Pseudo relative velocity spectra of earthquake ground motion at high frequencies

The currently available empirical scaling laws for estimation of spectral amplitudes are limited to periods longer than 0–04 s. However, for design of equipment and stiff structures on multiple and distant supports, exposed to strong shaking near faults where peak accelerations can exceed 1g, specification of design ground motions at higher frequencies is required. This paper presents a method for extrapolation of pseudo-relative velocity spectral amplitudes of strong earthquake shaking to short periods (0–01 < T < 0–04 sec). The extrapolated spectra can be used as a physical basis for defining design spectral amplitudes in this higher-frequency range. The analysis in this paper implies that for typical strong motion accelerations, particularly on sedimentary sites in California, the peak ground accelerations are projected to be unaffected by frequencies higher than those recorded. Consequently, in California, the high-frequency pseudo-acceleration spectra can be approximated from the recorded absolute peak accelerations.     

Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk‐based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20‐story reinforced concrete frame structure. It is shown here that risk‐based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS‐based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously. Copyright © 2013 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.     

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.     

Strong ground motion from the November 12, 2017, <Emphasis Type="Bold">M</Emphasis> 7.3 Kermanshah earthquake in western Iran

In this paper, we analyzed the strong ground motion from the November 12, 2017, Kermanshah earthquake in western Iran with moment magnitude (M) of 7.3. Nonlinear and linear amplification of ground motion amplitudes were observed at stations with soft soil condition at hypocentral distances below and above 100 km, respectively. Observation of large ground motion amplitudes dominated with long-period pulses on the strike-normal component of the velocity time series suggests a right-lateral component of movement and propagation of rupture towards southeast. Comparison of the horizontal peak ground acceleration (PGA) from the M 7.3 earthquake with global PGA values showed a similar decay in ground motion amplitudes, although it seems that PGA from the M 7.3 Kermanshah earthquake is higher than global values for NEHRP site class B. We also found that the bracketed duration (D_b) was higher in the velocity domain than in the acceleration domain for the same modified Mercalli intensity (MMI) threshold. For example, D_b reached ~?30 s at the maximum PGA while it was ~?50 s at the maximum peak ground velocity above the threshold of MMI?=?5. Although the standard design spectrum from Iranian Code of Practice for Seismic Resistant Design of Buildings (standard No. 2800) seems to include appropriate values for the design of structures with fundamental period of 1 s and higher, it is underestimated for near-field ground motions at lower periods.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

Engineering implications of the 1985 nahanni earthquakes

A series of strong ground motions was recorded during a set of earthquakes which occurred in the North Nahanni River area of the Northwest Territories of Canada in late 1985. The strongest of these motions were recorded within 10 km of the epicentre of a magnitude 6.9 event; peak accelerations were well above 1g and peak velocities exceeded 0.4 m/s. This paper describes a study of the engineering characteristics of the Nahanni strong motions, particularly as they affect the response of building structures. The response characteristics are analysed in terms of the response spectra and the unit velocity base shear coefficients for multi-degree-of-freedom elastic frame structures. An analysis of the strong motion durations of the records and several measures of intensity is also included. The characteristics of the Nahanni records are compared with those of typical strong seismic ground motions and an ensemble of epicentral region seismic motions recorded under similar conditions. Comparisons are also made with the equivalent parameters in the 1985 edition of the National Building Code of Canada. It is concluded that the Nahanni records are very strong seismic ground motion records with relatively unusual response characteristics, even when compared with those of other records obtained within the epicentral region. The impact of these characteristics on engineering design is most significant for low period structures in epicentral regions. The specifications of typical design codes do not adequately describe the response to such records for very low periods.     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.     

Correlation in spectral accelerations for earthquakes in Europe

The shape of a uniform hazard spectrum has been criticized to be unrealistic for a site where the spectral ordinates of the uniform hazard spectrum at different periods are governed by different scenario events and conservative for long‐return‐period earthquake shaking. The conditional mean spectrum considering epsilon (CMS‐ε) takes into account the correlation of spectral demands (represented by values of ε) at different periods, to address these issues. This paper proposes new prediction models for the correlation coefficient of ε(T₁) and ε(T₂), a key component for developing a CMS, using Pan‐European earthquake records from a European ground motion database. Epsilon (ε) for each record is computed using the 2005 Ambraseys ground‐motion prediction equation. The model can be used to develop CMS for European sites, and it can be incorporated in the European seismic standards. Copyright © 2012 John Wiley & Sons, Ltd.     

