Upper bound analysis of longitudinally inclined EPB shield tunnel face stability in dense sand strata

Earth pressure balance (EPB) shield machine frequently drives along a route with a longitudinal inclination angle (δ) during tunnel construction. The tunnel face stability is a crucial issue for controlling the safety of tunneling. In this paper, the finite difference method (FDM) is used to investigate the face stability of longitudinally inclined shield tunnel in dense sand strata. Based on the numerical results of soil failure pattern in front of tunnel face, a novel two-dimensional (2D) failure mechanism is conceived following the upper bound theorem. It is assumed that the failure zone consists of an upper loosen zone, an arc-shaped shear band, and a triangular rigid body, which can calculate the active limit face support pressure pu. A scale factor for pu is introduced to quantify the three-dimensional (3D) behavior from the 2D calculation, with respect to different analysis approaches, e.g., numerical simulation, limit analysis, and limit equilibrium method. By incorporating the measure of scale factor, the calculation accuracy of the proposed 2D failure mechanism can be improved to provide reasonable prediction for longitudinally inclined tunnel.