基于数字图像处理的矿物颗粒形态定量分析

矿物颗粒形态的评价一般采用目估法在显微镜下观测岩石薄片,其评价结果受主观影响.本文利用岩石薄片显微照片,基于图像处理技术提出了矿物颗粒形态定量分析方法.矿物颗粒形态参数主要包括球度、凸度、长宽比、磨圆度等.该方法利用图像分割技术将显微照片中的矿物颗粒区分开,提取颗粒的像素轮廓坐标进行离散几何分析,计算矿物颗粒形态参数....     

基于复数傅里叶分析的岩土颗粒细观特征识别与随机重构方法

岩土细观特征的识别与分析是岩土力学研究的重要内容。基于傅里叶变换原理,将任意岩土颗粒的二维轮廓变换为傅里叶描述符与相位进行分析,建立了基于复数傅里叶分析的细观特征表征与重构方法。通过两组不同颗粒的傅里叶细观特征统计,研究了不同阶傅里叶描述符与细观特征参量的对应关系。结果表明：-12～0及16～20阶对应的傅里叶描述符决定颗粒的形状;-23～-11及1～15阶对应的傅里叶描述符与颗粒粗糙度密切联系;傅里叶描述符曲线峰值与颗粒的粒径显著线性相关;高阶傅里叶系数与阶数近似呈对数线性关系,低阶系数则由不同颗粒形状决定。采用建立的傅里叶描述符对应关系进行颗粒相似重构研究,发现重构颗粒的外轮廓及傅里叶统计参量与实际颗粒十分接近,且反映颗粒的粗糙度、纹理等细部特征,其成果可用于大量岩土颗粒与力学特性的相关性研究。     

How round is round? A new approach to the topic ‘roundness’by Fourier grain shape analysis

Numerous methods for roundness measurement have been developed. None, however, has been generally accepted, because of conceptual and practical deficiencies. Modern image processing and Fourier grain shape analysis have eliminated the practical shortcomings, but the conceptual ones remained. Single, higher harmonics of the Fourier series, for example, fail to serve as reliable equivalents for roundness evaluation. The concept outlined in this paper recognizes three criteria for the evaluation of roundness. (1) All curvatures, convex as well as concave or plane elements, must be considered. (2) The positions of morphological elements are significant because salient parts of a particle are more easily abraded than protected ones. Consequently, the curvatures have to be weighted by their relative position on the particle. (3) Positions and curvatures of morphological elements have to be compared with the particle's ultimate abraded shape, which is assumed to be an ellipsoid. The ellipsoid reflects the aspect of form or sphericity. The distinction between sphericity and roundness is retained because there is no evidence that sphericity changes significantly during transport. The measurement is based on the outline of a particle's maximum projection plane, which is transformed to a Fourier series. Roundness data are derived from the complete amplitude spectrum. The aspect of sphericity is eliminated by subtracting the amplitude spectrum of the best approximating ellipse from the spectrum of the empirical shape. The residual amplitudes are normalized and summed. In a final step the resulting values are rescaled. This guarantees reasonable boundaries and a normal distribution of roundness values. The procedure is automated and its efficiency permits the calculation of large samples. Tests on fluvial and coastal gravel populations demonstrate that the method is sensitive to abrasional wear during all stages of roundness.     

Particle shape: a review and new methods of characterization and classification

Shape is a fundamental property of all objects, including sedimentary particles, but it remains one of the most difficult to characterize and quantify for all but the simplest of shapes. Despite a large literature on the subject, there remains widespread confusion regarding the meaning and relative value of different measures of particle shape. This paper re‐examines the basic concepts of particle shape and suggests a number of new and modified methods which are widely applicable to a range of sedimentological problems; it is shown that the most important aspects of particle form are represented by the I/L ratio (elongation ratio) and S/I ratio (flatness ratio). A combination of these two ratios can be used to classify particles in terms of 25 form classes. A method of obtaining a quantitative measure of particle roundness using simple image analysis software is described, and a new visual roundness comparator is presented. It is recommended that measurements of both roundness and circularity (a proxy measure of sphericity) are made on grain images in three orthogonal orientations and average values calculated for each particle. A further shape property, irregularity, is defined and a classification scheme proposed for use in describing and comparing irregular or branching sedimentary particles such as chert and coral.     

