Three Dimensional Digital Sieving of Asphalt Mixture Based on X-Ray Computed Tomography

applied sciences

Article Three Dimensional Digital Sieving of Asphalt Mixture Based on X-ray Computed Tomography

Chichun Hu 1,*, Jiexian Ma 1 ID and M. Emin Kutay 2 1 College of Civil and Transportation Engineering, South China University of Technology, Wushan Road, Guangzhou 510641, China; [email protected] 2 Department of Civil and Environmental Engineering, Michigan State University, 3554 Engineering Blvd., East Lansing, MI 48824, USA; [email protected] * Correspondence: [email protected]; Tel.: +86-20-8711-1030

Academic Editor: Feipeng Xiao Received: 30 June 2017; Accepted: 12 July 2017; Published: 18 July 2017

Abstract: In order to perform three-dimensional digital sieving based on X-ray computed tomography images, the definition of digital sieve size (DSS) was proposed, which was defined as the minimum length of the minimum bounding squares of all possible orthographic projections of an aggregate. The corresponding program was developed to reconstruct aggregate structure and to obtain DSS. Laboratory experiments consisting of epoxy-filled aggregate specimens were conducted to investigate the difference between mechanical sieve analysis and the digital sieving technique. It was suggested that concave surface of aggregate was the possible reason for the disparity between DSS and mechanical sieve size. A comparison between DSS and equivalent diameter was also performed. Moreover, the digital sieving technique was adopted to evaluate the gradation of stone mastic asphalt mixtures. The results showed that the closest proximity of the laboratory gradation curve was achieved by calibrated DSS, among gradation curves based on calibrated DSS, un-calibrated DSS and equivalent diameter.

Keywords: asphalt mixture; aggregate gradation; sieve analysis; image processing; X-ray computed tomography

1. Introduction Aggregate microstructure and gradation have great impacts on the performance of asphalt mixture, which also influences the pavement durability, stiffness, and fatigue behavior [1–3]. Traditionally, gradation is evaluated by passing the aggregates through a series of sieves. The sieve retains particles larger than the sieve opening, while smaller ones pass through. In practice, the non-uniform distribution of coarse and fine aggregate components within the asphalt mixture is called aggregate segregation [4,5]. The solvent extraction method or the ignition oven method is often used to measure segregation. However, these laborious and time-consuming tests involve a specially-equipped laboratory, as well as the use of solvents hazardous to workers’ health [6]. With the development of the digital image processing (DIP) technique, which has advantage of high efficiency, convenience, automation, and reducing manpower, many researchers have attempted to evaluate the gradation of asphalt mixture through the DIP technique. In early years, the research was toward two dimensional (2D) images of vertical or horizontal plane cross-sections that were cut from field cores or laboratory-prepared asphalt concrete (AC) specimens. Different parameters were used to describe the size of aggregate in order to obtain a size distribution. Yue et al. applied the DIP technique to quantify the distribution, orientation, and shape of coarse aggregates in AC mixtures [7]. Area gradations on different cross-sections were obtained based on the minor axis length, major axis length, and equivalent circular diameter.

Appl. Sci. 2017, 7, 734; doi:10.3390/app7070734 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 734 2 of 12

As the gradation estimated from a cross-section is dependent on the position at which the slice was taken, the average gradations of multiple sections were used to evaluate gradation. Masad et al. characterized the internal structure of AC in terms of aggregate gradation. The volume gradation based on the equivalent circular diameter was obtained from the analysis of 2D vertical sections [8]. In volume calculations, the thickness of the aggregate was taken as the average diameter measured in two dimensions. It was found that two specimens (six sections) was sufficient to satisfactorily capture the actual gradation of coarse aggregate. Bruno et al. estimated mixture gradation using the length of the minor axis of the ellipse that had the same normalized second central moments as the aggregate [6]. The average gradation curve obtained from 22 planar slices was compared with the laboratory gradation. One of the major problems with the two dimensional DIP technique is that only the area gradation is computed. Since volume gradation has a better correlation with traditional weight gradation, a stereological method was developed to acquire the volume gradation [9,10]. Guo et al. adopted the minor axis of the circumscribed ellipse of the aggregate to calculate the planar gradation of the mixture [10]. Then the planar area gradation was transformed to a three-dimensional volume gradation by the stereological method with the assumption of ellipsoidal particles. The results indicated that aspect ratio of the aggregate affected the stereological coefficients significantly. Although the X-ray computed tomography (CT) technique has been applied to the study of the internal structure of asphalt mixtures since 1999, it was not until 10 years ago that CT images began to be used in calculation of the three dimensional (3D) size and volume gradation. The improvement in image resolution and particle segmentation algorithms were the main reasons. Kutay et al. presented the filtered watershed transform method to overcome the problem of touching aggregates [11]. Gradations by equivalent diameter, major principal axis, minor principal axis, and average axial length were estimated from the CT images. The results showed that the closest match was achieved by the gradation based on the equivalent diameter. In other areas, Wang et al. developed an image segmentation method for multi-size particles and calculated dimensions along three principal axes, which was determined from the analysis of moments [12]. The gradation curves based on traditional sieve analysis, equivalent diameter, maximum dimension, intermediate dimension, and minimum dimension were compared. However, these techniques, based on indirect parameters, utilized only partial characteristics of aggregate shape to evaluate gradation, making them unable to exactly capture the real sieve opening that the aggregate passed through. In addition, there is a need to study the potential error brought by indirect parameter in describing particle size. The aim of this study is to develop 3D digital sieving technique used to evaluate the gradation of the asphalt mixture in X-ray CT images, which considers both the shape of aggregate particles and the square opening of the mechanical sieve. For this purpose, the definition of digital sieve size was proposed and the corresponding program was developed using Matlab™ (Natick, MA, USA) to obtain the digital sieve size. After that, laboratory experiments consisting of epoxy-filled aggregate specimens were conducted to calibrate the program. Moreover, the digital sieving technique was used to estimate the gradation of stone mastic asphalt mixtures.

