Stability mechanism on shield tunnel excavation face in layered soils with earthquake action considering upper bound limit analysis

In the study of the stability of shield tunnel excavation face in urban environment, most of the construction stratum is assumed to be homogeneous soils, and the coupled effects of layered characteristics and earthquake action are seldom considered. Therefore, this paper provides a 3D logarithmic spiral mathematical model to evaluate the excavation face stability considering earthquake action in layered soils. Firstly, the pseudo-static approach simplifies the dynamic reaction brought by the earthquake to the inertial forces operating in horizontal and vertical directions. Secondly, a 3D logarithmic spiral mathematical model that may be applied to layered soils is developed based on the 3D logarithmic spiral mathematical model in homogeneous soils. Then, according to the upper limit theorem, the upper limit solution of the support force on the excavation surface of the shield tunnel can be obtained by introducing the power generated by the earthquake inertia force into the imaginary work equation under the layered soils and earthquake action conditions. Lastly, the upper limit analytical solution is compared with the 3D numerical simulation results and existing model experimental results, and good consistency is obtained. Additionally, the key physical characteristics are analyzed for earthquake, geotechnical, and tunneling parameters.