## 3 Experiment Results and Discussion
### Internal Vibration Velocity Response of the Track and Pile-Raft Foundation  
Figure 9 illustrates the variation of the vibration velocities at different locations (V5, V6, V7, V11) with the time history. It can be found in Figures 7 and 8 that the velocity responses are consistent with the characteristics of the dynamic loading curve for both low and high train speeds, and similar results can also be found in Figure 9. For the case of \(v=90\) km/h, the maximum vibration velocity at location V5 (0.15 m under the roadbed surface) is 0.6 mm/s, which decreases by 50% compared with that at V2 (on the roadbed surface). The maximum velocity values at the raft (V6), cushion (V7), and at the bottom of the subsoil (V11) are 0.58, 0.48, 0.08 mm/s, respectively. The attenuation ranges of the velocity from the roadbed bottom to the subsoil bottom (i.e., V6 to V11) reach 86.7%. In contrast, the amplitude and intensity of the velocity are increased for the case of \(v=270\) km/h. The vibration velocity amplitudes at V5, V6, V7, and V11 are 4.2, 2.55, 1.58, and 0.45 mm/s, which are 7, 4.4, 3.3, and 5.6 times more than those at the corresponding position of \(v=90\) km/h. The attenuation ratio of the velocity from the roadbed bottom V5 to the subsoil V11 is 82.4%. The vibration velocity propagates down along the embankment and attenuates gradually. Vibration isolation and attenuation phenomena occur in the embankment and pile-raft foundation. The vibration waves move along the subsoil, and decrease to a very low level at the subsoil, which is much lower than that at the roadbed surface. The frequency contents of the vibration velocities at the road, raft, and subsoil are shown in Figure 10. For \(v=90\) km/h, the peak values appear at a frequency point below 10 Hz, including 1, 3, and 9 Hz, reflecting the characteristic frequencies of the geometry of the train compartment. The peak values of the vibration velocity frequency spectrum are distributed in low-frequency and medium-frequency regions, respectively. In Figure 10a, there is a small amplitude of vibration energy in the 27-40 Hz region of the roadbed, and the vibration wave is enhanced in this frequency band, indicating that the characteristic frequency of the vibration of the roadbed packing is distributed in this region. In Figure 10b, for \(v=270\) km/h, information of the frequency contents shows peaks at about 3, 9, and 27 Hz. Compared with the low speed, the peak points of the vibration speed spectrum gradually move to the medium-frequency area, and increase with the increase of the train speed. Larger velocity spectrum peaks occur in the range of 27-40 Hz, which is 8 times more than that at low speed, and the ratio of vibration energy is higher than that at low speed. Figure 9: Time history curves of vibration velocities at different locations of the pile–raft foundation. (**a**) Roadbed (V5, v = 90 km/h), (**b**) Roadbed (V5, v = 270 km/h), (**c**) Raft (V6, v = 90 km/h), (**d**) Raft (V6, v = 270 km/h), (**e**) Cushion (V7, v = 90 km/h), (**f**) Cushion (V7, v = 270 km/h), (**g**) Bottom of subsoil (V11, v = 90 km/h), (**h**) Bottom of subsoil (V11, v = 270 km/h). Figure 10: Frequency spectrum analysis of vibration velocities at different locations of a track embankment pile–raft foundation. (**a**) Roadbed (V5, v = 90 km/h), (**b**) Roadbed (V5, v = 270 km/h), (**c**) Raft (V6, v = 90 km/h), (**d**) Raft (V6, v = 270 km/h), (**e**) Cushion (V7, v = 90 km/h), (**f**) Cushion (V7, v = 270 km/h), (**g**) Bottom of subsoil (V11, v = 90 km/h), (**h**) Bottom of subsoil (V11, v = 270 km/h). For low speed and high speed, the frequency contents of the vibration velocity are mainly distributed in the low and medium region, the peak values of which respectively correspond to the passing frequency of the train carriage geometry (\(l_{c}\) = 25 m), bogie (\(l_{ab}\) = 7.5 m), and axle distance (\(l_{wb}\) = 2.5 m), reflecting the characteristic frequencies of the train compartment, adjacent bogie, and wheel load passing through.