Seismological evidence for nonlinear elastic ground behavior during large earthquakes

Amplification of earthquake-induced seismic waves by soft superficial deposits often causes significant damages in the urban areas. In predicting this effect for large future earthquakes, the linear elastic response of soils is customarily assumed. To check this assumption, we have analyzed surface and downhole acceleration data from the SMART1 and SMART2 strong motion arrays in Taiwan, covering peak accelerations of up to 0·3 g. First, frequency-dependent amplification induced by the alluvial deposits at the SMART1 array was estimated using spectral ratio technique, where the records at rock site were taken as a reference motion. Statistically validated reduction in soil amplification in the strong motion relative to the weak motion in the frequency range between approximately 1 and 9 Hz was detected. Secondly, relative site responses between the Pleistocene and recent sedimentary deposits at the SMART2 array were studied. Relative amplification was shown to be clearly dependent on the excitation level. Thirdly, we compared experimentally recorded uphole/downhole spectral ratios on weak and strong ground motion with the theoretical response yielded by the geotechnical code DESRA2 which assumes hysteretic constitutive relationship of soil. Major symptoms of nonlinear ground behavior predicted by the model were found in the observed data. Back-calculation of the shear wave velocities to the depth of 47 m shows nearly 50% decrease in the strongest quakes, also accounted for by the nonlinear soil behavior.     

ON THE CHARACTERISTICS OF NON-LINEAR SOIL RESPONSE AND DYNAMIC SOIL PROPERTIES USING VERTICAL ARRAY DATA IN JAPAN

Non-linear response of the soil is investigated by comparing the spectral ratios (uphole/downhole) using weak and strong motions. Data from seven vertical arrays in Japan are analysed in this study. The frequency-dependent transfer function of soil is calculated as a ratio of the spectrum at uphole to the spectrum at downhole, considering the horizontal component of shear wave. In spectral ratio analysis auto- and cross-spectra are employed. The reduction in the predominant frequency of the transfer function with increases in excitation level reflects the non-linear response of the soil. Results of analysis demonstrate a significant non-linear ground response at six sites with surface PGA exceeding 90 gal. However, the results of one site show the linear response up to 130 gal surface PGA. Furthermore, the in situ strain-dependent soil behaviour is examined through the shear modulus – shear strain relationship. When compared, the actual and laboratory results of the shear strain – shear modulus relationship are in agreement. Additionally, a good consistency between the tendency of reduction in shear modulus ratio with shear strain increases, and reduction of predominant frequency with ground motion increases, confirms the significance of non-linearity in site effects study.     

Inverse analysis of weak and strong motion downhole array data from the Mw7.0 Sanriku-Minami earthquake

A hybrid optimization scheme, comprising a genetic algorithm in series with a local least-squares fit operator, is used for the inversion of weak and strong motion downhole array data obtained by the Kik-Net Strong Motion Network during the M_w7.0 Sanriku-Minami Earthquake. Inversion of low-amplitude waveforms is first employed for the estimation of low-strain dynamic soil properties at five stations. Successively, the frequency-dependent equivalent linear algorithm is used to predict the mainshock site response at these stations, by subjecting the best-fit elastic profiles to the downhole-recorded strong motion. Finally, inversion of the mainshock empirical site response is employed to extract the equivalent linear dynamic soil properties at the same locations. The inversion algorithm is shown to provide robust estimates of the linear and equivalent linear impedance profiles, while the attenuation structures are strongly affected by scattering effects in the near-surficial heterogeneous layers. The forward and inversely estimated equivalent linear shear wave velocity structures are found to be in very good agreement, illustrating that inversion of strong motion site response data may be used for the approximate assessment of nonlinear effects experienced by soil formations during strong motion events.     