2. X-ray Computed Tomography X-ray CT is a non-destructive technique that can be used to conduct 3D reconstruction of a sample and obtain information about its geometry. Compact-225 (YXLON, Hamburg, Germany) industrial CT equipment at the road material laboratory of South China University of Technology was used in this work (Figure1). X-rays from different directions were detected through detectors, processed by electronic components, and then saved in a computer. The X-ray intensities are measured before they enter the specimen and after they penetrate through it. The attenuation intensity depends on the overall linear attenuation properties of the penetrated material. The attenuation or intensity variation was identiﬁed as the contour information, which was processed to obtain the CT image for each layer. Appl. Sci. 2017, 7, 734 3 of 12

The CT image is the spatial distribution of the linear attenuation coefficients, and brighter regions Appl. Sci. 2017, 7, 734 3 of 12 indicate a higher value of the attenuation coefficient. Therefore, the differentiation of features within thedifferentiation specimen is of possible features because within thethe linearspecimen attenuation is possible coefficient because at the each linear point attenuation depends directlycoefficient on theat each density point of depends the specimen directly at thaton the point densit [13,y14 of]. the specimen at that point [13,14].

Figure 1. Industrial CT. Figure 1. Industrial CT.

The linear attenuation coefficient varies with the component and density of the material. CT is sensitiveThe linearfor characterizing attenuation coefﬁcientmaterials with varies different with the densities. component In anda typical density CT ofimage the material. of an asphalt CT is sensitivemixture, the for aggregate characterizing is the materialsbrightest, withfollowed different by the densities. asphalt mastic, In a typical and then CT the image air voids. of an asphaltThe CT mixture,slices can the beaggregate put together is the for brightest, 3D reconstruction. followed by Th theere asphalt are four mastic, parameters and then that the are air voids.critical The to CT slicesimage can quality: be put spatial together resolution, for 3D reconstruction. comparison resolution, There are fournoise, parameters and ring artifact that are [15]. critical to CT image quality: spatial resolution, comparison resolution, noise, and ring artifact [15]. 3. Three Dimensional Reconstruction of Aggregates 3. Three Dimensional Reconstruction of Aggregates After CT slices are obtained from industrial CT equipment, the traditional image threshold After CT slices are obtained from industrial CT equipment, the traditional image threshold method method can be used to separate the aggregates from the mastic and air voids. Based on the binary can be used to separate the aggregates from the mastic and air voids. Based on the binary image image of aggregates, connected components will be detected and labeled. However, in an asphalt of aggregates, connected components will be detected and labeled. However, in an asphalt mixture mixture where the aggregates are in close proximity to each other, multiple aggregates are often where the aggregates are in close proximity to each other, multiple aggregates are often incorrectly incorrectly considered and labeled as a single particle. In order to eliminate the problem of clustering considered and labeled as a single particle. In order to eliminate the problem of clustering of the of the aggregates, the digital image processing (DIP) method proposed by Kutay et al. [11] was aggregates, the digital image processing (DIP) method proposed by Kutay et al. [11] was adopted to adopted to separate aggregates in this paper. There were two parameters (standard deviation of the separate aggregates in this paper. There were two parameters (standard deviation of the Gaussian ﬁlter Gaussian filter and the height of the H-maxima transform) that needed careful selection in this and the height of the H-maxima transform) that needed careful selection in this segmentation method. segmentation method. Hence, a trial and error process was used to determine these parameters until Hence, a trial and error process was used to determine these parameters until the best separation was the best separation was achieved based on visual inspection. achieved based on visual inspection.

4. Three-Dimensional Digital Sieving In the laboratory, a gradation test is performed by mechanical size analysis. A representative In the laboratory, a gradation test is performed by mechanical size analysis. A representative sample of aggregates is poured into a column of sieves, which is typically placed in a mechanical sample of aggregates is poured into a column of sieves, which is typically placed in a mechanical sieve shaker. During the shaking process, the mechanical device would move the sieves to cause the sieve shaker. During the shaking process, the mechanical device would move the sieves to cause the particles to bounce, tumble, or otherwise turn so as to present different orientations to the sieving particles to bounce, tumble, or otherwise turn so as to present different orientations to the sieving surface [16]. As a result, aggregate larger than the sieve opening remains on the sieve, while the surface [16]. As a result, aggregate larger than the sieve opening remains on the sieve, while the smaller ones pass through. Due to numerous particles in the mixture, high-frequency interaction smaller ones pass through. Due to numerous particles in the mixture, high-frequency interaction between the sieve mesh and particles, and the very large computation consumption, it is impractical between the sieve mesh and particles, and the very large computation consumption, it is impractical to to simulate the laboratory sieve analysis based on the mechanical model. However, if the sieving simulate the laboratory sieve analysis based on the mechanical model. However, if the sieving process process is possible to be simplified as a mathematical problem, the digital gradation test could be is possible to be simpliﬁed as a mathematical problem, the digital gradation test could be solved by solved by numerical calculation. numerical calculation.

