###### Abstract  
While existing analytical methods provide solutions for calculating vertical pressures in soil, calculating lateral stresses remains a critical challenge. Therefore, experimentally measuring stress values is essential, considering the various factors influencing these stresses. This study investigates the lateral stress variations occurring beneath foundations placed on sandy soil and assesses the ultimate bearing capacity and settlement behavior of these foundations. Additional lateral stresses were measured beneath square shallow foundations on the sand with varying relative densities. The model tests were conducted in a square-sectioned sand tank. The results revealed that the lateral stress values tended to increase with both the foundation size and soil density, with this effect being most pronounced at a relative density of 90%. Furthermore, the lateral stresses decreased with increasing depth beneath the foundation for all foundation sizes. Loading tests were performed on square  
soil density, stress history, and direction of retaining wall movement [4; 5; 6]. Considering that the soil is a homogeneous, isotropic, and semi-infinite medium, the vertical stress increases in the soil mass were determined using elastic solutions. Laboratory test methods have been developed to examine stress changes in field conditions and the parameters that affect stress. The primary purpose of these test methods is to accurately predict the mechanical behavior of samples under field conditions in a laboratory environment [7]. Experimental studies have been conducted to investigate the effects of parameters such as soil type, relative soil density, pore water pressure, and soil stress history on the coefficient of earth pressure at rest (K\({}_{0}\)) [8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. To understand the earth's pressure at rest, he analyzed laboratory test data on more than 170 different soil types and developed empirical relationships that are valid for various soil types, particularly clay, silt, and sand [17]. It was stated that the K\({}_{0}\) value for these soils can be estimated only by using the internal friction angle (\(\varphi\)'). The K0-internal friction relationship obtained as a result of this study was similar to the formulation proposed by [PERSON] in 1948 [9]. Therefore, it is necessary to determine the lateral stress variations caused by changes in soil properties. Lateral stresses occurring at different relative densities and depths under a square foundation have been investigated experimentally [18]. It has been determined that increases in lateral stresses do not change at the same rate as increases in vertical stresses and that lateral stresses change with changes in parameters such as the relative density and depth of sand. It is known that the bearing capacity and stresses may change depending on the degree of compaction of the soil [19; 20; 21]. Researchers have investigated the stresses occurring under square foundations resting on sand. [PERSON] et al. [22] investigated the vertical stress changes under the square foundation. In these experiments, sand was placed using the dynamic compression method at a relative density of 65 %. The vertical stresses formed at different depths under the foundation were measured using pressure transducers. The stresses under the foundation decreased with increasing depth [23]. The well-known K\({}_{0}\) equation proposed by [PERSON] 1948 [9] is widely adopted to determine the K\({}_{0}\) values for the internal friction angle. The simplified form used in current engineering practice is as follows:  
\[\text{K}_{0}=(1-\text{sin}\varphi) \tag{1}\]  
The validity of Equation (1) has been experimentally investigated and analyzed using various methods [17; 24]. Lateral stress is a critical design factor [25]. For this purpose, a centrifuge model test was used to examine the K\({}_{0}\) values of sand soils with varying relative densities.