Focusing of ground vibrations generated by trans-Rayleigh trains travelling with acceleration

In the present work, the effect of focusing of ground vibrations generated by high speed trains travelling with acceleration at trans-Rayleigh speeds, i.e. under the condition of ground vibration boom, is considered theoretically. This effect is similar to the effect of focusing of sound waves radiated by supersonic aircraft flying with acceleration, sometimes called a 'superboom', and it may occur 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. Under such conditions, the effect of train acceleration results in concentration of the energy of generated ground vibrations, mainly Rayleigh waves, along the simple caustic lines located symmetrically at both sides of the track. This concentration causes the increase in generated ground vibration levels, in addition to the already strong vibrations associated with ground vibration boom. The above-mentioned focusing mechanism is investigated in detail using the Green’s function formalism and the expression for space-time distribution of track-train-induced dynamic forces that takes into account train acceleration. It is shown that the effect of focusing can result in noticeable increase in generated ground vibrations. The obtained results are illustrated by numerical calculations. It is noted that in densely populated countries, with relatively short distances between railway terminals, a significant proportion of high-speed railway routes will be covered by trains travelling with acceleration and deceleration. Therefore, in principle, focusing of ground vibrations due to train acceleration could happen rather frequently.