Seismic response analysis of embedded structure at Hualien, Taiwan

Predictive and correlative analyses of the forces vibration tests (‘FVT’ for short, hereafter:) and seismic response of the large-scale embedded structure were performed as one of the analytical phases of an international large-scale seismic test (LSST) program (Tang et al., 1991) at Hualien, Taiwan. Consequently, the following was clarified; (1) FVT analysis using unified ground model (UMFVT2) predicted the fundamental system frequency (ƒ₀) about 20% higher than the test. (2) After careful investigation on several items cited as the presumed causes of (ƒ₀) discrepancy between the test and the prediction, it was attributed to the V_s of the backfill, and best correlated ground model (BCFVT2) was formed, based on it. (3) Seismic response analysis using BCFVT2 brought a bit better agreement with the observation than using UMFVT2, but from another viewpoint, both analysis results agreed fairly well with the observation, indicating that backfill V_s does not affect seismic response so much as during FVT.     

Seismic response of flexible cylindrical liquid storage tanks

Liquid slosh and tank wall flexural vibrations are studied in a flexible model storage tank subject to simulated earthquake environments. Emphasis is placed on determining the influence of wall flexural vibrations on induced stresses. The approach is basically experimental, whereby similitude considerations are first presented. Then, a series of scale model experiments are conducted, and preliminary observations are evaluated. These evaluations allow formulation of an approximate analytical model for prediction of seismically induced stress. Validity range for this model is established by comparison of various predicted responses with observed results.     

Seismic response analysis of RCC structure with yielding dampers using linearization techniques

Passive energy dissipating devices like elasto-plastic dampers (EPDs) can be used for retrofitting of structures subjected to seismic loads. A model of reinforced concrete structure is tested on shake table with and without EPDs attached in its frames. Using a finite element model of the structure, linear and nonlinear time history analysis is carried out using Newmark's time integration technique. However, the most viable approach used by designers is response spectrum approach. Hence equivalent linearization techniques are used to address the nonlinearity of dampers and iterative response spectrum method is used for evaluating the response of the structure using equivalent damping and stiffness. The analytical maximum storey response of the structure is compared with experimental values and time history analysis values. It has been concluded that, iterative response spectrum technique using equivalent linearization techniques is simple and results in reasonably acceptable response of the structures retrofitted with energy dissipaters.     

Seismic response of a structure subjected to rotational base excitation

A modal superposition method which can perform the seismic analysis of a structure subjected to translational and rotational base excitation is presented. Discussed are two different approaches to derive the equations of motion. In the first approach, the reference axes are fixed in space. While in the second approach, they are rigidly fixed at the base of the structure. For rotational base excitation, it is shown that the application of second approach results in equation of motion with asymmetric, time-dependent coefficient matrix due to presence of the Coriolis acceleration term.Analytic integration is used to integrate the modal equations of motion derived by the first approach. Most of the mode shapes have to be included in the time history analysis.The modal superposition method is applied to the seismic analysis of a building subjected to translational and rotational excitation. The displacement results and the computer cost of this analysis are compared with those of using the direct integration method. The computer cost associated with the modal superposition method is lower than that associated with the direct integration method.     

Seismic response analysis of full-scale boiling water reactor using three-dimensional finite element method

This paper presents the three-dimensional finite element seismic response analysis of full-scale boiling water reactor BWR5 at Kashiwazaki-Kariwa Nuclear Power Station subjected to the Niigata-ken Chuetsu-Oki earthquake that occurred on 16 July 2007. During the earthquake, the automatic shutdown system of the reactors was activated successfully. Although the monitored seismic acceleration significantly exceeded the design level, it was found that there were no significant damages of the reactor cores or other important systems, structures and components through in-depth investigation. In the seismic design commonly used in Japan, a lumped mass model is employed to evaluate the seismic response of structures and components. Although the lumped mass model has worked well so far for a seismic proof design, it is still needed to develop more precise methods for the visual understanding of response behaviors. In the present study, we propose the three-dimensional finite element seismic response analysis of the full-scale and precise BWR model in order to directly visualize its dynamic behaviors. Through the comparison between both analysis results, we discuss the characteristics of both models. The stress values were also found to be generally under the design value.     

Seismic analysis of liquid storage container in nuclear reactors

Seismic analysis of liquid storage containers is always difficult in the seismic design of nuclear reactor equipment. The main reason is that the liquid will generate significant seismic loads under earthquake. These dynamic liquid loads usually form the main source of the stresses in the container. For this kind of structure–fluid coupling problem, some simplified theoretical methods were usually used previously. But this cannot satisfy the requirements of engineering design. The Finite Element Method, which is now full developed and very useful for the structural analysis, is still not mature for the structure–fluid coupling problem. This paper introduces a method suitable for engineering mechanical analysis. Combining theoretical analysis of the dynamic liquid loads and finite element analysis of the structure together, this method can give practical solutions in the seismic design of liquid storage containers.     

