# Experimental and Numerical Studies of Vertical Stresses
## 2 Experimental Investigation  
Model tests carried out within the scope of this study were conducted using the experimental setup designed in the Geotechnical Laboratory of Cukurova University Civil Engineering Department. The facility is shown in Figure 2. Vertical stress measurements at certain depths beneath the centerline of the circular footing were carried out in a reduced-scale, square-shaped test tank with a plan length of 0.7 m, a width of 0.7 m and a height of 0.7 m. In order to prevent lateral movements that may occur during the placement of the sand in the test box and the static loading of the circular footing, the bottom and vertical edges of the test box were stiffened by using angled sections. The front and back surfaces of the test box consist of 8 mm thick glass plate, and the side surfaces consist of 20 mm thick wooden plate. The inner walls of the tank have been smoothed to minimize the friction that may occur on the side surfaces. Static vertical loads were applied to the model circular footing resting on the sand, with a mechanical jack attached to a loading beam mounted on the test box. Static load values applied to the circular model footing were measured using a comparator and a load ring placed between the jack and the model footing. In the tests, model footings were loaded with a loading rate of 1 mm/min. Loading tests were carried out on circular rigid model footings made of steel material. The diameters of the model footings were 85 and 150 mm, and the thickness was 20 mm (Figure 3). The loads were transferred to the circular model footing by means of a bearing ball. This produces a hinge, which allows the footing to rotate freely as it approaches failure and eliminates any potential moment transfer from the loading system. Figure 2: Test set-up: (**1**) mechanical jack; (**2**) proving ring; (**3**) model plate; (**4**) datalogger; (**5**) steel profile; (**6**) sand bed; (**7**) reaction beam. In the experimental study, uniform, clean and fine sand taken from the Seyhan riverbed was used as soil. After the sand material was subjected to pre-washing and sieving processes, it was dried in air, and a sieve analysis test was carried out to determine the particle size distribution in accordance with ASTM D422-63 [24]. It is shown in Figure 4. The classification of the sand material was determined as poorly graded sand (SP) according to the Unified Soil Classification System (USCS). In Table 1, the general physical properties of the sand used in the experiments are summarized. and to prevent crushing of sand grains, a 13 \(\times\) 13 cm sized and 2.0 cm thick plastic plate was mounted on the tip of the vibration compactor. The glass and wooden sides of the test box were scaled for convenience during the placement of the sand. After compacting each layer of sand, the next lift height was checked using scaled lines on the glass and wood plates of the test box. After the compaction process was completed and the sand bed was prepared, the areas beneath the circular model footing were leveled carefully. The leveling process was carried out in order to ensure full contact of the model footing with the sand and the applied load on the model footing to act vertically [25]. Care was taken to apply the same compression force to each sand layer during the compaction of the sand in the test box to have a uniform density. In the control tests performed on the compacted sand layers, it was determined that the difference between the densities was less than 1%. With the sand compaction technique applied in the experimental study, a uniform relative density of approximately 65% with a unit weight of 17.1 kN/m\({}^{3}\) was achieved. In order to determine the shear strength properties of the sand, which was compacted by layers in the test box, direct shear and consolidated-drained triaxial compression tests were carried out on the samples in accordance with ASTM D3080 [26]. The estimated internal friction angle was determined to be 41\({}^{\circ}\) at the same relative density used in the tests.