Journal of Marine Science and Engineering
Article Shape Characteristics of Coral Sand from the South China Sea
Xing Wang 1,2 , Yang Wu 1,2,*, Jie Cui 1,2,*, Chang-Qi Zhu 3 and Xin-Zhi Wang 3
1 School of Civil Engineering, Guangzhou University, Guangzhou 510006, China; [email protected] 2 Guangdong Provincial Engineering and Technology Research Center of Geo-Structure Safety and Protection, Guangzhou University, Guangzhou 510006, China 3 State Key Laboratory of Geotechnical Mechanics and Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [email protected] (C.-Q.Z.); [email protected] (X.-Z.W.) * Correspondence: [email protected] (Y.W.); [email protected] (J.C.)
Received: 1 September 2020; Accepted: 14 October 2020; Published: 15 October 2020
Abstract: The particle shape of coral sand is a crucial factor that affects its accumulation characteristics. Two-dimensional particle images of coral sand with different particle sizes were obtained through optical imaging, and the basic size parameters of particles were measured by digital image processing. The particle shape parameters were created, and on this basis, the variation of shape parameters with size, the distribution characteristics, and the sensitivity of shape parameters were analyzed by mathematical statistics and the fractal theory. In addition, a comparative analysis was conducted for the particle shape and bulk density of coral sand and quartz sand with the same particle size. The results show that (1) for coral sand with particle size ranging from 0.5 to 5.0 mm, as the particle size augments, its overall profile coefficient grows, while the flatness, angularity, and roughness diminish and the particle shape deviates more from the regular circle. (2) The shape of coral sand particles exhibits good fractal characteristics, and the particle shape gets more complex as the particle size grows as evidenced by the fact that the fractal dimension enlarges. (3) All the shape parameters obey a skewed distribution. Concerning the sensitivity to the change in particle shape, the flatness occupies the first place, the overall profile coefficient and angularity come second, and the roughness ranks third, accordingly. It is suggested that flatness should be preferred as the evaluation parameter of the particle shape. (4) Compared with that of quartz sand, the particle shape of coral sand is more irregular, and the intergranular pores are larger under the same accumulation conditions, which is the primary reason why the specific gravity of coral sand is greater than that of quartz sand while the bulk density is smaller than that of quartz sand.
Keywords: coral sand; quartz sand; particle shape; particle size; bulk density; digital image analysis
1. Introduction Recent years have seen large-scale hydraulic reclamation projects launched by China in the South China Sea. For these projects, the coral sand deposited in reefs and lagoons is the only reclaimed material [1,2]. Originated from marine organisms (corals, seaweeds, shells, etc.), coral sand is a special geotechnical material that is abundant in insoluble carbonates, such as calcium carbonate and magnesium carbonate [3,4]. Particle size, gradation, and shape are essential attribute parameters of sandy granular materials. Numerous studies have been conducted on the influence mechanism of the first two attribute parameters (i.e., particle size, gradation) on the engineering properties of sand [5–18]. However, relatively few studies were conducted on particle shape and its influence on the physical and mechanical properties of sand. The results of relevant studies [19–25] indicate
J. Mar. Sci. Eng. 2020, 8, 803; doi:10.3390/jmse8100803 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 803 2 of 24 that a change in the particle shape of sand may lead to a change in the particle arrangement and intergranular pores, thereby exerting a remarkable impact on its physical and mechanical properties. Therefore, the study on the morphological characteristics of particles of coral sand serves not only to understand its physical and mechanical properties but also to explore the micro mechanism of its macro physical and mechanical behavior. The relationship between the shape characteristics and physical and mechanical parameters of granular materials has been systematically studied from the perspectives of theoretical research and experimental testing technology by previous researchers. In terms of theoretical research, computational geometry theory [26], Fourier series description method [27,28], and fractal theory [29] have been proposed to quantitatively describe the particle shape. However, due to the complexity of computational geometry theory and Fourier series description method, they have not been widely used in practical engineering. On the contrary, the calculation method of fractal theory is relatively simple, and it can reflect the shape distribution characteristics of granular materials to a large extent [29]. Therefore, researchers often establish the relationship between particle shape and physical and mechanical parameters of granular materials by fractal theory on the basis of quantitative acquirement of particle shape parameters. For example, Chan and Page [30] studied the influence of the particle shape of copper powder on its internal friction angle, and found that there was a good correlation between fractal dimension of particle shape complexity and coefficient of internal friction. Gori and Mari [31] studied the relationship between the internal friction angle of sandy materials and particle shape, and concluded that there was a linear relationship between the internal friction angle of sandy materials and fractal dimension. Rausch et al. [32] studied the fractal characteristics of particle shape of the volcanic ash based on the fractal theory to conclude that the particle shape of volcanic ash bore multifractal characteristics. In terms of experimental testing technology, two-dimensional particle shape scanning equipment and digital image processing technology are widely used to obtain the basic two-dimensional size parameters of particle materials. Compared with two-dimensional particle shape, three-dimensional particle shape can more truly reflect the shape characteristics of granular materials, especially in the thickness direction of granular materials. However, the testers for extracting the basic three-dimensional size parameters of granular materials require high costs, and the construction process of three-dimensional particle shape parameters is relatively complex. More scholars tend to use two-dimensional particle shape scanner and digital image processing technology to study the two-dimensional shape of granular materials and its impact on the physical and mechanical properties, achieving abundant research results. For example, based on the comparative analyses about the effectiveness of convexity, roundness, and shape factor in describing particle edges and corners, Mora and Kwan [33] believed that convexity could better reflect the convexity degree of the edges and corners around the particles. Sukumaran and Ashmawy [34] proposed two parameters to describe the particle shape and angularity of granular materials, and on this basis found that drained friction angle and pluviated void ratio of granular materials increased with the increase of the two parameters. Cho et al. [35] studied the relationship between the shape parameters of sand particles and its bulk density and believed that the increase of angularity or eccentricity of sand particles would lead to the minimum and maximum void ratio increases. Cox and Budhu [36] measured the particle shape parameters of eight kinds of sand and found that circularity, roundness, compactness, sphericity, aspect ratio, and modratio were the key shape parameters for distinguishing the different sand. With the aid of the digital image processing technology, Felekoglu [37] and Altuhafi et al. [38] proposed the quantitative approaches of particle shape parameters such as length-to-width ratio, roundness, and convexity. Shin and Santamarina [39] studied the mechanical response of sand particles made of round and angular grains, and pointed out that the void ratio and internal friction angle of mixed sand increased in addition to the mass fraction of angular particles. Yang and Luo [40] performed multiple sets of dynamic triaxial shear tests on quartz sand with different particle shapes and found that the more regular the particle shape was, the more likely it was to liquefy. A comparative study on the particle shape of manufactured sand and river sand was conducted by Shen et al. [41] J. Mar. Sci. Eng. 2020, 8, 803 3 of 24 who noted that the roundness and aspect ratio of manufactured sand were higher than those of river sand and its distribution range was also wider than that of river sand, but its roughness was smaller. After conducting multiple triaxial compression tests on geotechnical materials with different particle shapes, Keramatikerman and Chegenizadeh [42] pointed out that critical friction angle (φcs) of the sample decreased with the increase of its roundness, sphericity, and regularity. Xu et al. [43] revealed the micro mechanism of the mechanical behavior of a sand–gravel mixture in a single shear test from the perspective of particle shape. Ren et al. [44] analyzed the influence of the particle shape of manufactured sand on the diffusion coefficient of manufactured mortar, which proved that the more regular the particle shape of manufactured sand, the higher the diffusion coefficient. Sarkar et al. [45] carried out a series of triaxial shear tests and direct shear tests on granular materials with different particle shapes (i.e., crushed glass, Rhein sand, and round glass beads) and found that the particle shape had a significant effect on the shear strength, peak friction and dilation angle of granular materials. Zhang et al. [46] made a quantitatively analysis of particle breakage and compressibility behavior of calcareous sand and completely decomposed granite under one-dimensional compression test condition, and pointed out that carbonate sand was stronger than completely decomposed although carbonate sand had extremely irregular particle shape. In summary, a series of studies on the relationship between the shape characteristics of granular materials and their physical and mechanical properties that have been made by the previous researchers generally used quartz sand, volcanic ash, and other terrigenous geotechnical materials as the objects. Meanwhile, studies on the particle shape of coral sand are reported minimally. Owing to its special marine biological origin, coral sand, which is often accompanied with cementation [47,48], features high porosity ratio [49,50], easy breakage [51,52], and other physical and mechanical properties that are significantly different from those of terrigenous sediments. However, it has not been confirmed by experimental data whether the above research results are applicable to coral sand. Therefore, based on the basic size parameters of coral sand particles extracted by the digital image processing technology and construction of particle shape parameters, a quantitative study on the impact of particle size on the shape of coral sand particles was conducted, and the sensitivity and distribution characteristics of particle shape parameters were analyzed through mathematical statistics and fractal theory. Further, a comparative study of the particle shape of coral sand and quartz sand was performed to reveal the microscopic and microscopic mechanisms of their difference in bulk density from the perspective of particle shape. The research results provide a deep understanding of the sedimentation characteristics of coral sand from microscopic and mesoscopic level.