Seismic fragility of reinforced concrete structures in nuclear facilities

The failure and fragility analyses of reinforced concrete structures and elements in nuclear reactor facilities within the Seismic Safety Margins Research Program (SSMRP) at the Lawrence Livermore National Laboratory are evaluated. Receiving special attention are uncertainties in material modeling, behavior of low shear walls, and seismic risk assessment for nonlinear response. Problems with ductility-based spectral deamplification and prediction of the stiffness of reinforced concrete walls at low stress levels are examined. It is recommended that relatively low damping values be used in connection with ductility-based response reductions and that static nonlinear force-deflection curves be studied for better nonlinear dynamic response predictions.     

Seismic analysis of a reactor coolant pump by the response spectrum method

Current nuclear steam supply systems (NSSS) are designed to remove the heat of fission by circulating coolant in closed loops from the reactor. For water reactors, this prime function is designated to the reactor coolant pump (RCP). The Westinghouse Type 93A RCP is analyzed for seismic response. Briefly described, this RCP is a vertical, single-stage, centrifugal pump designed to move 90 000 gpm (568 m³/sec) of water and driven by a 6000 hp motor for use in the PWR primary system. The RCP assembly is generally axisymmetric and is modeled using three-dimensional finite elements of the types normally found in general-purpose computer programs such as ANSYS or NASTRAN. The structural frame and the rotating shaft are the principal branches of the model. Each consists of a series of pipe elements complemented by mass elements. Orthogonal sets of linear spring elements connect the branches at the bearings and possibly at each labyrinth. Fluid elements are added to include the interaction between the shaft and the pump case through the intervening water mass. Beam elements are used to account for unsymmetry of the motor stand. To complete the model, stiffness matrix elements representing the support structure and the neighboring loop piping are attached. It is impractical to idealize faithfully each geometric irregularity. Several adjacent sections are combined into one suitable element with total stiffness and equivalence. The number of elements in the model is thus minimized. Shear deflection of the pipe elements is considered; mass and mass inertia are lumped at nodal points, as needed to compensate for the actual material distribution. The RCP model contains 82 nodes, 155 elements and 140 master dynamic degrees of freedom. A modal frequency analysis is first run to identify the mode shapes.The seismic analysis is performed by the response spectrum method in ANSYS, with seismic velocity as the input excitation parameter. The model is excited by a set of three orthogonal spectra. For each load excitation, the modal displacements, forces and moments are computed at each node. A post-run subroutine calculates the absolute sum of nodal response quantities at each mode for one horizontal and the vertical seismic excitations. The resultant modal values are then combined using the square root of the sum of the squares (RSS) to record the final values: SSE X-Y and SSE Y-Z. Nodal stresses are computed; absolute displacements are reviewed for selected nodes along the model branches. The relative displacements at bearings and labyrinths are determined. Finally, the accelerations of nodes previously chosen are found.This paper assesses the effects of a given seismic excitation on the overall structural integrity of an RCP. The in-depth analysis has found the RCP adequate to withstand the imposed seismic loading. All component stresses are within the applicable faulted criteria and the relative movements between closely mated parts fall inside their nominal clearance limits.     

Seismic response analysis of soil-structure interactive system using a coupled three-dimensional FE-IE method

This paper proposes a slightly new three-dimensional radial-shaped dynamic infinite elements fully coupled to finite elements for an analysis of soil-structure interaction system in a horizontally layered medium. We then deal with a seismic analysis technique for a three-dimensional soil-structure interactive system, based on the coupled finite-infinite method in frequency domain. The dynamic infinite elements are simulated for the unbounded domain with wave functions propagating multi-generated wave components. The accuracy of the dynamic infinite element and effectiveness of the seismic analysis technique may be demonstrated through a typical compliance analysis of square surface footing, an L-shaped mat concrete footing on layered soil medium and two kinds of practical seismic analysis tests. The practical analyses are (1) a site response analysis of the well-known Hualien site excited by all travelling wave components (primary, shear, Rayleigh waves) and (2) a generation of a floor response spectrum of a nuclear power plant. The obtained dynamic results show good agreement compared with the measured response data and numerical values of other soil-structure interaction analysis package.     

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.     

Seismic response of temporary structures

An unanchored temporary structure has five modes of response to base excitation: rest, slide, rock, slide–rock, and free-flight. This paper is concerned with the conditions under which an unanchored object will respond in these modes and, in a rock mode, the maximum amount of tilting and the probability of toppling. The conditions for the five modes of response are derived based on equations of equilibrium and of motion. The rocking response and toppling probability are obtained by the Monte Carlo simulation technique by solving the equations governing rocking response numerically and repeatedly using simulated base motion. Details of the derivation and computation are not presented. Toppling probabilities are given graphically for a number of values specifying dimension of the object.     

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.     

Seismic response of annular cylindrical tanks

A study is made of the dynamic response of liquid containing, upright annular cylindrical tanks subjected to the horizontal component of a seismic excitation at its base. The tank is assumed to be rigid. Critical response quantities for rigid annular tanks are evaluated over wide ranges of parameters involved and the results presented in a form convenient for use in practical applications. The effect of tank flexibility on the response is then assessed by the procedure proposed by Veletsos and Yang (1977). Simple approximation equations for estimating the fundamental frequency of the outer tank wall-liquid and inner tank wall-liquid systems are proposed.     

