## 3 Results and Discussion
### Compressibility Curve
#### 3.2.1 Saturated Condition  
Figure 7a shows the compressibility curve of the tailings sample subjected to an oedometer test. It reveals a progressive decrease in the void ratio as the vertical load increases, indicating that the soil compresses under load.  
Up to 10 kPa, the void ratio reduction reaches e = 0.78, corresponding to a 2% decrease relative to its initial void ratio. From 10 kPa onward, a significant change in the curve's slope is observed, reflecting increased soil compressibility. At the end of the final load application (3200 kPa), the void ratio reaches e = 0.38, corresponding to a 52% decrease  
Figure 7: Compressibility curve for saturated models: (**a**) Experimental model. (**b**) Experimental and Soft Soil. (**c**) Experimental and Hardening Soil. (**d**) Experimental and HS = 99%.  
from e0. During the unloading phase, the void ratio recovers to a maximum of e = 0.41 at 50 kPa.  
Figure 7b,c illustrate how both constitutive models behave similarly throughout most of the load range, suggesting that the models may be suitable for representing the actual behavior of the soil under the specified conditions [35]. The SS_Sat model shows a void ratio reduction similar to the experimental model across the load range, with only an average deviation of 0.01%. The most significant discrepancies occur at the beginning and end of the virgin compression phase, where the Soft Soil model shows a 1% reduction compared to the experimental model.  
On the other hand, the Hardening Soil model exhibits a noticeable void ratio reduction at the end of its recompression phase compared to the experimental curve (Figure 7c), corresponding to a 3% difference. Among the saturated models, Soft Soil and Hardening Soil align at only one point in their void ratio within the load range, occurring at 200 kPa. The greatest divergences are at the beginning and end of the virgin compression phase, differing by 3%.  
Figure 7d shows the volumetric strain of the saturated models and the Sr = 99% model. The three models display similar behavior (up to 50 kPa); however, beyond this point, significant variations occur between the curves, with the most notable difference observed at 400 kPa. At this load, the HS_99% model increases by 9% compared to the HS_Sat and SS_Sat models.  
The Soft Soil model exhibits lower recovery because it assumes dominant plastic compression with a relatively low elastic response [15]. This implies that, after being subjected to a range of loads (10-3200 kPa), the soil modeled by Soft Soil does not recover as much volume as other models.  
On the other hand, the Hardening Soil model has a more advanced and robust formulation that accounts for compression hardening, allowing it to capture a nonlinear and load-dependent response [10; 36]. This model may exhibit more significant expansion during unloading because it incorporates more detailed elastoplastic components, enabling the soil to recover more of the deformation experienced [16].  
These two behaviors can be seen in Figure 8, which shows that, during the unloading phase, the SS_Sat model displays an almost horizontal slope, maintaining a volumetric strain of \(\epsilon_{\mathrm{v}}=-24\%\), whereas the HS_Sat model shows greater recovery in this phase, reaching \(\epsilon_{\mathrm{v}}=-21\%\).  
Figure 8: Volumetric deformation (\(\epsilon\mathrm{v}\)) at each vertical stress for saturated models and Sr = 99%.  
As the load increases, the HS_99% model reaches a maximum difference of 13% during loading and 24% during unloading, implying greater volume recovery, as shown in Figure 8.