## 2 Materials and Methods
### Asphalt Mixture
#### 2.3.2. Gradation Evaluation Methods  
Gradation is an important factor that affects the performance of asphalt mixtures. It is of great significance to quantify the effect of gradation and evaluate the performance of mixtures using suitable evaluation parameters. The current methods for grading evaluation can be mainly classified into two categories: the key sieve method and the grading fractal method. The key sieve method evaluates the gradation by using the passing rates or ratios of certain key sieves or sieves in the mineral gradation. The grading fractal method evaluates the gradation by using the fractal theory to obtain the fractal dimension of composite gradation (\(D\)), the fractal dimension of coarse aggregate gradation (\(D_{c}\)), and the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Gradations**} & **Optimal** & \multicolumn{2}{c}{**Theoretical**} & \multicolumn{2}{c}{**Bulk**} & \multirow{3}{*}{**VV/\%**} & \multirow{3}{*}{**VMA/\%**} & \multirow{3}{*}{**VFA/\%**} & \multirow{3}{*}{**Stability/kN**} & \multirow{3}{*}{**Flow**} & \multirow{3}{*}{**Arbahit Film**} \\  & **Asphalit-** & & & & & & & & & \\
**Types** & **Aggrate** & **Density of** & **Density of** & **Avphalit** & & & & & & \\
**Ratio/\%** & **Asphalit** & **Asphalit** & & & & & & & & \\
**Mixture** & **Mixture** & & & & & & & & & \\ \hline
10A-1 & 6.95 & 2.394 & 2.333 & 2.5 & 16.82 & 85.15 & 9.48 & 2.87 & 0.94 & 10.06 \\
10B-1 & 6.10 & 2.425 & 2.364 & 2.5 & 15.11 & 83.41 & 8.65 & 2.76 & 1.08 & 9.70 \\
10C-1 & 7.49 & 2.381 & 2.333 & 2.5 & 17.64 & 85.66 & 7.66 & 3.14 & 0.45 & 21.24 \\
10C-2 & 6.55 & 2.410 & 2.343 & 2.5 & 15.93 & 84.38 & 7.81 & 3.33 & 1.35 & 9.71 \\
10C-MZ & 7.49 & 2.377 & 2.316 & 2.5 & 17.70 & 85.90 & 7.05 & 4.07 & 0.88 & 15.28 \\
10C-GG & 7.00 & 2.403 & 2.340 & 2.5 & 16.65 & 85.00 & 6.84 & 2.87 & 0.93 & 9.53 \\
10C-3 & 6.46 & 2.409 & 2.350 & 2.5 & 15.78 & 84.18 & 7.84 & 3.78 & 1.02 & 11.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Asphal mixture volume parameters. Figure 2: Gradation of AR-SAMI. fractal dimension of aggregate (\(D_{f}\)) of the gradation. The grading parameters used in this chapter are as follows:  
1. Key sieve passing ratios. As shown in Figure 2, there is a large difference in the passing ratios at the 4.75 mm sieve among different gradations. According to JTG F40-2004 [28], the 10-type gradation uses the 2.36 mm sieve as the key sieve to distinguish between coarse and fine aggregates. The passing rates at the 4.75 mm and 2.36 mm sieves affect the voids in the mineral aggregate (VMA) and the air voids (VV) of the mixture, and VMA and VV affect the mixture properties. Therefore, \(P_{4.75\text{mm}}\) and \(P_{2.36\text{mm}}\) were selected as key sieve passing rates. 2. Key particle size aggregate content. The content of coarse aggregate above 2.36 mm affects the skeleton structure of the mixture and determines the initial voids in the mixture. Therefore, 4.75-9.5 mm and 2.36-4.75 mm were selected as key particle sizes. 3. The primary control sieve index (\(PCSI\)) [39] \[PCSI=P_{PCS}-P_{PCS,MDL}\] (1) where \(PCSI\) is the difference in percentage passing between the given gradation and the point on the maximum density line at the primary control sieve; \(P\) is the passage ratio of the corresponding sieve, %; \(d\) is the maximum nominal particle size, mm; the primary control sieve (\(PCS\)) is 0.22 \(\times\)\(d\), mm; \(P_{PCS,MDL}\) is the passage ratio of the maximum density curve at \(PCS\), taken as 47%, %. 4. Parameters of the Bailey method \[CA=\frac{P_{D/2}-P_{PCS}}{100-P_{D/2}}\] (2) \[FA_{c}=\frac{P_{SCS}}{P_{PCS}}\] (3) \[FA_{f}=\frac{P_{TCS}}{P_{SCS}}\] (4) where \(CA\) is the coarse aggregate ratio; \(FA_{c}\) is the fine aggregate coarse ratio; \(FA_{f}\) is the fine aggregate fine ratio; the secondary control sieve (\(SCS\)) is 0.22 \(\times\)\(PCS\); the third control sieve (\(TCS\)) is 0.22 \(\times\)\(TCS\). 5.