On the reliability of long‐period response spectral ordinates from digital accelerograms

Using records from co‐located broadband and digital strong motion (SM) instruments, it is first shown that the displacement waveforms obtained by double integration of the accelerogram need not be free of unrealistic baseline drift to yield reliable spectral ordinates up to at least 10 s. Secondly, to provide objective criteria for selecting reliable digital SM records for ground motion predictions at long periods, a set of synthetic accelerograms contaminated by random long‐period noise has been used, and the difference between the original accelerograms and the spurious ones in terms of response spectra has been quantified, by introducing a noise index that can be easily calculated based on the velocity waveform of the record. The results of this study suggest that high‐pass filtering the digital acceleration record from a cutoff period selected to suppress baseline drifts on the displacement waveform appears to be in most cases too conservative and unduly depletes reliable information on long‐period spectral ordinates. Copyright © 2007 John Wiley & Sons, Ltd.     

基于分解方法的脉冲型地震动非弹性反应谱分析

本文旨在分析脉冲型地震动中不同频率的地震动分量对于原始地震动幅值及其非弹性反应谱的影响.首先以近期12次大地震的53条典型脉冲型地震动为数据基础,基于多尺度分解方法获取脉冲型地震动中的高频分量和低频分量.为与传统方法对比,本文获取了能够表征地震动脉冲特性的卓越分量及滤除卓越分量的剩余分量.然后对比分析原始地震动和4种地震动分量的幅值特征和非弹性反应谱的特性,以讨论地震动分量对原始地震动幅值参数及其非弹性反应谱的影响.最后结合简谐地震动模型和地震动分量的性质,讨论脉冲型地震动非弹性反应谱诸多特征的产生原因.分析发现,低频分量不仅是控制脉冲型地震动速度和位移幅值的主要因素,其对原始地震动的加速度幅值也具有不可忽略的影响.低频分量也是导致脉冲型地震动非弹性位移比谱偏大以及强度折减系数谱偏小的直接原因,从而造成结构在脉冲型地震动作用下需要具有更大的非弹性位移以及更高的强度需求.     

弹塑性地震反应谱的长周期特性研究

在基于性能抗震设计中弹塑性反应谱在计算结构地震位移反应方面越来越受到重视。利用统计分析方法研究了等强度的延性需求谱和等延性的强度折减系数谱的长周期(至5 s)区段的特性,关注的重点是等位移准则和场地条件影响。给出了若干具有工程价值的结论:一是周期介于1.5Tg(地震动特征周期)和2.5 s之间的结构可近似认为等位移准则成立且与场地条件关系不大,这样确定的强度折减系数当位移延性系数小于等于4时结果将是偏于安全的;二是结构周期大于2.5 s后以硬土场地等延性强度折减系数谱或等强度延性需求谱代替软土场地谱求解系统强度需求或延性需求,将会得到偏于安全的结果。     

Effects of hanging wall and forward directivity in the 1999 Chi-Chi earthquake on inelastic displacement response of structures

The characteristics of the inelastic response of structures affected by hanging wall and forward directivity in the 1999 Chi-Chi earthquake are investigated. Inelastic displacement ratios (IDRs) for ground motions impacted by these near- field effects are evaluated and comprehensively compared to far-field ground motions. In addition, the inelastic displacement responses to hanging wall and footwall ground motions are compared. It is concluded that the inelastic displacement response is significantly affected in the short period range by hanging wall and in the long period range by footwall. Although high peak ground acceleration was observed at hanging wall stations, the IDRs for structures on hanging wall sites are only larger than footwall sites in the very long period range. Forward directivity effects result in larger IDRs for periods longer than about 0.5s. Adopting statistical relationships for IDRs established using far-field ground motions may lead to either overestimation or underestimation in the seismic evaluation of existing structures located in near-field regions, depending on their fundamental vibration periods.     

