*4.1. Testing Area*

Table 2 shows di fferent constructions of tested model asphalt slabs with dimensions of 50 cm × 50 cm × 22 cm. Each slab consists of three layers with a total thickness of 22 cm. The slabs di ffer in their wearing course type, which is: MA—mastic asphalt being the most tight asphalt mix, SMA—stone mastic asphalt, AC—asphalt concrete, BBTM (*fr. beton bitumineuse trés mince*)—asphalt concrete for thin layers, and PA—porous asphalt, being the most porous asphalt mix. The slabs were placed on a metal plate to intensify wave reflection from the bottom of the slab (see Figure 2). The metal plate has a dielectric constant higher than asphalt; hence, during propagation by asphalt media, the wave phase does not change. This is important from the point of view of marking the bottom level of the slab.

Table 3 shows the atmospheric conditions when performing di fferent GPR tests. The reference measurement was made at 28 ◦C (wI). Other measurements were made at a temperature below zero in the following order: on the dry surface of the slab (wII), after pouring water onto the slab (wIII), after ice formation on the slab surface (wIV), in the presence of a thin layer of fluffy snow on the slab (wV), and in the presence of de-icing salt on the surface of the slab (wVI). Measurements were carried out using a GSSI (Geophysical Survey Systems, Inc., Nashua, NH, USA) air-coupled antenna with a central frequency of 1.0 GHz.


**Table 2.** Constructions of model asphalt slabs.

**Figure 2.** Tested model asphalt slabs.



#### *4.2. A-Scans from m1–m5 Slabs Measurements in Various Atmospheric Conditions*

In Figures 3–5, A-scans from measurements of slabs m1–m5 in conditions wI–wVI are shown. As a zero level, the minimum amplitude of the wave reflected from the slab surface was assumed. The bottom level is the minimum amplitude of the wave reflected from the bottom of the metal plate under the asphalt slab. Based on the A-scans, it is visible that both the propagation time through the slab and the reflection amplitude from the surface vary depending on the weather conditions.

**Figure 3.** A-scans of m1 (**a**) and m2 (**b**) slabs in atmospheric conditions wI, wII, wIII, wIV, wV, and wVI; green arrow—assumed zero level, blue arrow—assumed bottom of the slab.

**Figure 4.** A-scans of m3 (**a**) and m4 (**b**) slabs in atmospheric conditions wI, wII, wIII, wIV, wV, and wVI; green arrow—assumed zero level, blue arrow—assumed bottom of the slab.

**Figure 5.** A-scans of m5 slab in atmospheric conditions wI, wII, wIII, wIV, wV, and wVI; green arrow—assumed zero level, blue arrow—assumed bottom of the slab.

### *4.3. Dielectric Constants of HMA*

4.3.1. Dielectric Constants Calculated based on Propagation Time through the Slab of Known Thickness, Hereinafter Named the "B" Method

Table 4 shows two-way travel time through the slabs m1–m5 read directly from the GPR measurement. Knowing that the thickness of slabs m1–m5 is equal to 22 cm, and transforming Equation (1), their dielectric constants (<sup>ε</sup>*rB*) were calculated. The results are summarized in Table 5.


**Table 4.** Two-way travel time through the slabs.

**Table 5.** Dielectric constants calculated based on propagation time through the slabs ('B' method).


The di fferences in dielectric constants depending on the atmospheric conditions during the measurement calculated by the "B" method are not large (Figure 6), but they cannot be ignored. The following trends of apparent increases and decreases of the dielectric constant of the HMA are noted: temperature below zero (wII) causes an apparent decrease of the dielectric constant determined by the "B" method. Pouring the slab with water (wIII) causes an apparent increase in the dielectric constant. Freezing of the formed water film (wIV) causes the apparent decrease of the dielectric constant determined by the "B" method. The presence of snow (wV) on the surface causes an apparent increase in dielectric constant (except slab m3). The presence of salt on the slab surface (wVI) also causes an apparent increase in HMA dielectric constant marked by method "B".

**Figure 6.** Dielectric constants calculated based on propagation time through the slabs ("B" method).

For calculations of dielectric constants using the "B" method, knowledge of thickness is required, which in road practice translates into drilling and taking cores from roads for being measured. The following are dielectric constants calculated based on measurements of the same slabs, under the same atmospheric conditions, but based on the amplitude of the wave reflected from the surface, i.e., by a method that does not require taking cores.

