# Three Dimensional Digital Sieving of Asphal Mixture Based on 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; 2; 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. [PERSON] 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. 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. [PERSON] 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. [PERSON] 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]. [PERSON] 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. [PERSON] 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, [PERSON] et al.