基于能量耗散机制的粗粒土圆度损伤特性分析

圆度损伤是研究粗粒土力学特性变化的重要指标,为探索剪切过程中粗粒土圆度损伤的演化过程,定性及定量从能量角度对损伤本质进行分析。根据能量耗散原理,分析了剪切系统及单个颗粒剪切过程中能量的耗散与传递。结合弹塑性力学与热力学定律,定义粗粒土圆度损伤因子Dr,建立了基于能量耗散下的圆度损伤模型。采用剪切试验研究不同圆度的花岗岩和卵石颗粒的强度特性,以观测效果较好的花岗岩颗粒为研究对象,研究不同法向应力下的圆度损伤演化过程,运用MATLAB对模型及试验数据分析。结果表明:圆度不同的颗粒(花岗岩、卵石)随圆度减小,传递到颗粒内部积聚的塑性势能增大,更易在颗粒边界棱角处产生微裂纹使颗粒磨损,从而增大粗颗粒圆度,强度特性减小;剪切试验粗粒土圆度损伤演化过程存在2次损伤拐点,可分为圆度损伤响应、圆度损伤演化、圆度损伤稳定3个阶段;同一类型颗粒法向应力增大,达到损伤临界状态圆度损伤所需能量增大,圆度损伤因子减小。基于能量耗散下建立的圆度损伤模型阐述了剪切过程中的圆度损伤,试验结果能合理地反应圆度损伤演化过程中颗粒力学特性响应。     

多尺度内聚颗粒模型破碎过程研究

岩石破碎过程涉及到多个变量（应力、应变和孔隙率等）变化和裂纹的产生、拓展和聚集,是研究岩石破碎机制的重要途径。为了克服现有研究中岩石颗粒模型未考虑岩石内部特征问题,针对岩石内部颗粒非均匀分布、聚集的特点,开展了岩石轴压破碎试验和岩石岩相分析试验,并在此基础上,构建符合真实岩石内部特征的多尺度内聚颗粒模型。根据离散元的颗粒黏结模型（BPM）理论,求解了多尺度内聚颗粒模型不同粒级颗粒间黏结键的力学关系,发现与二级颗粒形成的黏结键断裂判据为 ≥ 2 GPa,三级颗粒之间形成的黏结键断裂判据为 ≥ 6 GPa,并基于该判据建立了用于模拟颗粒模型破碎的演化模型。通过模拟轴压破碎试验,破碎演化模型可以从细观角度得到颗粒模型各颗粒间黏结键承受力的实时变化和岩石破碎过程中黏结键从外而内的断裂顺序;从宏观角度得到岩石内部裂纹呈V形从上表面两端延伸并相交于岩石中部。通过与岩石轴压破碎试验结果对比发现,模拟试验得到的岩石裂纹特征与岩石轴压破碎试验结果相似,验证模型的可靠性,实现了从细观和宏观角度分析岩石破碎过程。     

岩石中纳米粒子层的观察厘定及其地质意义

纳米粒子具有个体极小(≤ 100nm), 大小均一, 多元物质和功能繁多的特点。岩石剪切滑移面纳米粒子层最早发现于美国圣安德列斯断裂带的花岗质糜棱岩中, 后相继在国内外一些地区的不同岩类中观察到。在剪切滑动作用下, 具有圆度和球度的纳米粒子可被变异, 并形成层状结构和各种构造型式。对岩石中纳米粒子层的成因有着不同的观点, 我们倾向于剪切摩擦的主导作用, 纳米粒子层可称谓摩擦-粘性薄层带。纳米级尺度粒子的力学、物理和化学效应是多种的、新奇的, 因此, 岩石纳米粒子层的研究有着重要的理论和实践意义。目前有关方面的研究工作, 国内外都处在起步阶段。      