4.3.2. Dielectric Constants Calculated based on the Amplitude of the Wave Reflected from the Surface, Hereinafter Named the "A" Method

Calculations were made based on Equation (2). Table 6 shows the ratio of the wave amplitude reflected from the surface of the slab to the wave amplitude reflected from the metal plate (reference amplitude). Table 7 shows dielectric constants calculated based on amplitudes.

**Table 6.** Ratio of the wave amplitude reflected from the surface of the slab to the wave amplitude reflected from the metal plate.



**Table 7.** Dielectric constants calculated based on the amplitudes ("A" method').

Based on the summaries in Table 7 and Figure 7, it is noted that the dielectric constants calculated based on the reflected wave amplitudes are significantly different from those calculated based on propagation time and known slab thickness. The temperature below zero (wII) of the HMA causes a significant decrease in the apparent value of its dielectric constant. Pouring the slab with water and the presence of a water film on the surface (wIII) causes an increase in dielectric constants calculated with the "A" method. Freezing of water on the surface (wIV) causes a decrease in dielectric constant again. The presence of snow (wV) decreases the dielectric constant (except for slab m5). The presence of salt on the surface (wVI) causes a significant increase in dielectric constant determined based on the amplitude of the wave reflected from the surface.

**Figure 7.** Dielectric constants calculated based on the amplitudes ("A" method).

4.3.3. Calculated Slabs Thicknesses Based on the Wave Amplitude Reflected from the Surface

Table 8 summarizes the thicknesses calculated based on dielectric constants determined based on the amplitudes of waves reflected from the surface. Table 9 shows the relative thickness determination error caused by calculating the dielectric constant based on amplitudes.

**Table 8.** Calculated slabs thicknesses based on the wave amplitude reflected from the surface.


**Table 9.** Relative thickness determinations error caused by calculating the dielectric constant based on amplitudes.


The measurement error in the conditions adopted as a reference is up to −10%, and it is the accuracy of determining the thickness of layers by the method based on the amplitudes of the wave reflected from the surface. Measurements in temperature below zero cause the calculated thickness to be smaller than the actual thickness up to −11%, except for slab m5. The presence of water film on the slab's surface caused the calculated thickness to be up to −11% smaller than the actual thickness, except for slab m5. An icy slab surface caused the calculated thickness to be up to −7% smaller than the actual thickness, except for slab m5. The presence of snow on the slab surface caused the calculated thickness to be greater than the actual thickness of the slab (up to 10% greater), except for slab m5 (thickness −16% smaller). As a result of the decrease in freezing temperature during the presence of de-icing salt on the HMA surface of the asphalt mixture, apparently smaller thicknesses are obtained (up to −29%). 4.3.4. Correction Coefficients for Dielectric Constants Determined based on the Amplitudes Reflected from the Surface

Based on Equation (4), the correction coefficients for dielectric constants determined based on amplitudes to dielectric constants determined based on propagation time through the slab of known thickness were calculated. Their values are summarized in Table 10. The reference conditions were the wI conditions (28 ◦C, dry slab surface). The dielectric constant determined based on amplitudes in all conditions other than wI should be multiplied by the correction coefficient k.

$$\mathbf{k} = \frac{\varepsilon\_{r\_B}}{\varepsilon\_{r\_A}}.\tag{4}$$

where: 

k[−] correction coefficients for dielectric constants determined based on the amplitudes

<sup>ε</sup>*rB* [−] dielectric constants calculated based on propagation time through the slabs ("B" method)

<sup>ε</sup>*rA* [−] dielectric constants calculated based on the amplitudes ("A" method).

**Table 10.** Correction coefficients for dielectric constants determined based on the wave amplitude reflected from the surface.


During determinations of the dielectric constant based on the amplitudes in a reference condition, a dielectric constant correction factor k = 0.87 should be adopted. During determinations of the dielectric constant based on the amplitudes at the temperature of −5 ◦C on the dry slab surface, a dielectric constant correction factor k = 0.97 should be adopted. During measurements at −5 ◦C and with water film presence on the slab surface, a dielectric constant correction coefficient k = 0.92 should be used. During measurements at −5 ◦C and with ice presence on the slab surface, a dielectric constant correction coefficient k = 0.98 should be used. During measurements at −2 ◦C and snow on the slab surface, a dielectric constant k = 1.02 correction coefficient should be adopted. During measurements at −2 ◦C and de-icing salt on the slab surface, a dielectric constant correction factor k = 0.55 should be used.

