考虑SSI效应的层间隔震结构自振特性及随机响应分析

基于水平摇摆阻尼系统模型,建立土-层间隔震结构简化分析模型,将地基土等效到上部结构,推导得到简化模型动力特性参数表达式,并通过对结构周期比及振型参与位移进行分析,讨论质量比及土体剪切波速对层间隔震结构自振特性的影响规律。利用虚拟激励法及均匀调制非平稳随机响应分析方法,分别从时域和频域角度分析不同场地条件下SSI效应对层间隔震结构的振动响应影响。结果表明：在刚性地基下,结构质量比对结构周期比及振型参与位移的影响较小,SSI效应放大了各子结构响应,尤其对下部子结构响应影响最大,各子结构在场地土差异下变化明显,软土场地下各子结构响应变大。     

软土层几何特性与剪切波速对场地峰值加速度的影响

软土层对场地地震动的影响一直以来是地震工程学的研究重点。本文应用一维真非线性场地反应分析方法,对某单层匀质场地内软土层的几何特征(厚度与埋深)和剪切波速变化对地面峰值加速度的影响进行了数值分析。研究结果表明:软土层的存在使得场地加速度幅值分布在软土层处发生突变,随着软土层几何特性和剪切波速的不同,这种突变可能使得地面峰值加速度增大或减小;存在一个由软土层厚度、埋深和相对剪切波速三个参数构成的临界状态面,当软土层的状态位于临界面以内时,软土层对地面峰值加速度起放大效应,且加速度效应系数随着上述三个变量的增大表现出先增大后减小的变化规律;当软土层位于临界面以外时,其对地面峰值加速度起衰减效应,加速度效应系数随着上述三个变量的增大而减小。根据算例的参数分析建立了其临界面方程,并提出了估计软土层加速度效应系数的经验公式,可为类似问题提供参考。     

埋地管道-场地地震反应振动台试验研究的场地响应

基于多子台台阵系统,北京工业大学于近期开展了多点地震动输入、不同场地条件下埋地管道振动台试验。试验中连续体模型箱固定于3个振动台台面上,相邻台面上的箱体能在水平双方向(纵向、横向)相对运动;3个振动台相互独立,通过分别对3个振动台输入各自的加速度记录实现了多点地震动输入。本文针对其中的横向水平地震激励作用下的场地响应进行研究,分析了一致和非一致地震作用下有无埋地管线时的场地地震响应规律。试验结果表明,非一致激励作用将增大场地土体的相对位移,致使相邻地震动输入点间场地土体受到剪切作用;随着输入地震动强度的增加,场地土体的一阶固有频率持续降低,阻尼比不断增大;非自由场的阻尼比、一阶固有频率等参数略大于自由场。     

土层场地的放大作用随深度的变化规律研究——以金银岛岩土台阵为例

为了探究土层场地放大作用的机制,利用金银岛岩土台阵在四次地震中记录的26组弱震动的三分量加速度时程,采用考虑上行波场与下行波场相消干涉作用的传统谱比法,研究了土层场地的放大作用随深度的变化规律.结果表明：（1）地震波从基岩传播到土层中时,土层的多个振型被激励,放大作用随深度的变化是按照不同振型的特征而有规律地变化.自下而上直至地表,一阶振型的场地放大作用是逐渐增大的;二阶振型的场地放大作用经历了逐渐减小和逐渐增大两个过程;三阶振型的场地放大作用经历了逐渐增大、逐渐减小和逐渐增大三个过程;四阶振型的场地放大作用经历了逐渐减小、逐渐增大、逐渐减小和逐渐增大四个过程;更高阶振型的场地放大作用可以据此类推.（2）四次地震中同一振型的NS和EW两个水平分量的自振频率相差很小;二阶到六阶5个振型与一阶振型的自振频率之比小于相应的理论模型之比.（3）四次地震中均存在一些高阶振型的放大系数大于其一阶振型相应分量的放大系数的现象.目前的场地反应分析中,往往将最大放大系数对应的频率作为场地的卓越频率,这么做的结果,很有可能将不同振型的自振频率作为场地的卓越频率,导致同一地震中不同水平分量的卓越频率相差较大,或者在不同地震中同一水平分量的卓越频率差别较大,难以描述场地的固有特性;而按照不同振型分析场地放大作用的特征,可以从本质上揭示场地的固有特性.     