2. Materials and Methods
2.1. Experimental Material The on-site geological survey of a reclamation island reef in the South China Sea found that the most abundant sediment possessed by the reclamation layer is sand, whose particle size is mostly distributed within 0.5–5.0 mm [1]. To better serve the engineering practice, in this study, the coral sand from the island reclamation site was screened to be used as research objective with particle sizes of 0.5–1.0 mm (coral medium sand), 1.0–2.0 mm (coral coarse sand), and 2.0–5.0 mm (coral gravel sand). Meanwhile, for a comparative analysis of the particle shape of coral sand and quartz sand, the same screening test was performed on quartz sand from the Yangtze River in Wuhan, China, and quartz sand with different particle sizes ranging from 0.5 to 5.0 mm were obtained (Figure1). J.J. Mar. Mar. Sci. Sci. Eng.Eng.2020 2020,,8 8,, 803 x FOR PEER REVIEW 44 of of 24 25
FigureFigure 1.1. CoralCoral sandsand andand quartzquartz sandsand withwith didifferentfferent particle particle sizes. sizes.
FigureFigure2 2shows shows the the particle particle size size distribution distribution curves curves of of coral coral sand sand and and quartz quartz sand sand with with di differentfferent graingrain groups. groups. TableTable1 1lists lists the the particle particle gradation gradation parameters parameters of of the the tested tested material. material. It It can can be be seen seen from from FigureFigure2 2and and Table Table1 that1 that within within each each grain grain group, group, the the particle particle size size distribution distribution curves curves of of coral coral sand sand andand quartzquartz sandsand areare completelycompletely coincident,coincident, andand thethe correspondingcorresponding particleparticle gradationgradation parametersparameters areare alsoalso identical.identical.
100 Coral medium sand Quartz medium sand Coral coarse sand Quartz coarse sand Coral gravel sand Quartz gravel sand 80
60
40
Finer Percent (%) Finer Percent
20
0 0.001 0.01 0.1 1 10 Particle size D (mm) FigureFigure 2.2.Particle Particle sizesize distributiondistribution curvescurves ofof thethe testedtested materials.materials.
1
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Table 1. Particle gradation parameters of the tested materials.
D D D D D Nonuniformity Curvature Sample 10 30 50 60 (mm) (mm) (mm) (mm) (mm) Coefficient Cu Coefficient Cc Coral medium sand 0.5–1.0 0.55 0.65 0.75 0.80 1.45 0.96 Coral coarse sand 1.0–2.0 1.10 1.30 1.50 1.60 1.45 0.96 Coral gravel sand 2.0–5.0 2.30 2.90 3.50 3.80 1.65 0.96 Quartz medium sand 0.5–1.0 0.55 0.65 0.75 0.80 1.45 0.96 Quartz coarse sand 1.0–2.0 1.10 1.30 1.50 1.60 1.45 0.96 Quartz gravel sand 2.0–5.0 2.30 2.90 3.50 3.80 1.65 0.96
The coral sand and quartz sand presented in Figure1 were tested by X-ray di ffraction, and the difference in their mineral composition was quantitatively analyzed. Figure3 shows the X-ray diffraction patterns of coral sand and quartz sand. It is seen from Figure3 that the mineral composition of coral sand is relatively simple, which is composed of aragonite, calcite, and magnesium calcite. Specifically, the chemical composition of aragonite or calcite is CaCO3, and magnesium calcite also harbors CaCO3. From the calculation, the content of CaCO3 in the coral sand tested amounts to approximately 99%, confirming that this is a type of special geotechnical material with extremely high content of CaCO3. Conversely, the mineral composition of quartz sand is relatively complex, which is composed of quartzite, albite, plagioclase, mica, montmorillonite clay minerals, and actinolite carbonate minerals, along with SiO2, which is the main chemical constituent of quartz sand. The difference in mineral composition between coral sand and quartz sand renders the color and single particle strength of coral sand distinct from those of quartz sand, and the specific gravity of coral sand (2.78–2.84) is also higher than that of quartz sand (2.65).
2.2. Experiment Apparatus and Operations The entire experiment process can be divided into three steps: preparation before experiment, acquisition of particle images, and extraction of basic size parameters of particles. (1) Prior to the experiment, coral sand and quartz sand with different particle sizes were washed with clean water and then dried to prevent measurement error of particle shape caused by fine particles adhering to the surface of coarse particles. Meanwhile, to remove the influence of sample quantity on the test results, for each grain group of coral sand and quartz sand, 200 particles were randomly selected as the samples of this experiment. (2) Under the condition of ample light, sand particles of the different grain groups were pictured with the digital camera to acquire clear particle images. It is worth noting that as both coral sand and quartz sand are geotechnical materials with uniform and bright color, a black plate was laid under the sand particles to be measured during the shooting process to eliminate the influence of image background color on the measurement results. To facilitate the subsequent image processing to calibrate the particle size, two scaleplates with clear scale were placed within the lens coverage (Figure4). The test apparatus (Figure4) is a Canon 6D digital camera manufactured by Canon Inc. with as many as 20.2 million pixels and image resolution of 5472 3648 pixels per inch (PPI). The tripod, × which can be inverted, is provided with a ball head on which the camera can be fixed through a quick mounting plate. Based on the level vacuole on the ball head, the camera can shoot vertically by adjusting the relative positions of the three legs of the tripod. The pixel value of the digital camera determines that the particle image of geotechnical materials with particle size more than 0.25 mm can be obtained by using this device. Zhang et al. [53] studied the particle shape of gravel soil with a similar experimental device and obtained good experimental results, indicating this method can be used to measure the particle shape of geotechnical materials and the test accuracy can meet the test requirements. (3) The basic size parameters of the particle were extracted using Image Pro Plus (IPP), which is a powerful image processing, enhancement, and analysis software complete with various image J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 5 of 25
Table 1. Particle gradation parameters of the tested materials.
D D10 D30 D50 D60 Nonuniformity Curvature Sample (mm) (mm) (mm) (mm) (mm) Coefficient Cu Coefficient Cc Coral medium sand 0.5–1.0 0.55 0.65 0.75 0.80 1.45 0.96 Coral coarse sand 1.0–2.0 1.10 1.30 1.50 1.60 1.45 0.96 Coral gravel sand 2.0–5.0 2.30 2.90 3.50 3.80 1.65 0.96 Quartz medium sand 0.5–1.0 0.55 0.65 0.75 0.80 1.45 0.96 Quartz coarse sand 1.0–2.0 1.10 1.30 1.50 1.60 1.45 0.96 Quartz gravel sand 2.0–5.0 2.30 2.90 3.50 3.80 1.65 0.96
The coral sand and quartz sand presented in Figure 1 were tested by X-ray diffraction, and the difference in their mineral composition was quantitatively analyzed. Figure 3 shows the X-ray diffraction patterns of coral sand and quartz sand. It is seen from Figure 3 that the mineral composition of coral sand is relatively simple, which is composed of aragonite, calcite, and magnesium calcite. Specifically, the chemical composition of aragonite or calcite is CaCO3, and magnesium calcite also harbors CaCO3. From the calculation, the content of CaCO3 in the coral sand tested amounts to approximately 99%, confirming that this is a type of special geotechnical material with extremely high content of CaCO3. Conversely, the mineral composition of quartz sand is relatively complex, which is composed of quartzite, albite, plagioclase, mica, montmorillonite clay minerals, and actinolite carbonate minerals, along with SiO2, which is the main chemical constituent J. Mar. Sci. Eng. 2020, 8, 803 6 of 24 of quartz sand. The difference in mineral composition between coral sand and quartz sand renders the color and single particle strength of coral sand distinct from those of quartz sand, and the specific measurementgravity of coral tools, sand analysis (2.78–2.84) plates, is andalso macrohigher andthan plug-insthat of quartz for specific sand (2.65) applications. that allow users to write their own code (Figure5). 2500 A: Aragonite B: Calcite, syn C: Calcite, magnesium 2000
)
-1
S 1500
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I
A C 1000
Intensity
A A A
500 A A A B A A A A C C A C C A C A C A C 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW Diffraction Angle 2q (°) 6 of 25 (a) 3500 A: Quartz, syn
A B: Albite 3000 C: Montmorillonite (Clay) D: Actinolite E: Microcline maximum 2500 F: Muscovite
)
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1500 A
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1000 B B B 500 C F D E E B B E F A A A A C E F A A 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Diffraction Angle 2q (°)
(b)
FigureFigure 3. 3.X-ray X-ray didiffractionffraction patterns patterns of of coral coral sand sand and and quartz quartz sand: sand: ( (aa)) coral coral sand sand and and ( b(b)) quartz quartz sand. sand.
2.2. Experiment Apparatus and Operations The entire experiment process can be divided into three steps: preparation before experiment, acquisition of particle images, and extraction of basic size parameters of particles. (1) Prior to the experiment, coral sand and quartz sand with different particle sizes were washed with clean water and then dried to prevent measurement error of particle shape caused by fine particles adhering to the surface of coarse particles. Meanwhile, to remove the influence of sample quantity on the test results, for each grain group of coral sand and quartz sand, 200 particles were randomly selected as the samples of this experiment. (2) Under the condition of ample light, sand particles of the different grain groups were pictured with the digital camera to acquire clear particle images. It is worth noting that as both coral sand and quartz sand are geotechnical materials with uniform and bright color, a black plate was laid under the sand particles to be measured during the shooting process to eliminate the influence of image background color on the measurement results. To facilitate the subsequent image processing to calibrate the particle size, two scaleplates with clear scale were placed within the lens coverage (Figure 4).
