| The metro traffic induced vibrations have become an environmental concern in urban areas, as waves propagate through the soil and interact with nearby buildings, where the damage to buildings and the malfunctioning of sensitive equipment, as well as the discomfort to people may be caused. Therefore, it is important to predict the vibrations in the tunnel, soil and buildings induced by passage of metro trains.The Line 4 of Beijing metro, which is currently under construction, is planned to pass in close proximity of the physics laboratory of Peking University. There is a lot of important sensitive equipment which is sensitive to traffic induced vibrations in the laboratory, and the future operation of Line 4 is a matter of great concern. A numerical model was developed to predict the dynamic response in the tunnel and the free field in this paper, and then it was used to calculate the vibrations and analyze the isolation efficiency of floating slab track north of East Gate of Peking University station on Line 4.In this paper, a three-dimensional coupled periodic finite element (FE)-boundary element (BE) model in the frequency-wavenumber domain was developed to predict the dynamic response in the tunnel and the free field. In this model, the dynamic tunnel-soil interaction problem was solved based on the finite element method for the tunnel and the boundary element method for the soil. And the periodicity or invariance of the tunnel and the soil in the direction of tunnel axis was exploited with the Floquet transform to limit the discretization effort to a single bounded generic cell, so the calculation can be efficiently made in this model. The inverse Floquet transform can be used to obtain the response in the special domain. And the Craig-Bampton substructuring technique was used to model efficiently the track inside the tunnel, which avoided the recomputation of the soil impedance.The direct stiffness method was used to establish the Green function in the homogeneous full space and the horizontally-layered half space, and the Green function was then introduced into the three-dimensional coupled periodic FE-BE model to calculate the boundary integral equation.The dynamic response in the tunnel and the free field induced by the moving metro trains was presented in the frequency-wavenumber domain. Through the Fourier transform and the Floquet transform, the vibrations induced by passage of metro trains can be calculated if the transfer function in the frequency-wavenumber domain and the moving loads in the frequency domain can be obtained. The transfer function was calculated using the three-dimensional coupled periodic FE-BE model, and the moving loads were considered as the contact force between wheel and rail due to the rail unevenness.The in-situ vibration measurements outside and inside the laboratory on metro Line 4 and at a site between Dongdan station and Jianguomen station on metro Line 1 were presented in this paper. The environmental vibrations outside and inside the laboratory, the vibrations generated only by cars, buses and trains and the combined vibrations of road traffic and metro traffic on Line 1 were elaborated.The dynamic response in the tunnel and the free field between Dongdan station and Jianguomen station on Line 1 was calculated, and then was compared with response in the in-situ vibration measurements. The results show that the numerical model in this paper has the good applicability.The vibrations induced by metro trains in the tunnel north of East Gate of Peking University station on Line 4 was predicted, and then was combined with the measured environmental vibrations inside and outside the physics laboratory. The effect on the sensitive equipment in the laboratory was studied due to the environmental vibrations at present and the metro traffic induced vibrations after operation of metro Line 4. At last, the isolation efficiency of floating slab track installed in the tunnel north of East Gate of Peking University station was analyzed.
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