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.     

基于振动台试验的黄土场地效应研究

地震作用下黄土场地对地震波不同分量的放大效应影响显著。针对黄土高原典型黄土场地在地震作用下的放大效应,设计并完成大型地震模拟振动台试验,通过输入不同强度的地震动荷载,研究黄土场地加速度（PGA）放大系数、傅里叶谱、加速度反应谱、H/V谱比与地震动强度和场地高度的变化规律,揭示地震波不同分量对黄土场地效应的影响。结果显示：黄土场地对地震波的水平分量具有明显的放大效应,对地震波垂直分量的放大效应影响较小;随着高程的增加,地震波水平分量PGA放大系数呈现非线性变化;随着地震动强度和高程的增加水平分量卓越频率的频段和幅值逐渐增加,卓越频率向低频偏移,放大倍数呈现出非线性特性。     

南北地震带川滇甘陕地区竖向与水平向加速度反应谱比的统计分析

本文收集了从南北地震带川滇甘陕地区263个有详细场地资料的强震台站获得的802组强震动记录,按照场地、震级和震中距等因素统计分析了竖向与水平向加速度反应谱比的形状以及不同场地、震级和震中距下不同周期段内的谱比平均值,并与建筑抗震规范GB50011—2010规定的0.65进行了比较。结果表明:竖向与水平向加速度反应谱比受场地、震级和震中距等因素的影响; Ⅰ类和Ⅱ类场地在全周期段的谱比均值基本上大于0.65;无论何种分组情况谱比均值在0.1—1.0 s周期范围内基本低于定值0.65,周期大于1.0 s的谱比均值基本上远高于0.65。因此对于大部分抗震规范直接把竖向地震作用取为水平向地震作用的0.65倍,有待商榷。本文建议根据水平向反应谱的标定方式来确定现有竖向强震动记录的竖向地震作用。      

An alternative construction of normalized seismic design spectra for near-fault regions

This paper presents a methodology for constructing seismic design spectra in near-fault regions.By analyzing the characteristics of near-fault pulse-type ground motions,an equivalent pulse model is proposed,which can well represent the characteristics of the near-fault forward-directivity and fling-step pulse-type ground motions.The normalized horizontal seismic design spectra for near-fault regions are presented using recorded near-fault pulse-type ground motions and equivalent pulse-type ground motions,which are derived based on the equivalent pulse model coupled with ground motion parameter attenuation relations.The normalized vertical seismic design spectra for near-fault regions are obtained by scaling the corresponding horizontal spectra with the vertical-to-horizontal acceleration spectral ratios of near-fault pulse-type ground motions.The proposed seismic design spectra appear to have relatively small dispersion in a statistical sense.The seismic design spectra for both horizontal and vertical directions can provide alternative spectral shapes for seismic design codes.     

Scaling of spectral displacement ordinates with damping ratios

The next generation of seismic design codes, especially those adopting the framework of performance‐based design, will include the option of design based on displacements rather than forces. For direct displacement‐based design using the substitute structure approach, the spectral ordinates of displacement need to be specified for a wide range of response periods and for several levels of damping. The code displacement spectra for damping values higher than the nominal value of 5% of critical will generally be obtained, as is the case in Eurocode 8 and other design codes, by applying scaling factors to the 5% damped ordinates. These scaling factors are defined as functions of the damping ratio and, in some cases, the response period, but are independent of the nature of the expected ground shaking. Using both predictive equations for spectral ordinates at several damping levels and stochastic simulations, it is shown that the scaling factors for different damping levels vary with magnitude and distance, reflecting a dependence of the scaling on the duration of shaking that increases with the damping ratio. The options for incorporating the influence of this factor into design code specifications of displacement response spectra are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

中、美、欧抗震规范底部剪力法的对比研究

目前,底部剪力法是各国计算水平地震作用的基本方法,应用该方法时需要使用各自国家的抗震设计反应谱。本文汇总了中、美、欧抗震设计规范的反应谱和底部剪力法,在相同重现期和场地条件的基础上,对比了不同烈度下3本规范反应谱的异同,并通过算例对比了分别采用3本规范的底部剪力法算出的不同设防烈度下同一结构的底部地震剪力和层间地震剪力。对比结果表明,3本规范的反应谱和底部剪力法在本质上是相同的,只在表达形式和参数设置上存在差异。     

