## 3 Results and Discussion  
### Evaluation of Lateral Stress Values  
In this section, model experiments are used to investigate the effects of relative density and foundation size on additional lateral stresses under square foundations on sand. The lateral stress in the soil increases due to the loading of shallow foundations measured at five different depths (z\({}_{1}\) = 1.25 B, z\({}_{2}\) = 2.5 B, z\({}_{3}\) = 3.75 B, z\({}_{4}\) = 5 B, z\({}_{5}\) = 6.25 B). As the foundation size increased, the vertical load also increased. Accordingly, the lateral stresses also increased. The maximum lateral stresses for all foundation sizes were measured at a depth of z = 2.5 B (Figure 9b-d) in (Dr \(\geq\) 40%). The maximum lateral stresses in the case of (Dr = 10%) are observed at a depth of z = 3.75 B, as shown in Figure 9a. This situation can be explained as the load applied through the foundation being transmitted a distance from the foundation due to the loose soil. Except for the very loosely dense soil, the maximum stresses at all other densities are observed in Figure 9b-d at z = 2.5 B. As shown in Figure 10a-c, for all foundation dimensions, as the relative density increased, the additional lateral stress also increased. Starting at the foundation base, the additional lateral stresses gradually decreased along the z depth and formed a pressure bulb shape, as described in the literature. Figure 9: Variation of measured lateral stresses with depth and relative density, comparison with [PERSON]’s calculations: (**a**) Dr: 10%, (**b**) 40%, (**c**) 65% and (**d**) 90%. In the B3 foundation, the maximum lateral stress was determined as \(\sigma_{\rm h}\) = 9.84 kPa in soil with a relative density (Dr = 90%). The maximum lateral stress value under the same foundation was \(\sigma_{\rm h}\) = 4.10 kPa (Dr = 10%). Consequently, the relative density increased, and the lateral stresses at the same depth increased by 140%. The other foundations were compared similarly, and the lateral stresses increased by 106% for foundation B1 and 145% for foundation B2. All lateral stresses measured using the model experiments were compared with Equation (5), which gives the lateral stress increase occurring under a rectangular loaded area. Figures 9 and 10 show that the experimental and theoretical results changed proportionally with depth. Additionally, it was observed that at (Dr = 10%), the Giroud equation [45] produced similar results for different foundations (Figure 9a). According to the model test results, as the relative density (Dr) increased for all foundation dimensions (B), the additional lateral stresses in the soil also increased. This situation can be explained by the fact that more loads are carried in denser soils, and therefore, greater stress transfer occurs. Similarly, as the foundation size increased, the increase in the applied vertical loads caused the load to be transmitted to deeper levels and higher lateral stress. These findings are consistent with the load transfer and pressure distribution models defined by [PERSON] (1973) and [PERSON] (2010) [19; 56]. In particular, in soils with a relative density of \(\geq\)40%, maximum lateral stresses occurred at a depth of z = 2.5 B. This finding is consistent with the \"pressure bulb\" model, which describes the distribution of the load from the foundation base to the soil at an angle [57]. However, in the case of very loose soil (Dr = 10%), the maximum lateral stress occurred at z = 3.75 B. This situation can be attributed to the load being transmitted to deeper depths due to the higher deformation capacity of loose sands. This observation is consistent with the studies of [PERSON] and [PERSON] (1978) on foundation load transfer in loose soils [58]. In addition, for all densities and foundation sizes, the additional lateral stresses gradually decreased with increasing depth from the foundation base, forming a classical pressure bulb.