Method for calculating limit support pressure of face of shield tunnels considering principal stress axis rotation and soil arching effects in dry sand

For the deep-buried shield tunnels in dry cohesionless soils, it is critical to determine the support pressure acting on the tunnel face due to the significant soil arching effects. Based on the limit equilibrium method and the wedge theory, a multi-layer parabolic bearing arch model is proposed. According to the characteristics of failure zone of the tunnel face and the category of soil arch under different buried depths, the tunnel state is divided into shallow buried tunnel, transition tunnel and deep buried tunnel, respectively. By considering the continuity of the principal stress deflection angle and lateral earth pressure coefficient in the multi-layer parabolic bearing arch and assuming the parabolic bearing arch as a three-hinged structural arch with reasonable arch axis, the load transfer expression for the multi-layer parabolic bearing arch is derived in transition zone and deep buried zone respectively, and then the limit support pressure is calculated. By comparing the proposed model with the existing model, model tests and numerical model, the rationality of the limit support pressure and failure zone of the tunnel face obtained by the proposed model is verified. Finally, the influences of the internal friction angle on the boundary between shallow and deep burials and the limit support pressure are discussed through parameter analysis. This study may provide a theoretical basis for predicting the limit support pressure acting on the tunnel face in dry sand.