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Powder Technology 291 (2016) 262275
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3D quantitative shape analysis on form, roundness, and compactnesswith CT
Budi Zhao, Jianfeng Wang Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China
Corresponding author.E-mail address: firstname.lastname@example.org (J. Wang).
http://dx.doi.org/10.1016/j.powtec.2015.12.0290032-5910/ 2015 Elsevier B.V. All rights reserved.
a b s t r a c ta r t i c l e i n f o
Article history:Received 29 October 2015Received in revised form 18 December 2015Accepted 19 December 2015Available online 29 December 2015
Particle shape plays an important role in determining the engineering behaviour of granular materials. In thisregard, characterisation and quantification of particle shape are essential for understanding the behaviour ofgranular materials. X-ray micro-computed tomography (CT) enables observation of particle morphology atever-greater resolutions. The challenge has thus become extracting quantified shape parameters from theserich three-dimensional (3D) images. In this paper, we implement X-ray CT to obtain 3D particle morphologyand utilize image processing and analysis techniques to quantify it at different scales. A novel framework isproposed to measure 3D shape parameters of form, roundness, and compactness. New 3D roundness indexeswere formulated from the local curvature on reconstructed triangular surface mesh. Subsequently, this methodis utilized to study the change of particle shape by single particle crushing tests on Leighton Buzzardsand (LBS) particles. It is found that compactness value (i.e., sphericity) could be influenced by both form androundness. Then, the distributions of shape parameters are characterised by Weibull statistics. It shows thatsingle particle crushing tests generate more irregular fragments which have smaller shape parameters withlarger variance for the measured shape parameters.
2015 Elsevier B.V. All rights reserved.
Keywords:CompactnessFormReconstructed surface meshRoundnessVoxel assemblyX-ray tomography
The analysis of particle shape and its influence on themechanical be-haviour of granular materials has been the subject in geology and engi-neering science for a long time. Particle shape influences attainabledensity, stiffness, compressibility and critical state parameters, such ascritical state friction angle (e.g., ). The end resistance of cone pen-etration test (CPT) at a given relative density and stress level is affectedsignificantly by particle shape . On the other hand, particle damageunder elevated stress levels changes particle shape, e.g. smaller particleswhich are less spherical, less convex and with lower aspect ratio aregenerated when particles suffer catastrophic splitting . Numericalmodelling, e.g. discrete elementmethod andmolecular dynamicsmeth-od, has been shown to constitute an important way to understand theinfluences of particle shape on the behaviour of granular materials(e.g., ). Although comprehensive laboratory and numerical testshave been conducted, there are few techniques to predict the mechan-ical behaviour of irregularly shaped particles. The lack of models andcorrelations can be attributed to the difficulty of defining andmeasuringshape descriptors for a wide variety of complex particle shapes.
Most of widely implemented rules to quantify particle shapehave been developed by sedimentary geologists, which are qualitative
shape determinations made by two-dimensional (2D) visual classifica-tion. Thesemethods are time-consuming and too subjective to generateparameters that could be utilized for simulating and modelling for geo-technical engineering purposes. Acknowledging these drawbacks,manyresearchers adopted advanced devices (e.g., optical microscopy, laserbeam systems, interferometer, and X-ray CT) and robust numericalmethods to obtain more comprehensive quantitative particle shape in-dexes. These shape quantification methods can be divided into twogroups, i.e. two-dimensional (2D) methods and three-dimensional(3D) methods.
Two-dimensional methods collect 2D projections from scanningelectron microscope (SEM), optical microscopy or laser beam systemsand implement digital image processing techniques to quantify particleshape. Various approaches have been proposed for characterising parti-cle shape from the collected 2D projections. Generally, common 2Dshape factors indicate the aspect ratio of two dimensions (e.g., Feret di-mensions and principal dimensions) or describe the deviations of theshape of a particle from the circular shapes (e.g., the area-equivalent cir-cle and the inscribed circle). This kind of evaluation technique has beencombinedwith high-speed camera inmany commercial 2D particle sizeand particle shape analysis systems, e.g., DiaInspect.OSM (Vollstdt-Diamant GmbH), CAMSIZER (Retsch Technology) and QICPIC(Sympatec GmbH). Examples of these systems' application includeobtaining the database of sand particles  and quality control of abra-sivematerials . Theoretical model is also shown to have significancein examining the relationship between these shape factors .
