Parametric modeling of earthquake response spectra

A mathematical model for the response spectra is determined using statistical analysis. The form of the model is first established using fifty computer simulated accelerograms. The final form is then used on twenty-five accelerograms from fifteen past United States earthquakes. This model smooths out peaks and valleys which are characteristic of the response spectrum of any single earthquake. Thus it serves as a ‘smooth design spectrum’ and can be used to approximate structural response to a future seismic event.     

Rotation-invariant measures of earthquake response spectra

A new procedure for combining the response spectra of two horizontal components of recorded ground motion is presented. The presented formulation accounts for different orientations of accelerometer sensors and derives the maximum and the expected (mean) horizontal response spectra at a site, both of which are invariant to rotation of sensor axes. The maximum response spectrum is derived as the peak resultant response of single degree of freedom oscillators subjected to the as-recorded ground acceleration. The expected spectrum is derived by projecting the displacement response (due to as-recorded motion) along two orthogonal axes to a principal axes in which the displacement responses are uncorrelated. This property is used to formulate an approximation for the expected response spectrum over all possible sensor orientations. A large set of accelerometric data from Europe and the Middle East is used to demonstrate the applicability of the proposed response spectral measures.     

双规准化地震动加速度反应谱研究

本文提出了双规准反应谱的概念。在统计了美国西部大量强震记录的基础上,分别研究了规准反应谱和双规准反应谱的特性,并进行了详细的对比分析。研究结果表明,双规准反应谱比通常的规准反应谱有更好的规律性,这不仅有利于认识地震动的特性,还可使基于场地的抗震设计反应谱大大简化,更便于广大工程设计人员应用。     

不同地震水准反应谱之间的关系和罕遇地震作用设计反应谱的确定

不同地震作用水准的设计反应谱长期以来一直采用各水准谱形完全一致的假定。这与地震危险性分析的一般结论不符。《建筑抗震设计规范》(GB50011-2001)对此作出了修订。本文基于设计反应谱的三参数标定模型推导了罕遇和多遇地震作用设计反应谱的关系，指出两者谱值之比在高频、中频和低频段分别对应于峰值加速度、速度和位移之比。引入地震动衰减规律进行了罕遇和多遇地震作用设计谱关系的近似估计，提出了基于多遇地震作用设计谱确定罕遇地震作用设计谱的调整方案，验证了现行规范将反应谱特征周期适当延长以得到罕遇地震作用设计谱的做法的合理性。     

场地类别划分与抗震设计反应谱的讨论

介绍了新的抗震设计规范(2001—07—20发布，2002—01—01实施)中场地类别划分和地震影响系数的有关内容，指出其中一些不相协调之处。最后，针对不同的问题建议相应的解决办法。     

地震动双规准速度反应谱研究

本文在统计了大量强震记录的基础上,分别研究了双规准加速度反应谱和双规准速度反应谱的特性,进行了对比分析,并分别得出了定量分析的结果。研究结果表明,双规准加速度反应谱在短周期段有很好的统一性,而双规准速度反应谱在长周期段的统一性较好,这种规律性对于认识地震动的特性、改进抗震设计反应谱具有重要的意义。     

Prediction of response spectra via real-time earthquake measurements

The development and implementation of an earthquake early warning system (EEWS), both in regional or on-site configurations can help to mitigate the losses due to the occurrence of moderate-to-large earthquakes in densely populated and/or industrialized areas. The capability of an EEWS to provide real-time estimates of source parameters (location and magnitude) can be used to take some countermeasures during the earthquake occurrence and before the arriving of the most destructive waves at the site of interest. However, some critical issues are peculiar of EEWS and need further investigation: (1) the uncertainties on earthquake magnitude and location estimates based on the measurements of some observed quantities in the very early portion of the recorded signals; (2) the selection of the most appropriate parameter to be used to predict the ground motion amplitude both in near- and far-source ranges; (3) the use of the estimates provided by the EEWS for structural engineering and risk mitigation applications.In the present study, the issues above are discussed using the Campania–Lucania region (Southern Apennines) in Italy, as test-site area. In this region a prototype system for earthquake early warning, and more generally for seismic alert management, is under development. The system is based on a dense, wide dynamic accelerometric network deployed in the area where the moderate-to-large earthquake causative fault systems are located.The uncertainty analysis is performed through a real-time probabilistic seismic hazard analysis by using two different approaches. The first is the Bayesian approach that implicitly integrate both the time evolving estimate of earthquake parameters, the probability density functions and the variability of ground motion propagation providing the most complete information. The second is a classical point estimate approach which does not account for the probability density function of the magnitude and only uses the average of the estimates performed at each seismic station.Both the approaches are applied to two main towns located in the area of interest, Napoli and Avellino, for which a missed and false alarm analysis is presented by means of a scenario earthquake: an M 7.0 seismic event located at the centre of the seismic network.Concerning the ground motion prediction, attention is focused on the response spectra as the most appropriate function to characterize the ground motion for earthquake engineering applications of EEWS.     

