## 3 Results and Discussion
### Excess Pore Pressure (\(\Delta u\))  
Excess pore pressure occurs when the applied stress on the soil is transferred to the pore water rather than to the soil structure. This is common in saturated or partially saturated soils under rapid and undrained loading [40]. This section shows that excess pore pressure is not evenly distributed within the soil and varies in depth due to the soil's boundary conditions from the beginning to the end of the applied load duration for each  
Figure 9: (**a**) Compressibility curve under unsaturated condition. (**b**) Volumetric deformation (\(\varepsilon\
u\)) under unsaturated condition. vertical stress [41]. The pressure concentration tends to be higher in deeper areas where pore water has less opportunity to flow due to the confinement effect, which traps and compresses the water. Since the soil was modeled to allow drainage through the top and bottom boundaries, this \"deeper\" zone corresponds to the middle height of the soil. As the applied stress increases, this middle zone decreases size [1,40]. A vertical cross-section was taken through the middle of the model to observe the excess pore pressure within the soil. Additionally, to evaluate the behavior under all applied loads (10-3200 kPa), excess pore pressure was plotted against the model's height immediately after the load was applied. In Figure 10, only the loads of 800, 1600, and 3200 kPa are shown to demonstrate that the excess pore pressure at the boundary is zero. Lower loads exhibit the same behavior as those plotted, so they were omitted for better visualization of the graph, assuming that all analyses also apply to these smaller loads. Figure 10a shows that the difference between the Soft Soil and Hardening Soil models under saturated conditions is minimal. In all cases, excess pore pressure increases with progressively applied loads, reaching maximum values equal to the applied load in the middle zone of the soil. This is consistent with [PERSON]'s consolidation principle [1,42], where pore pressure directly depends on the magnitude of the applied load. Figure 10: \(\Delta u\) immediately after each vertical stress is applied: (**a**) \(\Delta u\) for SS y HS in saturated condition; (**b**) \(\Delta u\) for SS and HS Sr = 60% [10–50 kPa]; (**c**) \(\Delta u\) for SS y HS Sr = 60% [100–400 kPa]; and (**d**) \(\Delta u\) for SS and HS Sr = 60% [800–3200 kPa]. From the same Figure 10a, it is demonstrated that, with each increment in applied stress, there is a reduction in the constant range of excess pore pressure along the height. For instance, the constant range of excess pore pressure at 10 kPa occupies 70% of the modeled specimen height, and this percentage decreases to 37% at 3200 kPa (see Figure 10a). Figure 10b-d show the excess pore pressure under unsaturated conditions (HS_60%). It can be observed that the excess pore pressure values are significantly lower than those in saturated soils, specifically in the range of 10 to 400 kPa. According to Table 5, relevant effective suction values are present during this range of applied stress, indicating the reduction in hydrostatic pressure generated by the interstitial water [2]. As the vertical stress increases, the excess pore pressure also increases, while the effective suction decreases due to the rise in the degree of effective saturation. However, this pore pressure distribution is less uniform than saturated soils. Unlike the saturated condition, with a 60% degree of saturation, the excess pore pressure does not reach the value of the applied load. Compared to the saturated condition, this excess pore pressure is 14% lower for HS_60%_3200 and 21% lower for SS_60%_3200. Under the same initial degree of saturation, at stress levels of 3200 kPa, effective saturation reaches 100% in the models (see Table 5). However, for stress levels below 3200 kPa, where effective saturation decreases and approaches its initial value, a reduction of 14% or more is anticipated in the Hardening Soil model and 21% in the Soft Soil model.