## 3 Results and Discussion
### Comparison of Ultimate Bearing Capacity with Existing Theoretical Methods  
The ultimate bearing capacities obtained from the model tests were compared with the equations presented by [PERSON], [PERSON], [PERSON], and [PERSON] [63; 64; 65; 66] (Table 5). It was observed that there was good agreement between the values obtained from the Vesic equation and the experimental results at higher relative densities (Dr = 65% and 90%). In contrast, the theoretical approaches of [PERSON] [63] and [PERSON] [65] are the closest to the experimental results at low relative densities (Dr = 10% and 40 %) (Figure 12). The [PERSON] theory bearing capacities in Table 5 were eliminated from the graphs because they were extremely high compared to all other data. It is known that as the foundation size increases, the results obtained in model experiments will be closer to reality [25]. In the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Dr (\%)** & **This Study** & **[PERSON]** & **[PERSON] [64]** & **[PERSON] [65]** & **[PERSON] [66]** \\ \hline \multirow{4}{*}{B = B1 = 80 mm} & 10 & 30.9 & 81.8 & 183.7 & 47.3 & 64.4 \\  & 40 & 173.0 & 163.7 & 358.1 & 81.9 & 110.8 \\  & 65 & 380.6 & 440.1 & 1083.5 & 197.1 & 264.7 \\  & 90 & 504.2 & 642.8 & 2262.6 & 348.4 & 466.7 \\ \hline \multirow{4}{*}{B2} & 10 & 34.5 & 122.8 & 275.6 & 71.0 & 96.6 \\  & 40 & 347.2 & 245.5 & 537.1 & 122.9 & 166.2 \\  & 65 & 496.3 & 660.1 & 1625.3 & 295.7 & 397.0 \\  & 90 & 592.2 & 964.3 & 3393.8 & 522.6 & 700.0 \\ \hline \multirow{4}{*}{B3} & 10 & 52.3 & 163.7 & 367.4 & 94.6 & 128.8 \\  & 40 & 375.4 & 327.3 & 716.2 & 163.9 & 221.6 \\ \cline{1-1}  & 65 & 597.9 & 880.2 & 2167.1 & 394.2 & 529.3 \\ \cline{1-1}  & 90 & 859.5 & 1285.7 & 4525.1 & 696.8 & 933.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Theoretical and experimental ultimate bearing capacities. model experiments, it was observed that as the foundation size increased, the experimental and theoretical data (especially with the Vesic equation [56]) became closer to each other. [PERSON] (1975) presented a broader theoretical framework by considering the foundation dimensions, load distribution, and soil properties, thus enabling more accurate results to be obtained at high relative densities [66]. This finding is also supported in the literature; for example, [PERSON]'s theory shows that the load-bearing capacity increases depending on the soil properties, and the effect of the foundation size becomes more pronounced in high-density soils ([PERSON], 1975) [66]. However, [PERSON]'s (1943) and [PERSON]'s (1970) theories provided better agreement at low relative densities (Dr = 10%, 40%) [65; 63]. This indicates that both theories are more effective in predicting foundation behavior when the soil density is low. While [PERSON]'s (1943) [63] bearing capacity theory can accurately model soil behavior, especially at low densities, by focusing on the bearing capacity, [PERSON]'s (1970) [65] approach more accurately reflects the effects of foundation dimensions and soil properties. Furthermore, this finding supports the notion that these theories may be more suitable for evaluating foundation performance in soils with low relative density. Figure 12: (a) B= 80 mm (b) 120 mm (c) 160 mm Comparison of the experimental ultimate bearing capacity with the available theoretical calculations. [PERSON]'s bearing capacity [64] calculations often yield extremely high values in the literature [67; 68; 69]. It is emphasized that the [PERSON] method yields overconfident results and that alternative calculation methods should be used for more accurate estimates. Therefore, [PERSON]'s theory, when compared to other theoretical results, overestimated the bearing capacity and was inconsistent with the experimental data. In [PERSON]'s theory, assumptions regarding the foundation size and load distribution can lead to overestimations under certain soil conditions. This finding shows that [PERSON]'s theory is invalid in some cases, and lower bearing capacity results can be obtained in model experiments.