Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.     

基于物理的随机地震动模型研究

基于物理联系研究地震动随机性,建立了随机地震动与基底输入傅氏谱、场地固有圆频率和场地等价阻尼比之间的物理关系,从随机傅氏谱函数角度描述了地震动随机过程的随机性本质。结合Ⅳ类工程场地的实测地震动记录资料,由数值方法识别了给出基本随机变量的概率分布参数。与实测记录对比表明,本文建立的随机地震动模型具有明确的物理概念,可充分反映地震动的变异性特征。     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

基于强度和能量控制的随机地震动模型

考虑地震动的随机性和频率与强度非平稳性,通过理论分析,提出了一般随机地震动模型,并给出了确定模型参数的原则和方法。该模型以地震动强度、地震动能量以及地震动持时等宏观指标作为控制随机地震动模型参数的指标,而对其内在的频谱组成等指标只要求满足一般地震动的特征。该模型可以用于描述平稳随机过程、强度非平稳随机过程以及强度和频率完全非平稳随机过程。通过与常用功率谱模型的比较,验证了该模型的合理性。     

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.     

Conditional simulation of spatially variable seismic ground motions based on evolutionary spectra

This paper proposes a computational procedure for the conditional simulation of spatially variable seismic ground motions for long span bridges with multiple supports. The seismic ground motions, with part of their time histories measured at some supports, are regarded as zero‐mean nonstationary random processes characterized by predefined evolutionary power spectral density. To conditionally simulate unknown seismic ground motion time histories at other supports, the Kriging method is first described briefly for the conditional simulation of a random vector comprised of zero‐mean Gaussian variables. The multivariate oscillatory processes characterized by the evolutionary power spectral density matrix are then introduced, and the Fourier coefficients of the oscillatory processes and their covariance matrix are derived. By applying the Kriging method to the random vector of the Fourier coefficients and using the inverse Fourier transform, unknown nonstationary seismic ground motion time histories can be simulated. A numerical example is selected to demonstrate capabilities of the proposed simulation procedure, and the results show that the procedure can ensure unbiased time‐varying correlation functions, especially the cross correlation between known and unknown time histories. The procedure is finally applied to the Tsing Ma suspension bridge in Hong Kong to generate ground accelerations at its multiple supports using limited seismic records. Copyright © 2012 John Wiley & Sons, Ltd.     

基于进化策略算法拟合多阻尼比反应谱的地震动仿真

拟合多阻尼比反应谱的人造地震波是新抗震规范提出的要求。本文引入多目标优化概念和进化策略算法，提出拟合多阻尼比反应谱的地震动仿真方法，解决了传统地震动仿真中的多阻尼比反应谱拟合精度较差的问题。算例表明，该方法可获得优化问题的近似Pareto最优解集，在拟合多阻尼比反应谱的人造地震波集系的仿真方面有传统方法所不能比拟的优势，产生的人造波或人造波集系可满足工程抗震设计需要。     

Simulation of orthogonal horizontal components of near‐fault ground motion for specified earthquake source and site characteristics

A procedure to generate horizontal pairs of synthetic near‐fault ground motion components for specified earthquake source and site characteristics is presented. Some near‐fault ground motions contain a forward directivity pulse; others do not, even when the conditions for such a pulse are favorable. The proposed procedure generates pulse‐like and non‐pulse‐like motions in appropriate proportions. We use our recent stochastic models of pulse‐like and non‐pulse‐like near‐fault ground motions that are formulated in terms of physically meaningful parameters. The parameters of these models are fitted to databases of recorded pulse‐like and non‐pulse‐like motions. Using these empirical “observations,” predictive relations are developed for the model parameters in terms of the earthquake source and site characteristics (type of faulting, earthquake magnitude, depth to top of rupture plane, source‐to‐site distance, site characteristics, and directivity parameters). The correlation coefficients between the model parameters are also estimated. For a given earthquake scenario, the probability of occurrence of a directivity pulse is first computed; pulse‐like and non‐pulse‐like motions are then simulated according to the predicted proportions using the empirical predictive models. The resulting time series are realistic and reproduce important features of recorded near‐fault ground motions, including the natural variability. Moreover, the statistics of their elastic response spectra agree with those of the NGA‐West2 dataset, with the additional feature of distinguishing between pulse‐like and non‐pulse‐like cases and between forward and backward directivity scenarios. The synthetic motions can be used in addition to or in place of recorded motions in performance‐based earthquake engineering, particularly when recorded motions are scarce.     

