predictionofsettlingvelocityofnonsphericalsoilparticles ...2018/08/29 · 4.conclusions...

Research ArticlePrediction of Settling Velocity of Nonspherical Soil ParticlesUsing Digital Image Processing

Donggeun Kim 1 Younghwan Son 2 and Jaesung Park3

1Department of Rural Systems Engineering Seoul National University Seoul KS013 Republic of Korea2Department of Rural Systems Engineering Research Institute for Agriculture and Life Sciences Seoul National UniversitySeoul KS013 Republic of Korea3Department of Bioresource Engineering McGill University Ste-Anne-de-Bellevue QC Canada H9X 3V9

Correspondence should be addressed to Younghwan Son syh86snuackr

Received 29 August 2018 Accepted 6 November 2018 Published 9 December 2018

Academic Editor Giuseppe Oliveto

Copyright copy 2018DonggeunKim et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Digital image processing (DIP) is used to measure shape properties and settling velocity of soil particles Particles with diametersof 1 to 10mm are arbitrarily sampled for the test e size of each particle is also measured by a Vernier caliper for comparisonwith the classification results using the shape classification table e digital images were taken with a digital camera (Canon EOS100d) Shape properties are calculated by image analysis software Settling velocity of soil particles is calculated by displacementand time difference of images during settling e fastest settling particles are spherical shaped Shape factors well explain thedifference of settling velocity by a particle shape In particular the aspect ratio has a high negative correlation with residual ofsettling velocity versus mean diameter Especially DIP has a higher applicability than classification using the shape classificationtable because it can measure a number of particles at once e settling velocity of soil particles is expressed as a function of meandiameter and aspect ratio

1 Introduction

e settling velocity of sediment particles is one of the keyvariables in the study of sediment transport and is importantin understanding suspension deposition mixing and ex-change processes It is affected by the size density shape ofsediment particles and physical properties of fluid [1]

e aim of many researches on the study of the settlingvelocity is to make precise general formula for prediction ofsettling velocity [1ndash6]e shape of sediment particles can bedivided into ideal spherical and nonspherical e settlingvelocity of spherical particles can be predicted to be morethan 98 accurate [7] Recent studies on the settling velocityof spherical particles have been an underway to investigatetheir acceleration motions analytically [8] especially theeffects of initial velocity on spherical particle acceleration ina fluid [9 10]

A sphere with the nominal diameter of a nonsphericalgrain 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 particlesresearchers propose a shape index to explain the effect of theparticle shape on settling velocity [11ndash20] e shape indexof the particle is a coefficient representing various shapeproperties of the particle such as circularity sphericityroundness and flatness ese shape indexes are calculatedby major intermediate and minor axes to consider a 3-dimensional shape of particles Most of the shape indexeswell represent the difference in settling velocity according tothe particle shape but they have a poor applicability becausethe measurement of the 3-dimensional particle shape isinconvenient

A digital image processing (DIP) can be a proper al-ternative method for particle shape measuring e DIP isa method to perform specific operations on digital imagesto extract information in digital images by computeralgorithms e DIP has been widely used to measure

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 4647675 8 pageshttpsdoiorg10115520184647675

displacement and shape of particles in geotechnical engi-neering by many researchers [21ndash30]

e objective of this paper was to measure particle shapeand settling velocity of nonspherical soil by DIP and developthe empirical prediction formula of settling velocity con-sidering the particle shape and diameter To compare withthe classification result using the shape classification tablethe particle shape is measured by a Vernier caliper and DIPmethod e settling velocity equation uses shape propertiesmeasured by the DIP method instead of 3-dimensionalshape indexes for high applicability

2 Materials and Methods

21 Materials and Experimental Procedure Two differentnonspherical soils were used in this study One is used forformulation of the settling velocity equation using the digitalimage processing method and the other is used for verifi-cation of the settling velocity equation e nonsphericalsoils were classified as SW by the Unified Soil ClassificationSystem Physical properties of nonspherical soils are sum-marized in Table 1

