## 3 Results and Discussion
### Simulated GPR Data  
gprMax is an open-source simulation software developed by [PERSON] and others based on the Finite-Difference Time Domain (FDTD) and Perfectly Matched Layer (PML) absorbing boundary [60, 61]. Its primary function is to simulate the propagation of GPR electromagnetic waves. Due to its advantages of solid professionalism, high computational efficiency, convenient parameter setting, and realistic simulation results, gprMax is very suitable for simulating GPR for road structure detection. In this study, defects of different types and sizes located in the road interior were taken as the primary research objects, and the basic parameters of the gprMax model are shown in Table 1. Four media layers were set in the model, and the parameters of each layer are shown in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline The model size (m) & 5.4 \(\times\) 2.0 \(\times\) 3.0 \\ The grid step (m) & 0.02 \(\times\) 0.02 \(\times\) 0.02 \\ The width of PML (m) & 0.2 \\ Time window (ns) & 44 \\ Center frequency (MHz) & 300 \\ Type of excitation source & Ricker \\ The initial coordinate of transmitting antenna (m) & (0.2, 1.0, 2.8) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of the gprmax model. Figure 7: Basic flow of K-means clustering algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Structural Layer** & **Relative Permittivity** & **Electrical Conductivity (S/m)** \\ \hline Air & 1 & 0 \\ Surface & 6 & 0.005 \\ Base & 8 & 0.005 \\ Subgrade & 12 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the medium at each layer of the model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model No.** & **Type of Defect** & **Location** & **Size (m)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: Type, size, and location of defects in the model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline The initial coordinate of transmitting antenna (m) & (0.2, 1.0, 2.8) \\ The moving step of the antenna (m) & 0.02 \\ The number of measured lines & 251 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._After the models were established, an XZ section was selected along the Y-axis every 20 cm, and the transmitting antenna and receiving antenna were placed above each section  
Figure 8: Defect model. for the GPR detection. After the gprMax processing, a group of B-Scan images were obtained, which were preprocessed as shown in Figure 9.  
Figure 9: _Cont_. The above images were processed by BP imaging, and the processing results are shown in Figure 10. It can be seen that after the pretreatment and BP image processing, the concentrated position of the reflected signal in the image was consistent with the actual position of the defect. Figure 10: _Cont_. Figure 9: B-Scan images. Figure 10: Results of BP imaging. Next, the radar data of each section after the preprocessing and BP imaging processing were interpolated in MATLAB to construct a 3D data set. Then, the K-means-AHC algorithm was used to calculate the threshold. All data were divided into background data and effective reflection data according to the threshold, and all background data were set to 0. Finally, the upper and lower surfaces of the effective reflection data were extracted and imaged in MATLAB, as shown in Figure 11. The red or blue part of the diagram represents the actual defect. Figure 11: Results of 3D reconstruction. The central position of the reconstructed defects is shown in Figure 8:0 Combined with the image, the size and position of the reconstructed defect were consistent with the actual size and position of the defect in the model.