地震动空间相干函数的极限性质

基于弹性理论中旋转与平移之间的微分关系，研究了当空间两点间距离趋于零时地震动空间相干函数的极限性质．结果表明，为满足这一微分关系，在建立小范围地震动随机场模型时，空间相干函数的选择必须满足一定的函数特征，不能完全凭经验统计方法来验定其函数形式．同时指出，基于随机地震动场估计旋转地震动分量功率谱密度的关键，是精确地确定地震动空间相干函数关于空间坐标的二阶导数．      

地震动空间变化随机描述及相干函数模型研究进展

本研究主要讨论地震动空间变化的随机描述.首先给出了基于密集地震台阵记录估计相干函数的方法,并对计算中需要关注的问题给出了相应的解释;然后对现有的经验和半经验相干函数模型的建立进行了详细的梳理,并对模型在工程应用中的适用性、有效性和局限性进行了讨论;最后通过对比分析不同相干函数模型对场址地震动空间相关性的模拟结果,对相干函数模型的选择提出了建议.     

基岩地震动的一个相干函数模型-走滑断层情形h

目前研究地震动空间变化的主要方法是利用密集台阵（如SMART1台阵等）的强震观测记录进行统计分析，由于地震动观测资料的不足，因而缺少基岩及不同场地类别地震动相干函数模型. 本文利用数值方法了模拟理论地震图，进而研究采用震源位错模型的基岩随机地震动的空间变化规律，并考虑震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响. 其具体思路为:首先对应于每个样本，用有限差分数值模拟方法计算弹性半空间近场地震动场，而后对所有样本的计算结果进行统计，给出了一个走滑断层情形下的近场基岩表面及沿基岩竖直方向水平分量地震动的相干函数模型.      

同一测点不同地震动分量空间相干性分析

利用SMART-1台阵的3次地震记录计算了同一测点三平动地震动分量问的相干值,并提出了相干函数模型。分析表明,同一测点各地震动分量间是低相干的,随频率衰减不明显;两水平分量问的相干性比水平分量与垂直分量间的相干性大。因此在工程计算中不计相干函数随频率的变化不会带来太大的误差。     

工程场地地震动相干函数的数值模拟

在确定性波动有限元分析基础上,结合随机振动分析的虚拟激励原理,可以形成工程场地随机波动分析方法。该方法将随机输入下的波动分析问题转换为多个虚拟激励下的确定性波动分析组合问题,从而可以方便地获得场地波动观测量之间的谱密度矩阵,进而计算给出工程场地的地震动相干函数。本文阐述了随机波动分析的基本原理,提出了该方法的正确性验证标准。将建议方法分别应用于具有一致随机激励与非一致随机激励的复杂工程场地的地震动相干函数分析之中,讨论了受局部场地条件影响的地震动相干函数的若干特征。     

非一致激励条件下工程场地地震动相干函数的数值模拟--Ⅱ分析方法的应用

在文《非一致激励条件下工程场地地震动相干函数的数值模拟———Ⅰ分析原理和方法》中,通过将随机振动的虚拟激励原理与工程波动理论散射问题的求解方法相结合,提出了开放系统中非一致激励条件下工程场地地震动随机场的数值模拟方法。本文将建议方法应用于具有非一致随机激励的复杂工程场地的地震动相干函数分析之中,讨论了受局部场地条件影响的地震动相干函数的若干特征。     

基于AR模型的相干函数有效频段范围的确定

目前人们在进行地震动相干函数模型参数的拟合时,选取的频段范围存在很大差异,而确定有效的频段范围对相干函数模型拟合结果的合理性很重要。本文利用AR模型(Autoregressive Model,自回归模型)计算地震动的功率谱,提出了根据功率谱"信噪比(SNR)"确定相干函数有效频段范围的方法。本文的信噪比中的"噪",专指AR模型中的激励白噪声,用于衡量AR模型中某一频率地震动功率谱与激励白噪声功率谱之间的比例。定义信噪比SNR=0时对应的频率为有效频段的最高频率,大于最高频率的频率成分,被当作是地震波中的随机成分,可以不考虑地震动的相关性。采用这一方法,对SMART-1第45次地震记录的不同台站间距下的地震波进行了功率谱估计,根据信噪比确定出了有效频段范围,并计算了相应的相干函数,结果表明此方法是可行的。     

空间相关的多点地震动合成(Ⅱ)合成实例

本文应用已提出的自功率谱、相干函数、视速度模型生成了空间相关的多点地震动时程。采用分段合成、乘强度包络函数的方法近似地考虑了地震动强度和频率尬发的非平稳性、生成的地震动符合空间相关性、传播性、随机性和非平稳性,可用于长结构多点输入地震反应分析。     

