Directional properties of polygons and their application to finite strain estimation

An eigenmethod for characterising the directional properties of convex polygons is described. Given a polygon, regular in the undeformed state, its image following a homogeneous strain transformation is an irregular polygon whose eigensolution (an ellipse) has the axis ratio and orientation of the strain ellipse. The eigenmethod can therefore be used for finite strain estimation using polygonal strain markers, and is compared with alternative methods recently proposed by Roder (1977) and Sanderson (1977).     

A generic method to organize boundaries of complex polygons for embedded devices

Based on an analysis of drawbacks in the existing graphical display of complex area objects in embedded system, the paper introduces a new method termed as consecutive boundary organization (CBO) which is able to convert a large number of separate polygons belonging to the same area object into a single consecutive stroke fitting for quick display. The working principle of the CBO method is demonstrated in three cases that can typically occur to the real-world concept “lake”: (1) a lake with an island in it, (2) a lake with multiple islands, and (3) the nested lake-island-lake. In spite of complicated inclusion relationships, the CBO method can always construct an integral stroke with neither information loss nor redundancy. Experiments with a real dataset of lakes and islands from North America have proved the feasibility and efficiency of the CBO method. Due to its generic nature, the CBO method can be applied to any other complex area objects with multiple polygons and inclusion levels.     

水位下降条件下黏性土边坡稳定性的图表法

库（河）岸边坡由于坡体迎水面水位下降经常造成坡体稳定性降低,建立快速评估水位变化条件下的边坡稳定性分析方法具有重要的工程实用价值。基于库（河）水位下降过程及坡体内非稳定渗流条件,通过对ABAQUS程序进行二次开发,发展了考虑地表水-地下水联动作用下的黏性土边坡强度折减有限元分析方法;在分析边坡土性参数、相对渗透比值、边界条件对边坡稳定性影响的基础上,建立了考虑土性参数、相对渗透比值、库水位下降比、坡角等一体化的相对稳定安全系数综合图表表示方法。该方法能够简便、快捷地查出实际涉水边坡在不同工况下的稳定安全系数及设计边坡坡比,可作为现有图表法的有益补充。     

地震数据重建方法原理及运用

在数值分析领域中,许多方法都是借助于插值公式导出的.几乎所有的经典数值微分、数值求积和常微分方程的数值积分公式,都可以从插值公式中推导出来.地震勘探领域常见的插值重建方法按照数学原理大致可以分为三类:适用于均匀采样的预测误差滤波插值方法,基于算子的插值方法(如DMO和偏移算子)和在最小二乘意义下估算特定数学变换系数进行插值的方法.这里从数学原理上系统地阐述了这几种插值方法的基本原理,并利用数值试验和实际数据进行了检验.     

畸变补偿法在滑坡模型试验中的应用可行性探索

传统的滑坡模型试验必须进行大规模的相似材料配比试验研究,要花费大量的人力物力,工作量是惊人的,并且常常伴随着由于介质性质难以控制或模拟所必然产生的畸变,这种畸变用传统的方法难以考虑,却在很大程度上影响了试验的精度。以调整滑坡物理模型渗透系数为例,探索了模型畸变补偿的方法,为采用与原型相同的材料开展滑坡物理模型试验提供了一种新的思路。该方法在滑坡物理模型试验中具有良好的应用前景。     

Application of a three-dimensional finite-element method to strain field analyses

I have programmed a three-dimensional finite-element model to spatially integrate distributed strains. The mathematics is based on Cobbold and Percevault (1983). The method finds the pre-strain configuration of a region by unstraining rectangular prisms into parallelepipeds, then rotating and translating them iteratively to minimize the interelement deviations. A numerical singular-value decomposition calculates the necessary rotations and the final cycle of further strains to make a best fit of the elements. The deviation of elements from holes formed by their nearest neighbors indicates the degree of compatibility of strain measurements.The program reproduces the rotations required in examples with analytic solutions. Even though only a single horizontal layer of elements is used, the fitting procedure correctly calculates rotations in all three dimensions from the constraints of strain compatibility.Three-dimensional strains measured in an Archean greenstone belt of northeastern Minnesota were integrated using a layer of nearly equant finite elements. Rotations calculated from the pre-tectonic configuration accord with field observations of fabrics indicating variable amounts of shear. Rotations about horizontal axes are minimal, precluding large vertical shears. An estimate of 40% true horizontal north-south shortening across the belt can be made from the undeformed configuration.     

Effect of grain packing tightness on strain estimation from the Fry method

How tightly should a sample be packed for strain estimation by the Fry method? We address this issue using synthetic simulations of 900 images such that each image contains 200 randomly distributed grains, but differs from other images with respect to the packing tightness and the degree of sorting. Each image is coaxially distorted by various known strain ratios and the strain estimates from distorted images are obtained by the Fry method. The statistical errors in the strain estimates are found to grow larger with the decrease in the packing tightness irrespective of the level of distortion. We demonstrate that a progressive decrease in the packing tightness results in an increasingly clustered nature of grain center distribution and hence the larger errors. These results, obtained from the synthetic images, are corroborated by two natural examples of sandstone, one loosely packed and the other tightly packed. Based on the results of tests on synthetic and natural examples, we recommend that the Fry method should be used only on those samples that have \({>}30\%\) packing density.     

