Earthquake Response Spectra Research Articles

Analysis of Seismic Response for an Extradosed Cable-Stayed Curved Bridge Based on Different Design Parameters

Based on the characteristics of low tower and few cables in extradosed Cable-Stayed bridges, simulation models are established for investigations of structural dynamic characteristics under different design parameters, which is related to the practical engineering of Longjing Bridge. As the design radius and pier beam connection form are chosen for the variable, the paper is focus on the influence of dynamic characteristics under the two parameters in extradosed cable-stayed curved bridges. Since the earthquake response spectrum data from National seismic code in 2008 and with the CQC vibration mode combination method, the diversified models are built by Midas/civil so as to explore the earthquake response mechanism under different design parameters. The result show that these two design parameters have some great impacts on dynamic characteristics of extradosed cable-stayed curved bridges, which has direct effect on the bridge seismic performance. The conclusion is the important reference for practical engineering and providing basis for seismic design parameters, but also for seismic design and construction in extradosed cable-stayed curved bridges.

Scaling ground motions using optimal feedback control for testing structures by shake table

Shake tables are widely used for testing structural models subjected to earthquakes. Time histories of real ground motions are reproduced by a moving shake table platform, controlled using an appropriate algorithm, considering the limitations in the platform's maximum displacement. As the real peak ground displacement is usually higher, compared with the platform's stroke, the earthquake records are scaled. Scaling yields distortion in the ground motion spectrum and consequently changes the influence of the earthquake on the tested structure. A method for minimization of the undesired effects, on the basis of linear models of a tested structure, was developed previously. Closeness of power spectral density to response spectra was chosen as the main criterion of scaling efficiency. However, strong earthquakes lead to nonlinear effects in structural response. Supplemental active and passive devices are widely applied for enhancing structural seismic response. Active and semi-active devices are activated according to structural dynamic behavior, measured during the earthquake. But if the accelerations in the measured feedback include high distortions, control will not be effective as desired. An earthquake record scaling method, proposed in this study, is based on criteria that are more consistent with the tested structure. A mathematical formulation of the problem is developed. Effectiveness of the proposed method is demonstrated by comparing the total earthquake energy and response spectra of real and scaled earthquakes as well as by comparative evaluation of the acceleration distortions of their time histories. Response of two multistory structural models to real and scaled seismic records is compared to demonstrate the proposed method's efficiency, accuracy and convenience. Copyright © 2012 John Wiley & Sons, Ltd.

DAMAGE EVOLUTION SPECTRA FOR SEISMIC ANALYSIS OF HIGH-RISE BUILDINGS

Seismic response spectra are amongst one of the most important tools for characterizing earthquake ground motions. In design practice, the response spectra are presented without including any load history, hence the nonlinear analysis of structures based solely on conventional earthquake response spectra is theoretically unsound, particularly for long-period or vertically irregular high-rise buildings. In this paper, a concept of seismic damage evolution is introduced and the method of analysis for characterizing the process of seismic damage to structures under earthquakes is presented. Seismic damage evolution spectra for analysis and design of high-rise buildings are then developed as an effective means of describing and simplifying earthquake ground motions. These spectra are shown to be very useful in selecting the ground motion-time history and, particularly, validating the equivalent static-load analysis and design of high-rise buildings under near-fault pulse-like ground motions. Case studies of the seismic inelastic performance of two vertically irregular, tall buildings are presented considering the seismic damage evolution spectra.

Research on the Stiffness Optimization of the Reinforced Concrete’s Shear Wall Structure Based on the Earthquake Response Spectrum

Optimization design is the significant development in the structure design which could adopt the better from several plans in the same task. This paper build the finite element model of sixteen-floors shear wall structures, which control the deformation as the restraint condition, to make the thickness of shear wall as the design variable and to take the light structure as the objective function in order to execute the optimization. After the optimization, the bottom and internal stress become higher, whereas the centralized stress will occur in the corner and the middle of the rooftop and the opening of the shear wall. The horizontal earthquake of the various floors presents the curve like S with the increasing of the floors. And the floor which occur earthquake effect and the biggest displacement angle is in the middle of the structure and the whip tip effect will emerge in the top of the structure.