结构Pushover分析的侧向力分布及高阶振型影响

Pushover分析方法是逐渐得到广泛应用的一种评估结构抗震性能的简化方法,已被引入我国新的建筑结构抗震设计规范。侧向力分布的选取是结构Pushover分析中的一个关键问题,尤其高阶振型影响显著时其选取直接影响Pushover分析的结果。本文通过拟合规范反应谱,挑选了适用Ⅱ类场地的4条地震动记录和4条人工波,对比了典型地震动下非线性时程分析和采用5种不同侧向力分布的Pushover分析的5层、10层和15层钢筋混凝土结构在不同地震动强度时的反应。通过结构振型参与系数量化了各个结构的高阶振型的影响。研究发现,随着结构层数的增加和地震动强度的增加高阶振型的影响变大,侧向力的选取变得十分重要。本文对在高阶振型影响下钢筋混凝土框架结构的Pushover分析中侧向力的选取提出了建议。     

区域性场地V_s30及峰值加速度放大系数估算方法

地震动速报评估方法中常常考虑场地的影响,为了提高地形坡度模型的区域性地表30m的平均剪切波速Vs30估算精度,本文提出了基于工程钻孔资料的Vs30的修正方法。通过计算实际钻孔的Vs30值与坡度模型估算的Vs30值之间的残差,分析了残差的空间变化趋势,利用克里金插值对所研究区域的Vs30残差趋势面进行插值,并与估算的Vs30进行空间叠加,实现了Vs30的修正。选取K-net和Kik-net台网中台站的剪切波速资料和强震记录回归了峰值加速度放大系数与场地Vs30的经验关系,将其应用于基于ShakeMap框架的地震动快速评估系统绘制了汶川地震影响区域的基岩和地表加速度峰值,分析场地条件对于地震动的实际影响,结果表明区域性场地Vs30及峰值加速度放大系数估算方法具有一定的适用性。     

应用强震动观测资料估算2014年鲁甸MS6.5地震震源参数

通过对2014年鲁甸MS6.5地震13个强震动台站观测记录的谱分析,估算了地震矩、矩震级等震源参数,得到的平均矩震级MW=6.3。讨论了震源Brune模型位移谱形状系数以及局部场地条件对估算参数的影响,结果显示,谱形状系数对参数估算影响不大,但ω2和ω3源谱模型分别能与远场和近场记录获取的源谱吻合更好;同时,仅在场地的卓越频率小于1 Hz时,场地条件影响参数的估算,由于13个台站均处于Ⅰ~Ⅱ类场地上,局部场地条件对本文参数计算结果影响不大。     

关于结构振型参与系数和振型贡献的分析

采用振型分解反应谱法求解多自由度弹性体系的地震反应时,为了在满足所需计算精度的前提下减少工作量,需要对振型数量进行合理的选择,而振型数的确定主要取决于结构各阶振型对总体反应的贡献。通过数学推导,对振型贡献及振型数量的选择问题进行了研究。首先,讨论了振型参与系数的性质,在此基础上给出了能够反映结构振型贡献参数的数学表达式,对这些参数的力学含义进行了解释,并给出了相关证明;其次,对有效质量法、振型位移控制法等基于不同振型贡献标准的确定振型数的方法进行了分析比较,指出了其合理性和不足。本文研究对进一步理解结构振型贡献和振型数的选择问题具有一定的理论意义。     

场地脉动卓越周期在工程抗震中的应用

根据工程项目场地地震安全性评价工作中所进行的场进脉动卓越周期试和剪切波速测试结果,以及地震反应分析计算结果的研究分析,根据现行工程抗震设计规范,将场地脉动卓越周期作为工程抗震中场地土类型,场地类别划分的参考标准,以及与工程场地震反应分析计算结果回归分析,结合场地地震危险性概率分析,估算场地地震动峰值加速度,应用于工程抗震设计中。     

