Simplified Tunnel–Soil Model Based on Thin-Layer Method–Volume Method–Perfectly Matched Layer Method

Abstract

In order to analyze the ground vibration responses induced by the dynamic loads in a tunnel, this paper proposes a new simplified tunnel–soil model. Specifically, based on the basic theory of the thin-layer method (TLM), the basic solution of three-dimensional layered foundation soil displacement was derived in the cylindrical coordinate system. The perfectly matched layer (PML) boundary condition was applied to the TLM. Subsequently, a tunnel–soil dynamic interaction analysis model was established using the volume method (VM) in conjunction with the TLM-PML method. The displacement frequency response function of the foundation soil around the tunnel foundation was derived. Finally, a ground vibration test under an impact load in a tunnel was carried out. The test and calculated results were compared. The comparison results show that the ground vibration acceleration response values within 25 m from the load are similar. Compared with the test results, the theoretical calculation results exhibit a decreasing trend in the range of 40–80 Hz between 25 and 60 m, with the maximum reduction being approximately one order of magnitude. In addition, the experimental comparison demonstrates that the model can be used to analyze the ground vibrations caused by underground loads.