A numerical model for ground-borne vibrations and re- radiated noise in buildings from underground railways

An efficient and modular numerical prediction model is presented to predict vibrations and re-radiated noise in buildings due to metro trains. The approach comprises of three weakly coupled problems: the dynamic vehicle-track-tunnel-soil interaction problem, the dynamic soil-structure interaction problem and the calculation of the acoustic response inside the rooms. The three-dimensional dynamic tunnel-soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. The Craig-Bampton substructuring technique is used to efficiently incorporate a track in the tunnel. The track-tunnel-soil interaction problem is solved in the frequency-wavenumber domain and the wave field radiated into the soil is computed. This incident wave field is used to solve the dynamic soil-structure interaction problem on the receiver side and to determine the vibration levels in the structure. The receiver side dynamic soil-structure interaction problem is solved by means of a 3D boundary element method for the soil coupled to a 3D finite element method for the structural. A weak coupling between the structural and acoustic vibrations is accounted for and an acoustic spectral finite element method is used to predict the acoustic response. To demonstrate the efficiency of the approach, the Bakerloo line tunnel of London Underground has been modelled using the coupled periodic FE-BE approach. It is a deep bored segmented tunnel, with a cast iron lining, embedded in the London clay. The response in the free-field due to a moving vehicle on an uneven rail is predicted. Subsequently, the re-radiated noise in a hypothetic multi-story portal frame office building is estimated. This numerical model enables to investigate the inherent physics of the generation and propagation of vibrations and re-radiated noise in buildings from underground railways.