基于典型地质特征分析的大同盆地VS30预测研究

土体剪切波速是进行土层地震反应分析的动力学参数，对场地地震动参数确定具有重要意义。基于地质地貌分析，将大同盆地划分为5类典型地质单元。对盆地1429个钻孔剪切波速资料进行分析，探讨V_S30与V_S20的相关性，研究土体埋深、岩性、地质单元、标贯击数及密实度等地质特征对V_S的影响，并基于地质单元、剪切波速比、密实度系数及第四系上部覆盖层厚度相关性分析给出土体V_S30预测模型。研究结果表明，基于典型地质特征的V_S30预测模型拟合优度R2>0.90，预测精度很高，对于离散性较大、直接拟合估算较差及无剪切波速场地来说，以区分地质单元及土体类型的方式进行V_S30分解预测是良好的研究思路。首次在区分地质单元及土体类型的前提下提出剪切波速比及密实度系数，并将其与第四系上部覆盖层厚度综合应用于V_S30预测研究。研究结果可为大同盆地城市防震减灾规划、震害预测、区域性地震安全评价提供重要技术支撑。     

Dynamic properties of planar,coupled shear walls

The paper is a study of the natural frequencies and mode shapes of planar, coupled shear walls, a common lateral resistive element in building construction. The equations of motion are derived for the general case, and the eigenvalue problem associated with free vibrations of equal, constant shear walls is solved, both with and without the inclusion of the inertia of vertical motion. Explicit solutions are presented for the characteristic equation and the mode shapes and the results are illustrated with figures, including an example calculation based on the shear walls of the Mt. McKinley Building, damaged by the Alaskan earthquake of 1964. The results affirm the necessity of including vertical displacement of the shear walls in the analysis of such systems, and suggest that the inertia of vertical motion also must be considered in the analysis for certain ranges of the parameters.     

MODAL ANALYSIS OF SOFT-SOIL SITES INCLUDING RADIATION DAMPING

For the one-dimensional analysis of soft-soil layers on an elastic half-space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half-space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd.     

Oscillatory large-scale dynamos from Cartesian convection simulations

We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of α² Ω type, which is generally expected to be relevant for the Sun, whereas the latter case refers to α² dynamos that are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated regimes when the negative ratio of shear to rotation rates, q?≡??S/Ω, is between 1.5 and 2, i.e. when shear and rotation are of comparable strengths. Other regions of oscillatory solutions are found with small values of q, i.e. when shear is weak in comparison to rotation, and in the regime of large negative qs, when shear is very strong in comparison to rotation. However, exceptions to these rules also appear so that for a given ratio of shear to rotation, solutions are non-oscillatory for small and large shear, but oscillatory in the intermediate range. Changing the boundary conditions from vertical field to perfect conductor ones changes the dynamo mode from oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution exists only in the kinematic regime whereas in the nonlinear stage the mean fields are stationary. However, the cases with rotation and no shear are always oscillatory in the parameter range studied here and the dynamo mode does not depend on the magnetic boundary conditions. The strengths of total and large-scale components of the magnetic field in the saturated state, however, are sensitive to the chosen boundary conditions.     

Dynamic characteristics of coupled wall-frame systems

The paper presents the first three natural frequencies and the corresponding mode shapes for fixed-base multistorey buildings which can be idealized as an equivalent planar coupled shear wall connected in series to an equivalent frame. The coupled wall is modelled as a continuum of uniform properties and the frame as a uniform shear beam, the connection between the two elements being taken as continuous. Solutions are obtained by treating the structure as a lumped parameter system with twenty equidistant discrete masses having only translational inertia. The relevant flexibility matrix is, however, generated from the exact solution of the governing differential equation for the continuum subjected to point loading. The results are presented for various combinations of the three non-dimensional parameters which are sufficient to describe all the geometric and material properties of the system. The mode shapes are presented in terms of the first three normal modes of a uniform slender cantilever. The non-dimensional base shears required for the response spectrum analysis of buildings of the type under consideration are also given for the three modes and for the various combinations of the three non-dimensional parameters mentioned above. The use of the results is illustrated by an example.     