The thicknesses calculated based on dielectric constants corrected by the mentioned coefficients and the relative thickness measurement error are presented in Tables 11 and 12, respectively.

**Table 11.** Calculated slabs thicknesses based on the corrected dielectric constant.



**Table 12.** Relative thickness determinations error after correction of dielectric constant.

It is noted that the thickness measurements error has been significantly reduced in the case of the slab covered with de-icing salt. Attention is drawn to the fact that the correction coe fficients have been calculated as the average of the coe fficients for 5 slabs with di fferent HMA wearing courses for the determined atmospheric conditions. To significantly reduce the error, a factor calculated for a specific HMA wearing course should be applied.

The coe fficients presented above are a proposal for specific slab geometry (m1–m5), specific measurement conditions (wI–wVI), and selected frequency and antenna design (1.0 GHz air-coupled). The observed trends thrive to expand the base of dielectric constants in controlled atmospheric conditions with a constant change in temperature, amount and type of precipitation, and the amount of de-icing salt used.

When measuring using GPR on large sections, the atmospheric conditions of the surface usually are not known; it is not known if and in which sections the surface was covered with water film, ice, snow, or de-icing salt. Of course, video cameras are helpful in recording the surface atmospheric condition; while it will be possible to record where the water film was on the surface during the measurements, the presence of salt on the surface will not be recognized based on the video image.

In determining the surface conditions, wavelet analysis may be a useful tool to correctly select the proposed correction coe fficient.

### *4.4. Wavelet Analysis of the GPR Signal*

Wavelet analysis was performed using the Db6 wavelet. The type of wavelet was chosen based on a literature review and the selection of the group of wavelets that are most useful in GPR signal analysis as well as the thorough initial empirical analysis of the authors.

Wavelet analysis was performed on the unscaled signal from m3 slab measurements. Figures 8–10 compare the distribution of energy into individual wavelet coe fficients as a function of scale and time. It was noticed that in some cases, the scale coe fficients of signals obtained in di fferent atmospheric conditions at a slab surface di ffer in magnitude. The largest magnitudes have signal scale factors from the measurement of a slab covered with de-icing salt, which is a positive result, because it is the presence of salt on the surface that strongly a ffects the value of the dielectric constant determined based on the amplitude, and, as previously noted, the presence of salt is not detectable by video recording. The results of the conducted analysis thrive at defining the atmospheric conditions on the surface (dry, covered with water film, ice, snow, and salt), which was obtained during the GPR survey.

There is a di fference between the scalograms from the measurement signals taken at temperatures above zero (Figure 8a) and below zero (Figure 8b). Scale factors 9–60 at a distance of 180–250 samples have higher magnitudes when the measurement is performed at a temperature above zero. Scale factors 9–60 at a distance of 200–400 samples have higher magnitudes when the measurement is performed at a temperature below zero.

The scalograms from the measurement signals taken at temperatures below zero on a dry slab surface (Figure 8b), temperatures below zero and water film on the slab surface (Figure 9a), and temperatures below zero and a thin layer of ice on the slab surface (Figure 9b) do not di ffer significantly.

**Figure 8.** Wavelet analysis of A-scan from measurements in conditions (**a**) wI (temp. 28 ◦C, dry slab surface); (**b**) wII (temp. −5 ◦C, dry slab surface).

**Figure 9.** Wavelet analysis of A-scan from measurements in conditions (**a**) wIII (temp. −5 ◦C, water film on the slab surface); (**b**) wIV (temp. −5 ◦C, thin layer of ice on the slab surface).

**Figure 10.** Wavelet analysis of A-scan from measurements in conditions (**a**) wV (temp. −2 ◦C, thin layer of fresh snow on the slab surface); (**b**) wVI (temp. −2 ◦C, de-icing salt on the slab surface).

Snow on the pavement at a temperature below zero (Figure 10a) results in the fact that the majority of energy falls on scale factors 9–60 at a distance of 200–300 samples. The e ffect of salt (Figure 10b) on the surface is that the scale factors 9–60 at a distance of 0–150 samples have very large amplitudes: the largest of those obtained during all other surface conditions.
