Focusing of ground vibrations generated by high-speed trains travelling at trans-Rayleigh speeds

In the present paper, the effects of focusing of ground vibrations generated by high speed trains travelling at trans-Rayleigh speeds, i.e. under the condition of ground vibration boom, are considered theoretically. These effects are similar to the effects of focusing of sound waves radiated by supersonic aircraft. In particular, if a railway track has a bend, e.g. to provide the possibility of changing direction of train movement, the Rayleigh surface waves generated by high-speed trains under the condition of ground vibration boom may become focused. This results in concentration of their energy along a simple caustic line at one side of the track and in the corresponding increase in ground vibration amplitudes. The effect of focusing of Rayleigh waves may occur also if a train moves along a straight line with acceleration a and its current speed v(t) is higher than Rayleigh wave velocity in the ground. In the present paper, both the above-mentioned focusing mechanisms are investigated in detail using the Green's function formalism and the expressions for space-time distributions of track-train-induced dynamic forces that take into account either track curvature or train acceleration. It is shown that in both these cases the effect of focusing can result in noticeable increase in generated ground vibrations. The obtained results are illustrated by numerical calculations.