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.

中文翻译：

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地铁列车隧道和地面振动预测的时频随机方法

本文提出了一种时频随机方法来预测地铁列车引起的隧道和地面振动。这是作者先前提出的随机方法的发展，它考虑了离散轨道支持、奇异轨道缺陷等。所提出的方法是使用两步法开发的。首先，将伪激励法（PEM）与二维多体系统/有限元法模型有效结合，利用轨道不规则度的功率谱密度推导轨道-隧道拟相互作用力。其次，隧道-土壤系统的随机振动是通过波数-频域中的 PEM 获得的。为了提高计算效率，提出了一种基于多点同步算法的快速计算策略。使用数值示例，通过将其与完全耦合的时间相关三维方法进行比较来验证所提出的时频混合建模过程。此外，通过将所提出的方法预测的结果与先前开发的方法预测的结果进行比较，讨论了离散轨道支撑对隧道和地面的随机振动的影响。