## 2 Materials and Methodology
### Geometric Characteristic Evaluating Methods
#### 2.2.2 Direct Methods  
As mentioned above, the indirect tests are based on the measurement of bulk property which is due to the combined effect of form, angularity and texture, and it is fairly difficult to separate the effect of the individual components. By contrast, the DIP-based direct methods can quantify the aggregate geometric characteristics separately and accurately, and thus determine the relative contribution of different geometric characteristics to mixture performance [17]. In this research, the stereomicroscopy and area light were combined to capture the images of FA. The image capturing device is shown in Figure 1 and the detailed steps are as following:  
* Wash the prepared fine aggregates with water and filter out the filler part. Sieve and obtain the required fine aggregates with specific representative size for use. The determination method for the representative size is to be given in the next section;
* Adjust the focal length to the required revolution and rotate the focus knob until the aggregates are showed clearly;
* Take and save the pictures for further use.  
For each kind of FA, 150 aggregate particles were selected for scanning and the 150 high-resolution (0.003 mm/pixel) images were taken for every single aggregate particle, and 25 low-resolution (0.015 mm/pixel) images were taken for every group of 6 aggregate particles as shown in Figure 2.  
A number of parameters have been proposed based on imaging analysis. In this research, 7 indexes were selected to describe the form, angularity and texture characteristics of FA, respectively. The employed index system was detailed in Table 3. Among these indexes, the surface parameter \(SP\) was calculated through the erosion-dilation method which was implemented by using MATLAB coding while the others were calculated through Image-Pro Plus (IPP) software. In the Erosion-Dilation method, erosion is a morphologic operation in which pixels are removed from the binary image according to the number of neighboring pixels that have different color and dilation is the reverse of erosion. The area lost after a certain number of erosion and dilation operations is proportional to the percentage of aggregates smaller than a certain size and surface irregularity. For the last five indicators, calculations based on low-resolution images describe the angularity characteristic of the FA, and calculations based on high-resolution images describe the texture characteristic of the FA. The definitions and physical meanings of the indexes are given in what follows.  
Figure 1: The image-capturing device.  
Figure 2: The obtained digital images of FA with different resolutions.  
The form indexes ratio of equivalent ellipse axis \(E\) and rectangularity \(R\) are given by:  
\[E=\frac{a}{b} \tag{7}\]  
\[R=\frac{A_{i}}{A_{r}} \tag{8}\]  
These two indicators describe the degree of similarity between the shape of aggregate and circle and rectangle respectively, as shown in Figure 3.  
The surface parameter \(SP\), perimeter ratio of equivalent ellipse \(A_{I}\), convex ratio \(C_{R}\), shape factor \(SF\) and fractal dimension \(D\) were defined respectively as:  
\[SP=\frac{A_{1}-A_{2}}{A_{1}}\times 100\% \tag{9}\]  
\[A_{I}=\frac{L_{1}}{L_{2}} \tag{10}\]  
\[A_{I}=\frac{L_{1}}{L_{2}} \tag{11}\]  
\[SF=\frac{L_{1}}{4\pi S} \tag{12}\]  
\[D=\frac{2}{k} \tag{13}\]  
Figure 3: Schematic of the equivalent ellipse.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Geometric Characteristic** & **Index** & **Methods** \\ \hline Form index & \(E\) & IPP \\  & \(R\) & IPP \\ \hline  & \(SP\) & MATLAB \\  & \(A_{I}\) & IPP \\ Angularity index 1  & \(C_{R}\) & IPP \\  & \(SF\) & IPP \\  & \(D\) & IPP \\ \hline  & \(SP\) & MATLAB \\  & \(A_{I}\) & IPP \\ Texture index 2  & \(C_{R}\) & IPP \\  & \(SF\) & IPP \\  & \(D\) & IPP \\ \hline \hline \end{tabular}
\end{table}
Table 3: Indexes of fine aggregate geometric characteristic.