In this study digital image processing is adopted tomeasure the particle shape properties and the settling ve-locities of particles Particles with diameters of 1 to 10mmare arbitrarily sampled in sample A and B 343 particles aresampled in sample A and 106 particles in sample B e sizeof each particle is also measured by a Vernier caliper forcomparison with the classification result using the shapeclassification table e experimental procedure is shown inFigure 1

22 Digital Image Acquisition It is important to take aproper digital image of target in digital image processinge quality of the digital image is influenced by the shootingcondition e apparatus for acquisition of the digital imageto get shape properties of soil is shown in Figure 2(a) edigital images were taken with a digital camera (Canon EOS100d) To separate soil from image background properly ablack background plate is used e digital camera is in-stalled in the vertical direction of the background plate Twoled lights are used to illuminate uniformly for shooting

e apparatus for acquisition of the digital image to getsettling velocity of soil is shown in Figure 2(b) e di-mension of the settling tank is 300mm (width) times 80mm(length) times 1000mm (height) A soil particle is settled downunder the surface of water by pincette to minimize the effectof surface tension e digital camera is installed in thehorizontal direction of the settling tank To acquire digitalimages of settling soil particle shoot high definition video at25 frames per second and divide video by frame

23 Digital Image Processing An image analysis software(Media Cybernetics Image Pro Plus Version 60) is used todetermine shape properties of soil particles such as diameterarea perimeter roundness and aspect ratio Description ofshape properties of soil particles is summarized in Table 2

e resolution of the digital image is 0077mmpixelProcedure of acquisition of soil shape properties is sum-marized in Figure 3

To determine settling velocity of soil the R-pro-gramming language is used to analyze the digital image setAn original image is cropped in order to remove un-necessary parts for DIP e procedure of calculation ofsettling velocity by DIP is as follows First select a digitalimage set of the settling particle e digital image set hasN frames of the digital image Second perform binar-ization to segmentation of target (soil particle) andbackground After binarization the soil particle in thedigital image is converted to a set of white pixels Todetermine the position of the soil particle in each imagecalculate centroid of white pixels in each image edisplacement is the difference of the position of the soilparticle in two consecutive images and the time differenceis 125 second because the original image is taken 25frames per second Finally settling velocity is calculated bydividing the displacement into time difference e pro-cedure of acquisition of settling velocity is summarized inFigure 4

3 Results and Discussion

31 Classification of the Particle Shape by the Shape Classi-fication Table e size of a soil particle could be given by 3-dimensional as the shape of particle is commonly non-spherical e major (A) intermediate (B) and minor (C)axes of the particle are measured by a Vernier caliper andeach particle is classified by the shape classification table[31]e shape classification table classifies soil into 9 groupsaccording to elongation ratio (BA) and flatness ratio (CB)e shape classification table is plotted in Figure 5(a)eshapes of nonspherical soil are classified into 4 groups suchas sphere short rod thick plate and ellipsoid (Figure 5(b))e other shape groups such as plate blade and needle arean extreme case in natural soil particles erefore the soilparticles used in this study represent almost all shapes of soilin nature

32 Shape Properties Measured by Digital Image Processinge shape properties of nonspherical soil such as diameter(maximum mean and minimum) area perimeterroundness and aspect ratio are measured by digital imageprocessing e statistic properties of shape properties areshown in Table 3

e mean diameter of soil particles is 841mm (max)461mm (average) 133mm (min) and 157mm (SD) emaximum diameter and minimum diameter are 592mm(average) and 297mm (average) respectively and showsimilar distribution with mean diameter e area of soilparticles is 1949mm2 (average) e roundness is distrib-uted between 06 and 10 mostly as shown in Figure 6(a)Sampled soil particles are classified to well-rounded parti-cles e aspect ratio is 224 (average) and is distributedbetween 15 and 35 mostly as shown in Figure 6(b) It meansthat the shape of soil particles is elongated vertically

