In-structure Response Spectra Research Articles

Degradation assessment of corroded RC frames using in-structure response spectra from shake table tests and numerical simulation

Degradation assessment of corroded RC frames using in-structure response spectra from shake table tests and numerical simulation

지반 임피던스 함수를 고려한 원전 구조물기반 질량집중모델에 대한 시간영역 지진응답해석

In this paper, a seismic analysis method of nuclear reactor containment buildings (RCBs), considering both soil-structure interaction (SSI) and structural nonlinearity, is proposed and verified. To consider the SSI effect, a frequency-dependent soil impedance function is calculated and transformed into an impulse response in the time domain, which is applied to the structure in sway-rocking model form. Seismic analysis of the structure considering structural nonlinearity is then conducted in the time domain. As a structural model, a beam-stick model based on OPR1000, an in-service RCB in Korea, is used. The IMK hysteretic model is adopted for seismic analysis to consider the structural nonlinearity of the RCB, which is mainly composed of concrete shear wall. Three different soil profiles are used for the comparison, and a series of analyses are performed with PGA = 0.3 g and 2 g. The seismic responses of the structure are represented as in-structure response spectra and compared.

Considerations for the Generation of In-Structure Response Spectra in Seismically Isolated Structures

Considerations for the Generation of In-Structure Response Spectra in Seismically Isolated Structures

Experimental study on the floor responses of a base-isolated frame structure via shaking table tests

Seismic isolation represents one of the innovative means to improve the seismic safety of nuclear power plants (NPPs) against strong earthquakes. Many difficulties remain, though, in applying seismic isolation systems to real NPP structures due to the variability of the material properties of seismic isolators and the nonlinear behavior characteristics of the base isolation system in spite of the elastic behavior of the superstructure. Specifically, there is a limit to estimate the dynamic properties of base isolation systems for numerical analysis. The in-structure response of a base isolated-structure, which is related to equipment safety installed on the floors, is more sensitive than the base shear of the superstructure to the nonlinear properties of the isolation system. In this study, the complex behavioral characteristics of a base-isolated elastic frame structure are experimentally investigated through shaking table tests. Variation in response according to the frequency contents of the input earthquake is investigated, and the earthquake responses of the base-isolated structure for each frequency range are analyzed. In addition, the nonlinear increment of the in-structure response spectra to input ground motion intensity is evaluated, along with the nonlinear behavior of the seismic isolators. The experimental results obtained in this study can help identify various behavioral characteristics of base-isolated structures, with the nonlinear properties examined here acting as important references for evaluating the seismic safety of base-isolated NPPs.

Benefits of Seismic Isolation for Nuclear Structures Subjected to Severe Earthquake

The Fukushima accident has reiterated that the seismic safety is a clear necessity in the design of nuclear power plants. To overcome the weaknesses of the plant design, appropriate measures or interventions have thus to be put in place to improve the nuclear safety. In this study, seismic isolation, widely adopted for conventional constructions, is considered as retrofit measure to provide superior performance of plant itself, even when exceptional events occur. In this paper, we numerically investigate the dynamic behaviour of a Small Modular Reactor (SMR) plant subjected to 0.6g PGA; in doing that time-history analysis has been performed assuming the reactor building with and without isolators. For that purpose, a suitable FEM model has been implemented to provide in-structure response spectra at safety relevant locations and subsystem supports. Adequate steel and concrete properties as well as isolators properties, experimentally determined, have been assumed. Results have shown the benefits of seismic isolation for NPP that can so sustain levels of loading beyond the design input and demonstrated that failure of an isolation system cannot occur before failure of the isolated structure. However, the large horizontal displacements of the structure require appropriate considerations in the layout and interfaces for interconnected systems.