地震动多点差异输入对架空管道地震响应影响研究

架空管道由于地震波传递、地震动衰减以及场地不均匀产生各支撑点地震动差异,为了研究这种差异对架空管道地震响应的影响,通过有限元软件ADINA建立架空管道有限元模型,利用MATLAB软件编写具有相干效应的人工地震波,计算分析了多点地震动相干函数法输入、行波输入与一致输入下地震响应。结果表明:①随着视波速的增加管道轴向应变变小,有接近一致激励情况的趋势;②同一相干函数模型,考虑和忽略场地效应,管道轴向应变最大值存在差异;不同相干函数模型,管道轴向应变最大值也存在差异。结论认为,如果场地比较均匀且管段较短,可采用行波法进行地震输入;长柔管道应采用相干法进行地震响应分析,场地不均匀的长柔管道,应同时考虑场地效应。     

地震动空间相干函数模型中拟合参数的修正

采用SMART-1台阵第5次和第45次地震的水平向分量加速度记录,首先计算了不同间距台站对的地震动空间相干函数;然后讨论了台站距离对相干函数拟合结果的影响,即某一特定距离的相干函数与所有不同距离的相干函数的拟合结果存在明显差异。为减小这一差异,提出了一种对各个不同距离的相干函数拟合参数进行二次回归的方法,并选用Loh相干函数模型进行了验证,最后给出了基于Loh相干函数模型的拟合参数的修正结果。结果表明本文提出的修正方法将大大提高相干函数模型中参数的拟合精度。      

Influence of irregular topography and random soil properties on coherency loss of spatial seismic ground motions

Coherency functions are used to describe the spatial variation of seismic ground motions at multiple supports of long span structures. Many coherency function models have been proposed based on theoretical derivation or measured spatial ground motion time histories at dense seismographic arrays. Most of them are suitable for modelling spatial ground motions on flat‐lying alluvial sites. It has been found that these coherency functions are not appropriate for modelling spatial variations of ground motions at sites with irregular topography (Struct. Saf. 1991; 10 (1):1–13). This paper investigates the influence of layered irregular sites and random soil properties on coherency functions of spatial ground motions on ground surface. Ground motion time histories at different locations on ground surface of the irregular site are generated based on the combined spectral representation method and one‐dimensional wave propagation theory. Random soil properties, including shear modulus, density and damping ratio of each layer, are assumed to follow normal distributions, and are modelled by the independent one‐dimensional random fields in the vertical direction. Monte‐Carlo simulations are employed to model the effect of random variations of soil properties on the simulated surface ground motion time histories. The coherency function is estimated from the simulated ground motion time histories. Numerical examples are presented to illustrate the proposed method. Numerical results show that coherency function directly relates to the spectral ratio of two local sites, and the influence of randomly varying soil properties at a canyon site on coherency functions of spatial surface ground motions cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

A stochastic approach to site-response component in seismic ground motion coherency model

In order to account for the site-response part of the seismic ground motion coherency for sites of interest, an analytical stochastic methodology is proposed in this paper. By combining the pseudo-excitation method with wave motion finite element simulation techniques, a numerical approach for the computation of the coherency function between observation points is developed firstly. Then the orthogonal expansion method is introduced into this approach to study the effect of the uncertainty in soil properties on the coherency function. Finally some numerical examples are given to show the applicability of the methodology. The computational results demonstrate that the lagged coherency values tend to decrease in the vicinity of the resonant frequencies of the site.     

非一致激励条件下非线性工程场地地震动相干函数研究

将土非线性分析的等效线性化方法与随机工程波动散射问题的求解方法相结合，建立了开放系统中非一致激励条件下考虑岩土介质非线性的工程场地地震动随机场数值模拟方法并研究了介质非线性对场地地震动相干性的影响。分析结果表明：与不考虑非线性相比，在地震过程中，场地土介质的非线性改变了复杂场地的局部特性从而导致场地地震动空间相干性的变化，因此有必要在场地地震动相干函数的分析中考虑场地介质非线性特性对地震动相干性的影响。     

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.     

Modeling of soil heterogeneity and its effects on seismic response of multi-support structures

This paper addresses the analytical evaluation of soil lateral heterogeneity effects,especially the random fluctuations of the soil layer's predominant frequency,on the spatial coherency of ground motion and the seismic response of multi-support structures.A coherency probabilistic model is proposed.In this model,the spatial variation of motion is attributed to wave passage effects,effects of loss of coherence in the bedrock motion and particularly site response effects(based on the assumption of vertically propagating shear-waves through a horizontal layer with random characteristics).The results indicate that soil lateral heterogeneity effects tend to cause diminution of the values of the total coherency function.This diminution is not limited to the vicinity of the mean resonant frequency of the layer,but reaches considerably high frequencies even for relatively low values of coefficient of variation(CV of 5 to 15%).Therefore,the trend of the total coherency function(exponential decay) can be influenced significantly by site effects.Finally,the proposed coherency model is applied for two different support seismic excitations.Study results indicate that the greater the soil heterogeneity,the larger are the dynamic displacements and shear forces in the columns of the oscillator(i.e.,support structure).Furthermore,these two components of the response are influenced differently by soil heterogeneity effects.     

