## 3 Database Construction
### Data Statistical Analysis  
To understand the distribution characteristics and intrinsic correlations among parameters within the database, this study conducted a detailed statistical analysis of relevant parameters. As illustrated in Figure 2, each parameter exhibits distinct distribution patterns and variability characteristics in the density distribution plots. The median particle size demonstrates a highly concentrated unimodal distribution, with data primarily clustered around 0.15 mm and a relatively narrow distribution width, indicating that the database samples predominantly consist of fine sand. The uniformity coefficient also presents a relatively compact unimodal distribution, with a peak value of approximately 1.8. The initial void ratio distribution is comparatively broad, mainly concentrated between 0.5 and 0.8, with multimodal characteristics, reflecting sample diversity in compaction states and density conditions.  
Among microbial-related parameters, bacterial optical density varies within the 0.5-3.5 range, forming distinct bimodal structures around 1.5 and 2.5, while urease activity distribution exhibits the greatest complexity, with the primary peak located in the 10-15 U/mL interval and overall multimodal characteristics, revealing significant differences among various bacterial strains and cultivation conditions. Regarding nutrient solution parameters, both urea concentration and calcium chloride concentration demonstrate concentrated and regular unimodal distributions. Calcite content is primarily concentrated in the 4-10% range, but the distribution tail extends beyond 25%, presenting pronounced long-tail characteristics. Unconfined compressive strength is concentrated in the 1-4 MPa  
Figure 2: Density distributions of input and output parameters in the MICP database.  
range with tail extension to 15 MPa, indicating that most samples exhibit relatively low strength values, with extremely high strength values being relatively rare.  
The correlation analysis presented in Figure 3 illustrates the quantitative relationships among the input parameters used in the MICP dataset. The lower-left off-diagonal panels display scatter plots between variable pairs, the upper-right panels present the corresponding correlation heatmaps, and the diagonal panels show individual parameter distributions as histograms. Overall, most input parameters exhibit relatively weak pairwise correlations, with a few notable exceptions. For example, urease activity (UA) shows a strong positive correlation with bacterial concentration (OD\({}_{600}\)) (r = 0.833), while the correlation between urea concentration (Mu) and calcium chloride concentration (M\({}_{\text{Ca}}\)) is extremely high (r = 0.975), reflecting their typical use in fixed molar ratios during MICP treatments. This coupling is expected, as urea and calcium chloride, respectively, serve as the primary sources of carbonate and calcium ions in the precipitation process. In contrast, variables such as median particle size (D\({}_{50}\)) exhibit weak or inconsistent correlations with other parameters, suggesting that their influence on the MICP process is more complex and may not follow simple linear patterns. Moderate positive associations are also observed between initial void ratio (e\({}_{0}\)) and microbial-related parameters (OD\({}_{600}\) and UA), indicating potential interactions related to pore space availability and microbial activity.