剪切波速对场地地表地震动参数的影响

本文以江淮地区典型场地资料为原型,将土层剪切波速实测值按照一定比例进行增减,构造多种场地土层地震反应分析模型,选择Taft、E1centro和Kobe三条强震记录作为地震输入,采用一维频域等效线性化波动方法进行了土层地震反应分析.研究结果表明,剪切波速的变异性与场地地表地震动的影响程度与输入基岩地震动的频谱特性、幅值、土层结构等因素有关.地表峰值加速度随着剪切波速的增大而逐渐增大,地表加速度反应谱的特征周期随着剪切波速的增大而逐渐减小.     

Nonlinear behaviour of scoria soil sediments evaluated from borehole records in eastern Shizuoka prefecture,Japan

We evaluate the non-linear behaviour of soil sediments, analysing five weak and four strong motions observed at depths of 1 m and 28 m, in eastern Shizuoka prefecture, Japan. We identify S-wave velocities and frequency-dependent damping factors by minimizing the residual between observed and theoretical spectral ratios, based on a linear one-dimensional model. We find that S-wave velocities identified from strong motions, whose peak ground acceleration are 440, 210, 176, and 140 cm/s², are significantly smaller than those identified from weak motions. The shear modulus reduction ratios estimated from identified S-wave velocities become clear above an effective shear strain of 10^-4 and agree with laboratory test results below an effective shear strain of 8×10^-4. The differences of damping factors between weak and strong motions are not clear below this effective shear strain, as the laboratory test suggested. The equivalent linear one-dimensional model, with frequency-dependent damping factors, is confirmed to be valid to simulate strong motions at least an effective shear strain of less than 4×10^-4. © 1997 John Wiley & Sons, Ltd.     

Equivalent linear method considering frequency dependent characteristics of stiffness and damping

Equivalent linear dynamic response analysis of ground is based on complex moduli and Fourier series expansion; therefore, it is not an equivalent method but an approximate method. Two deficiencies in the conventional equivalent linear method represented by SHAKE are described first. The maximum shear strength is overestimated, resulting in overestimation of the peak acceleration under a strong ground motion, and the amplification is underestimated at high frequency. The latter sometimes results in underestimation of the peak acceleration under weak ground shaking, and gives an incident wave with unrealistic large accelerations or a divergence of analysis in deconvolution analysis under strong ground motion. Both deficiencies are shown to come from the same cause, i.e. computing the effective strain as a constant fraction of the maximum strain. Since this is a key concept of the equivalent linear analysis, one cannot overcome both deficiencies at the same time in the conventional method. An apparent frequency dependence in stiffness and damping is shown to appear in the dynamic response, although soil itself does not show frequency dependent characteristics. Following this observation, the effective strain is expressed in terms of frequency from the similarity concept of the strain–frequency relationship between time domain and frequency domain. This enables the reduction of both deficiencies at the same time, resulting in a marked improvement in the equivalent linear analysis. The accuracy of the proposed method is examined by the simulations of three vertical array records during large earthquakes. The proposed method always gives much better prediction than conventional equivalent linear methods for both convolution and deconvolution analyses, and it is confirmed to be applicable at more than 1% shear strain.     

Site response analyses using downhole arrays at various seismic hazard levels of Singapore

Local site conditions can significantly influence the characteristics of seismic ground motions. In this study, site response analyses using one-dimensional linear elastic (LE), equivalent-linear (EQL) and nonlinear (NL) approaches are performed at different seismic hazard levels of Singapore. Two seismic stations, namely, the KAP and BES stations located at soft soil sites, are selected from the national network of Singapore. Firstly, site response estimates using the LE, EQL (SHAKE04) and NL (DEEPSOIL) approaches are compared with the borehole recordings. Results show favorable matches between the predictions and the observations at the KAP site, while under-predictions are observed for all the three site effect approaches at the BES site. Secondly, the applicability of the LE, EQL and NL models is examined at different hazard levels of Singapore. It is found that for the hazard level at a return period of 475 years, the computed maximum strain (γ_max) is 0.06% and then the EQL model can provide accurate site response predictions. However, for the hazard level at a return period of 2475 years, the calculated γ_max is larger than 2%, resulting in notable differences in the predictions of different site response models. This study highlights the importance of site effects in seismic hazard analysis of Singapore.     

