Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media

In viscoelastic media, the slowness vector p of plane waves is complex-valued, p = P + iA. The real-valued vectors P and A are usually called the propagation and the attenuation vector, repectively. For P and A nonparallel, the plane wave is called inhomogeneousThree basic approaches to the determination of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium are discussed. They differ in the specification of the mathematical form of the slowness vector p. We speak of directional specification, componental specification and mixed specification of the slowness vector. Individual specifications lead to the eigenvalue problems for 3 × 3 or 6 × 6 complex-valued matrices.In the directional specification of the slowness vector, the real-valued unit vectors N and M in the direction of P and A are assumed to be known. This has been the most common specification of the slowness vector used in the seismological literature. In the componental specification, the real-valued unit vectors N and M are not known in advance. Instead, the complex-valued vactorial component p of slowness vector p into an arbitrary plane with unit normal n is assumed to be known. Finally, the mixed specification is a special case of the componental specification with p purely imaginary. In the mixed specification, plane represents the plane of constant phase, so that N = ±n. Consequently, unit vector N is known, similarly as in the directional specification. Instead of unit vector M, however, the vectorial component d of the attenuation vector in the plane of constant phase is known.The simplest, most straightforward and transparent algorithms to determine the phase velocities and slowness vectors of inhomogeneous plane waves propagating in viscoelastic anisotropic media are obtained, if the mixed specification of the slowness vector is used. These algorithms are based on the solution of a conventional eigenvalue problem for 6 × 6 complex-valued matrices. The derived equations are quite general and universal. They can be used both for homogeneous and inhomogeneous plane waves, propagating in elastic or viscoelastic, isotropic or anisotropic media. Contrary to the mixed specififcation, the directional specification can hardly be used to determine the slowness vector of inhomogeneous plane waves propagating in viscoelastic anisotropic media. Although the procedure is based on 3 × 3 complex-valued matrices, it yields a cumbersome system of two coupled equations.     

First-order P-wave ray synthetic seismograms in inhomogeneous weakly anisotropic media

We propose approximate equations for P -wave ray theory Green's function for smooth inhomogeneous weakly anisotropic media. Equations are based on perturbation theory, in which deviations of anisotropy from isotropy are considered to be the first-order quantities. For evaluation of the approximate Green's function, earlier derived first-order ray tracing equations and in this paper derived first-order dynamic ray tracing equations are used.
The first-order ray theory P -wave Green's function for inhomogeneous, weakly anisotropic media of arbitrary symmetry depends, at most, on 15 weak-anisotropy parameters. For anisotropic media of higher-symmetry than monoclinic, all equations involved differ only slightly from the corresponding equations for isotropic media. For vanishing anisotropy, the equations reduce to equations for computation of standard ray theory Green's function for isotropic media. These properties make the proposed approximate Green's function an easy and natural substitute of traditional Green's function for isotropic media.
Numerical tests for configuration and models used in seismic prospecting indicate negligible dependence of accuracy of the approximate Green's function on inhomogeneity of the medium. Accuracy depends more strongly on strength of anisotropy in general and on angular variation of phase velocity due to anisotropy in particular. For example, for anisotropy of about 8 per cent, considered in the examples presented, the relative errors of the geometrical spreading are usually under 1 per cent; for anisotropy of about 20 per cent, however, they may locally reach as much as 20 per cent.     

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A spatial data model design for feature-based geographical information systems

Abstract

In state-of-the-art GIS, geographical features are represented as geometric objects with associated topological relations and classification attributes. Semantic relations and intrinsic interrelations of the features themselves are generally neglected. In this paper, a feature-based model that enhances the representation of geographical features is described. Features, as the fundamental depiction of geographical phenomena, encompass both real world entities and digital representation. A feature-based object incorporates both topological relations among geometric elements and non-topological (semantic) relations among features. The development of an object-oriented prototype feature-based GIS that supports relations between feature attributes and feature classes is described. Object-oriented concepts such as class inheritance and polymorphism facilitate the development of feature-based GTS.     

An analytical continuum model for axially loaded end-bearing piles in inhomogeneous soil

An approximate static solution is derived for the elastic settlement and load-transfer mechanism in axially loaded end-bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed-form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth-dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth-independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.     

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按Voronoi算法分析不均匀土层上的桩筏基础

现有桩筏基础分析方法仅能利用地基分层考虑土层的竖向不均匀性,对土层水平向不均匀性的分析却是无能为力。为了改进现有方法,首先计算地基多个勘察孔在水平面上的Voronoi图,利用Voronoi图最近影响范围特性,通过把多边形范围内土层按最近勘察孔的土层资料替代的方法,近似分析水平向不均匀土层上的桩筏基础。分析时按Bowyer-Watson算法计算Delaunay三角形,然后用间接法得到Voronoi图,借助C++计算机语言编制程序分析桩筏基础。通过一个桩筏基础计算模型,对比分析采用多个勘察孔和一个勘察孔土层资料桩筏基础的分析结果,发现土层水平向差异较大时,基础沉降、桩顶反力分布,筏板弯矩等结果差别较大。故对土层不均匀性较明显地基上的桩筏基础设计,宜采用Voronoi图算法应用全部勘察孔资料进行分析。     

基于能量耗散原理的非均质岩石损伤破坏元胞自动机模型研究

基于能量耗散理论建立非均质岩石的动态损伤破坏元胞自动机,分析单轴压缩试验中岩石破坏截面的损伤状态,得到该情况下的岩石裂隙微观动态发展过程、损伤演化关系以及全程应力应变曲线。研究发现：①加载过程中,均质度较低的岩样裂纹的萌生和扩展较为分散,损伤速率低;均质度较高的岩样裂纹的萌生和扩展非常集中,表现为脆性破坏。②损伤演化曲线呈3阶段S形发展。③随着岩石均质度参数的增加,岩石的峰值强度和峰值应变都有所提高,峰后曲线越来越陡。④给出的衡量岩石脆性破坏强弱程度的指标参数,能够较好地描述岩石破坏形式随着均值度参数m变化的规律。     

地震断层面上凹凸体和障碍体含义的解析

由凹凸体和障碍体研究引入的非均匀地震破裂模式,可解释主震前破裂的成因及主破裂之后的应力集中,对地震危险性分析具有重要的理论价值。本文在国内外研究成果的基础上,深入研究了凹凸体和障碍体在地震破裂过程中的作用和意义,解析了凹凸体和障碍体的本质含义,对比分析了两种模式的异同之处,给出了两种模式在不同滑动模型中的适用性,为地震安全性评价提供了有力的理论依据。