Support vector regression for estimating earthquake response spectra

This study uses support vector regression (SVR), a supervised machine learning algorithm, to model the average horizontal response spectrum as a nonparametric function of a set of predictor ground motion variables. Traditional ground motion prediction equations (GMPEs) are derived using parametric regression, where a fixed functional form is selected, and the model coefficients are determined by minimizing the errors on the training set. The SVR model is nonparametric; there is no need to assume a fixed functional form. Using nonlinear basis functions, the data points are mapped into a high dimensional feature space, where nonlinear input-output relationships can be expressed as a linear combination of nonlinear functions, using a subset of the data points. The combination weights are determined by minimizing the generalization error, using a formal mechanism to characterize the trade-off between the model complexity and the quality of fit to the data. Minimization of the generalization error instead of the fitting error leads to better generation to unseen data, and thus reduces the risk of over-fitting for a given number of data points. The SVR model is not based on a specific probability distribution, and is readily applicable to non-Gaussian data. An example application is presented for vertical strike-slip earthquakes, and the predictions from the SVR model are compared to the recently developed GMPEs. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion prediction models.

Earthquake response spectra for performance based design—A critical review

After briefly reviewing the history of the development of design codes and the contemporary performance based objectives for earthquake-resistant structures, this paper considers the linear elastic design spectra exemplified by the Eurocode 8. The amplitudes and shapes of the spectra are examined relative to what is known about strong ground motion and its empirical scaling equations. The estimation of seismic hazard is then discussed, and it is shown that hazard mapping in terms of one scaling parameter (e.g., peak ground acceleration) is neither reliable nor uniformly conservative, and is also in contradiction with the performance based design objectives. It is suggested that a reliable and robust seismic hazard mapping for use with national earthquake-resistant design guidelines (e.g. Eurocode 8) can be carried out using the Anderson–Trifunac Uniform Hazard Spectrum method.

Near-source strong ground motions observed in the 22 February 2011 Christchurch earthquake

This manuscript provides a critical examination of the ground motions recorded in the near-source region resulting from the 22 February 2011 Christchurch earthquake. Particular attention is given to reconciling the observed spatial distribution of ground motions in terms of physical phenomena related to source, path and site effects. The large number of near-source observed strong ground motions show clear evidence of: forward-directivity, basin generated surface waves, liquefaction and other significant nonlinear site response. The pseudo-acceleration response spectra (SA) amplitudes and significant duration of strong motions agree well with empirical prediction models, except at long vibration periods where the influence of basin-generated surface waves and nonlinear site response are significant and not adequately accounted for in empirical SA models. Pseudo-acceleration response spectra are also compared with those observed in the 4 September 2010 Darfield earthquake and routine design response spectra used in order to emphasise the amplitude of ground shaking and elucidate the importance of local geotechnical characteristics on surface ground motions. The characteristics of the observed vertical component accelerations are shown to be strongly dependent on source-to-site distance and are comparable with those from the 4 September 2010 Darfield earthquake, implying the large amplitudes observed are simply a result of many observations at close distances rather than a peculiar source effect.

Digital Filters for Simulation of Seismic Ground Motion and Structural Response

Discrete time series representations for some commonly used relations in earthquake engineering and engineering seismology are presented and the advantages, compared with their continuous time counterparts, are discussed. Seismic source models derived by Brune are presented in discrete time form, as well as a model by Savage, which includes directivity. The discrete time series models are presented as recursive filters (ARMA models) that simplify the simulation process and do not involve the numerical Fourier transform. Furthermore, a demonstration is made of the use of discrete time representations for a SDOF system and their use for the computation of earthquake response spectra.

Reliability analysis of uncertain structures using earthquake response spectra

This paper develops a probabilistic methodology for the seismic reliability analysis of structures with random properties. The earthquake loading is assumed to be described in terms of response spectra. The proposed methodology takes advantage of the response spectra and thus does not require explicit dynamic analysis of the actual structure. Uncertainties in the structural properties (e.g. member cross-sections, modulus of elasticity, member strengths, mass and damping) as well as in the seismic load (due to uncertainty associated with the earthquake load specification) are considered. The structural reliability is estimated by determining the failure probability or the reliability index associated with a performance function that defines safe and unsafe domains. The structural failure is estimated using a performance function that evaluates whether the maximum displacement has been exceeded. Numerical illustrations of reliability analysis of elastic and elastic-plastic single-story frame structures are presented first. The extension of the proposed method to elastic multi-degree-of-freedom uncertain structures is also studied and a solved example is provided.

Database of Processed Time Series and Response Spectra Data for Canada: An Example Application to Study of 2005 MN 5.4 Riviere du Loup, Quebec, Earthquake

The Engineering Seismology Toolbox ( ) is a virtual laboratory that provides processed seismographic data, including time series and spectral information. A variety of programs and tools for signal processing and various applications are also provided. The products of the toolbox are updated continuously and are freely available to all researchers. A key resource provided by the Toolbox is a database of processed time series and Fourier and response spectra for moderate earthquakes recorded on seismographic stations across Canada. We describe herein the data available in this online database, and provide an example application of the database to study of the ground motions from the 2005 MN (Nuttli magnitude) 5.4 Riviere du Loup, Quebec, earthquake.

