# Unsteady-State Creep of an Asphalt Concrete
## 4 Results and Discussion
### Unsteady-State Creep Duration  
An important characteristic of the unsteady-state creep of a material is its duration t\({}_{1}\). The whole creep process occurs in time, including the unsteady-state creep one. The unsteady-state creep is continued only to the time t\({}_{1}\), after which another characteristic type of the creep of a material (steady-state creep) with different physical mechanisms and parameters starts. Therefore, it is very important to study the dependence of the unsteady-state creep duration on the effecting factors, and it is desirable to have a mathematical expression which describes it for practical use. The graphs showing the dependence of the unsteady-state creep duration of the asphalt concrete on a stress at all the considered temperatures are represented in Figure 6. As it is seen, the unsteady-state creep duration depends greatly on temperature as well as on stress. As one should expect, it decreases with the stress increase and the temperature increase. The dependences of the unsteady-state creep duration on stress at all the considered temperatures are satisfactorily described by the power function of the following form:  
\[t_{1}=B\cdot\sigma^{m}, \tag{8}\]  
where \(t_{1}\) is the unsteady-state creep duration, sand \(\sigma\) are stress and MPa, \(B\) and \(m\) are correlation coefficients. The correlation coefficients \(B\) and \(m\) are of physical nature. The coefficient \(B\) is numerically equal to the unsteady-state creep duration of the asphalt concrete at the stress equal to 1 MPa. Having taken the logarithm of Expression (8), we will have:  
\[\text{log}t_{1}=\text{log}B+m\cdot\text{log}\sigma. \tag{9}\]  
Figure 5: Sensitivity analysis of Equation (5): (**a**) change in \(\alpha\); (**b**) in \(\delta\); (**c**) in \(\epsilon_{0}\). It is seen from Expression (9) that the correlation coefficient \(m\) characterizes the variation rate of the unsteady-state creep duration with the stress variation, and it shows to which order the duration decreases with the stress increase by one order. The values of the correlation coefficients \(B\) and \(m\) of Equation (8) at the considered temperatures calculated by the least square method are represented in Table 5. One can see from the table that there is a reliable correlation relationship between the unsteady-strain creep duration of the asphalt concrete and a stress at all the considered temperatures. As it is seen from Equation (8), the unsteady-state creep duration \(t_{1}\) is directly proportional to the coefficient \(B\). The higher the temperature and the less the unsteady-state creep duration, the coefficient \(B\) decreases with the temperature increase. Meanwhile, it should be noted that the coefficient \(B\) is strongly varied at low temperatures; statistically it has a constant value at high temperatures (from +36 to +60 \({}^{\circ}\)C): only from the temperature of +24 \({}^{\circ}\)C it increases fast with the temperature decrease. For example, within the range of the temperatures of +24 \({}^{\circ}\)C and \(-\)24 \({}^{\circ}\)C, it increases by more than four orders. Figure 6: Graphs for the dependence of the unsteady-state creep duration for the asphalt concrete on stress at various temperatures. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Temperature, \({}^{\circ}\)C**} & \multicolumn{3}{c}{**Coefficients**} \\ \cline{2-4}  & \(B\) & \(m\) & \(\mathbf{R^{2}}\) \\ \hline +60 & 0.0046 & \(-\)2.4156 & 0.8819 \\ \hline +48 & 0.0023 & \(-\)3.1739 & 0.9627 \\ \hline +36 & 0.0072 & \(-\)3.5787 & 0.9754 \\ \hline +24 & 0.7639 & \(-\)3.4318 & 0.8277 \\ \hline +12 & 9.2648 & \(-\)4.8324 & 0.9877 \\ \hline 0 & 107.6331 & \(-\)4.4062 & 0.9820 \\ \hline \(-\)12 & 449.6749 & \(-\)4.1046 & 0.6895 \\ \hline \(-\)24 & 29,865.4511 & \(-\)6.6253 & 0.6623 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Values of the coefficients \(B\) and \(m\). Coefficient \(m\) has a negative sign, and its absolute value increases with the temperature decrease.