Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.     

A simple ground‐motion prediction model for cumulative absolute velocity and model validation

Cumulative absolute velocity (CAV) is an important ground motion intensity measure used in seismic hazard analysis. Based on the Next Generation Attenuation strong motion database, a simple ground‐motion prediction equation is proposed for the geometric mean of as‐recorded horizontal components of CAVs using mixed regression analysis. The proposed model employs only four parameters and has a simple functional form. Validation tests are conducted to compare the proposed model with the recently developed Campbell–Bozorgnia (CB10) model using subsets of the strong motion database, as well as several recent earthquakes that are not used in developing the model. It is found that the predictive capability of the proposed model is comparable with the CB10 model, which employs a complex functional form and more parameters. The study also corroborates previous findings that CAV has higher predictability than other intensity measures such as the peak ground acceleration. The high predictability of CAV warrants the use of the proposed simple model as an alternative in seismic hazard analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

According to the current seismic codes, structures are designed to resist the first damaging earthquake during their service life. However, after a strong main shock, a structure may still face damaging aftershocks. The main shock‐aftershock sequence may result in major damage and eventually the collapse of a structure. Current studies on seismic hazard mainly focus on the modeling and simulation of main shocks. This paper proposes a 3‐step procedure to generate main shock‐aftershock sequences of pairs of horizontal components of a ground motion at a site of interest. The first step generates ground motions for the main shock using either a source‐based or site‐based model. The second step generates sequences of aftershocks' magnitudes, locations, and times of occurrence using either a fault‐based or seismicity‐based model. The third step simulates pairs of ground motion components using a new empirical model proposed in this paper. We develop prediction equations for the controlling parameters of a ground motion model, where the predictors are the site condition and the aftershock characteristics from the second step. The coefficients in the prediction equations and the correlation between the model parameters (of the 2 horizontal components of 1 record and of several records in 1 sequence) are estimated using a database of aftershock accelerograms. A backward stepwise deletion method is used to simplify the initial candidate prediction equations and avoid overfitting the data. The procedure, based on easily identifiable engineering parameters, is a useful tool to incorporate effects of aftershocks into seismic analysis and design.     

Empirical attenuation relationship for Arias Intensity

Arias Intensity is a ground motion parameter that captures the potential destructiveness of an earthquake as the integral of the square of the acceleration–time history. It correlates well with several commonly used demand measures of structural performance, liquefaction, and seismic slope stability. A new empirical relationship is developed to estimate Arias Intensity as a function of magnitude, distance, fault mechanism, and site category based on 1208 recorded ground motion data from 75 earthquakes in active plate‐margins. Its functional form is derived from the point‐source model, and the coefficients are determined through non‐linear regression analyses using a random‐effects model. The results show that for large magnitude earthquakes (M > 7) Arias Intensity was significantly overestimated by previous relationships while it was underestimated for smaller magnitude events (M ? 6). The average horizontal Arias Intensity is not significantly affected by forward rupture directivity in the near‐fault region. The aleatory variability associated with Arias Intensity is larger than that of most other ground motion parameters such as spectral acceleration. However, it may be useful in assessing the potential seismic performance of stiff engineering systems whose response is dominated by the short‐period characteristics of ground motions. Copyright © 2003 John Wiley & Sons, Ltd.     

地震动竖向分量对铁路房屋的地震响应性能影响

为了提高铁路房屋的抗震能力,分析地震动竖向分量对铁路房屋的地震响应性能,提出基于荷载—变形关系联合评估的地震动竖向分量对铁路房屋的地震响应评估模型。构建地震动竖向分量的力学响应评估模型,识别铁路房屋的地震屈服响应参数,采用荷载—变形关系和极限荷载结合的方法进行铁路房屋的地震屈服响应应力评估,分析地震动竖向分量对铁路房屋的响应。建立动量平衡方程和弯矩平衡方程,构建铁路房屋的地震响应的三阶段荷载—变形模式,实现地震动竖向分量对铁路房屋的地震响应性能评估模型的优化设计。测试结果表明,采用该模型能有效分析地震动竖向分量对铁路房屋的地震响应性能影响,Simulink仿真结果和有限元模拟结果的准确性较高,力学参数辨识性能优越,计算结果准确可靠。     

Ground motion and probabilistic hazard

It might be thought that an empirical ground motion prediction model has only to describe the variations in the input data set as accurately as possible in order to be useful, with the proviso that the data set is reasonably extensive and well-selected. If the model is to be used in probabilistic seismic hazard assessment, however, the model will probably be subject to extrapolation beyond the parameter space within which it was constructed, especially for hazard at low annual probabilities. In this case, features of the model, especially its functional form, may turn out to have unexpected and undesirable implications. The end result can be conclusions about the hazard that are clearly not in accordance with commonsense. In this study, two test cases are used to examine the application of some recent ground motion models to probabilistic hazard studies. Problems are found that suggest that, although a ground motion model may be a correct representation of its data set, the effects of the functional form applied can be such that it becomes doubtful whether the model should be used for probabilistic hazard purposes.     