Dynamic characteristics of shear buildings on laminated rubber bearings

Analytical solutions are derived for the dynamic characteristics of base-isolated shear buildings supported on laminated rubber bearings. The solution process takes into account the combined effects of the superstructure flexibility and the base raft inertia on the dynamic characteristics. A series of parametric studies is carried out and the effects of varying the stiffness and mass of the base-isolation system on the frequencies and mode shapes are identified. Approximate solutions for the fundamental base-isolated frequency and mode shape are obtained, which are suitable for use in the preliminary design of non-rigid base-isolated buildings.     

Site effect on vulnerability of high-rise shear wall buildings under near and far field earthquakes

Worldwide experience repeatedly shows that damages in structures caused by earthquakes are highly dependent on site condition and epicentral distance. In this paper, a 21-storey shear wall-structure built in the 1960s in Hong Kong is selected as an example to investigate these two effects. Under various design earthquake intensities and for various site conditions, the fragility curves or damage probability matrix of such building is quantified in terms of the ductility factor, which is estimated from the ratio of storey yield shear to the inter-storey seismic shear. For high-rise buildings, a higher probability of damage is obtained for a softer site condition, and damage is more severe for far field earthquakes than for near field earthquakes. For earthquake intensity of VIII, the probability of complete collapse (P) increases from 1 to 24% for near field earthquakes and from 1 to 41% for far field earthquakes if the building is moved form a rock site to a site consisting a 80 m thick soft clay. For intensity IX, P increases from 6 to 69% for near field earthquake and from 14 to 79% for far field earthquake if the building is again moved form rock site to soft soil site. Therefore, site effect is very important and not to be neglected. Similar site and epicentral effects should also be expected for other types of high-rise structures.     

1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

中、美、欧抗震规范底部剪力法的对比研究

目前,底部剪力法是各国计算水平地震作用的基本方法,应用该方法时需要使用各自国家的抗震设计反应谱。本文汇总了中、美、欧抗震设计规范的反应谱和底部剪力法,在相同重现期和场地条件的基础上,对比了不同烈度下3本规范反应谱的异同,并通过算例对比了分别采用3本规范的底部剪力法算出的不同设防烈度下同一结构的底部地震剪力和层间地震剪力。对比结果表明,3本规范的反应谱和底部剪力法在本质上是相同的,只在表达形式和参数设置上存在差异。     

On faulting in a medium containing an inhomogeneity inplane and antiplane strain models

Faulting in a medium with an inhomogeneity is analysed applying two-dimensional models consisting of a shear crack in a presence of a circular inclusion. The stress drop and the stress intensity factor are calculated for mode II and III cracks of various positions in relation to the inclusion. The results demonstrate that the effect of an inhomogeneity on a shear zone strongly depends on the location of a zone for either mode II or mode III shear zone. This effect is mostly due to the spatial distribution of external effective shear stress around an inhomogeneity. Depending on the position, an inhomogeneity may have either a destabilizing effect (the stress intensity factor becomes greater) or a stabilizing influence (the stress intensity factor is decreased or faulting is prohibited so the inhomogeneity acts as an asperity or a barrier). There is a substantial difference, however, between mode II and mode III shear zones approaching an inhomogeneity centrally. Namely, the effect of inhomogeneity on the mode III shear zone located in the immediate vicinity of the inhomogeneity is in this case considerably more pronounced than that for mode II shear zone and depends to a far greater extent on the rigidity contrast between the inhomogeneity and the surrounding medium. Another important conclusion is that the quantitative effect of an inhomogeneity on faulting depends essentially on the initial value of the stress drop of a shear zone approaching an inhomogeneity, being decidedly higher for a shear zone of small stress drop. It means that in specified areas in the proximity of medium inhomogeneities one should expect substantially greater faulting activity in which weak events prevail than in other regions surrounding inhomogeneities where such activity should be distinctly reduced. Such conclusions apply to both high rigidity inhomogeneities, which, in particular, may be associated with intrusions from the upper mantle, and to low rigidity inhomogeneities such as volcanos. The present model sets forth the plausible explanation regarding why earthquakes from the same region are occasionally characterized by various values of the stress drop. The model also presents the quantitative insight concerning how heterogeneity of the medium, in the sense of spatial variation of elastic constants, affects faulting.     

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。