Prediction of Settling Velocity of Nonspherical Soil Particles Using Digital Image Processing

Digital image processing (DIP) is used to measure shape properties and settling velocity of soil particles. Particles with diameters of 1 to 10mm are arbitrarily sampled for the test. ,e size of each particle is also measured by a Vernier caliper for comparison with the classification results using the shape classification table. ,e digital images were taken with a digital camera (Canon EOS 100d). Shape properties are calculated by image analysis software. Settling velocity of soil particles is calculated by displacement and time difference of images during settling. ,e fastest settling particles are spherical shaped. Shape factors well explain the difference of settling velocity by a particle shape. In particular, the aspect ratio has a high negative correlation with residual of settling velocity versus mean diameter. Especially, DIP has a higher applicability than classification using the shape classification table because it can measure a number of particles at once. ,e settling velocity of soil particles is expressed as a function of mean diameter and aspect ratio.


Introduction
e settling velocity of sediment particles is one of the key variables in the study of sediment transport and is important in understanding suspension, deposition, mixing, and exchange processes.It is affected by the size, density, shape of sediment particles, and physical properties of fluid [1].
e aim of many researches on the study of the settling velocity is to make precise, general formula for prediction of settling velocity [1][2][3][4][5][6].e shape of sediment particles can be divided into ideal spherical and nonspherical.e settling velocity of spherical particles can be predicted to be more than 98% accurate [7].Recent studies on the settling velocity of spherical particles have been an underway to investigate their acceleration motions analytically [8], especially the effects of initial velocity on spherical particle acceleration in a fluid [9,10].
A sphere with the nominal diameter of a nonspherical grain has the same weight, so that the difference between their settling velocities must be due to shape effects alone [11].
To predict settling velocity of nonspherical particles, researchers propose a shape index to explain the effect of the particle shape on settling velocity [11][12][13][14][15][16][17][18][19][20].e shape index of the particle is a coefficient representing various shape properties of the particle such as circularity, sphericity, roundness, and flatness.ese shape indexes are calculated by major, intermediate, and minor axes to consider a 3dimensional shape of particles.Most of the shape indexes well represent the difference in settling velocity according to the particle shape, but they have a poor applicability because the measurement of the 3-dimensional particle shape is inconvenient.
A digital image processing (DIP) can be a proper alternative method for particle shape measuring.e DIP is a method to perform specific operations on digital images to extract information in digital images by computer algorithms.
e DIP has been widely used to measure displacement and shape of particles in geotechnical engineering by many researchers [21][22][23][24][25][26][27][28][29][30].e objective of this paper was to measure particle shape and settling velocity of nonspherical soil by DIP and develop the empirical prediction formula of settling velocity considering the particle shape and diameter.To compare with the classification result using the shape classification table, the particle shape is measured by a Vernier caliper and DIP method.e settling velocity equation uses shape properties measured by the DIP method instead of 3-dimensional shape indexes for high applicability.

Materials and Experimental
Procedure.Two different nonspherical soils were used in this study.One is used for formulation of the settling velocity equation using the digital image processing method, and the other is used for verification of the settling velocity equation.
e nonspherical soils were classified as SW by the Unified Soil Classification System.Physical properties of nonspherical soils are summarized in Table 1.
In this study, digital image processing is adopted to measure the particle shape properties and the settling velocities of particles.Particles with diameters of 1 to 10 mm are arbitrarily sampled in sample A and B. 343 particles are sampled in sample A and 106 particles in sample B. e size of each particle is also measured by a Vernier caliper for comparison with the classification result using the shape classification table.e experimental procedure is shown in Figure 1.

