Analytical layer element solutions for deformations of transversely isotropic multilayered elastic media under nonaxisymmetric loading   总被引：1，自引：0，他引：1  

Zhi Yong Ai  Dong Liang Feng  Nai Rui Cang 《国际地质力学数值与分析法杂志》2014,38(15):1585-1599

This paper presents the analytical layer element solutions for deformations of transversely isotropic elastic media subjected to nonaxisymmetric loading at an arbitrary depth. The state vectors for the nonaxisymmetric problem are deduced through the substitution of the Hu Hai‐chang solutions into the basic equations for the transversely isotropic elastic media. From the state vectors, the analytical layer element of a single layer is obtained in the Hankel transformed domain. The analytical layer element is an exact and symmetric stiffness matrix whose elements are without positive exponential functions, which can not only simplify the calculation but also improve the stability of computation. On the basis of the continuity conditions between adjacent layers, the global stiffness matrix is obtained by assembling the interrelated layer elements. The solutions for the multilayered elastic media in the transformed domain are obtained by solving the algebraic equation of the global stiffness matrix, which satisfies the boundary conditions. The actual solutions in the physical domain are further obtained by inverting the Hankel transform. Finally, some cases are analyzed to verify the solutions and evaluate the influences of the transversely isotropic character and stratified character of the media on the load–displacement responses. The numerical results show that the variations of the elastic properties between layers have a great effect on the displacements of the multilayered media. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

横观各向同性岩土材料的应变局部化分析          下载免费PDF全文

丁巍  楚锡华  常江芳 《地震工程学报》2017,39(3):481-487,508

为分析横观各向同性岩土材料的应变局部化行为,推导对应于Lade横观各向同性屈服准则向前欧拉算法的迭代格式及本构矩阵,通过有限元软件ABAQUS的UMAT接口实现相应的程序代码。数值算例调查分析材料主方向对横观各向同性岩土结构的极限承载力和变形局部化模式的影响。结果表明该模型能较好地模拟横观各向同性岩土结构的应变局部化行为。  相似文献   

薄互层弹性波反演面临的困境   总被引：2，自引：0，他引：2       下载免费PDF全文

王赟  杨春  芦俊 《地球物理学报》2018,61(3):1118-1135

对于薄互层地震传播特征的研究我们已有了充分的认识,这是一种完全不同于现有的基于厚层单阻抗差界面地震反射理论的、具有频率依赖性的调谐反射.因而也使得对具有N层结构的弹性介质薄互层反演时,现有有限带宽的基于空间-频率域采样的地震观测难以规避多解性问题.长波长假设下的薄互层VTI近似似乎可以为我们提供一种待反演弹性参数只有5个的可行性方案,使得我们可以将薄互层背景下任一目标薄层的反演看作VTI厚层介质背景下单薄层的反演.但是,我们首先面临薄互层VTI近似的误差和适用性条件等问题;其次,既使对于单薄层厚度的反演,目前地震领域也未能提供一种通用有效的解决方案,实际地震勘探中薄层厚度的预测依然是一个悬而未决的难题.因此在此基础上再进行单薄层的物性参数、裂缝隙和流体的预测则更叠加了难以预知的多解性.显然单纯P波已难以应对,弹性波的介入成为必然;而且单薄层含裂缝与流体的预测更需要横波分裂和双相介质理论的支撑.可以预见的是,除了纵、横波速度,薄互层反射系数的频率依赖性是我们试图给出相对可靠的、单薄层物性精细刻画必须使用的一种重要地震属性.  相似文献   

随钻四极源声波测井多模式采集测量TTI地层各向异性的研究          下载免费PDF全文

卫建清  何晓  陈浩  王秀明 《地球物理学报》2018,61(2):792-802

本文应用三维柱坐标时域有限差分方法模拟了多极子随钻声波测井的波场,提出了在横向各向同性（TI）慢速地层倾斜井中,使用四极源激发、多模式采集进行各向异性参数反演的方法.模拟结果表明：在强各向异性地层大角度倾斜井中使用四极源能够激发出多极模式波,并且井孔内的声场会随着声源方向角β（声源方向和快横波偏振方向的夹角）的改变而发生变化.使用四极子采集方式记录时,可以发现波形会分裂成快慢两种波;并且在声源方向与地层快横波偏振方向成45°时,分裂的两种波形的速度更趋近于地层快慢横波波速,用此可反演地层各向异性值大小.使用单极子采集方式记录时,其波形能量与声源方向角β大致成cos²2β的关系,在声源方向角为45°时,其波形幅度最小,用此可判断与快横波偏振方向成45°角的方向.使用AC方向（与声源同方向）偶极子采集方式记录时,当声源方向与快横波偏振方向一致时,采集到的波形幅度最小;而与快横波偏振方向垂直时,波形幅度最大,所以通过偶极子采集方式记录的波形可以判断快横波偏振方向.因此,在强各向异性倾斜井中进行随钻四极子测量时,可以使用多模式采集方式来进行地层各向异性的反演.  相似文献   

Practical and robust experimental determination of c13 and Thomsen parameter δ          下载免费PDF全文

Fuyong Yan  De‐Hua Han  Xue‐Lian Chen 《Geophysical Prospecting》2018,66(2):354-365

We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c₁₃ and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c₁₃ and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c₄₄ and c₁₃ in determining the directional dependence of the seismic velocities. The quasi‐P‐wave or quasi‐S‐wave velocities can be approximated by three elastic parameters.  相似文献   

Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium     

Munirdin Tohti  Yibo Wang  Evert Slob  Yikang Zheng  Xu Chang  Yi Yao 《Geophysical Prospecting》2020,68(6):1927-1943

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.  相似文献   

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks     

Sabrina C.Y. Ip  Ronaldo I. Borja 《国际地质力学数值与分析法杂志》2022,46(1):23-46

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.  相似文献