Ground motion selection for simulation‐based seismic hazard and structural reliability assessment

This paper examines four methods by which ground motions can be selected for dynamic seismic response analyses of engineered systems when the underlying seismic hazard is quantified via ground motion simulation rather than empirical ground motion prediction equations. Even with simulation‐based seismic hazard, a ground motion selection process is still required in order to extract a small number of time series from the much larger set developed as part of the hazard calculation. Four specific methods are presented for ground motion selection from simulation‐based seismic hazard analyses, and pros and cons of each are discussed via a simple and reproducible illustrative example. One of the four methods (method 1 ‘direct analysis’) provides a ‘benchmark’ result (i.e., using all simulated ground motions), enabling the consistency of the other three more efficient selection methods to be addressed. Method 2 (‘stratified sampling’) is a relatively simple way to achieve a significant reduction in the number of ground motions required through selecting subsets of ground motions binned based on an intensity measure, IM. Method 3 (‘simple multiple stripes’) has the benefit of being consistent with conventional seismic assessment practice using as‐recorded ground motions, but both methods 2 and 3 are strongly dependent on the efficiency of the conditioning IM to predict the seismic responses of interest. Method 4 (‘generalized conditional intensity measure‐based selection’) is consistent with ‘advanced’ selection methods used for as‐recorded ground motions and selects subsets of ground motions based on multiple IMs, thus overcoming this limitation in methods 2 and 3. Copyright © 2015 John Wiley & Sons, Ltd.     

A generalized conditional intensity measure approach and holistic ground‐motion selection

A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

A stochastic model of the Fourier phase of strong ground motion

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Detection of soil liquefaction from strong motion records

During the recent earthquakes in Japan and the U.S.A. a number of records from liquefied‐soil sites have been obtained. The ground motion parameters from these sites were studied and several methods for detection of liquefaction from seismic records were developed. The methods, however, focus mainly on the horizontal ground motion and may interpret as liquefaction‐induced some records from soft‐soil deposits or records with dominant surface waves, at which sites the phenomenon was not observed. Besides, not all of the available records from liquefied sites were processed. In this paper, after examination of the ability of different types of ground motion parameters to indicate alone soil liquefaction we propose a new liquefaction detection method that simultaneously analyses instantaneous frequency content of the horizontal and the vertical ground acceleration. We also compare performance of the proposed method with that of the other liquefaction detection methods. The computations are carried out using a common data set including records from liquefied and non‐liquefied sites. Results show that the frequency‐related parameters and the proposed method detect more efficiently the occurrence of liquefaction from the seismic records. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

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.     

竖向地震动对大跨度高断面Y形柱地铁车站地震响应分析研究

以北京地铁6号线新华大街站公共区Y型柱地铁车站为工程背景,利用FLAC3D有限差分程序数值模拟分析,研究超浅埋大跨度、高断面、Y形柱地铁车站结构分别在仅输入水平向地震动和同时输入水平向与竖向地震动情况下的地震响应特性。结果表明:(1)与仅输入单向地震动相比,双向地震动耦合作用下车站各测点的峰值加速度和应力值均增大,而相对水平位移减小,且随着输入地震动强度的增加,竖向地震动影响率呈递减趋势;(2)双向地震动作用下,同一工况Y形柱叉支处各测点的竖向位移明显增大,且各测点的竖向位移值较为均匀,而单向水平地震动作用下各测点竖向位移差异较大;(3)与单向水平地震动相比,竖向地震动的输入对各测点间的水平方向地震动特性规律影响较小。     

基于实测记录分析场地因素对海底地震动特性影响

目前基于海底实测记录的分析发现海底与陆地地震动特性存在明显差异,但难以进一步确定海底地震动特性的影响因素。在以往研究的基础上对比同次地震中相邻海底台站间地震动特性的差异,并分析造成差异的原因。以日本K-NET地震台网中6个海底强震台站及其相邻不同场地条件陆地台站监测的8次强震记录为研究对象,通过分析强震记录的峰值加速度、水平放大系数谱、竖向与水平反应谱的比谱等,对比分析不同海底台站地震动的特性,以及海底台站与相邻不同场地条件陆地台站地震动特性的差别。研究发现：（1）海底与陆地竖向地震动存在明显差异;（2）不同海底台站间地震动特性亦存在较大差异和明显的规律性,海底场地条件、地形等场地因素对海底地震动特性的影响较大;（3）海底水平向地震动反应谱的特征周期较大,谱特性介于陆地中硬土与软土场地间。     

Collapse assessment of moment frame buildings,considering vertical ground shaking

While many cases of structural damage in past earthquakes have been attributed to strong vertical ground shaking, our understanding of vertical seismic load effects and their influence on collapse mechanisms of buildings is limited. This study quantifies ground motion parameters that are capable of predicting trends in building collapse because of vertical shaking, identifies the types of buildings that are most likely affected by strong vertical ground motions, and investigates the relationship between element level responses and structural collapse under multi‐directional shaking. To do so, two sets of incremental dynamic analyses (IDA) are run on five nonlinear building models of varying height, geometry, and design era. The first IDA is run using the horizontal component alone; the second IDA applies the vertical and horizontal motions simultaneously. When ground motion parameters are considered independently, acceleration‐based measures of the vertical shaking best predict trends in building collapse associated with vertical shaking. When multiple parameters are considered, Housner intensity (SI), computed as a ratio between vertical and horizontal components of a record (SI_V/SI_H), predicts the significance of vertical shaking for collapse. The building with extensive structural cantilevered members is the most influenced by vertical ground shaking, but all frame structures (with either flexural and shear critical columns) are impacted. In addition, the load effect from vertical ground motions is found to be significantly larger than the nominal value used in US building design. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of seawater on incident plane P and SV waves at ocean bottom and engineering characteristics of offshore ground motion records off the coast of southern California,USA

The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).     

Regional variation of spectral parameters for seismic design from broadband probabilistic seismic hazard analysis

The characterisation of the seismic hazard input is a critical element of any seismic design code, not only in terms of the absolute levels of ground motion considered but also of the shape of the design spectrum. In the case of Europe, future revisions of the seismic design provisions, both at a national and a pan‐European level, may implement considerable modifications to the existing provisions in light of recent seismic hazard models, such as the 2013 European Seismic Hazard Model. Constraint of the shape of the long‐period design spectrum from seismic hazard estimates on such a scale has not been possible, however, owing to the limited spectral period range of existing ground motion models. Building upon recent developments in ground motion modelling, the 2013 European Seismic Hazard Model is adapted here with a new ground motion logic tree to provide a broadband Probabilistic Seismic Hazard Analysis for rock sites across a spectral period range from 0.05 seconds to 10.0 seconds. The resulting uniform hazard spectra (UHS) are compared against existing results for European and broadband Probabilistic Seismic Hazard Analysis and against a proposed formulation of a generalised design spectrum in which controlling parameters can be optimised to best fit the uniform hazard spectra in order to demonstrate their variability on a European scale. Significant variations in the controlling parameters of the design spectrum are seen both across and within stable and active regions. These trends can help guide recalibrations of the code spectra in future revisions to seismic design codes, particularly for the longer‐period displacement spectrum.     

台湾集集地震近场地震动的上盘效应

1999年9月21日（当地时间）台湾集集7.6级地震是一个逆断层型地震．用回归分析法对台湾集集地震的加速度峰值数据进行分析，得出了这次地震的水平与垂直向的加速度峰值衰减关系．从残差分布上看，位于断层上盘和下盘上的加速度峰值与从衰减关系所得到的结果相比存在不同的系统偏差，断层上盘地表的加速度峰值较高，而下盘地表的加速度峰值较低．从这次地震的加速度峰值分布等值线图上也可以看出，加速度峰值的分布相对于断层呈现明显的不对称性，上盘衰减较慢而下盘衰减较快．在近断层强地面运动研究、地震危险性分析、设定地震研究与震害预测等工作中，应考虑可能地震的震源机制特点，以便使所用的衰减模型更能反映不同地震环境地区的地震动分布特征．      

旋转地震合成及其在大跨度悬索桥中的应用

为探究旋转地震动在大跨度悬索桥中的应用,首先,从线弹性理论和功率谱角度基于随机振动理论提出了6维地震动加速度功率谱模型;其次,基于MATLAB编制旋转地震动人工地震合成程序,从反应谱角度对合成地震动进行了正确性验证和拟合精度迭代调整;最后,分析了旋转地震动与地震动入射角对桥梁结构地震响应的影响。研究表明：人工合成的地震动平动分量反应谱与实测地震动的平动分量反应谱吻合度较高;六维地震动的主梁跨中竖向位移越是三维平动地震动的3倍,而主缆轴力峰值接近2.25E+05kN,约是三维平动地震动的1.3倍;旋转地震动和地震动入射角将会加大桥梁结构的位移响应和内力响应,且会减小塔底截面和桩最不利截面的安全性。