## 3 Results and Discussion
### Creep Characteristics of the Three Asphalt Mixtures  
#### 3.2.1 Fitting Analyses of Creep Compliance  
To better characterize the creep properties of the three types of asphalt mixtures, the Burgers model and the generalized Kelvin model are used to fit the curve of the creep compliances (\(J(t)\)) of the asphalt mixtures with time. The expressions of the Burgers model and the generalized Kelvin model are shown in Equation (12) and (13), respectively [25; 41; 42].  
\[J(t)=\frac{1}{E_{1}}+\frac{t}{\eta_{1}}+\frac{1}{E_{2}}[1-\exp(-\frac{E_{2}t}{ \eta_{2}})] \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types** & \(A\) & \(E\) **(k))** & \(\mathbf{R^{2}}\) & **Equation** \\ \hline AM & 0.3768 & 122.22 & 0.99963 & \(\alpha_{\text{T}}=0.3768\times\exp[14701\times(1/\text{T-1/323.15})]\) \\ DBFAM & 0.2804 & 146.01 & 0.99999 & \(\alpha_{\text{T}}=0.2804\times\exp[17562\times(1/\text{T-1/323.15})]\) \\ SBSAM & 0.5238 & 156.14 & 0.99998 & \(\alpha_{\text{T}}=0.5238\times\exp[18781\times(1/\text{T-1/323.15})]\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: The fitting results of the shift factors.  
Figure 3: Creep compliances at different temperatures and the fitting results of generalized Kelvin model: (**a**) AM; (**b**) DBFAM; (**c**) SBSAM.  
The Burgers model is composed of a Maxwell model and a Kelvin model in series. \(E_{1}\) and \(\eta_{1}\) are the elastic modulus and the viscosity coefficient of the Maxwell model, respectively; \(E_{2}\) and \(\eta_{2}\) are the elastic modulus and the viscosity coefficient of the Kelvin model, respectively.  
\[J(t)=J_{0}+\frac{t}{\eta_{0}}+\sum_{i=1}^{n}J_{i}[1-\exp(-\frac{t}{\tau_{i}})] \tag{13}\]  
where \(J_{0}\) is the glassy compliance, \(\eta_{0}\) is the long-time viscosity or the zero-shear viscosity. For the viscoelastic solids, \(\eta_{0}\rightarrow\infty\)[43]. \(J_{i}\) and \(\tau_{i}\) are the retardation strengths and the retardation times, respectively. The retardation times \(\tau_{i}\) are fixed to the constants, \(\tau_{i}=2\times 10^{(i-3)}\) (\(i=1,\,2,\cdots,\,12\)).  
The 1 stopt software is used to fit the creep compliances of the three asphalt mixtures shown in Figure 3 based on the Burgers model and the generalized Kelvin model. The fitting results of the parameters are shown in Table 7 and Figure 3. It can be seen from the correlation coefficient R\({}^{2}\) of the parameters that both the Burgers model and the generalized Kelvin model can better reflect the creep deformation tendency of the asphalt mixtures under constant load. It can also be found that the generalized Kelvin model is superior to the Burgers model in characterizing the creep compliance variation of three asphalt mixtures at different temperatures. The parameters obtained by fitting the generalized Kelvin model can perfectly reflect the development trend of creep compliance of the asphalt mixtures with the loading time, which can provide more reliable material performance parameters for the finite element simulation calculation of asphalt mixtures. But, due to its excessive parameters, the generalized Kelvin model is difficult in reflecting the variation of asphalt mixture performance with the test temperature. However, the parameters obtained by the Burgers model can better reflect the changes of viscoelastic properties of three asphalt mixtures with temperature, which are characteristics not reflected in the generalized Kelvin model.