Efficient time–frequency approach for prediction of subway train-induced tunnel and ground vibrations

In this paper, an efficient time–frequency approach is presented for the prediction of subway train-induced tunnel and ground vibrations. The proposed approach involves two steps. In the first step, a time domain simulation of the vehicle–track subsystem is used to determine the track–tunnel interaction forces and, in the second step, the resulting forces are then applied to a 2.5 D FEM–PML model of the tunnel–soil system. There are two main aspects to the novelty and contribution of this work: First, the errors of the linearized Hertzian wheel–rail contact models in the calculation of the track–tunnel interaction forces are quantified by a comparison with the nonlinear Hertzian contact model. The results show that the relative errors are less than 2%. Second, an efficient time–frequency analysis framework is proposed, including the use of a strongly coupled model in the time domain solution and a 2.5 D FEM–PML model in the frequency–wavenumber domain solution. Finally, the accuracy and efficiency of the proposed approach are verified by comparison with a time-dependent 3 D approach, where three types of soil, i.e. soft, medium, and hard, are considered.