Appl. Sci. 2017, 7, 734 4 of 12

In order to simplify the problem, an assumption related to passage judgment of aggregate is made first. When an aggregate is right above a sieve opening, whether it can pass that sieve opening is assumed to be equivalent to whether its orthographic projection on the sieve plate can be surrounded by four sides of the square opening. Apparently, this could be determined by the length of the minimum bounding square (MBS) of the projection area. If the length of the MBS of the projection is smaller than the sieve size, the aggregate passes through. It should be noted that the MBS is obtained when the length of circumscribed square achieves the minimum value. Though the problem of particle passage judgment is solved, the displacement of aggregate during shaking is not considered. In the actual mechanical sieving process, the aggregate will experience rotation. Thus, orthographic projection in every direction might be the critical projection that determines the smallest sieve opening that aggregate passes through. In this paper, digital sieve size (DSS) is defined as the minimum length of the minimum bounding squares of all possible orthographic projections. Ideally, each aggregate has only one DSS because it corresponds to the smallest MBS. It could be thought as a virtual sieve opening that aggregate is just able to fit in. Hereinafter, whether an aggregate is able to pass through certain sieve opening is totally depend on the value of DSS of the aggregate. The numerical method used to obtain the DSS of an aggregate is described as follows:

1. Assume a local rectangular coordinate system x0y0z0, as shown in Figure2, where xyz is the global rectangular coordinate system of the voxel data of aggregate particle, (δ, θ) is used to describe the direction of z0 axis, δ is the angle between x axis and the projection of z0 axis on xy plane, and θ is the angle between the z0 axis and the xy plane. 2. Calculate Euler angles α, β, γ based on (δ, θ). Euler angles are used to describe the rotation of a coordinate system [17]. 3. Calculate the rotation matrix R through Euler angles α, β, γ, as shown in Equation (1). Perform coordinate conversion according to Equation (2). Hence, voxel data of the particle can be expressed in the local coordinate system x0y0z0 (see Figure3).

  cos β cos γ − cos β sin γ sin β   R =  sin α sin β cos γ + cos α sin γ − sin α sin β sin γ + cos α cos γ − sin α cos β , (1) − cos α sin β cos γ + sin α sin γ cos α sin β sin γ + sin α cos γ cos α cos β

    x0 x  0     y  = R y . (2) z0 z

4. Project voxel data to x0y0 plane (see Figure3). The three-dimensional problem is successfully converted into a two-dimensional problem. 5. Calculate the minimum bounding square for the aggregate projection (see Figure3). The process of ﬁnding the minimum bounding square is the same as the linear time algorithm for the minimum bounding rectangle [18]. First, the convex polygon of a particle projection area is solved using the Matlab function convhull. This is based on the observation that a side of a minimum enclosing box must be collinear with a side of the convex polygon [18]. After corner points of the convex polygon are obtained, two vertical calipers are rotated [19] around the aggregate projection until the minimum square is found. The length of the minimum square is recorded. 6. Assume another local rectangular coordinate system. Repeat Steps 1–5 until the minimum length is obtained, which is the DSS. Appl.Appl. Sci. Sci. 2017 2017, ,7 7, ,734 734 55 of of 12 12

Appl. Sci. 2017, 7, 734 5 of 12 Appl. Sci. 2017, 7, 734 5 of 12

Figure 2. Rotation of the rectangular coordinate system. FigureFigureFigure 2. 2. Rotation2.Rotation Rotation of of of the thethe rectangular rectangular coordinatecoordinate coordinate system. system. system.

