Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

阻尼对应力波传播的影响

基于一维应力波理论，本文讨论了材料粘性（内阻尼）及作用于杆侧表面外阻尼对应力波传播的影响，应力波在外阻尼作用下，向上传播－应力波，该应力波在端面质点速度方向与入射波质点速度相反，而内阻尼则使材料具有松弛、蠕变行为，作用力终止后，端面质点速度缓慢地回复到零。无论是内阻尼还是外阻尼。受其影响，应力波在向下传播过程中，能量有一定程度的耗损     

Effects of seismic wave propagation on a long and narrow building: Body wave and surface wave propagation

In the case of the dynamic analysis of the structures using the recorded earthquake ground motions, it is usually assumed that the ground motion consists of body waves propagating vertically. However, the response of a long and narrow structure may be influenced by the oblique propagation of body waves and the dispersion of surface waves. In this paper, the effects of the seismic wave propagation on the response of this kind of structure are investigated. The characteristics of the wave propagation were verified using the recorded motions and soil information at the building site. The ground motion at every input point of the building was evaluated using the difference of arrival time of seismic waves calculated by assuming the velocity and the direction of the wave propagation. Using these ground motions, response analyses of the lumped mass model for the structure were performed. By considering the characteristics of the seismic wave propagation, the average response decreased but the local response increased around the end of the roof. Further studies of the structure were also performed in order to restrain the response around the end of the roof.     

基于微形态理论的各向异性散体波动分析

基于散粒体微观力学理论,忽略颗粒转动引起的相对位移,考虑颗粒接触的组构各向异性,根据宏微观能量守恒推导得到了散体材料各向异性微形态本构关系,进而通过单位接触方向积分的递推公式推导出了各向异性本构张量表达式;在此基础上,根据哈密顿原理得到了各向异性散体材料的运动平衡方程和边界条件,从而求得了平面波在各向异性散粒体中的传播规律和频散关系,最后对波的频散关系和频率带隙进行了详细的参数分析。研究表明：该模型预测了散体中包含3类12种位移波：3种纵波、6种横波和3种平面内横向剪切波;横观各向同性条件下,接触各向异性参数a20越大,纵波和横波的频率越大,而平面内横向剪切波的频率越小;正交各向异性条件下,随着接触各向异性参数a22的增大,与2方向运动相关的横波频率增大,而与3方向运动相关的横波频率则减小;但a22的变化对纵波频率影响很小。材料各向异性程度对横波带宽影响不大,但对纵波带宽影响较大：a20的增大使得声?光学波间的带宽减小,而光学波间的带宽增大,当a20>0.84时,声?光学波间的带隙消失;但是a22的增大则使得声?光学波间的带宽增大,而光学波间的带宽减小。退化为各向同性模型后,预测3类波的频散曲线与其他各向同性模型的结果基本一致。     

应力波在平台-桩系统中传播的实验研究

分析了应力波在平台－桩系统中的传播图案。对有限尺寸的平台来说，应力波在平台边界面上会发生反射，反射波不仅有同类波同时还有转换波，除此之外，平台表面的响应还受桩及桩土相互作用的影响。除非桩身反射波走时较长，可以避开平台上的各种干扰波，否则，由平台实测波形特征来分析平台下桩的完整性是很困难的。通过对平台上完整桩实测波形与异常桩波形进行比较，可以提高波形识别的准确度，此外，根据桩侧面测点及平台表面测点走时，相位、幅值间关系，将两者信号进行比较，可以从复杂的信号中辨别出桩身反射波信号。     

地下爆炸地震效应的评价标准探讨

在对地下爆炸地表震动特性进行分析的基础上,对地下爆炸地震效应的评价标准进行了分析与探讨,通过解析的方法,建立了地下爆炸地表运动计算模型和震动反应谱。计算结果表明：地下爆炸地表运动存在两组波群,在评价波对于建筑物的作用时应当考虑到第2波群中粒子运动的周期比第1波群的粒子运动周期长1.5～2.0倍;地面建筑物的响应取决于建筑物的固有频率、阻尼和地震的频率、振幅;对于小当量一次性爆破,震动频率高而震动时间短,可以忽略地表震动频率对结构的影响;但是对于大当量爆炸地震安全问题,不应当忽略频率的影响;对于双层建筑物,第2层结构的不稳定运动有大振幅的特点。     