In-structure response spectra considering nonlinearity of RCC structures: Experiments and analysis

Many devastating earthquakes exceeding the design basis levels have occurred in the past. Safety assessment of equipments and piping systems of industrial/nuclear safety related structures subjected to earthquakes beyond design basis levels necessitates consideration of the structural nonlinearity. The In-structure or floor response spectra (FRS) are the input required for qualification of these systems and hence it is essential to generate this input considering structural nonlinearity. This paper addresses the experimental and analytical work on generation of FRS for nonlinear Reinforced Cement Concrete (RCC) structure. Push over and shake table experiments are performed on three storeyed RCC framed structure. A simplified analytical approach is proposed to derive earthquake-induced In-structure response spectra for the structure deforming beyond elastic limits. In this approach, initially, the performance of the structure is evaluated using pushover analysis. Floor spectra of the structure are then obtained considering the degraded stiffness and increased damping evaluated at each performance level iteratively from pushover curve. The floor spectra of the structure generated by the proposed method are validated using experimentally simulated results from shake table tests.

Research on the attribution evaluating methods of dynamic effects of various parameter uncertainties on the in-structure floor response spectra of nuclear power plant

Consideration of the dynamic effects of the site and structural parameter uncertainty is required by the standards for nuclear power plants (NPPs) in most countries. The anti-seismic standards provide two basic methods to analyze parameter uncertainty. Directly manually dealing with the calculated floor response spectra (FRS) values of deterministic approaches is the first method. The second method is to perform probability statistical analysis of the FRS results on the basis of the Monte Carlo method. The two methods can only reflect the overall effects of the uncertain parameters, and the results cannot be screened for a certain parameter’s influence and contribution. In this study, based on the dynamic analyses of the floor response spectra of NPPs, a comprehensive index of the assessed impact for various uncertain parameters is presented and recommended, including the correlation coefficient, the regression slope coefficient and Tornado swing. To compensate for the lack of guidance in the NPP seismic standards, the proposed method can effectively be used to evaluate the contributions of various parameters from the aspects of sensitivity, acuity and statistical swing correlations. Finally, examples are provided to verify the set of indicators from systematic and intuitive perspectives, such as the uncertainty of the impact of the structure parameters and the contribution to the FRS of NPPs. The index is sensitive to different types of parameters, which provides a new technique for evaluating the anti-seismic parameters required for NPPs.

Effects of structural nonlinearity and foundation sliding on probabilistic response of a nuclear structure

This paper examines the effects of structural nonlinearity and foundation sliding on the results of probabilistic structural analysis of a typical nuclear structure where structural nonlinearity, foundation sliding and soil-structure interaction (SSI) are explicitly included. The evaluation is carried out for a soil and a rock site at 104, 105, and 106 year return periods (1E−4, 1E−5, and 1E−6 hazard levels, respectively). The input motions at each considered hazard level are deaggregated into low frequency (LF) and high frequency (HF) motions and a sample size of 30 is used for uncertainty propagation. The statistical distribution of structural responses including story drifts, and in-structure response spectra (ISRS) as well as foundation sliding displacements are examined. The probabilistic implementation of explicit structural nonlinearity and foundation sliding in combination with the SSI effects are demonstrated using nonlinear response history analysis (RHA) of the structure with the foundation motions obtained from elastic SSI analyses, which are applied as input to fixed-base inelastic analyses. This approach quantifies the expected structural nonlinearity and sliding for the particular structural configuration and provides a robust analytical basis for the estimation of the probabilistic distribution of selected demands parameters both at the design level and beyond design level seismic input. For the subject structure, the inclusion of foundation sliding in the analysis is found to have reduced both structural and nonstructural seismic demands and their corresponding dispersion. This reduction is more pronounced for the structure on the rock site.

Significance of structure–soil–structure interaction for closely spaced structures