263B. Zhao, J. Wang / Powder Technology 291 (2016) 262275
Recently, a novel method has been proposed to quantify roundness, ascale dependent variable, by fitting circles to the identified corners ofa particle outline . A more complex and theoretical method, Fouriermathematical method, has also been developed. It was found that Fou-rier descriptors, which are determined by taking the Fourier transfor-mation of the outline of sand particles, were closely related to shapefactors [15,16]. Although 2D methods can characterise and quantifyshape characteristics, noticeable difference between 2D and 3D shapeindexes have been found [17,18]. Indexes based on 2D projects mayhighly depend on the choice of observing directions, which will resultin non-unique shape descriptors for a given individual particle.
Three-dimensional particle morphology is usually measured by X-ray CT or 3D laser scanner, and then processed to retrieve particlesurface information. Image analysing methods are implemented toquantify particle shape from the surface information. In general, thesemethods could be classified into three groups. The first one has beenperformedon voxel assembly to obtain particle orientation, principal di-mensions, volume and surface area . This method usually leadsto a large variance in estimated surface area due to the fact that differenttypes of boundary voxels are not well distinguished and classified. Thisproblem has been solved by identifying the local configuration of eachboundary voxel using Marching Cubes algorithm, and assigning a sur-face area weight to each configuration . The second method isbased on reconstructed surface, which is composed of triangular surfacemeshes. It can be obtained by a three-dimensional laser scanner  orperformingMarching Cube algorithmon voxel assembly . The trian-gular mesh surface provides a more accurate representation of particlesurface than the voxel assembly, which resulted in a more precise
Fig. 1. Flowchart illustrating image processin
surface area estimation. A more complex and theoretical method per-forms 3D spherical harmonic analysis to mathematically characterisethe morphology of particles, and then calculates shape factors .However, it does not seem to provide an efficient way to obtain shapedescriptors after applying complex algorithms to approximate themor-phology of particles.
The aim of this work is to perform comprehensive 3D particle shapequantification at different shape scales. We first introduced a frame-work to quantify 3D particle shape with X-ray CT images. A series ofimage processing techniques were used to generate voxel assemblyand reconstructed surface mesh to characterise particle morphology.Then image analysis techniques were implemented on reconstructedsurface to quantify particle shape, specifically on form, roundness andcompactness. Secondly, this frameworkwas applied to analyse themor-phology changemade by single particle crushing tests on Leighton Buz-zard sand (LBS) particles. The shape parameters of LBS particles and LBSfragments were characterised statistically.
X-ray CT and 3D laser scanner are two common instruments thatcan be used to acquire 3D surface information for particle shape analy-sis. Due to the limited resolution, 3D laser scanner is not suitable forsmall sand particles, e.g. 1 mm2 mm LBS particles measured in thisstudy. Therefore, we implemented X-ray CT scanning to obtain 3Dgrey-level CT images. These images were put through a series ofimage processing and analysis methods to obtain different 3D particlemorphology data and shape factors, respectively. This procedure is
g and analysing with X-ray CT images.
264 B. Zhao, J. Wang / Powder Technology 291 (2016) 262275
shown in Fig. 1, andwill be described in detail in the followingparts. Thegrey-level CT images were first processed to generate the voxel assem-bly, which represents sand particles with a group of discrete voxels.Then, surface reconstruction methods were implemented to extract asmooth isosurface, representing more precise particle surface with tri-angular meshes. The reconstructed surface was simplified to removesurface texture for evaluating the scale-dependent particle roundness.In summary, three types of data were obtained after image processing,i.e., voxel assembly, smooth triangular s