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.     

定量表征河流砂颗粒的形状——在西藏帕隆藏布的尝试

河流搬运体系中,颗粒的形状属性可以反映其来源、搬运、沉积的过程。长期以来沉积学界缺乏相对统一的定量的、多维的颗粒形状参数。本研究以西藏雅鲁藏布江支流帕隆藏布为例,运用图像分析、软件分析等计算机辅助技术,对8个天然河流砂样品中的2276个颗粒开展碎屑成分鉴定和形状参数量化等工作。重点评估了11个颗粒形状参数,通过因子分析等统计方法提取并定义了3个形状信号,包括圆形度因子、规则度因子和平滑度因子。这些参数可用于表征颗粒宏观形状上接近圆形的程度、中观尺度上轮廓规则的程度及轮廓平滑的程度。挖掘天然河流砂的重要形状特征后,进一步探索了这些形状参数与颗粒成分、粒度的关系。本研究成果为解释河流系统中颗粒的形状信号、理解颗粒自身微观属性和外部物理过程等提供重要借鉴。     

定量表征河流砂颗粒的形状——在西藏帕隆藏布的尝试

河流搬运体系中,颗粒的形状属性可以反映其来源、搬运、沉积的过程。长期以来沉积学界缺乏相对统一的定量的、多维的颗粒形状参数。本研究以西藏雅鲁藏布江支流帕隆藏布为例,运用图像分析、软件分析等计算机辅助技术,对8个天然河流砂样品中的2276个颗粒开展碎屑成分鉴定和形状参数量化等工作。重点评估了11个颗粒形状参数,通过因子分析等统计方法提取并定义了3个形状信号,包括圆形度因子、规则度因子和平滑度因子。这些参数可用于表征颗粒宏观形状上接近圆形的程度、中观尺度上轮廓规则的程度及轮廓平滑的程度。挖掘天然河流砂的重要形状特征后,进一步探索了这些形状参数与颗粒成分、粒度的关系。本研究成果为解释河流系统中颗粒的形状信号、理解颗粒自身微观属性和外部物理过程等提供重要借鉴。     

Quantitative characterization of grain shape: Implications for textural maturity analysis and discrimination between depositional environments

Grain shape plays an important role in textural analysis of sedimentary grains. Textural analysis helps to determine the formation, transportation and deposition processes of sedimentary rocks. However, there is a lack of standardized methodology for quantitative characterization of grain shapes. The utility of fully automated image analysis for grain shape measurement is assessed in this paper. This research aimed to identify the most useful shape parameters for textural characterization of populations of grains and determine the relative importance of the parameters. A key aspect of this study is to determine whether, in a particular sedimentary environment, textural maturity of the samples can be ranked based on their grain shape data. Furthermore, discrimination of sedimentary depositional environments is explored on the basis of grain shape. In this study, 20 loose sediment samples from four known depositional environments (beach, aeolian, glacial and fluvial) were analysed using newly implemented automatic image analysis methods. For each sample, a set of 11 shape parameters were calculated for 200 grains. The data demonstrate a progression in textural maturity in terms of roundness, angularity, irregularity, fractal dimension, convexity, solidity and rectangularity. Furthermore, statistical analysis provides strong support for significant differences between samples grouped by environment and generates a ranking consistent with trends in maturity. Based on novel application of machine learning algorithms, angularity and fractal dimension are found to be the two most important parameters in texturally classifying a grain. The results of this study indicate that textural maturity is readily categorized using automated grain shape parameter analysis. However, it is not possible to absolutely discriminate between different depositional environments on the basis of shape parameters alone. This work opens up the possibility of detailed studies of the relationship between textural maturity and sedimentary environment, which may be more complicated than previously considered.     

Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis

This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two‐dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles. Copyright © 2003 John Wiley & Sons, Ltd.     