Nuclear facilities typically consist of many closely spaced structures with different sizes and depths of embedment. Seismic response of each structure could be influenced by dynamic structure–soil–structure interaction (SSSI) behavior of adjacent closely spaced structures. This paper examines the impact of SSSI on the in-structure response spectra (ISRS) and peak accelerations of a light structure adjacent to a heavy structure and of a heavy structure adjacent to a similar heavy structure for several soil cases, foundation embedment depths, and separation distances. The impacts of a heavy surface or embedded structure on adjacent ground motions were studied. The analyses demonstrated the adjacent ground motions are sensitive to foundation embedment, soil profile, response frequency, and distance from the structure. Seismic responses of a light structure located near a heavy structure are calculated either by modeling both structures subjected to free field motions, or performing a cascade analysis by considering the light structure model subjected to modified ground motions due to the heavy structure. Cascade SSSI analyses are shown to adequately account for the effect of the heavy structure on the light structure without explicitly modeling both structures together in a single analysis. To further study the influence of SSSI behavior, this paper examines dynamic response of two adjacent heavy structures and compares this response to response of a single heavy structure neglecting adjacent structures. The SSSI responses of the two heavy structures are evaluated for varying soil conditions and structure separation distances using three-dimensional linear SSI analyses and considering anti-symmetry boundary conditions. The analyses demonstrate that the SSSI response of a light or a heavy structure can be influenced by the presence of a nearby heavy structure. Although this study considers linear analysis methodology, the conclusion of SSSI influences on dynamic behavior is similar to that reported in nonlinear experimental SSSI studies (Trombetta et al., 2012).

Evaluation of Soil Stiffness Variability Effects on Soil-Structure Interaction Response of Nuclear Power Plant Structure

This study investigated the influence of probabilistic variability in stiffness and nonlinearity of soil on response of nuclear power plant (NPP) structure subjected to seismic loads considering the soil-structure interaction (SSI). Both deterministic and probabilistic methods have been employed to evaluate the dynamic responses of the structure. For the deterministic method, SRP min method given in USNRC SRP 3.7.2(2013) (envelope of responses using three shear modulus profiles of lower bound(G LB ), best estimate(G BE ) and upper bound(G UB )) and SRP max method (envelope of responses by more than three ground profiles within range of G LB ≤ G≤ G UB ) have been considered. The probabilistic method uses the Latin Hypercube Sampling (LHS) that can capture probabilistic feature of soil stiffness defined by the median and the standard deviation. These analysis results indicated that 1) number of samples shall be larger than 60 to apply the probabilistic approach in SSI analysis and 2) in-structure response spectra using equivalent linear soil profiles considering the nonlinear behavior of soil medium can be larger than those based on low-strain soil profiles.

Probabilistic and deterministic soil structure interaction analysis including ground motion incoherency effects

Soil-structure interaction (SSI) is a major step for seismic design of massive and stiff structures typical of the nuclear facilities and civil infrastructures such as tunnels, underground stations, dams and lock head structures. Currently most SSI analyses are performed deterministically, incorporating limited range of variation in soil and structural properties and without consideration of the ground motion incoherency effects. This often leads to overestimation of the seismic response particularly the In-Structure-Response Spectra (ISRS) with significant impositions of design and equipment qualification costs, especially in the case of high-frequency sensitive equipment at stiff soil or rock sites. The reluctance to incorporate a more comprehensive probabilistic approach is mainly due to the fact that the computational cost of performing probabilistic SSI analysis even without incoherency function considerations has been prohibitive. As such, bounding deterministic approaches have been preferred by the industry and accepted by the regulatory agencies. However, given the recently available and growing computing capabilities, the need for a probabilistic-based approach to the SSI analysis is becoming clear with the advances in performance-based engineering and the utilization of fragility analysis in the decision making process whether by the owners or the regulatory agencies.This paper demonstrates the use of both probabilistic and deterministic SSI analysis techniques to identify important engineering demand parameters in the structure. A typical nuclear industry structure is used as an example for this study. The system is analyzed for two different site conditions: rock and deep soil. Both deterministic and probabilistic SSI analysis approaches are performed, using the program SASSI, with and without ground motion incoherency considerations. In both approaches, the analysis begins at the hard rock level using the low frequency and high frequency hard rock input motions obtained from Probabilistic Seismic Hazard Analysis (PSHA) and the site response analysis is conducted with simulated soil profiles and accompanying soil nonlinearity curves. The deterministic approach utilizes three strain-compatible soil profiles (Lower Bound (LB), Best Estimate (BE) and Upper Bound (UB)) determined based on the variation of strain-compatible soil profiles obtained from the probabilistic site response analysis and uses SSI analysis to determine a conservative estimate of the required response as the envelope of the SSI results from LB, BE and UB soil cases. In contrast, the probabilistic SSI analysis propagates the uncertainty in the soil and structural properties and provides rigorous estimates for the statistical distribution of the response parameters of interest. The engineering demand parameters considered are the story drifts and ISRS at key locations in the example structure. The results from the deterministic and probabilistic approaches, with and without ground motion incoherency effects, are compared and discussed. Recommendations are made regarding the efficient use of statistical methods in probabilistic SSI analysis and the use of such results in Integrated Soil-Structure Fragility Analysis (ISSFA) and performance-based design.

