## 4 Feature Importance  
Two methods were used to evaluate the importance of the selected variables: the SHapley Additive ExPlanations (SHAP) values [102] and the algorithm's inherent computation of traditional feature importance. In the latter approach, following algorithm training, relative relevance scores for each input characteristic can be derived [103]. A higher score indicates a greater impact on prediction. The analysis results are shown in Table 10, indicating that across all models, saturation degree holds the highest influence on \(q_{u}\) and \(E_{t}\), followed by void ratio and dry unit weight, with liquid limit and sand percentage having the least influence. Notably, XGBoost places saturation degree on top, followed by void ratio and liquid limit, with dry unit weight and sand percentage at the bottom.  
Additionally, the SHAP method was employed, providing a consistent approach to explaining the output of any tree-based model and offering distinct advantages over other methods. Figures 23 and 24 illustrates the combination of feature importance with feature effects. Each point in the graph represents a SHAP value for a feature and prediction, with the y-axis displaying features in descending order of importance. SHAP values are plotted along the x-axis, where a value of zero indicates no contribution to the prediction, with increasing contributions as the SHAP value moves away from zero. Furthermore, color gradation from low (blue) to high (red) feature values provides insight into the directional impact of features. The distribution of blue and red dots offers an overall understanding of the directionality impact of features [55].  
According to the random forest regression (RFR) model, the degree of saturation emerges as the most influential variable impacting both \(q_{u}\) and \(E_{t}\), showing a negative correlation, consistent with findings from [104; 105]. Following closely is the void ratio, exhibiting a smaller yet still significant negative correlation, as observed in the study by [106].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**DTR**} & \multicolumn{2}{c}{**RFR**} & \multicolumn{2}{c}{**GBR**} & \multicolumn{2}{c}{**XGBoost**} & \multicolumn{2}{c}{**Correlation**} & \multirow{2}{*}{**Correlation According to SHAP**} & \multirow{2}{*}{**CoPrevious Research**} \\ \cline{2-2} \cline{6-9}  & \(q_{u}\) & \(E_{t}\) & \(q_{u}\) & \(E_{t}\) & \(q_{u}\) & \(E_{t}\) & \(q_{u}\) & \(E_{t}\) & & \\ \hline \(SR\) & 0.406 & 0.677 & 0.429 & 0.67 & 0.394 & 0.662 & 0.291  
Figure 23: Relative importance of features with SHAP values in XGBoost model for (**A**) \(E_{t}\) and (**B**) \(q_{u}\).  
Figure 24: Relative importance of features with SHAP values in RFR model for (**A**) \(E_{t}\) and (**B**) \(q_{u}\).  
Additionally, the dry unit weight emerges as another influential factor affecting \(q_{u}\) and \(E_{t}\), demonstrating a positive correlation, as indicated in previous studies such as those by [106, 107]. The sand content parameter shows a negative correlation, aligning with the findings of [108]. Conversely, the liquid limit variable demonstrates the least impact on both \(q_{u}\) and \(E_{t}\), with a positive correlation, consistent with studies by [106, 107].  
These observations suggest that the models have effectively captured the relationships between each independent variable and \(q_{u}\) and \(E_{t}\), in line with existing technical literature. A concise summary of the feature importance analysis conducted using the two approaches is presented in Table 10.