碎石颗粒形态特征及其与堆积特性的关系

颗粒形态对碎石集料宏观力学性质有显著影响,准确描述其形态特征是从微细观层面研究材料宏观力学行为的基础性工作。针对颗粒形状、棱角、纹理3个尺度的形态特征,探讨了基于颗粒几何尺寸的量化表征参数;分析了不同粒组碎石颗粒形态特征表征参数的分布规律;结合单粒组颗粒堆积试验,讨论了颗粒形态特征与堆积孔隙率的关系。有以下结论：（1）提出的以周长为核心表征的颗粒形态特征量化参数,对颗粒形态以及形状、棱角、纹理3个尺度形态特征具有较好甄选能力;（2）基于每个粒组1 000个颗粒样本统计分析表明,描述颗粒形态及形状、棱角、纹理特征的参数均符合对数正态分布;（3）颗粒集合体的综合棱角、纹理指数与松堆和密堆条件下的孔隙率具有较好的映射关系,颗粒棱角与纹理是影响堆积孔隙率的主控因素。     

K0条件下颗粒形状特征对砂土剪切模量的影响

为了研究颗粒形状特征对砂土剪切模量的影响,选取4种形状不同的砂样（福建标准砂和人工石英砂）作为研究对象,通过扫描电镜获取其颗粒微观图像,使用Image Pro Plus软件和自编Matlab程序提取试样颗粒的形状特征。采用改进的半径角和轮廓指数综合描述颗粒偏离圆或椭圆的程度以及棱角变化程度,并基于这两个参数提出颗粒形状因子来综合表征颗粒的形状特征。之后在K0条件下通过弯曲元试验获得不同竖向荷载对应的4个试样的剪切模量,试验结果表明,砂土颗粒的形状因子与砂土的剪切模量具有良好的相关性。最后基于Hertz-Mindlin接触模型,推导出引入形状因子的砂土剪切模量理论计算公式,该计算公式与实测值吻合良好。     

Estimating the settling velocity of bioclastic sediment using common grain‐size analysis techniques

Most techniques for estimating settling velocities of natural particles have been developed for siliciclastic sediments. Therefore, to understand how these techniques apply to bioclastic environments, measured settling velocities of bioclastic sedimentary deposits sampled from a nearshore fringing reef in Western Australia were compared with settling velocities calculated using results from several common grain‐size analysis techniques (sieve, laser diffraction and image analysis) and established models. The effects of sediment density and shape were also examined using a range of density values and three different models of settling velocity. Sediment density was found to have a significant effect on calculated settling velocity, causing a range in normalized root‐mean‐square error of up to 28%, depending upon settling velocity model and grain‐size method. Accounting for particle shape reduced errors in predicted settling velocity by 3% to 6% and removed any velocity‐dependent bias, which is particularly important for the fastest settling fractions. When shape was accounted for and measured density was used, normalized root‐mean‐square errors were 4%, 10% and 18% for laser diffraction, sieve and image analysis, respectively. The results of this study show that established models of settling velocity that account for particle shape can be used to estimate settling velocity of irregularly shaped, sand‐sized bioclastic sediments from sieve, laser diffraction, or image analysis‐derived measures of grain size with a limited amount of error. Collectively, these findings will allow for grain‐size data measured with different methods to be accurately converted to settling velocity for comparison. This will facilitate greater understanding of the hydraulic properties of bioclastic sediment which can help to increase our general knowledge of sediment dynamics in these environments.     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

Laboratory-on-a-smartphone for estimating angularity of granular soils

Particle angularity significantly affects the macro-mechanical behavior of granular soils. However, due to the difficulty of characterizing particle angularity, this fundamental soil property is commonly ignored by researchers and practitioners in geotechnical applications. This study develops a smartphone application allowing the automatic evaluation of the particle angularities of soils. Therefore, this technique is termed as laboratory-on-a-smartphone. A total of 75,000 various granular soil images are collected in this study. Based on their roundnesses, these images are labeled into six classes including very angular, angular, subangular, subrounded, rounded, well-rounded soils, following the Powers’ chart. Then, machine learning techniques, including speed up robust features, k-means, and support vector machine, are used to train a soil image classifier. This soil image classifier automatically analyzes the sharpnesses of particle corners in three-dimensional soil assembly images and classifies images based on Powers’ chart with a high classification accuracy of 93%. This technique does not require a specialized device to capture images other than a smartphone. It can achieve real-time angularity evaluations without demanding computations. It is fully automated without human intervention. These features ensure that researchers and practitioners can easily implement this technique in the field and laboratory.