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion, including its evaluation for tall buildings

AbstractThe modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.

Site dependence of far-source ground motions during the Wenchuan earthquake

This paper aimed to examine the site dependence and evaluate the methods for site analysis of far-source ground motions. This was achieved through the examination of frequency content estimated by different methods based on strong ground motions recorded at twelve far-source stations in Shandong province during the Wenchuan earthquake. The stations were located in sites with soil profiles ranging from code classes I to III. Approaches used included the Fourier amplitude spectrum (FAS), the earthquake response spectrum (ERS), the spectral ratio between the horizontal and the vertical components (H/V), the spectral ratio between the spectra at the site and at a reference site (SRRS), and coda wave analysis (CWA). Results showed that major periods of these ground motions obtained by FAS, ERS and H/V ratio methods were all evidently larger than site dominant periods; the periods were also different from each other and mainly reflected the frequency content of long period components. Prominent periods obtained by the SRRS approach neither illuminated the long period aspect nor efficiently determined site features of the motions. The CWA resulted in a period close to site period for stations with good quality recordings. The results obtained in this study will be useful for the evaluation of far-source effect in constructing seismic design spectra and in selecting methods for ground motion site analysis.

A probabilistic approach for the construction of regional earthquake response spectra

Five scenario earthquakes plausible for the Los Angeles metropolitan region, and one numerical approximation of the 1994 Northridge M w 6.7 event, provide the database of the proposed methodology that is applied for the construction of regional earthquake response spectra. The methodology involves two main stages of data compaction. In the first stage, the Karhunen–Loève (K–L) decomposition of the excitation temporal covariance matrix is performed. In the second stage, the dominant eigenvectors are analytically approximated with Chebyshev polynomials, thus being converted from eigenvectors to eigenfunctions. This compact analytical representation of the nonstationary excitation data provides an exact closed-form solution for the nonstationary response of linear multi-degree-of-freedom systems. Furthermore, statistical inference analysis for the response variables is conducted, which leads to the construction of regional probabilistic response spectra based on the Log-Normal probability model for the response variables.

The Next Generation of Seismic Isolation Going Beyond Seismic Design Dominated by Earthquakes

Seismic isolation can provide superior building safety and dynamic response during strong earthquakes, however, performance is only assured below the design earthquake intensity level. This paper opens with a study of observed strong, near-source ground motions and long-period earthquake waves proposed by researchers. Through the examination of a widerange of earthquake response and input energy spectra, up to a period of 100 seconds, the most suitable range of damping values and isolation periods are found. The optimal period range is further confirmed by evaluating earthquake-wave amplification features during propagation from bedrock to the ground surface. Three types of next-generation seismic isolation systems are proposed along with new parameters to evaluate the dynamic response of seismically isolated structures. By comparing the dynamic response performance of four isolation systems, including a "conventional" 4-second period system, the superior seismic performance of the three next-generation isolation systems is confirmed. The paper shows the direction for a new generation of seismically isolated structures, with periods exceeding 10 seconds, and which minimize the elastic strain energy stored in the structure. Seismically isolated structures possessing these properties will survive strong earthquake input regardless of the uncertainty inherent in earthquake ground motions.

Improvement of the seismic safety of existing nuclear power plants by an increase of the component seismic capacity: A case study

This case study produces the scenario earthquakes for an example nuclear power plant (NPP) site and suggests the effective seismic capacity of safety-related equipment and components which significantly contribute to a core damage to improve the seismic safety of an existing NPP by using a probabilistic safety assessment. The response spectra for the scenario earthquakes show greater spectral accelerations than those for the design response spectrum in the frequency range higher than about 12 Hz. In order to improve the seismic safety of an example NPP, the effects of the seismic capacity of safety-related equipment and components on the core damage frequency (CDF) are investigated, and their effective seismic capacities are determined. The results of the case study show that an increase of the seismic capacity of the equipment reduces the CDF considerably. The effective seismic capacities for the diesel generator, offsite power, condensate storage tank and battery rack are determined as 0.84, 0.35, 0.63 and 0.63 g, respectively.

