## 3 Results  
### Void Characteristics Analysis  
The comparison of void ratios obtained through digital image processing and the water weight method is presented in Table 2. The term \"errors\" refers to the mathematical difference between the observed values and the true values, representing the prediction or estimation error of the model. The minor discrepancy between these measurements confirms the high accuracy of the digital image analysis approach. This verification demonstrates the effectiveness of the image segmentation methodology used in this study, particularly in achieving precise threshold segmentation and accurate void identification. The microstructural analysis provides valuable insights into the performance variations among different CPAM formulations, enabling the establishment of quantitative relationships between void characteristics and macroscopic material properties. * Strength Properties Correlation  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group Number** & **Test Void Ratio** & **Digital Void Ratio** & **Errors** \\ \hline CPAM1 & 7.45\% & 7.15\% & 0.30\% \\ CPAM2 & 10.53\% & 9.53\% & 1.00\% \\ CPAM3 & 11.13\% & 9.98\% & 1.15\% \\ CPAM4 & 15.33\% & 13.88\% & 1.45\% \\ CPAM5 & 17.10\%  
Marshall stability, a primary indicator of CPAM's load-bearing capacity, exhibits a moderate quadratic relationship with the void ratio, as shown in Figure 6 (R\({}^{2}\) = 0.76). The initial stability increase with the void ratio indicates the development of a load-bearing skeleton structure requiring optimal void participation. However, beyond a critical threshold, excessive void content compromises structural integrity, resulting in stability reduction. This nonlinear relationship emphasizes the necessity of maintaining an optimal void ratio for maximizing load-bearing capacity. * Moisture Susceptibility Correlation  
The moisture resistance of CPAM, measured by stability retention, shows a pronounced negative exponential relationship with the void ratio in Figure 7. This indicates that a higher void ratio leads to a looser internal structure, making the material more susceptible to water intrusion and thereby reducing its water stability. The coefficient of determination (R\({}^{2}\) = 0.998) demonstrates an excellent fit between the model and the experimental data, suggesting that air void content is a key factor influencing the water stability of cold patch materials. Specifically, when the air void content is relatively low (e.g., below 10%), the residual stability approaches 100%, indicating strong water resistance. However, as the void content increases, residual stability drops rapidly, underscoring the requirement for accurate void content control in the mix design. * Cohesive Properties Correlation  
The cohesion characteristics, expressed through residual rate, exhibit a negative linear correlation with increasing void ratio in Figure 8. The residual ratio decreases linearly with increasing air void content. The coefficient of determination (R\({}^{2}\) = 0.901) suggests that the linear model has good fitting accuracy and effectively captures the overall trend between air voids and residual cohesion. Although the fit is slightly lower than that observed in the exponential model for water stability (Figure 7), it still provides strong explanatory  
Figure 6: Relationship between void ratio and strength. Figure 7: Relationship between void ratio and stability retention. power. When the air void content is high, the internal structure becomes looser, reducing the contact area between aggregates and weakening the bonding strength, which leads to a lower residual ratio. Conversely, a lower void content results in a denser structure and better bonding among aggregates, thereby improving the residual ratio. This correlation highlights the essential importance of void content control for improving long-term pothole repair performance, especially under wet environmental conditions.