Digital Image Acquisition.
It is important to take a proper digital image of target in digital image processing.
e quality of the digital image is influenced by the shooting condition.e apparatus for acquisition of the digital image to get shape properties of soil is shown in Figure 2(a).e digital images were taken with a digital camera (Canon EOS 100d).To separate soil from image background properly, a black background plate is used.e digital camera is installed in the vertical direction of the background plate.Two led lights are used to illuminate uniformly for shooting.
e apparatus for acquisition of the digital image to get settling velocity of soil is shown in Figure 2(b).
e dimension of the settling tank is 300 mm (width) × 80 mm (length) × 1000 mm (height).A soil particle is settled down under the surface of water by pincette to minimize the effect of surface tension.
e digital camera is installed in the horizontal direction of the settling tank.To acquire digital images of settling soil particle, shoot high definition video at 25 frames per second and divide video by frame.

Digital Image
Processing.An image analysis software (Media Cybernetics Image Pro Plus, Version 6.0) is used to determine shape properties of soil particles such as diameter, area, perimeter, roundness, and aspect ratio.Description of shape properties of soil particles is summarized in Table 2.
e resolution of the digital image is 0.077 mm/pixel.Procedure of acquisition of soil shape properties is summarized in Figure 3.
To determine settling velocity of soil, the R-programming language is used to analyze the digital image set.An original image is cropped in order to remove unnecessary parts for DIP. e procedure of calculation of settling velocity by DIP is as follows.First, select a digital image set of the settling particle.e digital image set has N frames of the digital image.Second, perform binarization to segmentation of target (soil particle) and background.After binarization, the soil particle in the digital image is converted to a set of white pixels.To determine the position of the soil particle in each image, calculate centroid of white pixels in each image.e displacement is the difference of the position of the soil particle in two consecutive images, and the time difference is 1/25 second because the original image is taken 25 frames per second.Finally, settling velocity is calculated by dividing the displacement into time difference.e procedure of acquisition of settling velocity is summarized in Figure 4.

Classification of the Particle Shape by the Shape Classification Table.
e size of a soil particle could be given by 3dimensional as the shape of particle is commonly nonspherical.e major (A), intermediate (B), and minor (C) axes of the particle are measured by a Vernier caliper, and each particle is classified by the shape classification table [31].e shape classification table classifies soil into 9 groups according to elongation ratio (�B/A) and flatness ratio (�C/ B). e shape classification table is plotted in Figure 5(a).e shapes of nonspherical soil are classified into 4 groups such as sphere, short rod, thick plate, and ellipsoid (Figure 5(b)).
e other shape groups such as plate, blade, and needle are an extreme case in natural soil particles.erefore, the soil particles used in this study represent almost all shapes of soil in nature.

Shape Properties Measured by Digital Image Processing.
e shape properties of nonspherical soil such as diameter (maximum, mean, and minimum), area, perimeter, roundness, and aspect ratio are measured by digital image processing.e statistic properties of shape properties are shown in Table 3.
e mean diameter of soil particles is 8.41 mm (max), 4.61 mm (average), 1.33 mm (min), and 1.57 mm (SD).e maximum diameter and minimum diameter are 5.92 mm (average) and 2.97 mm (average), respectively, and show similar distribution with mean diameter.e area of soil particles is 19.49mm 2 (average).e roundness is distributed between 0.6 and 1.0 mostly as shown in Figure 6(a).Sampled soil particles are classified to well-rounded particles.
e aspect ratio is 2.24 (average) and is distributed between 1.5 and 3.5 mostly as shown in Figure 6(b).It means that the shape of soil particles is elongated vertically.

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Variation of Settling Velocity through Particle Shape
Properties by DIP. Figure 7 shows relationship of settling velocity and particle mean diameter measured by the digital image processing method.Settling velocity of soil particle has a large variation even though the mean diameter of particles is similar to each other.e fastest settling particles are spherical shaped.is means that settling velocity of soil particles is affected by the particle shape, even when particles have the same mean diameter.e particles with mean diameter smaller than 6 mm have a significant variation of settling velocity through a difference in the particle shape.erefore, particle shape classification by the shape classification table well explains variation of settling velocity through a difference in the particle shape.But particle shape classification by the shape classification table has a poor applicability because it needs 3-dimensional size of every single particle.
As the settling velocity is related with particle diameter and shape, to analysis relationship between settling velocity and particle shape, the relationship between settling velocity and mean diameter of the particle should be excluded.For this reason, the residual of settling velocity versus mean   Advances in Civil Engineering diameter (Figure 8) is calculated with the regression curve of settling velocity and mean diameter.e residual is distributed independent of mean diameter and varies up to 54%, down to 43% even for the same mean diameter.
e correlation coefficient between shape factors and residual is shown in Figure 9. e aspect ratio has a high negative correlation with residual, and its correlation coefficient is -0.72.In common with the result using the shape classification table (Figure 7), settling velocity is affected by the particle shape in case of each particle having a same mean diameter.It means that the settling velocity can be explained with shape properties which acquired by a 2-dimensional digital image instead of using the 3-dimensional shape classification method.Especially, DIP has a higher applicability than the shape classification table because it can measure a number of particles at once.

