## 5 Model Results
### Variable Importance Analysis
Figure 10 illustrates how the predicted \(w_{opt}\) changes in relation to the \(\text{C}_{\text{F}}\) (%), the LL (%), the PL (%), and the E (kJ/m\({}^{3}\)). Notably, as the \(\text{C}_{\text{F}}\) (%), the LL (%), and the PL (%) rise, the forecasted \(w_{opt}\) also goes up. In contrast, when the E (kJ/m\({}^{3}\)) grows, the predicted value goes down. These consistent changes align with the patterns observed for the \(w_{opt}\) in relation to each soil property as seen in the figure, indicating that the proposed model is accurate. Figure 11 displays the parametric analysis of the anticipated \(\rho_{\text{dmax}}\) in relation to each input variable. Contrary to the \(w_{opt}\), the forecasted \(\rho_{\text{dmax}}\) goes down as the \(\text{C}_{\text{F}}\) (%), LL (%), or PL (%) rises and as the E (kJ/m\({}^{3}\)) reduces. This trend mirrors the monotonic observations from the actual database illustrated in the figure. Such a parallel between the parametric study and the database in predicting the \(\rho_{\text{dmax}}\) further confirms the accuracy of the model introduced. Figure 9: Influence of different independent variables on MARS model: (a) for \(\rho_{\text{dmax}}\); (b) for \(w_{opt}\). The findings from the variable importance analysis are consistent with previously published literature. A respected study explored the influence of C\({}_{\rm F}\) on the mechanical response of CDG (completely decomposed granite) subjected to dynamic compaction grouting [65]. Through integrating varying proportions of kaolin clay with CDG, this study aimed to understand the implications of fines concentrations on its compactive behavior. The findings indicated that an increment in C\({}_{\rm F}\) correspondingly results in a diminished  
Figure 11: Parametric analysis of the predicted \(w_{opt}\) versus: (**a**) C\({}_{\rm F}\) (%); (**b**) PL (%); (**c**) LL (%); (**d**) E (kJ/m\({}^{3}\)). Figure 10: Parametric analysis of the predicted \(w_{opt}\) versus: (**a**) C\({}_{\rm F}\) (%); (**b**) PL (%); (**c**) LL (%); (**d**) E (kJ/m\({}^{3}\)). \(\rho_{\rm{dmax}}\), while concurrently elevating the \(w_{opt}\). In another study, sand-kaolin blends were compressed to investigate the connection between \(\rho_{\rm{dmax}}\), C\({}_{\rm{F}}\), and specific gravity (Gs) across different moisture levels, with C\({}_{\rm{F}}\) ranging from 20% to 70% [66]. A prominent linear correlation (R\({}^{2}\) = 0.99) was found between \(\rho_{\rm{dmax}}\) and the C\({}_{\rm{F}}\)/Gs\({}^{2}\) ratio. For PL, a respected paper investigates which index properties best correlate with compaction traits. Incorporating both the study's findings and the existing literature, it was determined that the plastic limit correlates strongly with compaction features, such as optimum moisture content and maximum dry unit weight, more effectively than either the liquid limit or plasticity index. For the plastic limit (PL), a notable study examined which index properties have the strongest correlation with compaction characteristics [23]. Through integrating the study's results with the established literature, it was ascertained that the plastic limit shows a significant correlation with compaction attributes, particularly \(w_{opt}\) and \(\rho_{\rm{dmax}}\), surpassing the correlations seen with either the liquid limit or the plasticity index.