J. Mar. Sci. Eng. 2020, 8, 803 7 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 7 of 25
Tripod Level vacuole
Ball head
Canon 6D digital camera
Scaleplate Black plate
FigureFigure 4. 4.Two-dimensional Two-dimensional image shooting shooting device. device. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 25 The test apparatus (Figure 4) is a Canon 6D digital camera manufactured by Canon Inc. with as many as 20.2 million pixels and image resolution of 5472 × 3648 pixels per inch (PPI). The tripod, which can be inverted, is provided with a ball head on which the camera can be fixed through a quick mounting plate. Based on the level vacuole on the ball head, the camera can shoot vertically by adjusting the relative positions of the three legs of the tripod. The pixel value of the digital camera determines that the particle image of geotechnical materials with particle size more than 0.25 mm can be obtained by using this device. Zhang et al. [53] studied the particle shape of gravel soil with a similar experimental device and obtained good experimental results, indicating this method can be used to measure the particle shape of geotechnical materials and the test accuracy can meet the test requirements. (3) The basic size parameters of the particle were extracted using Image Pro Plus (IPP), which is ① a Determination powerful image of scale processing, enhancement, and analysis software complete with various image measurement tools, analysis plates, and macro and plug-ins for specific applications that allow users to write their own code (Figure 5).
③ Measurement of basic size parameters of particles
②Extraction of particle contour
FigureFigure 5.5. Digital image image processing processing software software (IPP). (IPP).
In the subsequent analysis, the quantification of particle basic size parameters was completed using the built-in measurement tools and analysis plates of IPP. First, the plotting scale (pixel value: physical length) was determined based on the pixel value and real physical length of the scaleplate in the image so that the pixel value used to describe the particle shape could be converted into the actual geometric size in the subsequent parameter extraction process. Note that adjusting the vertical distance between the digital camera and the particles during the shooting process is not allowed to avoid frequent verification of the scale of each image during extraction of the basic siz11e parameters of the particle; otherwise, the scale of the images obtained after the adjustment should be corrected again. Second, the black-and-white binarization was performed on the captured image (Figure 6) to extract the two-dimensional projection contour of the particles. Relevant research results [54] show that pixel count has a significant effect on the calculation of particle shape parameters. In order to obtain the accurate values of particle shape parameters after converting raw images to binary images, the raw images taken should have enough high pixel value.
(a) (b)
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①Determination of scale
③ Measurement of basic size parameters of particles ②Extraction of particle contour
J. Mar. Sci. Eng. 2020, 8, 803 Figure 5. Digital image processing software (IPP). 8 of 24
In the subsequent analysis, the quantification of particle basic size parameters was completed usingIn the the built subsequent-in measurement analysis, tools the quantificationand analysis plates of particle of IPP. basic First, size theparameters plotting scale was (pixel completed value: physicalusing the le built-inngth) was measurement determined tools based and on analysisthe pixel plates value of and IPP. real First, physical the plotting length scale of the (pixel scaleplate value: inphysical the image length) so that was the determined pixel value based used on tothe describe pixel valuethe particle and real shape physical could length be converted of the scaleplate into the actualin the geometric image so thatsize thein the pixel subsequent value used parameter to describe extraction the particle proce shapess. Note could that beadjusting converted the intovertical the distanceactual geometric between sizethe indigital the subsequent camera and parameter the particles extraction during process. the shooting Note process that adjusting is not allowed the vertical to avoiddistance frequent between verification the digital of camerathe scale and of each the particlesimage during during extraction the shooting of the process basic siz11e is not parameters allowed to ofavoid the particle frequent; otherwise, verification the of thescale scale of the of eachimages image obtained during after extraction the adjustment of the basic should siz11e be parameters corrected again.of the Second, particle; the otherwise, black-and the-white scale binarization of the images was obtained performed after on the the adjustment captured shouldimage (Figure be corrected 6) to extractagain. Second,the two- thedimensional black-and-white projection binarization contour of was the performed particles. Releva on thent captured research image result (Figures [54] show6) to thatextract pixel the count two-dimensional has a significant projection effect on contour the calculation of the particles. of particle Relevant shape research parameters. results In [ 54order] show to obtainthat pixel the accurate count has values a significant of particle eff ectshape on parameters the calculation after of converting particle shape raw images parameters. to binary In orderimages, to theobtain raw the images accurate taken values should of particlehave enough shape high parameters pixel value. after converting raw images to binary images, the raw images taken should have enough high pixel value.
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 25 (a) (b)
(c) (d)
FigureFigure 6. 6. DigitalDigital images images and and black black-and-white-and-white binarization binarization images images of coral of coral sand sand and quartz and quartz sand with sand awith diameter a diameter of 2.0– of5.0 2.0–5.0 mm: (a mm:) digital (a) images digital of images coral sand, of coral (b) sand, digital (b images) digital of images quartz sa ofnd, quartz (c) black sand,- and(c) black-and-white-white binarization binarization images of images coral sand, of coral and sand, (d) black and (-dand) black-and-white-white binarization binarization images imagesof quartz of sand.quartz sand.
Finally,Finally, the basic size parameters, parameters, such such as as particle particle area, area, perimeter, perimeter, Feret Feret diameter, diameter, and and radius radius of of thethe circumscribed andand inscribedinscribed circles, circles, of of the the particle particle to beto extractedbe extracted were were selected selected in the in analysisthe analysis plate plateof the of IPP the software. IPP software. Table2 presents Table 2 thepresents basic size the parametersbasic size parameters of the particle of andthe particle their descriptions; and their descriptions;Figure7 displays Figure a schematic 7 displays view a schematic of the basic view size of parametersthe basic size of parameters the particle. of the particle.
Table 2. Basic size parameters of the particle.
Basic size Parameters Symbol Description Area A Area of the graph surrounded by the outer contour points of a particle Perimeter of the graph surrounded by the outer contour points of a Perimeter P particle Maximum Ferret Maximum distance between two boundary parallel lines of a particle Feretmax diameter projection contour Minimum Ferret Minimum distance between two boundary parallel lines of a particle Feretmin diameter projection contour Radius of Rc Radius of the smallest circumscribed circle circumscribed circle Radius of inscribed Ri Radius of the largest inscribed circle circle Perimeter of external Pc Perimeter of the smallest external polygon along the particle boundary polygon
Perimeter of ellipse Pe Perimeter of an ellipse with the same area and flatness as a particle
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Table 2. Basic size parameters of the particle.
Basic Size Parameters Symbol Description Area of the graph surrounded by the outer Area A contour points of a particle Perimeter of the graph surrounded by the outer Perimeter P contour points of a particle Maximum distance between two boundary Maximum Ferret diameter Feret max parallel lines of a particle projection contour Minimum distance between two boundary Minimum Ferret diameter Feret min parallel lines of a particle projection contour Radius of circumscribed circle Rc Radius of the smallest circumscribed circle Radius of inscribed circle Ri Radius of the largest inscribed circle Perimeter of the smallest external polygon along Perimeter of external polygon P c the particle boundary Perimeter of an ellipse with the same area and Perimeter of ellipse Pe J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW flatness as a particle 10 of 25
Circle with an area equal to that of the sand particle
Sand particle
Maximum Feret diameter
Maximum inscribed circle Minimum circumscribed circle FigureFigure 7. Schematic 7. Schematic view view of of the the basic basic size size parameters of of an an irregular irregular sand sand particle. particle.
2.3. Construction of Particle Shape Parameters 2.3. Construction of Particle Shape Parameters For particle shape analysis, selecting and constructing the proper shape parameters are crucial. TheFor buildingparticle shape parameters analysis, that selecting can reflect an thed constructing real shape of particlesthe proper are shape not necessarily parameters calculated are crucial. The buildingusing a sophisticated parameters formulathat can but reflect can describethe real theshape overall of particles shape at are the not macroscopic necessarily level, calculated edges and using a sophisticatedcorners at the formula microscopic but can level, describe and surface the overall texture shape at the at microscopicthe macroscopic level oflevel, the particlesedges and to corners the at thegreatest microscopic extent (Figurelevel, 8and). Among surface them, texture as the at first-level the microscopic description level of the of particlethe particles shape, theto the overall greatest extentshape (Figure at the 8). macroscopic Among them, level as represents the first-level the overall description appearance of the of particle the particle shape, contour, the overall which isshape at thegenerally macroscopic described level as represents a block, sheet, the branch,overall rod,appearance spindle, etc. of the As theparticle second-level contour, description which is ofgenerally the describedparticle as shape, a block, the angularitysheet, branch, reflects rod, the spindle, number of etc. edges As andthe cornerssecond around-level description the particle contour of the andparticle shape,the the degree angularity of prominence, reflects whichthe number can be of classified edges intoand thecorners mesoscopic around category. the particle As the contou third-levelr and the description of the particle shape, the texture structure of the particle surface mirrors the roughness degree of prominence, which can be classified into the mesoscopic category. As the third-level (or smoothness) of the particle surface. description of the particle shape, the texture structure of the particle surface mirrors the roughness (or smoothness) of the particle surface.
Surface textures at the micro level Edges and corners at the microscopic level
Edges and corners at Overall shapes at the the microscopic level macroscopic level
Figure 8. Multi-scale shape characteristics of the sand particle.
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 25
Circle with an area equal to that of the sand particle
Sand particle
Maximum Feret diameter
Maximum inscribed circle Minimum circumscribed circle Figure 7. Schematic view of the basic size parameters of an irregular sand particle.
