Upper Bound Solution of the Safety Factor for a Shield Tunnel Face Subjected to the Hoek–Brown Failure Criterion

Assessment of the stability of a tunnel face under a setting support pressure is a key challenge in shield tunneling engineering, especially when a tunnel is excavated in a heavily fractured rock mass. In this paper, a factor of safety is introduced for investigating the face stability of a tunnel using the upper bound theorem in combination with the Hoek–Brown nonlinear failure criterion. The factor of safety for the tunnel face is defined as the ratio of the rate of the energy dissipation and the external rate of work in the kinematically admissible velocity field. The upper bound solution of the factor of safety is obtained from the optimal computation. The solutions provided by the presented approach are compared with those derived from a numerical simulation. The values of the factor of safety derived from these two methods are found to be in agreement, indicating that the proposed method is valid. Furthermore, based on the measured data of the chamber pressure and the parameters provided by the geological survey report, the proposed method is used to evaluate the stability of the tunnel face for an actual project. The effects of different parameters on the factor of safety are also discussed.