Current empirical ground-motion prediction equations for Europe and their application to Eurocode 8

The first ground-motion prediction equation derived from European and Middle Eastern strong-motion data was published more than 30 years ago; since then strong-motion networks and the resulting databank of accelerograms in the region have expanded significantly. Many equations for the prediction of peak ground-motion parameters and response spectral ordinates have been published in recent years both for the entire Euro-Mediterranean and Middle Eastern region as well as for individual countries within this region. Comparisons among empirical ground-motion models for these parameters, developed using large regional datasets, do not support the hypothesis of there being significant differences in earthquake ground-motions from one area of crustal seismicity to another. However, there are certain regions within Europe—affected by different tectonic regimes—for which the existing pan-European equations may not be applicable. The most recent European equations make it possible to now implement overdue modifications to the presentation of seismic design actions in Eurocode 8 that allow an improved approximation to the target uniform hazard spectrum (UHS). Using these recent equations, this study outlines a new approach via which an approximation to the UHS may be constructed using hazard maps calculated for peak ground velocity and the corner period T _D in addition to the maps for peak ground acceleration that underpin the current stipulations of Eurocode 8.     

Empirical evaluation of peak ground velocity and displacement as a function of elastic spectral ordinates for design

In the framework of the revision of Part 1 of Eurocode 8, this study aims at developing new empirical correlations to compute peak values of ground velocity (PGV) and displacement (PGD) as a function of elastic spectral ordinates for design. At variance with the expressions for PGV and PGD currently adopted in the Eurocode 8, based solely on the peak ground acceleration (PGA), in this paper reference is made to spectral ordinates of the short and intermediate period range, namely S_s, which is the constant acceleration spectral ordinate, and S₁, which is the spectral ordinate at 1 s. On the one hand, a relationship between PGV and the product (S_s?S₁) was found based on the regression analysis on a high‐quality strong‐motion dataset. On the other hand, the PGD was estimated by extrapolating to long periods the constant displacement branch of the elastic response spectrum, introducing a correlation between the corner period T_D and S₁. For this purpose, results of a long period probabilistic seismic hazard assessment study for Italy, encompassing low to high seismicity areas, were considered. Furthermore, verification of the proposed relationship against strong‐motion records was carried out, and differences justified in terms of the concept of uniform hazard spectrum.     

桃夭门大桥基岩长周期设计反应谱

文中结合舟山市桃夭门大桥抗震设计在长周期频段的需要,研究分析了桃夭门大桥场地基本地震地质环境特点和长周期地面运动谱的研究现状,从强震记录长周期分量信息特点出发,以强震记录为基础,选用了11个有代表性的M≥65的强震,共72条强震地面运动记录,参照核法规HAF0101(1)特定场地谱的确定方法,通过统计分析建立了以均值反应谱为基础的长周期反应谱     

Consecutive combined response spectrum

Appropriate estimates of earthquake response spectrum are essential for design of new structures, or seismic safety evaluation of existing structures. This paper presents an alternative procedure to construct design spectrum from a combined normalized response spectrum(NRSC) which is obtained from pseudo-velocity spectrum with the ordinate scaled by different peak ground amplitudes(PGA, PGV, PGD) in different period regions. And a consecutive function f(T) used to normalize the ordinates is defined. Based on a comprehensive study of 220 strong ground motions recorded during recent eleven large worldwide earthquakes, the features of the NRSC are discussed and compared with the traditional normalized acceleration, velocity and displacement response spectra(NRSA, NRSV, NRSD). And the relationships between ground amplitudes are evaluated by using a weighted mean method instead of the arithmetic mean. Then the NRSC is used to define the design spectrum with given peak ground amplitudes. At last, the smooth spectrum is compared with those derived by the former approaches, and the accuracy of the proposed spectrum is tested through an analysis of the dispersion of ground motion response spectra.     

