## 6 FE Results and Analysis  
### Comparison of the FE with the Test Results in the Time and Frequency Domain at Different Locations  
In this section, the FE results are compared with the test results. For train speed \(v\) = 270 km/h, the vibration velocities at the track slab, roadbed, embankment, and pile-raft foundation were calculated in the numerical model.  
Figure 17b,d,f,h,j show the frequency domain analysis results corresponding to the vibration velocity time histories in Figure 16a,c,e,g,i, respectively. Figure 17a shows the time history of the vibration velocity at the track slab induced by the train moving at a speed of 270 km/h. The amplitudes of the vibration velocities are 41.48 mm/s in the FE simulation data and 32 mm/s in the model test data. In Figure 17b, the frequency contents of the vibration velocity for the model test and FE simulation present the same dominant frequencies within certain frequency ranges. Most of the spectral energy of the vibration velocity is concentrated at the frequency of about 3, 9, and 27 Hz. These three dominant frequencies 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.  
Figure 16: Dynamic loading wave (v = 270 km/). (**a**) waveform of dynamic loading wave, (**b**) frequency distribution of dynamic loading wave.  
Figure 17: _Cont._  
Figure 17: Comparisons of the vibration velocity between the FE and test results for train speed v = 270 km/h. (**a**) Track slab (V1, time domain), (**b**) Track slab (V1, frequency domain), (**c**) Roadbed (V5, time domain), (**d**) Roadbed (V5, frequency domain), (**e**) Raft (time domain), (**f**) Raft (frequency domain), (**g**) Cushion (time domain), (**h**) Cushion (frequency domain), (**i**) Bottom of subsoil (time domain), (**j**) Bottom of subsoil (frequency domain).  
In Figure 17c,d, the FE results and model test results still agree with each other in the time and frequency domain. The amplitudes of the vibration velocities are 3.35 mm/s in the FE simulation data and 2.72 mm/s in the model test data. The spectral energy of the vibration velocity in the model test is lower than that in the FE simulation at 3 and 6 Hz. It shows that the vibration attenuation of the model test is higher than that of the numerical simulation in some frequency ranges.  
In Figure 17e,f, the vibration velocities are 4.25 and 2.55 mm/s for the FE data and test data on the raft. Based on the influence of vibration superposition, interference, and attenuation, the vibration velocity energy for the test data displays fast attenuation of the amplitude at low frequency, and is lower than the FE data.  
The same law of the vibration response can also be obtained from Figure 17g,h,i,j. The low-frequency part of the frequency contents for the test data attenuates relatively fast. In general, the time history of the vibration velocity obtained from the numerical calculation agrees well with that from the model test regarding the vibration waveform, amplitude, and frequency characteristics. The water content, degree of compaction, and gradation size will have an impact on the vibration response characteristics of the embankment and pile raft foundation.