## 4 Mix Design of SPS Asphalt Mixture  
### Determination of Optimal Fiber Content and Optimal Asphalt Content  
To determine the optimal fiber and asphalt content, the optimal composition of the asphalt mixture without fiber was first determined by the Marshall test. Then, the polymer fiber, as the admixture, was added to the asphalt mixture at a certain interval of content, while the asphalt content should increase at an appropriate proportion. Hence, under each fiber content, Marshall samples were molded respective to a certain interval of asphalt content and the optimal asphalt-aggregate ratio was determined. Marshall test results of the mixture without fiber are shown in Tables 6-8: \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Grain Size/mm** & **9.5** & **4.75** & **2.36** & **1.18** & **0.6** & **0.3** & **0.15** & **0.075** \\ \hline Passing rate/\% & 100 & 73.2 & 53.4 & 39.1 & 28.9 & 21.1 & 15.5 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SMA-II gradation calculation. Figure 3: Gradation curves of SMA-I and SMA-II. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Particle Size/mm** & **9.5** & **4.75** & **2.36** & **1.18** & **0.6** & **0.3** & **0.15** & **0.075** \\ \hline Passing rate of SMA-I & 100 & 95 & 46.5 & 29 & 23 & 18.5 & 15.5 & 13.5 \\ Passing rate of SMA-II-1/\% & 100 & 76.7 & 55.6 & 36.3 & 23.3 & 18.3 & 13.5 & 9.5 \\ Passing rate of SMA-II-2/\% & 100 & 95 & 85 & 70 & 55 & 35 & 18 & 12 \\ Passing rate of SMA-II-3/\% & 100 & 88.2 & 67.6 & 47.1 & 47.1 & 29.4 & 16.5 & 10.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SMA-II gradation design. Air voids have a significant influence on the performance of the mixture and should be strictly controlled within a reasonable range. Thus, air voids in this test were decreased within the allowable range to enhance the crack resistance of the dense-graded mixture. According to specification JTG F40-2004 [39], the air voids should be between 3.5% and 4%. According to the Marshall test results, for SMA-II-1, the stability first increases from 10.65 kN to the maximum value of 11.12 kN with the increase of the asphalt-aggregate ratio from 5.3% to 6.3%, then the stability decreases to 10.41 kN with the increase of the asphalt-aggregate ratio from 6.3% to 7.3%. Similarly, the maximum values of stability for SMA-II-2 and SMA-II-3 are 10.35 kN when the asphalt-aggregate ratio is 8.1% and 10.67 kN when the asphalt-aggregate ratio is 7.1%. Thus, the optimal asphalt contents of SMA-II-1, SMA-II-2 and SMA-II-3 are 6.3%, 7.8% and 6.9%. Then, fiber was added to all SMA-II mixtures in different proportions; meanwhile, asphalt content should increase. The Marshall test results of SMA-II-1 are shown in Table 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Items** & \multicolumn{5}{c}{**Test Values**} \\ \hline Asphal-aggregate ratio/\% & 5.3 & 5.8 & 6.3 & 6.8 & 7.3 \\ Bulk density/(g-cm\({}^{-3}\)) & 2.393 & 2.427 & 2.445 & 2.438 & 2.422 \\ VV/\% & 5.4 & 4.2 & 3.4 & 2.7 & 1.5 \\ VMA/\% & 17.3 & 17.6 & 17.6 & 19.2 & 21.5 \\ VFA/\% & 68.9 & 75.9 & 80.6 & 85.7 & 92.9 \\ Stability/kN & 10.65 & 10.94 & 11.12 & 11.02 & 10.41 \\ FL/mm & 3.31 & 3.52 & 3.85 & 4.33 & 4.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Marshall test results of SMA-II-1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Items** & \multicolumn{5}{c}{**Test Values**} \\ \hline Asphal-aggregate ratio/\% & 7.1 & 7.6 & 8.1 & 8.6 & 9.1 \\ Bulk density/(g-cm\({}^{-3}\)) & 2.367 & 2.395 & 2.406 & 2.368 & 2.343 \\ VV/\% & 5.6 & 4.5 & 3.4 & 2.5 & 1.6 \\ VMA/\% & 20.1 & 19.0 & 18.6 & 20.0 & 20.2 \\ VFA/\% & 72.3 & 76.1 & 81.6 & 87.4 & 91.9 \\ Stability/kN & 9.31 & 9.82 & 10.35 & 9.91 & 9.73 \\ FL/mm & 4.22 & 4.58 & 5.15 & 5.74 & 6.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: [PERSON] test results of SMA-II-2.