2 Advances in Civil Engineering

33 Variation of Settling Velocity through Particle ShapeProperties by DIP Figure 7 shows relationship of settlingvelocity and particle mean diameter measured by the digitalimage processing method Settling velocity of soil particle

has a large variation even though the mean diameter ofparticles is similar to each other e fastest settling particlesare spherical shaped is means that settling velocity of soilparticles is affected by the particle shape even when particleshave the same mean diameter e particles with meandiameter smaller than 6mm have a significant variation ofsettling velocity through a difference in the particle shapeerefore particle shape classification by the shape classi-fication table well explains variation of settling velocitythrough a difference in the particle shape But particle shapeclassification by the shape classification table has a poorapplicability because it needs 3-dimensional size of everysingle particle

As the settling velocity is related with particle diameterand shape to analysis relationship between settling velocityand particle shape the relationship between settling velocityand mean diameter of the particle should be excluded Forthis reason the residual of settling velocity versus mean

Table 1 Physical properties of nonspherical soils considered in this study

Sample Specific gravity Liquid limit () Plasticity index ()Passing sieve

USCSa475mm () 0075mm ()

Alowast 260 Nonplastic Nonplastic 7958 958 SWBlowastlowast 267 Nonplastic Nonplastic 9500 1566 SWlowastSample for formulation of the settling velocity equation using digital image processing lowastlowastsample for verification of the settling velocity equation using digitalimage processing aUnified Soil Classification System

Sampling

Size measuringby digital image processing

Size measuringby vernier calipers

Calculate shape factor

Settling

Determine trajectory and settling velocityby digital image processing

Figure 1 Experimental procedure

LED light

Digital camera

Sample

(a)

Digitalcamera

Settlingtank

(b)

Figure 2 Apparatus for the acquisition of the digital image(a) measuring shape properties (b) measuring settling velocity

Table 2 Description of shape properties of soil particles

Shape properties DescriptionArea e area of the particle

Aspecte ratio between the major axis and theminor axis of the ellipse equivalent to the

particle

Major axis e length of the main axis of the ellipseequivalent to the particle

Minor axis e length of the minor axis of the ellipseequivalent to the particle

Maximumdiameter

e length of the longest line joining twooutline points and passing through the

centroid

Minimumdiameter

e length of the shortest line joining twooutline points and passing through the

centroid

Mean diametere average length of the diameters measuredat two degree intervals joining two outlinepoints and passing through the centroid

Maximum radius e maximum distance between particlersquoscentroid pixel position and its perimeter

Minimum radius e minimum distance between particlersquoscentroid pixel position and its perimeter

Perimeter e length of particlersquos outline

Radius ratio

e ratio between maximum radius andminimum radius for each particle as

determined by maximum radiusminimumradius

Roundness e roundness of each particle as determinedby (4lowast pilowast area)(perimeter2)

Fractaldimension e fractal dimension of the particlersquos outline

Advances in Civil Engineering 3

diameter (Figure 8) is calculated with the regression curve ofsettling velocity and mean diameter e residual is dis-tributed independent of mean diameter and varies up to54 down to 43 even for the same mean diameter

e correlation coefficient between shape factors andresidual is shown in Figure 9 e aspect ratio has a highnegative correlation with residual and its correlation co-efficient is ndash072 In common with the result using the shapeclassification table (Figure 7) settling velocity is affected bythe particle shape in case of each particle having a samemean diameter It means that the settling velocity can beexplained with shape properties which acquired by a 2-di-mensional digital image instead of using the 3-dimensionalshape classification method Especially DIP has a higherapplicability than the shape classification table because it canmeasure a number of particles at once

34 Prediction Formula of Settling Velocity by DIP esettling velocity of soil particles is a function of diameter and

aspect ratioe prediction formula for settling velocity (1) isan empirical formula derived with multiple nonlinear re-gression by Microsoft Excel Solver e form of the formulawas determined in the simplest form by trial and error eformula was developed for nonspherical soil particles withan average particle size range of 133mm to 841mm

V 145

DmeanDmin

Dmax1113888 1113889

1113971

(1)

where V is the settling velocity (cmsec) Dmean is the meandiameter (mm) and DminDmax is the inverse of aspect ratio

e coefficient of determination (R2) is 082 (Figure 10)is function has a high applicability because it needs onlytwo parameters (mean diameter and aspect ratio) derivedfrom DIP

