## 3 Correlation Analysis Between Macroscopic Mechanics and Microscopic Pore Characteristics
### Correlation Analysis Between Unconfined Compressive Strength and Microscopic Porosity  
To assess the strength and direction of the correlation between porosity and unconfined compressive strength, and to further validate the reliability of using porosity as an indicator for evaluating the engineering properties of soil, it is necessary to establish a direct univariate function prediction model between porosity and unconfined compressive strength. This will allow for a more accurate prediction of unconfined compressive strength and serve engineering applications. Therefore, an analysis of the correlation between microscopic porosity and unconfined compressive strength has been conducted. In our work, the data analysis software SPSS 24.0 (Statistical Product and Service Solutions) was utilized to analyze the correlation between the unconfined compressive strength and the microscopic porosity of 12 soil samples under different disturbance degrees. The means and standard deviations presented in Table 5 are the results of the SPSS software analysis, which describe the statistical measures that characterize the distribution of the experimental data. During the correlation analysis with SPSS, the overall characteristics of all variables were mainly reflected through the mean values of various samples, indicating the central tendency of the experimental data. At the same time, comparisons were made between different groups or cross-groups. In comparative analysis, the differences in mean values between different groups quantified the degree of difference between them, thereby facilitating the analysis of correlations. From Table 5, there is a significant correlation between the unconfined compressive strength of the soil sample and its porosity, as indicated by a \(p\)-value less than 0.001 and a correlation coefficient of \(-0.963\), demonstrating a strong negative linear correlation. Consequently, a linear regression analysis was conducted to assess the correlation relationship between microscopic porosity and unconfined compressive strength, using unconfined compressive strength as the dependent variable and porosity as the independent variable [33]. Through regression analysis, the following regression model was obtained. \[\tau=701.436-7.657m \tag{3}\]  
The regression equation's goodness of fit, with an \(R^{2}\) of 0.927, indicates a well-fitted model. Comparison of the regression curve values with the experimental data, as illustrated in Figure 5, reveals that the test data closely align with the fitted values, suggesting a high correlation between the fitted values and test values, and suggesting that the regression model is relatively reliable. Therefore, in actual engineering practice, on-site sampling followed by SEM analysis can be performed. Subsequently, based on the regression model between the microscopic porosity and the unconfined compressive strength of soil, the unconfined compressive strength from porosity data can be rapidly estimated, facilitating the assessment engineering properties of the soil. Correlation and regression analyses suggest that the unconfined compressive strength of Zhanjiang Formation structural clay is influenced by porosity, with higher porosity correlating with lower strength. This indicates that the unconfined compressive strength of soil is affected by its internal pore structure. Vibrational disturbances lead to an increase in pores within the sample, which enlarges the distance between soil particles, reduces the bonding force, and renders the soil more susceptible to damage. Consequently, the unconfined compressive strength of soil decreases continuously as the disturbance degree increases. In undisturbed samples with lower porosity, greater friction and stronger bonding force between soil particles result in a higher unconfined compressive strength. It is evident