Dispersion analysis in ballasted railway tracks and Anderson localization in granular media

International audience; This paper analyzes the dynamic behavior of a randomly-heterogeneous continuum model of a ballasted railway track through the numerical construction of dispersion curves along the axis of the track. At intermediate frequencies (50-100 Hz), the dispersion curves display a strong decrease of the group velocity. At higher frequencies (above 100 Hz), the wave are strongly localized and cannot propagate along the track. This behavior is coherent with experimental observations reported in the literature on ballasted railway tracks and other granular media. Additional simulations are performed to prove that the localization is not a consequence of the geometry of the track or the impedance mismatch between the ballast and the underlying soil, but is indeed Anderson localization due to the heterogeneity of the ballast.