## 3 Results and Discussion  
### Creep Compliance of Asphalt Mixtures at Different Temperatures  
According to the static creep tests, the creep compliances of three samples with each asphalt mixture were tested and calculated from 10 \({}^{\circ}\)C to 50 \({}^{\circ}\)C at 10 \({}^{\circ}\)C increments. The average results of the three asphalt mixtures are shown in Figure 2. It can be seen from Figure 2 that in the initial stage, the creep compliances of the three asphalt mixtures grow rapidly with the increase of the loading time and the test temperature, respectively, and grows slowly in the late stage. According to the TTEP, the creep compliances of asphalt mixtures at low temperatures can be obtained by horizontally shifting the high-temperature creep curves in logarithmic coordinates [37; 38]. The shifting distance is called the shift factor and can be obtained by the overlap area surrounded by the displacement curve and the reference curve. And the shift factors can be calculated by Equation (10) [39]. The calculation results of the shift factors of the three asphalt mixtures at different temperatures are shown in Table 5.  
According to the Arrhenius equation, there is a relationship between the shift factors of asphalt mixture and the experimental temperatures, which is shown in Equation (11) [25; 40]. Using the Origin numerical processing software, the trends of shift factors with test temperatures for three asphalt mixtures are fitted by the Arrhenius equation. The fitting results of the parameters are shown in Table 6. Using the fitting results of the Arrhenius equation in Table 6, the shift factors of 0 \({}^{\circ}\)C, \(-\)10 \({}^{\circ}\)C, \(-\)20 \({}^{\circ}\)C relative to 50 \({}^{\circ}\)C are calculated as shown in Table 5. The creep compliance curves at 0 \({}^{\circ}\)C, \(-\)10 \({}^{\circ}\)C, \(-\)20 \({}^{\circ}\)C can be obtained by the calculated shift factors and the creep results measured by experiments, as shown in Figure 3.  
\[\log\alpha_{T}=\frac{\sum\limits_{k=1}^{m+n}(x_{k}y_{k+1}-x_{k+1}y_{k})}{(y_{ m}-y_{1}+y_{m+1}-y_{m+n})} \tag{10}\]  
where \(\log\alpha_{T}\) is the shift factor of the shift creep curve at T \({}^{\circ}\)C relative to the reference creep curve at T \({}_{0}\)\({}^{\circ}\)C; m and n are the number of points on the reference curve and the shift curve in the overlap region, respectively; \(x_{k}\) and \(y_{k}\) are the horizontal and vertical coordinates on the creep curve in logarithmic coordinates, respectively; \(y_{1}\) and \(y_{m}\) are the minimum ordinate and the maximum ordinate of the overlap region of the reference curve in logarithmic coordinates, respectively; \(y_{m+1}\) and \(y_{m+n}\) are the maximum ordinate and the minimum ordinate of the overlap region of the reference curve in logarithmic coordinates; respectively. \[\alpha_{T}=A\times\exp[\frac{E}{R}\times(\frac{1}{T}-\frac{1}{T_{0}})] \tag{11}\]  
where \(A\) is a constant of the material; \(E\) is the creep activation energy, kJ; \(R\) is the universal gas constant, 8.314 J/(mol\(\cdot\)K); T and T\({}_{0}\) are the test temperature and the reference temperature, respectively, both of which are absolute temperature, K. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Comparison** & \multicolumn{4}{c}{**log \(\alpha_{\text{T}}\) Based on Tests**} & \multicolumn{4}{c}{**log \(\alpha_{\text{T}}\) Based on Arrhenius Equation**} \\ \cline{2-9}
**Temperature** & **40 °C** & **30 °C** & **20 °C** & **10°C** & **0 °C** & **-10 °C** & **-20 °C** \\ \hline AM & 0.4816 & 0.9981 & 1.5865 & 2.3674 & 3.1927 & 4.0809 & 5.0393 \\ DBFAM & 0.5076 & 1.0451 & 1.8972 & 2.8168 & 3.7683 & 4.8294 & 5.9744 \\ SBSAM & 0.7208 & 1.5078 & 2.3363 & 3.3218 & 4.3393 & 5.4741 & 6.6984 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The shift factors at 50 °C reference temperature. Figure 2: Creep compliances at different temperatures: (**a**) asphalt mixture (AM); (**b**) diatomite and basalt fibers reinforced asphalt mixture (DBFAM); (**c**) styrene-butadiene-styrene modified asphalt mixture (SBSAM).