An in-situ test to obtain vertical, transversal and longitudinal ground velocities and accelerations caused by high-speed trains was performed alongside the Chinese high-speed railway line between Beijing and Shanghai. The test results indicate that due to excellent track quaity and consolidated infrastructure, whether if the train speed is below or above the Rayleigh wave speed, the dominant frequencies of both the vertical ground velocity and acceleration are both integral multiples of the trainload frequency generated by the centre distance of two neigbouring cars. The frequency-domain distribution of the ground velocity is more sensitive to soil stiffness than is the ground acceleration; this is especially the case for the first dominant frequency. Whether the frequency amplitudes of the vertical ground vibration are higher than the horizontal vibrations depends on the soil stiffness. The greater the soil stiffness, the higher is the frequency-range of the vertical ground vibration compared with that for the horizontal vibration, and the smaller is the difference between the three-dimensional frequency-weighted ground vibration level and the vertical vibration. Thus, effects of horizontal ground vibrations cannot be ignored when the foundation soil is soft.

This study presents a measuring framework for railway transition zones using a case study on the Swedish line between Boden and Murjek. The final goal is to better understand the vertical dynamics of transition zones using hammer tests, falling weight measurements, and axle box acceleration (ABA) measurements. Frequency response functions (FRFs) from hammer tests indicate two track resonances, for which the FRF magnitudes on the plain track are at least 30% lower than those at the abutment. The falling weight measurements indicate that the track on the bridge has a much higher deflection than the track on the embankment. Two features from ABA signals, the dominant spatial frequency and the scale average wavelet power, show variation along the transition zone. These variations indicate differences in track conditions per location. Finally, the ABA features in the range of 1.05–2.86 m ⁻¹ are found to be related to the track resonance in the range of 30–60 Hz. The findings in this paper provide additional support for physically interpreting train-borne measurements for monitoring transition zones.

Employing theory on vehicle–track coupled dynamics, the equation of motion of a vehicle–track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle–track vertical coupled system was calculated under the excitation of the German low-interference spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German low-interference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel–rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle–track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the low-frequency vibrations of the vehicle system and track structure. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel–rail vertical force and track structure decrease at 50–80 Hz, while the mid-frequency and high-frequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel–rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel–rail vertical force and track structure.