Limit Analysis for the Face Stability of a Shallow-Shield Tunnel Based on a Variational Approach to the Blow-Out Failure Mode

The soil in front of a shield tunnel face can be pushed toward the ground surface if the support pressure is higher than the threshold that causes blow-out failure of the tunnel face. Most of the failure mechanisms used in the upper-bound analysis of a tunnel face have been derived from rigid-block failure mechanisms that are inconsistent with the failure mode observed in actual engineering practice. This article describes the construction of a new blow-out failure mechanism that is characterized by an arbitrary curve. Based on this failure mechanism and the Hoek–Brown (H-B) nonlinear failure criterion, an objective function that can be used to derive the upper-bound solution of the failure surface for a tunnel face is established in the framework of the upper-bound theorem. Using a variational approach, the equation of the failure surface that makes the objective function reach an extremum is obtained. On the basis of the analytical equation of the failure surface, the shapes of the failure surfaces for different parameters are plotted. By studying the influence of various parameters on the shape of failure surfaces, the changing laws of the shape of the failure surface for different parameters are obtained. To evaluate the validity of the upper-bound solution, the analytical results are compared with the numerical results provided by finite-difference software. By converting the parameters of the H-B failure criterion represented by normal and shear stresses into the parameters of the H-B failure criterion represented by the major and minor principal stresses, a comparison is made for equivalent conditions. The failure surface derived from the upper calculation and the shear-failure surface provided by the numerical simulation are found to be in agreement, which indicates that the method proposed is valid.