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.     

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....     

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。     

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.     

An evaluation of shape indices as palaeoenvironmental indicators using quartzite and metavolcanic clasts in Upper Cretaceous to Palaeogene beach, river and submarine fan conglomerates

The feasibility of using quantitative shape measurements to discriminate between clast populations from different depositional settings was evaluated using samples from 11 fluvial, six submarine fan and four beach conglomerates from south-west California; these origins had been established previously by facies analysis. Quartzite and metavolcanic clasts were characterized by the following indices: modified Wentworth roundness (R_w), maximum projection sphericity (δ_p), oblate-prolate index (OPI) and long (L), intermediate (I) and short (S) axial ratios. These indices were compared with those documented previously for modern gravels. The results show that certain indices are useful palaeoenvironmental indicators, despite inherited differences in shape due to texture, provided that multiple sites are sampled and a statistical approach is used. Statistically, the most effective shape indices are δ_p and S/L which give good results with the Zingg classification (I/L vs. S/I); better results are also obtained using quartzite clasts. The OPI is useful for discriminating between beach and river conglomerates, which consist largely of oblate and prolate clasts, respectively. The relative abundance of blade-shaped clasts is a useful index of sediment maturity, being greatest for river clast samples and smallest for submarine fan clast samples. The latter are dominated by spherical particles. No correlation between palaeoenvironment and R_w is observed, hence the abundance of disc-shaped clasts in the beach conglomerates studied is attributed to selective transport in suspension and sediment by passing during fluvial transport prior to deposition in the surf zone. Selective transport of rollers (spheres and rods) by traction in a shallow marine setting, prior to redeposition by mass transport, may be responsible for the dominance of spherical particles in submarine fan conglomerates.     

Computational Methods for the Determination of Roundness of Sedimentary Particles

A number of subjective and objective methods have been proposed to determine the roundness of rock particles, roundness being one of three properties describing the shape of a particle. Methods that make use of the Fourier transform of the polar coordinates of particles’ edge elements are proposed in this paper. Lowpass filters are used to smooth the profiles of rock particle, roundness is then determined from the differences between the original and smooth profiles. Further methods that are proposed make use of different measures of inequality to quantify the distribution of the energy among the transform coefficients of the profiles of rock particles. These values are then used to determine the roundness of the particles. Entropy and Emlen’s modified entropy are the measures of inequality that are used. Different methods of determining the centre point of a particle and different methods to interpolate the edge elements are compared. The sensitivity of the methods to different resolutions is also investigated. The results obtained with the proposed methods are comparable to those obtained with an existing Fourier transform based method, however it is shown that the proposed methods are computationally less demanding. It is also shown that the proposed methods are better than the existing method when the comparison is based on the correlation between the mean roundness of samples of particles and the actual roundness of the particles.     

THE PRESENTATION OF SUBJECTIVE SHAPE AND ROUNDNESS DATA

If a modified version of the Zingg system is used particles can be subjectively classified into four shape classes. The roundness of a particle can be estimated by assessing the flat/convex/concave ratio and can then be represented as a point on a triangular net; this point can also indicate the Zingg class of the particle.     

磨圆度定量表征在扇三角洲沉积微相判别中的应用

砾石颗粒的磨圆度对粗碎屑的沉积环境具有重要的指示意义。针对玛湖凹陷下三叠统百口泉组砾岩的地下钻井岩芯,运用去扁化De?flat磨圆度测量方法,通过定量获取砾石磨圆度参数对扇三角洲沉积中不同沉积微相的指示关系,分析黄羊泉扇的磨圆度及其方差的分布特征,讨论磨圆度定量表征指示扇三角洲沉积的科学性。研究结果表明,扇三角洲沉积的砾石磨圆度普遍较差,为次棱—次圆状和次棱角状。牵引流沉积的砾石磨圆度普遍好于重力流沉积的砾石磨圆度,且牵引流沉积的砾石磨圆度方差明显小于重力流沉积的方差,指示河道沉积中的砾石磨圆度更加集中。黄羊泉扇砾石磨圆度以棱角状和次棱角状为主。通过黄羊泉扇区砾岩砾石颗粒磨圆度及其方差的变化趋势,表明磨圆度对沉积相带具有指示意义。砾石磨圆度的定量表征可以为粗粒碎屑沉积相分析提供新的定量沉积学手段。     

Interference phenomena between particle flattening and particle rounding in free vertical sedimentation processes

In this paper interference phenomena between particle flattening and particle rounding during the free vertical sedimentation of natural particles are investigated. Particle flattening is measured by the Corey Shape Factor (CSF), particle rounding by the Powers Index (P). Using Dietrich's equation, the effect of the flattening and the effect of the rounding on the terminal fall velocity of the particle can be studied separately. This is done by examining the influence of particle flattening and particle rounding on the Particle Sedimentation Coefficient (PSC), which is the ratio of the nominal diameter D_n of the particle to the equivalent sedimentation diameter D_b. It appears that particle flattening and particle rounding are interdependent so that interference phenomena occur. In the case of positive interference, the combined effect of flattening and rounding on the PSC is larger than the sum of the effects of both parameters separately. If, on the other hand, the combined effect is smaller than the sum of the single effects, negative interference occurs. For fine-grained particles, the more the shape of a particle differs from a sphere in one variable (flattening or rounding), the higher will be the influence of the other variable on the free vertical fall. For coarse-grained particles, the inverse occurs. For very fine-grained particles (D_n < 200 μm (air) or < 370 μm (water)) the influence of particle rounding on free vertical settling is negligibly small. For coarser grained particles, flattening is the most important parameter if the grains are strongly flattened. If not, rounding will be the governing parameter.     