Potential of Winkler type platform models for SSI problems considering flexibility of base mat

Linear soil-structure interaction (SSI) analysis seems to be well understood nowadays and can be performed, for example, by convenient combined asymptotic method (CAM). However, CAM is asymptotically accurate for rigid base mats only – this is a limitation. So, the additional research is needed to find out (a) what is the impact of the base mat's flexibility to the seismic response; (b) how can one account for this impact using the conventional tools. In the first part of the paper a sample “wave” solution is obtained in the frequency domain using SASSI2000 code, without CAM at all. Different formats of the seismic response (e.g., in-structure response spectra, soil-structure interaction forces, in-structure internal forces) have proved to have different sensitivity to the base mat's flexibility. In the second part of the paper this wave solution is a benchmark for the different “platform” models with “soil” springs and dashpots distributed over the base mat (this is a broad definition of Winkler type model). Different shapes of distribution, starting from the conventional Winkler's flat shape and up to the “optimal” shape, are compared to each other in the second part of the paper. It is shown that even the most advanced “shaped” models of the Winkler type are limited in their ability to reproduce seismic response in the most sensitive format – the internal forces in the mat. This is the result of (a) local nature of Winkler's model, and (b) frequency independence of its’ parameters.

Seismic stability of cracked concrete dams using rigid block models

Several gravity dams subjected to severe ground motions are likely to experience cracking and sliding in the upper section where dynamic amplification is important. A high acceleration spike realistically applies large inertia forces computed from mass times the acceleration. However, these impulsive inertia forces might not be applied in the same direction for a sufficient long period of time to induce significant rotational or sliding displacements detrimental to the seismic or post-seismic structural stability of the cracked components. When it is of interest to estimate residual sliding displacements, a convenient and simple tool is to perform transient rigid body “sliding block” analysis of the “cracked” component. However, this requires the definition of proper seismic input motions at the base of the block with due consideration of dynamic amplification. The possibility to compute in-structure response spectra (ISRS) at the base of the block to define suitable spectra compatible accelerograms is presented in this paper. An important conclusion is that it is not conservative to use accelerograms compatible with the linear (uncracked) dam ISRS to perform transient rigid body sliding response analyses. Dam base and upper joint cracking affects its dynamic properties such that there are modifications of the intensities and frequency content of seismic motions as they propagate over the dam’s height. An envelope of nonlinear ISRS computed from cracked beam models of the dam is recommended to obtain compatible accelerograms and to provide a conservative estimate of upper block residual sliding displacements.

A study on the connection effects of subsurface slabs to exterior walls in the KNGR seismic analysis

The soil-structure interaction (SSI) analyses are being performed for the Korean next generation reactor (KNGR) design, because the KNGR is developed as a standard nuclear power plant concept enveloping various soil conditions. The SASSI program, which adopts the flexible volume method is used for the SSI analyses. Since the impedances are computed based on the assumption of a rigid foundation in the KNGR design, the impedances are computed at a single point around the center of the basemat. The base model used in the SSI analyses assumed that the subsurface slabs are free and not connected to the exterior walls. This results in a more flexible structure than reality. This study is performed to address the concern of the potential dynamic effect of this modeling assumption on the overall structural response. The super-structure model is modified with the subsurface portions of the sticks being laterally rigid, so that the entire subsurface cavity together with the super-structure model acts laterally rigid. For the comparison, the in-structure response spectra using the rigid subsurface model are compared with the original spectra without considering the connection effects.

