## 2 Materials and Methods  
### Material  
The data used in this study were obtained from references [21; 22; 23; 24; 25; 26]. After removing incomplete data, a dataset specifically tailored for this study was formed. This dataset comprises 182 sets of liquid and plastic limit data, 192 sets of mechanical property data, soil moisture content data, and corresponding mineral composition data. The corresponding soil types include various types of soils such as residual soil, soft soil, and reconstituted soil. Based on these data, a neural network was trained to construct a predictive model for the physical and mechanical properties of soils.  
Soils exhibit a wide range of mineral compositions, making it impractical to include the content of all mineral types as input conditions. Hydrophilicity refers to the ability of a mineral to combine with water and is related to the structure of a mineral. The hydrophilic ity of a mineral has a great impact on its various physical and mechanical properties. Therefore, the major minerals present in soils were classified into three categories based on their inherent strength characteristics and structural features. The first category consists of primary minerals with high particle strength and poor hydrophilicity, such as quartz and feldspar. The second category includes clay minerals with relatively lower particle strength and weaker hydrophilicity, such as kaolinite. The third category comprises clay minerals with relatively lower particle strength and stronger hydrophilicity, such as montmorillonite and illite. The structures of kaolinite and montmorillonite are depicted in Figure 1, respectively. Different clay minerals possess distinct mineral structures, hydrophilicity, and varying effects on mechanical properties. Therefore, it is necessary to categorize clay minerals into two groups and separately analyze the effects of their content rather than solely considering the overall clay content [27; 28].  
The mineral composition data were processed according to the classification criteria to obtain the required training dataset. The variables in this dataset include the percentages of different types of mineral composition and the moisture content, with values ranging from 0 to 100. It should be noted that the dataset includes some artificially prepared remolded soil data, and the distribution pattern of variables does not follow a normal distribution. The relationships between parameters in this dataset can be described using the Pearson correlation coefficient between variables, which is calculated as shown in Equation (1). In the equation, \(\operatorname{cov}(X,Y)\) represents the covariance between two variables, while \(\sigma_{X}\) and \(\sigma_{Y}\) represent the standard deviations of the two variables, respectively.  
\[\rho_{X,Y}=\frac{\operatorname{cov}(X,Y)}{\sigma_{X}\sigma_{Y}} \tag{1}\]  
By calculating the Pearson correlation coefficients between all pairs of variables, a corresponding heatmap of the Pearson correlation coefficients is plotted, as shown in Figure 2. From the heatmap, it can be observed that the Pearson correlation coefficients between mineral composition and different physical and mechanical properties are relatively low, indicating weak correlations. On the other hand, the correlation coefficients between different mineral compositions are relatively higher.