On the Modelling of Train Induced Ground Vibrations with Analytical Methods

Abstract: A novel analytical approach to model train induced ground vibrations is proposed. Integral transform solutions are combined with series solutions to obtain fast numerical algorithms, where a particular designed boundary condition for finite regions is seen to enable the solution procedure. The track superstructure is primarily modelled with an analytical approach with Euler-Bernoulli beams for the rails, an anisotropic Kirchhoff plate with transversal isotropy for the sleepers and two Kelvin models in series for the rail pads. Prescribed propagating wheel loads are accounted for by means of static moving forces. An embankment substructure is obtained by employing rectangular finite regions, which are situated on top of a layered semi-infinite ground domain. Low frequency vibrations for trains moving at constant velocities, but also accelerating trains, are treated. The displacement fields excited by moving loads are validated with measurements and very good agreement is obtained both at subcritical and supercritical train velocities. With buildings and people living close to railroads, vibration countermeasures are a necessity. A typical method to reduce the vibration levels is to construct some sort of wave barrier. The modelling technique is applied for low frequency assessment of open trenches. It is found that the trenches have significant attenuating effects on vibrations for propagating waves, whereas the effect is missing in the dominating frequency range when the subcritical velocity excites the quasi-static deflection. The analytical model for the ground and embankment is also utilized together with a numerical track model to simulate low-frequency train-track interaction problems in the time domain. A coupling of the two basically different models is made with a special stiffness formulation of the ground and embankment at interaction areas under the sleepers. It is found that the simple Winkler-foundation works well for low frequency ground vibrations as long as only one axle load is used. However, with two or more axle loads, the coupling to adjacent sleepers becomes important.