新疆喀什原场地地震动频谱特性研究

2020年1月19日和2020年2月21日在新疆喀什地区先后发生M_S6.4和M_S5.1地震,针对新疆强震动台网收集到的128条强震动记录进行统计分析,研究2次地震记录的幅值及反应谱特性,并与两个现行规范设计反应谱进行对比,结果表明：(1)震级相同时,震中距越小加速度反应谱越大,且加速度反应谱衰减速度越慢;震中距相同时,震级越大加速度反应谱越大,且加速度反应谱衰减速度越慢;(2)震级越大加速度谱值、速度谱值、位移谱值越大;(3)M_S6.4、M_S5.1地震波加速度反应谱及其平均值曲线相近,与我国现行规范加速度反应谱相比差别很大。建议在新疆喀什地区采用基于当地强震记录的加速度反应谱进行结构抗震设计。     

Ground-motion characterization for the probabilistic seismic hazard assessment in Turkey

This study describes the methodology implemented to establish the ground-motion logic-tree for national probabilistic seismic hazard map of Turkey for shallow active crustal regions. The presented procedure provides quantitative information to guide the hazard experts while establishing the logic tree to capture the epistemic uncertainty in ground-motion characterization. It uses non-data-driven and data-driven testing methods to identify and rank candidate ground-motion prediction equations (GMPEs) under a specific ground-motion database. The candidate GMPEs are subjected to visual inspection and are classified into center, body and range (CBR) spectral estimates for a proper consideration of epistemic uncertainty. The GMPEs classified into CBR are then used in a suite of seismic hazard sensitivity analysis to establish the most suitable GMPE logic-tree whose spectral estimates are not biased by any one of the GMPEs in the logic-tree structure. The sensitivity analysis considers normalized spectral ordinates and is not manipulated by the spectral amplitudes. The proposed procedure is inherited from the relevant studies of the Earthquake Model of the Middle East (EMME; www.efehr.org:8080/jetspeed/portal/emme.psml) regional seismic hazard project. This paper also highlights the similarities and differences in ground-motion characterization between EMME and our approach.     

缺乏近断层强震观测资料地区抗震设计规范反应谱研究

根据最近几次的近断层地震观测记录研究显示，在现行结构抗震设计规范中很少考虑近断层效应的影响，对于缺乏近断层强震观测资料地区，抗震设计规范的改进方法及近断层效应的设计参数还没有统一结论. 本文基于UBC97近断层因子设计理念， 在收集世界范围内近断层观测记录的基础上，按场地和震级进行分类，建立了中长周期关键点处的加速度谱需求的衰减关系式，推导给出了缺乏近断层观测资料地区近断层影响因子的震级和断层距的关系式. 并以我国现行的建筑抗震设计规范为基础，建议了近断层影响因子的参考取值和修正后的反应谱曲线，为我国结构抗震设计提供了参考.      

Response spectrum of seismic design code for zones lack of near-fault strong earth- quake records

It was shown from the study on the recently near-fault earthquake ground motions that the near-fault effects were seldom considered in the existing Chinese seismic code. Referring to the UBC97 design concept for near-fault factors, based on the collected world-widely free-site records of near-fault earthquakes ground motions classified by earthquake magnitude and site condition, the attenuation relationship expressions of the acceleration spectrum demand at the key points within the long period and moderate period were established in term of the earthquake magnitude and the site condition. Furthermore, the near-fault factors’ expressions about the earthquake magnitude and the fault distance were deduced for the area lack of near-fault strong earthquake records. Based on the current Chinese Building Seismic Design Code, the near-fault effect factors and the modified design spectral curves, which were valuable for the seismic design, were proposed to analyze the seismic response of structures.     

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.     

多层隔震结构的竖向地震作用研究

国外对隔震结构竖向地震反应的观测结果和对隔震结构竖向地震作用计算的规定,都与我国抗震规范有较大差别。本文通过反应谱和时程分析,讨论了多层隔震结构的竖向地震作用取值及竖向地震作用效应,对我国抗震规范的有关规定作了探讨,认为除位于近断层附近的隔震建筑外,其它隔震结构的竖向地震作用可取与不隔震结构相同;对于多层隔震建筑,多遇地震下可不考虑竖向地震作用,在罕遇地震下,应对所有隔震结构验算支座是否受拉或失稳,并且组合时应计入竖向地震作用效应。     

