## 4 Results and Discussion
### Assessment of Tyre Models Considering the Road Pavement Structure  
The stresses and strains in the flexible road pavement structure calculated by the two types of finite element tyre models, between two tyres of a twin tyre (at the axis of the twin tyre), are summarised in Table 9, while those straight below the tyre are summarised in Table 10. The first row of the tables' heading contains the analysed points (from A to F) in the road pavement structure, illustrated in Figure 7. A significant difference is visible in case of the vertical \(u_{zz}\) displacements or deflections below the tyre (Point D). This can be explained by the fact that the simplified tyre model had a higher contact stress at the direct contact point. The same explanation is valid for the higher \(\varepsilon_{yy}\) specific strains in the lower part of the asphalt layer (Point E). These differences decreased at the axis of the twin tyre (Points A and B), since the contact area of the simplified tyre model was smaller; therefore, it had less effect on more distant places. The \(\varepsilon_{zz}\) specific vertical compression values on the top of the subgrade (Points C and F) are in good correlation. In practical calculations, i.e., pavement strengthening design, the loaded area of twin tyres is substituted by a circle of an area identical to the real contact area. The  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\ \begin{tabular}{c} **F/2** \\ **(kPa)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **P** \\ **(kPa)** \\ \end{tabular}  } & \multicolumn{4}{c}{**D**} & \multicolumn{4}{c}{**E**} & \multicolumn{4}{c}{**F**} \\ \cline{3-14}  & & \multicolumn{2}{c}{\(\mathbf{u}_{zz}\)} & \multicolumn{4}{c}{\(\mathbf{\varepsilon}_{xx}\)} & \multicolumn{4}{c}{\(\mathbf{\varepsilon}_{yy}\)} & \multicolumn{4}{c}{\(\mathbf{\varepsilon}_{zz}\)} \\ \cline{3-14}  & & **Complex** & **Simple** & **Error** & **Complex** & **Simple** & **Error** & **Complex** & **Simple** & **Error** & **Complex** & **Simple** & **Error** \\ \hline
17.5 & 430 & \(-0.194\) & \(-0.207\) & 6.7\% & 61,187 & 65,135 & 6.5\% & 41,607 & 46,355 & 11.4\% & \(-161,948\) & \(-165,293\) & 2.  
diameter of this substituting circle was also calculated in our research study, using the following equation:  
\[a\approx 564\sqrt{F/q}, \tag{13}\]  
where \(a\) is in mm and \(q\) is in kPa. The average contact pressure \(q\) is given by Equation (7) for the complex twin tyre model. The stresses and strains in the critical points of the flexible road pavement structure were calculated via WESLEA software, and they were compared to the results of the complex finite element twin tyre simulation (see Tables 11 and 12). The greatest differences occurred in the case of the vertical \(u_{zz}\) displacements or deflections (Points A and D). The finite element pavement structure model--despite applying infinite elements--provided significantly lower (at 50-55%) values than the calculation based on the flexible-layer theory. This can be explained by the fact that WESLEA software, based on the theory of [13; 14; 15], summarises vertical specific displacements up to the infinite, providing supposedly higher displacement values than in reality. These high differences, observed in the case of deflections, require attention in the assessment of load-bearing capacity measurements based on vertical deflections, i.e., Benkelman beam, Lacroix, or Curviameter devices. The values of the horizontal x- and y-direction \(\varepsilon_{xx}\) and \(\varepsilon_{yy}\) specific strains in the lower part of the asphalt layer (Points B and E) are in very good agreement with the results of the WESLEA software. In case of the vertical \(\varepsilon_{zz}\) specific compression on the top of the