横观各向同性层状半空间中的弹性位错

本文在柱向量函数系下,利用传播矩阵法求解了层状横观各向同性半空间由内部点源位锚引起的变形;对六个基本点源位错,以等价体力法推出了横观各向同性情形下的点源函数,并且给出了内部任意剪切位错源引起的地表位移的积分表达式。为研究地球的层状结构,特别是其上部的横观各向同性对地表的地震位移、应变以及倾斜场的影响提供了计算公式。     

考虑各向异性的层土-盾构隧道地震反应数值模拟

在层状各向异性土体-盾构隧道地震反应分析中,引入了横观各向同性弹塑性模型理论,建立了适合于横观各向同性介质的双渐近-多向透射边界条件。针对地铁区间盾构隧道抗震设计的特点,基于横观各向同性弹塑性模型,研制了考虑层状土体各向异性和施工开挖效应,适合于盾构隧道动力计算的各向异性弹塑性动力有限元程序。在程序中对于不同的材料采用了不同的本构关系和不同的单元形式,并采用了关联流动法则和多种屈服准则,可同时进行各向异性土体与地下结构的二维平面应力、平面应变和轴对称问题的静力和动力数值分析。最后利用所研制的程序进行了上海地铁二号线石门一路站附近区间隧道在不同超越概率地震动输入下的隧道反应计算。结果表明,在层状土体-地铁区间隧道的抗震分析中考虑土体各向异性的影响是必要的,所提出的计算模型是可行的。     

横观各向同性饱和两相介质动力反应计算分析

针对横观各向同性饱和两相介质的弹性波动方程组,应用基于显式逐步积分计算格式的时域显式有限元方法对其在输入地震波作用下的动力反应进行计算和分析,并将计算结果与完全各向同性饱和两相介质的计算结果进行对比研究。结果显示横观各向同性饱和两相介质与完全各向同性饱和两相介质的动力反应具有较为显著的差异。同时表明时域显式有限元方法是进行横观各向同性饱和两相介质动力反应计算分析的一种有效方法。     

平面外振动周期性高架桥失谐局部化问题分析

考虑周期性高架桥结构由桥墩及两相邻的水平梁组成,分析平面外振动失谐引起局部化现象。首先建立水平梁-桥墩连接处的传递矩阵,结合Wolf算法推导描述周期性高架桥波场局部化的Lyapunov正指数,并讨论高架桥结构的桥墩高度、桥梁跨度失谐及材料阻尼变化对描述局部化因子的Lyapunov指数影响。计算结果表明:低频时桥墩高度及桥梁跨度失谐对Lyapunov指数几乎没有影响,而随频率增加,周期高架桥结构失谐引起局部化现象明显;在通带域,振动波局部化更容易受结构材料阻尼变化的影响;在禁带域,高架桥的桥墩高度、桥梁跨度失谐对振动局部化影响要大于结构材料阻尼。     

分形几何在岩土力学研究中的过去、现在与未来

首先简略地介绍了分形几何理论及其方法。从岩土材料结构的定量描述、流体在岩土体中的渗流问题、岩土材料强度的分形模型和分形空间的力学特征四个方面叙述了分形理论在岩土力学研究中取得的成果及应用。指出只有将岩土力学系统在欧氏空间的各种基本变量、原理和方法向分形空间推广和拓展,才能产生对岩土材料非线性力学行为的新认识,这也是分形理论在岩土力学研究中进一步深化的基础。     

平面外振动周期性高架桥失谐局部化问题分析

考虑周期性高架桥结构由桥墩及两相邻的水平梁组成,分析平面外振动失谐引起局部化现象。首先建立水平梁-桥墩连接处的传递矩阵,结合Wolf算法推导描述周期性高架桥波场局部化的Lyapunov正指数,并讨论高架桥结构的桥墩高度、桥梁跨度失谐及材料阻尼变化对描述局部化因子的Lyapunov指数影响。计算结果表明:低频时桥墩高度及桥梁跨度失谐对Lyapunov指数几乎没有影响,而随频率增加,周期高架桥结构失谐引起局部化现象明显;在通带域,振动波局部化更容易受结构材料阻尼变化的影响;在禁带域,高架桥的桥墩高度、桥梁跨度失谐对振动局部化影响要大于结构材料阻尼。     

桩土共同作用下桩长对结构抗震性能影响分析

桩基础是松软深厚地基上高层建筑的主要基础形式,其长度直接影响高层建筑的抗震性能。尽管桩基础有较广的应用范围,但桩长与结构整体抗震性能的相关性研究还颇为少见。根据上海某高层建筑地基基础结构数据建立软土地基上桩基础高层建筑平面动力有限元计算模型,以横观各向同性材料模拟软土地基,弹性阻尼人工边界模拟地基半无限体,薄膜单元模拟桩土间接触滑移性能,并考虑桩-土-结构共同作用,采用上海地铁某车站地震监测数据作为地震波输入,在其他条件不变的情况下选择各种桩长进行计算,根据计算结果分析讨论在该模型条件下桩长选择对上部结构以及桩基础整体抗震性能的影响,提出优化方案。     

钢板混凝土圆板结构非经典理论抗爆效应解析解

将沿厚度由钢板和混凝土组合而成的圆板化为一等效横观各向同性板件，应用弹性动力学和复合板件等效非经典理论，通过动力分析建立了基本振动方程，求得了自由振动和横向爆炸载荷作用下强迫反应的解析解。     

