A coupled finite element–infinite element boundary method performed by the harmonic analysis based on the commercial software ABAQUS was verified by comparing it with the thin layer method to address the issue of subway induced vibration, a major environmental concern in urban areas. In addition, an interface program was developed to automatically read the simulation result files in the harmonic analysis, and then put the data into MATLAB, achieving the frequency domain analysis. Moreover, a site measurement was performed on a practical engineering track bed-tunnel lining-surrounding formation located on Line 2, Shanghai Metro and rich vibration data were acquired. Then, the corresponding simulation model was established and the numerical results were compared with the measured data based on the developed program, which was verified applicable for the practical engineering of subway induced vibration on the soft site. The proposed prediction formula of the vibration level, by comparison with the measurement, is applicable for the prediction in subway induced vibration. The results show that there exists a vibration amplifying zone a certain distance to the tunnel under high frequency loads due to the wave propagation and reflection. Finally, a parametric study was conducted in an elastic half-space simulation to investigate the influence of model widths and depths with infinite element boundary on the numerical results. The higher performance of the combined finite element–infinite element boundary method, which can decrease the model sizes in widths and heights 50% effectively, was demonstrated. Consequently, the coupled finite element–infinite element boundary method and developed frequency analysis with interface program provide rational numerical methods for the models of subway induced vibration.

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It has been observed from previous large earthquakes that weakening the structural foundation can reduce the damage of the structure itself by allowing a rocking motion to release the seismic energy, and this seismic design philosophy is gradually applied to new constructions. In this paper, a simplified model of the motion process of a rigid rocking block is proposed, the rocking motion equation of rigid rocking block is derived, and the parameter analysis is carried out. It was found that the height–width ratio and damping have a great impact on the rocking response of the structure. On this basis, combined with the Winkler foundation model, the equation of motion of the rigid rocking block considering the flexibility of the foundation is established. Through the analysis of an example, it is found that damping plays an important role in the overturning resistance of high-rise buildings and the soil elastic coefficient has a greater impact on the higher structure.

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