(a)( b)(c) ((aa)()(bb)()(cc)) Figure 3. Illustration of 3D digital sieving of an aggregate: (a) voxel data in global coordinate; Figure(b ) 3.perform Illustration coordinate of 3Dconversion digital andsieving obtain of projection; an aggregate: (c) solve (a the) voxel minimum data bounding in global square. coordinate; FigureFigure 3. IllustrationIllustration of 3D3D digitaldigital sievingsieving ofof an an aggregate: aggregate: ( a()a voxel) voxel data data in in global global coordinate; coordinate; (b ) ((bb)) perform perform coordinate coordinate conversion conversion and and obtain obtain projection; projection; ( (cc)) solve solve the the minimum minimum bounding bounding square. square. performIt iscoordinate noted that, conversion in order to and improve obtain the projection; efficiency (c )of solve numerical the minimum method bounding used to calculate square. DSS, the voxel data of each aggregate is simplified to a point set of its convex hull using Matlab function ItIt isis notednoted that,that, inin orderorder toto improveimprove thethe efficienefficiencycy ofof numericalnumerical methodmethod usedused toto calculatecalculate DSS,DSS, Itconvhull is noted before that, the in above order mentioned to improve steps. the The efficiency possible oferror numerical of this simplification method used will tobe calculateexamined DSS, thethe voxelvoxel datadata ofof each each aggregateaggregate isis simplified simplified toto a a pointpoint setset ofof itsits convex convex hullhull usingusing MatlabMatlab function function the voxelin the data following of each section. aggregate The average is simplified calculation to atime point of DSS set offor its an convex aggregate hull with using 100,000 Matlab voxels function is convhullconvhull before before the the above above mentioned mentioned steps. steps. The The possible possible error error of of this this simplification simplification will will be be examined examined convhull1.4 s beforeon a 3.2 the GHz above single-core mentioned processor. steps. Since The the possible numerical error method of this is simplification based on heuristics will beonly, examined its inin the the following following section. section. The The average average calculation calculation time time of of DSS DSS for for an an aggregate aggregate with with 100,000 100,000 voxels voxels is is in therun following time can section.be further The improved average by calculation an iterative timeapproach of DSS [20]. for an aggregate with 100,000 voxels is 1.41.4 s s onon a a Two3.2 3.2 GHz GHzexamples single-coresingle-core of DSS are processor.processor. shown in Since SinceFigure thethe 4. numericalnumerical methodmethod is is basedbased onon heuristicsheuristics only,only, itsits 1.4 s on a 3.2 GHz single-core processor. Since the numerical method is based on heuristics only, its run runrun time time can can be be further further improved improved by by an an iterative iterative approach approach [20]. [20]. time can be further improved by an iterative approach [20]. TwoTwo examples examples of of DSS DSS are are shown shown in in Figure Figure 4. 4. Two examples of DSS are shown in Figure4.

(a) (b)

Figure 4. Examples of digital sieve size: (a) aggregate 1; (b) aggregate 2.

((aa)) ((bb))

Figure 4. Examples of digital sieve size: (a) aggregate 1; (b) aggregate 2. FigureFigure 4. 4. ExamplesExamples of of digital digital sieve sieve size: size: ( (aa)) aggregate aggregate 1; 1; ( (bb)) aggregate aggregate 2. 2. Appl. Sci. 2017, 7, 734 6 of 12

5. Calibration of Digital Sieving Technique Appl. Sci. 2017, 7, 734 6 of 12 As the shape of aggregate particles is quite complex and diverse, further investigation of the 5. Calibration of Digital Sieving Technique difference between mechanical sieve analysis and the digital sieving technique developed in this research is essential.As the shape In of order aggregate to accomplish particles is quite this, complex four groups and diverse, of epoxy-filled further investigation aggregate of specimensthe were prepareddifference using between aggregates mechanical retained sieve analysis on four and differentthe digital sieve sieving sizes technique (4.75 mm,developed 9.5 mm, in this 13.2 mm research is essential. In order to accomplish this, four groups of epoxy-filled aggregate specimens and 16 mm, respectively). The number and type of aggregates for different specimens are shown in were prepared using aggregates retained on four different sieve sizes (4.75 mm, 9.5 mm, 13.2 mm Table1.and The 16 specimen mm, respectively). dimension The was number 104 and± 1 type mm of in aggregates diameter, for and different the gaps specimens between are aggregatesshown in were filled usingTable epoxy1. The specimen resin (see dimension Figure 5was) which 104 ± 1 wouldmm in diameter, significantly and the enhance gaps between the contrastaggregates between were the aggregatesfilled and using background epoxy resin in(see the Figure X-ray 5) CTwhich images. would significantly enhance the contrast between the aggregates and background in the X-ray CT images. Table 1. The number and type of aggregates in specimens. Table 1. The number and type of aggregates in specimens.

GroupingGrouping Specimen Specimen 1 1 Specimen Specimen 2 2 Type Type Group 1Group (16~19 1 (16~19 mm) mm) 35 35 36 36 Limestone Limestone Group 2Group (13.2~16 2 (13.2~16 mm) mm) 73 73 80 80 Granite Granite Group 3Group (9.5~13.2 3 (9.5~13.2 mm) mm) 104 104 138 138 Granite Granite Group 4Group (4.75~9.5 4 (4.75~9.5 mm) mm) 211 211 - - Granite Granite

FigureFigure 5. 5.Epoxy-ﬁlled Epoxy-filled aggregate specimens. specimens.