利用微波侦测地下水位与河川变化

论文探讨藉由电磁波照射地表,从反射讯号中去判断地下水水位与土石流移动观测之可行性,期能提供一新的土石流预警方法.电磁波在土壤中的行为受土壤的介电系数所控制.我们首先以地下水模式仿真出地层中的含水量分布状况,同时搜集过去关于土壤介电系数的实验资料和模型,将其运用于层状介质法来仿真电磁波照射在不同含水量剖面下之反射波,以建立含水量分布与反射讯号间的对比模块.最后则是以砂箱实验,量测含水量剖面后,藉由天线与网络分析仪来发射电磁波与记录反射波.由理论计算与实验测量结果之比较可知所选择的土壤介电系数模型可以仿真简单潮湿土壤的电磁行为;而由实验量测可知电磁波至少可以打进50cm的微湿砂子.若以雷达扫瞄河道,可对土石流或洪水前锋的速度作准确之估计.     

地下洞室群对地面运动影响问题的级数解答:SH波入射

采用波函数展开法给出平面SH波入射下半空间中洞室群对地面运动影响问题的一个级数解答，并分析了入射波频率和入射角以及两洞室之间距离等参数对地面运动的影响。数值结果表明，地下洞室群对沿线地面运动具有显著的放大作用：两个洞室情况地面运动可以达到单个洞室情况的1．6倍、无洞室情况的3．5倍以上。建议地铁等地下工程在设计和规划时应考虑工程建设后对沿线设计地震动的影响。     

埋藏基岩地形对地震波动影响的模拟研究

本文以超声地震模型试验为基础,着重从地震波的强度方面来阐明埋藏基岩地形对地震波动的影响,提出了利用振动能量分析地震动问题的重要性,理论分析及实验结果表明,埋藏基岩地形对地震波动的影响表现为:一方面基岩面凹凸不平,致使基岩面上不同部位接收能量大小不同;另一方面,基岩的凹凸面对地震波产生汇聚与发散作用,这两方面共同作用的结果使得地表不同地点表现出不同的地震动强度。     

Comparison of transmitting boundaries in dynamic finite element analyses using explicit time integration

Explicit time integration schemes provide an efficient solution to non-linear dynamic finite element analyses of geotechnical problems especially when high frequency response is important. Such explicit time integration schemes require one of two distinct transmitting boundary formulations to overcome the problem of radiation damping. These are the superposition boundary approach, which involves the cancellation of the reflected waves by combining the solutions of two different boundary conditions and the viscous boundary approach, which involves the absorption of incident wave energy by frequency independent viscous dashpots. The theoretical justification of these two approaches and their means of implementation are reviewed. The solutions obtained using the two different boundary approaches to the problem of a rigid massless circular footing vibrating on an elastic half-space are compared with an independent theoretical solution. The performance of the boundaries for problems involving step loading is also examined and the implications for any loading pattern with a non-zero time average are discussed.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.     

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd.     

扭转导波在锚固锚杆中传播的数值模拟

采用有限元数值模拟的方法研究了扭转导波在锚固锚杆中的传播性质。建立了自由锚杆和锚固锚杆的有限元模型,在锚杆顶端激发20～60 kHz扭转导波信号,计算得到导波在自由锚杆和锚杆锚固段的传播速度值与理论值吻合很好,证明了扭转导波数值模拟方法的有效性。数值模拟结果表明：随着激发波频率的增大,扭转导波在自由锚杆和锚杆锚固段中的衰减值均呈线性递增趋势,导波在锚杆锚固段上界面的反射回波逐渐减弱;扭转导波在锚杆锚固段的衰减值较大,无法在锚杆顶端采集到锚杆底端反射回波信号,所以扭转导波不适用于锚杆长度的检测;随着锚固介质弹性模量的增大,同一频率扭转导波在锚杆锚固段上界面的反射波逐渐增强。通过检测扭转导波在锚杆锚固段上界面的反射回波,可以确定锚固介质弹性模量的大小。     

