## 4 Results and Discussion
### Evolution Law of Macro-Texture Characteristics  
According to Section 3.2, nineteen texture geometric parameters were calculated. These geometric parameters can be directly used to characterize macro-texture of the pavement. To investigate the potential relationship between pavement macro-texture and pavement compaction, this study conducted a correlation analysis between the compactness of the asphalt mixtures (measured by degree of compaction and number of roller passes) and the geometric parameters. The correlation coefficient (r) was commonly utilized to analyze the correlation between the two variables, and its calculation formula is as follows:  
\[r=\frac{\sum_{j}^{n}\left(x_{i}-\overline{x}\right)\left(y_{i}-\overline{y} \right)}{\sqrt{\sum_{i}^{n}\left(x_{i}-\overline{x}\right)^{2}}\sqrt{\sum_{i}^ {n}\left(y_{i}-\overline{y}\right)^{2}}} \tag{3}\]  
where the \(x_{i}\) is the geometric parameter value of the \(i\)-type asphalt mixture, and \(\overline{x}\) is the average geometric parameter value of the asphalt mixtures; \(y_{i}\) is the compactness value of the \(i\)-type asphalt mixture, and \(\overline{y}\) is the average compactness value of the \(i\)-type asphalt mixtures.  
Figure 9: Decomposition by 2D wavelet transform algorithm.  
(1) Figure 10 illustrates that most of the indicators display a negative or weak positive correlation with compaction. A larger geometric parameter value typically indicates a rougher surface texture. Theoretically, as compaction progresses, the macro-texture is influenced by applied forces resulting in a smoother surface and a decrease in the values of geometric parameters. However, some indicators present anomalous behavior in the case of large NMAS asphalt mixtures. Coarse aggregates occupy a significant proportion of mixtures, and their macro-texture is hard to alter during the compaction process.  
(2) Figure 10 reveals that the asphalt mixtures with a lower void content exhibit stronger correlations with a larger number of indexes. The changes in geometric parameters of macro-texture exhibit regularity. This suggests that these mixtures form a denser structure early in the compaction process where aggregates are fixed in place and the macro-texture is not affected during the later stages of compaction. Therefore, the formation and alteration of macro-texture in compacted asphalt mixtures exhibit regularity when the void content is low. Monitoring geometric parameters of the macro-texture can enable real-time control of compaction quality.  
(3) Figure 11 shows that the MPD curve decreases almost linearly throughout the compaction process, with R\({}^{2}\) values of 0.9452 for AC-13, 0.885 for AC-16, and 0.8703 for SMA-13. This phenomenon explains the common occurrence of insufficient MPD resulting from over-compaction in the field. Because MPD is an indicator of skid resistance, caution should be exercised to prevent over-compaction during field compaction procedures.  
(4) Additionally, Figure 12 shows that the convergence of the sp (maximum peak height) and vmp (peak material volume) parameters implies that they can be used to monitor compaction progress. The convergence of these two parameters signifies that the compaction process has essentially been completed, particularly in asphalt mixtures AC-16 and VMA-13, where this phenomenon is more pronounced. Furthermore, the variation in the sp and vmp parameters is similar to that of the compaction degree curve. It indicates that the reduction in volume and height of the macro-texture peaks is regular during the compaction process.  
Figure 12: (**a**,**b**) Fitted curve of compaction and \(Sp/Vmp\) from AC-16; (**c**,**d**) Fitted curve of compaction and \(Sp/Vmp\) from SMA-13.