After the voxel data of each aggregate was extracted from X-ray CT images of epoxy-filled After the voxel data of each aggregate was extracted from X-ray CT images of epoxy-ﬁlled aggregate specimens, the properties such as volume, equivalent diameter, and DSS were computed. aggregateThe specimens,following equations the properties were used such to calculate as volume, volume equivalent and equivalent diameter, diameter: and DSS were computed. The following equations were used to calculate volume and equivalent diameter: =, (3)

V = Nvoxelsdxdydz , (3) = 2( ), (4) 1 where V is the volume, ED is the equivalent diameter,3V Nvoxels3 is the number of voxels that the given ED = 2( ) , (4) aggregate is made of, and dx, dy and dz are the dimensions4π of one voxel (mm). Figure 6 shows the results of the DSS for four different groups. It can be seen that, in each where Vspecimen,is the volume, there wasED a certainis the equivalentpercent of aggregates diameter, whoseNvoxels DSSis was the larger number than ofthe voxels upper thatlimit theof given aggregatetheir is mechanical made of, andsize. dxThat, dy percentageand dz are (counted the dimensions by number) of ranged onevoxel from 5.69% (mm). to 31.43% in seven Figurespecimens,6 shows with the the maximum results of ratio the achieved DSS for by four Grou differentp 1, Specimen groups. 1. Additionally, It can bethose seen aggregates that, in each specimen,having there the waslargest a DSS certain in Group percent 2, Specimen of aggregates 2 and Group whose 3, both DSS specimens, was larger should than be noted the upperbecause limit of their mechanicaltheir DSS were size. over That the percentagemid-value of (countedtheir superior by sieve number) size range. ranged For frominstance, 5.69% the largest to 31.43% DSS in in seven Group 3, Specimen 1 was 14.8985 mm, and its superior sieve size range was 13.2~16 mm. As the specimens, with the maximum ratio achieved by Group 1, Specimen 1. Additionally, those aggregates smallest DSS in Group 3, Specimen 1 was quite close to the lower limit (9.5 mm), the above having thephenomenon largest DSS was innot Group caused 2,by Specimen the selection 2 andof the Group threshold 3, bothvalue specimens,in the segmentation should process be noted thatbecause their DSSmay were increase over the the dimension mid-value of aggregate of their data. superior It was also sieve observed size range. that there For were instance, overlaps the between largest DSS in Groupthe 3, DSS Specimen distribution 1 was ranges 14.8985 of three mm, different and groups its superior of granite. sieve size range was 13.2~16 mm. As the smallest DSS in Group 3, Specimen 1 was quite close to the lower limit (9.5 mm), the above phenomenon was not caused by the selection of the threshold value in the segmentation process that may increase the dimension of aggregate data. It was also observed that there were overlaps between the DSS distribution ranges of three different groups of granite. Appl. Sci. 2017, 7, 734 7 of 12 Appl. Sci. 2017, 7, 734 7 of 12 Appl. Sci. 2017, 7, 734 7 of 12

Figure 6. Size of seven specimens based on the digital sieving technique.

Figure 6. Size of seven specimens based on the digital sieving technique. In order to investigate the simplification of voxel data of each aggregate to its convex hull, 70 aggregates (10 from each specimen) were chosen to calculate the DSS with or without the In order to investigateinvestigate the simplificationsimplification of voxe voxell data of each aggregate to its convex hull, simplification.70 aggregates It (10 was from found each that specimen) the relative were erro chr broughtosen to bycalculate the simplifica the DSStion with was or less without than one the 70 aggregates (10 from each specimen) were chosen to calculate the DSS with or without the billionth,simplification. indicating It was that found treating that thethe aggregaterelative erro asr convexbrought hulls by the was simplifica entirelytion feasible was lessfor thethan DSS one simplification. It was found that the relative error brought by the simplification was less than one computation.billionth, indicating Considering that treatingthe definition the aggregate of DSS involvedas convex orthographic hulls was entirely projection feasible and forminimum the DSS billionth, indicating that treating the aggregate as convex hulls was entirely feasible for the DSS boundingcomputation. square, Considering both hid the convexdefinition basis, of DSSthe aboveinvolved approaching-zero orthographic projection relative errorand minimumwas not computation. Considering the definition of DSS involved orthographic projection and minimum unexpected.bounding square, It can be both concluded hid the that convex the concave basis, thsuerface above of aggregateapproaching-zero was the possiblerelative reasonerror wasfor the not bounding square, both hid the convex basis, the above approaching-zero relative error was not disparityunexpected. between It can DSS be concludedand mechanical that the sieve concave size, assu rfaceshown of inaggregate Figure 7. was the possible reason for the unexpected. It can be concluded that the concave surface of aggregate was the possible reason for the disparity between DSS and mechanical sieve size, as shown in Figure 7. disparity between DSS and mechanical sieve size, as shown in Figure7.

Figure 7. Effect of concave surface on sieving. Figure 7. Effect of concave surface on sieving. Due to difference betweenFigure the digital 7. Effect and of mechanicalconcave surface sieve on size,sieving. the digital sieving technique was requiredDue to to difference be calibrated between before the it can digital be employed and mechan to evaluateical sieve the size, gradation the digital of thesieving asphalt technique mixture. wasFor required granite,Due to thedifferenceto maximumbe calibrated between and before minimum the digitalit can DSS andbe inemployed mechan each specimenical to sieveevaluate and size, their the the gradation correspondingdigital sieving of the uppertechnique asphalt and mixture.lowerwas required bounds For granite, ofto mechanicalbe calibratedthe maxi sievemum before size and wereit minimumcan used be employed for DSS calibration. in eachto evaluate Thespecimen result the ofand gradation linear their ﬁtting corresponding of the is shown asphalt in upperFiguremixture. and8. Forlower granite, bounds the of maxi mechanicalmum and sieve minimum size were DSS used in for each calibration. specimen The and result their of corresponding linear fitting isupper shown and in Figurelower bounds 8. of mechanical sieve size were used for calibration. The result of linear fitting is shown in Figure 8. Appl. Sci. 2017, 7, 734 8 of 12 Appl. Sci. 2017, 7, 734 8 of 12

Figure 8. Linear calibration curve for granite. Figure 8. Linear calibration curve for granite.

