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A simple and fast prediction scheme is presented for train-induced ground and building vibrations. For the emission, finite-element boundary-element or multiple-beam-on-continuous-soil models of the track have been analysed and approximated by faster track-on-Winkler-soil models. The vehicle-track interaction due to irregularities yields the excitation forces. For the transmission of waves in the soil, the wavenumber integral of the compliance of layered soils has been evaluated. The calculation time is reduced for the prediction by using the solution of a homogeneous half-space with a frequency-dependent wave velocity (the dispersion) of the soil. For the immision, many 2 and 3-dimenisonal finite-element building models have been investigated, and a good approximation has been established by a 1-dimensional soil-wall-floor model. In addition, the axle sequence of the train, the quasi-static and the “scattered” response of the soil, and the wave propagation from a tunnel to a pile foundation of a building have been included.
This contribution presents some principles and some examples of the mitigation of railway-induced ground vibrations. The principles are different for the mitigation measures at the track, in the soil or at the building. Force transfer functions of isolated and un-isolated track-soil systems, reflected and transmitted wave amplitudes at walls and trenches in the soil, and the transfer of the (free-field) vibration amplitudes to the foundation amplitudes of the building are analysed. The mitigation effect can be calculated by exact or simplified formulas. Some examples with 3D (finite-element boundary-element), 2D (beam-on-support), and 1D track models, 2D and 1D soil models, detailed 3D building models and finite or infinite 1D wall-floor models are investigated to find out if simple models can be used for a satisfactory prediction of the mitigation effect. The 1D track examples show that the force transfer of the track without vehicle can be exactly calculated, whereas the total force transfer can be calculated approximately if appropriate wheelset masses per track length are used for the isolated and the un-isolated track. The mitigation effect of a filled trench is calculated by a 2D finite element model and the results compare with simple transmission formula if the stiffness per area rather than the wave impedances are used for the infill material. The base isolation of a building is analysed by a detailed 3D model and the results are similar to the analytic results of a single wall with floors on the soil. Other reduction measures as different floor and column dimensions are usually less effective so that the clearly best mitigation solution at a building is a partly or a complete base isolation.