Face Stability Analysis of Shield Tunnel in Cohesive–Frictional Soils Considering Soil Arch Evolution

Face instability models considering the gradual evolution of the soil arching effect and the characteristics of face instability under different cover-to-diameter ratios are proposed in this paper. The face instability combined-model includes the upper cylinder and lower logarithmic spiral for shallow buried shield tunnels considering the overall soil slipping failure. The two-phase face instability model is proposed for deep buried shield tunnels based on the evolution of the upper soil arching shape and soil local slipping failure. The first-phase combined model is composed of the upper catenary and lower logarithmic spiral. The second-phase combined model consists of the upper cone and lower logarithmic spiral. The earth pressures on the bottom of the upper cylinder, physical catenary, and cone arch are calculated based on the Terzaghi loose earth pressure calculation method and the arch theory, respectively. The carrying capacity at the top surface of the lower logarithmic spiral was calculated according to the slicing method considering the intersection between the logarithmic spiral and tunnel section is in full-section contact. The limit equilibrium equation is established and the calculation model derived by using MATLAB is used to obtain the numerical solution for the limit face supporting pressure of the shield tunnel. The reliability of the theoretical calculation method based on arch theory and the validity of face instability combined model are verified by comparing the calculated values with the measured values of centrifuge model tests and literatures. The influence of cohesion, inner friction angle, and cover-to-diameter ratio on limit face supporting pressure is analyzed. The results provide a basis for determination of limit face supporting pressure at different phases during face instability.