## 5 Results and Discussion
### Sensitivity Analysis
#### 5.2.2 Feature Dependency Relationship Analysis  
Figure 10 further presents the dependency relationships between main input variables and their corresponding SHAP values, facilitating an in-depth understanding of the variation patterns of each factor's influence on model outputs. In each subplot, the horizontal axis corresponds to the variable's own values, while the vertical axis represents the variable's contribution to sand strength prediction results, with the overlaid red curve reflecting the overall influence trend.  
From the figure, it can be observed that FCaCO3, as the most important influencing factor, exhibits a significant positive correlation with SHAP values. When calcite content increases from approximately 5% to 25%, SHAP values rise from near zero to above six, with an influence magnitude far exceeding other input parameters. This approximately linear positive trend indicates that calcite content is a key factor determining MICP treatment effectiveness, and its generation efficiency and distribution uniformity should be prioritised in practical engineering applications. UA demonstrates distinct staged influence characteristics. Within the lower range (0-5), UA contributes positively to model outputs, with SHAP values mainly distributed between 0.2 and 1.3, indicating that low-level urease activity promotes the strength of MICP-treated sand. This trend aligns with experimen  
Figure 10: Dependency analysis of key variables for MICP-treated sand strength.  
tal observations by [PERSON] et al. [40], whose research demonstrated that under identical calcium carbonate precipitation amounts, lower urease activity resulted in higher UCS.  
As UA gradually increases to the 5-18 transition interval, SHAP values rapidly decline, with the fitting curve showing a typical negative exponential decay trend, reflecting rapidly diminishing marginal gains. When urease activity exceeds 20, the model's response tends to stabilise, with SHAP values approaching zero. D\({}_{50}\) also exhibits complex, non-monotonic variation trends. Within the low particle size range near 0, SHAP values are highly dispersed, reflecting significant uncertainty in prediction results. As particle size increases to 0.4-0.7, the contribution gradually stabilises with a slight decline. However, upon further increase to the 0.8-1.7 range, SHAP values rise again, indicating significant nonlinear inflection points located approximately around 0.7. OD\({}_{600}\) presents a clear positive influence trend, with SHAP values continuously increasing from approximately \(-\)0.75 to 0.5. This result aligns with MICP reaction mechanisms, where higher bacterial concentrations facilitate improved calcium carbonate precipitation efficiency, thereby enhancing sand cementation performance. Therefore, in engineering implementation, bacterial cultivation conditions should be rationally optimised to achieve appropriate bacterial density. e\({}_{0}\) demonstrates a negative correlation with SHAP values. As the void ratio increases from 0.4 to 1.0, its SHAP values gradually decrease, indicating that larger pore spaces may result in uneven distribution of bacteria and nutrient solutions, subsequently weakening cementation effectiveness.  
In contrast, the remaining input parameters (Mu, Cu, Mc\({}_{\text{a}}\)) have relatively limited influence on strength prediction results. For instance, Mu's SHAP values are mainly distributed between \(-\)0.6 and 0.6, with the overall trend slightly negative. Although these factors' individual contributions are not significant, their synergistic effects with dominant factors should still be comprehensively considered in actual engineering design to achieve optimal sand improvement results. In summary, this analysis provides theoretical support for MICP parameter optimisation, emphasising that calcite generation, urease activity control, and particle size characteristic adjustment should be prioritised in strength prediction and engineering practice.