A comparison between un-calibrated DSS and equivalent diameter was also performed, A comparison between un-calibrated DSS and equivalent diameter was also performed, as demonstrated in Figure 9. The maximum value of absolute difference between DSS and equivalent as demonstrated in Figure9. The maximum value of absolute difference between DSS and equivalent diameter for Group 1 to Group 4 was 4.272 mm, 3.638 mm, 2.871 mm and 1.398 mm, respectively. diameter for Group 1 to Group 4 was 4.272 mm, 3.638 mm, 2.871 mm and 1.398 mm, respectively. As particle size increased, the absolute difference increased. Therefore, estimation of the gradation of As particle size increased, the absolute difference increased. Therefore, estimation of the gradation the coarse-grained asphalt mixture based on equivalent diameter might lead to significant errors. of the coarse-grained asphalt mixture based on equivalent diameter might lead to signiﬁcant errors. However, it might be feasible to obtain gradation of the fine-grained mixture based on equivalent However, it might be feasible to obtain gradation of the ﬁne-grained mixture based on equivalent diameter with rigorous calibration. diameter with rigorous calibration.

Figure 9. Comparison between digital sieve size and equivalent diameter.

6. Application The 3D digital sieving technique developed in this paper was adopted to estimate the gradation of two specimensspecimens of stonestone masticmastic asphaltasphalt mixturemixture (SMA-13).(SMA-13). The gradation of the asphalt mixture used is listed in Table2 2.. TheThe granitegranite aggregatesaggregates utilizedutilized herehere werewere fromfrom the the samesame constructionconstruction sitesite (Zhanjiang(Zhanjiang City)City) as as the the granite granite mentioned mentioned in lastin last section, section, thus thus the calibration the calibration curve cancurve be usedcan be directly. used Thedirectly. specimens The specimens were 101.6 were mm (diameter) 101.6 mm by (diameter) 63.5 mm (height) by 63.5 in mm dimension (height) and in weredimension compacted and usingwere compacted using the Marshall compactor. After demolding, specimens were sent for X-ray CT scanning. The resolutions of the resulting images were approximately 0.0878 mm/pixel in the Appl. Sci. 2017, 7, 734 9 of 12 Appl. Sci. 2017, 7, 734 9 of 12 the Marshall compactor. After demolding, specimens were sent for X-ray CT scanning. The resolutions horizontal and vertical direction. The results of 3D reconstruction are shown in Figure 10. It was of the resulting images were approximately 0.0878 mm/pixel in the horizontal and vertical direction. observed that most of clustering coarse aggregates were separated successfully, whereas a certain The results of 3D reconstruction are shown in Figure 10. It was observed that most of clustering coarse amount of fine aggregates still adhered to the surface of coarse aggregate. The emphasis of future aggregates were separated successfully, whereas a certain amount of fine aggregates still adhered to study should be placed upon the segmentation of aggregates in X-ray CT images. In addition, the the surface of coarse aggregate. The emphasis of future study should be placed upon the segmentation aggregate structure (see Figure 10) can also be used to establish mechanical model for micromechanical of aggregates in X-ray CT images. In addition, the aggregate structure (see Figure 10) can also be used behavior analysis. For example, after aggregate and mastic phases are identified from 3D images, to establish mechanical model for micromechanical behavior analysis. For example, after aggregate triangular surface meshes for each phase can be created, and then finite element meshes can be and mastic phases are identified from 3D images, triangular surface meshes for each phase can be generated [21]. created, and then finite element meshes can be generated [21]. Considering the breakage of aggregates during Marshall compaction has an effect on gradation [22], Considering the breakage of aggregates during Marshall compaction has an effect on aggregates were extracted from mixtures by ignition method (T0735-2011 [23]) after scanning, and gradation [22], aggregates were extracted from mixtures by ignition method (T0735-2011 [23]) after laboratory gradations were determined (T0725-2000 [24]) for further analysis. scanning, and laboratory gradations were determined (T0725-2000 [24]) for further analysis.

(a) (b)(c)(d)

Figure 10. 3D reconstruction of aggregate structure: (a) CT slices; (b) volume rendering; (c) binary Figure 10. 3D reconstruction of aggregate structure: (a) CT slices; (b) volume rendering; (c) binary image after thresholding; and (d) connected-component detection. image after thresholding; and (d) connected-component detection.