A direct boundary element method for plane strain poroelasticity

This paper presents a direct boundary element method (BEM), formulated in the Laplace transform space, for plane strain poroelasticity. The paper expands on work by Cheng and Liggett by recasting the theoretical foundation of BEM within the framework of Rice and Cleary's formulation of the Biot theory of poroelasticity. Furthermore, the numerical algorithm is generalized to deal with both interior and exterior domain problems, and a method for indirectly calculating the Cauchy principal value of the singular integrals is presented. Formulae for the stress and flux inside the domain are also derived. Finally, the algorithm is validated by comparing the numerical results with the analytical solution of a borehole subject to a far-field deviatoric stress (exterior domain) and with the solution of Mandel's problem (interior domain). These two examples provide a critical test of the algorithm.     

Extending the strain path method analogy for modelling penetrometer installation

The Strain Path Method (SPM) is an approximate framework for simulating the disturbance caused by piles or penetrometers in soil. The key conceptual assumption of the SPM is that the deformation and strain fields caused during these penetration processes are strongly kinematically constrained (especially during undrained penetration of clays) and can be estimated independently from the actual constitutive properties of the surrounding soil. Previous applications of SPM have estimated strain fields for a variety of penetrometer geometries using velocity fields of ideal inviscid fluids. This paper refines the strain field for penetrometers with 60° conical tips using numerically computed velocity fields in viscous fluids with a variety of boundary conditions imposed on the penetrometer shaft. Following a parametric study, a set of flow conditions is selected which provides a best fit between computed soil deformations and physical displacement measurements made in three separate experiments. The approach is simple and rapid and, while highlighting some of the inaccuracies associated with the existing SPM solution, may also be used for comparative purposes to assist the development of other approaches to the deep penetration problem. Copyright © 2000 John Wiley & Sons, Ltd.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明:初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

河南朱庄金矿区化探规则测网的布设方法

运用导线分层次逐步布设控制点，测距与视距测量相结合布设基测点的方法，解决通视困难的金矿区布设土壤地球化学测量规则测网效率不高，精度低的问题，使用该方法，数据大大减少，便于计算机随机运算，检查，平差，也便于随时发现问题随时纠正，在河南朱庄金矿区1：1万土壤地球化学测量工作中，各项技术指标均符合规范要求，与传统方法相比，节约一半以上工期，返工率低，该方法建立在有先进的测量仪器和先进的计算工具基础上，仪器越先进，方法的优势越明显。     

Evaluation of geochemical data acquired from regular grids

Geochemical data obtained during mineral exploration often are biased by systematic as well as random errors; these may result in failures when usual methods of evaluation are used. This is true particularly in soil surveys carried out in regions where a long history of prospecting and mining activity has occurred and/or where aerial chemical pollution is likely to have occurred.A satisfactory evaluation of geochemical data even in such an unfavorable case requires sampling on a relatively dense grid and utilization of all available knowledge of types of mineralization. The evaluation procedure proposed consists of five consecutive phases: (1). Dividing the area of interest into subareas of a relatively homogeneous geological nature. (2). Processing by multivariate methods (factor analysis, in particular) without consideration of geographic relations. (3). A preliminary interpretation and search for a geochemical explanation of factors. (4). Processing of individual factors in two-dimensional geographic space by directional and frequency linear filtering methods. (5). Final interpretation and construction of a geochemical model. The procedure is illustrated by an example from a geochemical exploration survey in the vicinity of Píbram (Middle Bohemia).     

Tectonic strain of a deformed conglomerate determined from a single pebble

Individual rounded pebbles of schist or foliated gneiss included in a conglomerate can each be used as strain markers when the conglomerate has been deformed subsequently. The shape, orientation and the attitude of the earlier schistosity within a single pebble allow one to determine the strain ratio assuming passive behaviour during deformation. The method may also be applicable to certain individual lava pillows containing paleo-horizontal “lava-level” markers.     

Population polygons of tektite specific gravity for various localities in Australasia

Measurements of specific gravity by the method of liquid flotation have been made on about 6000 tektites from 18 different localities in Australasia, from 1 locality in Texas and 2 in Czechoslovakia. Comparison of specific-gravity population polygons for various localities has led to the unanticipated conclusion that the australite population in southwest Australia is essentially the same as the philippinite population, rather than the population elsewhere in Australia. The javanite population appears closely related to certain populations in Australia. In several localities the presence of two superimposed populations is demonstrated. The specific-gravity evidence indicates that the Australasian tektites represent a single event comprising many distinguishable clusters, some of which have partially overlapped.     

Some guidelines for the practical application of Fry's method of strain analysis

A systematic analysis of patterns in artificial and natural point distributions is presented in order to demonstrate how the nature and degree of anticlustering of point distributions affect the character of Fry diagrams derived from them. Ideally anticlustered artificial point distributions illustrate the nature of the dependence between the degree of anticlustering and the minimum number of points required in such a distribution if it is to reveal strain accurately by Fry's method. In addition, these distributions provide straightforward results which aid in the interpretation of less ideally anticlustered natural point distributions.The results from the artificial distributions may be used to estimate the minimum number of points required for strain determination in natural distributions of varying degrees of anticlustering, as long as the anticlustering is sufficiently strong. However, application of the results from the artificial distributions to less strongly anticlustered natural point distributions shows not only that the existence of a vacancy field is an insufficient criterion for determining whether or not Fry's method is appropriate for strain determination but also that the nature of the anticlustering in these natural distributions limits the effectiveness of enhancing strain definition by increasing the number of points composing the distribution.