A framework is developed in this article to predict the nonstationary random ground vibrations induced by high-speed trains, by combining the pseudo-excitation method with the two-and-a-half-dimensional finite element method. This development contains two steps. First, the power spectral density of the wheel–rail dynamic force is accurately obtained through the combination of the pseudo-excitation method and a vehicle–slab-track–ground theoretical model. Second, the nonstationary random ground vibrations are efficiently solved by combining the pseudo-excitation method and the two-and-a-half-dimensional finite element method, where the power spectral density of the wheel–rail dynamic force obtained in the former step is used to constitute the pseudo-loads. In the numerical examples, the accuracy and efficiency of the proposed approach are validated through the comparison to the fast three-dimensional random method for train–track–soil system developed previously. The results show that the proposed approach can predict the train-induced random ground vibrations with sufficient accuracy and has three-to-five times increase in efficiency in comparison to the fast three-dimensional random method.

本文开发了一个框架，通过将伪激励方法与二维半有限元方法相结合，来预测高速列车引起的非平稳随机地面振动。此开发包含两个步骤。首先，通过伪激励方法和车辆-平板-轨道-地面理论模型的组合，可以精确地获得轮-轨动力的功率谱密度。其次，结合拟激励方法和二维半有限元方法，有效地解决了非平稳随机地面振动问题，前一步获得的轮轨动力功率谱密度为用于构成伪负载。在数字示例中，通过与之前开发的列车-轨道-土壤系统的快速三维随机方法进行比较，验证了所提方法的准确性和效率。结果表明，与快速三维随机方法相比，该方法能够以足够的精度预测列车引起的随机地面振动，并且效率提高了三到五倍。