# Settlement Foundations by Exploring the Collapse of Unsaturated Soils
## 3 Validation of the Theoretical Framework
### Collapse Settlements  
Figure 8 illustrates the variation in \(\uplambda\)(s), the compression index, at the current suction within the soil layer. Before the rain, \(\uplambda\)(s) is only governed by the initial conditions and is adopted in the numerical model. However, when the infiltration starts, \(\uplambda\)(s) is determined from the suction calculated by the hydraulic model. During the infiltration, the \(\uplambda\)(s) values change, leading to deformation in the foundation. After 60 days of infiltration, the \(\uplambda\)(s) values, except in some parts below the footing, become nearly the same as \(\uplambda\)(0) in almost all parts of the soil profile. The footing pressure versus the settlement after the infiltration is shown in Figure 9. As can be seen, infiltration causes an additional settlement at a constant footing pressure. This additional settlement reproduces the behavior of the unsaturated soil upon wetting, known as wetting-induced collapse, as shown in Figure 9. This indicates that when the soil is gradually wetted, the suction is reduced, resulting in additional settlement until it becomes fully saturated. The apparent pre-consolidation stress and cohesion diminish as a result of the decreased suction, which in turn decreases the soil's yield surface and, eventually, the strength of the soil. This poses a major stability concern, even in soils like sandy soil [61]. This phenomenon is captured by the EBBM model, which takes into account the reduction in suction caused by infiltration and the corresponding decrease in strength. The vertical displacement of the top layer due to rainfall is presented in Figure 10. It is worth mentioning that the maximum vertical displacement is not centered on the footing but displaced toward the corner. This is because the corner of the footing is exposed to more infiltration and experiences a greater reduction in suction, as depicted in Figure 7. According to the results, the profile of suction at 30 and 60 days nearly remains unchanged. This trend can be attributed to most of the soil collapse occurring within 30 days of infiltration. However, at the center of the footing, the suction profile shows less reduction, which results in a less deformation (see Figure 10). Figure 11 shows the settlement induced by infiltration in the shallow foundation. Initially, the rate of collapse potential is high, but toward the final days, the soil layer experiences minimal settlement,  
Figure 8: The evolution of the compression index (\(-\)): (**a**) before infiltration and (**b**) after infiltration. Figure 7: Suction profile changes with depth due to wetting: (**a**) at the corner of the footing and (**b**) at the center of the footing. with insignificant volumetric changes. This is because when the suction approaches zero, the structure experiences insignificant settlement and negligible volumetric changes. Figure 12 shows the volumetric plastic strain of the soil profile. Generally, during the loading phase (before raining), the peak values of volumetric plastic are concentrated around the footing. However, the collapse of the soil layer induces a considerable expansion of the plastic zone after 60 days of infiltration, with the maximum plastic deformations occurring around the corner of the footing at the surface. Under such conditions, infiltration triggers plastic yielding, resulting in a reduction in the soil volume. This behavior, which contributes to the collapse of the soil, is effectively represented by the EBMM model. Figure 11: Induced settlement by infiltration in a shallow foundation. Figure 10: Vertical Displacement of Soil due to Infiltration. Figure 9: Footing pressure versus settlement. To evaluate the collapse potential of this studied soil, the following simple equation can be used:  
\[CP=\frac{\Delta H}{H}\times 100 \tag{11}\]  
H is the layer's height and \(\Delta\)H is its maximum vertical settlement. If we assume that the active layer is above the groundwater and that the entire layer is wetted, then H0 = 1.35 m and \(\Delta H=17\) mm.