## 3 Results and Discussion
### Analysis of Response Output Index Results
#### 3.1.2 Air Voids  
The comparison of the fitting degrees of various fitting equations in the air voids analysis is consistent with the method selected in the density analysis process in the previous section, and will not be repeated in this section. Table 15 is the variance test situation of each variable after fitting through the quadratic equation. Figure 4: Contour map and response surface map of density and influencing factors. (**a**) Contour map between basalt fiber content, NTC content and density; (**b**) Three-dimensional surface graph between basalt fiber content, NTC content and density; (**c**) Contour map between basalt fiber content, asphalt–aggregate ratio and density; (**d**) Three-dimensional surface graph between basalt fiber content, asphalt–aggregate ratio and density; (**e**) Contour map between asphalt–aggregate ratio, NTC content and density; (**f**) Three-dimensional surface graph between asphalt–aggregate ratio, NTC content and density. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Project** & **Sum of Squares** & **Degrees of Freedom** & **Mean Square Error** & **F Value** & **P Value** & **Significant** \\ \hline Model & 77.35 & 9 & 8.59 & 35.59 & \(<\)0.0001 & \(\surd\) \\ A: Fiber Content & 4.32 & 1 & 4.32 & 17.9 & 0.0039 & \(\surd\) \\ B: Nano-Material Content & 10.46 & 1 & 10.46 & 43.31 & 0.0003 & \(\surd\) \\ C: Asphal-Aggregate Ratio & 29.83 & 1 & 29.83 & 123.52 & \(<\)0.0001 & \(\surd\) \\ AB & 1.42 & 1 & 1.42 & 5.87 & 0.0459 & \(\surd\) \\ AC & 1.01 & 1 & 1.01 & 4.2 & 0.0797 & \(\times\) \\ BC & 0.86 & 1 & 0.86 & 3.56 & 0.1013 & \(\times\) \\ A? & 0.13 & 1 & 0.13 & 0.53 & 0.4909 & \(\times\) \\ B2 & 2.2 & 1 & 2.2 & 9.11 & 0.0194 & \(\surd\) \\ C2 & 25.86 & 1 & 25.86 & 107.08 & \(<\)0.0001 & \(\surd\) \\ Residual & 1.69 & 7 & 0.24 & — & — & — \\ Mismatch & 1.69 & 3 & 0.56 & — & — & — \\ Pure Error & 0 & 4 & 0 & — & — & — \\ Total Deviation & 79.04 & 16 & — & — & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Air voids variance test table. According to the analysis of variance results, the fitting equation for the air voids can be obtained: Air voids = 42.12238 + 0.45739 \(\times\) A \(-\) 0.51128 \(\times\) B \(-\) 12.56855 \(\times\) C \(+\) 0.049613 \(\times\) A \(\times\) B \(-\) 0.111 \(\times\) A \(\times\) C \(-\) 0.077228 \(\times\) B \(\times\) C \(+\) 0.0193422 \(\times\) A\({}^{2}\) \(+\) 0.045175 \(\times\) B\({}^{2}\) \(+\) 1.10135 \(\times\) C\({}^{2}\)  
The distribution of the predicted and measured values is shown in Figure 5.  
It can be seen from the above figure that the fit between the predicted value and the measured value is good, indicating that the fitting equation was selected accurately. There are 5 test groups with air void contents greater than 6% in the figure, exceeding the \"Technical Specifications for Highway Asphalt Pavement Construction\" (JTG F40-2004) regulations [42]; therefore, it is necessary to limit the scope when optimizing the impact factor. Using the same method as Section 3.1.1, the contour plot and the response surface plot between the air voids and each influencing factor were drawn. The results are shown in Figure 6.  
Figure 5: The measured and predicted values of the air voids. Figure 6: _Cont._  
According to Figure 6, the addition of BF leads to an increase of the air voids in the asphalt mixture, while the addition of NTC reduces the air voids in the asphalt mixture; the interaction between NTC and the BF modifier is obvious. On the premise that the asphalt-aggregate ratio is 5.5%, when the NTC content is 1.0% the fiber content increases from 1.0% to 7.0%, while the air voids only increase by about 1.0%. When the NTC content is 9.0%, the fiber content increases from 1.0% to 7.0% and the air voids increase by about 3.0%. When the fiber content is 1.0%, during the increase of the NTC content the air voids decreases by about 4.0% and the effect is more obvious. When the fiber content is 7.0%, the increase of NTC reduces the air voids by about 1.0% and the effect is greatly reduced.