## 4 Mix Design of SPS Asphalt Mixture
### Determination of Optimal Fiber Content and Optimal Asphalt Content
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Items** & \multicolumn{5}{c}{**Test Values**} \\ \hline Asphal-aggregate ratio/\% & 6.1 & 6.6 & 7.1 & 7.6 & 8.1 \\ Bulk density/(g-cm\({}^{-3}\)) & 2.397 & 2.422 & 2.433 & 2.418 & 2.402 \\ VV/\% & 5.1 & 4.3 & 3.6 & 2.4 & 1.5 \\ VMA/\% & 19.2 & 18.0 & 17.3 & 18.2 & 19.7 \\ VFA/\% & 73.7 & 76.3 & 79.5 & 86.6 & 92.5 \\ Stability/kN & 9.72 & 10.51 & 10.67 & 10.26 & 9.83 \\ FL/mm & 3.37 & 3.96 & 4.33 & 4.75 & 5.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Marshall test results of SMA-II-3. According to Marshall test results in Table 9 and calculation methods in the Chinese specification JTG40-2004 [39], OAC (the optimal asphalt content), OAC\({}_{\text{min}}\) and OAC\({}_{\text{max}}\) of SMA-II-1 with different fiber contents are shown in Figure 4:  
In Figure 4, before the peak of the curve, the optimal asphalt content (OAC) increases with increasing fiber content. At the peak, OAC increases by about 0.4% because of the presence of the fiber. After the peak, OAC reduces gradually with increasing fiber content. Figure 5 shows that there is an extremum for the Marshall stability of the asphalt mixture with different fiber contents and asphalt-aggregate ratios. The reason is that the specific surface area of the fiber will increase with the addition of fiber that will adsorb a certain amount of asphalt, then the OAC will increase. But with a further increase of fiber content, the specific surface area of the fiber will decrease because excess fiber can reduce the dispersity so OAC will decrease accordingly. Therefore, in this test, the optimal amount of polyester fiber is 0.18% while the optimal asphalt-aggregate ratio is 6.6%. Figure 4: Relationship between fiber content and asphalt-aggregate ratio of SMA-II-1. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mixture**} & \multirow{2}{*}{\begin{tabular}{c} **Fiber** \\ **Content/\%** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Asphal-** \\ **Aggregate** \\ **Ratio/\%** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Bulk** \\ **Density** \\ **g/cm\({}^{3}\)** \\ \end{tabular} } & \multirow{2}{*}{**VV/\%**} & \multirow{2}{*}{**VWA/\%**} & \multirow{2}{*}{**VFA/\%**} & \multirow{2}{*}{**Stability/kN**} & \multirow{2}{*}{**FL/mm**} \\ \hline \hline \multirow{8}{*}{SMA-II-1} & \multirow{8}{*}{0.1} & 6.2 & 2.441 & 3.62 & 17.6 & 79.4 & 10.52 & 3.52 \\  & & 6.5 & 2.437 & 3.23 & 18.3 & 82.4 & 10.73 & 3.76 \\  & & 6.8 & 2.416 & 2.64 & 18.8 & 86.0 & 10.15 & 4.21 \\ \cline{2-8}  & \multirow{8}{*}{0.15} & 6.3 & 2.438 & 3.42 & 17.7 & 80.7 & 10.47 & 3.35 \\  & & 6.6 & 2.431 & 2.71 & 17.9 & 84.9 & 10.98 & 3.57 \\  & & 6.9 & 2.409 & 2.43 & 18.6 & 87.0 & 10.15 & 4.12 \\ \cline{2-8}  & \multirow{8}{*}{0.2} & 6.4 & 2.436 & 3.31 & 17.4 & 81.0 & 10.59 & 3.54 \\  & & 6.7 & 2.433 & 3.03 & 17.5 & 82.7 & 11.06 & 3.88 \\  & & 7.0 & 2.420 & 2.33 & 18.1 & 87.1 & 10.71 & 4.36 \\ \cline{2-8}  & \multirow{8}{*}{0.25} & 6.4 & 2.435 & 3.52 & 17.4 & 79.8 & 10.84 & 3.67 \\  & & 6.7 & 2.421 & 3.11 & 17.2 & 81.9 & 10.75 & 4.06 \\  & & 7.0 & 2.402 & 2.73 & 18.2 & 85.0 & 10.23 & 4.63 \\ \cline{2-8}  & \multirow{8}{*}{0.3} & 6.4 & 2.425 & 3.23 & 17.7 & 81.8 & 10.63 & 3.73 \\ \cline{2-8}  & & 6.8 & 2.406 & 2.61 & 17.2 & 84.8 & 10.41 & 4.39 \\ \cline{2-8}  & & 7.0 & 2.398 & 2.23 & 17.9 & 87.5 & 9.97 & 4.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Basic parameters and Marshall volumetric indicators of the mixture. In Table 10, the asphalt content for three gradations (without fiber) are still 6.5%. As a control variable for each gradation, the passing rates of the 1.18-mm sieve are 36.3%, 55.3% and 47.1% in SMA-II-1, SMA-II-2 and SMA-II-3, respectively. The mineral filler content of each gradation is 8.5%, 9.5%, 10.5 %, respectively. Specimens of all gradations are made by way of the gyratory compaction method (125 times compaction). Table 11 presents the test results of the air voids of gyratory compaction specimens.