地震荷载下土层变形等级预测方法研究

以计算结果可靠的土层反应结果为基础数据,基于随机森林算法（Random Forest,简称“RF”）,建立地震动、场地土层参数特征量与土层变形特征的关系,提出一种依据常规地震动和场地土层参数为特征量的地震荷载下土层变形等级预测新方法,给出了典型场地土体发生大应变的地震动阈值。结果表明:基于RF模型对土体的变形程度预测结果较为理想,各项评价指标始终保持一个较高水平;对于软土、中硬土及硬土场地,输入地震动分别大于0.05 g、0.15 g及0.19 g时,将产生大应变。同时,本文方法可在不进行土层地震反应数值模拟的情况下,得到场地各土层的剪应变等级,为强地震作用下土体实际力学状态的界定和认识提供新的分析手段,而且也可为地下结构抗震设计问题提供指导和参考。     

Dynamic responses of structure–soil–structure systems with an extension of the equivalent linear soil modeling

A three-dimensional problem of cross interaction of adjacent structures through the underlying soil under seismic ground motion is investigated. The story shears and lateral relative displacements (drifts) are the targets of the computations. These are calculated using a detailed modeling of soil, the foundations and the two adjacent structures. An equivalent linear behavior is assumed for the soil by introducing reduced mechanical properties consistent with the level of ground shaking for the free-field soil. Then a distinctive soil zone (the near-field soil) is recognized in the vicinity of the foundations where the peak shear strain under the combined effect of a severe earthquake and the presence of structures is much larger than the strain threshold up to which the soil can be modeled as an equivalent linear medium. It is shown that it is still possible to use an equivalent linear behavior for the near-field soil if its shear modulus is further reduced with a factor depending on the dynamic properties of the adjacent structures, the near-field soil, and the design earthquake. Variations of the dynamic responses of different adjacent structures with their clear distances are also discussed.     

Analysis of nonlinear site response using the LSST downhole accelerometer array data

Both linear and nonlinear behaviors of soil deposits were evaluated by strong and weak motion data observed on the surface and at depths of 6, 11, 17, 47 m at the Large Scale Seismic Test (LSST) array in Lotung, Taiwan. The soil properties measured by well logging and by the shear wave velocity profile measured by uphole and cross-hole methods are available. Both one-dimensional equivalent-linear method and nonlinear method are used for the evaluation have been used. The synthetic records at various depths are obtained by using the records at the bottom as input motion. These synthetic records are then compared with actual records at corresponding depths. Records of 13 earthquakes are used. We find that the synthetic records obtained from a linear model match well with actual records for small input motions, but the results obtained from a nonlinear model match poorly. On the other hand, the synthetic records using both the nonlinear model and equivalent-linear model are in good agreement with the observed records for large input motions. In these cases, the predicted response spectra using the linear model consistently overestimate the observed records. The threshold distinguishing the large and small input motions is 0.04 g at depth of 47 m for the LSST data. Thus, the nonlinearity started at 0.04 g and occurred unequivocally at 0.075 g. Furthermore, the dominant frequencies shift toward lower values when input motions become large. Clearly, the observed records at the LSST site manifest nonlinearity of soil response. The hysteresis loops evaluated by the nonlinear method show a permanent strain of about 0.01% in soil layers at higher ground motion input levels in this case.     

天津滨海软土场地的大震远场作用

利用天津滨海地区丰富的地震地质钻孔资料及测试数据,建立了相应的地震反应模型.选取美国加州1992年Landers地震的远场记录P0841作为基底输入,采用工程上常用的等效线性化方法进行了土层地震反应分析,以期对天津滨海软土场地的大震远场作用得到一些定性的认识．结果显示,天津滨海软土场地对远场大震地震动峰值加速度的放大作用比较显著,但不同场地条件放大作用有明显差异,Ⅳ类场地的放大效应明显减弱.对基岩与地表反应谱比的分析显示, 滨海场地对基岩地震动的不同频率分量的放大作用具有明显的不同,对短周期分量甚至出现了缩减,但当滨海软土场地受到与场地卓越周期相吻合的地震动影响时,可能会产生很可观的放大作用,这对建在其上的高层、超高层建筑可能会构成较大的威胁．      

