Three-dimensional morphological characterization of sand particles based on a multiangle projection method
XIE Weiqiang1,2, ZHANG Xiaoping3, LIU Xiaoli1, ZHOU Xiaoxiong1, LIU Quansheng3
1. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; 2. Yunlong Lake Laboratory of Deep Underground Science and Engineering, Xuzhou 221116, China; 3. The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, Wuhan University, Wuhan 430072, China
Abstract：[Objective] The morphological characteristics (size and shape) of sand particles are critical for the evaluation of the mechanical properties of sand. Accurate quantification of these morphological characteristics is a prerequisite to investigating the mechanical properties of sand. Compared with the three-dimensional (3-D) test method, the two-dimensional (2-D) counterpart has the advantages of rich test types, simple procedures, and low cost. [Methods] To investigate the feasibility of 2-D images for 3-D morphological characterization of sand particles, 3-D laser scanning technology is employed in the present study to obtain the point cloud data of sand particles. Furthermore, a computer algorithm is developed to reconstruct the 3-D models of the sand particles. Thus, the 3-D morphological characteristics of the particles are accurately and quickly obtained. Three 2-D methods, namely the random single projection method, maximum and minimum projected area method (selected from 1 000 projections), and three orthogonal direction projection methods, are proposed for obtaining the 2-D morphological parameters of sand particles. [Results] Computer algorithms for reconstructing the 3-D model of sand particles based on a point cloud were proposed. The algorithms were used to automatically acquire the 3-D and 2-D morphological parameters. Thereafter, the correlations between the 3-D and 2-D parameters were analyzed. A practical method was proposed to obtain the 3-D morphological characteristics of the granular material based on the corresponding 2-D morphological characteristics. [Conclusions] The results reveal that there is a large gap between the 2-D parameters obtained from various angle projections, especially the area parameters in various projections. Notably, the error between the maximum and minimum area is as high as 40%. The random single angle projection method does not provide accurate 3-D information. A strong linear correlation exists between the 3-D and 2-D size parameters of the particles, and a moderate correlation exists between the shape parameters. An empirical relationship for estimating the 3-D morphology of sand particles using 2-D parameters is established. The 3-D parameters, namely the length, width, and thickness of the granular material, can be estimated using the corresponding 2-D parameters (R2=0.735-0.994). The fitting effects of the particle size parameters are better than those of the shape parameters. Additionally, the fitting effects of the maximum and minimum projected area and three orthogonal directional projection methods are better than those of the random single projection method. Among the three 2-D methods, the maximum and minimum projected area and three orthogonal direction projection methods can more accurately estimate the 3-D morphological characteristics of sand particles; thus, these are practical methods for the morphological quantification of granular materials.
[1] 高金翎. 砂土抗剪强度的主要影响因素及其研究现状分析[J]. 科教文汇, 2013(33):110-115, 122. GAO J L. Analysis of the main factors on the shear strength of sandy soil and the current research situation [J]. The Science Education Article Collects, 2013(33):110-115, 122. (in Chinese) [2] 周博. 基于能量耗散机制的砂土微观力学特性研究[D]. 武汉:华中科技大学, 2013. ZHOU B. Analysis of the microscopic mechanical property of sandy soils based on the energy dissipation mechanism [D]. Wuhan:Huazhong University of Science and Technology, 2013. (in Chinese) [3] 彭仁. 颗粒形状对砂土力学性质影响的PFC模拟及定量分析研究[D]. 银川:宁夏大学, 2011. PENG R. PFC simulation and quantitative analysis of influence of particle shape on mechanical properties of sand [D]. Yinchuan:Ningxia University, 2011. (in Chinese) [4] 刘清秉, 项伟, BUDHU M, 等. 砂土颗粒形状量化及其对力学指标的影响分析[J]. 岩土力学, 2011, 32(S1):190-197. LIU Q B, XIANG W, BUDHU M, et al. Study of particle shape quantification and effect on mechanical property of sand [J]. Rock and Soil Mechanics, 2011, 32(S1):190-197. (in Chinese) [5] 付茹, 胡新丽, 周博, 等. 