2.3. Construction of Particle Shape Parameters For particle shape analysis, selecting and constructing the proper shape parameters are crucial. The building parameters that can reflect the real shape of particles are not necessarily calculated using a sophisticated formula but can describe the overall shape at the macroscopic level, edges and corners at the microscopic level, and surface texture at the microscopic level of the particles to the greatest extent (Figure 8). Among them, as the first-level description of the particle shape, the overall shape at the macroscopic level represents the overall appearance of the particle contour, which is generally described as a block, sheet, branch, rod, spindle, etc. As the second-level description of the particle shape, the angularity reflects the number of edges and corners around the particle contour and the degree of prominence, which can be classified into the mesoscopic category. As the third-level J. Mar.description Sci. Eng. 2020of the, 8, 803particle shape, the texture structure of the particle surface mirrors the roughness10 of 24 (or smoothness) of the particle surface.
Surface textures at the micro level Edges and corners at the microscopic level
Edges and corners at Overall shapes at the the microscopic level macroscopic level
J. Mar. Sci. Eng. 2020, 8Figure,Figu x FORre PEER 8. 8. Multi-scaleMulti REVIEW-scale shape characteristics of of the the sand sand particle. particle. 11 of 25
BasedBased on on the the researchresearch findings findings of Liu of et al.Liu [22], et Zhang al. [22 et], al. Zhang [53], Mark et al. and [53 Neil], [55], Mark and and Chen Neil [55], and Chenet al. et [56], al. [the56], following the following four particle four shape particle parameters shape parameters are constructed are (Figure constructed 9). (Figure9).
FigureFigure 9. Diagram9. Diagram of of thethe particle shape shape parameters. parameters.
22 × √√(A (×A π) π) (1) The(1) overall The overall contour contour coe coefficientfficient α 훼= = × ×, a rough, a rough description description of the particle of the shape particle at the shape at P P the macroscopicmacroscopic level, level, is is thethe ratio of of the the circumference circumference of an of equal an equalarea circle area to circle the circumference to the circumference of the of the particle.particle. As As the the circumference circumference of a a circle circle is is the the smallest smallest in the in thecontext context of a certain of a certain area, the area, overall the overall profileprofile coeffi cientcoefficient of sand of sand particles particles is is generallygenerally less less than than 1.0, 1.0,and andthe closer the closerthe particle the shape particle to the shape to circle, the closer the overall contour coefficient to 1.0. the circle, the closer the overallFeretmax contour coefficient to 1.0. (2) Flatness Feret퐸 = max , which represents the elongation property of the particles, is the ratio of (2) Flatness E = Feret,min which represents the elongation property of the particles, is the ratio of Feretmin the maximumthe maximum Feret Feret diameter diameter to theto the minimum minimum FeretFeret diameter. diameter. The The flatter flatter and andnarrower narrower the particles, the particles, the larger the value; conversely, the closer the particle contour to the circle, the closer the value to 1.0. the larger the value; conversely, Pc the closer the particle contour to the circle, the closer the value to 1.0. (3) Angularity AP g = , defined as the ratio of the minimum perimeter of a circumscribed c Pe (3) Angularity Ag = P , defined as the ratio of the minimum perimeter of a circumscribed polygon polygon to the perimetere of an ellipse with the same area and flatness, is an important shape to the perimeter of an ellipse with the same area and flatness, is an important shape parameter to parameter to characterize the number and protrusion degree of the edges and corners of the particles. characterizeThe larger the numberthe number and of protrusion edges and corners degree and of the the edgesgreater and the cornersdistance of the protruding particles. Theparticle larger the numberedge, of edges the greater and cornersthe angularity. and the greater the distance of the protruding particle edge, the greater 푃 2 the angularity.(4) Roughness 푅 = ( ) refers to the square of the ratio of the perimeter of the particle to the 푃푐 minimum perimeter of the circumscribed polygon. The more complex the grain boundary curve, the greater the roughness; conversely, the smoother the particle surface, the smaller the roughness. Based on the physical meaning of each shape parameter, it can be observed that the overall contour coefficient (α) and flatness (E) are part of the first-level particle shape parameters, and the angularity (Ag) and roughness (R) are the second- and third-level particle shape parameters, respectively. Subsequently, the fractal dimensions of coral sand and quartz sand with different particle sizes were calculated using the perimeter–area method based on the fractal theory to evaluate quantitatively the variation of sand particle shape with particle size and mineral composition. For irregular sand particles, the expression of the perimeter–area method [56] is as follows: 푃1⁄퐷푝 퐴1⁄2, (1)
where Dp is the fractal dimension of particle shape. Equation (1) can also be expressed as
J. Mar. Sci. Eng. 2020, 8, 803 11 of 24
2 (4) Roughness R = P refers to the square of the ratio of the perimeter of the particle to the Pc minimum perimeter of the circumscribed polygon. The more complex the grain boundary curve, the greater the roughness; conversely, the smoother the particle surface, the smaller the roughness. Based on the physical meaning of each shape parameter, it can be observed that the overall contour coefficient (α) and flatness (E) are part of the first-level particle shape parameters, and the angularity (Ag) and roughness (R) are the second- and third-level particle shape parameters, respectively. Subsequently, the fractal dimensions of coral sand and quartz sand with different particle sizes were calculated using the perimeter–area method based on the fractal theory to evaluate quantitatively the variation of sand particle shape with particle size and mineral composition. For irregular sand particles, the expression of the perimeter–area method [56] is as follows:
P1/Dp A1/2, (1) ∝ where Dp is the fractal dimension of particle shape. Equation (1) can also be expressed as
P = aADp/2, (2)
Dp lgP = lgA + lga. (3) 2
Equation (3) shows that the fractal dimension (Dp), which reflects the curvature degree of the particle profile, is twice the slope of the straight line in the lgP–lgA plane. The more complex the particle profile, the larger the fractal dimension, and the more irregular the particle shape.
3. Shape Analysis of Coral Sand Particles
3.1. Effect of Particle Size To investigate the influence of particle size on the shape of coral sand particles, the frequency distribution histograms of the overall profile coefficient (α), flatness (E), angularity (Ag), and roughness (R) of coral sand with different particle sizes were drawn, as shown in Figure 10. This figure shows that the particle shape parameters of coral sand with different particle sizes only satisfies some characteristics of normal distribution, but not strictly normal distribution, and they change regularly with the increase in particle size. We analyzed the evolution law of the particle shape with the particle size through the change of the arithmetic mean value (µ) of the particle shape parameter with the particle size. From the perspective of statistics, the arithmetic mean value of a group of data is equal to the expected value under the condition of normal distribution. That is, the abscissa corresponding to the peak value in the normal distribution fitting curve in Figure 10 is not only the expected value when the particle shape parameter distribution meets the normal distribution, but also the arithmetic average value of the particle shape parameter. In combination with the position of the peak value of the normal distribution curve and the arithmetic mean value (µ) of the particle shape parameters of coral sand with different particle sizes in Figure 10, we can clearly see that (1) the overall profile coefficient (α) of coral sand decreases as the particle size becomes larger; that is, with the enlargement in particle size, the ratio of the circumference of an equal area circle to the perimeter of the particle grows smaller, indicating that the deviation between the particle shape of large-size coral sand and the circle is larger than that of small-size coral sand, and the shape is more irregular. (2) The flatness (E) of coral sand grows with the increment in particle size. The arithmetic mean value of flatness (E) of coral medium sand with particle size of 0.5–1.0 mm and coral coarse sand with particle size of 1.0–2.0 mm are 1.474 and 1.481, respectively, while the arithmetic mean value of flatness (E) of coral gravel sand with particle size of 2.0–5.0 mm can reach 1.606. The flatness (E) of coral medium sand and coarse sand is less than 2.5, while there are particles with flatness (E) greater than 2.5 in coral gravel sand. The findings of Li et al. (2001) and Lv et al. (2001) demonstrate that the flatness (E) of 2.5 is the boundary to distinguish particles with different shapes; the flatness (E) of massive, flaky, J. Mar. Sci. Eng. 2020, 8, 803 12 of 24 and spindle particles is generally between 1.0 and 2.5, while that of dendritic and rod-shaped particles is greater than 2.5. It can be observed that the grain shapes in coral medium sand and coarse sand are mainly massive, flaky, and spindle, while those in coral gravel sand are branched and rod-shaped (Figure 11). (3) The angularity (Ag) rises as the particle size increases, indicating that the surface of large-size coral sand particles exhibits higher angularity protrusion; that is, the particle sphericity is poor and the shape is irregular. (4) The roughness (R) mounts with the increase in particle size, indicating that the complexity of surface roughness, irregularity, and boundary curve fluctuation of large-size coral sand are greater than that of coral sand with small particle size, and the particle surface is more unsmooth. In summary, the change trend of the four shape parameters with particle size reveals that the smaller the particle size, the more regular the particle shape, the less edges and corners, the lower the protruding degree around the particle contour, and the smoother the particle surface. This is because coral sand is a special sediment of marine origin. The large-size coral sand retains some structural characteristics of the protozoa (i.e., hermatypic coral, seaweeds, and shells), resulting in highly irregular grain shapes. Unlike large-size coral sand, most of the small-size coral sand, as the product of particle breakage of large-size coral sand, experienced more particle breakage in the process of deposition.J. Mar. Sci. Eng. The 20 particle20, 8, x FORbreakage PEER REVIEW that is often accompanied by the interaction between13 of 25 particles reducesbreakage the coral that sand is often particle accompanied size. Meanwhile, by the interaction the surrounding between particles corners reduces and edges the coral are sand frequently brokenparticle and ground, size. Meanwhile, which renders the surrounding the particle corners shape and more edges regular are frequently and reduces broken and the ground, intergranular resistancewhich in renders relative the motion. particle s Therefore,hape more regular the small-size and reduces coral the sandintergranular is more resistance regular in than relative large-size coral sand.motion. Therefore, the small-size coral sand is more regular than large-size coral sand.