To verify the prediction function for settling velocity 106soil particles are sampled Compared with other researches[1 6 15 18] the prediction formula of settling velocity byDIP is much simpler and has a higher accuracy (Figure 11)

Particles

Camera

Digital image Preparation of camera and particles Shape properties

Diameter Area

Roundness Aspect ratio

Perimeter

Dmax

Dmin

4πA

P2

Figure 3 Procedure of acquisition of shape properties

Camera

Particle

Settling

Settling tank

Perform binarization

Select ith image

Calculate center of particle

Start

i = 1

i = N

i = i + 1

NoYes

Calculate settling velocity

End

Settling of particle

Video (25fps)

Digital image set

Divide videoby frame

Number of frames= N

Get digital image Calculation of settling velocity by DIP

Figure 4 Procedure of acquisition of settling velocity


Table 3 Statistic properties of shape properties

Maximum Average Minimum Standard deviationMaximum diameter (mm) 1179 592 160 203Minimum diameter (mm) 749 297 080 136Mean diameter (mm) 841 461 133 157Area (mm2) 5852 1949 157 1286Perimeter (mm) 3708 1722 443 618Roundness 090 072 020 013Aspect ratio 470 223 118 067

Roundness02 03 04 05 06 07 08 09

0

20

40

60

80

Freq

uenc

y

(a)

Aspect ratio10 15 20 25 30 35 40 45

0

10

20

30

40

50

60

Freq

uenc

y

(b)

Figure 6 Histogram of shape properties of nonspherical soil (a) roundness (b) aspect ratio

Flatness ratio (CB)00 02 04 06 08 10

00

02

04

Elon

gatio

n ra

tio (B

A)

06

08

10

Plate Thick plate Sphere

Elliptical plate Ellipsoid Short rod

Blade Thick blade Needle

(a)


Elon

gatio

n ra

tio (B

A)

00

02

04

06

08

10

SphereShort rod

Thick plateEllipsoid

(b)

Figure 5 Shape classification table and classification result of nonspherical soil (a) shape classification table [31] (b) shape of nonsphericalsoil


4 Conclusions

In this study the digital image processing method has beenused as an alternative measure to predict settling velocity ofsoil particles e following conclusions were obtainedeshapes of nonspherical soil are classified into 4 groups suchas sphere short rod thick plate and ellipsoid Measure-ment method of soil shape properties and settling velocityby digital image processing is evaluated as a simple fasteralternative rather than using the shape classification tablee settling velocity of the soil particle has a large variationeven though the mean diameter of particles is similar toeach other In case particles have a same mean diameter

sphere shape particles have higher settling velocity thanthat of other shape particles e particles smaller than6mm have a significant variation of settling velocitythrough a difference in the particle shape e settlingvelocity is affected by mean diameter and aspect ratiomeasured by digital image processing e predictionformula for settling velocity is derived with multiplenonlinear regression and it is simple and accurate com-pared to results of previous researches

Mean diameter (mm)0 2 4 6 8 10

0

10

20

30

40

Settl

ing

velo

city

(cm

sec

) Furguson amp church 2004 [15] (Sand)

Gibbs

1971

[1] (

Glass s

pher

e)

Zhiyao et al 2008 [6]

(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod

Figure 7 Settling velocity of nonspherical soil classified with theshape classification table


ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)

Figure 8 Residual of settling velocity versus mean diameter

Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t

1 Area2 Aspect ratio3 Major axis4 Minor axis5 Maximum diameter6 Minimum diameter

7 Maximum radius8 Minimum radius9 Perimeter10 Radius ratio11 Roundness12 Fractal dimension

Figure 9 Correlation coefficients between shape factors and re-siduals of settling velocity

Observed settling velocity (cms)0 10 20 30 40

0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)

Figure 10 Comparison of observedpredicted settling velocity


Data Availability

e data used to support the findings of this study are in-cluded within the article

Disclosure

is manuscript is based on a part of the first authorrsquosmasterrsquos thesis from Seoul National University [32]

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by the Bio-Industry TechnologyDevelopment Program (no 114147ndash3) Ministry for FoodAgriculture Forestry and Fisheries Republic of Korea and by aNational Research Foundation of Korea (NRF) grant funded bythe Korea government (MEST no 2014R1A2A1A11051680)

