## 3 Experiment Results and Discussion
### Velocity Response of the Track and Pied Raff Foundation  
Figures 7 and 8 refer to the time history and frequency contents of the vibration velocities at the track slab V1, roadbed V2, road shoulder V3, and slop toe V4, for the low speed (e.g., 90 km/h) and high speed (e.g., 270 km/h), respectively. Figure 7 (v = 90 km/h) shows the cycle time \(T_{3}=1\) s, representing the time during which one carriage passes the monitoring point. The peak value of the vibration velocity varies with the moving train's axle loads. The maximum values of the track slab, roadbed, road shoulder, and slop toe were measured as 12.5, 1.58, 1.25, 0.84 mm/s, respectively. It is obvious that the peak value decreases quickly from the track slab to the roadbed with an amplitude of 87.4%, and then slows down gradually along the roadbed to the slope toe. For the case of v = 270 km/h (Figure 7b,d,f,h), the cycle time is T\({}_{3}\) = 0.333 s, representing one carriage passing time. At the same locations, V1, V2, V3, and V4, maximum vibration velocities were obtained as 37.5, 4.22, 3.12, 3.45 mm/s, respectively. The peak vibration velocity decreases quickly by 88.8% from the track slab to the roadbed, and then slows down gradually along the roadbed to the slope toe. There is a certain fluctuation of the velocity at the structural break of the raft and embankment. The structural break has an influence on the vibration response of the track, embankment, and pile-raft foundation system. The variation pattern of the vibration velocity corresponds to loading from the bogies. The vibration velocity of the roadbed, shoulder, and slope toe follows a pattern similar to that of the track slab. The difference is that the vibration velocity at a train speed of 270 km/h is higher than that at a train speed of 90 km/h. The vibration velocity at each location can reflect the applied M-wave load and the vibration state of the pile-raft foundation well. The intensity of the vibration velocity curves at each location under the high-speed load is clearly higher  
Figure 6: Dynamic loading hydraulic servo control and digital data acquisition system. than that under the low-speed load, including the amplitude, similarity, and fluctuations of the intensity, which are associated with the increase of the train speed. Figure 7: Time history curves of the vibration velocities at the track slab, roadbed, road shoulder, and slope toe for different train speeds. (**a**) Track slab (V1, \(\
u\) = 90 km/h), (**b**) Track slab (V1, \(\
u\) = 270 km/h), (**c**) Roadbed (V2, \(\
u\) = 90 km/h), (**d**) Roadbed (V2, \(\
u\) = 270 km/h), (**e**) Road shoulder (V3, \(\
u\) = 90 km/h), (**f**) Road shoulder (V3, \(\
u\) = 270 km/h), (**g**) Slop toe (V4, \(\
u\) = 90 km/h), (**h**) Slop toe (V4, \(\
u\) = 270 km/h). Figure 8: Frequency spectrum analysis of vibration velocities at the track slab, roadbed, road shoulder, and slope toe for different train speeds. (**a**) Track slab (V1, v = 90 km/h), (**b**) Track slab (V1, v = 270 km/h), (**c**) Roadbed (V2, v = 90 km/h), (**d**) Roadbed (V2, v = 270 km/h), (**e**) Road shoulder (V2, v = 90 km/h), (**f**) Road shoulder (V3, v = 270 km/h), (**g**) Slop toe (V4, v = 90 km/h), (**h**) Slop toe (V4, v = 270 km/h). In the case of low speed (90 km/h) and high speed (270 km/h), the peak value of the track slab increases three-fold. With the vibration velocity moving to the roadbed and the shoulder in turn, the proportion value of the peak velocity at high speed and low speed decreases gradually. The velocity attenuation is relatively large from the track slab to the roadbed but is relatively small from the roadbed to the slope toe. The frequency spectrum curves of the vibration velocity for the low and high train speeds are compared in Figure 8. For the case of \(v=90\) km/h, typical characteristic frequencies of the vibration velocity are 1, 3, and 9 Hz, corresponding to the passing frequency of the train carriage geometry (\(l_{c}=25\) m), bogie (\(l_{ub}=7.5\) m), and axle distance (\(l_{wb}=2.5\) m), respectively.