汶川地震远场地震动场地相关性与分析方法评价

为考查远场地震动的场地相关性并评价一些场地特性分析方法的适用性,采用不同方法对汶川地震山东省12个远场台站的强震记录进行了分析.选取台站分别位于按建筑抗震设计规范(CBC)场地划分中的Ⅰ—Ⅲ类场地上.地震动记录的分析方法包括傅里叶幅值谱法,地震反应谱法,水平与竖向谱比率法,参考点谱比率法,以及尾波分析等.结果表明,按傅里叶幅值谱法,地震反应谱法,水平与竖向谱比法计算得到的卓越周期均远大于台站场地的卓越周期,不同方法得到的结果之间也有较大差别,且主要反映长周期地震动的卓越频率;参考点谱比率法的结果未反映地震动的卓越周期,也与场地的卓越周期差别较大;对完整记录尾波分析所得的结果比较接近场地的卓越周期.希望本文能为考虑远场地震作用时设计谱的建立,以及场地特性估计时地震动分析方法的选取提供参考依据.     

A vector‐valued ground motion intensity measure consisting of spectral acceleration and epsilon

The ‘strength’ of an earthquake ground motion is often quantified by an Intensity Measure (IM), such as peak ground acceleration or spectral acceleration at a given period. This IM is used to predict the response of a structure. In this paper an intensity measure consisting of two parameters, spectral acceleration and epsilon, is considered. The IM is termed a vector‐valued IM, as opposed to the single parameter, or scalar, IMs that are traditionally used. Epsilon (defined as a measure of the difference between the spectral acceleration of a record and the mean of a ground motion prediction equation at the given period) is found to have significant ability to predict structural response. It is shown that epsilon is an indicator of spectral shape, explaining why it is related to structural response. By incorporating this vector‐valued IM with a vector‐valued ground motion hazard, we can predict the mean annual frequency of exceeding a given value of maximum interstory drift ratio, or other such response measure. It is shown that neglecting the effect of epsilon when computing this drift hazard curve leads to conservative estimates of the response of the structure. These observations should perhaps affect record selection in the future. Copyright © 2005 John Wiley & Sons, Ltd.     

Empirical correlations between cumulative absolute velocity and spectral accelerations from NGA ground motion database

Considering multiple ground motion intensity measures is important in seismic hazard analysis and ground motion selection process. Using the NGA strong motion database and recently developed ground-motion prediction models, empirical correlations are developed between cumulative absolute velocity (CAV) and spectral accelerations (Sa) at periods from 0.01 to 10 s. The CAV–Sa correlations at long periods are significantly influenced by rupture distance due to modification of the frequency content and duration of the acceleration time history through travel path. Similarly, the presence of strong velocity pulses in near-source ground motions also affects the correlations at moderate to long periods. On the other hand, the correlations are not particularly sensitive to the earthquake magnitude, orientation of the ground-motion recordings, selection of ground-motion prediction models and local site conditions. Piecewise linear fitting equations are provided to quantify the correlations for various cases. The application of the CAV–Sa correlations in ground motion selection process is also discussed.     

Ground motion simulations for seismic stations in southern and eastern Romania and seismic hazard assessment

This research focuses on the evaluation of soil conditions for seismic stations in southern and eastern Romania, their influence on stochastic finite-fault simulations, and the impact of using them on the seismic hazard assessment. First, the horizontal-to-vertical spectral ratios (HVSR) are evaluated using ground motions recorded in 32 seismic stations during small magnitude (M _W  ≤ 6.0) Vrancea seismic events. Most of the seismic stations situated in the southern part of Romania exhibit multiple HVSR peaks over a broad period range. However, only the seismic stations in the eastern-most part of Romania have clear short-period predominant periods. Subsequently, stochastic finite-fault simulations are performed in order to evaluate the influence of the soil conditions on the ground motion amplitudes. The analyses show that the earthquake magnitude has a larger influence on the computed ground motion amplitudes for the short- and medium-period range, while the longer-period spectral ordinates tend to be influenced more by the soil conditions. Next, the impact of the previously evaluated soil conditions on the seismic hazard results for Romania is also investigated. The results reveal a significant impact of the soil conditions on the seismic hazard levels, especially for the sites characterized by long-period amplifications (sites situated mostly in southern Romania), and a less significant influence in the case of sites which have clear short predominant periods.     

