An analytical model for face stability of shield tunnel in dry cohesionless soils with different buried depth

For deep-buried shield tunnels in dry cohesionless soils, it is critical to determine the support pressure acting on a tunnel face due to the significant soil arching effect during excavation. In this paper, a new analytical model of the multi-layer parabolic bearing arch is proposed to predict the limit support pressure based on the limit equilibrium method and the wedge model. The model consists of the multi-layer parabolic bearing arch, the friction arch and the wedge. According to the different buried depth of tunnel, the tunnel state is divided into shallow buried zone, transition zone and deep buried zone. By assuming the multi-layer parabolic soil arch as a three-hinged structural arch with reasonable arch axis, the load transfer expression of multi-layer parabolic soil arch is derived in transition zone and deep buried zone respectively. Then, the rationality and effectiveness of the proposed model were verified by comparing with model tests, existing theoretical methods and numerical model. Finally, the effects from the internal friction angle phi of soil on the inclination angle beta, tunnel state and limit support pressure were also discussed. It is shown that with the increase of internal friction angle phi, the boundaries in between the shallow zone and the deep buried zone declines linearly, the inclination angle beta increases linearly and the limit support pressure decreases nonlinearly. This study provides a significant reference for predicting the value of limit support pressure acting on the tunnel face in dry cohesionless soils.