The development of the floor response spectra using large 3D model

This paper presents the development of the synthetic ground motion, the set up of a large 3D model for the reactor building and the development of the in-structure response spectra without any reduction of the model size by either condensation methods or component mode synthesis methods.

Nonlinear dynamic analysis of reinforced concrete shear wall structures

During strong ground motions, structural members made of reinforced concrete undergo cyclic deformations and experience permanent damage. Members may lose their initial stiffness as well as strength. Recently, Los Alamos National Laboratory has performed experiments on scale models of shear wall structures subjected to recorded earthquake signals. In general, the results indicated that the measured structural stiffnesses decreased with increased levels of excitation in the linear response region. Furthermore, a significant reduction in strength as well as in stiffness is also observed in the inelastic range. Since the in-structure floor response spectra which are used to design and qualify safety equipment have been based on calculated structural stiffness and frequencies, it is possible that certain safety equipment could experience greater seismic loads than were specified for qualification due to stiffness reduction. In this research, a hysteresis model based on the concept of accumulated damage has been developed to account for this stiffness degradation both in the linear and inelastic ranges. Single and three-degrees-of-freedom seismic Category I structures were analysed and compared with equivalent linear stiffness degradation models in terms of maximum displacement responses, permanent displacement, and floor response spectra. The results indicate significant differences in response between the hysteresis model and equivalent linear stiffness degradation model at PGA levels of greater than 0.8 g. The hysteresis model is used in the analysis of reinforced concrete shear-wall structures to obtain the in-structure response spectra. Results of both cumulative and one shot tests are compared.

High frequency, high amplitude and low energy earthquake study of nuclear power plants

Nuclear power plants are designed for a seismic input spectrum based on U.S. acceleration time histories. However, data recorded near several recent earthquakes, mostly in the Eastern U.S., are richer in high frequency energy. This paper focuses on the evaluation of one of these events, i.e., the 1986 Ohio earthquake approximately 10 miles from the Perry nuclear power plant. The Perry Seismic Category I structures were reanalyzed using the in-structure recorded earthquake motions. The calculated in-structure response spectra and recorded response spectra have the same general trends, which shows the buildings are capable of responding to high frequency earthquake motion. Dynamic stresses calculated using the Ohio earthquake recorded motions are substantially lower than the design stresses. The seismic qualification of a wide sample of equipment was reassessed using the Ohio earthquake recorded motions and the margins were found to be larger than one. The 1986 Ohio earthquake was also shown to possess much lower energy content and ductility demand than the design spectra. For the Perry case, the seismic design was shown to have adequate safety margins to accommodate the 1986 Ohio earthquake, even though the design spectra were exceeded at about 20 Hz. The NRC is evaluating the need to generically modify design spectra in light of the recent high frequency recordings.

Seismic response of multiply connected MDOF primary and MDOF secondary systems

New algorithms are presented to evaluate the mode shapes and frequencies of a coupled system, given the mode shapes and frequencies of the uncoupled primary and secondary systems. These coupled mode shapes can be used to obtain the dynamic response of the total system given the input to the primary system. This information can also be used to develop instructure response spectra (IRS) at the connecting DOF, along with the correlation between the motions at the connecting DOF.

Mutual pounding of adjacent structures during earthquakes

The seismic response of a structure which, in addition to earthquake loading, is subjected to the impact force resulting from pounding by an adjacent building, is determined. At first, simple models are used to examine the characteristics of the pounding phenomenon. The pounding structure is modelled as a nonlinear 1-DOF system and the neighbouring building is represented by an impact-spring-dashpot mechanism. Parametric studies, varying the structural parameters, are performed both for steady-state and transient excitions. Finally, the pounding of a typical reactor building by an adjacent auxialiary building during an earthquake is analysed using a simple 2-DOF system and a very detailed dynamic model. The stresses and in-structure response spectra are compared to those for the case in which no pounding occurs, as well as to the results obtained for aircraft impact. Different types of running devices which reduce the response of pounding are examined.

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.