High-frequency filtering of strong-motion records

The influence of noise in strong-motion records is most problematic at low and high frequencies where the signal to noise ratio is commonly low compared to that in the mid-spectrum. The impact of low-frequency noise (<1 Hz) on strong-motion intensity parameters such as ground velocities, displacements and response spectral ordinates can be dramatic and consequentially it has become standard practice to low-cut (high-pass) filter strong-motion data with corner frequencies often chosen based on the shape of Fourier amplitude spectra and the signal-to-noise ratio. It has been shown that response spectral ordinates should not be used beyond some fraction of the corner period (reciprocal of the corner frequency) of the low-cut filter. This article examines the effect of high-frequency noise (>5 Hz) on computed pseudo-absolute response spectral accelerations (PSAs). In contrast to the case of low-frequency noise our analysis shows that filtering to remove high-frequency noise is only necessary in certain situations and that PSAs can often be used up to 100 Hz even if much lower high-cut corner frequencies are required to remove the noise. This apparent contradiction can be explained by the fact that PSAs are often controlled by ground accelerations associated with much lower frequencies than the natural frequency of the oscillator because path and site attenuation (often modelled by Q and κ, respectively) have removed the highest frequencies. We demonstrate that if high-cut filters are to be used, then their corner frequencies should be selected on an individual basis, as has been done in a few recent studies.     

Displacement spectra and displacement modification factors,based on records from Greece

Elastic and inelastic displacement spectra (for periods up to 4.0 s) are derived, using a representative sample of acceleration records from Greece, carefully selected based on magnitude, distance and peak ground acceleration criteria, and grouped into three ground type categories according to the Eurocode 8 (EC8) provisions. The modification factor for the elastic design spectrum adopted in EC8 for accounting for damping is verified herein and is found to be satisfactory in the short to medium period range and less so in the long period range. The equivalent viscous damping ratio concept is also evaluated and is found to lead to underestimation of inelastic displacement spectra. Finally, based on the previously derived elastic and inelastic spectra, equations suitable for design and/or assessment purposes, are proposed for the corresponding displacement modification factors.     

利用等位移原则估计高层结构的非弹性地震反应(一)

高层建筑非弹性地震反应估计是当前结构抗震研究迫切希望解决的课题。本文概略介绍了常用非弹性地震反应分析方法在高层结构分析中应用的主要问题,从而引出利用等位移原则(对于长周期体系,弹性与非弹性地震位移反应近似相等)进行高层结构非弹性地震反应估计研究的原因,并以长周期单自由度和多自由度体系弹性与非弹性地震反应之间关系的有关研究结果论述了其可行性。     

绝对和相对输入能量谱对比及延性系数的影响研究

利用266条强震记录,在研究绝对输入能量谱和相对输入能量谱衰减规律的基础上,对由衰减关系所确立的两种输入能量谱进行对比分析,讨论了延性系数对这两种输入能量谱的影响. 研究发现,在弹性情况下,两种输入能量谱在周期0.5~1.0 s范围内相差不大; 在非弹性情况下 两种输入能量谱在周期0.5 s处相差不大. 周期较小时,绝对输入能量谱要大于相对输入能量谱;周期较大时,绝对输入能量谱小于相对输入能量谱. 延性系数对这两种输入能量谱影响均比较大, 对绝对输入能量谱而言,周期小于0.3 s时,随着延性系数的增大, 能量谱升高;周期大于0.3 s时,随着延性系数的增大能量谱降低. 不同延性系数的绝对输入能量谱在分界点0.3 s左右相等. 相对输入能量谱受延性系数影响与绝对输入能量谱相似, 但分界点在0.5 s左右. 与绝对输入能量谱相比, 相对输入能量谱在短周期段受延性系数的影响较大, 特别是当场地较软时更为明显.      

Prediction of elastic displacement response spectra in Europe and the Middle East

Empirical equations are presented for the prediction of displacement response ordinates for damping ratios of 2, 5, 10, 20 and 30% of critical and for response periods up to 4s, using 532 accelerograms from the strong‐motion databank from Europe and the Middle East. The records were all re‐processed and only employed for regressions at periods within the usable range, defined as a fraction of the filter cut‐off and depending on the instrument type (digital or analogue), earthquake magnitude and site class. The equations can be applied to predict the geometric mean displacement and pseudo‐acceleration spectra for earthquakes with moment magnitudes ( M ) between 5 and 7.6, and for distances up to 100km. The equations also include style‐of‐faulting and site class as explanatory variables. The predictions obtained from these new equations suggest that earlier European equations for spectral displacements underestimate the ordinates at longer periods as a result of severe filtering and the use of the spectral ordinates at periods too close to the filter cut‐off. The results also confirm that the period defining the start of the constant displacement plateau in the Eurocode 8 (EC8) spectrum is excessively short at 2s. The results not only show that the scaling factor defined in EC8 for estimating the spectral ordinates at damping ratios different from 5% of critical are a good general approximation, but also that this scaling varies with magnitude and distance (reflecting the influence of duration) and also displays a mild dependence on response period. Copyright © 2007 John Wiley & Sons, Ltd.     

