## 3 Numerical Simulation and Laboratory Testing
### Numerical Simulation  
Concrete, as a typical composite material, has a high degree of non-uniformity, and changes in its internal structure can significantly affect its dielectric properties. The different components of concrete (such as cement, aggregates, additives, etc.) have different dielectric constants, and changes in the proportion of components can lead to changes \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Information** & **Number** & \begin{tabular}{c} **Defective** \\ **Layout** \\ \end{tabular} & \begin{tabular}{c} **Measurement** \\ **Method** \\ \end{tabular} & \begin{tabular}{c} **Strength \& Dimensions** \\ \end{tabular} \\ \hline (a) & H\_B0 & - & scan after loading & \\ \hline (b) & H\_BF1 & \begin{tabular}{c} PVC, \\ Wooden box \\ \end{tabular} & Direct scan & \
\begin{tabular}{c} Strength: C30 \\ Dimensions: \\ \end{tabular} \\ \hline (c) & H\_BF2 &
\begin{tabular}{c} PVC, \\ Styrofoam \\ \end{tabular} & Direct scan & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Concrete beam defect information and measurement methods. Figure 7: (**a**) H_B0: reinforced concrete beam; (**b**) H_BF1: 40 mm diameter PVC pipe and 60 mm side length of non-confined solid; (e) H_BF2: 25 mm diameter PVC pipe and 30 mm side length plastic foam. in the overall dielectric constant [31; 32]. Therefore, it is crucial to develop more accurate and heterogeneous electromagnetic field propagation material models [33]. This article proposes a three-dimensional numerical model of heterogeneous concrete (See Figure 8), where the distribution of different materials in concrete is random. By writing Python scripts, the specific positions of different materials in concrete structures are randomly generated. In the model, materials such as coarse aggregate, fine aggregate, and cement are defined, and they have different volume fractions and particle size ranges in concrete. For example, the particle size of coarse aggregate is greater than or equal to 5 mm, while the particle size of fine aggregate is between 1 mm and 5 mm. In addition, each material is assigned different dielectric parameters, and after setting the aggregate parameters, the remaining space in the concrete model is filled with cement material. This script is implemented in the input file of gprMax [34; 35]. The specific internal material parameters of concrete are shown in Table 2, and the internal material information of concrete is shown in Table 3.  
The thickness of PVC pipes and square wooden boxes in the model with built-in defects is 2 mm, and the concrete beam model with built-in defects is shown in Figure 9. We divided three sampling lines, L1, L2, and L3, on the surface of each concrete beam (see Figure 10). Due to the unevenness inside the concrete, the A-scans of L1, L2, and L3 are not the same in the cross-section of the concrete structure. Therefore, collecting multiple \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Materials** & **Dielectric Constant** & **Electric Conductivity** & **Relative Permeability** & **Magnetic Loss** & **Volume Proportion** & **Particle Size (mm)** \\ \hline Coarse aggregate & 7.0 & 0 & 1.0 & 0 & 55\% & 6–20 \\ \hline Fine aggregate & 6.0 & 0 & 1.0 & 0 & 20\% & 2–5 \\ \hline Cement & 6.5 & 0 & 1.0 & 0 & 20\% & - \\ \hline Air & 1.0 & 0 & 1.0 & 0 & 5\% & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties in 3D models. Figure 8: A heterogeneous numerical model of concrete. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Defective Material** & **Dielectric Constant** & **Size** \\ \hline PVC & 4 & Diameter size: 40 mm, 25 mm \\ \hline Wooden box & 2.5 & Length: 60 mm \\ \hline Crushed stone & 7 & - \\ \hline Styrofoam & 3 & Length: 30 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of build-in materials in concrete beams. measurement lines ensures the repeatability of the data and enrich the datasets available for training CNN models. Table 4 shows the parameter settings for the gprMax 3.0 orthotropic simulation.