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.     

复阻尼地震反应谱的计算方法及其它

本文阐述了为什么要研究复阻尼地震反应谱问题,并给出了复阻尼地震反应谱计算的精确方法．实例计算结果表明,复阻尼反应港与常用的粘性阻尼反应谱之间存在着相当大的差异．文中还简述了复阻尼系统运动方程的建立方法。     

A note on the fast computation of response spectra estimates

An algorithm is presented for fast computation of estimates of response spectra. It is based on the formalism of random vibration theory. Numerical results show that estimates are reliable and useful for practical applications.     

地震动群延时不确定性对反应谱的影响研究

为了考察外部激励群延时对反应谱的影响,分别从确定性的角度和统计的角度分析了群延时对线性单自由度结构体系位移响应最大值的影响。推导出了对应于给定单自由度结构体系在任意外部激励作用下最大位移响应的群延时。据此可以利用任意外部激励的群延时与结构体系的最大位移响应群延时的关系评估体系在该外部激励作用下位移响应峰值的大小。统计分析的结果表明:激励群延时的均值和方差对结构体系位移响应最大值的影响具有明显的规律性;激励群延时的分布频数与结构体系最大位移响应之间也存在着显著的关系。     

Analysis of strong earthquake ground motion for prediction of response spectra

Prediction of response spectra for earthquake engineering purposes is considered from a new point of view based on the dislocation theory of earthquakes. It is shown that the traditional scaling of response spectra by the predicted peak acceleration should be limited to the high-frequency end of the spectrum, and that the peak acceleration in the near field is not strongly correlated with earthquake magnitude. The amplitude of the long-period end of response spectrum at source to station distances greater than about 10 source dimensions should be scaled with seismic moment, while for distances less than about one source dimension this amplitude should be proportional to the permanent ground displacement. To reconcile the existing extensive data on seismicity of active regions based on magnitude scale, it is shown that magnitude can be used to determine approximately the seismic moment.     

汶川地震动弹性和弹塑性反应谱分析

利用汶川地震获得的数字强震记录研究了汶川近场无速度脉冲、近场含速度脉冲和远场(盆地效应)地震动的弹性和弹塑性反应谱,后者包括等延性强度折减系数谱Rμ、等延性位移比谱Cu和等强度折减系数位移比谱CR.与相同场地条件PEER近场无速度脉冲、集集近场含速度脉冲地震动的谱进行了比较.汶川近场含速度脉冲地震动的弹性反应谱在0.2～0.8s周期内明显偏小,而它的弹塑性反应谱在短周期段(0.1 ～0.4 s)与汶川近场无速度脉冲地震动谱差别不大,但等延性强度折减系数谱Ru要大于集集地震含速度脉冲地震动的谱,而等延性位移比谱Cu和等强度折减系数位移比谱CR则小于集集地震动情况,此后随周期增长(至0.6 ～1.Os后)它们都逐渐过渡至与集集地震动的谱相当.汶川远场(盆地效应)地震动的弹性反应谱具有较宽并随周期缓慢增长的平台值和较长的特征周期,可达1.7s及以上.提出了远场(盆地效应)与近场地震动的弹性反应比谱和弹塑性位移比谱的概念.     

Inelastic earthquake spectra

This paper presents a procedure for computing inelastic design spectra in terms of yield displacement. The procedure results in substantial computational savings as compared to the current procedures for computing the inelastic spectra in terms of displacement ductility. The proposed method is used to obtain inelastic design spectra for alluvium and rock. The results for alluvium are compared to those from the Newmark and Hall,¹⁰ Riddell and Newmark¹² and Lai and Biggs⁴ studies. The findings indicate that for given ductility and frequency one may de-amplify the elastic response or reduce the elastic forces more for a structure on rock than for a structure on alluvium. A technique is presented so that the inelastic design spectrum can be scaled to any desired yield displacement and acceleration. An example is presented to illustrate how the proposed inelastic spectra can be used to compute the required ductility for a given system.     

地震动反应谱变异系数分析

利用随机振动理论,分别考虑3种地震动随机过程模型,本文对反应谱变异系数及相关问题进行了深入分析。研究结果表明：在一定范围内,地震动模型、场地条件和结构体系阻尼比对结构加速度反应越零率有明显影响,但这三者对反应谱变异系数的量值影响不大。在工程设计中,可以采用白噪声模型按本文给出公式计算反应谱变异系数。     

