## 3 Results and Discussion  
### Experimental Work Results and Discussion  
The relationship between the swelling amplitude and the dry unit weight of the soil samples was examined for each percentage of added sand, with an initial degree of saturation of 75%, as shown in Figure 12. The results indicate that the swell amplitude increases as the dry unit weight of the soil samples increases, for all percentages of added sand. It should be noted that the swelling values decrease with an increase in the applied stress to the soil. Similar observations were made for the other initial degree of saturation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Hyperparameter**} & \multirow{2}{*}{**Values Range**} & \multicolumn{2}{c}{**Optimal Values**} \\ \cline{3-5}  & & & \(\sigma_{min}\) & \(\gamma_{max}\) \\ \hline \multirow{3}{*}{**DTR**} & max\_depth & 5 to 15 & 14 & 13 \\  & min\_samples\_leaf & 1 to 5 & 1 & 1 \\  & min\_samples\_split & 1 to 5 & 3 & 1 \\ \hline \multirow{3}{*}{**RFR**} & max\_depth & 5 to 15 & 14 & 10 \\  & min\_samples\_leaf & 1 to 5 & 1 & 1 \\  & min\_estimators & 50 to 150 & 110 & 130 \\ \hline \multirow{3}{*}{**GBR**} & subsample & 0.5 to 1 & 0.8 & 0.9 \\  & n\_estimators & 50 to 250 & 250 & 200 \\  & min\_samples\_split & 2 to 20 & 17 & 10 \\  & min\_samples\_leaf & 1 to 20 & 3 & 2 \\  & max\_depth & 3 to 15 & 10 & 5 \\  & learning\_rate & 0.01 to 0.4 & 0.1 & 0.2 \\ \hline \multirow{3}{*}{**XGBoost**} & subsample & 0.6 to 1 & 1 & 0.8 \\  & learning\_rate & 0.01 to 0.4 & 0.1 & 0.2 \\  & max\_depth & 1 to 15 & 7 & 6 \\  & n\_estimators & 50 to 250 & 200 & 200 \\  & subsample & 0.5 to 1 & 0.8 & 0.6 \\ \hline \multirow{3}{*}{**SVR**} & C & 0.1 to 10,000 & 1000 & 10 \\  & epsilon & 0.001 to 100 & 10 & 0.01 \\  & kernel & linear, poly, rbf & rbf & rbf \\ \hline \multirow{3}{*}{**ANN**} & number of neurons in layer1 & 2 to 100 & 8 & 8 \\  & number of neurons in layer2 & 2 to 100 & 56 & 56 \\  & learning\_rate & 0.01 to 0.4 & 0.05 & 0.025 \\  & batch size & 10 to 50 & 16 & 12 \\ \cline{1-1}  & hidden layers function & ReLU, tanh, linear, Sigmoid & ReLU & tanh \\ \cline{1-1}  & linkage between the hidden layer and the & ReLU, tanh, linear, Sigmoid & linear & ReLU \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The optimal hyperparameters for models. For each applied stress considered as \(\sigma_{min}\), the dry unit weight (\(\gamma_{max}\)) at which volumetric changes become insignificantly small (indicated by a swelling amplitude of 0) was determined. This determination is illustrated in Figure 13, which presents the correlation between dry unit weight and the percentage of added sand at various applied stress levels that lead to a swelling amplitude of 0, while maintaining a degree of saturation at 75%. An analysis of Figure 13 reveals that, under the same applied stress resulting in minimal volumetric changes (swelling amplitude = 0), the necessary dry unit weight increases proportionally with the increase in sand content up to approximately 30%. Beyond this point, the rate of increase becomes less prominent. Furthermore, it is noteworthy that as the dry unit weight increases, the required applied stress to achieve zero swell amplitude also increases. Similar results hold true for other degrees of saturation as well. Consequently, structures with varying weights require a careful consideration of foundation dimensions. This ensures that the applied stress aligns with the initial dry density and degree of saturation, ultimately minimizing foundation heave. In view of the complexity of the swelling phenomenon and the significant variability in the results obtained through statistical methods, machine learning is proposed to assist in predicting the applied stress required to minimize volumetric changes.