The shape of rock particles, a critical review

An attempt was made to distinguish aspects of the shape of rock particles, and to discover by analysis and empirical considerations the most appropriate parameters for describing these aspects. The shape of a rock particle can be expressed in terms of three independent properties: form (overall shape), roundness (large-scale smoothness) and surface texture. These form a three-tiered hierarchy of observational scale, and of response to geological processes. Form can be represented by only two independent measures from the three orthogonal axes normally measured. Of the four pairs of independent measures commonly used for bivariate plots, the two sphericity/shape factor pairs appear to be more efficient discriminators than simple axial ratios. Of the two, the most desirable pair is the maximum projection sphericity and oblate-prolate index for both measures show an arithmetic normal distribution for the range investigated. A measure of form that is independent of the three orthogonal axes, and measures derived from them, is the angularity measure of Lees. Roundness has measures of three types, those estimating average roundness of corners, those based on the sharpest corner, and a measure of convexity in the particle outline. Although each type measures a different aspect, they are not independent of each other. Only roundness from corners is considered in detail. As neither average nor sharpest corner measures are inherently more objective or more quantitative, purpose should determine which is more appropriate. Of the visual comparison charts for average roundness, Krumbein's appears best. The Modified Wentworth roundness is the most satisfactory for estimating roundness from the sharpest corner. The Cailleux Roundness index should not be used because it includes aspects of roundness and form. Shape is a difficult parameter to use for solving sedimentological problems. Even the best of the commonly used procedures are limited by observational subjectivity and a low discriminating power. Unambiguous interpretation of particle shape in terms of source material and processes will always be made difficult by the large number of natural variables and their interactions. For ancient sediments satisfactory results can be expected only from carefully planned studies or rather unusual geological situations.     

一种改进的光滑粒子动力学法在地震条件下岩质边坡中的验证与应用

开发一种改进损伤框架的粒子流算法,被称为核断裂的光滑粒子流法（kernel-broken smoothed particle hydrodynamics,KBSPH）,用于模拟地震条件下岩质边坡的裂纹扩展和变形破坏过程.在KBSPH中,提出一种改进的损伤框架,通过引入断裂标志来改进损伤粒子的核函数,使损伤粒子的虚拟应力键直接断裂,裂纹在断裂的应力键间生成,从而模拟岩石的裂纹扩展过程.在地震边界上采用了双层边界,将动力输入边界与黏滞边界分离.首先通过薄板振动实验验证KBSPH的动力特性.其次以单裂隙岩体单轴压缩试验验证KBSPH的断裂力学特性.最后模拟地震条件下多节理岩质边坡中裂纹扩展过程和动力响应.薄板振动实验验证了KBSPH的动力特性的准确性.单裂隙岩体单轴压缩试验,证明了KBSPH可以正确模拟预制裂隙尖端的翼型裂纹.通过对比以往数值模拟方法和现场案例,表明KBSPH正确揭示了加速度放大效应以及地震条件下岩质边坡的裂纹扩展过程.KBSPH避免了传统算法的网格畸变,损伤粒子应力分量重新分配的问题,降低了编程难度,提高了运行速率,可为SPH在地震条件下岩石力学中的应用和理解岩石断裂机理提...     

砂土颗粒三维形态的定量表征方法

颗粒形态是影响砂土力学特性的重要因素,特别是影响砂土在低应力状态下的抗剪强度、剪胀效应和临界状态行为,以及高应力状态下的颗粒破碎行为。因此,准确地重构砂粒的三维形态,并量化计算其形态表征参数是研究砂粒形态效应的前提工作。借助于高精度的CT扫描技术和图像处理技术,获得近海石英砂和风化花岗岩残积砂这两类砂土颗粒的三维形态信息。采用球谐函数序列实现两种砂颗粒三维形态的准确重构,并通过球谐函数分析计算砂土颗粒的体积来验证该方法的有效性。基于球谐重构的三维砂粒表面,提出了实用性的方法来计算砂粒的表面积、表面曲率和三维尺寸等,进而计算砂粒的三维球度、圆度和伸长率等形态表征参数。结果表明,当球谐函数阶达到15时,其重构的砂粒基本形状和表面纹理均与真实砂粒非常接近;近海石英砂在水流搬运和磨蚀的作用下颗粒形态较为规则和圆滑,球度和圆度较大,而风化花岗岩残积砂则在物理风化和剥蚀作用下颗粒形态较为复杂和粗糙,球度和圆度较小;而这两种地质作用对砂土颗粒的伸长率则没有明显的影响。     

