## 2 Materials and Methods
### Machine Learning Algorithms Used in the Study
#### 2.5.1 Decision Tree Regression  
Decision tree regression, or DTR, represents a hierarchical data structure characterized by a dynamic arrangement of branches and nodes. Within this structure, nodes exhibit lines going outwards, and some nodes, termed 'leaves', lack such extensions. The mechanism involves the division of data points intended for regression or categorization into two or more distinct categories using specific internal nodes. In the training phase, input variable values undergo comparisons against designated functions. The algorithm systematically endeavors to construct optimal decision trees by iteratively minimizing the fitness function. At various junctures within each context of independent variables, the dataset undergoes division. During this process, the algorithm computes prediction errors, representing disparities between projected and actual values, guided by the fitness function. The determination of the optimal split point hinges on identifying the variable that yields the smallest fitness function value, a process that entails evaluating split point errors across each variable. In the context of decision tree regression, several key hyperparameters play pivotal roles in shaping the model's performance. One such parameter is the'max_depth,' which dictates the maximum depth of the decision tree. A deeper tree can capture intricate relationships in the training data but risks overfitting. On the other hand,'min_samples_split' determines the minimum number of samples required to split an internal node. It influences the threshold for further division, thereby affecting the model's  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **LL (\%)** & **SR (\%)** & \(\gamma_{d}\) **(kN/m3)** & \(\gamma_{dmax}\) **(kN/m3)** & **Applied Stress** (\(\sigma\) **(kN/m2)**) \\ \hline mean & 59.82 & 78.9 & 15.14 & 15.69 & 164.59 \\ std & 13.02 & 17.1 & 1.22 & 1.20 & 83.43 \\ min & 41.00 & 44.5 & 12.05 & 13.95 & 25.00 \\
25\% & 48.60 & 65.0 & 14.26 & 14.66 & 87.50 \\
50\% & 55.80 & 75.0 & 15.11 & 15.95 & 170.00 \\
75\% & 72.10 & 88.0 & 16.05 & 16.73 & 240.00 \\ max & 78.80 & 100.0 & 17.80 & 18.20 & 300.00 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the statistical characteristics of the variables.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{4}{c}{**Models to Predict Dry Unit Weight (\(\gamma_{max}\))**} & **Models to Predict Applied Stress (\(\sigma_{min}\))** \\ \hline
**Parameters** & **Minimum** & **Maximum** & **Minimum** & **Maximum** \\ \hline  & \multicolumn{3}{c}{Input parameters} & \multicolumn{3}{c}{Input parameters} \\ \hline LL (\%) & 41 & 79 & 41 & 79 \\ \hline SR (\%) & 45 & 100 & 45 & 100 \\ \hline \(\sigma\) (kN/m2) & 25 & 300 & & \\ \hline \(\gamma_{dry}\) (kN/m3) & & & 12 & 17.8 \\ \hline \(\gamma_{dmax}\) & 13.95 & 18.2 & 13.95 & 18.2 \\ \hline  & \multicolumn{3}{c}{Output parameter} & \multicolumn{3}{c}{Output parameter} \\ \hline \(\gamma_{max}\) (kN/m3) & 12 & 17.8 & & \\ \hline \(\sigma_{min}\) (kN/m2) & & & 25 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Boundaries, inputs, and outputs used for the developed models.  
generalization capability. Additionally, the'min_samples_leaf' parameter establishes the minimum number of samples necessary to constitute a leaf node [72].