Analysis of Train-induced Dynamic Response of Metro Tunnel in Saturated Foundation Based on the Wave Function Transformation Method

[Objective] The train-induced metro tunnel vibration may affect adversely the normal life of residents along the line, the use of precision instruments, and the structural safety of ancient buildings. In order to clarify the propagation law of the entire process of train-induced metro tunnel vibration, analyze the implementation effects of various vibration isolation and reduction measures, it is necessary to establish an efficient calculation model for the train-induced dynamic response of metro tunnels. [Method] The Biot wave equation is used to simulate the vibration characteristics of the foundation, and the vibration equation of the double-layer thin-walled shell is used to simulate the vibration characteristics of the metro tunnel and the tunnel grouting layer. The transformation formula of the wave functions for plane and cylindrical waves is introduced to solve the basic solution of the dynamic response of the tunnel embedded in the half-space foundation. Based on the basic solution of the dynamic response of the foundation-tunnel, the Euler beam with continuous line support is used to simulate the track structure, and the multi-body dynamics model is used to simulate the vehicle load. Subsequently, the structures such as vehicles and tracks are further coupled, and an analytical calculation model for the train-induced dynamic response of metro tunnels is proposed. Based on this model, the vibration reduction effects of vibration reduction measures such as the floating slab track of the metro tunnel are analyzed. [Result & Conclusion] While exerting the vibration reduction effect, different vibration reduction measures will lead to an increase in the vibration response of some sub-structures of the system to a certain extent. When analyzing the vibration reduction of the system, the vibration reduction design should be carried out from the perspective of systemic safety to avoid damage caused by the local vibration amplification.