Study on comparison between absolute and relative input energy spectra and effects of ductility factor

Introduction Estimation of an attenuation relationship for strong ground motion parameters has been an interesting research subject in the field of engineering seismology and has played a very important role in seismic safety evaluation, seismic zoning, seismic hazard evaluation of major constructions, etc. At present, the generally used parameters include peak acceleration, peak velocity and elastic response spectrum. Such parameters mentioned above are essentially independent of the duration…     

Evaluation of seismic displacement demands from the September 19, 2017 Puebla‐Morelos (Mw = 7.1) earthquake in Mexico City

This short communication presents the assessment of seismic inelastic and elastic displacement demands computed from earthquake ground motions (EQGMs) recorded in Mexico City during the intermediate‐depth intraslab Puebla‐Morelos earthquake on 19 September 2017 (Mw = 7.1). Evaluation is conducted by means of peak elastic and inelastic displacement demand spectra, inelastic displacement ratio, C_R, spectra, and generalized interstory drift spectra computed for selected recording stations located in different soil sites of Mexico City, including those located in areas of reported collapsed buildings. Results of this study confirm previous observations made from interplate (subduction) EQGMs that peak inelastic displacement demands are greater than corresponding elastic counterparts for short‐to‐medium period structures, while the opposite is true for medium‐to‐long period structures. Possible basin site effects were identified from generalized interstory drift spectra. It is also shown that an equation introduced in the literature to obtain estimates of C_R developed from interplate EQGMs provides also a good estimate for mean C_R computed from the intermediate‐depth intraslab EQGMs.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.     

从中国、美国、欧洲抗震设计规范谱的比较 探讨我国的抗震设计反应谱

本文分析了中国、美国、欧洲 3 种抗震设计规范的地震动参数取值,并比较了 3 种抗震设计反应谱。结果表明,总体上说,欧洲、美国规范的加速度短周期反应谱高于中国规范。但随着周期的扩大,由于中国规范中反应谱的下降指数较小,导致了中国规范中的反应谱逐渐接近并可能超过了欧洲、美国规范。本文的结果可为我国未来抗震设计规范修订,以及地震安全性评价工作中确定设计反应谱提供参考。     

设计反应谱长周期区段的研究

本文利用近20年国内外大地震时获得的数字强震仪记录分析强震动的长周期分量特性,给出了不同场地上的平均加速度反应谱及其拟合曲线。结果表明,现行抗震设计规范中设计谱的特征周期和长周期谱值明显偏小。在此基础上提出了长周期设计反应谱的修正建议。文中还根据统计分析提出了不同阻尼比的反应谱修正公式。     

A new model for spectral velocity ordinates at long periods

The estimation of peak linear response via elastic design (response) spectra continues to form the basis of earthquake‐resistant design of structural systems in various codes of practice all over the world. Many response spectrum‐based formulations of peak linear response require an additional input of the spectral velocity (SV) ordinates consistent with the specified seismic hazard. SV ordinates have been conventionally approximated by pseudo spectral velocity (PSV) ordinates, which are close to the SV ordinates only over the intermediate frequency range coinciding with the velocity‐sensitive region. At long periods, PSV ordinates underestimate the SV ordinates, and this study proposes a formulation of a correction factor (>1) that needs to be multiplied by the PSV ordinates in order to close the gap between the two sets of ordinates. A simple model is proposed in the form of a power function in oscillator period to estimate this factor in terms of two governing parameters which are in turn estimated from two single‐parameter scaling equations. The parameters considered for the scaling equations are (1) the period at which the PSV spectrum is maximized and (2) the rate of decay of the pseudo spectral acceleration (PSA) amplitudes at long periods. For a given damping ratio, four regression coefficients are determined for the scaling equations with the help of 205 ground motions recorded in western USA. A numerical study undertaken with the help of several design PSA spectra and ensembles of spectrum‐compatible ground motions illustrates the effectiveness of the proposed correction factor, together with the proposed scaling models, in comparison with the PSV approximation in a variety of design situations. Both the input parameters mentioned above can be easily obtained from the specified design spectrum, and thus the proposed model is convenient to use.     