Estimating ground motion incoherence through finite source simulation: a case study of the 1980 El-Asnam Earthquake

Spatial variability of ground motions has significant influence on dynamic response of extended structures such as bridges and tunnels. In this study, the widely used finite-source ground motion simulation approach, the so-called Empirical Green’s Function (EGF) method, is extended to synthesize seismic motions across an array of stations located at bedrock in the epicentral region of the 1980 El-Asnam region (North-West Algeria). The target event being simulated is the October 10 1980 \( M_{s} = 7.2 \) Earthquake, and the EGF is obtained from the ground motion recorded at Sogedia Factory station during the 8 November 1980 \( M_{L} = 5.6 \) aftershock. Coherency functions are then estimated from the simulated ground accelerations. A parametric study investigating the influence of shear wave velocity, earthquake magnitude, and epicentral distance is conducted by simulating ground acceleration for different scenarios using the Hybrid Green’s Function method. The main finding of the study is that finite source effects can cause significant loss in coherency at bedrock in the near-field. In the far-field, the source effect alone does not seem to produce incoherent motion, which implies that scattering and local site effects could be dominating there. Furthermore, coherency functions are found to be more sensitive to inter-station separation in the near-field than in the far-field. Increasing shear wave velocity seems to increase coherency functions, and larger earthquakes seem to produce more incoherent motion than smaller ones. The simulation method presented here produces incoherent motion mainly due to the finite source effect, while path effects are partially accounted for through the EGF, and local site effects are not considered. In this sense, the estimated coherency functions represent that of plane waves. A parametric model of plane wave coherency is calibrated and presented based on the simulation results. The results indicate that the parametric model can be used as a first approximation, and at least an upper bound of lagged coherency in the near-field region of the El-Asnam Earthquake scenario. This model could be useful in random vibration analysis or generation of spatially variable ground motion for time history analysis of lifeline structures in the study area.     

考虑岩土介质随机特性的工程场地地震动相干函数研究

将随机结构正交展开理论和随机振动分析的虚拟激励原理运用于场地波动有限元分析，形成了一种可以考虑岩土介质随机特性对工程场地地震动相干函数影响的分析方法。实例分析表明，非严格均匀分布的随机介质场地对场地表面的迟滞相干函数值有重要影响，这种影响可由场地的随机影响因子来衡量，在进行工程场地地震动随机场研究时应当考虑场地介质随机特性的影响。     

A coherency function model of ground motion at base rock corresponding to strike-slip fault

IntroductionEarthquakedamagesurveyandresearchresultshavedemonstratedthatspatialdistributiondifferenceofgroundmotionisoneoftheimportantreasonswhichcausedlongstructure(eglongspanbridge,undergroundpipe)destroy.Thathowtoprovideareasonableinputofgroundmotionfieldforaseismicdesignoflongstructureisaurgentprobleminearthquakeengineeringfield.Atpresent,themethodtostudyspatialvariationofgroundmotionsisadoptingstatisticanalysisbasedondensearrayrecordssuchasSMART-1array,etc,togetcoherencyfunctionofground…     

Spatial variation and conditional simulation of seismic ground motion

Spatially varying ground motion (SVGM) may have influence on certain civil engineering structures with spatially extended superstructure and/or substructures. Conditional simulation of spatially varying ground motion (CSSVGM) may be viewed from two different perspectives. Most procedures available in the literature neglect the spatial variability in auto-spectral density (ASD) and estimate the SVGM through cross-spectral density (CSD) which was computed using the empirical coherency models. This paper proposes a coherency model that accounts for the spatial variability of ASD. A framework has been developed for the CSSVGM, through the mapping of both proposed coherency model and ASD over the footprint of an array. Current framework (existing in the literature) accounts for only the phase variability of SVGM while proposed framework accounts for both phase and amplitude variability. Ground motion generated from both perspectives is then assessed with the data recorded over SMART1 and LSST arrays. For the purpose of assessment, a definition of target spectrum based on the direction of arrival is explored. The effect of choice of coherency model on the simulated spatially varying ground motion is investigated first. Spectra resulting from both the perspectives are assessed against the target spectrum. An attempt has been made to predict the SVGM for a future event using a coherency model calibrated against a past event and an estimate of ASD of the seed ground motion. Finally, the effect of form of ASD (of a seed ground motion) on SVGM simulated is investigated by considering the ASD in different forms. Simulating SVGM through the mapping of both coherency model and ASD seems to be more appropriate than through CSD.