# Three Dimensional Digital Sieving of Asphal Mixture Based on X-ray Computed Tomography
## 6 Application  
The 3D digital sieving technique developed in this paper was adopted to estimate the gradation of two specimens of stone mastic asphalt mixture (SMA-13). The gradation of the asphalt mixture used is listed in Table 2. The granite aggregates utilized here were from the same construction site (Zhanjiang City) as the granite mentioned in last section, thus the calibration curve can be used directly. The specimens were 101.6 mm (diameter) by 63.5 mm (height) in dimension and were compacted using  
Figure 8: Linear calibration curve for granite.  
Figure 9: Comparison between digital sieve size and equivalent diameter.  
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 horizontal and vertical direction. The results of 3D reconstruction are shown in Figure 10. It was observed that most of clustering coarse aggregates were separated successfully, whereas a certain amount of fine aggregates still adhered to the surface of coarse aggregate. The emphasis of future study should be placed upon the segmentation of aggregates in X-ray CT images. In addition, the aggregate structure (see Figure 10) can also be used to establish mechanical model for micromechanical behavior analysis. For example, after aggregate and mastic phases are identified from 3D images, triangular surface meshes for each phase can be created, and then finite element meshes can be generated [21].  
Considering the breakage of aggregates during Marshall compaction has an effect on gradation [22], aggregates were extracted from mixtures by ignition method (T0735-2011 [23]) after scanning, and laboratory gradations were determined (T0725-2000 [24]) for further analysis.  
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 gradation can be directly estimated from X-ray CT images. After each aggregate was classified into a different standard size range based on their equivalent diameter or DSS, the total volume of the aggregates in each standard size range and the accumulative passing percentage were computed. It is noted that the aggregates smaller than 4.75 mm will not be considered in the calculation, which is acceptable because they are components of asphalt mortar.  
The gradation curves based on different methods are presented in Figures 11 and 12.The results showed that the gradation based on calibrated DSS was closer to the laboratory gradation curve than the curve based on DSS or equivalent diameter, indicating the calibration of DSS was necessary. In the case of specimen 1 (see Figure 11), although a significant difference existed between the mix design and laboratory gradation, the calibrated DSS was able to capture the variability. Moreover, the gradation curves based on DSS and equivalent diameter were quite close. This result was owing to the finding in Figure 9 that there was a good statistical correlation between these two parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline Sieve size (mm) & 16 & 13.2 & 9.5 & 4.75 & 2.36 & 1.18 & 0.6 & 0.3 & 0.15 & 0.075 \\ \hline Passing ratio (\%) & 10 & 95 & 62.5 & 27 & 20 & 19 & 16 & 13 & 12 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Gradation of the mixture.  
Figure 10: 3D reconstruction of aggregate structure: (**a**) CT slices; (**b**) volume rendering; (**c**) binary image after thresholding; and (**d**) connected-component detection.