基于颗粒识别分析系统的碎屑流堆积物颗粒识别和统计方法研究

碎屑流堆积物颗粒识别和统计是碎屑流灾害的研究重点。文章基于图像处理孔隙（颗粒）及裂隙图像识别与分析系统（PCAS）,以贵州纳雍普洒村崩塌-碎屑流为例,结合纳雍崩塌堆积物粒径实测结果,通过阐释识别过程中阈值、孔喉封闭半径、最小孔隙面积的参数意义,研究PCAS软件在碎屑流颗粒识别与统计中的应用,并提出了颗粒识别时这些参数的选取方法。分析结果表明:（1）PCAS能自动准确地识别碎屑流堆积物颗粒与孔隙,相比人工计数更精细,所识别堆积物各区小颗粒比重较大,0～2 m颗粒粒径各区占比都在50%以上;（2）当阈值为170（像素）时能获得精细的二值图像,颗粒与孔隙得到了准确地区分;（3）不同参数取值下获得堆积物颗粒粒径分布结果不同,碎屑流堆积物颗粒识别宜采用较大的孔喉封闭半径和较小孔隙面积,当二者比值为3/30（像素）时能更好地反应颗粒粒径分布情况;（4）PCAS具有较高的可行性,统计结果显示,各粒径含量变化趋势与人工统计相近,两种统计方法各粒径占比、分布规律基本吻合,说明利用PCAS可以实现对崩塌碎屑流颗粒粒径分布的高效便捷分析。     

泥石流浆体与大颗粒冲击力特征的试验研究

开展了密度为1 400～2 200 kg/m3的泥石流浆体、浆体与大颗粒混合流体的冲击力试验,获取了流速为2.8～4.9 m/s条件下31组冲击力试验数据。采用小波分析方法有效地去除了冲击力数据中的噪声信号,依据离散傅里叶变换（FFT）为基础的频谱分析结果,将低频泥石流浆体冲击和高频大颗粒冲击的临界频率值界定为2 Hz,实现了浆体和大颗粒冲击信号的分离。目前水动力学公式中待定系数α缺乏统一的确定方法,以不同地区157组泥石流观测和试验数据为基础,建立了待定系数?与流体Fr数的幂函数关系,形成可表征不同流态,且弱化尺度效应的浆体动压力计算公式。与泥石流浆体平滑信号相比,大颗粒冲击压力具有一定随机性。泥石流大颗粒冲击次数与频率随大颗粒的质量比增加而增大,其质量比从0.05增至0.21时,冲击总次数从1 305次增至2 838次,冲击频率从82次/s增至195次/s,且龙头段大颗粒的冲击频率高于后续泥石流体。测得大颗粒的压力约为60 kPa,是相同密度和流速下浆体动压力的3倍。随着大颗粒比例的增加,上部1#和2#传感器测得大颗粒冲击频率增加量明显高于下部3#～6#。说明随着流体中大颗粒比例上升,颗粒物质多集中于泥石流上部或表层运动,也佐证了泥石流运动中大颗粒多集中在龙头顶部的认识。对大颗粒和浆体冲击规律的分析可为固液两相流运动机制研究和防治工程设计以及承灾体易损性定量评估提供合理参数。     

