## 3 Experimental Results and Analysis
### Correlation Between Cone Tip Resistance (\(q_{\text{c}}\)) and CBR Values  
Figure 4 presents a comparison of \(q_{\text{c}}\) and CBR values at various temperatures (\(T\)) and moisture contents (\(\omega\)) for soil samples. It is evident that for compaction degrees of 80%, 85%, and 90%, both \(q_{\text{c}}\) and CBR values initially increase and then stabilize as the \(T\) decreases or \(\omega\) increases. This is similar to the results of [PERSON]'s research [24], which states that there is a functional relationship between \(CBR\) and \(q_{\text{c}}\). Although permafrost is different from non-permafrost soil, from the mechanical point of view, the change pattern of both tests is a reflection of the bearing capacity of the soil. This similarity in trends is because both test methods are penetration tests. Despite differences in probe dimensions, penetration rates, and depths, the penetration process is influenced by the soil's particle structure and moisture content. Both test metrics reflect the compressive resistance and localized shear strength of the soil under a given load. Consequently, changes in temperature and moisture content positively correlate with CBR values and \(q_{\text{c}}\). Thus, the Pearson correlation coefficient method is used for further analysis. The Pearson correlation coefficient (\(r\)) quantifies the strength of a linear relationship between two variables, with \(\left|r\right|\) closer to 1 indicating a stronger linear correlation. Using Equation (7), the Pearson correlation coefficients were calculated and are presented in Table 3, showing values of 0.927, 0.934, and 0.94 for the three compaction levels, respectively, all close to 1. The corresponding significance levels (\(Sig\)) are all less than 0.05, indicating statistically significant positive correlations with strong linear relationships. Regression analysis can thus establish a functional relationship between the two.  
\[r=\frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{\sum_{ i=1}^{n}{(  
The regression analysis results between \(q_{\rm c}\) and CBR values are depicted in Figure 5, showing a robust linear relationship with a regression equation correlation coefficient (\(R^{2}\)) of 0.87, which accurately reflects the association between the two. Consequently, the functional model relating soil \(q_{\rm c}\) to CBR values is given by Equation (8). Figure 6 illustrates the histogram-based log-normal distribution of predicted CBR (\(CBR_{\rm p}\)) versus actual \(CBR\) ratios. A 20% accuracy level, defined as a \(CBR_{\rm p}/CBR\) range of 0.8 to 1.2, covers 81% and 51.3% of the area under the histogram and log-normal distribution, respectively, indicating that the model predicts CBR values with minimal error using \(q_{\rm c}\).  
\[CBR_{p}=0.57q_{\rm c}+0.35,R^{2}=0.87 \tag{8}\]  
where: \(CBR_{\rm p}\) is the CBR value of the soil sample obtained by cone tip resistance calculation, and \(q_{\rm c}\) is the cone tip resistance of the soil sample.  
Figure 5: Fit between \(q_{\rm c}\) and CBR values. The \({}^{\star}\) in the figure represents the multiplication symbol.  
Figure 6: Histogram and log-normal distribution of \(CBR_{\rm p}\) versus \(CBR\).