## 4 Conclusions  
In this study, the additional lateral stress values formed in the soil by loading square foundations resting on sandy soil were investigated experimentally. The 60 lateral stress values obtained from the experiments were compared with those calculated using [PERSON]'s Equation (5). Comparisons were made between the ultimate bearing capacities found in the model experiments and the current theoretical relationships proposed by [PERSON], [PERSON], [PERSON], and [PERSON] [63; 64; 65]. Multivariate regression analyses were conducted to estimate the experimental lateral stress values, and a usable equation for calculating the lateral stress increase is presented. The results obtained from this study are as follows:  
Figure 14: (a) Lateral stress due to finite area load [38], (b) Experimental lateral stresses for Dr = 10%. 1. Lateral Stress Distribution Depending on Depth: The results of the model experiments showed that the measured lateral stresses changed systematically depending on both the relative density and foundation width. In particular, in the measurements made in the loosest case (Dr = 10%), the highest lateral stress value was \(\sigma_{\text{h}}\) = 4.10 kPa, and this value was measured at a depth of z = 3.75 B. In the same foundation size and very dense case (Dr = 90%), the maximum lateral stress value reached\(\sigma_{\text{h}}\) = 9.84 kPa, which was recorded at a depth of z = 2.5 B. While the maximum stresses in all foundation dimensions for Dr = 40%, 65%, and 90% are concentrated at the level of z = 2.5 B, these values are around z = 3.75 B in the case of Dr = 10%. 2. Multivariate Regression for Lateral Stress Prediction: Multivariate regression analysis was performed to estimate the lateral pressure increases measured in the experiments. Considering the environmental geometric parameters and relative soil density, an equation was developed to determine the lateral stress increases under a square shallow foundation. 3. Effect of Soil Density and Foundation Size: Its lateral stresses and ultimate bearing capacity increased significantly with increasing relative density and foundation size. At the largest foundation size (B3), when Dr is increased from 10% to 90%, there is an increase of 140% in lateral stress. Similarly, a more than 1500% increase in the bearing capacity was observed. 4. Agreement with Theoretical Models: At high relative densities, the experimental results were in good agreement with [PERSON]'s theory. The ultimate bearing capacity values obtained from the model tests were compared with classical theoretical approaches, and the levels of agreement with different models were evaluated according to soil density. At Dr = 90% density, the experimental bearing capacity was calculated as 504.2 kPa for the B1 foundation size, while the Vesic bearing capacity was calculated as 466.7 kPa. The error rate was approximately 7.4%. In particular, the Vesic theory provides results that are very close to the experimental data in the experiments carried out on dense sands. At low densities, the [PERSON] and [PERSON] methods yield more realistic results. In contrast, [PERSON]'s method consistently overestimated the carrying capacity and did not agree with the experimental data. 5. Load-Settlement Behavior: The load settlement curves exhibited nonlinear behavior with no obvious inflection points in the loose state (Dr = 10%). However, post-peak softening behavior was observed when the density increased steadily to 90%. Higher relative densities resulted in higher carrying capacity values at the same settlement level. However, the ultimate bearing capacity was reached at about 10% of the normalized settlement value when the settlement values were normalized with the foundation width. H.S.A. : Writing--review and editing, writing--original draft, validation, methodology, investigation, statistical analysis; D.K.K. : Writing--review and editing, writing--original draft, investigation, conducting experiments.