Inelastic displacement ratios for evaluation of existing structures

Results of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single‐degree‐of‐freedom systems with different levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180m/s are considered. The influence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain‐hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible influence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1s earthquake magnitude and soil conditions have a moderate influence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1.0s while it decreases maximum inelastic displacement non‐linearly as the period of vibration shortens and as the relative‐strength ratio increases for periods of vibration shorter than 1.0s. Finally, results from non‐linear regression analyses are presented that provide a simplified expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on firm sites. Copyright © 2003 John Wiley & Sons, Ltd.     

近断层速度脉冲的地震动特性研究

在搜集了大量近断层具有速度脉冲的记录后,对有速度脉冲和无速度脉冲的记录的反应谱和特征周期进行了对比,将近断层记录的反应谱与我国规范标准反应谱进行了比较, 还将各次地震有速度脉冲记录的反应谱和特征周期与规范标准谱及规范给出的特征周期进行了比较. 通过比较可知,在长周期段（大约在1.5 s以后）,有速度脉冲记录的反应谱值要比无速度脉冲记录的反应谱值大;计算特征周期时,对于近断层记录,T1和T2有后延的趋势, 采用不固定频段的方法计算更加合理; 无论是相对我国规范的Ⅰ类还是Ⅱ类场地, 有速度脉冲记录的特征周期比规范中给出的值都要大,均在规范值的2倍以上.      

Evaluation of simulated ground motions for predicting elastic response of long period structures and inelastic response of structures

The response of linear elastic and non-linear hysteretic systems having a single degree of freedom to recorded and simulated ground motions is studied. The objective is to evaluate whether the commonly used simulated motions are appropriate for predicting inelastic response of structures and elastic response of long period structures. Eight simulated motions were generated to model properties of horizontal ground motions recorded during four earthquakes. The simulated motions are sample functions of a stationary, Gaussian white noise process, multiplied by a temporal intensity function and passed through a linear single-degree-of-freedom filter. Two versions, corresponding to parabolic and ‘standard’ base line corrections (BLC), of each of the simulated and recorded accelerograms were considered. The following general conclusions are deduced. Simulated ground motions should be subjected to the standard BLC, because it results in more reliable ground velocities and displacements, which in turn would lead to more reliable predictions of response of long period structures. Furthermore, the spectral density of the underlying random process, from which the simulated motions are obtained, should be modified to be more representative of the frequency content of recorded motions, especially in the low frequency range. Such an improved model can be expected to lead to better agreement, over a broad range of periods, in the average response spectra of simulated and recorded motions, for elastic as well as inelastic systems.     

芦山地震强地面运动频谱特征及致灾相关性分析

以芦山地震震中距100km内20个台站的60条原始强震记录为依据,采用零交法计算台站处三方向卓越周期,采用线性加速法计算台站处阻尼比为0.05的三方向反应谱,考察反应谱峰值周期、卓越周期和放大系数在各台站位置处的分布以及在断裂上、下盘的均值。通过研究发现:芦山地震动卓越周期、反应谱峰值周期和放大系数在各台站不同方向上的分量不同;各台站处反应谱的计算表明地震动具有上盘效应以及上盘衰减迅速的特征;地震动卓越周期在芦山地震震中100km的上、下盘上差别不大,其中上盘EW和UD向卓越周期均值略小于下盘,而上盘NS向均值略大于下盘,断裂两盘UD向卓越周期总体小于水平向,断裂两盘三方向卓越周期变化范围为0.013~0.275s;计算得到的放大系数表明80%台站NS向放大系数大于EW向,因此NS向放大系数较大可能是芦山地震诱发崩滑地质灾害的主要因素。     

Ground-Motion Prediction Equations (GMPEs) for inelastic displacement and ductility demands of constant-strength SDOF systems

The objective of this paper is to present ground-motion prediction equations for ductility demand and inelastic spectral displacement of constant-strength perfectly elasto-plastic single-degree-of-freedom (SDOF) oscillators. Empirical equations have been developed to compute the ductility demand as a function of two earthquake parameters; moment magnitude, and source-to-site distance; one site parameter, the ground type; and three oscillator parameters, an undamped natural period, critical damping ratio, and the mass-normalized yield strength. In addition, a comparative study of the proposed model with selected previous studies and recommendations of Eurocode 8 is presented. Proposed equations can easily be incorporated in existing probabilistic seismic hazard analysis (PSHA) software packages with the introduction of an additional parameter. This leads to hazard curves for inelastic spectral displacement, which can provide better estimates of target displacement for nonlinear static procedures and an efficient intensity measure for probabilistic seismic demand analysis (PSDA). Proposed equations will be useful in performance evaluation of existing structures.