不同饱和度土层分界面上剪切波的反射与透射

基于多相孔隙介质弹性理论,给出了非饱和土中不同弹性波的传播方程。根据分界面上的边界条件,建立了各势函数波幅值之间的关系式,讨论了入射剪切波在不同饱和度土层分界面上的反射与透射问题。在无限空间非饱和土体中存在3种压缩波和1种剪切波,因此,当剪切波传播到不同饱和度的非饱和土层分界面上将分别在上、下土层激发产生4种反射波和4种透射波。推导出不同反射波和透射波的振幅比例系数和能量比例系数的理论表达式,并且在此基础上进行数值分析。在数值算例中分别研究了各反射波与透射波的能量比例系数（即能量反射率和能量透射率）受入射频率、入射角度以及上、下土层土体饱和度变化的影响情况。计算结果表明：各能量反射率和能量透射率不仅与入射角和入射频率有关,而且其受上、下土层饱和度变化的影响也同样不能忽视。     

二维条件下颗粒柱体崩塌入水堆积过程

在我国西南地区,以塔柱状危岩体崩塌为扰动源的涌浪次生灾害时有发生。涌浪特征与其扰动源的初始形状和破坏模式关系密切,塔柱状危岩体由下至上、空中崩解的破坏模式与颗粒柱体崩塌相似。区别于以往多试验采用的刚体材料和利用运动距离获得初始动力状态的涌浪试验,本研究设计并进行了不同高度和宽度的颗粒柱体在不同水深下自然崩塌的物理模型试验。运用PIV技术分析了颗粒体及水体的运动特征,按颗粒体与水体的相互作用关系将整个过程大致分为了3个阶段,并研究了颗粒柱体初始形态对试验结果的影响。结果表明,颗粒柱体崩塌后的残余体积受颗粒体初始形态影响较大,水深对其影响较小。涌浪产生早期,首浪位置与颗粒运动位置有着良好的对应关系;而后,两者的位置逐渐拉开。颗粒柱体高度越高,首浪最大波高出现时的位置与崩塌颗粒群前端位置的差值越大。这可能与流固相互作用后期水体流速大于颗粒流动速度有关。试验产生的涌浪大多具有完整波形,这与柱状颗粒体的散体性及其覆盖堆积特征对水体的作用呈不均匀性有关。涌浪传播过程中,水体在z方向上抬升幅度具有一定的渐变性。试验分析结果揭示了柱状危岩体引发涌浪的机制特点,为涌浪灾害防治提供了基础资料。     

高频纵向导波在钢杆中传播的数值模拟

锚固锚杆中高频导波（大于1 MHz）的低衰减使其具有巨大的潜在应用价值,但高频导波数值计算的复杂性使得确定其传播特征非常困难,只依赖试验确定不同锚固锚杆中的最优激发波并不现实,因此建立高频导波传播的数值模型具有重要意义。应用有限元软件构建钢杆的数值模型,分别研究径向和轴向的单元网格密度和材料阻尼对高频导波传播过程的影响情况,采用所有截面节点幅值叠加和经验模态分解（empirical mode decomposition,简称 EMD 分解）的方法进行数据处理,获得了与文献理论结果及试验测试结果相吻合的高频导波在钢杆中的基本传播特征。研究结果表明,单元网格密度、材料阻尼值设置及不同位置质点的振动叠加是再现高频导波基本传播特征的关键。     

Numerical and analytical investigation of compressional wave propagation in saturated soils

In geotechnical earthquake engineering, wave propagation plays a fundamental role in engineering applications related to the dynamic response of geotechnical structures and to site response analysis. However, current engineering practice is primarily concentrated on the investigation of shear wave propagation and the corresponding site response only to the horizontal components of the ground motion. Due to the repeated recent observations of strong vertical ground motions and compressional damage of engineering structures, there is an increasing need to carry out a comprehensive investigation of vertical site response and the associated compressional wave propagation, particularly when performing the seismic design for critical structures (e.g. nuclear power plants and high dams). Therefore, in this paper, the compressional wave propagation mechanism in saturated soils is investigated by employing hydro-mechanically (HM) coupled analytical and numerical methods. A HM analytical solution for compressional wave propagation is first studied based on Biot’s theory, which shows the existence of two types of compressional waves (fast and slow waves) and indicates that their characteristics (i.e. wave dispersion and attenuation) are highly dependent on some key geotechnical and seismic parameters (i.e. the permeability, soil stiffness and loading frequency). The subsequent HM Finite Element (FE) study reproduces the duality of compressional waves and identifies the dominant permeability ranges for the existence of the two waves. In particular the existence of the slow compression wave is observed for a range of permeability and loading frequency that is relevant for geotechnical earthquake engineering applications. In order to account for the effects of soil permeability on compressional dynamic soil behaviour and soil properties (i.e. P-wave velocities and damping ratios), the coupled consolidation analysis is therefore recommended as the only tool capable of accurately simulating the dynamic response of geotechnical structures to vertical ground motion at intermediate transient states between undrained and drained conditions.     

