Rail movement and ground waves caused by high-speed trains approaching track-soil critical velocities

The increased speeds of modern trains are normally accompanied with increased transient movements of the rail and ground, which are especially high when train speeds approach some critical wave velocities in the track±ground system. These transient movements may cause large rail deflections, as well as structural vibrations and associated noise in nearby buildings. There are two main critical wave velocities in the track±ground system: the velocity of the Rayleigh surface wave in the ground and the minimum phase velocity of bending waves propagating in the track supported by ballast, the latter velocity being referred to as the track critical velocity. Both these velocities can be exceeded by modern high-speed trains, especially in the case of very soft soil where both critical velocities become very low. The discussion in this paper focuses on the effects of transient rail deflections on associated ground vibrations in the cases of train speeds approaching and exceeding Rayleigh wave and track critical velocities. The obtained theoretical results are illustrated by numerical calculations for TGV and Eurostar high-speed trains travelling along typical tracks built on soft soil.