine their influence on the computed interaction coefficients were made. From the calculations, it has been determined that the primary requirement of the mesh is a transmitting boundary formulation. For low damping conditions, roller support boundary conditions must be placed exceedingly far from the structure to ensure convergence of the results to the analytic solution. In addition, with such boundary conditions, the addition of artificial hysteretic soil damping cannot be used to simulate radiation damping behavior of the continuum. A frequency dependent criteria is also presented to determine minimum size elements that must be used in any calculation.     

Nonlinear seismic response analysis of an embedded reactor building based on the substructure approach

A practical method to calculate the elasto-plastic seismic response of structures considering the dynamic soil-structure interaction is presented. The substructure technique in the time domain is utilized in the proposed method. A simple soil spring system with the coupling effects which are usually evaluated by the impedance matrix is introduced to consider the soil-structure interaction for embedded structures. As a numerical example, the response of a BWR-MARK II type reactor building embedded in the layered soil is calculated. The accuracy of the present method is verified by comparing its numerical results with exact solutions. The nonlinear behavior and the soil-structure interaction effects on the response of the reactor building are also discussed in detail. It is concluded that the present method is effective for the seismic design considering both the material nonlinearity of the nuclear reactor building and the dynamic soil-structure interaction.     

Response of equipment in nuclear power plants to airplane crash

Nuclear power plants in Germany are to be designed against airplane crash. Two problems arise: first, the local problem of penetration as well as local destruction of the building and secondly the airplane induced vibrations of the whole building which cause loadings for secondary systems (equipment). This paper deals especially with the second problem. Floor response spectra due to airplane crash are presented for two different power plant buildings. The influence of various parameters (time history of excitation, direction and location of impact, mathematical model, soil, damping, etc.) are discussed. A comparison with the results of earthquake loading is given. Suggestions are made for developing suitable floor design spectra and using them to analyse multidegree-of-freedom systems. However, the paper gives only a partial answer to the questions arising because of some important restrictions which had to be made. Studies concerning these restrictions are still being conducted and will be presented in a separate paper.     

Short-term degradation mechanisms of piping

The operation of PWR-type EDF plants has shown that components have been subjected to loadings higher than the design basis loads. For example, localized degradations on nuclear system pipes were found after relatively short times (10-10⁴ hours). The main damage mechanisms involved are:

&#x02022; - erosion—cavitation arising from the type of hydraulic flow,

&#x02022; - vibrational fatigue arising from the flow or operation of mechanical

&#x02022; - corrosion fatigue occurring in some confined spaces (dead ends).

This paper addresses these damage modes and the mitigating steps taken to cope with them, together with the initiatives taken for future reactors.     

Benchmarking results of the COMETHE code

The validation of a code for fuel rod behaviour prediction requires a comparison of its results with corresponding experimental data. Benchmarking of the COMETHE code has been done in parallel with its development, but more time has been spent on that work than in the development of the models themselves. Three experiments are presented; they have been selected from amongst those used by BN for the calibration as being good examples of various features:

1. (1) The ELP2 experiment, performed in the EL3 reactor by CEA-Saclay and related to fuel restructuring. Results show that behaviour is very well modelled in COMETHE.

2. (2) The BR3/VN post-irradiation data, which show a large sensitivity of the fission gas release to the power level and reveal that coupling between the fission gas release model and the gaseous swelling model is beneficial.

3. (3) The BM01 low density fuel BN pin, irradiated in the FBR RAPSODIE: close agreement is found between the cracking pattern computed by the “pivot model” and the experimental cold state results.

A lot of the benchmarking results arise from the EPRI RP 397 Fuel Rod Modeling Code Evaluation Project.