## 2 Methodology  
In the case of unsaturated conditions, the soil's porous spaces contain both water and air, which is normal for soils above the water table. In this situation, capillarity and matrix suction play a crucial role. Capillarity allows water to rise through the soil pores, while matric suction retains water within the pores [17]. The experimental foundation of this research was based on the results of [PERSON] et al. [13], who conducted oedometer tests under saturated and unsaturated conditions. In the experimental test, the one-dimensional deformation of the soil under constant vertical stress increments provided essential data on compressibility and consolidation rate in both conditions. The load was applied to record the corresponding deformations at each increment, allowing maximum detail with the settlement data obtained over time. The constitutive models used aim to replicate the actual behavior of the material under different conditions to match the experimental response [15]. Maintaining a single set of constant parameters reduces errors or biases, increasing the model's credibility and prediction confidence. It is well known that discrepancies between experimental and modeling results are more often attributed to model assumptions or boundary conditions than parametric inconsistencies [18]. Table 1 presents the soil sample parameters used in numerical modeling with Plaxis2\(\otimes\) for both models. These parameters are the same as those used in the work of [PERSON] et al. [13]. According to the Plaxis2D\(\otimes\) manuals [12; 15], the Soft Soil model is suitable for simulating primary compressibility and long-term consolidation effects, capturing high plasticity and time-dependent deformation. In contrast, the Hardening Soil model provides a more detailed representation of nonlinear stiffness and soil hardening, providing a more comprehensive analysis under different loading and drainage conditions. These models effectively represent the experimental results observed in the oedometer test under \begin{table}
\begin{tabular}{c c} \hline \(\phi^{\prime\circ}\) (Friction angle) & 35.2 \\ \(c^{\prime}\) [kN/m\({}^{2}\)] (Cohesion) & 0 \\ \(\psi^{\circ}\) (Dilatancy angle) & 2.5 \\ \(e\) (Void ratio) & 0.8 \\ _Gs_ (Specific gravity) & 2.97 \\ \(k\) [m/s] (Permeability coefficient) & \(5\times 10^{-7}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Soil parameters used in both constitutive models. saturated and unsaturated conditions. Figure 1 shows the number of executed models (6) and their saturation conditions to analyze the simulation results of a one-dimensional consolidation test. Two models were created for the saturated condition and four for the unsaturated condition. For the latter, two models were set with an initial saturation of 60% and two more with initial saturation of 80% and 99% to compare the behavior and variation in results based on the degree of saturation. The modeling in Plaxis2D(r) was performed using an axisymmetric representation of the soil to simulate the specimen with a vertical symmetric axis. This two-dimensional representation, shown in Figure 2, was transformed into a three-dimensional model by rotating the section around its symmetry axis. This approach allows for an efficient soil and structural behavior analysis, avoiding needing a full three-dimensional model, which could be more computationally demanding [19; 20]. Figure 1: Modeling diagram. Figure 2: (a) Cylindrical laboratory specimen. (b) Applied asymmetry. (c) Hydraulic boundary conditions. (d) Displacement boundary conditions. It is well known that the displacement boundary conditions established during the oedometer test cause the soil to experience deformations only along its vertical axis (one-dimensional consolidation) when a load is applied. This occurs because pore water can only drain through the top and bottom faces of the sample, facilitated by the porous stones used in the test, which promote flow in these directions [1].