References

[1] R J Gibbs M D Matthews and D A Link ldquoe relationshipbetween sphere size and settling velocityrdquo Journal of Sedi-mentary Research vol 41 no 1 pp 7ndash18 1971

[2] J P Ahrens ldquoA fall-velocity equationrdquo Journal of WaterwayPort Coastal and Ocean Engineering vol 126 no 2 pp 99ndash102 2000

[3] N-S Cheng ldquoSimplified settling velocity formula for sedi-ment particlerdquo Journal of Hydraulic Engineering vol 123no 2 pp 149ndash152 1997

[4] E J Farrell and D J Sherman ldquoA new relationship betweengrain size and fall (settling) velocity in airrdquo Progress inPhysical Geography vol 39 no 3 pp 361ndash387 2015

[5] W Wu and S S Wang ldquoFormulas for sediment porosity andsettling velocityrdquo Journal of Hydraulic Engineering vol 132no 8 pp 858ndash862 2006

[6] S Zhiyao W Tingting X Fumin and L Ruijie ldquoA simpleformula for predicting settling velocity of sediment particlesrdquoWater Science and Engineering vol 1 no 1 pp 37ndash43 2008

[7] J Le Roux ldquoSettling velocity of spheres a new approachrdquoSedimentary Geology vol 81 no 1-2 pp 11ndash16 1992

[8] M Jalaal D Ganji and G Ahmadi ldquoAnalytical investigationon acceleration motion of a vertically falling spherical particlein incompressible Newtonian mediardquo Advanced PowderTechnology vol 21 no 3 pp 298ndash304 2010

[9] J Guo ldquoMotion of spheres falling through fluidsrdquo Journal ofHydraulic Research vol 49 no 1 pp 32ndash41 2011

[10] Z G Yin Z L Wang B C Liang and L Zhang ldquoInitialvelocity effect on acceleration fall of a spherical particlethrough still fluidrdquo Mathematical Problems in Engineeringvol 2017 Article ID 9795286 8 pages 2017

[11] J Le Roux ldquoSettling velocity of ellipsoidal grains as related toshape entropyrdquo Sedimentary Geology vol 101 no 1pp 15ndash20 1996

[12] J Baba and P D Komar ldquoMeasurements and analysis ofsettling velocities of natural quartz sand grainsrdquo Journal ofSedimentary Research vol 51 no 2 pp 631ndash640 1981

[13] B Camenen ldquoSimple and general formula for the settlingvelocity of particlesrdquo Journal of Hydraulic Engineeringvol 133 no 2 pp 229ndash233 2007

[14] W E Dietrich ldquoSettling velocity of natural particlesrdquo WaterResources Research vol 18 no 6 pp 1615ndash1626 1982

[15] R Ferguson and M Church ldquoA simple universal equation forgrain settling velocityrdquo Journal of Sedimentary Researchvol 74 no 6 pp 933ndash937 2004

[16] N Janke ldquoEmpirical formula for velocities and Reynoldsrsquonumbers of single settling spheres NOTESrdquo Journal ofSedimentary Research vol 35 no 3 pp 749-750 1965

[17] S Joshi G P Duffy and C Brown ldquoSettling velocity andgrain shape of maerl biogenic gravelrdquo Journal of SedimentaryResearch vol 84 no 8 pp 718ndash727 2014

[18] W W Rubey ldquoSettling velocities of gravel sand and siltparticlesrdquo American Journal of Science vol 25 no 148pp 325ndash338 1933

[19] H Wadell ldquoVolume shape and roundness of rock particlesrdquoJournal of Geology vol 40 no 5 pp 443ndash451 1932

[20] H Wadell ldquoSphericity and roundness of rock particlesrdquoJournal of Geology vol 41 no 3 pp 310ndash331 1933

[21] Y W Choo J-H Kim H-I Park and D-S Kim ldquoDevel-opment of a new asymmetric anchor plate for prefabricatedvertical drain installation via centrifuge model testsrdquo Journalof Geotechnical and Geoenvironmental Engineering vol 139no 6 pp 987ndash992 2012