60 D = 0.5 - 1.0 mm D = 0.5 - 1.0 mm 50 D = 1.0 - 2.0 mm D = 1.0 - 2.0 mm D = 2.0 - 5.0 mm 50 D = 2.0 - 5.0 mm -----D = 0.5 - 1.0 mm -----D = 0.5 - 1.0 mm 40 m = 0.933 m = 1.474
n -----D = 1.0 - 2.0 mm n 40 -----D = 1.0 - 2.0 mm m = 0.908 m = 1.481 30 -----D = 2.0 - 5.0 mm -----D = 2.0 - 5.0 mm 30 m = 0.870 m = 1.606 20
Particle number Particle
Particle number Particle 20
10 10
0 0 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.0 1.5 2.0 2.5 3.0 Overall profile coefficient a Flatness E (a) (b)
100 D = 0.5 - 1.0 mm 90 D = 1.0 - 2.0 mm D = 2.0 - 5.0 mm 80 -----D = 0.5 - 1.0 mm 70 m = 1.014
n -----D = 1.0 - 2.0 mm 60 m = 1.016
50 -----D = 2.0 - 5.0 mm m = 1.019 40
Particle number Particle 30
20
10
0 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 Roughness R (c) (d)
FigureFigure 10. Shape 10. Shape parameter parameter distribution distribution of of coralcoral sand with with different different particle particle sizes: sizes: (a) overall (a) overall profile profile coefficient α, (b) flatness E, (c) angularity Ag, and (d) roughness R. coefficient α,(b) flatness E,(c) angularity Ag, and (d) roughness R.
(a)
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 25 breakage that is often accompanied by the interaction between particles reduces the coral sand particle size. Meanwhile, the surrounding corners and edges are frequently broken and ground, which renders the particle shape more regular and reduces the intergranular resistance in relative motion. Therefore, the small-size coral sand is more regular than large-size coral sand.
60 D = 0.5 - 1.0 mm D = 0.5 - 1.0 mm 50 D = 1.0 - 2.0 mm D = 1.0 - 2.0 mm D = 2.0 - 5.0 mm 50 D = 2.0 - 5.0 mm -----D = 0.5 - 1.0 mm -----D = 0.5 - 1.0 mm 40 m = 0.933 m = 1.474
n -----D = 1.0 - 2.0 mm n 40 -----D = 1.0 - 2.0 mm m = 0.908 m = 1.481 30 -----D = 2.0 - 5.0 mm -----D = 2.0 - 5.0 mm 30 m = 0.870 m = 1.606 20
Particle number Particle
Particle number Particle 20
10 10
0 0 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.0 1.5 2.0 2.5 3.0 Overall profile coefficient a Flatness E (a) (b)
100 D = 0.5 - 1.0 mm 90 D = 1.0 - 2.0 mm D = 2.0 - 5.0 mm 80 -----D = 0.5 - 1.0 mm 70 m = 1.014
n -----D = 1.0 - 2.0 mm 60 J. Mar. Sci. Eng. 2020 m, 8= ,1.016 803 13 of 24
50 -----D = 2.0 - 5.0 mmJ. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 25 m = 1.019 40
Particle number Particle 30
20
10
0 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 Roughness R (c) (d)
Figure 10. Shape parameter distribution of coral sand with different particle sizes: (a) overall profile coefficient α, (b) flatness E, (c) angularity Ag, and (d) roughness R. (b)
(a) (c)
Figure 11. Coral sand withFigure di 11.fferent Coral particle sand wi sizes:th different (a) D particle= 0.5–1.0 sizes:mm, (a) D (=b 0.5) D–1.0= mm,1.0–2.0 (b) mm,D = 1.0–2.0 mm, and (c) D and (c) D = 2.0–5.0 mm. = 2.0–5.0 mm.
3.2. Analysis of Particle Fractal3.2. Analysis Dimension of Particle Fractal Dimension The perimeter and areaThe of theperimeter two-dimensional and area of projectionthe two-dimensional contour of projection coral sand contour particles of coral were sand particles were calculated using the imagecalculated analysis using software the imag IPP,e analysis and the software lgP–lgA IPP,fitting and curves the lgP for–lg theA fitting three curves grain for the three grain groups of coral sand weregroups drawn, of coral as shownsand were in Figure drawn, 12 as. Theshown figure in Figure shows 12. that The the figure perimeter shows andthat the perimeter and area of the experimentalarea coral of sandthe experimental present a linear coral relationshipsand present ina linear the double relationship logarithmic in the coordinatedouble logarithmic coordinate system with a correlationsystem coeffi cientwith ofa correlation approximately coefficient 0.9, indicating of approximately that coral 0.9, sand indicating with particle that coral sizes sand with particle in the range of 0.5–1.0 mm,sizes 1.0–2.0 in the range mm, andof 0.5 2.0–5.0–1.0 mm, mm 1.0 features–2.0 mm, good and fractal2.0–5.0 characteristics.mm features good fractal characteristics. Using Equation (3), theUsing fractal dimensionEquation (3), of coral the fractal sand with dime dinsionfferent of particle coral sand sizes waswith calculated, different particle sizes was as presented in Table3. calculated, as presented in Table 3.
As presented in the table, the fractal dimension of0.85 coral sand with different particle sizes ranges D = 0.5 - 1.0 mm from 1.07 to 1.10, and as particle size grows, the fractal dimension Fitting line of coral sand increases. According to the physical meaning of fractal dimension, the larger0.80 the fractal dimension, the more complex the
(mm)
particle shape. Furthermore, the particle shape of coralP 0.75 sand becomes more irregular with the increase
lg in particle size, which is consistent with the results of the statistical analysis of particle shape parameters of coral sand with different particle sizes. 0.70 lgP = 0.53469lgA + 0.57126 3.3. Distribution Characteristics and Sensitivity Analysis0.65 of Particle Shape Parameters R2 = 0.90313
Preliminary analysis of the distribution characteristics circumference Particle 0.60 of each particle shape parameter of three grain
groups of coral sand found that the shape parameters are0.55 concentrated in a specific range, although discrete 0.00 0.10 0.20 0.30 0.40 0.50 in numerical value. To uncover the distribution characteristics of the coral2 sand particle shape, Particle area lgA (mm ) the mean value, standard variance, coefficient of variation, concentrated(a) distribution interval, and interval length of various shape parameters of coral sand with different particle sizes were statistically analyzed, as presented in Table4.
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 25
(b)
J. Mar. Sci. Eng. 2020, 8, 803 14 of 24 (c) J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 15 of 25 Figure 11. Coral sand with different particle sizes: (a) D = 0.5–1.0 mm, (b) D = 1.0–2.0 mm, and (c) D 1.00 = 2.0–5.0 mm. D = 1.0 - 2.0 mm Fitting line 0.95
3.2. Analysis of Particle Fractal Dimension (mm)
P 0.90
lg The perimeter and area of the two-dimensional projection contour of coral sand particles were calculated using the image analysis software IPP, and the lgP–lgA fitting curves0.85 for the three grain groups of coral sand were drawn, as shown in Figure 12. The figure shows that the perimeter andlg P = 0.54634lgA + 0.56802 area of the experimental coral sand present a linear relationship in the double0.80 logarithmic coordinate R2 = 0.89705 system with a correlation coefficient of approximately 0.9, indicating that coral sand with particle Particle circumference Particle 0.75 sizes in the range of 0.5–1.0 mm, 1.0–2.0 mm, and 2.0–5.0 mm features good fractal characteristics. Using Equation (3), the fractal dimension of coral sand with different0.70 particle sizes was 0.30 0.40 0.50 0.60 0.70 calculated, as presented in Table 3. Particle area lgA (mm2) (b) 0.85 D = 0.5 - 1.0 mm D = 2.0 - 5.0 mm Fitting line 1.40 Fitting line 0.80
(mm) (mm) 1.30
P P 0.75
lg
lg
1.20 0.70
lgP = 0.53469lgA + 0.57126 lgP = 0.55166lgA + 0.55287 1.10 0.65 R2 = 0.90313 R2 = 0.93571
Particle circumference Particle 1.00 0.60 circumference Particle
0.55 0.90 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.80 1.00 1.20 1.40 1.60 2 Particle area lgA (mm ) Particle area lgA (mm2) (a) (c)
Figure 12. lgP–lgA fittingFigure curve 12. oflgP coral–lgA sandfitting with curve di offferent coral particlesand with sizes: different (a) D part= 0.5–1.0icle sizes: mm, (a) D = 0.5–1.0 mm, (b) D = (b) D = 1.0–2.0 mm, and (1.0c) D–2.0= 2.0–5.0mm, and mm. (c) D = 2.0–5.0 mm.