Prediction Formula of Settling Velocity by DIP.
e settling velocity of soil particles is a function of diameter and aspect ratio.e prediction formula for settling velocity (1) is an empirical formula derived with multiple nonlinear regression by Microsoft Excel Solver.e form of the formula was determined in the simplest form by trial and error.e formula was developed for nonspherical soil particles with an average particle size range of 1.33 mm to 8.41 mm: where V is the settling velocity (cm/sec), D mean is the mean diameter (mm), and D min /D max is the inverse of aspect ratio.e coefficient of determination (R 2 ) is 0.82 (Figure 10). is function has a high applicability because it needs only two parameters (mean diameter and aspect ratio) derived from DIP.
To verify the prediction function for settling velocity, 106 soil particles are sampled.Compared with other researches [1,6,15,18], the prediction formula of settling velocity by DIP is much simpler and has a higher accuracy (Figure 11).

Conclusions
In this study, the digital image processing method has been used as an alternative measure to predict settling velocity of soil particles.e following conclusions were obtained.e shapes of nonspherical soil are classified into 4 groups such as sphere, short rod, thick plate, and ellipsoid.Measurement method of soil shape properties and settling velocity by digital image processing is evaluated as a simple, faster alternative rather than using the shape classification table.e settling velocity of the soil particle has a large variation even though the mean diameter of particles is similar to each other.In case particles have a same mean diameter, sphere shape particles have higher settling velocity than that of other shape particles.
e particles than 6 mm have a significant variation of settling velocity through a difference in the particle shape.
e settling velocity is affected by mean diameter and aspect ratio measured by digital image processing.

Table 2 :
Description of shape properties of soil particles.the major axis and the minor axis of the ellipse equivalent to the particle Major axis e length of the main axis of the ellipse equivalent to the particle Minor axis e length of the minor axis of the ellipse equivalent to the particle Maximum diameter e length of the longest line joining two outline points and passing through the centroid Minimum diameter e length of the shortest line joining two outline points and passing through the centroid Mean diameter e average length of the diameters measured at two degree intervals joining two outline points and passing through the centroid Maximum radius e maximum distance between particle's centroid pixel position and its perimeter Minimum radius e minimum distance between particle's centroid pixel position and its perimeter Perimeter e length of particle's outline Radius ratio e ratio between maximum radius and minimum radius for each particle, as determined by maximum radius/minimum radius Roundness e roundness of each particle, as determined by (4 * pi * area)/(perimeter 2 ) Fractal dimension e fractal dimension of the particle's outline

Figure 3 :Figure 4 :
Figure 3: Procedure of acquisition of shape properties.

Figure 7 :
Figure 7: Settling velocity of nonspherical soil classified with the shape classification table.

Figure 8 :
Figure 8: Residual of settling velocity versus mean diameter.

Figure 9 :
Figure 9: Correlation coefficients between shape factors and residuals of settling velocity.

Figure 11 :
Figure 11: Comparison of prediction formula by DIP (this study) and other research studies.

Table 1 :
Physical properties of nonspherical soils considered in this study.Sample for formulation of the settling velocity equation using digital image processing; * * sample for verification of the settling velocity equation using digital image processing; a Unified Soil Classification System.

Table 3 :
Statistic properties of shape properties.