## 3 Results and Discussion
### Distribution Characteristics of the Dominant Frequency and Amplitude of Subgrade Vibrations  
In Section 3.2, the time-domain curves of subgrade vibration acceleration were analyzed. However, frequency-domain analysis can provide additional and distinct information. By performing a Fourier transform on the time-domain curves of vertical vibration acceleration, frequency-domain curves were obtained. The characteristic values, dominant frequency, and corresponding maximum amplitude from the frequency-domain curves were then analyzed. The spectra of the vibration acceleration at different measuring points at different measurement points on survey line 1 at the toe of the slope under both conditions are shown in Figure 13. As shown in Figure 12, the dominant frequency under the condition without a soil hole was 20.91 Hz, while the dominant frequencies under the condition with a soil hole were 22.27 Hz, 23.18 Hz, and 22.73 Hz, respectively. This suggests that the dominant frequency is slightly higher under the condition with a soil hole compared to the condition without a soil hole, and the closer the position is to the soil hole, the higher the dominant frequency becomes. The maximum amplitudes at the three positions under the condition without a soil hole were 33.72 mm/s\({}^{2}\), 36.66 mm/s\({}^{2}\), and 47.68 mm/s\({}^{2}\), respectively, while under the condition with a soil hole, the maximum amplitudes were reduced to 24.02 mm/s\({}^{2}\), 19.14 mm/s\({}^{2}\), and 32.76 mm/s\({}^{2}\), representing attenuations of 28.76%, 47.79%, and 31.29%, respectively. These results indicate that the maximum amplitude is higher under the condition without a soil hole, while under the condition with a soil hole, the amplitude attenuation is more pronounced, particularly near the soil hole. Figure 12: Spatial distribution of vibration acceleration amplitude at measurement points on survey lines 1 and 3. The spatial relationship curves of the dominant frequency and corresponding amplitude at the measurement points on survey lines 1 and 3 are shown in Figure 14. Comparing the dominant frequencies, it can be seen that the frequencies at the toe of the slope were concentrated in the 20-24 Hz range, while at the position 10 m from the toe of the slope on survey line 3, the frequency at the soil hole location dropped to 5 Hz, indicating that high-frequency vibrations have been largely absorbed by the soil. Comparing the amplitudes of the frequency-domain curves, it was evident that the farther the position was from the vibration source, the smaller the amplitude. The maximum amplitudes at the \(-\)16 m, 0 m, and 16 m positions on survey line 3, 10 m from the toe of the slope, under the condition without a soil hole were 21.8 mm/s\({}^{2}\), 22.35 mm/s\({}^{2}\), and 24.02 mm/s\({}^{2}\), respectively, while under the condition with a soil hole, the maximum amplitudes were 16.45 mm/s\({}^{2}\), 14.85 mm/s\({}^{2}\), and 25.85 mm/s\({}^{2}\), respectively. Compared to the condition without a soil hole, the amplitudes under the condition with a soil hole had attenuated by 24.54%, 33.56%, and \(-\)7.62%. Under the condition with a soil hole, the central position  
Figure 13: Spectra of the vibration acceleration at different measuring points. had a smaller maximum amplitude and a greater degree of attenuation compared to other positions, consistent with the characteristics observed at the toe of the subgrade. In summary, the dominant frequency and corresponding amplitude of the vertical vibration acceleration frequency-domain curves at positions 0-10 m from the toe of the slope can also serve as dynamic monitoring indicators for assessing the health of the subgrade. Under karst subgrade conditions, the dominant frequency tends to decrease significantly as the distance from the monitoring point to the toe of the slope increases, with a corresponding decrease in amplitude.