## 3 Results and Discussions  
In order to determine the relative dielectric constant value, two undriven piles were selected on the ground surface, and 100 MHz antennas were used for the radar test, respectively. Since the test pile length is known (11.5 m), the top-bottom interface was determined according to the reflection characteristics of radar images at the top and bottom of the sheet pile, and the depth \(h\) (m) corresponding to the bottom interface was set as 11.5 m. The electromagnetic wave propagation time \(t\) (ns) can be directly read by the ordinate of the radar image, the electromagnetic wave propagation speed \(v\) (m/ns) can be obtained by the formula \(v=2\,h/t\), and then the relative dielectric constant \(\varepsilon=\big{(}C/v\big{)}^{2}\) can be obtained by the formula \(v=C/\sqrt{\varepsilon}\). Where \(C\) is the velocity of light (\(C\) = 0.3 m/ns). The average relative permittivity \(\overline{\varepsilon}=(\varepsilon_{1}+\varepsilon_{2})/2\) can be acquired from the two piles. Where \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are the relative dielectric constant values of the two piles, respectively. Taking into account the fact that reinforced concrete U-shaped sheet piles were used, through the radar measurement of undriven piles on the ground, the average relative permittivity was set at 5.5 to obtain depth information when GPR was used with its own software. The non-destructive testing results of 400 and 100 MHz antennas are shown in Figures 7 and 8, respectively. The abscissa of all the radar images is the measurement line length and the vertical coordinates are the testing depth. These black vertical lines are the connection between piles. The black oval frames are the middle damaged position in Figure 7. The black horizontal line indicates the position of the pile bottom in Figure 8.  
As can be seen from the two figures, the high frequency components of the radar signal are not well suppressed and there are many burrs, which cause certain interference to the normal reflected signals. There is serious crushing in the middle and the pile bottom reflection is invisible in Figure 7. While the pile bottom interface is visible in Figure 8, and the bottom is seriously broken. These results indicate that the detection depth of the 400 MHz antenna is limited and the situation of pile bottom cannot be seen, but the detection depth of the 100 MHz antenna is deeper and can better reflect the situation of the pile bottom. Figure 8: GPR image of 100 MHz (B-Scan). Figure 7: GPR image of 400 MHz (B-Scan). As can be seen from the following figures (Figures 9 and 10), the interference signal of the left image is relatively obvious, while the right image is smooth. The interference is filtered out, and the location of the pile foundation damage is easier to determine. For the non-destructive testing image of the 400 MHz antenna, the damage is mainly in the upper and middle parts; the damage location of the pile foundation processed by wavelet transform is relatively clear. It is shown in the white curve box in Figure 9. For detecting the image of the 100 MHz antenna, the white curve box shows the areas of severe damage. After the wavelet transform processed, the damage location and status are clearly visible, interference filtered, which is on the right side of the image in Figure 10. The bottom of Pile#1, Pile#2 and Pile#5 are the most damaged. As shown in Figures 7 and 8, the high frequency radar signal is not well suppressed, and there are many burrs, which cause certain interference to the normal reflected signal. Wavelet transform was applied to the GPR data in Figures 7 and 8, and the processing results are shown in Figures 9 and 10. After the wavelet transform processing, the processed data is converted into the format of the original radar data file so that the processed data can be displayed by means of the build-in software of the radar system.