Seismic Performance of a 62-Story Steel Frame Hotel Tower

This paper introduces the seismic design and performance of a 62-story hotel tower in Beijing, China, and discusses conceptual conflicts that arose during the design process between code provisions and expected seismic behavior. For instance, while the IBC 2000 requires such a tower to be designed as a Special Moment Resisting Frame, pushover analysis studies (not permitted by FEMA 350 for such a tall building, but allowed by the design review board for collapse analysis during this design process) suggested that inelastic rotation demands were on the order of the 2002 AISC requirements for Intermediate Moment Resisting Frames. Furthermore, while axial force demands in the columns resulting from the pushover analyses exceeded the demands calculated according to the AISC building overstrength factor of 3.0, these high axial load demands clearly resulted from the pushover analysis loading pattern derived from the tower's fundamental mode shape. Time history analyses showed that both the extent of plastic hinging and the magnitude of overturning forces under actual earthquake demands were significantly lower than the levels produced from response spectrum and pushover analyses. Finally, in a capacity spectrum assessment under maximum considered earthquake (MCE) response spectrum loads, ductile capacity in the beams did very little to enhance the tower's performance. Several of these results were easily explained by the fact that the Chinese Code response spectrum controlling the design was artificially high for longer periods. This code requirement implied that increased strength, not increased ductility, would improve the tower's ability to withstand MCE demands according to a capacity spectrum assessment. The purpose of this paper is to identify these conflicts in the context of a real project where circumstances prevented the coordination of consistent seismic design criteria.

Energy density spectra in actively controlled inelastic structures—application

An accurate method of predicting peak structural responses and energy forms in actively controlled structures using generated response spectra and energy density spectra developed in the first part of this research is proposed for both elastic and inelastic structures. The accuracy of the predicted responses is compared with that obtained using inelastic time history analysis. Conventional analysis of controlled structures generally uses structural models that are simplified to a significant extent such that the results usually do not represent the actual behaviour of real moment resisting frames. In this research, inelastic structural control analysis based on force analogy method is extended to analyse real moment-resisting frames with plastic hinges offsets from the member ends. By using static condensation, additional degrees of freedom in real moment resisting frames are condensed out, and thereby the procedure of force analogy method in analysing inelastic structural response remains unchanged. Numerical simulation is performed using the modified 1940 El Centro earthquake time history and response spectra for both elastic and inelastic structural models to study the controlled responses using both optimal linear control and ad hoc control algorithms. Results show that the proposed method of predicting the maximum structural responses gives very accurate results for both elastic and inelastic structural systems. Copyright © 2005 John Wiley & Sons, Ltd.

Typical uniform hazard spectra for eastern North American sites at low probability levels

Seismic design for nuclear power facilities is generally based on a prescribed earthquake response spectrum, which defines the response of a simple oscillator of a given natural frequency to the expected motions. To develop standard designs that may be suitable in a number of possible future locations, it is useful to develop standard spectra that describe typical environments. The adequacy of the standard design for a particular location may then be judged based on comparison of the standard spectrum with a site-specific "uniform hazard spectrum" (UHS). In this paper, UHS results from selected publicly available studies are used to develop a standard spectral shape that describes moderate-seismicity sites in eastern North America, on hard-rock site conditions. Compared with a standard spectrum that has been suggested for future nuclear plants on rock sites (modified Canadian Standards Association CSA/CAN-N289.3), the spectral shape proposed herein has higher amplitudes at high frequencies and lower amplitudes at low frequencies.Key words: earthquake ground motion, response spectrum, nuclear power plant, spectral shape, design ground motion.

Dynamic behaviors of corrugated steel plate structures in open-cut tunnels

This research focuses on this soil-steel composite mechanism of CSPS. The results form conventional equations, computational analysis and model tests were cross checked with the variations in the following factors, such as the height of cover according to earthquake loads, open-cut slope inclination, degree of compaction, spacing between CSPS supports in order to examine the safety and dynamic behaviors of CSPS linings. From the results of earthquake response spectrum according to CSPS support spacing, there were little or no differences in compression forces but as spacing between the supports decreases the moment and shear forces increased. Canadian Highway Bridge Design Code (CHBDC) was used as the conventional equation. The results from the earthquake analysis using CHBDC were compared with the results form the dynamic time dependent on time history analysis. The comparison showed that even though the CHBDC results were relatively smaller than the time history analysis, the difference was minimal. The results from seismic displacement method and Mononobe-Okabe method showed that the increase in the height of cover increases extremely the compression stresses, showing different results from the CHBDC and dynamic time history analysis results. The differences in the results are caused from not considering the restraining effects of the surrounding soil and just implementing the dynamic soil pressures and the ground relative displacement in the analysis. In order to verify the results of this research, a 1/40 scale static model chamber test and dynamic shaking table test were carried out. The results from the tests showed similar trend to the results of the analyses. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.

Brief history of computation of earthquake response spectra

The methods for computation of response spectrum amplitudes are reviewed for the period preceding the modern digital computer age. The mechanical and electrical analog methods that preceded the modern digital calculations were time consuming, inaccurate, and difficult to verify. Modern studies of response and of the nature of strong ground motion became possible after mid-1960 with accumulation of strong-motion records and with accurate digitization and digital data processing.