Table 3. Fractal dimension of coral sand with different particle sizes. Table 3. Fractal dimension of coral sand with different particle sizes. Particle size D (mm) 0.5–1.0 1.0–2.0 2.0–5.0 Particle Size D (mm) 0.5–1.0 1.0–2.0 2.0–5.0 Fractal dimension Dp 1.06938 1.09268 1.10332 Fractal Dimension Dp 1.06938 1.09268 1.10332 As presented in the table, the fractal dimension of coral sand with different particle sizes ranges from 1.07 to 1.10, and as particle size grows, the fractal dimension of coral sand increases. According to the physical meaning of fractal dimension, the larger the fractal dimension, the more complex the particle shape. Furthermore, the particle shape of coral sand becomes more irregular with the increase in particle size, which is consistent with the results of the statistical analysis of particle shape parameters of coral sand with different particle sizes.
3.3. Distribution Characteristics and Sensitivity Analysis of Particle Shape Parameters Preliminary analysis of the distribution characteristics of each particle shape parameter of three grain groups of coral sand found that the shape parameters are concentrated in a specific range, although discrete in numerical value. To uncover the distribution characteristics of the coral sand particle shape, the mean value, standard variance, coefficient of variation, concentrated distribution interval, and interval length of various shape parameters of coral sand with different particle sizes were statistically analyzed, as presented in Table 4.
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Table 4. Probability statistics table of the shape parameters of coral sand with different particle sizes.
Particle Size 0.5–1.0 mm 1.0–2.0 mm 2.0–5.0 mm Overall Overall Overall Contour Flatness Angularity Roughness Contour Flatness Angularity Roughness Contour Flatness Angularity Roughness Shape Parameters Coefficient E Ag R Coefficient E Ag R Coefficient E Ag R α α α Mean value 0.93267 1.47363 1.01789 1.01425 0.90845 1.48061 1.04102 1.01556 0.86955 1.60616 1.06444 1.01926 Standard variance 0.03814 0.25311 0.01995 0.01294 0.03414 0.24156 0.02654 0.01217 0.05695 0.39946 0.03827 0.01910 Coefficient of variation 0.04089 0.17176 0.01960 0.01276 0.03758 0.16315 0.02550 0.01198 0.06549 0.24871 0.03595 0.01874 Concentrated 0.92737– 1.43846– 1.01512– 1.01246– 0.90372– 1.44713– 1.03734– 1.01388– 0.86166– 1.5508– 1.05914– 1.01661– distribution interval 0.93797 1.50879 1.02066 1.01605 0.91318 1.514090 1.04469 1.01725 0.87744 1.66152 1.06974 1.02190 Interval length 0.01060 0.07033 0.00554 0.00360 0.00946 0.06696 0.00736 0.00337 0.01578 0.11072 0.01061 0.00529 SK 0.76594 1.09211 0.80144 3.45728 -0.39706 1.03294 1.09371 2.12617 -0.77176 1.55492 1.02152 2.88351 − negative positive positive positive negative positive positive positive negative positive positive positive Skewness type skewness skewness skewness skewness skewness skewness skewness skewness skewness skewness skewness skewness J. Mar. Sci. Eng. 2020, 8, 803 16 of 24
The distribution interval of the shape parameters of particles accounting for 95% of the total particles is also displayed in the table. The interval length, referring to the value range of shape parameters under certain probability, and the coefficient of variation, meaning the dispersion degree of shape parameters, can simultaneously reflect the sensitivity of shape parameters. The larger the coefficient of variation and the longer the interval length, the stronger the sensitivity of the corresponding shape parameters. As also presented in Table4, (1) although the particle sizes in the three grain groups of coral sand are different, the sensitivity of shape parameters to the change in particle shape is completely consistent. Regarding the coefficient of variation and interval length, together with the sensitivity to the change in particle shape, flatness ranks first, the overall profile coefficient and angularity are second, and roughness is third. In other words, compared with the other three shape parameters in this study, flatness can better distinguish the particle shape of coral sand. (2) Except for individual scattered points, as the particle size increases, the variation coefficient and interval length of each shape parameter of coral sand also increase, indicating that as the particle size grows, the shape parameters of coral sand are more widely distributed and more discrete. That is, as the particle size grows, the shape of coral sand is more diversified, the odd-shaped particles in the sample augments, and the overall shape is more irregular, which also verifies the conclusion drawn from the above analysis in terms of coefficient of variation and interval length that the larger the particle size, the more irregular its shape. Furthermore, in the process of statistical analysis of particle shape parameters, it was found that although several characteristics of normal distribution are met, the shape parameters are not strictly subject to a normal distribution (Table4). Using Equation (4) [ 57] and the distribution range of various shape parameters, the three grain groups of coral sand with 200 particles in each grain group were divided into 16 groups. k = 1.87(n 1)0.4, (4) − where k is the number of groups and n is the total amount of samples. The frequency distribution histograms of each particle shape parameter of coral sand were drawn. Owing to space limitation, the statistical results of four shape parameters of coral gravel sand with particle size between 2.0 and 5.0 mm were plotted in Figure 13, in which a comparative analysis was conducted for the peak value corresponding to the average value of particle shape parameters in the fitting curve of the normal distribution and the actual peak value. The figure demonstrates that in the frequency distribution histograms of the shape parameters of coral sand particles, the fitting peak value of the normal distribution curve corresponding to the average value does not coincide with the actual peak value, and the parameter distribution is skewed. The skewness coefficient (SK) represents the deviation degree between the particle shape parameter value corresponding to the actual peak value and the particle shape parameter value corresponding to the normal distribution fitting peak value (i.e., mean value of the particle shape parameter), which is often adopted to reflect the symmetry degree of the probability density curve of the actual particle shape parameter distribution. The actual peak value of the overall contour coefficient (α) is on the right side of the fitting peak value, and the long tail extends to the left side of the coordinate axis; therefore, the SK is less than 0 (Table4), showing a negative skew distribution. Conversely, the SK of flatness (E), angularity (Ag), and roughness (R) is greater than 0 (Table4), showing a positive skew distribution. According to the physical meaning of each shape parameter, the overall contour coefficient (α) of non-standard sphere particles is less than 1.0, whereas their flatness (E), angularity (Ag), and roughness (R) are all greater than 1.0; that is, the closer the shape parameter to 1.0, the closer the particle shape to the standard sphere. The statistical results show that the distribution of the overall profile coefficient (α) of the particles tends to the right, that is, to 1.0, whereas the distributions of flatness (E), angularity (Ag), and roughness (R) tend to the left, that is, to 1.0. This indicates that, although characterized by heterogeneous particles, coral sand still tends to be composed of spherical particles in the overall distribution. The same results were obtained from the statistical analysis of the particle shape parameters of other sizes of coral sand, which will not be repeated here. J. Mar. Sci. Eng. 2020, 8, 803 17 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 18 of 25
35 45 D = 2.0 - 5.0 mm Actual peak Actual peak D = 2.0 - 5.0 mm Normal distribution fitting curve Normal distribution fitting curve m = 0.92204 40 m = 1.606 30 35 Peak of the fitting curve 25 Peak of the fitting curve
n n 30
20 25
15 20
Particle number Particle
Particle number Particle 15 10 10 5 5
0 0 0.75 0.80 0.85 0.90 0.95 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Overall profile coefficient a Flatness E
(a) (b) 35 90 Actual peak D = 2.0 - 5.0 mm Actual peak D = 2.0 - 5.0 mm Normal distribution fitting curve Normal distribution fitting curve m = 1.064 80 m = 1.019 30 Peak of the fitting curve 70 25
n Peak of the fitting curve n 60
20 50
15 40
Particle number Particle Particle number Particle 30 10 20 5 10
0 0 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.00 1.02 1.04 1.06 1.08 1.10 1.12 Angularity A g Roughness R (c) (d)
FigureFigure 13.13. DistributionDistribution diagram diagram of ofthe the shape shape parameters parameters of coral of coralsand with sand the with particle the particle size of 2.0 size–5.0 of mm: (a) overall profile coefficient α, (b) flatness E, (c) angularity Ag, and (d) roughness R. 2.0–5.0 mm: (a) overall profile coefficient α,(b) flatness E,(c) angularity Ag, and (d) roughness R.