[22] J M R Fernlund ldquoe effect of particle form on sieveanalysis a test by image analysisrdquo Engineering Geologyvol 50 no 1-2 pp 111ndash124 1998

[23] Y Higo C-W Lee T Doi et al ldquoStudy of dynamic stability ofunsaturated embankments with different water contents bycentrifugal model testsrdquo Soils and Foundations vol 55 no 1pp 112ndash126 2015

[24] S Lam S Haigh and M Bolton ldquoUnderstanding grounddeformation mechanisms for multi-propped excavation insoft clayrdquo Soils and Foundations vol 54 no 3 pp 296ndash3122014

Observed settling velocity (cms)0 20 40 60

0

20

40

60

This studyRubey 1933 [16]Gibbs 1971 [1]

Furgerson amp Church 2004 [15]Zhiyao et al 2008 [6]

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)

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


[25] C Mora A Kwan and H Chan ldquoParticle size distributionanalysis of coarse aggregate using digital image processingrdquoCement and Concrete Research vol 28 no 6 pp 921ndash9321998

[26] A-L Persson ldquoImage analysis of shape and size of fine ag-gregatesrdquo Engineering Geology vol 50 no 1-2 pp 177ndash1861998

[27] H Takahashi S Sassa Y Morikawa D Takano andK Maruyama ldquoStability of caisson-type breakwater founda-tion under tsunami-induced seepagerdquo Soils and Foundationsvol 54 no 4 pp 789ndash805 2014

[28] J Yoneda M Hyodo N Yoshimoto Y Nakata and A KatoldquoDevelopment of high-pressure low-temperature plane straintesting apparatus for methane hydrate-bearing sandrdquo Soilsand Foundations vol 53 no 5 pp 774ndash783 2013

[29] N Yoshimoto M Hyodo Y Nakata R P Orense T Hongoand A Ohnaka ldquoEvaluation of shear strength and mechanicalproperties of granulated coal ash based on single particlestrengthrdquo Soils and Foundations vol 52 no 2 pp 321ndash3342012

[30] G Zhang R Wang J Qian J-M Zhang and J Qian ldquoEffectstudy of cracks on behavior of soil slope under rainfallconditionsrdquo Soils and Foundations vol 52 no 4 pp 634ndash6432012

[31] I K Lee W White and O G Ingles Geotechnical Engi-neering Pitmans Books Limited London UK 1983

[32] D Kim Analysis of Settling Characteristic of Landfill Soil usingDigital Image Processing Seoul National University SeoulSouth Korea 2016


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Submit your manuscripts atwwwhindawicom

displacement and shape of particles in geotechnical engi-neering by many researchers [21ndash30]

e objective of this paper was to measure particle shapeand settling velocity of nonspherical soil by DIP and developthe empirical prediction formula of settling velocity con-sidering the particle shape and diameter To compare withthe classification result using the shape classification tablethe particle shape is measured by a Vernier caliper and DIPmethod e settling velocity equation uses shape propertiesmeasured by the DIP method instead of 3-dimensionalshape indexes for high applicability

2 Materials and Methods

21 Materials and Experimental Procedure Two differentnonspherical soils were used in this study One is used forformulation of the settling velocity equation using the digitalimage processing method and the other is used for verifi-cation of the settling velocity equation e nonsphericalsoils were classified as SW by the Unified Soil ClassificationSystem Physical properties of nonspherical soils are sum-marized in Table 1

In this study digital image processing is adopted tomeasure the particle shape properties and the settling ve-locities of particles Particles with diameters of 1 to 10mmare arbitrarily sampled in sample A and B 343 particles aresampled in sample A and 106 particles in sample B e sizeof each particle is also measured by a Vernier caliper forcomparison with the classification result using the shapeclassification table e experimental procedure is shown inFigure 1