A morphometric analysis of terrace gravels in Santa Ynez basin,Santa Barbara County,California

An analysis of 6,300 pebbles from eighteen river terraces within the five subareas of the Santa Ynez River basin has revealed significant differences in particle sphericity and roundness of the various terrace gravels.Using the Cailleux technique of pebble measurement, Krumbein's sphericity ratio formula (Y) and the author's own roundness ratio or the I/L¹ ratio (R) the computed values derived for $\text{Y}$ range from 0.92 to 1.11, and for $\text{R}$ from 0.66 to 0.79 on these benches.An analysis of variance, based on the F-test applied to samples has established that: (a) gravel sphericity and roundness increase significantly from upstream to the river mouth; (b) in the subareas themselves pebble sphericity and roundness vary significantly from bench to bench indicating varied energy conditions of deposition; (c) all terrace gravels measured show higher sphericity and roundness than the underlying Orcutt gravels. This suggests a reworking of the latter by the Santa Ynez River.     

Three-dimensional quantitative analysis on granular particle shape using convolutional neural network

To identify all desired shape parameters of granular particles with less computational cost, this study proposes a three-dimensional convolutional neural network (3D-CNN) based model. Datasets are made of 100 ballast and 100 Fujian sand particles, and the shape parameters (i.e., aspect ratio, roundness, sphericity, and convexity) obtained by conventional methods are used to label all particles. For the model training, by feeding the slice images of particles into the model, the contour of particles is automatically extracted, thereby the shape parameters can be learned by the model. Thereafter, the model is applied to predict shape parameters of new particles as model testing. All results indicate the model trained based on slice images cut from three orthogonal planes presents the highest prediction accuracy with an error of less than 10%. Meanwhile, the accuracy for concave and angular particles can be guaranteed. The rotation-equivariant of the model is confirmed, in which the predicted values of shape parameters are roughly independent of orientations of the particle when cutting slice images. Superior to conventional methods, all desirable shape parameters can be obtained by one unified 3D-CNN model and its prediction is independent of particle complexity and the number of triangular facets, thus saving computation cost.     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Mathematical theory of counting two-dimensional grains by line and ribbon methods

Currently popular line and ribbon methods yield grain counts that are differentially biassed in regard to sizes and orientations of the maximum projection diameter of the grains in the sample. Bias correction factors covering the entire range of counting situations are obtained using probability theory and coordinate geometry. The corrected numbers are true unbiassed Fleet counts that are suitable for estimating true statistical measures and for estimating economic potential of mineral(s). Irregular grains can be counted by classifying them into either elliptical or rectangular shapes by means of nondimensional discriminant equations based on area or length measurements. Wadell roundness (ρ) for elliptical and rectangular outlines shows inconsistency, but the modified Wadell roundness (ρ′) proposed herein is a consistent measure of roundness for all types of shapes, and hence the latter is recommended for use. Theoretically, roundness is linearly correlated with the form factor (B/A) for elliptical outlines and hence, a linear correlation of average roundness and average form factor in sediments is to be expected. The entire spectrum of shape comprising two continuous variables, form factor and modified Wadell roundness, may be classified into two discrete shape states (elliptical and rectangular) or into several discrete shape states having ranges of ρ′ and B/A values.     

大理冲积扇含水层非均质性分布规律研究

洪-冲积扇的非均质性分布规律对含水层渗流和污染物迁移研究、地下水污染管理、控制及修复具有重要意义。本文以大理点苍山东麓隐仙溪洪-冲积扇为例,对其水动力条件、沉积构造模型、地形坡度与运移距离的关系进行探讨。研究表明,冲积扇沉积非均质受水动力条件影响,当水动力较好时,沉积颗粒物为砾石和漂砾,填充泥质和粉砂质,水动力较弱时沉积多为砂质和粘土颗粒,扇面整体以水流河道为中心轴呈扇形沉积;冲积扇沉积颗粒物的分选性和磨圆度受地形坡度的影响,地形坡度大沉积颗粒物分选性和磨圆度差,搬运距离越远分选性和磨圆度越好;扇顶因水动力强,坡度大,沉积物分选性和磨圆度差,层理不发育,扇中扇缘随着水动力条件及地形坡度减弱,沉积物分选性和磨圆度逐渐变好,层理较为发育,沉积为水平或均匀层理。     

