## 2 Sampling and Methodology
### Quantitative Analysis of Loess Microstructure in Different Regions under Natural Conditions  
Table 2 presents the calculated quantitative parameters of the loess microstructure before and after soaking in different regions. Figure 10 illustrates the corresponding trends in these parameters. Quantitative analysis of the microstructure, based on the data presented in the tables and figures, yielded the following results:  
Figure 9: Comparison between the original image and the binary image. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sampling Site** & **State of Soil** & **Average Form** & **Probability** &
\begin{tabular}{c} **Porosity** \\ **Distribution** \\ **Factor** \\ \end{tabular} & **Pore Area Ratio** \\ \hline \multirow{2}{*}{Shanzhou} & Before soaking & 0.398 & 0.991 & 2.8 & 39.21\% \\  & After soaking & 0.357 & 0.988 & 2.5 & 22.78\% \\ \hline \multirow{2}{*}{Mianchi} & Before soaking & 0.388 & 0.987 & 2.6 & 35.86\% \\  & After soaking & 0.355 & 0.985 & 2.2 & 21.77\% \\ \hline \multirow{2}{*}{Gongyi} & Before soaking & 0.342 & 0.984 & 2.2 & 17.86\% \\  & After soaking & 0.323 & 0.983 & 1.9 & 7.57\% \\ \hline \multirow{2}{*}{Xingyang} & Before soaking & 0.343 & 0.979 & 1.9 & 16.15\% \\  & After soaking & 0.329 & 0.977 & 1.5 & 8.32\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative parameters of microstructures in different regions. Figure 10: Variation curves of quantitative microstructure parameters in different regions. (**(a)** average form factor, **(b)** probability entropy, **(c)** porosity distribution dimension, **(d)** pore area ratio). 1. Average form factor. In this paper, the shape coefficient of the pore is defined as \(\text{F}_{\text{i}}=\text{S}/\text{C}\). In the formula, C is the circumference of the circle with equal area to the image contact area, and S is the actual circumference of the image contact area. The value of the pore shape coefficient is between 0 and 1. The larger the value, the closer the pore shape is to the circle, and the smaller the value, the narrower the pore shape. The complexity of pore morphology makes the shape coefficient of a single pore to often show a large error, and the shape of a single pore cannot reflect the total pore characteristics of the soil. Therefore, the average shape coefficient is usually used to quantitatively describe the pore morphology of a soil. The formula for calculating the average shape coefficient is as follows: \[F=\frac{1}{n}\sum_{i=1}^{n}F_{i}\] where n is the statistical number of particle contact points. Larger F-values indicate that the pore features are closer to circular, and vice versa for narrower and longer. A pore shape close to circular means that the larger the pore size, the looser the particle arrangement is. The average form factor serves as an indicator of pore shape. Results suggest that under the influence of overlying load and immersion, the soil's pore structure undergoes a transformation, shifting from a predominantly wide and open configuration to one characterized by narrower and more constricted pores. This observation points to the gradual disappearance of larger pore structures. The aforementioned findings highlight the spatial variability in the microstructure of loess across western Henan, with a corresponding inconsistency in initial water content. Notably, the roundness of loess pores in all four regions shows a general decreasing trend before and after immersion. However, this decline is less pronounced in the Xingyang and Gongyi areas compared to Shanzhou and Minachi. In particular, Shanzhou loess experiences the most significant reduction in pore roundness. This observation suggests that loess particles in the Xingyang and the Gongyi areas are arranged in a denser configuration, rendering their pore morphology less susceptible to alteration. 2. Probability entropy [36]. This parameter serves as a measure of the orderliness of pore and particle distribution within the soil.