等效线性场地响应程序对比研究

为了评价4种等效线性场地响应软件的适用性,选取深厚场地作为研究对象,将基岩地震波作为地震输入,根据土层剪切波波速和容重确定初始剪切模量并设置对应的模量衰减和阻尼比曲线,分别用SHAKE 2000、 DEEPSOIL、EERA和Strata 4种等效线性场地响应程序计算得到地表的加速度时程及相应的加速度反应谱和傅里叶幅值谱\,场地的最大剪应变和峰值加速度随深度的变化曲线。计算结果表明,由4种场地响应软件得到的地表加速度时程对应的加速度反应谱和傅里叶幅值谱一致,由于土层划分方式不同,Strata软件得到的峰值加速度和最大剪应变深度曲线不同。总结4种软件的不同,DEEPSOIL可以较全面考虑土的动力特性,Strata提供随机振动理论进行场地响应分析并可以考虑土层参数的变异性。     

土体地震反应分析的简化有效应力法

本文提出了一个计算二维土体地震反应的简化有效应力法。该方法将整个地震特时分成若干时段，对每个时段用等效线性迭代进行次线性分析，等效剪应变幅值取该时剪应变均方根值的√２倍。     

基于等效线性化方法的一维土层地震反应通用计算程序对比

基于等效线性化的一维土层地震反应计算是目前国内外普遍采用的方法,国外的SHAKE91、DEEPSOIL和我国的LSSRLI-1即是根据这一方法编制的通用计算程序。本文采用这3个程序进行了不同地震波、不同输入地震动幅值下不同场地类型的土层地震反应计算,并对三者的结果进行了全面的比较分析。结果表明:①SHAKE91和DEEPSOIL程序的计算结果完全相同;②当土层最大剪应变均采用时域计算时,LSSRLI-1程序的计算结果与SHAKE91和DEEPSOIL程序基本相同,但有微小差别,其原因是:在基于等效剪应变通过离散形式的剪切模量和阻尼比随等效剪应变变化的关系曲线确定等效剪切模量和阻尼比时,DEEPSOIL和SHAKE91采用的插值方法与LSSRLI-1不同;③当LSSRLI-1程序采用频域经验关系计算土层最大剪应变时,特别是在强地震动输入下得到的土层地表加速度峰值和加速度反应谱与另外两个程序的计算结果有差别,且土层最大剪应变随着输入加速度的增大出现较大的差别。因此,本文建议:当采用LSSRLI-1程序计算土层地震响应时,应使用程序中的时域解方法代替以往默认的频域经验关系方法。     

浅硬场地剪切波速测试标准差对地震动影响初探

采用Shake 2000程序,以Turkey Flat试验场地为模型,通过输入不同类型下多种强度的地震波,计算研究多工况下剪切波速测试标准差对地表加速度反应谱和峰值加速度的影响。结论为:(1)浅硬场地上剪切波速测试标准差对地震动的影响很大,影响程度与输入地震波的强度和频率以及场地剪切波速计算值有关;(2)如果将反应谱残差大于20%或加速度峰值差别大于20%定义为统计意义上的不可忽略,那么剪切波速测试标准差对计算结果的影响在大多数情况下均不可忽略;(3)当输入波的卓越周期与场地特征周期接近时,浅硬场地上剪切波速测试标准差引起的反应谱变化非常显著;(4)只有当输入波的卓越周期与场地特征周期相差较大且输入波强度偏小时,剪切波速测试标准差引起的反应谱变化才可略去;(5)当浅硬场地上剪切波速实测结果低于统计均值时,地震动计算结果的偏差一般明显大于剪切波速实测结果,高于统计均值时引起的偏差,且地震输入越强表现越明显。     