22 Digital Image Acquisition It is important to take aproper digital image of target in digital image processinge quality of the digital image is influenced by the shootingcondition e apparatus for acquisition of the digital imageto get shape properties of soil is shown in Figure 2(a) edigital images were taken with a digital camera (Canon EOS100d) To separate soil from image background properly ablack background plate is used e digital camera is in-stalled in the vertical direction of the background plate Twoled lights are used to illuminate uniformly for shooting

e apparatus for acquisition of the digital image to getsettling velocity of soil is shown in Figure 2(b) e di-mension of the settling tank is 300mm (width) times 80mm(length) times 1000mm (height) A soil particle is settled downunder the surface of water by pincette to minimize the effectof surface tension e digital camera is installed in thehorizontal direction of the settling tank To acquire digitalimages of settling soil particle shoot high definition video at25 frames per second and divide video by frame

23 Digital Image Processing An image analysis software(Media Cybernetics Image Pro Plus Version 60) is used todetermine shape properties of soil particles such as diameterarea perimeter roundness and aspect ratio Description ofshape properties of soil particles is summarized in Table 2

e resolution of the digital image is 0077mmpixelProcedure of acquisition of soil shape properties is sum-marized in Figure 3

To determine settling velocity of soil the R-pro-gramming language is used to analyze the digital image setAn original image is cropped in order to remove un-necessary parts for DIP e procedure of calculation ofsettling velocity by DIP is as follows First select a digitalimage set of the settling particle e digital image set hasN frames of the digital image Second perform binar-ization to segmentation of target (soil particle) andbackground After binarization the soil particle in thedigital image is converted to a set of white pixels Todetermine the position of the soil particle in each imagecalculate centroid of white pixels in each image edisplacement is the difference of the position of the soilparticle in two consecutive images and the time differenceis 125 second because the original image is taken 25frames per second Finally settling velocity is calculated bydividing the displacement into time difference e pro-cedure of acquisition of settling velocity is summarized inFigure 4

3 Results and Discussion

31 Classification of the Particle Shape by the Shape Classi-fication Table e size of a soil particle could be given by 3-dimensional as the shape of particle is commonly non-spherical e major (A) intermediate (B) and minor (C)axes of the particle are measured by a Vernier caliper andeach particle is classified by the shape classification table[31]e shape classification table classifies soil into 9 groupsaccording to elongation ratio (BA) and flatness ratio (CB)e shape classification table is plotted in Figure 5(a)eshapes of nonspherical soil are classified into 4 groups suchas sphere short rod thick plate and ellipsoid (Figure 5(b))e other shape groups such as plate blade and needle arean extreme case in natural soil particles erefore the soilparticles used in this study represent almost all shapes of soilin nature

32 Shape Properties Measured by Digital Image Processinge shape properties of nonspherical soil such as diameter(maximum mean and minimum) area perimeterroundness and aspect ratio are measured by digital imageprocessing e statistic properties of shape properties areshown in Table 3

e mean diameter of soil particles is 841mm (max)461mm (average) 133mm (min) and 157mm (SD) emaximum diameter and minimum diameter are 592mm(average) and 297mm (average) respectively and showsimilar distribution with mean diameter e area of soilparticles is 1949mm2 (average) e roundness is distrib-uted between 06 and 10 mostly as shown in Figure 6(a)Sampled soil particles are classified to well-rounded parti-cles e aspect ratio is 224 (average) and is distributedbetween 15 and 35 mostly as shown in Figure 6(b) It meansthat the shape of soil particles is elongated vertically







USCSa475mm () 0075mm ()


Sampling




Settling



LED light

Digital camera

Sample

(a)

Digitalcamera

Settlingtank

(b)





particle



Maximumdiameter


centroid

Minimumdiameter


centroid





Radius ratio










V 145

DmeanDmin

Dmax1113888 1113889

1113971

(1)




Particles

Camera


Diameter Area


Perimeter

Dmax

Dmin

4πA

P2


Camera

Particle

Settling

Settling tank


Select ith image


Start

i = 1

i = N

i = i + 1

NoYes


End


Video (25fps)

Digital image set


Number of frames= N






Roundness02 03 04 05 06 07 08 09

0

20

40

60

80

Freq

uenc

y

(a)

Aspect ratio10 15 20 25 30 35 40 45

0

10

20

30

40

50

60

Freq

uenc

y

(b)



00

02

04

Elon

gatio

n ra

tio (B

A)