ByBy introducing introducing the the basicbasic sizesize parametersparameters of a regular polygon into into the the particle particle shape shape parameters parameters defineddefined above, above, the the sensitivity sensitivity of the of theregular regular polygon polygon to the to change the change of particle of particle shape is shape further is explored. further Figureexplored 14a. Figure shows 14 thea shows shape thesketch shape of asketch regular of a quadrilateral, regular quadrilateral, regular hexagon, regular hexagon, regular octagon, regular regularoctagon, decagon, regularregular decagon, dodecagon, regularand dodecagon, regular hexagon. and regular Figure hexagon.14b shows Figure the comparison 14b shows diagram the ofcomparison the shape parameter diagram of of the the shape regular parameter polygons. of It the can regular be observed polygons. from It Figure can be 14 observed that (1) as from the numberFigure of14 regular that (1) polygon as the number edges increases, of regular the polygon overall edges contour increases, coefficient the (α overall) increases contour gradually, coefficient and ( theα) increases gradually, and the flatness (E) and angularity (Ag) gradually decrease, which can be flatness (E) and angularity (Ag) gradually decrease, which can be explained by the fact that the higher theexplained number by of regularthe fact polygonthat the higher edges, t thehe number closer it of is toregular the circle. polygon However, edges, the the roughness closer it is (toR) the fluctuates circle. withHowever, the increase the roughness in number (R of) fluctuates regular polygon with the edges. increase The in roughness number of (R regular) is related polygon to the edges. undulating The complexityroughness of(R the) is contourrelated lineto the of theundulating two-dimensional complexity projection of the contour image. Althoughline of the the two regular-dimensi polygononal tendsprojection to be image.a regular Although circle with the the regular increase polygon in number tends toof edges,be a regular the wrinkle circle withdegree the of increase its contour in linenumber will enterof edges, the coursethe wrinkle of constant degree increase of its contour and decrease, line will enter and when the course it evolves of constant into a smoothincrease circle, and decrease, and when it evolves into a smooth circle, the roughness (R) reaches the minimum value. (2)
J. Mar. Sci. Eng. 2020, 8, 803 18 of 24
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 19 of 25 the roughness (R) reaches the minimum value. (2) To quantitatively evaluate the sensitivity of various shapeTo quantitatively parameters, evaluate a statistical the magnitudesensitivity of (δ) various was defined, shape whichparameters, can be a calculatedstatistical magnitude by (δ) was defined, which can be calculated by ∂max ∂min δ = ∂max−-∂min 100%, (5) δ = ∂max ×× 100%, (5) ∂max wherewhereα maxαmaxand andαmin αminare are the maximumthe maximum and minimum and minimum values of values a particle of shape a particle parameter, shaperespectively. parameter, Therespectively. sensitivity The of each sensitivity shape parameterof each shape is analyzed parameter by iscomparing analyzed the by δ comparingvalues of di thefferent δ values shape of parametersdifferent shape under parameters the same conditions. under the same After conditions. substituting After the data substituting in Figure the 14 intodata Equation in Figure (5), 14 itint iso foundEquation that (5), the itδ valuesis found of that the overallthe δ values contour of coethe ffioverallcient ( αcontour), flatness coefficient (E), angularity (α), flatness (Ag), and (E), roughnessangularity (R(A)g are), and 9.03%, roughness 27.44%, (R) 8.71%, are 9.03%, and 27.44%, 1.76%, respectively.8.71%, and 1.76%, It can respectively. also be observed It can also that be the observed sensitivity that ofthe flatness sensitivity (E) is of the flatness strongest, (E) is thethe overallstrongest, profile the overall coefficient profile (α) coefficient and angularity (α) and (A angularityg) are the second, (Ag) are andthe second, the sensitivity and the ofsensitivity roughness of roughness (R) is the weakest, (R) is the whichweakest, is which consistent is consistent with the with conclusion the conclusion of the aboveof the analysis.above analysis.
(a) 1.45 Overall contour coefficient a 1.40 Flatness E
1.35 Angularity Ag Roughness R 1.30 1.25 1.20 1.15 1.10 1.05 1.00
Particle shape parameterParticle values 0.95 0.90 0.85 4 6 8 10 12 16 Number of regular polygon edges (b)
FigureFigure 14. 14.Comparison Comparison of shapeof shape parameters parameters for regular for regular polygons: polygons (a) schematic: (a) schematic diagram diagram of regular of polygons, regular (bpolygons) variation, (b of) variation particle shape of particle parameter shape valueparameter with thevalue number with the of regularnumber polygon of regular edges. polygon edges.
4.4. ComparativeComparative AnalysisAnalysis ofof thethe ParticleParticle ShapeShape ofof CoralCoral SandSand andand QuartzQuartz Sand Sand TheThe basic basic sizesize parametersparameters of of coralcoral sandsand particlesparticles andand quartzquartz sandsand particlesparticles withwith didifferentfferent particleparticle sizessizes that that were were extracted extracted using using IPP IPP were were implemented implemented the particle the particle shape shape parameters parameters constructed constructed above. The overall contour coefficient (α), flatness (E), angularity (A ), roughness (R), and fractal dimension above. The overall contour coefficient (α), flatness (E), angularityg (Ag), roughness (R), and fractal (D ) and their arithmetic mean values (i.e., the expected value (µ) under normal distribution) were dimensionp (Dp) and their arithmetic mean values (i.e., the expected value (μ) under normal statisticallydistribution) analyzed, were statistically as shown analyzed, in Figure as 15 shown. It can in beFigure observed 15. It fromcan be the observed figure that,from under the figure the samethat, particleunder the size, same the particle overall size, profile the coe overallfficient profile (α) of coefficient coral sand (α is) smallerof coral thansand that is smaller of quartz than sand. that Accordingof quartz sand. to the According physical to meaning the physical of the meaning overall of profile the overall coeffi cientprofile (α coefficient), in the case (α), ofin the the case same of projectionthe same projection area, the edges area, andthe edges corners and around corner corals around sand particlescoral sand are particles prominent are andprominent its number and isits alsonumber higher, is also rendering higher, a rendering larger perimeter a larger value. perimeter Therefore, value. theTherefore, value of the the value overall of contourthe overall coe contourfficient (α) of coral sand is smaller. This is consistent with the result that the angularity (A ) of coral sand of coefficient (α) of coral sand is smaller. This is consistent with the result that the gangularity (Ag) of eachcoral grain sand group of each is greatergrain group than thatis greater of quartz than sand. that Theof quartz flatness sand. (E) of The coral flatness sand in(E each) of coral grain sand group in each grain group is greater than that of quartz sand, indicating that the content of rod- and branch- shaped particles in coral sand is higher than that in quartz sand and the overall shape deviates more from the circle. The roughness (R) of coral sand in each grain group is also higher than that of quartz
J. Mar. Sci. Eng. 2020, 8, 803 19 of 24
is greater than that of quartz sand, indicating that the content of rod- and branch-shaped particles J. Mar.in Sci. coral Eng. sand 2020, is8, higherx FOR PEER than REVIEW that in quartz sand and the overall shape deviates more from the circle.20 of 25 The roughness (R) of coral sand in each grain group is also higher than that of quartz sand with the sandsame with particle the same size, particle implying size, that implying the surface that of the coral surface sand is of more coral undulating sand is more and lessundulating smooth. Theand less smooth.fractal The dimension fractal dimension of coral sand of is coral larger sand than thatis larger of quartz than sand, that which of quartz indicates sand, that which the grain indicates profile that the grainof coral profile sand isof more coral complex sand is thanmore that complex of quartz than sand. that of quartz sand.
1.6 1.4736 D = 0.5 - 1.0 mm 1.4 1.3990 Coral sand Quartz sand
1.2
1.01791.0097 1.01431.0138 1.0 0.93270.9501
0.8
0.6 0.53470.5106
0.4
Particle shape parameterParticle values 0.2
0.0
α E Ag R Dp Particle shape parameter (a) 1.6 1.4806 D = 1.0 - 2.0 mm 1.4146 1.4 Coral sand Quartz sand
1.2
1.04101.0156 1.01561.0140 1.0 0.9450 0.9084
0.8
0.6 0.5463 0.5178
0.4
Particle shape parameterParticle values 0.2
0.0
α E Ag R Dp Particle shape parameter (b) 1.8 D = 2.0 - 5.0 mm 1.6 1.6062 Coral sand Quartz sand
1.4267 1.4
1.2 1.0644 1.0325 1.01931.0150 1.0 0.9297 0.8695 0.8
0.6 0.55170.5202
0.4
Particle shape parameterParticle values 0.2
0.0
α E Ag R Dp Particle shape parameter (c)
FigureFigure 15. 15.ComparisonComparison of of shape shape parameters for for coral coral sand sand and quartzand quartz sand with sand di ffwitherent different particle sizes: particle sizes:(a ()aD) D= 0.5–1.0= 0.5–1.0 mm, mm, (b) D(b=) D1.0–2.0 = 1.0– mm,2.0 mm, and (cand) D =(c2.0–5.0) D = 2.0 mm.–5.0 mm.
In summary, coral sand possesses more rod- and branch-shaped particles than quartz sand with the same particle size, and the particle surface has more edges and corners, the angular protrusion grain edge distance is larger, and the particle surface has more undulation and is rougher than those of quartz sand. The grain shape of coral sand is very different from that of quartz sand, which is closely related to its genesis and sedimentary environment. Quartz sand from the Yangtze River, which migrates continuously with the flow during the deposition process, often collides and rubs with other particles, and this is coupled with the scouring action of the flow, which makes its particle surface smooth and round with less edges and corners. The special marine biological origin of coral
J. Mar. Sci. Eng. 2020, 8, 803 20 of 24
In summary, coral sand possesses more rod- and branch-shaped particles than quartz sand with the same particle size, and the particle surface has more edges and corners, the angular protrusion grain edge distance is larger, and the particle surface has more undulation and is rougher than those J. Mar. Sci.of Eng. quartz 2020 sand., 8, x FOR The PEER grain REVIEW shape of coral sand is very different from that of quartz sand, which is 21 of 25 closely related to its genesis and sedimentary environment. Quartz sand from the Yangtze River, sand, formedwhich migratesby the biological continuously remains with the afte flowr the during death the of deposition the hermatypic process, often coral collides group and through rubs a long with other particles, and this is coupled with the scouring action of the flow, which makes its particle geologicalsurface process, smooth leads and to round the withirregular less edges shape and of corners. coral sand The specialin the marineinitial formation biological origin and ofto the low possibilitycoral of sand, large formed-scale by and the biological long-distance remains migration after the death in of the the seabed. hermatypic In coral addition, group through it still a retains a certain angularitylong geological after process, particle leads breakage to the irregular under shape the of action coral sand of external in the initial forces. formation Meanwhile, and to the the river sand, whichlow possibility is hard and of large-scale may not and be subjected long-distance to migrationlarge-scale in the particle seabed. breakage, In addition, is it mainly still retains composed a of certain angularity after particle breakage under the action of external forces. Meanwhile, the river SiO2. When interacting with the external world, the edges and corners of quartz sand are polished to sand, which is hard and may not be subjected to large-scale particle breakage, is mainly composed make itself more regular. of SiO2. When interacting with the external world, the edges and corners of quartz sand are polished to make itself more regular. 5. Influence of Particle Shape on Accumulation Characteristics 5. Influence of Particle Shape on Accumulation Characteristics According to the specifications of the Chinese National Standard of Soil Test Method (GB/T50123- According to the specifications of the Chinese National Standard of Soil Test Method 2019) [58],(GB 700/T50123-2019) g of dry [coral58], 700 sand g of and dry quartz coral sand sand and of quartz each sandgrain of group each grain were group taken were for taken bulk density test (or minimumfor bulk density dry testdensity (or minimum test). The dry results density test).are shown The results in Figure are shown 16. in Figure 16.