脉冲地震动中竖向加速度对场地液化的影响

为研究近断层脉冲地震动中竖向加速度对砂土场地液化的影响,基于有限元平台OpenSees开发的边界面塑性本构模型,建立了动单剪单元试验模型和饱和砂土三维有限元模型。选取台湾Chi-Chi地震中10条具有速度脉冲特性的地震波,对比分析了水平双向脉冲波与三向脉冲波作用下土柱竖向位移、循环应力比、孔压比及等效循环周数的差异性,继而明确了脉冲地震动中竖向加速度对砂土液化的影响规律。研究表明,三向脉冲地震波中竖向加速度分量对场地永久位移值影响较小,但使永久位移的发展持时明显增大;土柱循环应力比受竖向地震动影响较小,因此分析脉冲地震动对场地剪切特性的影响时,可将三向脉冲地震动简化为水平双向地震动;考虑竖向地震动的三向脉冲地震波引起的孔压比变化幅度较大,孔压消散时间较长;三向脉冲地震波对应的等效循环周数较大,地震动发展持时长,可认为竖向加速度对场地液化有促进作用。     

表面波有效相速度近似分析方法

分层介质中瑞利面波有多个模态,表面瞬态响应是多个模态响应的叠加。在近场,面波模态响应传播速度随传播距离而变化;在远场,其趋于模态相速度。由分层介质表面两不同点响应互谱分析(SASW)得到的有效相速度并不对应于面波基阶模态相速度,它与波场中高阶模态能量分配比例有关。有效相速度随传播距离而变化,近场体波对有效相速度影响较大。对分层介质在简谐荷载下表面质点位移响应进行了互谱分析,得到了有效相速度理论值,通过理论值与测试值匹配分析可估算分层参数,该分析方法考虑了近场及高阶面波模态对有效相速度的影响。     

Source signature and elastic waves in a half‐space under a momentary shear line impulse

The transient deformation of an elastic half‐space under a line‐concentrated impulsive vector shear load applied momentarily is disclosed in this paper. While in an earlier work, the author gave an analytical–numerical method for the solution to this transient boundary‐value problem, here, the resultant response of the half‐space is presented and interpreted. In particular, a probe is set up for the kinematics of the source signature and wave fronts, both explicitly revealed in the strained half‐space by the solution method. The source signature is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Fourteen wave fronts exist behind the precursor shear wave S: four concentric cylindrical, eight plane, and two relativistic cylindrical initiated at propagating centres that are located on the stationary boundaries of the solution domain. A snapshot of the stressed half‐space reveals that none of the 14 wave fronts fully extend laterally. Instead, each is enclosed within point bounds. These wave arresting points and the two propagating centres of the relativistic waves constitute the source signature. The obtained 14 wave fronts are further combined into 11 disparate wave fronts that are grouped into four categories: an axis of symmetry wave—so named here by reason of being a wave front that is contiguous to the axis of symmetry, three body waves, five surface waves and two inhibitor waves—so named here by reason that beyond them the material motion dies out. Of the three body waves, the first is an unloading shear wave, the second is a diffracted wave and the third is a reflected longitudinal two‐branch wave. Of the two inhibitor waves, the first is a two‐joint relativistic wave, while the second is a two‐branch wave. The wave system, however, is not the same for all the dependent variables; a wave front that appears in the behaviour of one dependent variable may not exist in the behaviour of another. It is evident from this work that Saint–Venant's principle for wave propagation problems cannot be formulated. Therefore, the above results are valid for the particular proposed model for the momentary line‐concentrated shear load. The formulation of the source signature, the wave system, and their role in the half‐space transient deformation are presented here. Copyright © 2003 John Wiley & Sons, Ltd.