地震动功率谱与反应谱的转换关系

本文详细评述了现今常用的几种加速度反应谱与功率谱的转换关系。对于小阻尼单质点体系而言，考虑到输入地震动是一非平稳的随机过程，又由于其传递函数的窄频带滤波特性，它的加速度反应将是一窄频带的非平稳随机过程。对于峰值系数水平的超越不是独立的，而是成群超越。据此本文考虑非平稳效应和对峰值系数水平的成群效应，对前人的转换关系进行了修正，并基于随机振动理论，给出了对工程上常用的频率平稳、强度非平稳的地震;动模型的功率谱和反应谱的转换关系。此转换关系对于长、短持时的地震动记录和反应谱长、短周期部分以及不同阻尼比的反应谱都能给出精度较高的结果。     

Constant‐ductility response spectra for sequential earthquake and tsunami loading

Simplified approaches for examining structural system response under sequential earthquake and tsunami loading are helpful for understanding response trends. To aid understanding, nonlinear (constant‐ductility) response spectra are developed for elastoplastic single degree of freedom systems subjected to seismic loads followed by hydrodynamic tsunami loads. The forcing function is composed of long‐duration earthquake motion concatenated with a range of tsunami hydrodynamic forces that are proportional to the pseudo‐spectral acceleration produced by the earthquake motion. The constant‐ductility spectra are thus constructed for scenarios where the loading imposed by one hazard is not dominant over the other. The spectra and basic intensity measures indicate that the amplification of response for sequential earthquake and tsunami loading over the earthquake only case is most significant for systems with long natural periods and high‐ductility capacity under seismic loading. Copyright © 2017 John Wiley & Sons, Ltd.     

Revisiting design earthquake spectra

For several decades, seismologists and engineers have been struggling to perfect the shape of design spectra, analyzing recorded signals, and speculating on probabilities. This research effort produced several improvements, for example, suggesting to adopt more than one period to define a spectral shape or proposing different spectral shapes as a function of the return period of the design ground motion. The spectral shapes recommended in most modern codes are driven by considerations on uniform hazard; however, the basic assumption of adopting essentially three fundamental criteria, ie, constant acceleration at low periods, constant displacement at long periods, and constant velocity in an intermediate period range, has never been really questioned. In this opinion paper, the grounds of a constant velocity assumption is discussed and shown to be disputable and not physically based. Spectral shape based on different logics are shown to be potentially consistent with the experimental evidence and to lead to possible differences of 100% in terms of displacement and acceleration demand in the wide intermediate period range that characterizes the vast majority of structures. In this framework, the historical development of linear and nonlinear spectra is critically revisited, proposing a novel original way of defining seismic demand.     

Characteristics of response spectra for long-periods of main-shock recordings of the Chi-Chi earthquake

Current practice uses predictive models to extrapolate long-period response spectra based on far-field recordings in moderate and weak earthquakes. However, the spectra are not long enough and the data are often not reliable, which means that the seismic design code cannot accurately define seismic design requirements for long-period structures. The near-field recordings in the main-shock of the Chi-Chi earthquake have a large signal-to-noise ratio (SNR), which makes them suitable for studying the long-period acceleration response spectrum up to 20 sec. The acceleration response spectra from 246 stations within 120 km of the causative fault are statistically analyzed in this paper. The influence of distance and site conditions on long-period response spectrum is discussed, and the shapes of the amplification spectra are compared with the standard spectra specified in the seismic design code of China. Finally, suggestions for future revisions to the code are proposed.     

Distance scaling of vertical and horizontal response spectra of the Loma Prieta earthquake

Attenuations of the vertical and horizontal response spectra of the 17 October 1989 Loma Prieta, California, earthquake are developed through analyses of the ground motion at 53 sites within a 100 km radius of the source. The analyses are performed on the spectral ordinates for 16 incremental periods ranging from 0.05 to 2.0 sec. The response spectra are modelled empirically for two different site conditions characterized by rock and stiff-soil geologies. Data analysis is performed by the application of a non-linear multivariate regression procedure allowing for distance and site factor as independent variables. Variation of the vertical-to-horizontal (V/H) spectral ratios with wave frequency and distance shows the same behaviour as observed previously in the widely separated geographic regions of northeastern Taiwan and east-central Iran. The predicted ratios at sites underlain by stiff soil are generally higher than the commonly used value of 2/3 at high frequencies ( > 5 Hz) in the near-source region (R < 30 km), but reduce to 1/2 or less at longer periods and farther distances. This behaviour is also observed at rock sites; however, it is somewhat less pronounced. With a faster attenuation of spectral ordinates at higher frequencies, the shape of the response spectrum is found to change with distance. As expected, the spectral attenuation with distance is generally higher for the vertical spectrum than for the horizontal spectrum. The difference is particularly significant at the higher-frequency end of spectrum. Site amplification factors for stiff soil with respect to rock geology varies between 1.17 and 1.72 for horizontal spectrum and 1.01 and 1.81 for vertical spectrum. Spectral amplifications at four sites underlain by soft soil and artificial fill, are also evaluated. This is done by a comparison of the observed spectra with those predicted for rock geology at corresponding distances. As expected, the resulting amplification factors at soft-soil sites show significant increase relative to those at sites underlain by rock.