随机地震动作用下的结构振动控制试验设计

研究了随机地震动作用下基于MR阻尼器的结构振动控制振动台试验设计的若干问题。首先,由原型结构按动力相似关系进行了模型结构的设计,基于ANSYS模态分析的结果识别出了其结构参数;其次,基于物理随机地震动模型生成了试验地震动样本,根据试验要求调整了各地震动样本的加速度峰值;然后,基于MATLAB对试验模型进行了随机地震动作用下无控与主动控制数值仿真分析;最后,结合ANSYS弹塑性动力时程分析,研究了试验模型的动力稳定性。介绍的振动控制试验设计方法可供进行类似试验设计的研究人员参考。     

地震动强度对场地地震反应的影响

通过对场地地震反应的研究发现,地震动强度不同,同样的场地对地震动的影响也不同,得到的反应谱形状也不同。目前我国抗震设计规范中不同烈度下的设计反应谱形状完全一致,没有考虑地震动强弱对相同场地反应谱形状的影响。     

基于EMD和VARMA模型的地震动仿真

通过EMD方法将地震动分解成若干固有模态函数,提出了用固有模态函数的时变VARMA建模实现地震动仿真的思路。算例分析表明,该方法充分利用了固有模态函数的特性,解决了直接基于ARMA或VARMA模型建模的仿真方法所面临的模型判阶的难题,并可同时考虑地震动的强度和频率非平稳特性,使仿真地震动与实际地震动在能量时频分布特性上具有较好的一致性且样本统计性较好,弹性及弹塑性反应谱拟合精度较高。     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Stochastic model for simulation of near‐fault ground motions

A parameterized stochastic model of near‐fault ground motion in two orthogonal horizontal directions is developed. The major characteristics of recorded near‐fault ground motions are represented. These include near‐fault effects of directivity and fling step; temporal and spectral non‐stationarity; intensity, duration, and frequency content characteristics; directionality of components; and the natural variability of ground motions. Not all near‐fault ground motions contain a forward directivity pulse, even when the conditions for such a pulse are favorable. The proposed model accounts for both pulse‐like and non‐pulse‐like cases. The model is fitted to recorded near‐fault ground motions by matching important characteristics, thus generating an ‘observed’ set of model parameters for different earthquake source and site characteristics. A method to generate and post‐process synthetic motions for specified model parameters is also presented. Synthetic ground motion time series are generated using fitted parameter values. They are compared with corresponding recorded motions to validate the proposed model and simulation procedure. The use of synthetic motions in addition to or in place of recorded motions is desirable in performance‐based earthquake engineering applications, particularly when recorded motions are scarce or when they are unavailable for a specified design scenario. Copyright © 2016 John Wiley & Sons, Ltd.     

平稳地震动过程具分段均布随机频率的谱拟合模型

本文首先针对平稳随机地震动谱拟合问题建立了一个统一的谱拟合模型,在此基础上,提出了一新的具分段均布随机频率的拟合模型,并与几类常用的谱拟合模型进行了比较研究,指出拟合模型的频率特性对拟合功率谱与反应谱具有显著的影响。算例表明,当结构的自振频率与拟合模型的分量频率接近时,计算的响应值明显偏大,对于小阻尼情况,这一现象更为明显。     

基于强震记录的核电厂抗震标准反应谱研究

依据基岩场地上的汶川地震强震记录,分析了地震动地面峰值和核电站抗震标准反应谱的特性,证明了在推导和使用标准反应谱时所考虑的地面峰值加速度与地面峰值速度之比(PGA/PGV)受地面峰值加速度和震中距的影响,将对标准反应谱形状产生明显的影响.另外还发现了基岩场地的竖向峰值加速度可能要远比通常认为水平向峰值加速度的2/3大....     

A new attenuation model of near-fault ground motions with consideration of the hanging wall effect in the Wenchuan earthquake

The hanging wall effect is an important factor that impacts the characteristics of strong ground motions in near-fault areas. Based on a residual analysis of ground motion parameters characterizing the hanging wall effect and in recognition of the nature of the effect, many models have been developed. In this study, after a comprehensive analysis of two existing models, a new model is proposed and used to model the hanging wall effect in horizontal peak ground acceleration (PGAH) and spectral acceleration (SAH) at a period of 0.1s in the Wenchuan earthquake. Finally, comparisons between the modeling results of the hanging wall effect in the Wenchuan earthquake and the results predicted by using Abrahamson and Silva’s NGA model (AS NGA) indicate that the AS NGA model predicts a much higher hanging wall effect than the model developed in this paper. Furthermore, the AS NGA model predicts a large hanging wall effect even at great distances, while the proposed model more accurately captures the trend of the effect.     

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。     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

基于相位差谱的时-频非平稳人造地震动的反应谱拟合

本文根据相位差谱对地震动时程非平稳性的影响，反应谱、功率谱和傅里叶幅值谱间的数学关系以及加速度时程单谐波分量对反应谐拟合精度和拟合效率的作用，提出了一种可直接拟合目标反应谱的具有时－频非平稳性的人工地震动的高效方法，算例说明了其有效性。