Ground vibrations from operating railway in tunnels is a significant obstacle to sustainable development of subway. The backfill grouting layer, formed during shield tunneling, serves as a critical medium in propagation of tunnel vibrations, highlighting its potential in vibration mitigation. A semi-analytical model for the tunnelgrouting layer-soil system is proposed in this study, in order to clarify the influence of backfill grouting layer on the dynamic responses in a half-space, subjected to tunnel vibrations. In establishment of the closed-form solution, the tunnel and grouting layer are considered as two nested hollow cylinders embedded in a halfspace, with applying the Fourier transform and wave transformation. As a validation, the numerical results from the proposed semi-analytical model are compared with those reported in literature. Parametric studies, with respect to the geometric configuration (i.e., the thickness) and material parameters (i.e., the Young's modulus, material damping, and density) of the backfill grouting layer in the mitigation of tunnel vibrations, are carried out. It is found that incorporation of the backfill grouting layer significantly changes the dynamic responses of the soil and, by appropriately designing its material parameters, especially the Young's modulus, effective mitigation of tunnel vibrations can be achieved.

Large-scale cooling towers in inland nuclear power plants (NPPs) may collapse under extreme conditions. The collapse-induced ground vibrations threat the safety operations of the adjacent nuclear related facilities. Therefore, prediction and possible mitigation of the ground vibrations are significant in the NPP planning. This study proposed a novel method to arrange a water pool as a cushion underneath the cooling tower to mitigate the ground vibrations. The planar dimension of the water pool is determined by the debris distribution of the collapsed cooling tower. To achieve this, first, the mitigation effect was tested using a steel ball impacting on a concrete pedestal. Then, to obtain the complete debris distribution, a technique was developed to reproduce the disappearing elements in the finite element method-based simulation, and was validated against the tests of vase debris. Finally, the cooling tower-water pool cushion-soil models were established to demonstrate the vibration mitigation using the water pool cushion. For the concerned case with the water pool of 6 m depth, the vibration reduced by 56 % and 59 % for the maximum and average of the ground peak accelerations in the horizontal direction, as well as by 65 % and 60 % for those in the vertical direction, respectively.

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