Active Stability Analysis of 3D Shallow Tunnel Face with Longitudinally Inclined Ground Surface Based on Nonlinear Mohr–Coulomb Failure Criterion

Abstract

The longitudinally inclined (the tunnel excavation direction) ground surface often appearing at the shallow tunnel entrance and exit zone threatens and reduces the tunnel face stability. However, studies on this stability have rarely accounted for this inclined angle. Therefore, the effect of this inclined angle on the shallow tunnel face stability is considered, and the corresponding three-dimensional (3D) failure mode is constructed in this article. Then, the expression of active failure pressure is obtained using a nonlinear Mohr–Coulomb failure criterion based on the principle of virtual work. The upper-bound solution of it is examined based on the sequential quadratic programming method. The active failure pressure and failure mechanism are presented based on a series of studies of the key parameters. The results demonstrate that the shallow tunnel face stability is more dependent on the inclined angle (δ), tunneling length (L), and nonlinear shear strength parameters. Under nonlinear conditions, the influence is more significant. When the ground surface failure region is zero, the dimensionless parameter (C/D), tunneling length, and ground surcharge (σs) have no effect on the result. In addition, the longitudinally inclined ground surface is easy to induce the active failure of the shallow tunnel face.