Pseudo-Mach angles for Rayleigh ground waves generated by trains moving at conventional speeds

Spatial distributions of ground vibrations (mostly Rayleigh surface waves) generated by railway trains travelling at conventional speeds have been investigated theoretically at frequencies close to sleeper passage frequencies defined by train speeds and sleeper periodicity. It has been demonstrated that generated ground vibrations at such frequencies are plane Rayleigh waves propagating symmetrically away from the track at certain angles in respect of the track. In particular, for frequency components slightly higher than sleeper passage frequencies, these radiation angles resemble the well-known frequency-independent Mach angles for Rayleigh ground waves generated by trains moving at speeds that are higher than Rayleigh wave velocity in the supporting ground. The above-mentioned angles associated with Rayleigh wave radiation at conventional speeds, that are dependent on frequency, can be called 'pseudo-Mach angles'. These radiation angles can be used for better understanding of railway-generated ground vibrations around sleeper passage frequencies and for their more efficient experimental observation.