N个薄层介质组合引起的视各向异性

作者详细推导了N个薄层介质组合时所引起的视各向异性介质的弹性参数,扩展了J.E.white先生在《Underground Sound》一书中关于双层介质组合的视各向异性介质的弹性参数应用范围,并计算了2个薄层各向同性的弹性介质组合时视各向异性介质中地震波速度随波动传播方向而变化的关系曲线,说明了薄层组合确实可以引起介质的视各向异性。     

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.     

计算分层介质中位错点源静态位移场的广义反射、透射系数矩阵和离散波数方法

本文将计算合成地震图的广义反射、透射系数矩阵和离散波数方法应用于静态问题,给出了分层介质中位错点源产生的静态位移场的计算方法。该方法保留了反射、透射矩阵方法的原有优点,通过将数值结果与解析解的对比表明,该方法具有较高的数值精度,可用于研究地震断层活动造成的地表形变。     

横向各向同性介质中的弹性波方程逆时偏移及其成像条件

作者在本文中导出了在横向各向同性介质情况下，二维弹性波逆时传播的高阶差分格式，实现了弹性波在数值空间中的逆时延拓，从snell定量出发，采用插值法求取网格空间中各点的直达波旅行时，以此作为弹性波逆时偏移的成像条件，实现多波多分量资料的逆时偏移，数值试验表明，逆时偏移能够使地表接收到的波场准确归位，提高资料处理的精度。     

Seismic Moment Tensor Resolution on a Local Scale: Simulated Rockburst and Mine-induced Seismic Events in the Kopanang Gold Mine, South Africa

Seismic records contain information about the effect of the source as well as the effect of wave propagation through the rock mass. The effect of wave propagation is usually not well known as only simplified models of geological structures are available. Therefore, the information about the source retrieved by inverting seismograms may include errors due to incomplete knowledge of the rock mass along the propagation path, which in turn cause a distortion in the calculated moment tensor (MT). The distortion of the MT on a local scale was observed by inverting records of a simulated rockburst conducted at the Kopanang gold mine in South Africa. A dominant isotropic component of the explosive characteristics was found from the inversion. The deviatoric components retrieved from the blast are spurious. A test of their stability indicated that they are not significant, assuming an uncertainty above 5% for velocities and 10% for attenuation within the homogeneous model available for the mine. Thus, the retrieval of the MT from records of local networks in mines using a homogeneous model of the rock mass seems to be feasible. However, the homogeneous model of the rock mass can only be applied to close stations, within a few kilometers of the source. The seismic records from distant stations were too complex to be modelled by a homogeneous rock mass. Records of six mine-induced seismic events recorded at the Kopanang gold mine were also inverted. A vertical linear dipole along the pressure (P) axis was found for three of the events, suggesting a pillar burst. The mechanism of two events contains an isotropic implosion together with a nearly vertical dip-slip, and seems to indicate a combination of a cavity collapse with a down dip-slip along a nearly vertical fault. One event corresponds to a dipole along the tensional (T) axis. However, it is vertical, thus its association with tensile faulting of the hangingwall is uncertain.     

基于Hoek-Brown的岩石横观各向同性屈服准则研究

为了描述岩石强度的各向异性特征,通过引入材料的微结构张量,考虑单轴抗压强度σ_cβ随层理倾角β而变化,提出了基于微结构张量的修正Hoek-Brown屈服准则。开展不同层理倾角(0°、15°、30°、45°、60°、75°和90°)的页岩试样不同围压(0、5、10、15和20 MPa)下的三轴压缩试验,结果显示,页岩峰值强度与层理倾角β呈"U"形曲线关系,在围压较低时呈"肩"形曲线关系,弹性模量E_t和泊松比ν对围压不敏感,其平均值随层理倾角β的变化关系分别呈倒"U"形、"肩"形。页岩的微观和宏观破坏图像表明,其破坏模式受围压和层理倾角双重控制。试验值与模型预测值的对比表明,修正的Hoek-Brown屈服准则可较好地对页岩强度的各向异性进行模拟。同时,采用Koteshwar千枚岩、Koteshwar板岩、绿泥石片岩等层状结构岩石的单轴和三轴压缩试验数据,进一步验证了提出的修正Hoek-Brown屈服准则对多数具有层理结构的横观各向同性岩石峰值强度模拟具有普遍适用性,并对屈服准则在试验数据较多和较少情况下的峰值强度模拟效果进行了评价。     

Moving load response of an axially loaded Timoshenko beam on a multilayered transversely isotropic half-space comprising different media

This paper investigates the dynamic response of an axially loaded Timoshenko beam coupled with a multilayered transversely isotropic (TI) half-space subjected to a moving load. An axial force induced by the thermal expansion is taken into account in the Timoshenko beam. The half-space considers the alternate distribution of an arbitrary number of TI elastic and poroelastic layers to model foundation soils with different properties and moisture conditions. To solve the governing equations, Fourier transform is adopted. The stratified foundation is formulated by extending an “adapted stiffness matrix method” to a more general scenario with an arbitrary number of layers. The beam is then coupled with the foundation to derive solutions to the system in the frequency-wavenumber domain. The final results in the time-spatial domain are recovered by the inverse Fourier transform. After confirming the accuracy of the method in this study, the influences of the pore water existence, the transverse isotropy of different parameters, and the axial force are investigated. It can be observed that the effect of pore water existence on the maximum beam deflection can reach 22% in this study. The transverse isotropy of the elastic and shear moduli influences the critical speed of the beam deflection by altering the phase velocity of the first wave propagation mode of the beam-foundation system. The vertical permeability coefficient is more important than the horizontal one in determining the excess pore pressure. The rise of the beam temperature (axial force) decreases the critical speed and magnifies the vibrations.     

A stress and displacement discontinuity element method for elastic transversely anisotropic rock

The paper presents closed‐form solutions for stress and displacement influence functions for stress discontinuity (SD) and displacement discontinuity (DD) elements, for a two‐dimensional plane‐strain elastic, transversely anisotropic medium. The solutions for SD elements are based on Kelvin's problem and for DD elements on the concept of dipoles. Stress and displacement influence functions are derived for the following elements: constant SD, linear SD, constant DD, linear DD, square root DD, parabolic DD, constant DD surface, and linear DD surface elements. The formulations are incorporated into FROCK, a hybridized boundary element method code, and are validated by providing comparisons between the results from FROCK and the finite element code ABAQUS. A limited parametric analysis shows the effects of slight anisotropy on the stress field around the tip of a crack and of the orientation of the crack with respect to the axes of elastic symmetry. Copyright © 2014 John Wiley & Sons, Ltd.     

Vertical dynamic response of a disk on a saturated poroelastic half-space

This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform.