## 2 Materials and Methods
### Void Characteristic Analysis  
Moisture-induced damage is a critical factor in pavement pothole deterioration, closely related to the void characteristics of repair materials. In cold patch asphalt mixtures (CPAMs), voids form an essential component of the internal structure, representing the volumetric space not occupied by aggregate particles and asphalt mortar. The three-dimensional visualization model allows accurate quantification and analysis of void characteristics, including void ratio and spatial distribution. To verify the accuracy of void  
Figure 2: Digital image processing results: (**a**) aggregate extraction visualization; (**b**) coarse aggregate edge detection.  
ratio determination through CT image processing and 3D reconstruction, a comparative analysis was performed using two independent methods: the digital void ratio obtained from CT scanning digital image analysis and the test void ratio measured by the water weight method (T 0706-2021) [34].  
The test void ratio can be expressed as:  
\[VV=(1-\frac{r_{f}}{r_{t}})\times 100\% \tag{1}\]  
where \(VV\) is the text void ratio; \(r_{f}\) is the relative density of asphalt mixture; and \(r_{t}\) is the bulk relative density of compacted specimens.  
This study utilizes two fundamental geometric parameters--equivalent diameter [25] and void area--for quantitative void morphology characterization. The complex void structures identified in CT images were simplified through circular approximations, where each void's cross-sectional area was represented by an equivalent circular area. The diameter of this representative circle, defined as the equivalent diameter, serves as a standardized metric for void size assessment.  
The equivalent diameter is calculated as:  
\[D{=2\sqrt{\frac{A}{\pi}}} \tag{2}\]  
where \(D\) is the equivalent diameter, and \(A\) is the void area.  
CT imaging enables comprehensive characterization of void characteristics beyond mere size quantification, particularly in assessing spatial distribution uniformity within CPAM specimens. This analysis incorporates three key aspects: (1) radial distribution patterns, (2) longitudinal distribution patterns, and (3) fractal dimension quantification of void networks.  
* Radial Distribution Analysis  
The 3D visualization model was systematically divided into four concentric regions of equal area using circular boundaries with radii of \(\frac{1}{2}R\), \(\frac{\sqrt{2}}{2}R\), \(\frac{\sqrt{3}}{2}R\), and \(R\) (Figure 4), where \(R\) represents the specimen radius. This partitioning scheme facilitates the detailed characterization of void distribution gradients from the specimen center to its periphery.  
Figure 3: The three-dimensional reconstruction results: (**a**) 3D image of CPAM specimen; (**b**) 3D void model of CPAM specimen.  
* Longitudinal Distribution Analysis  
With a total specimen height of 63.5 mm, longitudinal scanning was conducted at 0.7 mm intervals, yielding 90 CT images per specimen. After excluding incomplete images near the upper and lower surfaces (where porosity variations are most pronounced [39]), 85 complete cross-sectional images were selected for analysis.
* Fractal Dimension Quantification  
Fractal dimension analysis was employed to characterize void network complexity and spatial uniformity. As a robust metric for quantifying irregular geometric patterns [40], the fractal dimension provides insights into void area distribution continuity. Lower fractal dimension values indicate more uniform void distribution with fewer large, continuous void areas.  
The void cycle length can be expressed as:  
\[lnP=C+(\frac{B}{2})lnA \tag{3}\]  
where \(P\) is the void cycle length; \(A\) is the void area; \(B\) is the fractal dimension; and C is a constant.