## 2 Materials and Methods
### Experimental Methods  
#### 2.3.1 Test Methods  
In order to evaluate the design for these five kinds of bituminous mixture, a series of laboratory tests were carried out, including a high-temperature rutting test, a low-temperature bending test, an immersion Marshall test, a freeze-thaw splitting test and a fatigue test. (1) High-temperature rutting test \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Type** & \multicolumn{6}{c}{**Percentage (\%) of Quality Passing the Following Sieve Size (mm)**} \\ \cline{2-10}  & **26.5** & **19** & **16** & **13.2** & **9.5** & **4.75** & **2.36** & **1.18** & **0.6** & **0.3** & **0.15** & **0.075** \\ \hline AC-20 & 100 & 95.1 & 80.0 & 72.4 & 58.7 & 36.0 & 24.7 & 19.4 & 14.7 & 10.6 & 6.7 & 4.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Aggregate gradation composition of bituminous mixture selected in this study. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **M-9467** & **PR Module** \\ \hline Density (g/cm\({}^{3}\)) & 0.90–0.98 & 0.91–0.96 \\ Melting point (\({}^{\circ}\)C) & 120–130 & 140–150 \\ Particle size (mm) & 2–4 & 2–4 \\ Melt index at 190 \({}^{\circ}\)C (g/10 min) & 5–11 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of anti-rutting modifiers. Based on (T0719-2011) [50], the rutting test was carried out. The test conditions were set as 60 \({}^{\circ}\)C \(\pm\) 0.5 \({}^{\circ}\)C. The dynamic stability (\(DS\)) and relative deformation (\(\varepsilon_{r}\)) of the specimen were calculated and recorded based on Equations (1) and (2). \[DS=\frac{(t_{2}-t_{1})\times N}{d_{2}-d_{1}}\times C_{1}\times C_{2} \tag{1}\]  
\[\varepsilon_{r}=\frac{d_{2}}{D}\times 100 \tag{2}\]  
where \(DS\) is the dynamic stability (times/mm); \(d_{1}\) is the deformation corresponding at \(t_{1}\) (mm); \(d_{2}\) is the deformation corresponding at \(t_{2}\) (mm); \(C_{1}\) and \(C_{2}\) are the coefficients, \(C_{1}\) = 1.0, \(C_{2}\) = 1.0; \(N\) is the round-trip rolling speed, \(N\) = 42 times/min; \(D\) is the thickness of the rutting plate (mm). (2) Low-temperature bending test  
Based on (T0715-2011) [50], the low-temperature bending test was carried out. The test conditions were set as (\(-10\)\(\pm\) 0.5) \({}^{\circ}\)C and a loading rate of 50 mm/min. The maximum bending tensile strain (\(\varepsilon_{B}\)) and the critical bending strain energy density (\(dW/dV\)) when the specimen fails were recorded through Equations (3) and (4), respectively. A diagram of the low-temperature bending test is shown in Figure 2.  
\[\varepsilon_{B}=\frac{6 hd}{L^{2}} \tag{3}\]  
\[\frac{\mathrm{d}W}{\mathrm{d}V}=\int_{0}^{\varepsilon_{0}}\sigma_{ij}\mathrm{ d}\varepsilon_{ij} \tag{4}\]  
where \(\varepsilon_{B}\) is the maximum bending tensile strain when the specimen fails (\(\mu\varepsilon\)); \(h\) is the height of the midspan section (mm); \(d\) is the mid-span deflection when the specimen is damaged (mm); \(L\) is the span of the specimen (mm); \(\mathrm{d}W/\mathrm{d}V\) is the critical bending strain energy density (kJ-m\({}^{3}\)); \(\varepsilon_{0}\) is the strain value corresponding to the maximum stress (i.e., the critical strain value). (3) Immersion Marshall test and freeze-thaw splitting test  
Based on (T0709-2011 and T0709-2011) [50], the immersion Marshall test and the freeze-thaw splitting test were also carried out. The temperature of the immersion Marshall test was (60 \(\pm\) 1) \({}^{\circ}\)C, the temperature of the freeze-thaw splitting test was (25 \(\pm\) 1) \({}^{\circ}\)C. Furthermore, the Marshall immersion residual stability (\(MS_{0}\)) and freeze-thaw splitting tensile strength ratio (\(TSR\)) of the specimens were also recorded through Equations (5) and (6), respectively. \[MS_{0}=\frac{MS_{1}}{MS}\times 100 \tag{5}\]  
Figure 2: Diagram of low-temperature bending test.