This paper investigates the relation between unevenness at different locations in a railway track and the unevenness perceived by a train, for the particular case of a slab track. The different types of unevenness considered are: slab and track bed unevenness, bent rail and bent slab, variation of rail pad stiffness, variation of slab bearing stiffness, and variation of rail and slab bending stiffness. The unevenness perceived by the wheels of a moving train is the result of all these types of unevenness. When vibration countermeasures, such as resilient elements (e.g. soft rail pads), are introduced in a track, the perceived unevenness is modified.The slab track is modelled as a double beam supported on a rigid foundation. Analytical expressions are derived to relate the input and perceived unevenness. It is shown that in-track vibration countermeasures always introduce a change in perceived unevenness, which may turn out to be an increase or decrease and, consequently, result in a change of the performance of vibration countermeasures. This is illustrated for the particular case of a slab track on elastic supports on metro line M1 of ATM in Milan (Italy).This paper shows that prediction of vibration insertion loss based on conventional models may lead to inaccuracies in absence of information about different sources of unevenness. After the installation of vibration countermeasures, it is advised to measure the perceived unevenness in order to interpret differences between predicted and measured insertion loss.

This paper introduces the circle fit method for the determination of multi-modal Rayleigh dispersion and attenuation curves as part of a Multi-Channel Analysis of Surface Waves (MASW) experiment. The wave field is transformed to the frequency-wavenumber (fk) domain using a discretized Hankel transform. In a Nyquist plot of the fk-spectrum, displaying the imaginary part against the real part, the Rayleigh wave modes correspond to circles. The experimental Rayleigh dispersion and attenuation curves are derived from the angular sweep of the central angle of these circles. The method can also be applied to the analytical fk-spectrum of the Green's function of a layered halfspace in order to compute dispersion and attenuation curves, as an alternative to solving an eigenvalue problem. A MASW experiment is subsequently simulated for a site with a regular velocity profile and a site with a soft layer trapped between two stiffer layers. The performance of the circle fit method to determine the dispersion and attenuation curves is compared with the peak picking method and the half-power bandwidth method. The circle fit method is found to be the most accurate and robust method for the determination of the dispersion curves. When determining attenuation curves, the circle fit method and half-power bandwidth method are accurate if the mode exhibits a sharp peak in the fk-spectrum. Furthermore, simulated and theoretical attenuation curves determined with the circle fit method agree very well. A similar correspondence is not obtained when using the half-power bandwidth method. Finally, the circle fit method is applied to measurement data obtained for a MASW experiment at a site in Heverlee, Belgium. In order to validate the soil profile obtained from the inversion procedure, force-velocity transfer functions were computed and found in good correspondence with the experimental transfer functions, especially in the frequency range between 5 Hz and 80 Hz.

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In situ characterization of dynamic soil characteristics by means of surface wave tests frequently involves the determination and inversion of dispersion and attenuation curves. The inverse problem is formulated as a non-linear least squares problem minimizing the misfit between theoretical and experimentally obtained dispersion and attenuation curves, which is often solved using gradient based techniques. A new analytical and computationally efficient methodology is presented for the determination of the sensitivities of the Rayleigh and Love phase velocities and attenuation coefficients with respect to the shear wave velocity, the dilatational wave velocity, the material damping ratios in volumetric and shear deformation and the thickness of the layers. The expressions are based on the direct stiffness method for elastodynamic wave propagation. The proposed analytical method requires only a fraction of the calculation cost of the dispersion and attenuation curves. Sensitivities of Rayleigh dispersion and attenuation curves are computed for four soil profiles, including two shallow soil profiles, a very deep profile and an inverse profile with a soft layer trapped in between two stiffer layers. Results obtained with the proposed method are shown to be in perfect correspondence with sensitivities reported in the literature and obtained with a finite difference method.