## 5 Numerical Analysis
### Modeling Procedure  
Numerous geotechnical issues are addressed with the Mohr-Coulomb model (MC model) as it only needs a small number of input parameters that may be obtained by laboratory experiments [55]. The Mohr-Coulomb (MC) model is widely used in the numerical modeling of embankments [56]. The MC model is suitable for sand as well as clay [57]. Therefore, the Mohr-Coulomb model, a perfect plastic model for analyzing such soils, was employed here for subgrade, and foundation. The material properties are shown in Table 3.  
In this study, the numerical analysis was carried out for the road section at Km 38+000 using the Abaqus CAE 2021 software using reinforced and unreinforced cases. In this analysis, the vertical deformations were calculated for the new road during one year of construction and nine years of operation. The construction phases of the new and old roads were not considered, and it was assumed that consolidation of the old road had already been completed. The finite element model was set so as to make it an actual representation of N-120. In the numerical analysis, the old road plus the foundation was considered part 1 and the new road part 2 in the Abaqus software environment. The overall analysis progress was divided into three steps. The old road was set to be active since the geostatic phase, and the widened part was set to be active since the first year of operation. The  
Figure 11: Geometry of the model (units in mm). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & **Density** & **Modulus of** & **Poisson** & **Cohesion** & **Dilation** & **Friction** & **Permeability** & **Void** \\  & **(kg/m\({}^{3}\))** & **Elasticity** & **Ratio** & **(kPa)** & **Angle (\({}^{\circ}\))** & **Angle (\({}^{\circ}\))** & **Angle (\({}^{\circ}\))** & **(m/s)** & **Ratio** \\ \hline Natural Ground & 2140 & 16.3 & 0.32 & 20 & 1 & 31 & \(1\times 10^{-9}\) & 0.43 \\ \hline New Road & 2060 & 20.4 & 0.32 & 25 & 0 & 30.1 & \(1\times 10^{-9}\) & 0.44 \\ \hline Old Road & 2210 & 13.6 & 0.32 & 0 & 0 & 28.8 & \(1\times 10^{-9}\) & 0.39 \\ \hline \multirow{2}{*}{Pavement} & 1900 & 1400 & & & & & \(1\times 10^{-20}\) & 0.3 \\  & [36] & [36] & 0.4 & & & & & \\ \hline \multirow{2}{*}{Geogrid} & \multirow{2}{*}{–} & 38,700 & 0.25 & & & & & \\  & [18] & [18] & [18] & & & & & \\ \hline \multirow{2}{*}{CFG} & 2447 & 150 & 0.15 & & & & & \\  & [18] & [18] & [18] & & & & & \\ \hline Lightweight & 699 & 285 & 0.10 & & & & & \\ foamed concrete & [33] & [33] & [33] & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties. boundary conditions and traffic loads are shown in Figure 12. The bottom of the model was constrained for horizontal and vertical displacement. The horizontal displacement was limited for the left and right vertical sides of the model. Geostatic stresses were created in the geostatic step. The gravity load was applied on the new road, and the traffic load was applied since the geostatic step on the old road surface and in the second step on the new road surface. The numerical analysis used a 4-node plane strain quadrilateral, bilinear displacement, and bilinear pore pressure (CPE4P) for parts 1 and 2, as described above. The mesh size of the element used was 0.2 for both parts having quad and structured shapes. The mesh density for part 1 was 2252 elements with 0% errors. The mesh density for the new road was 197 elements, with 0% errors and 10% warnings. The unreinforced model was the basis; therefore, geogrid was considered part 3 and CFG piles as part 4 in the remaining cases for parametric study. The geogrid was modeled in a 4-node bilinear plane strain quadrilateral, reduced integration unit in Abaqus (CPE4R). The CFG piles with a diameter of 0.5 m [18] were modeled in a 4-node bilinear plane stress quadrilateral, reduced integration (CPS4R). The mesh element shape was quad and structured, and the element size used was 0.2 units for both geogrid and CFG piles.