Coral sand Quartz sand 1.4 1.32 1.32 1.35
1.2
)
3
1.0
g/cm
(
0.86 0.83 dmin 0.80 r 0.8
0.6
0.4
Bulk density
0.2
0.0 0.5–1.0 1.0–2.0 2.0–5.0 Particle size D (mm) Figure 16.Figure Comparison 16. Comparison of bulk of bulk density density betweenbetween coral coral sand sand and quartz and sandquartz with sand different wi particleth different sizes. particle sizes. Figure 16 shows that as the particle size increases, the bulk density of coral sand decreases evenly by 6.98%, while that of quartz sand slightly increases (by 2.27%); that is, in the context of the same Figureparticle 16 size,shows the that bulk densityas the particle of quartz size sand increases, is greater than the that bulk of coral density sand, of and coral the disandfference decreases grows evenly by 6.98%,with while an increase that of in particlequartz size.sand slightly increases (by 2.27%); that is, in the context of the same particle size,When the bulk the mass density is constant, of quartz the bulk sand density is greater depends than on the that gradation of coral and sand, specific and gravity the ofdifference particles and the volume of internal and intergranular pores [47,49]. The mineral composition of the grows with an increase in particle size. sand is the decisive factor of its specific gravity. When the volume of the internal and intergranular Whenpores the is themass same, is theconstant, greater the the specific bulk gravity, density the depends greater the on bulk the density gradation of the sand. and For specific the same gravity of particlesmineral and the type volume of sand, of the internal larger the and volume intergranular of the internal pores and intergranular [47,49]. The pores mineral is, the composition smaller the of the sand is thebulk decisive density becomes. factor of its specific gravity. When the volume of the internal and intergranular pores is the Thesame, special the marine greater biogenesis the specific of coral gravity, sand contributes the greater to a massthe bulk of internal density pores of in the the sand. coral For the sand particles. Both internal pores and intergranular pores exist simultaneously in the process of same mineral type of sand, the larger the volume of the internal and intergranular pores is, the smaller the bulk density becomes. The special marine biogenesis of coral sand contributes to a mass of internal pores in the coral sand particles. Both internal pores and intergranular pores exist simultaneously in the process of natural accumulation. The larger the size of coral sand particles, the greater the probability of internal pores, the greater the number and volume of the corresponding internal pores, and the more irregular the shape of coral sand particles. This leads to the larger the volume of the intergranular pores in the natural accumulation process of large-size coral sand than those of small-sized coral sand. Therefore, the bulk density of coral sand decreases with the increase in particle size. Relevant research results [59–61] show that the influence of nonuniformity coefficient (Cu) on the bulk density of granular materials is greater than that of the median particle size (d50), and the bulk density of granular materials increases gradually with the increase of nonuniformity coefficient (Cu) within limits. In this paper, the nonuniformity coefficient (Cu) of coral sand with particle size in the range of 0.5–1.0 mm, 1.0–2.0 mm and 2.0–5.0 mm increases slightly with the increase of particle size (see Table 1), but the bulk density does not increase with the slightly increase of nonuniformity coefficient (Cu), indicating
J. Mar. Sci. Eng. 2020, 8, 803 21 of 24 natural accumulation. The larger the size of coral sand particles, the greater the probability of internal pores, the greater the number and volume of the corresponding internal pores, and the more irregular the shape of coral sand particles. This leads to the larger the volume of the intergranular pores in the natural accumulation process of large-size coral sand than those of small-sized coral sand. Therefore, the bulk density of coral sand decreases with the increase in particle size. Relevant research results [59–61] show that the influence of nonuniformity coefficient (Cu) on the bulk density of granular materials is greater than that of the median particle size (d50), and the bulk density of granular materials increases gradually with the increase of nonuniformity coefficient (Cu) within limits. In this paper, the nonuniformity coefficient (Cu) of coral sand with particle size in the range of 0.5–1.0 mm, 1.0–2.0 mm and 2.0–5.0 mm increases slightly with the increase of particle size (see Table1), but the bulk density does not increase with the slightly increase of nonuniformity coefficient (Cu), indicating that the influence of particle shape on the bulk density of coral sand is stronger than that of nonuniform coefficient (Cu) in the case of little difference in the nonuniformity coefficient (Cu). As there are almost no internal pores in quartz sand, the variation in bulk density with particle size hinges on the variation of intergranular pores and particle gradation. The particle shape of quartz sand is also more irregular with the increase of particle size, which leads to the increase of intergranular pore volume in the sample with the increase of particle size. However, the bulk density of quartz sand shows a slight increase trend with the increase of particle size. This is because the particle shape of quartz sand is relatively smooth, and the influence of particle gradation on the bulk density of quartz sand is greater than that of particle shape. The nonuniformity coefficient (Cu) of quartz sand increases slightly with the increase of particle size (see Table1), which is the essential reason why the bulk density of quartz sand increases slightly with the increase of particle size. Determination of the specific gravity of coral sand and quartz sand in this test shows that the specific gravity of coral sand is 2.785, which is greater than that of quartz sand (2.698). If the coral sand and quartz sand do not have internal pores and intergranular pores, the bulk density of these two types of sand is the same as its specific gravity; that is, the bulk density of coral sand should be greater than that of quartz sand. It can be observed that owing to the existence of internal pores and intergranular pores, the bulk density of coral sand significantly decreases. With the decrease in particle size, their difference in bulk density gradually decreases, which occurs because the number (or volume) of the internal pores of coral sand decrease with the decrease in particle size, and at this point, the key factors restricting their bulk density are the specific gravity of particles and the volume of the intergranular pores. Even in the case of small particle size, the bulk density of coral sand is still less than that of quartz sand, indicating that the intergranular pore volume of coral sand is much larger than that of quartz sand under the same particle size. The volume of internal pores of coral sand is determined by its marine origin, and the volume of the intergranular pores is associated with its irregular particle shape. From the above analysis, it can be observed that owing to the irregular shape of coral sand particles, the bulk density of small-size coral sand is still smaller when its specific gravity is larger than that of quartz sand.
6. Conclusions (1) In this study, four shape parameters, namely, overall profile coefficient, flatness, angularity, and roughness, were constructed to study the change in particle shape with particle size ranging from 0.5 to 5.0 mm. It was proved that the larger the particle size of coral sand, the more evident the difference in shape between coral sand and the standard circle. (2) The shape of coral sand exhibits good fractal property, and the fractal dimension of coral sand with particle size of 0.5–5.0 mm is between 1.07 and 1.10; thus, the larger the particle size, the greater the fractal dimension, and the more complex the particle profile. (3) Although the distribution of each shape parameter presents certain discreteness, it generally obeys the skewed distribution. The flatness renders the greatest sensitivity to the change in particle shape, J. Mar. Sci. Eng. 2020, 8, 803 22 of 24 followed by the overall profile coefficient and angularity and then the roughness. It is suggested that flatness should be preferred as the evaluation parameter of the particle shape. (4) Coral sand particles are mainly massive, flaky, and spindle shaped. In comparison with the quartz sand, the coral sand harbors more contents of rod- and branch-shaped particles, more edges and corners, larger roughness, and a more irregular grain shape. (5) The irregular particle shape of coral sand makes its bulk density smaller than that of quartz sand under the same conditions, and it is also more difficult for coral sand to reach the dense state. The larger the particle size, the more irregular the particle shape, the larger the intergranular pore volume, the smaller the corresponding bulk density, and the greater the difference of bulk density between coral sand and quartz sand. The irregular particle shape of coral sand functions as the main reason why its specific gravity is higher than that of quartz sand, but its bulk density is less than that of quartz sand.
Author Contributions: Conceptualization, X.W. and Y.W.; methodology, X.W.; validation, X.W.; formal analysis, X.W. and Y.W.; investigation, Y.W.; resources, X.W.; data curation, X.W.; writing—original draft preparation, J.C.; writing—review and editing, C.-Q.Z.; visualization, X.-Z.W.; supervision, C.-Q.Z.; project administration, Y.W.; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Consultative Project by Chinese Academy of Engineering(2019-XZ-18), the National Natural Science Foundation of China (Nos. 41877271, 51908153), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA13010301), and Guangzhou City Technology and Science Program (201904010278). Conflicts of Interest: All the authors have read and approved this version of the article, and due care has been taken to ensure the integrity of the work. All the authors have no conflicts of interest to declare.
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