# Numerical Study of Geotextile-Reinforced Flexible Pavement Overlying Low-Strength Subgrade
## 2 Materials and Methods
### Finite Element Modeling  
Abaqus/CAE software was used to conduct three-dimensional modeling based on the Finite Element Method as shown in. The Abaqus environment is made up of modules which define logical aspects in the modeling process, such as model geometry, material properties, and the mesh.  
The dimensions of the pavement model section considered in the study were 3500 mm in the x-direction and 5000 mm in the z-direction. In contrast, the y-direction dimension varied based on the reinforcement schemes. The expression for the global governing equation is as follows [31]:  
\[[\text{K}][\text{t}]=[\text{T}] \tag{1}\]  
where:  
\([\text{K}]=\text{global stiffness matrix}\).  
\(\{\text{t}\}=\text{global displacement vector}\).  
\(\{\text{T}\}=\text{global load vector}\).  
A linear elastic constitutive model described the material behavior of the asphalt concrete. The Mohr-Coulomb model described the characteristics of base and subgrade materials. An Equivalent Single Axle Load (ESAL) of 80 kN was considered. A static loading with an amplitude of 40 kN was applied over a square area with a side length of 2.64 mm [32] at the center of the pavement model to simulate heavy vehicular traffic. This represented half of the ESAAL considered.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Course/Layer** & **Model** & **Poisson Ratio, v** & **Elastic Modulus, E (MPa)** & **Density, \(\Upsilon\)** & **Thickness (mm)** \\ \hline AC & Linear Elastic Model & 0.35 & 2200 & 2240 & 40 \\ Base & Mohr–Coulomb Model & 0.35 & 50 & 1850 & 300 \\ Subgrade & Mohr–Coulomb Model & 0.35 & 10 & 1282 & 2000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties for the base, subgrade [26; 27], and AC [28].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & \multicolumn{3}{c}{**Mohr Coulomb Plasticity Model**} \\  & **Plasticity** & **Cohesion** \\  & **Friction Angle (\(\varphi\))** & **Dilation Angle (\(\psi\))** & **Cohesion Yield Stress (MPa)** \\ \hline Base & 40 & 10 & 0.15 \\ Subgrade & 10 & 0 & 0.0436 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mohr–Coulomb Plasticity model parameters for the base and subgrade [27].  
In defining model boundary conditions, all nodes parallel to the y-axis were free to move vertically but were constrained against horizontal movement. Encastre boundary conditions were applied at the bottom of the model, and this ensured that all degrees of freedom were constrained in the specified area (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0). The boundary conditions are shown in Figure 1a.  
A fine mesh was used at the loading area to capture the strain and stress gradients well as shown in Figure 1b. A general-purpose linear hexahedron type C3D8R was used for the elements. This type of element is advantageous because of its reduced integration. A membrane element was used to characterize the behavior of the geotextile, a three-dimensional deformable shell planar.  
The interaction feature utilized in this study is based on'master' and'slave' surfaces. The master surface defines the rigid surface, while the slave represents a deformable surface. Interaction properties included normal and tangential interactions. A tie condition was introduced to simplify the model. This ensures that every node on the slave surface is tied to the nearest node on the master surface in order to achieve perfect bonding between the pavement layers. In this case, the nodes of pavement layers at the interface experience the same magnitude of displacement in all directions, thus avoiding slippage.