# Experimental Study on the Bearing Capacity of Gas Oil-Contaminated Coastal Sand
## 2 Laboratory Investigation
### Physical Modeling Tests  
Reduced-scale tests offer precise control for studying foundation behavior but require careful interpretation due to \"scale effects\" arising from (I) foundation stress on the subgrade, (II) the footing size relative to the soil grains, (III) soil anisotropy affecting the failure plane orientation, and (IV) progressive failure and nonuniform soil strains. Among the mentioned effects, the difference in the stress level between reduced- and full-scale footings, as highlighted by [PERSON] and [PERSON] [30], is of paramount significance. Larger footings generate greater stress within their influence zone. Due to the nonlinearity of the Mohr-Coulomb (MC) failure envelope--resulting in higher \(\varphi\) values at lower stress levels--the friction angle at failure is greater in reduced-scale footings compared to full-scale footings [42]. Several strategies have been proposed in prior studies to account for these scale effects. [PERSON] and [PERSON] [30] suggested determining the \(N_{\gamma}\) factor based on friction angles as a function of the applied pressure. Additionally, [PERSON] et al. [43], [PERSON] [44], and [PERSON] and [PERSON] [45] advocated adopting \(N_{\gamma}\) values based on the footing size. Another influential factor affecting the bearing capacity is the ratio of the footing width (B) to the median grain size of the soil particles (B/D50). To mitigate particle size effects, [PERSON] [46] recommends maintaining a minimum B/D50 ratio of 50-100. Furthermore, in the case of unsaturated subgrades, the distribution of suction (or the saturation level) should be considered when interpreting the results of the physical modeling of shallow footings. In such subgrades, the average matrix suction should be considered in the determination of the bearing capacity, which may be a function of the footing dimension, as larger foundations influence the underneath soil to greater depth and may have a different average matric suction compared to smaller foundations. Nonetheless, in case the profile of the matric suction distribution is uniform in depth, the average matric suction will be constant for different foundation sizes [47; 48]. The above-mentioned scaling effects were taken into account in the physical model experiments in the present research. As previously mentioned in Section 2.1, grain size effects are not an issue in this study, as the ratio is well above the recommended value. Moreover, subgrade layers were prepared with a uniform profile of degree of saturation in depth in order to achieve a constant average degree of saturation in all layers. The foundation width effect is also considered in the determination of the \(N_{\rm Y}\) values and interpretation of the predicted bearing capacity results in Section 4. The physical modeling tests were conducted in the soil dynamics laboratory at the Amirkabir University of Technology. These experiments utilized a rectangular tank as the foundation subgrade container, with specific dimensions of 100 \(\times\) 80 \(\times\) 65 cm (length \(\times\) width \(\times\) height), as illustrated in Figure 3. The tank's interior featured a smooth, impermeable membrane to prevent gas oil leakage and minimize friction between the tank wall and sand grains. The foundation model consisted of a 2 cm thick, 15 cm wide square steel plate. Given the stress levels in the bearing capacity tests, the foundation exhibited a rigid response. An abrasive sheet was affixed to the foundation's bottom to replicate the friction between an actual concrete foundation and its subgrade. All tests were conducted with the foundation placed on the subgrade surface without any embedment considered. A standard vertical loading system was utilized to measure the bearing capacity of the square foundation on various subgrade conditions. After preparing the subgrade, the foundation model was attached to the vertical loading system and placed on the subgrade.