## 3 Materials and Methods
After performing the in situ measurements, the relative permittivity values were exported from the PaveScan device at every 0.5 m, starting at the lane edge and moving towards the road axis in the sequence of: 2.9 m, 2.3 m, 1.7 m, 1.3 m, 0.7 m, 0.6 m, 0.1 m, and 0 m.  
The spatial relative permittivity values were recalculated as air void content values by applying the recommended model in this work, as shown in Equation (10). Finally, the in situ relative compactness (relative density) of the analysed layers was calculated [12; 41] using the following formula:  
\[RD=1-AV=\frac{G_{mb}}{G_{mm}} \tag{14}\]  
where \(RD\) is the relative density of the mixture; \(AV\) is the air void content of the mixture; \(G_{mb}\) is the bulk density of the compacted mixture; and \(G_{mm}\) is the theoretical maximum density of the mixture without air void. It is clear from Equation (14) that the density level reached at a construction site and the air void content are two inversely related condition parameters: the higher the compactness, the lower the air void content. This is why the air void content of the built-in asphalt layers is usually characterised based on the relative compactness or the relative density. According to [PERSON] (1990) [41], the initial air void content of a newly built layer cannot exceed 8%, and after compaction, it cannot be less than 3%. Based on these limits, the \(RD\) relative compactness of new layers typically varies between 0.92 and 0.97. Immediately after construction, it is regarded as optimal if the relative compactness is 0.93-0.94. Figure 4: Scheme of the measurements performed on the residential street. Figure 5: A drilled core sample on the base course and measurement of the relative permittivity at its place. Based on the adjusted \(R_{*}^{2}\) and the \(S_{e}/S_{y}\) quotient, every analysed model achieves good performance in predicting the air void content of both asphalt mixture types. Only the HD model shows a slightly lower performance, but the difference to the other models is negligible. However, there are significant differences in the uncertainty of model parameters. The parameters of the HD and MnDOT models vary in a rather wide range, which suggests they are characterised by high uncertainty. A good example for this is the HD model for the AC 22 asphalt mix, where the 95% confidence interval widens at both low and high values of relative permittivity. A similar phenomenon can be observed for the MnDOT model, mainly in the case of the AC 11 asphalt mix. The model recommended in the present paper shows less uncertainty compared to the other two models. The recommended model is characterised by a very narrow confidence interval for both asphalt mixtures, which provides the possibility for more accurate population predictions (Figure 8). The data points of the drilled core samples are indicated on the figures in lime green colour. These data points were not used for model fitting. There are differences between the laboratory and field dielectric constants. The results of the laboratory tests are limited to a certain degree. Thus, the density values obtained from the laboratory tests using  
Figure 8: The recommended model fitted to the laboratory data: (**a**) AC 11 and (**b**) AC 22 asphalt mixtures. Figure 7: The MnDOT model fitted to the laboratory data: (**a**) AC 11 and (**b**) AC 22 asphalt mixtures. the available compaction equipment are much lower than the field values. With in situ compaction, the air void content usually ranges between 4% and 5%. In the laboratory, it is also necessary to consider the scattering of the GPR signal from the edge of the sample under test. Despite this fact, the recommended model fits well even when using such data in the case of the AC 22 asphalt mix. The HD and MnDOT models underestimate the results of the in situ tests (Figures 6 and 7). For the AC 11 wearing course, only one core sample was taken; therefore, detailed analysis could not be performed.