# Unsteady-State Creep of an Asphalt Concrete
## 4 Results and Discussion
### Unsteady-State Creep Approximation  
The graphs of Figure 3 represent the unsteady-state creep curve of the asphalt concrete constructed according to the experimental data obtained at various stresses and different temperatures. The experimentally obtained strain values are dotted in these figures, and the lines represent the relevant approximations according to Expression (5). As it is seen, the compliance of the approximating curves and the experimental strains is very good. Such good compliance of the experimental and the calculated strains is obtained practically at all the considered stresses and temperatures. Figure 3: Unsteady-state creep curves of the asphalt concrete: (**a**)—T = 24 \({}^{\circ}\)C, (**b**)—T = 36 \({}^{\circ}\)C, (**c**)—T = 48 \({}^{\circ}\)C, (**d**)—T = 60 \({}^{\circ}\)C: \(\circ\) experiment, — approximation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation of** & **Description of a Characteristic** \\ \hline I & unsteady-state creep site \\ \hline II & steady-state creep site \\ \hline III & accelerating creep site \\ \hline \(\Delta\)t\({}_{1}\) & unsteady-state creep site duration \\ \hline \(\Delta\)t\({}_{2}\) & steady-state creep site duration \\ \hline \(\Delta\)t\({}_{3}\) & accelerating creep site duration \\ \hline \(\epsilon\)\({}_{1}\) & strain in the end of Site I (in the beginning of Site II) of a creep curve \\ \hline \(\epsilon\)\({}_{2}\) & strain in the end of Site II (in the beginning of Site III) of a creep curve \\ \hline \(\epsilon\)\({}_{3}\) & failure strain corresponding to failure time \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of the creep curve characteristics. The values of the parameters \(\varepsilon_{0}\), \(\alpha\) and \(\delta\) for the unsteady-state creep curves shown in Figure 3 and found according to the method specified in the Section 3.3 are represented in Table 4.  
Figure 4 shows the dependence of the parameter \(\alpha\) on a stress. It is seen that the average values of the parameter \(\alpha\) at all the stresses and temperatures are concentrated near the value of 0.5. Meanwhile, the scatter of the average values of the parameter \(\alpha\) decreases with the temperature reduction. Meanwhile, the scattering in the values of the parameter \(\alpha\) at temperatures from \(-12\) to \(+12\)\({}^{\circ}\)C is insignificant, and there are significant scatters at temperatures from \(+24\) to \(+60\)\({}^{\circ}\)C. Therefore, it is recommended in the calculations to accept the parameter \(\alpha\) value equal to 0.5 at different stresses in the temperature range from \(-12\) to \(+12\)\({}^{\circ}\)C and to accept its values determined experimentally for specific stresses in the temperature range from \(+24\) to \(+60\)\({}^{\circ}\)C.  
Therefore: (1) it can be stated that Expression (5) with the parameters \(\varepsilon_{0}\), \(\alpha\) and \(\delta\) determined according to the method specified in Section 3.3 describes the unsteady-state creep of the asphalt concrete with a high accuracy; (2) we have the analytical expression (5) for the unsteady-state creep of the asphalt concrete which can be used for the analysis of its other physical and mechanical characteristics. Figure 5 represents graphical data showing sensitivity of Expression (5) for the unsteady-state creep of the asphalt concrete to variations of the parameters: \(\alpha\), \(\delta\) and \(\varepsilon_{0}\). The following four values of parameters have been adopted in the sensitivity calculations: reduced by 5 and 10%and increased by 5 and 10%. As can be seen, the strain is more sensitive to variation of the parameter \(\alpha\); especially, a reduction in its value by 10% causes a lot of scattering. The scattering increases with time fast; it can achieve the value of 220% at long duration of the stress.