Upper bound analysis of factor of safety for shield tunnel face subjected to underground water seepage

Based on the numerical simulation technique, the seepage fields of shield tunnel face are simulated, and the pore water pressures of the nodes adjacent to the tunnel face are obtained. Using the pore pressures of the nodes, the work rate of the pore pressures of the upper bound failure mechanism is derived. The work rate of the pore pressures regarded as a work rate of external force is included in the equation for virtual work rate, and the objective function for factor of safety for tunnel face is established in the framework of upper bound theorem. Using the nonlinear sequential quadratic programming, the upper bound solution of the factor of safety is obtained. By comparing the solution with the results derived from strength reduction method, the validation of the proposed method is verified. Moreover, this method is applied to a shield tunnel which takes account of the effect of seepage to investigate the stability of the tunnel face. The study indicates the factor of safety for tunnel face increases with the increase of cohesion, friction angle and supporting pressure, but decreases with the increase of underground water level. The failure range of the tunnel face decreases with the increase of friction angle observably, but the underground water level has slight influence on the failure range of the tunnel face.