Seismic response of structures by the response spectrum method

The problems of the acceleration profile at the lower elevations of cantilever structures and the response of relatively rigid structures are explored. It is shown that the use of the conventional methods for the above problems provide very approximate results. An alternate combination of the modal responses is proposed that not only resolves the above problems but also provides better estimates of response for the complete range of structure frequencies. The procedure treats the relative and rigid body responses separately and then appropriately combines the two results. For the rigid range of frequencies (fundamental frequencies greater than about 2 Hz), the proposed procedure does not encounter any numerical difficulties because of the additive nature of the component responses; however, the application of the proposed procedure for very flexible structures causes accuracy problems since the rigid body effects tend to be subtractive from the flexural response of about equal magnitude. For this latter class of problems, the conventional approach of modal combination provides adequate results and avoids the above mentioned numerical difficulties.     

SSRF储存环共架机构热-力耦合分析

上海同步辐射光源(SSRF)工程中,束流稳定性是提高SSRF性能指标的关键因素,影响束流稳定性的一个主要因素就是工作状态下温度变化引起的支架和磁铁的变形.本文以上海光源储存环共架机构为研究对象,采用参数化有限元法、借助有限元分析软件ANSYS WORKBENCH,对不同工况下的共架机构进行热-力耦合仿真,得出共架机构的温度场和应力场,为控制支架的稳定性进而保证上海光源束流稳定性提供依据.     

Seismic fragility analyses of nuclear power plant structures based on the recorded earthquake data in Korea

By nature, the seismic fragility analysis results will be considerably affected by the statistical data of design information and site-dependent ground motions. The engineering characteristics of small magnitude earthquake spectra recorded in the Korean peninsula during the last several years are analyzed in this paper. An improved method of seismic fragility analysis is evaluated by comparative analyses to verify its efficiency for practical application to nuclear power plant structures. The effects of the recorded earthquake on the seismic fragilities of Korean nuclear power plant structures are also evaluated from the comparative studies. Observing the obtained results, the proposed method is more efficient for the multi-modes structures. The case study results show that seismic fragility analysis based on the Newmark's spectra in Korea might over-estimate the seismic capacities of Korean facilities.     

Uncertainty analysis of system fragility for seismic safety evaluation of NPP

In this study, a Seismic Probabilistic Safety Assessment (SPSA) methodology considering the uncertainty of fragilities was studied. A system fragility curve is estimated by combining component fragilities expressed by two variance sources, inherent randomness and modeling uncertainty. The sampling based methods, Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS), were used to quantify the uncertainties of the system fragility. The SPSA of an existing nuclear power plant (NPP) was performed to compare the two uncertainty analysis methods. Convergence of the uncertainty analysis for the system fragility was estimated by calculating High Confidence Low Probability of Failure (HCLPF) capacity. Alternate HCLPF capacity by composite standard deviation was also verified. The annual failure frequency of the NPP was estimated and the result was discussed with that from the other researches. As a result, the criteria of the uncertainty analysis and its effect was investigated.     

Seismic failure probability evaluation of redundant fast breeder reactor piping system by probabilistic structural response analysis

The seismic failure probability and the correlation coefficient of the multiple failure mode of the heat transport system of a three-loop fast breeder reactor have been evaluated based on a probabilistic structural response analysis. It has been found that the most probable failure mode of the heat transport system has less impact on the core cooling capability than other modes. The correlation coefficient of the heat transport system loops is approximately 0.9. It is found that the correlation comes from the common structural properties rather than the common seismic input. The present approach is useful for quantifying the correlation coefficient and the seismic fragility of the redundant component failure that is used in the systems analysis.     

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.     

Core response of a PWR to a slug of under-borated water

A parameter study, incorporating stationary and transient core calculations, was carried out for a hypothetical boron dilution event in a pressurized water reactor, using the three-dimensional (3D) neutron kinetics core model DYN3D in combination with a fast running semi-analytical coolant mixing model. It was assumed that a slug of deborated water was formed in one of the loops, due to a secondary-to-primary steam generator leakage during outage. It was further assumed that this slug is not recognised and that the first main coolant pump is started, in preparation to returning to power. At the initiation of pump start-up, the reactor is still in the cold and deeply sub-critical state. By varying the initial slug volume, it was found in stationary calculations that, for the given core configuration, slugs of less than 14 m³ do not lead to re-criticality. Transient core calculations with larger slug volumes show a significant reactivity insertion and over-criticality. However, according to the calculations, even an over-criticality of about 2$ did not lead to safety-relevant consequences. The power excursion is mitigated and stopped by Doppler feedback. The influence of the cross-section library on the course of the transient was investigated, applying an alternative library. Differences in the global core parameters lead to quantitative differences in the time and height of the power excursion. In addition, it is shown that numerical diffusion has to be suppressed in order to describe the boron transport correctly, especially at low flow velocities. Otherwise the neutron kinetic core behaviour cannot be correctly modelled.