颗粒体材料在压缩位移控制加载条件下的力学行为及界面参数对它的影响

采用连续介质快速拉格朗日分析程序（FLAC）,模拟了颗粒体材料在压缩位移控制加载条件下的力学行为及破坏过程。颗粒及它们之间的界面被离散为尺寸相同的单元。颗粒被视为各向同性的弹性材料,而界面被视为弹性-应变软化-理想塑性材料。界面完全破坏之后,其内聚力为零而内摩擦角不为零,因而适于模拟颗粒之间的摩擦行为。在双轴压缩条件下的计算结果表明,压应力通过颗粒之间的接触,以应力线的方式在试样的垂直方向上传递,最终形成了清晰、有序的图案,而剪切应变增量的高值区主要位于一些界面上。从剪切应变增量的高值区中能发现试样中的最薄弱环节。此外,还研究了试样两侧的压应力、界面的初始内聚力及内摩擦角对试样的应力—时步曲线的影响。     

横观各向同性层状半空间中凹陷地形对平面SH波的散射

沉积风化作用下土体表现出明显的成层特性和横观各向同性(TI)特性。将更为符合实际的TI介质模型引入到局部地形对地震波的散射问题研究有着重要的理论意义和工程实用价值。本文在TI土层平面外动力刚度矩阵的基础上,推导了斜线均布荷载动力格林函数,进而以该格林函数为基本解建立间接边界元方法研究了TI层状半空间中凹陷地形对平面SH波的散射问题。文中验证了方法的正确性,并分别在频域和时域内进行了数值计算分析。研究表明,TI介质中凹陷地形对SH波的散射与各向同性介质情况存在较大差异,凹陷附近地表位移幅值依赖于SH波的入射角度、入射频率和竖向与水平剪切模量比值;另外土体竖向与水平剪切模量比值对基岩上单一土层场地动力特性有着显著影响,进而使得TI层状场地凹陷附近位移幅值与各向同性情况差异变得更为复杂。     

Determination of the reference symmetry axis of a generally anisotropic medium which is approximately transversely isotropic

For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we estimate to what extent the medium is transversely isotropic (uniaxial) and determine the direction of its reference symmetry axis expressed in terms of the unit reference symmetry vector. If the medium is exactly transversely isotropic (exactly uniaxial), we obtain the direction of its symmetry axis. We can also calculate the first–order and second–order spatial derivatives of the reference symmetry vector which may be useful in tracing the reference rays for the coupling ray theory. The proposed method is tested using various transversely isotropic (uniaxial) and approximately transversely isotropic (approximately uniaxial) media.     

Seismic anisotropy analysis at the Low-Noise Underground Laboratory (LSBB) of Rustrel (France)

Seismic anisotropy of a fractured karstic limestone massif in sub-parallel underground galleries is studied. As the fractures are mostly vertically oriented, the seismic properties of the massif are approximated by horizontal transverse isotropy (HTI). Several data inversion methods were applied to a seismic dataset of arrival-times of P and S-waves.The applied methods include: isotropic tomography, simple cosine function fit, homogeneous Monte-Carlo anisotropic inversion for the parameters of horizontal transverse isotropy and anisotropic tomography for tilted transversely isotropic bodies. All methods lead to the conclusion that there is indeed an anisotropy present in the rock massif and confirm the direction of maximum velocity parallel to the direction of fracturing. Strong anisotropy of about 15% is found in the studied area. Repeated measurements show variations of the P-wave parameters, but not of the S-wave parameters, which is reflecting a change in water saturation.     

基于walkaway VSP下行P波的TTI各向异性参数反演

本文基于弱各向异性（WA）介质的正反演公式和qP波的坐标变换,推导了利用qP波反演任意倾斜对称轴的横向各向同性（TTI）介质的各向异性参数和对称轴方向的公式.理论和数值实验表明,利用2个相互正交的变井源距垂直地震剖面（walkaway VSP）可以完全确定钻井中TTI介质qP波的3个WA参数和对称轴的2个方向参数.我们完成了几个由不同数量剖面组成的walkaway VSP模拟实验,使用TTI模型和一般各向异性模型对模拟数据进行了反演,证明了反演公式的正确性和可靠性.使用这些公式,对来自Java Sea的由3条剖面组成的walkaway VSP观测数据进行了各向异性反演,获得了钻井中接收点处介质的WA参数.     

ELASTIC WAVE PROPAGATION IN MEDIA WITH PARALLEL FRACTURES AND ALIGNED CRACKS1

A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

Anisotropic azimuthal surface-wave inversion for a vertically fractured and transverse isotropy medium: Theory and examples from a controlled field experiment

Fractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh-wave equations for a vertically transverse isotropic media can be used to model surface-wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first-break analysis and azimuthal anisotropic Rayleigh-wave inversion can be used to estimate P-wave and S-wave velocities, Thomsen's ε, and Thomsen's δ along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S-wave velocities with Thomsen's parameters ε and δ along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the in situ normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh-wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known a priori.     

Reference transversely isotropic medium approximating a given generally anisotropic medium

For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we can estimate the extent to which the medium is transversely isotropic, and determine the direction of its reference symmetry axis. In this paper, we rotate the given stiffness tensor about this reference symmetry axis, and determine the reference transversely isotropic (uniaxial) stiffness tensor as the average of the rotated stiffness tensor over all angles of rotation. The obtained reference transversely isotropic (uniaxial) stiffness tensor represents an analytically differentiable approximation of the given generally anisotropic stiffness tensor. The proposed analytic method is compared with a previous numerical method in two numerical examples.