## 2 Test Method  
### GPR Detection and Forward Simulation  
GPR technology operates by transmitting high-frequency broadband electromagnetic pulses into a subsurface through a transmitting antenna. As shown in Figure 1, upon encountering subsurface structures with differing electrical properties, these electromagnetic waves undergo reflection and refraction at interfaces, subsequently being received by the receiving antenna upon returning to the surface. By analyzing parameters such as the signal waveform, intensity, and two-way travel time, the depth, spatial position, structure size, electrical properties, and geometric shape of subsurface anomalies can be determined, thereby facilitating the detection of hidden subsurface targets [16; 17]. The GPR frequency range encompasses the electromagnetic waves emitted by the radar, utilizing scattered echoes from the targets for signal detection and parameter estimation. The center frequency denotes the peak operating frequency of the radar antenna [18; 19].  
The propagation time of the electromagnetic pulse is described in Equation (1). When the medium's electrical conductivity is very low, the wave speed can be approximated using Equations (2) and (3) [20]. However, when the medium's electrical conductivity is non-negligible, the wave speed \(v\) depends on both the electrical conductivity and the dielectric constant of the medium, rendering the calculation more complex, and it is typically determined through empirical measurements [21].  
Figure 1: Principle of geological radar detection.  
\[t=\sqrt{4z^{2}+x^{2}}/v \tag{1}\]  
\[v=c/\sqrt{\mu_{r}\epsilon_{r}} \tag{2}\]  
\[c=1/\sqrt{\mu_{0}\epsilon_{0}}\approx 3\times 10^{8}\text{ m/s}=0.3\text{ m/ns} \tag{3}\]  
In the above equations, \(v\) is the propagation speed of the electromagnetic wave in the medium (m/ns); \(z\) is the burial depth of the subsurface target (m); \(x\) is the horizontal distance between the transmitting and receiving antennas (m); \(t\) is the propagation time of the electromagnetic pulse (ns); \(c\) is the speed of electromagnetic waves in a vacuum (m/ns); \(\mu_{r}\) is the relative magnetic permeability of the medium; \(\mu_{0}\) is the magnetic permeability of a vacuum; \(\varepsilon_{r}\) is the relative dielectric constant of the medium; and \(\varepsilon_{0}\) is the dielectric constant of a vacuum.  
This study employs the GprMax forward simulation software, based on the Finite Difference Time Domain (FDTD) method, to solve the 3D Maxwell equations and establish a forward simulation of GPR subgrade defects. The model simulates electromagnetic wave propagation in a semi-infinite space, using lossy media at the boundaries to absorb waves, achieving the desired effect within a finite grid. The model uses perfectly matched layer (PML) boundary absorbing conditions, where the electromagnetic waves entering the PML boundary absorption layer are attenuated rapidly, without reflection. Additionally, the model employs Ricker wavelets as the excitation source for the GprMax forward simulation, effectively simulating the detection of subgrade defect models. Ricker wavelets, which have the minimum phase input with positive and negative peak values, closely resemble the field source of the GPR transmitting antenna [22].