06

08

10




(a)


Elon

gatio

n ra

tio (B

A)

00

02

04

06

08

10

SphereShort rod


(b)



4 Conclusions




0

10

20

30

40

Settl

ing

velo

city

(cm

sec


Gibbs

1971

[1] (

Glass s

pher

e)


(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod



ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)


Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t





0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)



Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







USCSa475mm () 0075mm ()


Sampling




Settling



LED light

Digital camera

Sample

(a)

Digitalcamera

Settlingtank

(b)





particle



Maximumdiameter


centroid

Minimumdiameter


centroid





Radius ratio










V 145

DmeanDmin

Dmax1113888 1113889

1113971

(1)




Particles

Camera


Diameter Area


Perimeter

Dmax

Dmin

4πA

P2


Camera

Particle

Settling

Settling tank


Select ith image


Start

i = 1

i = N

i = i + 1

NoYes


End


Video (25fps)

Digital image set


Number of frames= N






Roundness02 03 04 05 06 07 08 09

0

20

40

60

80

Freq

uenc

y

(a)

Aspect ratio10 15 20 25 30 35 40 45

0

10

20

30

40

50

60

Freq

uenc

y

(b)



00

02

04

Elon

gatio

n ra

tio (B

A)

06

08

10




(a)


Elon

gatio

n ra

tio (B

A)

00

02

04

06

08

10

SphereShort rod


(b)



4 Conclusions




0

10

20

30

40

Settl

ing

velo

city

(cm

sec


Gibbs

1971

[1] (

Glass s

pher

e)


(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod



ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)


Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t





0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)



Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






V 145

DmeanDmin

Dmax1113888 1113889

1113971

(1)




Particles

Camera


Diameter Area


Perimeter

Dmax

Dmin

4πA

P2


Camera

Particle

Settling

Settling tank


Select ith image


Start

i = 1

i = N

i = i + 1

NoYes


End


Video (25fps)

Digital image set


Number of frames= N






Roundness02 03 04 05 06 07 08 09

0

20

40

60

80

Freq

uenc

y

(a)

Aspect ratio10 15 20 25 30 35 40 45

0

10

20

30

40

50

60

Freq

uenc

y

(b)



00

02

04

Elon

gatio

n ra

tio (B

A)

06

08

10




(a)


Elon

gatio

n ra

tio (B

A)

00

02

04

06

08

10

SphereShort rod


(b)



4 Conclusions




0

10

20

30

40

Settl

ing

velo

city

(cm

sec


Gibbs

1971

[1] (

Glass s

pher

e)


(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod



ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)


Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t





0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)



Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Roundness02 03 04 05 06 07 08 09

0

20

40

60

80

Freq

uenc

y

(a)

Aspect ratio10 15 20 25 30 35 40 45

0

10

20

30

40

50

60

Freq

uenc

y

(b)



00

02

04

Elon

gatio

n ra

tio (B

A)

06

08

10




(a)


Elon

gatio

n ra

tio (B

A)

00

02

04

06

08

10

SphereShort rod


(b)



4 Conclusions




0

10

20

30

40

Settl

ing

velo

city

(cm

sec


Gibbs

1971

[1] (

Glass s

pher

e)


(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod



ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)


Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t





0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)



Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


4 Conclusions




0

10

20

30

40

Settl

ing

velo

city

(cm

sec


Gibbs

1971

[1] (

Glass s

pher

e)


(Natural sediment)

Rubey 1933 [18]

(Gravel sand)

ick plate Sphere

Ellipsoid Short rod



ndash15

ndash10

ndash5

0

5

10

15

Resid

ual o

f set

tling

velo

city

(cm

s)


Shape factor0 1 2 3 4 5 6 7 8 9 10 11 12 13

ndash08

ndash06

ndash04

ndash02

00

02

Corr

elat

ion

coeffi

cien

t





0

10

20

30

40

Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)



Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Data Availability


Disclosure




Acknowledgments


References


























0

20

40

60



Pred

icte

d se

ttlin

g ve

loci

ty (c

ms

)














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


predictionofsettlingvelocityofnonsphericalsoilparticles ...2018/08/29 · 4.conclusions...

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