## 7 Conclusions  
In this paper, a series of dynamic large-scale model tests and three-dimensional finite element analyses were conducted to investigate the dynamic response of an XCC pile-raft composite foundation for a ballastless high-speed railway under train moving loads. The tests and FE results are presented and were compared regarding the variation of the vibration velocity to analyze the characteristics of the dynamic response, transmission, and attenuation for the XCC pile-raft composite foundation. The main findings can be summarized as follows:  
For the model test and FE simulation, the vibration velocity at each location reflects 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 at high speed is clearly higher than that at low speed, including the amplitude, similarity, and fluctuations of the intensity, which are associated with the increase of the train speed.  
The frequency contents of the vibration velocity for the model test and FE simulation present the same dominant frequencies in low and medium regions, the peak value of which respectively corresponds to the passing frequency of the train carriage geometry (l\({}_{\rm c}\) = 25 m), bogie (l\({}_{\rm ab}\) = 7.5 m), and axle distance (l\({}_{\rm wb}\) = 2.5 m), reflecting the characteristic frequencies of the train compartment, adjacent bogie, and wheel load passing through. The peak spectrum value at high speed is significantly higher than that at low speed.  
The peak velocity depends significantly on the distance from the track center in the horizontal direction, mainly decreasing by 89.3% and 87% from the track slab to the roadbed for train speeds of 90 and 270 km/h, respectively. The attenuations of the peak velocity follow the exponential curve distribution from low to high train speed. Most vibration attenuations were completed in the process of vibration propagation from the track slab to the roadbed. The velocity attenuation tendencies in the ballast, embankment, and ground are different due to their dynamic characteristics.  
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 velocity distribution and attenuation law obtained from the test and the FE simulation results are basically consistent. The vibration velocities decrease rapidly within the first 0.7 m of depth from the roadbed surface to the raft, and display a vibration enhancement region from the raft to a 1 m depth of the foundation soil. The vibration wave forms a small area with the vibration strengthening effect at 1 m of the foundation soil, and then decreases gradually along the subsoil foundation, to a very low level at the bottom of the subsoil, which is much lower than that at the track slab and roadbed. The pile-raft composite foundation can reduce the vibration level effectively, and improve the safety of trains running in soft soil areas.  
[PERSON] wrote the manuscript and performed the numerical analyses; [PERSON] investigated and reviewed the material parameters required for the numerical and other analyses. All authors have read and agreed to the published version of the manuscript. This work was funded by the National Natural Science Foundation of China (Grant No. 51908152). Not applicable. Not applicable. Not applicable. Not applicable.  
**Data Availability Statement**: Not applicable.  
**Conflicts of Interest**: The authors declare no conflict of interest.