## 3 Results and Discussion
### Load-Settlement Response  
The load-settlement (q-s) curves were used to determine the ultimate bearing capacity. At high relative densities, the peak point of the q-s curve is considered the ultimate bearing capacity. The test was terminated after the peak point, when the carrying capacity decreased, and the collapse increased rapidly. Since the load-settlement curve does not peak in loose soils, the ultimate bearing capacity is accepted as the stress value when the settlement equals 10% of the foundation size (B) [8]. The graphs in Figure 11 show the changes in the normalized settlement values with the stress applied to the model foundations. As mentioned above, the ultimate bearing capacity reached around 10% of the normalized settlement values (settlement/foundation width) (Figure 11b-d).  
When the load-settlement (q-s) curves presented in Figure 11 are examined, it is observed that the curves do not show a peak in loose sands (Dr = 10%), and the settlement continues with increasing load. In contrast, a peak point was evident in dense soils, followed by post-peak softening behavior. This situation causes dense sand to accumulate more energy in the structure and experience a sudden loss of resistance [62]. This transition can be explained by the fact that loose soils become denser when compressed under load, and thus, the bearing capacity increases. The results indicate that the bearing capacity behavior depends on both the relative density and foundation size and that these two parameters should be evaluated together in terms of soil-foundation interaction. The results  
Figure 11: Normalized load–displacement curves of the model foundation at different relative densities: (**a**) Dr: 10% (**b**) Dr: 40% (**c**) Dr: 65% (**d**) Dr: 90%.  
obtained show that foundation design should be optimized according to soil properties for engineering applications.  
The effect of the relative density and foundation size on the ultimate bearing capacity (qu) of the model foundations is shown in Table 5. The ultimate bearing capacity of the smallest-size foundation increased by 1531.7% when Dr increased from 10% (qu = 30.9 kPa) to 90% (qu = 504.2 kPa); it increased by 1616.5% when Dr increased from 10% (qu = 34.5 kPa) to 90% (qu = 592.2 kPa) in the B2 foundation size; and it increased by 1543.4% when Dr increased from 10% (qu = 52.3 kPa) to 90% (qu = 859.5 kPa) in the B3 foundation size. This indicates that a higher relative density significantly increases the ultimate bearing capacity of sandy soils. In addition, the effect of the foundation size is significant. Increasing the foundation size from 80 mm to 160 mm increases qu from 504.2 kPa to 859.5 kPa for the highest relative density (Dr = 90%). This result highlights the positive correlation between the ultimate bearing capacity and the increasing foundation size.  
As the foundation size increases, the ultimate bearing capacity and settlements increase (Table 3). As the density increases from Dr = 10% to 40%, a significant change, i.e., a significant increase in the bearing capacity and a noticeable difference in the damage patterns, is observed. While hardening behavior is observed in loose sand (Figure 11a), post-peak softening behavior is observed as the soil density increases (Figure 11b-d). It is known that loose soils become denser by decreasing the void ratio during loading [52]. Therefore, very high settlements were observed in soils with a relative density of Dr = 10%. The settlements were very low in dense soils (Dr = 65% and 90%) since the bearing capacity was very high. The largest settlements, however, occurred with a density of Dr = 40% because of their limited bearing capacity and high void ratio.