To mitigate the metro-induced vertical vibration of the indoor substation structure, this study proposes a gas-spring quasi-zero stiffness air damping isolator (AD-QZSI) with excellent low dynamic stiffness and high-static stiffness characteristics. The working principle and mechanical properties of the AD-QZSI are introduced and studied through theoretical and numerical methods. A model for substation considering soil-structure-equipment interaction is established using the software ABAQUS, its accuracy is validated based on a series of measured data from actual projects, and the AD-QZSI's simulation method and parameter design method are described in detail. The air damper's stiffness ka is integrated into the isolator's mechanical model, theoretically and numerically achieving an accurate simulation of AD-QZSI's nonlinear mechanical properties. The numerical results have an error of less than 5% with the measured data, indicating that the model is able to better capture the actual structure's dynamic characteristics and is reasonable to be employed for subsequent analysis. Numerical results show that AD-QZSI can significantly reduce the structural vertical vibration, and its control effect is better in the whole frequency band, in particular, the effect is also visible in the low-frequency band, indicating that its vibration isolation frequency band is wider than that of traditional QZS isolator. With the vibration source distance increasing, the control effect of AD-QZSI presents a tendency to decrease and then level off, and its vibration isolation gain is weakened by the continuous increase of the damping ratio greater than 0.01. Moreover, the equipment's dynamic amplification factor of the isolated structure decreases significantly. Finally, the proposed AD-QZSI can obtain ideal quasi-zero stiffness characteristics by adjusting the air pressure, and the adopted air damper belongs to the green low-carbon components, featuring great practical value and application prospects.

The vibrations generated by metro operations can cause structural damage and discomfort to occupants adjacent to the metro lines. In this study, a multigrid fully coupled method of metro vehicle-track-station-soil-building systems is proposed to predict and assess building vibrations before construction. This approach facilitates the efficient calculation of the fully coupled system, while ensuring precise simulations through the utilization of multigrid techniques for wheel-rail contact, track, station, soil, and building components. Using the newly built opera theatre along Beijing metro line 4 as a case, the study demonstrates that the multigrid fully coupled model can predict the dynamics characteristics of metro-induced vibrations and distribution with high accuracy compared with the field tests. Specifically, it was found that metro operations could result in vibrations exceeding specified limits in the opera theatre, particularly at 10 similar to 40 Hz (the building's natural frequency) and 60 similar to 80 Hz (the main frequency band of vibration caused by the metro). Finally, the mechanism of excessive vibration and the effectiveness of targeted vibration mitigation measures were analyzed with the proposed method. These findings have promising implications for wider applications in environmental assessments and control strategies for new metro lines or vibration-sensitive buildings. Graphical Abstract