适用于结构时程分析法的输入地震波

本文对建筑结构抗震设计时程法所需的输入地震波提出一种基于规范反应谱的、与设防烈度、场地条件、设计近震或远震、结构自振特性有关的选择原则和方法。按远、近震和四类场地标定了反应谱、延性谱和积累损伤谱。通过对六幢不同高度的剪切和弯曲型结构模型的弹塑性分析,表明离差很小。建议在进行结构时程法分析时,按地震加速度反应谱特定的分布规律选择4条加速度记录作为输入计算。两个实际的例子表明按上述方法计算的结果与按底部剪力法计算的结果基本相符。     

An evaluation of the applicability of the NGA models to ground-motion prediction in the Euro-Mediterranean region

The first phase of the Next Generation Attenuation (NGA) project has now finished, resulting in the publication of five new sets of empirical ground-motion models for PGA, PGV and response spectral ordinates. These models mark a significant advancement in the state-of-the-art in empirical ground-motion modelling and include many effects that are not accounted for in existing European equations. Under the assumption that the Euro-Mediterranean database from which the European relationships are derived is unlikely to drastically change in the near future, a prudent question to ask is: can the NGA models be applied in Europe? In order to answer this question, the NGA model of Boore and Atkinson (PEER Report 2007/01, Pacific Earthquake Engineering Research Center, Berkeley, CA, 234 pp., 2007), which is shown to be representative of the NGA models as a suite, is compared with the dataset used for the development of the most recent European empirical ground-motion models for response spectral ordinates and peak ground velocity. The comparisons are made using analyses of model residuals and the likelihood approach of Scherbaum et al. (Bull Seism Soc Am 94(6):2164–2185, 2004). The analyses indicate that for most engineering applications, and particularly for displacement-based approaches to seismic design, the NGA models may confidently be applied within Europe. Furthermore, it is recommended that they be used in conjunction with existing European models to provide constraint on finite-fault effects and non-linear site response within logic-tree frameworks. The findings also point to the potential benefits of merging the NGA and European datasets.     

Evaluation of combination rules for peak response calculation in three‐component seismic analysis

The responses, r_e, given by several multicomponent combination rules used in seismic codes for determining peak responses to three ground motion components are evaluated for elastic systems and compared with the critical response r_cr; this is defined as the largest response for all possible incident angles of the seismic components and obtained by means of the CQC3‐rule when a principal seismic component is vertical, or the GCQC3‐rule when it departs from the vertical direction. The combination rules examined are the SRSS‐, 30%‐, 40%‐ and IBC‐rules, considering different alternatives for the design horizontal spectrum. Assuming that a principal seismic component is along the vertical direction, the upper and lower bounds of the ratio r_e/r_cr for each combination rule are determined as a function of the spectral intensity ratio of the horizontal seismic components and of the responses to one seismic component acting alternately along each structural axis. Underestimations and overestimations of the critical response are identified for each combination rule and each design spectrum. When a component departs from the vertical direction, the envelopes of the bounds of the ratio r_e/r_cr for each combination rule are calculated, considering all possible values of the spectral intensity ratios. It is shown that the inclination of a principal component with respect to the vertical axis can significantly reduce the values of r_e/r_cr with respect to the case when the component is vertical. Copyright © 2003 John Wiley & Sons, Ltd.     

近断层竖向与水平向加速度反应谱比值特征

显著的竖向地震动是近断层地震动区别于远场地震动的重要特征之一,为更合理地确定竖向地震动作用,研究了近断层区域竖向地震动的反应谱特征及其与水平向反应谱比值的影响因素.首先,选取1952—1999年世界范围内震级在M5.4—7.6之间的18次地震的地震动记录,研究竖向地震加速度反应谱及其与水平向加速度反应谱比值特征;然后统计分析了断层距、场地条件、震级以及断层机制对竖向与水平向加速度反应谱比的影响.结果表明,一般情况下竖向加速度具有更丰富的短周期分量,并且竖向加速度反应谱衰减较慢;断层距在20km以内的近断层区域、软弱土层场地、中等震级地震和逆断层大震级中长周期范围等条件下,具有较大的竖向与水平向加速度反应谱比值;在近断层区域的结构抗震设计中应充分考虑竖向地震动的影响.