     

X‐ray tomography of tsunami deposits: Towards a new depositional model of tsunami deposits

X‐ray computed microtomography is used to obtain high resolution imagery of a historical tsunami deposit in Andalusia, Spain (1755 Lisbon tsunami). The technique allows characterization of grain‐size distribution, structures, component analysis and sedimentary fabric of fine‐grained unconsolidated tsunami deposits at resolutions down to particle scale. The results are validated by comparing to data obtained using other techniques such as laser diffraction, anisotropy of magnetic susceptibility and X‐ray microfluorescence on the same deposits. Specific technical details such as sampling, scanning and image processing methods, and further improvements are addressed. The use of X‐ray computed microtomography provides new insights into the stratigraphy of the deposits and gives access to significantly more detailed view of key sedimentary features such as mudlines, rip‐up clasts, crude laminations, convolutions, floating outsized clasts and contacts between successive units. This analysis of the 1755 tsunami deposits using X‐ray computed microtomography allows the proposal of new hypotheses for the sedimentary processes forming tsunami deposits. Deposition by settling is limited and the section analysed here is dominated by a high shear stress leading to the development of traction carpets, with laminated mudlines corresponding to the basal frictional region of these carpets. The onset of the tsunami backwash is marked by a micro‐vortex resembling Kelvin–Helmoltz instabilities.     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.     

Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis

Three‐dimensional particle morphology is a significant problem in the discrete element modeling of granular sand. The major technical challenge is generating a realistic 3D sand assembly that is composed of a large number of random‐shaped particles containing essential morphological features of natural sands. Based on X‐ray micro‐computed tomography data collected from a series of image processing techniques, we used the spherical harmonics (SH) analysis to represent and reconstruct the multi‐scale features of real 3D particle morphologies. The SH analysis was extended to some highly complex particles with sharp corners and surface cavities. We then proposed a statistical approach for the generation of realistic particle assembly of a given type of sand based on the principle component analysis (PCA). The PCA aims to identify the major pattern of the coefficient matrix, which is made up of the SH coefficients of all the particles involved in the analysis. This approach takes into account the particle size effect on the variation of particle morphology, which is observed from the available results of micro‐computed tomography and QICPIC analyses of sand particle morphology. Using the aforementioned approach, two virtual sand samples were generated, whose statistics of morphological parameters were compared with those measured from real sand particles. The comparison shows that the proposed approach is capable of generating a realistic sand assembly that retains the major morphological features of the mother sand. Copyright © 2016 John Wiley & Sons, Ltd.     

Rank exposure index on a Silurian carbonate tidal flat

Adequate discrimination between ancient intertidal and supratidal limestones and dolomites is often difficult because of vagueness of terms, problems of resolution, and the fact that most ‘diagnostic’sedimentary features are not restricted to narrow environmental zones. Furthermore, the rise and fall of sea-level in restricted, epeiric seas is usually due more to storm surges than to true tides, and hence the occurrence and extent of tidal-flat inundations are quite irregular. ‘Rank exposure index’is a concept introduced (1) to quantify the relative percentage of time that sediments are subaerially exposed and (2) to produce a more refined subdivision of shoreline carbonate rocks. The scheme employed to determine this index is a combination of numerical methods: cluster analysis separates 46 Tonoloway Limestone samples (Silurian of Maryland) into groups based on 16 sedimentary, mineralogic, and organic features, and minimum spanning tree produces a connected series of the five resultant groups. These groups are then ranked in sequence from 1 (greatest subaerial exposure) to 5 (least). Rocks of rank 1 are thought to have been deposited at the highest position within the tidal zone, as on a beach ridge. Rocks of decreasing rank reflect greater frequency of flooding. Those of rank 5 represent sediments deposited closest to low-water level, as in a tidal pond. Rock type, mineralogy, fossil content, algal stromatolites, and sedimentary structures are closely related to exposure rank as interpreted for the Tonoloway carbonates. Rank exposure index, therefore, is a semi-quantitative measure to aid in the detailed reconstruction of ancient shoreline environments.     

Segmentation of contacting soil particles in images by modified watershed analysis

Image-based soil particle size and shape characterization relies on computer methods to process and analyze the images. For contacting particles spread on a flat surface this requires delineation of particle boundaries through shape-based image segmentation. The traditional method using watershed analysis fails for particles that have constrictions (are peanut-shaped). The oversegmentation interprets such particles as being two, thereby underestimating the long particle dimension by about 50% and overestimating particle sphericity by about a factor of two. This paper presents a solution to the problem of oversegmentation through morphologic reconstruction. The key to this improvement is distinguishing the necks in peanut shaped particles from actual contacts between particles. A parameter α is defined to quantify the necks and contacts. Approximately 220,000 particles in a range of 2.0–35.0 mm having various shapes and angularities were studied to find typical α values for necks and contacts. An algorithm is proposed to correct the oversegmentation based on α. The results show that this improved watershed analysis accurately segments sand particles at contacts while preserving the continuity of peanut shaped particles. Example lab tests demonstrate the significance of the problem and its solution.     