Table 2. Gradation of the mixture. Table 2. Gradation of the mixture. Sieve size (mm) 16 13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 Passing ratioSieve (%) size (mm)10 1695 13.262.5 9.5 274.75 2.3620 1.1819 0.616 0.3 0.1513 0.07512 10 Passing ratio (%) 10 95 62.5 27 20 19 16 13 12 10 To convert the graphical volume-based gradation to a realistic weight-based gradation, it was assumed that all the aggregates in the specimen have the same specific gravity. Thus, the weight-based To convert the graphical volume-based gradation to a realistic weight-based gradation, it was gradation can be directly estimated from X-ray CT images. After each aggregate was classified into a assumed that all the aggregates in the specimen have the same specific gravity. Thus, the weight-based different standard size range based on their equivalent diameter or DSS, the total volume of the gradation can be directly estimated from X-ray CT images. After each aggregate was classified into aggregates in each standard size range and the accumulative passing percentage were computed. a different standard size range based on their equivalent diameter or DSS, the total volume of the It is noted that the aggregates smaller than 4.75 mm will not be considered in the calculation, which aggregates in each standard size range and the accumulative passing percentage were computed. It is is acceptable because they are components of asphalt mortar. noted that the aggregates smaller than 4.75 mm will not be considered in the calculation, which is The gradation curves based on different methods are presented in Figures 11 and 12.The results acceptable because they are components of asphalt mortar. showed that the gradation based on calibrated DSS was closer to the laboratory gradation curve than The gradation curves based on different methods are presented in Figures 11 and 12.The results the curve based on DSS or equivalent diameter, indicating the calibration of DSS was necessary. showed that the gradation based on calibrated DSS was closer to the laboratory gradation curve than In the case of specimen 1 (see Figure 11), although a significant difference existed between the mix the curve based on DSS or equivalent diameter, indicating the calibration of DSS was necessary. In the design and laboratory gradation, the calibrated DSS was able to capture the variability. Moreover, case of specimen 1 (see Figure 11), although a significant difference existed between the mix design and the gradation curves based on DSS and equivalent diameter were quite close. This result was owing laboratory gradation, the calibrated DSS was able to capture the variability. Moreover, the gradation to the finding in Figure 9 that there was a good statistical correlation between these two parameters. curves based on DSS and equivalent diameter were quite close. This result was owing to the finding in Figure9 that there was a good statistical correlation between these two parameters. Appl. Sci. 2017, 7, 734 10 of 12 Appl. Sci. 2017, 7, 734 10 of 12

Figure 11. GradationGradation curves for Specimen 1.

Figure 12. GradationGradation curves for Specimen 2.

7. Conclusions Conclusions The aim of this study study was was to to develop develop 3D 3D digital digital sieving sieving technique technique used used to to estimate estimate the the gradation gradation of asphalt asphalt mixture mixture in in X-ray X-ray CT CT images. images. For For this this purpose, purpose, a concept a concept named named digital digital sieve sieve size (DSS) size (DSS) was proposed,was proposed, which which was wasdefined defined as the asthe minimum minimum length length of ofthe the mini minimummum bounding bounding squares squares of of all possible orthographic projections of an aggregate.aggregate. The The corresponding numerical numerical method method used to obtain DSS was introduced. In In order to investigat investigatee the difference between mechanical sieve analysis and the digital sieving technique, technique, four four groups groups of of epoxy-filled epoxy-filled aggregate aggregate specimens were scanned and analyzed. As a a convex convex basis basis lurked lurked in in the the definition definition of of DSS, DSS, there there were were a a certain certain percent percent of of aggregates aggregates inin each specimenspecimen withwith theirtheir DSSDSS largerlarger thanthan the the upper upper limit limit of of their their mechanical mechanical size size in in the the result. result. It Itwas was suggested suggested that that the concavethe concave surface surface of aggregate of aggregate was the was possible the possible reason forreason the disparityfor the disparity between betweenDSS and DSS mechanical and mechanical sieve size. sieve After size. a linear After calibration a linear calibration of DSS was of performed DSS was performed for granite, for the granite, digital thesieving digital technique sieving wastechnique adopted was to adopted evaluate to the evaluate gradation the of gradation stone mastic of stone asphalt mastic mixtures. asphalt The mixtures. results Theshowed results that showed the closest that proximity the closest of proximity the laboratory of the gradation laboratory curve gradation was achieved curve bywas calibrated achieved DSS by calibratedamong the DSS gradation among curves the basedgradation on calibrated curves based DSS, un-calibratedon calibrated DSS, DSS, and un-calibrated equivalent diameter. DSS, and equivalent diameter.

Appl. Sci. 2017, 7, 734 11 of 12

Apart from good reliability after calibration and being easy to understand, the major advantage of DSS is that it considers the shape of the aggregate and the square opening of the mechanical sieve, as compared to the equivalent diameter. Although the beneﬁt of DSS for a dense-grained asphalt mixture is weakened by the large quantity and volume summation of aggregates in each standard size range, DSS is promising in capturing size distribution of coarse/medium-grained mixture. Moreover, DSS is much more sensitive to the clustering of coarse aggregates than the equivalent diameter since clustering particles often have strange shapes and large aspect ratios. The gradation curve based on DSS can be used to select the optimum parameters for the segmentation algorithm.

