## 3 Results and Discussion
### Master Curve Parameters  
On the basis of previous studies and literature review [10; 39; 40; 52; 53; 56], [PERSON] model was selected as the basic equation of master curves. \"Branching\" model modification [54] was also applied for all the tested mixtures, to take into account the deviations from the time-temperature superposition principle. Parameters for asphalt mixtures derived from the TCT are presented in Table 6. Parameters for asphalt mixtures derived from the BBCT are presented in Table 7. Shift factors used in the study are presented in Figure 10.  
Basic parameters of the master curve described by the [PERSON] model in which deviations are completely omitted are presented in the first row of results for each mixture (for T \(>-20\)\({}^{\circ}\)C or T \(>-10\)\({}^{\circ}\)C, depending on the mixture and test procedure). It is visible that in the case of higher temperatures for the TCT, the \"\(\delta\)\" parameter shows consistency between all the tested mixtures, and it is always higher than 0. Determination of the same parameter for the BBCT sometimes requires setting of the minimum value of \"\(\delta\)\" as 0, as the SOLVER unit of EXCEL used in the analysis sometimes suggests values lower than 0 [40], which is in contradiction to the physical meaning of the parameter. Additional \"branches\", deviating from the master curves due to shifting of stiffness curves obtained at lower test temperatures, are presented in further rows of the tables, according to their corresponding temperature ranges. Since the shape of the deviations in the TCT is different than in the BBCT, the values of the \"\(\delta\)\" parameter for the TCT are equal across all temperatures. The \"asymptotical\" phase is not correctly described, which suggests that for the TCT a new model needs to be developed. Results presented in this study for the BBCT show full consistency with the \"branching\" modification of [PERSON] model [54], and deviations are correctly described. Two models of shift factors commonly used for binders and asphalt mixtures were used in the study--WLF and Arrhenius [52]. Arrhenius model parameters are similar for both tests, but results obtained from the BBCT presented higher homogeneity. In both cases the results were similar, both in shape and in values, to the WLF function determined for the TCT (Figure 10b). The WLF function proved more reliable when applied to the TCT results than to the BBCT results. For the BBCT test, in the case of higher temperatures, the WLF function (Figure 10a) presents a significantly different shape. While in the case of temperatures of up to 0 \({}^{\circ}\)C, the course of the line is similar to the TCT test, in the case of +10 \({}^{\circ}\)C the values decrease strongly, probably due to limitation of the BBCT test. It was impossible to obtain reliable results at temperatures higher than +15 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mixture Designation**} & \multirow{2}{*}{**Test Temperature T, \({}^{\circ}\)C**} & \multicolumn{3}{c}{**Richards Model Parameters (“Branching” Modification)**} \\ \cline{3-6}  & & **Max** & \(\beta\) & \(\gamma\) & \(\delta\) & \(\lambda\) \\ \hline AC 11S & \(>-20\) & 4.712 & \(-10.075\) & \(-0.462\) & 0.367 & 0.000615 \\
70/100 LT & \(<-20\) & 4.712 & \(-17.217\) & \(-0.279\) & 0.367 & 0.000005 \\ \hline AC 11S & \(>-20\) & 4.789 & \(-9.735\) & \(-0.451\) & 0.441 & 0.000898 \\
50/70 MT & \(<-20\) & 4.789 & \(-16.478\) & \(-0.196\) & 0.441 & 0.000001 \\ \hline AC 11S & \(>-20\) & 4.823 & \(-9.584\) & \(-0.421\) & 1.175 & 0.000566 \\
45/80-55 MT & \(-20\div-30\) & 4.823 & \(-10.698\) & \(-0.366\) & 0.823 & 0.000226 \\
45/80-55 MT & \(<-30\) & 4.823 & \(-10.424\) & \(-0.212\) & 3.786 & 0.000066 \\ \hline AC 11W & \(>-10\) & 4.935 & \(-9.703\) & \(-0.369\) & 0.284 & 0.00055 \\
35/50 MT & \(-10\div-20\) & 4.935 & \(-6.737\) & \(-0.302\) & 0.284 & 0.01074 \\
35/50 MT & \(<-20\) & 4.935 & \(-11.818\) & \(-0.213\) & 0.284 & 0.00006 \\ \hline \hline \end{tabular}
\end{table}