## 3 Materials and Methods  
The potential application of GPR technology was demonstrated on an experimental section of a Hungarian residential street that was about 220-240 m in length. The measurements and their assessment aimed to control the prescribed compactness and air void content of freshly built asphalt layers. The composition of the road pavement structure of the analysed two-lane residential street was as follows:  
1. A 4.0 cm AC 11 wearing course. 2. A 7.0 cm AC 22 binder course. 3. An 8.0 cm AC 22 base course. 4. A 20.0 cm FZKA 0/63 unbound granular base. 5. A 20.0 cm sandy gravel protection layer. Samples were taken from the AC 11 and AC 22 asphalt mixtures and tested in the laboratory. The main characteristics of these asphalt mixtures were as follows:  
1. The AC 11 maximum density of the wearing course \(G_{mm}=2436\) kg/m\({}^{3}\). 2. The AC 22 maximum density of the binder course \(G_{mm}=2572\) kg/m\({}^{3}\). The proportion of the binder (bitumen) by weight was \(P_{b}=4.1\%\), with its relative density \(G_{b}=1050\) kg/m\({}^{3}\) in both mixes. The maximum density of the aggregates used was \(G_{sb}=2759\) kg/m\({}^{3}\). To determine the model parameters, either in situ drilled core samples or gyratory specimens obtained from a given asphalt mixture can be used [35]. In the present work, the latter method was chosen, and gyratory specimens were prepared in three ways from the transported asphalt material in the laboratory to calibrate the models for the air void content and the relative permittivity. The reference specimen had the prescribed mass and was compacted at 150 turns. The second specimen had a 10% increase in mass and was compacted at 408 turns. The third specimen had a 10% decrease in mass and was compacted at 12 turns. All specimens were split into three slices, and their \(G_{mb}\) bulk density and \(\varepsilon_{AC}\) relative permittivity were determined using a GSSI PaveScan device (Figure 2). The PaveScan device basically measures the dielectric characteristics of the analysed asphalt mixture with a 2 GHz middle-frequency antenna and estimates the bulk density. In the next phase of this research study, the correlation between the \(\varepsilon_{AC}\) relative permittivity measured in the laboratory and the \(AV\) air void content of the asphalt layer was determined. The air void content can be calculated from densities as follows:  
\[AV=\frac{G_{mm}-G_{mb}}{G_{mm}} \tag{8}\]  
The HD and MnDOT models were fitted to the data points of air void content and relative permittivity determined in the laboratory. Besides these two popular models, another \(S\)-shape function was investigated, which has been successfully applied in the field of rheology [37]:  
\[y=\frac{a}{1+\left(\frac{x}{c}\right)^{b}}+d \tag{9}\]where \(a\) denotes the difference between the upper and lower asymptotes of the function, \(b\) denotes the slope of the function between the upper and lower asymptotes, \(c\) shifts the total curve horizontally (left or right, depending on its value), and \(d\) is the lower asymptote of the function. The recommended model of this work, as described in Equation (9), possesses all the positive qualities of the MnDOT model and has only 4 parameters instead of 5. Moreover, considering the model constraints established by [36], the number of remaining free parameters has been decreased to 2 as follows:  
\[AV=\frac{0.20}{1+\left(\frac{e_{AC}}{c}\right)^{b}}+\frac{0.0005}{\left(e_{AC}- 1\right)} \tag{10}\]  
To determine the optimal parameters for these three nonlinear models, a program code was developed in Python, mainly applying the curve_fit procedure from the SciPy library. The confidence intervals of the parameter sets of the models fitted to the data were calculated using the NumPy function. The laboratory data and model parameters were determined by minimising the least square error, thereby providing the possibility of recalculating the relative permittivity data into bulk density or air void content.