Acknowledgments: Supports provided by National Natural Science Foundation (51578248) and Pearl River S&T Nova Program of Guangzhou were greatly appreciated. Author Contributions: Chichun Hu proposed the idea, designed the experiments and simulation; Jiexian Ma performed the experiments and simulation; M. Emin Kutay contributed image analysis tools and provided simulation suggestions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Masad, E.; Olcott, D.; White, T.; Tashman, L. Correlation of fine aggregate imaging shape indices with asphalt mixture performance. Transp. Res. Rec. 2001, 1757, 148–156. [CrossRef] 2. Sefidmazgi, N.R.; Tashman, L.; Bahia, H. Internal structure characterization of asphalt mixtures for rutting performance using imaging analysis. Road Mater. Pavement 2012, 13, 21–37. [CrossRef] 3. Haddock, J.; Pan, C.; Feng, A.; White, T. Effect of gradation on asphalt mixture performance. Transp. Res. Rec. 1999, 1681, 59–68. [CrossRef] 4. Williams, R.; Duncan, G.; White, T. Hot-mix asphalt segregation: Measurement and effects. Transp. Res. Rec. 1996, 1543, 97–105. [CrossRef] 5. American Association of State Highway and Transportation Officials (AASHTO). Segregation: Causes and Cures for Hot Mix Asphalt; AASHTO: Washington, DC, USA, 1997. 6. Bruno, L.; Parla, G.; Celauro, C. Image analysis for detecting aggregate gradation in asphalt mixture from planar images. Constr. Build. Mater. 2012, 28, 21–30. [CrossRef] 7. Yue, Z.Q.; Bekking, W.; Morin, I. Application of digital image processing to quantitative study of asphalt concrete microstructure. Transp. Res. Rec. 1995, 1492, 53–60. 8. Masad, E.; Muhunthan, B.; Shashidhar, N.; Harman, T. Internal structure characterization of asphalt concrete using image analysis. J. Comput. Civ. Eng. 1999, 13, 88–95. [CrossRef] 9. Wu, W.; Wang, D.; Zhang, X. Estimating the gradation of asphalt mixtures using X-ray computerized tomography and stereology method. Road Mater. Pavement 2011, 12, 699–710. [CrossRef] 10. Guo, Q.; Bian, Y.; Li, L.; Jiao, Y.; Tao, J.; Xiang, C. Stereological estimation of aggregate gradation using digital image of asphalt mixture. Constr. Build. Mater. 2015, 94, 458–466. [CrossRef] 11. Kutay, M.E.; Arambula, E.; Gibson, N.; Youtcheff, J. Three-dimensional image processing methods to identify and characterise aggregates in compacted asphalt mixtures. Int. J. Pavement Eng. 2010, 11, 511–528. [CrossRef] 12. Wang, Y.; Lin, C.L.; Miller, J.D. 3D image segmentation for analysis of multisize particles in a packed particle bed. Powder Technol. 2016, 301, 160–168. [CrossRef] 13. Masad, E.; Jandhyala, V.K.; Dasgupta, N.; Somadevan, N.; Shashidhar, N. Characterization of air void distribution in asphalt mixes using X-ray computed tomography. J. Mater. Civ. Eng. 2002, 14, 122–129. [CrossRef] 14. Hu, C.; Youtcheff, J.; Wang, D.; Zhang, X.; Kutay, E.; Thyagarajan, S. Characterization of asphalt mixture homogeneity based on X-ray computed tomography. J. Test. Eval. 2012, 40, 1–7. [CrossRef] 15. Krumm, M.; Kasperl, S.; Franz, M. Reducing non-linear artifacts of multi-material objects in industrial 3D computed tomography. NDT & E Int. 2008, 41, 242–251. 16. ASTM C136/C136M-14. Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates; ASTM International: West Conshohocken, PA, USA, 2014. 17. Goldstein, H. Classical Mechanics, 3rd ed.; Addison-Wesley Publishing: Reading, PA, USA, 2001. Appl. Sci. 2017, 7, 734 12 of 12

18. Freeman, H.; Shapira, R. Determining the minimum-area encasing rectangle for an arbitrary closed curve. Commun. ACM 1975, 18, 409–413. [CrossRef] 19. Toussaint, G.T. Solving geometric problems with the rotating calipers. In Proceedings of the IEEE Melecon’83, Athens, Greece, 24–26 May 1983. 20. Chan, C.K.; Tan, S.T. Determination of the minimum bounding box of an arbitrary solid: An iterative approach. Comput. Struct. 2001, 79, 1433–1449. [CrossRef] 21. Hu, J.; Qian, Z.; Wang, D.; Oeser, M. Inﬂuence of aggregate particles on mastic and air-voids in asphalt concrete. Constr. Build. Mater. 2015, 93, 1–9. [CrossRef] 22. Airey, G.D.; Hunter, A.E.; Collop, A.C. The effect of asphalt mixture gradation and compaction energy on aggregate degradation. Constr. Build. Mater. 2008, 22, 972–980. [CrossRef] 23. T 0735-2011. Test Method for Asphalt Content of Asphalt Mixture (Ignition Method); China Communication Press: Beijing, China, 2011. 24. T 0725-2000. Test. Method for Examining Mineral. Gradation of Asphalt Mixture; China Communication Press: Beijing, China, 2000.

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