## 2 Materials and Methods
### Loaded Swelling Pressure Tests  
The loaded swelling pressure tests were performed on samples with different densities and degrees of saturation for each sand mixing percentage. In this method, a procedure was employed involving the loading of three or more specimens at various pressures. This process enabled the specimens to absorb water, leading to either swelling or compression until equilibrium positions were achieved. These positions aligned linearly on the swell versus logarithmic pressure plot as shown in Figure 6. While this methodology mandates the use of a minimum of three identical specimens, it provides the advantage of comparably reduced time demands. In the context of the loaded swelling pressure tests, the soil specimens were meticulously placed within a cylindrical metal ring, characterized by dimensions measuring 71.4 mm in diameter and a height of 20 mm. To mitigate any potential effects of friction between the soil and the inner surface of the ring, a lubricant was applied to the lateral sides of the ring.  
Figure 5: Images of the sample formation process step-by-step: (**a**) mixing sand with expansive soil, (**b**) placing the sample in plastic bags for moisture retention, (**c**) positioning it within the ring, (**d**) applying meticulous static pressure through a hydraulic piston, and (**e**) presenting the final prepared specimen.  
After meticulous sample preparation, as illustrated in Figure 5, filter papers were inserted both above and below the soil sample to prevent the ingress of fine soil particles into the porous discs' interstices. Subsequently, a loading cap was installed atop the upper porous disc, and the entirety of this composite assembly was carefully positioned within the oedometer cell. Finally, the load transfer frame was installed onto the loading cap, as exemplified in Figure 7. The specimens were subjected to varying stress levels (25, 75, 150, 300 kPa). Afterwards, the specimens underwent immersion in distilled water, inducing swelling or settlement contingent upon the initial conditions and applied stress. Following the attainment of equilibrium in deformation, the swelling amplitude was meticulously recorded for each applied stress.  
The findings presented in Figure 6, specific to initial conditions (Fs = 10%, \(\gamma_{d}\) = 14.66 kN/m\({}^{3}\), SR = 75%), revealed a distinctive swelling pressure of 232 kPa. This observation signifies that, under these specified initial conditions, the optimal dry unit weight of 14.66 kPa should align with an applied stress of 232 kPa to achieve a swelling amplitude of 0. Correspondingly, for \(\gamma_{d}\) = 14.66 kN/m\({}^{3}\), the optimal applied stress for these specific initial conditions was determined to be 232 kPa. These outcomes contribute significantly to our understanding of the complex interplay between initial conditions, optimal applied stress, and optimal dry unit weight in expansive soils.  
Based on the results of the experiments, a dataset of 657 unconfined compression tests was created for use in developed machine learning models. The input data include: liquid limit (LL), clay content (Fc), silt content (Fsi), sand content (Fs), specific degree of saturation (SR), maximum dry unit weight (\(\gamma_{dmax}\)) of proctor test, applied stress (\(\sigma\)), and dry unit weight (\(\gamma_{d}\)), This dataset is used to predict the optimal applied stress (\(\sigma_{min}\)) and optimal dry unit weight (\(\gamma_{max}\)). The key steps of the applied methodology are depicted in Figure 8. Figure 9 displays the distribution histograms and density plots for the dataset.  
Figure 6: Relationship between swelling amplitude and applied stress in loaded swelling pressure test for initial condition (Fs = 10%, \(\gamma_{d}\) = 14.66 kN/m\({}^{3}\), SR = 75%).  
Figure 7: Consolidation test device (oedometer).