A new approximation for spectral velocity ordinates at short periods

Response spectrum methods in earthquake‐resistant design sometimes require information on the spectral velocity (SV) for a given single‐degree‐of‐freedom oscillator and specified seismic hazard. SV has been conventionally approximated as pseudo spectral velocity (PSV) in the case of lightly damped structures that are not too flexible. This study shows that the PSV approximation may lead to large overestimation errors when the structure is stiffer to the ground motion and the ground motion is a long‐period motion. It is also shown that a new approximation requiring the use of peak ground acceleration of the motion may significantly reduce these errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Probabilistic seismic hazard analysis: Early history

Probabilistic seismic hazard analysis (PSHA) is the evaluation of annual frequencies of exceedence of ground motion levels (typically designated by peak ground acceleration or by spectral accelerations) at a site. The result of a PSHA is a seismic hazard curve (annual frequency of exceedence vs ground motion amplitude) or a uniform hazard spectrum (spectral amplitude vs structural period, for a fixed annual frequency of exceedence). Analyses of this type were first conceived in the 1960s and have become the basis for the seismic design of engineered facilities ranging from common buildings designed according to building codes to critical facilities such as nuclear power plants. This Historical Note traces the early history of PSHA. Copyright © 2007 John Wiley & Sons, Ltd.     

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。     

集集地震近断层地震动频谱特性

利用5个反映地震动频谱特征的周期(反应谱卓越周期Tp, 平滑化反应谱卓越周期To, 傅氏幅值谱平均周期Tm, 等效速度脉冲周期Tv和拟速度反应谱卓越周期Tpv), 对集集地震的近断层三分量地震动进行研究. 结果表明, 上盘地震动的频谱周期小于下盘地震动; Tp小于To和Tm, 且Tp反映的三分量之间的关系与To和Tm不同; 在地表断裂带的北端,Tv和Tpv所反映的近断层地震动长周期分量的频谱特征, 与走滑断层中方向性效应作用的规律相类似. 得出的定性或定量结论可以为近场抗震设计谱的建立与地震危险性区划研究提供参考.      

Correlation model for spatially distributed ground‐motion intensities

Risk assessment of spatially distributed building portfolios or infrastructure systems requires quantification of the joint occurrence of ground‐motion intensities at several sites, during the same earthquake. The ground‐motion models that are used for site‐specific hazard analysis do not provide information on the spatial correlation between ground‐motion intensities, which is required for the joint prediction of intensities at multiple sites. Moreover, researchers who have previously computed these correlations using observed ground‐motion recordings differ in their estimates of spatial correlation. In this paper, ground motions observed during seven past earthquakes are used to estimate correlations between spatially distributed spectral accelerations at various spectral periods. Geostatistical tools are used to quantify and express the observed correlations in a standard format. The estimated correlation model is also compared with previously published results, and apparent discrepancies among the previous results are explained. The analysis shows that the spatial correlation reduces with increasing separation between the sites of interest. The rate of decay of correlation typically decreases with increasing spectral acceleration period. At periods longer than 2 s, the correlations were similar for all the earthquake ground motions considered. At shorter periods, however, the correlations were found to be related to the local‐site conditions (as indicated by site V_s30 values) at the ground‐motion recording stations. The research work also investigates the assumption of isotropy used in developing the spatial correlation models. It is seen using the Northridge and Chi‐Chi earthquake time histories that the isotropy assumption is reasonable at both long and short periods. Based on the factors identified as influencing the spatial correlation, a model is developed that can be used to select appropriate correlation estimates for use in practical risk assessment problems. Copyright © 2009 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.