## 4 Results and Discussion
### Assessment of Tyre Models Considering the Road Pavement Structure
\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** \\ **(kN)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} \(q\) \\ **(kPa)** \\ \end{tabular} } & \multicolumn{4}{c}{**A**} & \multicolumn{4}{c}{**B**} & \multicolumn{4}{c}{**C**} \\ \cline{3-14}  & & & \(u_{zz}\) & & & \(\varepsilon_{xx}\) & & & \(\varepsilon_{yy}\) & & \(\varepsilon_{zz}\) \\ \cline{2-14}  & & **FEM** & **MLEA** & **Error** & **FEM** & **MLEA** & **Error** & **FEM** & **MLEA** & **Error** \\ \hline
17.5 & 385 & \(-0.190\) & \(-0.293\) & 54.5\% & 64,231 & 62,750 & \(-2.3\%\) & 37,338 & 35,800 & \(-4.1\%\) & \(-172,790\) & \(-179,150\) & \(3.7\%\) \\
20.0 & 408 & \(-0.217\) & \(-0.335\) & 54.5\% & 72,651 & 71,230 & \(-2.0\%\) & 43,006 & 41,280 & \(-4.0\%\) & \(-196,978\) & \(-204,390\) & \(3.8\%\) \\
22.5 & 430 & \(-0.244\) & \(-0.377\) & 54.6\% & 80,737 & 79,570 & \(-1.4\%\) & 48,678 & 46,840 & \(-3.8\%\) & \(-220,907\) & \(-229,540\) & \(3.9\%\) \\
20.0 & 415 & \(-0.217\) & \(-0.335\) & 54.5\% & 73,055 & 71,620 & \(-2.0\%\) & 42,195 & 40,990 & \(-2.9\%\) & \(-196,690\) & \(-204,670\) & \(4.1\%\) \\
22.5 & 438 & \(-0.243\) & \(-0.377\) & 55.2\% & 81,511 & 80,200 & \(-1.6\%\) & 47,808 & 46,390 & \(-3.0\%\) & \(-220,820\) & \(-229,990\) & \(4.2\%\) \\
25.0 & 460 & \(-0.270\) & \(-0.419\) & 55.2\% & 89,684 & 88,270 & \(-1.6\%\) & 53,424 & 52,140 & \(-2.4\%\) & \(-244,752\) & \(-254,950\) & \(4.2\%\) \\
22.5 & 445 & \(-0.242\) & \(-0.377\) & 55.9\% & 81,718 & 80,420 & \(-1.6\%\) & 46,998 & 46,230 & \(-1.6\%\) & \(-220,251\) & \(-230,150\) & \(4.5\%\) \\
25.0 & 468 & \(-0.269\) & \(-0.419\) & 55.8\% & 90,180 & 89,030 & \(-1.3\%\) & 52,563 & 51,610 & \(-1.8\%\) & \(-244,314\) & \(-255,490\) & \(4.6\%\) \\
27.5 & 491 & \(-0.296\) & \(-0.461\) & 55.7\% & 98,429 & 96,950 & \(-1.5\%\) & 58,142 & 57,460 & \(-1.2\%\) & \(-268,243\) & \(-280,330\) & \(4.5\%\) \\
25.0 & 475 & \(-0.268\) & \(-0.419\) & 56.4\% & 90,178 & 89,250 & \(-1.0\%\) & 51,714 & 51,450 & \(-0.5\%\) & \(-243,319\) & \(-255,640\) & \(5.1\%\) \\
27.5 & 498 & \(-0.294\) & \(-0.461\) & 56.8\% & 98,639 & 97,820 & \(-0.8\%\) & 57,240 & 56,850 & \(-0.7\%\) & \(-267,326\) & \(-280,950\) & \(5.1\%\) \\
30.0 & 521 & \(-0.321\) & \(-0.503\) & 56.7\% & 106,925 & 105,780 & \(-1.1\%\) & 62,776 & 62,680 & \(-0.2\%\) & \(-291,213\) & \(-305,830\) & \(5.0\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Critical stresses and strains between two tyres based on the twin tyre finite element simulation (FEM) and the substituting circular plate model (MLEA). \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** \\ **(kN)** \\ \end{tabular}  } & \multicolumn{4}{c}{**D**} & \multicolumn{4}{c}{**E**} & \multicolumn{4}{c}{**F**} \\ \cline{2-14}  & & & \(u_{zz}\) & & & \(\varepsilon_{xx}\) & & & \(\varepsilon_{yy}\) & & \(\varepsilon_{zz}\) & \\ \cline{2-14}  & & **FEM** & **MLEA** & **Error** & **FEM** & **MLEA** & **Error** & **FEM** & **MLEA** & **Error** & **FEM** & **MLEA** & **Error** \\ \hline
17.5 & 395 & \(-0.194\) & \(-0.295\) & 52.1\% & 61,187 & 60,080 & \(-1.8\%\) & 41,607 & 42,730 & 2.7\% & \(-161,948\) & \(-168,540\) & 4.1\% \\
20.0 & 412 & \(-0.220\) & \(-0.336\) & 52.7\% & 69,016 & 67,970 & \(-1.5\%\) & 46,945 & 48,270 & 2.8\% & \(-184,614\) & \(-192,280\) & 4.2\% \\
22.5 & 430 & \(-0.246\) & \(-0.378\) & 53.7\% & 76,520 & 75,690 & \(-1.1\%\) & 52,174 & 53,670 & 2.9\% & \(-207,093\) & \(-215,920\) & 4.3\% \\
20.0 & 440 & \(-subgrade (Points C and F), there was a slightly greater difference of 4-5%, the analytic solution being higher; however, it can still be regarded as being in good agreement. Based on the data in Tables 11 and 12, it can be stated that stresses and strains for asphalt layer fatigue (Points B and E) and for subgrade compression (Points C and F) criteria can be accurately estimated by applying an evenly distributed load system on two circular plates substituting twin tyres, choosing the average contact stress \(q\) in a realistic way.