Vibration reduction of high-speed railway subgrade with periodic structures based on complex dispersion curves

At present, the researches on the attenuation zone of periodic row piles only stay in the stage of dispersion curve analysis. Only a few scholars have studied complex dispersion curves of 2D model. The dispersion curve can only obtain the range of the attenuation zone, while the complex dispersion curve can obtain its attenuation degree. In this study, the COMSOL PDE module is used to solve the complex dispersion curve of 3D model. By analyzing the influence of arrangement forms and materials of piles, it is found that the piles in triangular arrangement have the widest attenuation zone and the best vibration reduction effect. When the material of piles is concrete or steel, the attenuation zone in high frequency can be obtained, and the attenuation zone in low frequency can be obtained when two-component piles are used. The vibration reduction degrees of the two-component piles and concrete piles are smaller than those of the steel piles. Finally, a finite-scale frequency domain response model for periodic row piles is established to verify the correctness of the complex dispersion curve. As the characteristic frequency of the foundation vibration caused by the high-speed railway is within 0~50 Hz, four types of piles with different attenuation zones and one kind of composite piles are put forward. The results show that the composite piles can combine the attenuation zones of four types of row piles, and the vibration reduction effect is good.