# Recognition of Rebar in Ground-Penetrating Radar Data for the Second Lining of a Tunnel
## 3 Experimental Study  
Due to the electromagnetic properties of the rebar, the part of the electromagnetic wave was totally reflected by the rebar, which resulted in the amplitude of the peak point  
Figure 7: The workflow of this study.  
being smaller than the amplitude of the adjacent peak points of the same phase. Therefore, the waveform variation of each A-scan could provide a basis for determining the rebar signal, as shown in Figure 8.  
When GPR detects the tunnel, electromagnetic waves first enter from the air to the second lining. The dielectric constant of air is approximately equal to 1, and the dielectric constant of concrete is approximately equal to 6-9 [18]. According to Equation (4), the phase of the reflected wave at the air-lining interface is opposite that of the incident wave. Then, the electromagnetic wave propagates in the concrete to the rebar. The dielectric constant of the rebar is much larger than that of the concrete, and the rebar totally reflects part of the electromagnetic wave. As a result, the reflected waves from the concrete change, as shown in Figure 8b. This variation is because the dielectric constant of the rebar is considered to be infinite [13], whereas the dielectric constant of concrete is 6-9. Therefore, according to Equations (1) and (4), the reflection coefficient is negative when the electromagnetic wave propagates from the concrete to the rebar. Electromagnetic waves propagating in concrete are interfered with by the rebar, causing the reflected waves from the concrete to fail to attenuate at a certain rate and to show up in the A-scan as peaks with the opposite phase of the incident wave having a smaller amplitude than the adjacent peaks. These peak points are simultaneous for the hyperbolic shape of the rebar, as shown in Figure 8a.  
According to these peak points, the hyperbolic shape of the rebar is reconstructed in the B-scan, as shown in Figure 9a. In Figure 9a, the reconstructed curve reflects the hyperbolic feature of the rebar, but discontinuities appear in some regions. Therefore, the A-scan was extracted from the discontinuous regions, as shown in Figure 9b. The reflection signal of the rebar was not detected in these regions, which is the reason for this phenomenon.  
A correction method was used to solve the problem due to discontinuities in the reconstructed rebar hyperbolas, due to the phenomenon that the medium in the B-scan would exhibit an in-phase axis characteristic. Therefore, it was assumed that the difference between the appearance times of the medium signals in the adjacent A-scan would not exceed a certain threshold. The threshold value \(k\) is expressed as  
\[k=\frac{|A_{i}-A_{mean}|}{A_{mean}} \tag{10}\]  
Figure 8: (a) B-scan with rebar’s hyperbolic features. (b) Waveform attenuation diagram at the letters a, b and c, where the reflected signal of the reinforcement corresponds to the hyperbolic feature appearing in the B-scan.  
where \(A_{i}\) is the two-way travel time of the rebar signal in the ith A-scan and \(A_{mean}\) is the average of the two-way travel times of the rebar signals in all A-scans.  
This method is performed by making a difference between adjacent data and comparing them with 20% of the mean value, where the comparison value is derived from several experiments. If this difference is greater than 20% of the mean value, then it is replaced by the value of the adjacent data. The effect of the correction is shown in Figure 10. On the one hand, the corrected curve reflects the curve feature of the rebar, and on the other hand, the corrected curve indicates that the rebar was located in the 5-7 ns region in the B-scan.