大位移剪切下钙质砂破碎演化特性

为了揭示钙质砂在大位移剪切作用下的破碎及形状演化规律,对南海钙质砂进行了系列不同剪切位移下的环剪试验。首先,利用筛分和激光粒度分析获取试验后的颗粒粒径分布,分析颗粒分布变化情况;其次,通过粒径分布对破碎进行定量分析;最后,运用图像处理技术计算颗粒圆度和扁平度,分析了颗粒形状的变化情况。试验结果表明,在不同的竖向压力下,颗粒会达到不同的稳定级配,但达到稳定所需的剪切位移相同;经历大位移剪切后,出现粒径为0.01～0.075 mm钙质砂破碎严重的现象;随剪切位移的增加,颗粒的圆度和扁平度减小。针对细小颗粒破碎严重的现象,修正了相对破碎率;修正后的相对破碎率能考虑粒径为0.01～0.075 mm颗粒发生的破碎。剪切后的钙质砂颗粒更为规则,整体轮廓趋于圆形、表面更光滑。     

An efficient approach to generating DEM samples having coincident void ratios with actual sand

The ranges of initial void ratios that can be achieved for numerical samples with the same grading as actual sand under gravity are explored using three-dimensional discrete element method (DEM). A corrected compressible accumulation model is proposed to predict the packing density of sand. Compared with the measured results, the errors of the prediction results are small. For three-dimensional DEM samples, when the ratio of sample size to particle size L/R is equal to or larger than 30, the maximum and the minimum void ratios are minimally affected by the sample size L. The maximum void ratios and the minimum void ratios of numerical samples with spherical particles are much smaller than those of actual sands. The generation method for numerical samples with non-spherical particles is proposed based on the theory of CPM. The variations of void ratios of numerical samples with non-spherical particles are wider than actual sands. So it can meet all the need of DEM simulation on the void ratio of actual sand.     

固结与荷载耦合作用下吹填土力学性质与微结构参数关联性

固结条件与荷载条件对吹填土的力学特性具有明显的影响,且土的微观结构特征是决定其宏观力学性质的本质因素,为了研究吹填软土力学特性在不同固结条件和荷载条件下的变化规律及与微结构参数的关联性,对天津滨海新区重塑吹填软土进行不同初始固结条件与荷载效应综合作用下的蠕变试验和微观结构测试,研究此条件下吹填土力学特性的变化规律,并通过灰色关联度理论建立宏观力学参数与微结构参数之间的关联性。试验结果表明:稳定性蠕变对吹填软土强度的增长起到积极作用,有偏压固结较无偏压固结强度增长更快,且初始固结越充分,强度增长越快;随蠕变时间的增加,颗粒的等效直径、形态比和圆度呈增大的趋势,而颗粒和孔隙的数量与周长、孔隙的等效直径、形态比和圆度则呈减小的趋势;抗剪强度指标C,φ值随颗粒等效直径、形态比和圆度的增大而增大,但随颗粒和孔隙的数量与周长、孔隙的等效直径、形态比和圆度的增大而减小。关联度分析表明,颗粒（孔隙）等效直径和圆度是影响吹填土力学性质演化的重要微结构参数,固结与蠕变越充分,土体微结构参数调整越稳定,强度越高。     

Equantcy versus sphericity

The shape of a particle is commonly characterized by its sphericity. In geology, sphericity is determined by comparing a grain's length, width and breadth diameters. This type of measurement does not indicate how close the particle is to a true spherical shape, and cubes, tetrahedrons, and true spheres all have the same degree of sphericity. Because the term sphericity is misleading, implying that its determination takes roundness into account, a different term should be used. I propose that whenever the shape of a grain is determined by measuring or estimating the lengths of its main axes, we regard this as determining its degree of equantcy.     

珊瑚砂颗粒形状特征分析

珊瑚砂粒形状及粗糙度等微细观特性影响着砂土的宏观力学性质,采用图像处理技术对珊瑚砂粒的长宽比、面积、圆度、分形维数进行了分析。使用3D测量显微镜对砂粒的表面粗糙度,界面扩展面积比、峰顶点的算数平均曲率进行了测量计算。试验结果表明:大部分珊瑚砂颗粒的长宽比介于1.2~1.5之间,且长宽比呈现出负偏态分布。砂颗粒的圆度则主要集中于0.75~0.9区间,其表现为负偏态分布。砂颗粒的面积主要在0.015~0.035 cm2之间,颗粒面积为正偏态分布。砂粒的分形维数D基本介于1.04~1.10之间,表明砂颗粒具有很强的自相似性。粗糙度的分析结果表明,珊瑚砂颗粒表面平整度差,分布有较多的侵蚀坑,局部存在尖锐的凸起,砂粒表面粗糙度S_a为20.078 μm。界面扩展比S_dr为0.167,砂颗粒表面分布有若干倾斜面。峰顶点的算数平均曲率S_pc为216.641 mm-1,显示出砂颗粒之间的接触较为尖锐。上述研究结果可为珊瑚砂宏微观力学特性研究提供参考。