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A numerical study of subgrade stiffening as a mitigation measure for railway induced vibrations through 2.5D and 3D FE-BE models

Abstract. This paper studies the efficiency of subgrade stiffening next to the track as a mitigation measure for railway induced vibrations. A computationally efficient two-and-a-halfdimensional (2.5D) methodology is first employed, assuming invariance of the geometry in the longitudinal direction. An analysis in the frequency–wavenumber domain reveals that an infinitely long block of stiffened soil next to the track can act as a wave impeding barrier. It is demonstrated that the wave impeding effect depends on the relation between the Rayleigh wavelength in the soil and the free bending wavelength in the block of stiffened soil, as the transmission of plane waves in the soil with a longitudinal wavelength smaller than the bending wavelength is hindered. This leads to a critical frequency from which this mitigation measure starts to be effective, depending on the stiffness contrast between the soil and the block of stiffened soil. The existence of a critical angle delimiting an area where vibration levels are reduced in case of harmonic excitation on the rail is also demonstrated. Fully three–dimensional (3D) calculations are finally performed to assess the vibration reduction efficiency if subgrade stiffening is only implemented along a finite length, indicating that the length of the block should be approximately two times the free bending wavelength of an infinitely long beam in order to ensure that a finite block can act as a wave impeding barrier.