DEM–SPH simulation of rock blasting

A numerical model is proposed for the simulation of rock blasting. A bonded particle system is utilized to mimic the behavior of rock. The particles interact at the contact points through normal and shear springs to simulate rock elasticity. To withstand the deviatoric stresses, the particles are glued to each other. If the applied force exceeds the contact strength, local failure occurs and microcracks are developed in the synthetic rock. For simulation of gas flow, the smooth particle hydrodynamic method is implemented. The interaction of gas particles with the rock grains is assumed to follow a perfect plastic collision model in which the initial momentum of the colliding particles is preserved. A detailed examination of the interaction of gas with blast hole is investigated. It is shown that the proposed hybrid model is capable of simulating the induced shock waves in the gas together with wave propagation in the rock material. The model successfully mimics crack propagation in rock. In particular, the crushed zone around the borehole, radial cracks, and surface spalling are all captured successfully. The results of numerical analysis suggest that gas–rock interaction can, in fact, generate a few successive compressive waves in the rock specimen, causing further extension of radial cracks with time as the weaker secondary and tertiary waves interact with the crack tips.     

Low energy trajectories for the Moon-to-Earth space flight

The Moon-to-Earth low energy trajectories of ‘detour’ type are found and studied within the frame of the Moon-Earth-Sun-particle system. These trajectories use a passive flight to the Earth from an initial elliptic selenocentric orbit with a high aposelenium. The Earth perturbation increases the particle selenocentric energy from a negative value first to zero and then to a positive one and therefore leads to a passive escape of the particle motion from the Moon attraction near the translunar libration pointL ₂. This results in the particle flight to a distance of about 1.5 million km from the Earth where the Sun gravitation decreases the particle orbit perigee distance to a small value that leads to the particle approaching the Earth vicinity in about 100 days of the flight. A set of the Moon-to-Earth ‘detour’ trajectories is defined numerically. Characteristics of these trajectories are presented. The ‘detour’ trajectories give essential economy of energy (about 150 m/s in Delta V) relative to the usual ones.     

A generalized three-dimensional Hoek–Brown strength criterion

Summary  Although the Hoek–Brown strength criterion has been widely used in rock mechanics and rock engineering, it does not take account of the influence of the intermediate principal stress. Much evidence, however, has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. Therefore, researchers have developed three-dimensional (3D) versions of the Hoek–Brown strength criterion. In this paper, three existing 3D versions of the Hoek–Brown strength criterion are reviewed and evaluated. The evaluation shows that all of the three 3D versions of the Hoek–Brown strength criterion have limitations. To address the limitations, a generalized 3D Hoek–Brown criterion is proposed by modifying the generalized Hoek–Brown strength criterion. The proposed 3D criterion not only inherits the advantages of the Hoek–Brown strength criterion but can take account of the influence of the intermediate principal stress. At a 2D stress state (triaxial or biaxial), the proposed 3D criterion will simply reduce to the form of the generalized Hoek–Brown strength criterion. To validate the proposed 3D strength criterion, polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature. Predictions of the proposed generalized 3D Hoek–Brown strength criterion are in good agreement with the test data for a range of different rock types. The difference of the proposed generalized 3D Hoek–Brown strength criterion from and its advantages over the existing 3D versions of the Hoek–Brown strength criterion are also discussed. It should be noted that the proposed 3D criterion is empirical in nature because it is an extension of the 2D Hoek–Brown strength criterion, which is empirical. Because of the non-convexity of the yield surface for a biaxial stress state, the proposed 3D criterion may have problems with some stress paths. Correspondence: L. Zhang, Department of Civil Engineering and Engineering Mechanics, The University of Arizona, Tucson, Arizona 85721, USA     

碎屑颗粒圆度的分形描述

碎屑颗粒圆度是指碎屑颗粒的原始棱角被磨圆的程度,用来表征碎屑沉积物的结构成熟度。目前普遍的做法是采用Powers 1953年作的一组图,表示从尖棱角状至滚圆状各级圆度的特征,这一做法属于定性描述。本文借助分形几何学理论,利用盒维数法实现了计算机对颗粒维数的自动统计计算,结果表明碎屑颗粒维数可以作为刻画碎屑颗粒圆度的定量指标。      

