Theoretical treatment of ground vibrations from high speed railways

The increased speeds of modern trains are normally accompanied by increased levels of generated ground vibrations that are especially high when train speeds approach two critical wave velocities in a track-ground system: the velocity of Rayleigh surface wave in the ground and the minimal phase velocity of bending waves propagating in a track supported by ballast, the latter velocity being often referred to as track critical velocity. Both these velocities can be overcome by modern high-speed trains, especially in the case of very soft soil where both critical velocities become very low. As has been earlier predicted by the present author (Krylov 1994, 1995), if a train speed exceeds the Rayleigh wave velocity in the supporting soil, then a ground vibration boom occurs which is associated with very large increase in generated ground vibrations, as compared to the case of conventional trains. The existence of a ground vibration boom has been confirmed experimentally in October 1997 on the newly opened high-speed railway line in Sweden for train speeds of only 160 km/h. If train speeds increase further and approach the track critical velocity, then rail deflections due to applied axle loads become especially large and an additional growth of generated ground vibrations takes place, as compared to the case of ground vibration boom. The obtained theoretical results are illustrated by numerical calculations for TGV and Eurostar high-speed trains travelling along typical tracks built on soft soil.