Hyperspectral image analysis of different carbonate lithologies (limestone,karst and hydrothermal dolomites): the Pozalagua Quarry case study (Cantabria,North‐west Spain)

Ground‐based hyperspectral imaging combined with terrestrial lidar scanning is a novel technique for outcrop analysis, which has been applied to Early and Late Albian carbonates of the Pozalagua Quarry (Cantabrian Mountains, Spain). An image processing workflow has been developed for differentiating limestone from dolomite, providing additional sedimentary and diagenetic information, and the possibility to quantitatively delineate diagenetic phases in an accurate way. Spectral absorption signatures can be linked to specific sedimentary or diagenetic products, such as recent and palaeokarst, hydrothermal karst, (solution enlarged) fractures and different dolomite types. Some of the spectral signatures are related to iron, manganese, organic matter, clay and/or water content. Ground‐truthing accessible parts of the quarry showed that the classification based on hyperspectral image interpretation was very accurate. This technique opens the possibility for quantitative data evaluation on sedimentary and diagenetic features in inaccessible outcrops. This study demonstrates the potential of ground‐based imaging spectroscopy to provide information about the chemical–mineralogical distribution in outcrops, which could otherwise not be established using conventional field methods.     

动态图像法与镜下测量法粒度分布结果对比研究

动态图像法、镜下测量法在地下沉积岩粒度分析中的应用研究较为薄弱。对塔里木轮南地区X100井三叠系水下分流河道12块砂岩样品分别采用以上两种方法进行粒度测试,将所测得的各组分含量、粒度曲线及粒度参数进行对比分析,并对镜下测量法粒度结果开展校正研究,以使这两种方法在今后能更广泛地运用于粒度分析。研究结果表明:相较于镜下测量法,动态图像法检测粗组分含量偏大而细组分含量偏小,黏土—粉砂组分和中砂组分是两种方法产生差异的分界线。检测颗粒数目的悬殊和岩石类型是两种方法存在差异的主要原因,测试方法的量程、测量原理和颗粒形状也会造成一定的影响。基于岩性的镜下测量法粒度结果校正,使两种方法的细砂—粗砂组分含量、粒径参数的相关系数从0.25~0.80提高到0.88~0.95,达到了校正基本目的,其准确性得到有效的提高。     

A new approach to the three-dimensional quantification of angularity using image analysis of the size and form of coarse aggregates

This paper describes a system for the acquisition and analysis of 3D data from the surfaces of coarse aggregate particles. The technique uses laser triangulation to acquire data from the upper hemispheres of particles passing along a conveyor belt. Methods of determining particle size and form in three dimensions are described and a new approach to the quantification of angularity is presented. The algorithm uses mathematical morphology to provide a geometrically meaningful interpretation of particle shape. The relative advantages of 2D and 3D analysis of aggregate particles are discussed, and results are presented which demonstrate the validity of this approach.     

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.     

3D finite element modeling of sand particle fracture based on in situ X‐Ray synchrotron imaging

Compressive loading of granular materials causes inter‐particle forces to develop and evolve into force chains that propagate through the granular body. At high‐applied compressive stresses, inter‐particle forces will be large enough to cause particle fracture, affecting the constitutive behavior of granular materials. The first step to modeling particle fracture within force chains in granular mass is to understand and model the fracture of a single particle using actual three‐dimensional (3D) particle shape. In this paper, the fracture mode of individual silica sand particles was captured using 3D x‐ray radiography and Synchrotron Micro‐computed Tomography (SMT) during in situ compression experiments. The SMT images were used to reconstruct particle surfaces through image processing techniques. Particle surface was then imported into Abaqus finite element (FE) software where the experimental loading setup was modeled using the extended finite element method (XFEM) where particle fracture was compared to experimental fracture mode viewed in radiograph images that were acquired during experimental loading. Load‐displacement relationships of the FE analysis were also compared with experimental measurements. 3D FE modeling of particle fracture offers an excellent tool to map stress distribution and monitors crack initiation and propagation within individual sand particles. Copyright © 2015 John Wiley & Sons, Ltd.