Stress–Strain Model for Carbonate Rocks Based on Haldane’s Distribution Function

Summary. This paper presents a model created by the author to predict stress–strain relationships for weak to strong carbonate rocks (σ_c < 100 MPa) exhibiting axial strains up to 1%. The stress–strain model based on Haldane’s distribution function (Haldane, 1919) relates the axial stress (or normalized axial stress) to the square of an exponential function where the exponent is axial strain. To obtain accurate stress–strain relationship over the whole pre-failure strain with the proposed stress–strain model, it is necessary to have only one datum point (peak axial stress and maximum axial strain at this peak stress). It is shown that the stress–strain relationships observed in laboratory compression tests on samples collected from six carbonate rock formations (chalk, dolomites and limestones) from different parts of Israel, agree well with the stress–strain prediction model proposed by the author.     

珊瑚颗粒形状对钙质粗粒土的压缩性能影响

珊瑚颗粒形状不规则是其显著区别于陆源土的一大特征。为揭示珊瑚颗粒形状对钙质粗粒土压缩性能的影响,人工挑选出不同形状(块状、枝状、棒状、片状)的珊瑚颗粒,以块状颗粒为基础,与其他3种不同形状的粗颗粒任意一种混合,控制不同颗粒形状配比制成钙质粗粒土试样,完成室内压缩试验,对比分析试验前后珊瑚颗粒的圆度、长宽比、扁平度和凹凸度等形状参数,评价颗粒形状对压缩性能的影响。结果表明:(1)粒径为10~20 mm钙质粗粒土的压缩模量是4~5. 5 MPa,回弹系数为42~53;(2)随枝状、棒状或片状颗粒掺量的增加(0、10%、20%、30%),试样压缩模量呈小幅波状变化,回弹系数呈持续减小趋势;(3)各加载区间应力-应变曲线包括应力快速增长阶段、应力-应变同步增长阶段、应变增长阶段共3个阶段和1个稳定点;(4)随枝状颗粒掺量的增加,试样的长宽比和凹凸度逐渐增加,圆度和扁平度基本无变化;因颗粒破碎的影响,试验后试样的长宽比及扁平度有所增加,圆度及凹凸度则有所减小。选择钙质粗粒土地基时,应考虑其压缩性能,避免施工初期的快速加载。     

A quantitative technique for assessing the roundness of pottery sherds in water currents

The shape property of transposed pottery sherds that changes most rapidly due to wear during water transport in natural sedimentary environments is roundness, the degree of curvature of edges and corners. of the many methods for the measurement of particle roundness, which are briefly reviewed, that proposed by Wadell (1932, 1933) is considered to specify roundness best. A simple and rapid procedure for the measurement of the Wadell projection roundness is described, which yields roundness values having a precision of the order of a few percent, the precision improving with the degree of roundness. the technique is therefore suitable for the analysis of large samples of transposed and transported sherds.     

Evaluation of equivalent medium methods for stress wave propagation in jointed rock mass

This paper evaluates the existing equivalent medium methods for jointed rock mass and further develops the equivalent viscoelastic medium method proposed by the authors. The advantages and limitations of different equivalences to the discontinuous rock mass are discussed. Theoretical derivation of stress wave propagation through the equivalent viscoelastic medium is carried out by adopting the Fourier transformation method, and the parameters of the equivalent viscoelastic medium method are determined analytically. The frequency dependence and the wave attenuation phenomenon can be properly described when the imaginary terms of the complex moduli of the rock mass are included. The results show that the equivalent viscoelastic medium method is able to predict the effective velocity and the stress wave transmission coefficient in a rock mass more accurately than the conventional effective elastic moduli methods. An example of the stress wave propagation through rock mass with parallel joints shows that the equivalent viscoelastic medium method is promising and worthy to be further explored for application in practical rock engineering problems. Copyright © 2011 John Wiley & Sons, Ltd.