中硬场地下两种土层地震反应方法与精确解的对比

基于谐波入射下的波动理论频域精确解,导出线性时域精确解,并在Matlab环境中编制相应的计算程序;选取8个简化的中硬场地剖面,用LSSRLI-1、精确解和SHAKE2000三种方法计算各场地在不同输入条件下的地震反应。结果表明:程序计算所得地表反应谱和土体剪应变分布与SHAKE2000结果一致;LSSRLI-1方法得到的地表反应谱与前二者结果一致;LSSRLI-1方法在某些情况下得到的土体剪应变分布与另外二者结果存在较大偏差,该偏差对地表反应谱有着不可忽略甚至非常显著的影响。     

地震反应分析中输入界面的选取对地表地震动参数的影响

地震反应分析中输入界面选取合理与否对设计地震动参数有重要影响。基于唐山地区钻孔剖面,分别选取剪切波速为500m/s的硬黏土和800m/s的岩石顶面作为基岩输入界面,采用一维等效线性化方法讨论中硬场地输入界面的选取对地表地震动参数的影响,结果表明:(1)地表峰值加速度放大倍数及地表加速度反应谱特征周期都随输入界面深度的增加而递增,且这种递增与输入地震动的强度及频谱特性都有密切联系;(2)随着输入界面深度的增加,地表加速度反应谱几乎全频段内增大,仅在短周期内出现减小的情况,但幅度十分有限;(3)中硬场地地震反应分析中基岩输入界面宜取剪切波速为800m/s的土层顶面。     

渤海海域软土层土对地震动参数的影响研究

渤海海域软土层土对场地设计地震动参数取值具有显著影响.选取渤海中部钻孔剖面作为计算场地模型基础,分别构建软土和硬土场地模型,并通过改变软土层厚度,构造新的场地模型.采用等效线性化方法(EL法)和非线性计算方法(NL法)分别对场地模型进行地震反应分析,分析了海底软土层土对地震动参数的影响.研究结果表明:海底软土层土对地震...     

Simultaneous identification of time and space variant dynamic soil properties during the 1995 Hyogoken-Nanbu earthquake

Time and space variant soil properties at a liquefied site were simultaneously identified in the time domain by using borehole array strong motion records. During soil liquefaction at a site, soils usually show a wide variety of non-linear behavior along the depth as well as non-stationary behavior. Strong ground motion records were obtained at Port Island borehole array observatory, Kobe, during the 1995 Hyogoken-Nanbu earthquake. In this study, the instrumented soil was modeled by the equivalent linear MDOF system, and an extended Kalman filter with local iteration was employed for the identification of the soils. The identification process was successfully conducted, and the stress–strain relationships of the soils at the liquefied site were obtained from different depths all at once.     

基于小田原试验场地数据的不同基岩输入模型对预测地震动特征的影响研究

随着强震台网的密布及观测记录的增加,为研究各类局部场地地震反应预测模型的合理性提供了有效的参考依据,也使利用强震记录及场地条件研究地震动特征成为可能。选取场地地质参数资料和地震记录数据齐全的日本小田原（Ashigara Valley）盲测试验场地,通过对比不同地震动输入方式及场地反应分析模型,研究地震动特征,分析现有模型的优劣。基于1990年8月5日M5.1强震事件的地表基岩记录和地下基岩地震记录,采用地下台强震记录直接输入、地表基岩台强震记录减半为基底地震动输入、地表基岩台强震记录反演为基底地震动输入作为3种基岩地震动输入。基于局部场地条件分别建立一维等效线性模型、二维黏弹性模型及二维时域等效线性化模型等工程中常用的场地数值分析模型,进行局部场地地震反应分析,预测该盲测场地的地表地震动特征,并与对应的实测强震记录结果进行对比,分析不同基岩地震动输入方式对预测地震动特征及地表土层反应谱特征的影响,重点分析地震动输入、土体非线性、场地横向不均匀性及几何与非线性特征共同作用等因素对地表地震动特征的影响,以期为地表地震动的合理预测提供参考。