## 2 Methodology
### Data Processing  
For each cube, grayscale images were semi-automatically binarized using an interactive watershed tool in combination with manual selection (Figure 6a). This human-involved approach provides more accurate differentiation of soil pores and particles compared to conventional segmentation methods. The binarized 3D microstructure was then processed to extract the pore structure (Figure 6b), which was further classified into connected pores (Figure 6c) and isolated pores (Figure 6d). The porosity (\(P_{\rm o}\)) refers to the ratio of pore voxels to all voxels. The connected porosity (\(P_{\rm c}\)) is the ratio of connected pore voxels to all voxels, and the isolated porosity (\(P_{\rm i}\)) is defined as the ratio of isolated pore voxels to all voxels.  
Afterward, the connected pore space was segmented into individual pores using pore throats identified through the watershed algorithm in the Avizo software (Figure 6e). The pore throat is defined as the minimum contact area between two adjacent pores. Based  
Figure 4: Workflow to generate the cubes to be analyzed: (**a**) 3D reconstruction; (**b**) noise reduction; (**c**) region-of-interest (ROI) selection.  
Figure 5: Cube partition scheme.  
on this segmentation, a pore network model was generated using the \"pore network\" command in Avizo (Figure 6f). In this model, the radius of each sphere corresponds to the radius of a sphere with the same pore volume, and the throats are modeled as cylinders connecting the pore centers. The cylinder radius matches the actual radius of the contact area (pore throat) between adjacent pores, and its length represents the linear distance between the centers of the two-pore spheres. Figure 6g illustrates the spherical pores in the pore network model, while Figure 6h depicts the pore throats. Rich information characterizing the 3D pore microstructure can be obtained from the pore network model, including the pore volume (\(V_{\text{P}}\)), pore equivalent radius (\(R_{\text{P}}\)), the coordination number (\(C_{\text{N}}\)), throat equivalent radius (\(R_{\text{t}}\)), throat channel length (\(L_{\text{t}}\)) and so on. \(V_{\text{P}}\) refers to the number of voxels in a single pore. \(R_{\text{P}}\) is the radius of a sphere that corresponds to the pore volume. \(C_{\text{N}}\) is the number of throats that are connected to a given pore, reflecting the connectivity of the specimen. The throat equivalent radius (\(R_{\text{t}}\)) refers to the radius of the smallest contact area between two connected pores. The throat channel length (\(L_{\text{t}}\)) is the distance between the centers of these two connected pores.  
For subsequent analyses aimed at determining the representative volume element, the following parameters are considered: total porosity (\(P_{o}\)), connected porosity (\(P_{c}\)), isolated porosity (\(P_{i}\)), average coordination number (\(C_{\text{N}}\)), median of pore volume (\(M_{\text{V}}\)), median of pore area (\(M_{\text{A}}\)), median of pore equivalent radius (\(M_{\text{R}}\)) and median of throat channel length (\(M_{\text{L}}\)). The use of medians ensures robustness to extreme values and enhances the representativeness of the parameters in the distribution sequence.