Mitigation of railway-induced vibrations by using periodic wave impeding barriers

Railway-induced vibrations can cause significant environmental issues. This paper proposes an efficient analytical method to investigate the mitigation of railway-induced vibrations by using periodic barriers in a layered half-space. The general solutions for layered ground and multiple inclusions are derived by using the potential decomposition and multiple scattering theory. The conversion equation between cylindrical and exponential functions and the addition theorem are introduced to achieve the transformation between plane and cylindrical wave functions and the translation between cylindrical wave functions. Combined with the transfer matrix method, the fundamental solution for the soil-inclusion dynamic interaction in a layered half-space is derived. The railway train and track are subsequently coupled to the ground-inclusion system. Numerical results demonstrate that the phononic crystal effect induced by the periodic distribution of barriers improves the mitigation efficiency at high frequencies. The increase in the number, size, and stiffness of barriers can give a higher mitigation efficiency in a wider frequency range. The mitigation efficiency of periodic barriers can be guaranteed when their depth is shorter than half the Rayleigh wavelength in the considered frequency range. Owing to the scattering of waves at layer interfaces, the periodic barriers beneath the track have a higher efficiency than those located next to the track, which does not appear in the homogeneous half-space. The performance of periodic barriers is significantly affected by the soil stiffness of the upper shallow layer, while it is less affected by the soil stiffness of the bottom stiffer layer.