砂土颗粒三维形态的定量表征方法[J]. 岩土力学, 2018, 39(2):483-490. FU R, HU X L, ZHOU B, et al. A quantitative characterization method of 3D morphology of sand particles [J]. Rock and Soil Mechanics, 2018, 39(2):483-490. (in Chinese) [6] BARRETT P J. The shape of rock particles, a critical review [J]. Sedimentology, 1980, 27(3):291-303. [7] 汪轶群. 钙质砂宏细观力学特性试验及离散元模拟[D]. 杭州:浙江大学, 2016. WANG Y Q. Macro-and micro-mechanical behavior of calcareous sand and discrete element method analysis [D]. Hangzhou:Zhejiang University, 2016. (in Chinese) [8] 孔亮, 彭仁. 颗粒形状对类砂土力学性质影响的颗粒流模拟[J]. 岩石力学与工程学报, 2011, 30(10):2112-2119. KONG L, PENG R. Particle flow simulation of influence of particle shape on mechanical properties of quasi-sands [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(10):2112-2119. (in Chinese) [9] 常在, 杨军, 程晓辉. 砂土强度和剪胀性的颗粒力学分析[J]. 工程力学, 2010, 27(4):95-104. CHANG Z, YANG J, CHENG X H. Granular mechanical analysis of the strength and dilatancy of sands [J]. Engineering Mechanics, 2010, 27(4):95-104. (in Chinese) [10] ZHANG X P, XIE W Q, CAI K Y, et al. Evaluation of rock muck using image analysis and its application in the TBM tunneling [J]. Tunnelling and Underground Space Technology, 2021, 113:103974. [11] XIE W Q, ZHANG X P, YANG X M, et al. 3D size and shape characterization of natural sand particles using 2D image analysis [J]. Engineering Geology, 2020, 279:105915. [12] 王步雪岩, 孟庆山, 韦昌富, 等. 多投影面下珊瑚砂砾颗粒形貌量化试验研究[J]. 岩土力学, 2019, 40(10):3871-3878. WANG B X Y, MENG Q S, WEI C F, et al. Quantitative experimental study of the morphology of coral sand and gravel particles under multiple projection surfaces [J]. Rock and Soil Mechanics, 2019, 40(10):3871-3878. (in Chinese) [13] ASAHINA D, TAYLOR M A. Geometry of irregular particles:Direct surface measurements by 3-D laser scanner [J]. Powder Technology, 2011, 213(1-3):70-78. [14] LANARO F, TOLPPANEN P. 3D characterization of coarse aggregates [J]. Engineering Geology, 2002, 65(1):17-30. [15] ERDOǦAN S T, GARBOCZI E J, FOWLER D W. Shape and size of microfine aggregates:X-ray microcomputed tomography vs. laser diffraction [J]. Powder Technology, 2007, 177(2):53-63. [16] LIN C L, MILLER J D. 3D characterization and analysis of particle shape using X-ray microtomography (XMT) [J]. Powder Technology, 2005, 154(1):61-69. [17] BAGHERI G H, BONADONNA C, MANZELLA I, et al. On the characterization of size and shape of irregular particles [J]. Powder Technology, 2015, 270:141-153. [18] YUE Z Q, BEKKING W, MORIN I. Application of digital image processing to quantitative study of asphalt concrete microstructure [M]. Transportation Research Board, 1995. [19] KWAN A K H, MORA C F, CHAN H C. Particle shape analysis of coarse aggregate using digital image processing [J]. Cement & Concrete Research, 1999, 29(9):1403-1410. [20] 陈海洋, 汪稔, 李建国, 等. 钙质砂颗粒的形状分析[J]. 岩土力学, 2005, 26(9):1389-1392. CHEN H Y, WANG R, LI J G, et al. Grain shape analysis of calcareous soil [J]. Rock and Soil Mechanics, 2005, 26(9):1389-1392. (in Chinese) [21] HENTSCHEL M L, PAGE N W. Selection of descriptors for particle shape characterization [J]. Particle & Particle Systems Characterization, 2003, 20(1):25-38. [22] FERNLUND J M R. Image analysis method for determining 3-D size distribution of coarse aggregates [J]. Bulletin of Engineering Geology & the Environment, 2005, 64(2):159-166. [23] ALTUHAFI F, O'SULLIVAN C, CAVARRETTA I. Analysis of an image-based method to quantify the size and shape of sand particles [J]. Journal of Geotechnical & Geoenvironmental Engineering, 2013, 139(8):1290-1307. [24] BLOTT S J, PYE K. Particle shape:A review and new methods of characterization and classification [J]. Sedimentology, 2008, 55(1):31-63. [25] 王东伟, 陆武萍, 唐朝生, 等. 砂土微观结构样品制备技术及量化方法研究[J]. 岩土力学, 2019, 40(12):4783-4792. WANG D W, LU W P, TANG C S, et al. Sample preparation technique and microstructure quantification method for sandy soil [J]. Rock and Soil Mechanics, 2019, 40(12):4783-4792. (in Chinese) [26] KOESAWE J. The minimal bounding box [Z/OL]. (2015-2-16) [2023-01-15]. http://www.mathworks.com/matlabcentral/fileexchange/18264-minimal-bounding-box. 2008. [27] WADELL H. Sphericity and roundness of rock particles [J]. The Journal of Geology, 1933, 41(3):310-331. [28] WADELL H. Volume, shape, and roundness of rock particles [J]. The Journal of Geology, 1932, 40(5):443-451.
2024, Vol. 64 
