## 3 Materials and Methods  
### Finite Element Model of the Road Pavement Structure  
The mechanical road pavement structure design is based on the theory reported in [13; 14; 15], modelling real road pavement structures as a flexible multi-layered system on a linear elastic, homogeneous, and isotropic half-space (multi-layer elastic analysis; MLEA). In this model, the mechanical behaviour of a layer of thickness \(h\) is given by the elastic or [PERSON]'s modulus \(E\) and the transverse contraction or [PERSON]'s ratio \(\mu\), according to [PERSON]'s law. Layers have absolute adhesion within the structure with no slipping at their boundaries. In addition to the MLEA theory, thanks to the work advanced in [16], finite element modelling has been implemented in the study of road pavement structures since the end of the 1960s because, among others, it allows one to consider the non-linear behaviour of materials. A typical feature of the finite element method is that the infinite domains used in analytic solutions become finite. This feature is, sometimes, not reasonable, mainly in tasks including infinite or half-infinite continuums. In the case of road pavement structures, the problem occurs at the lowest layer, the subgrade, modelled as a homogeneous infinite half-space. The solution is provided by infinite finite elements, suitable for describing even infinite partial domains. Table 2 summarises the layer system and mechanical characteristics of the layers of the analysed road pavement structure. The finite element model (Figure 2) prepared for this research study consisted of a cylindrical domain of the road pavement structure, where there were C3D8I (8-node linear) finite elements, surrounded, at the boundary in the radial direction, by CIN3D8 (8-node linear) infinite elements; additionally, at the bottom of the subgrade below, we considered there to be a transition into infinite elements (to control the size of the depression). In ABAQUS software, at the definition of infinite elements, the numbering of nodes needs to be considered, because only the first surface of an infinite element can be interconnected to the finite element mesh. Edges starting from boundaries head toward the direction considered as infinite and are located around a pole. According to the theory, the solution for the infinite space is approximated along these edges, while the elongations of these edges within the boundary meet in a pole. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type Types**} & \multicolumn{4}{c}{**Model Parameters**} \\ \cline{2-5}  & \(a_{1}\) & \(a_{2}\) & \(b_{1}\) & \(C^{{}^{\prime}}\) \\ \hline
07.50–15 Michelin Radial & \(-\)0.0029 & 13.0 & 0.520 & 52.0 \\ \hline
08.25–20 \(\times\) 10 Firestone Transport & 0.0130 & 10.5 & 0.119 & 125.9 \\ \hline
09.00–20 \(\times\) 10 Firestone & 0.0240 & \(-\)0.9 & \(-\)0.001 & 259.6 \\ \hline
10.00–20 \(\times\) 14 Papaleguas Goodyear Brazil & 0.0020 & 6.8 & 0.330 & 110.0 \\ \hline
11.00–20 \(\times\) 14 General SDT & 0.0080 & 2.3 & 0.040 & 313.0 \\ \hline
11.00–22 \(\times\) 14 General Jet Cargo & 0.0090 & 2.6 & 0.098 & 211.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Relationship among contact pressure, inflation pressure, and wheel load, according to [11]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer Name** & **Thickness, h (mm)** & **Young’s Modulus, E (MPa)** & **Poisson’s Ratio, \(\mu\) (-)** \\ \hline Asphalt wearing course & 40 & 4000 & 0.35 \\ \hline Asphalt binder and base & 200 & 5500 & 0.35 \\ \hline Crushed stone base & 250 & 350 & 0.40 \\ \hline Subgrade & infinite & 50 & 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Layers and their linear elastic material characteristics in the analysed road pavement structure. Consequently, the proper positioning of nodes in the infinite direction is important, as their distance from the pole is two-fold, compared to the nodes on the boundary.