## 3 Results and Discussion
### Analysis of Response Output Index Results
#### 3.1.3 Marshall Stability  
The quadratic equation was selected as the design model for the fitting calculation. Then, the variance test was performed. The results are shown in Table 16.  
Figure 6: Contour maps and response surface maps of the air voids and influencing factors. (**a**) Contour map between basalt fiber content, NTC content and air voids; (**b**) Three-dimensional surface graph between basalt fiber content, NTC content and air voids: (**c**) Contour map between basalt fiber content, asphalt–aggregate ratio and air voids; (**d**) Three-dimensional surface graph between basalt fiber content, asphalt–aggregate ratio and air voids; (**e**) Contour map between asphalt–aggregate ratio, NTC content and air voids; (**f**) Three-dimensional surface graph between asphalt–aggregate ratio, NTC content and air voids.  
\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 & 38.08 & 9 & 4.23 & 18.95 & 0.0004 & \(\surd\) \\ A: Fiber Content & 0.086 & 1 & 0.086 & 0.39 & 0.5543 & \(\times\) \\ B: Nano-Material Content & 0.11 & 1 & 0.11 & 0.48 & 0.5112 & \(\times\) \\ C: Asphal\(-\)aggregate Ratio & 1.25 & 1 & 1.25 & 5.61 & 0.0497 & \(\surd\) \\ AB & 0.29 & 1 & 0.29 & 1.29 & 0.2928 & \(\times\) \\ AC & 0.11 & 1 & 0.11 & 0.51 & 0.4982 & \(\times\) \\ BC & 0.076 & 1 & 0.076 & 0.34 & 0.5788 & \(\times\) \\ A? & 4.24 & 1 & 4.24 & 19 & 0.0033 & \(\surd\) \\ B2 & 2.46 & 1 & 2.46 & 11.04 & 0.0127 & \(\surd\) \\ C? & 26.79 & 1 & 26.79 & 119.98 & \(<\)0.0001 & \(\surd\) \\ Residual & 1.56 & 7 & 0.22 & — & — & — \\ Mismatch & 1.56 & 3 & 0.52 & — & — & — \\ Pure Error & 0 & 4 & 0 & — & — & — \\ Total Deviation & 39.64 & 16 & — & — & — & — \\ \hline \hline \end{tabular}
\end{table}
Table 16: Marshall stability variance test table.  
According to the analysis of variance, the fitting equation of the Marshall stability can be obtained:  
Marshall stability \(=-22.60123+0.832535\times\mathrm{A}+0.72266\times\mathrm{B}+12.03306\times\mathrm{ C}-0.022396\times\mathrm{A}\times\mathrm{B}+0.037500\times\mathrm{A}\times\mathrm{C}-0.022917 \times\mathrm{B}\times\mathrm{C}-0.1115278\times\mathrm{A}^{2}-0.047813\times \mathrm{B}^{2}-1.12111\times\mathrm{C}^{2}\)  
The distribution of the predicted and measured values is shown in Figure 7.  
It can be seen from the above figure that the fit between the predicted value and the measured value obtained by the equation is good, indicating that the fitting equation was selected accurately. Using the same method as Section 3.1.1, the contour plots and the response surface plots between the Marshall stability and each influence factor were drawn. The results are shown in Figure 8.  
Figure 8: _Cont_.  
Figure 7: The measured value and the predicted value for the Marshall stability.  
It can be seen from the surface graph that the incorporation of fiber and NTC significantly improves the Marshall stability of the asphalt mixture, but as the amount of both increases the Marshall stability first increases and then decreases. When the content of the fiber or NTC is too high or too low, the influence of other modifiers on the Marshall stability will become greater. The asphalt-aggregate ratio has a greater influence on the Marshall stability. The Marshall stability of the mixture will increase first and then decrease with the increase of the asphalt-aggregate ratio.