## 6 FE Results and Analysis
### Vibration Attenuation Pattern of the Pile-Raff Foundation  
Figure 18 shows the vibration velocity amplitudes at the track structure and underlying soils in the transversal direction from the track center at three different speeds. In Figure 18a,b, at the top of the track slab, the maximum velocities of the FE simulation at different train speeds are slightly higher than that of the model test. The attenuation law of the vibration velocity from the track center along the embankment is very consistent, showing only a slight difference in the velocity amplitude. The vibration velocity increases with the train speed. As shown in Figure 18b, for the model test, when the train speed is 270 km/h, the increase range of velocity is significantly higher than that at low speeds. The vibration velocity attenuation rate can reach 90 % from the track slab to the top of the roadbed. It is shown that the vibration intensity of the upper structure of the track slab is large, and decreases quickly to lower than 5 mm/s in the roadbed while the vibration velocity of the lower foundation bed and the embankment structure decreases rapidly to less than 5 mm/s. The influence of the vibration damping attenuation of the roadbed and embankment under different train speeds is consistent, which further verifies the accuracy of the numerical simulation method. The FE numerical simulation results are close to the model test results at high speed. Figure 19 shows the distribution of the vibration velocity along the depth from the roadbed in the middle cross-section, where velocity sensors were located under the track center. The peak value obtained from the FE simulation is slightly larger than that from the  
Figure 18: Comparison of the vibration velocity attenuation along the horizontal direction. (**a**) V1–V4, (**b**) V2–V4. model test, and the velocity distribution and attenuation law obtained by the two methods are basically consistent. This is related to the consistency between the parameters of the model test material and the FE simulation. As mentioned earlier, the water content, degree of compaction, and gradation size impact on the vibration characteristic of the embankment and pile-raft foundation, thus resulting in a certain increase of the damping coefficient, and leading to vibration attenuation. For the model test and FE simulation, the velocities decrease along the depth from the roadbed to the raft, and have a vibration enhancement region from the raft to the 1 m depth of the foundation soil. It shows that the vibration wave forms a small area with a vibration strengthening effect at 1 m of the foundation soil, and then decreases gradually along the foundation. For \(v=270\) km/h, the maximum velocity at the bottom of the subsoil is 0.45 and 1.57 mm/s, which is much lower than that at the embankment. The vibration attenuation rates of the velocity along the depth from the roadbed for the model test and FE simulation at different train speeds were calculated and are shown in Table 10. The vibration attenuation rates of the velocity from the roadbed to the bottom of the subsoil are 85.84% and 69.66% at a train speed of 180 km/h, 87.33% and 69.13% at a train speed of 225 km/h, and 89.34% and 69.81% at a train speed of 270 km/h, respectively. The vibration velocities decrease at much faster rates within the first 0.7 m of depth from the roadbed surface, and increase within the 1 m depth, and then the rates slow down. With the increase of the depth, the vibration velocities decrease and increase along the embankment-pile-raft foundation. Besides, the increase of the train speeds causes a certain increase of the velocity at different locations of the embankment and XCC pile-raft foundation.