Time-Frequency Random Approach for Prediction of Subway Train-Induced Tunnel and Ground Vibrations

A time-frequency random approach is proposed in this paper for the prediction of subway train-induced tunnel and ground vibrations. This is a development of the random approach previously proposed by the authors, which takes the discrete track support, singular track defects, etc., into consideration. The proposed approach is developed using a two-step method. First, the pseudo-excitation method (PEM) and the two-dimensional multibody system/finite element method model are effectively combined to derive the track-tunnel pseudo-interaction forces by employing the power spectral density of track irregularity. Second, the random vibrations of the tunnel-soil system are obtained via the PEM in the wavenumber-frequency domain. To improve the computational efficiency, a fast-computing strategy is proposed based on the multipoint synchronous algorithm. Using numerical examples, the proposed time-frequency hybrid modeling process is verified by comparing it with the fully coupled time-dependent three-dimensional approach. Furthermore, the influence of the discrete track support on the random vibrations of the tunnel and ground is discussed by comparing the results predicted by the proposed approach with those predicted by the previously developed approach.