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.

Planned tunnel excavation beneath piled buildings is common in actual projects. The excavation-induced deformation of the bearing stratum at the end of an existing pile end may decrease the ultimate bearing capacity of the pile, affecting its mechanical properties. Since previous studies on this topic have focused on the pile deformation induced by tunneling, the deformation mode of the bearing stratum at a pile end has not been thoroughly investigated. In this study, a new two-dimensional failure mechanism describing the failure characteristics of a bearing stratum at the end of an existing single pile induced by shield tunnel drilling beneath the pile is established. Based on this mechanism and the kinematic approach, an analytical equation for the failure surface of the bearing stratum during tunnel drilling beneath a single pile is obtained via a variational principle, and the shapes of the rupture surface of the bearing stratum at the pile end are plotted for various parameters. To validate the validity of the method in practice, an analytical expression for the failure surface of the bearing stratum is obtained and compared with numerical simulation solutions. The results of this comparison show that the presented method is effective for studying the failure characteristics of a bearing stratum at a pile end and can be used for predicting these failure characteristics in practice.

In accordance with the collapse characteristic of trench wall during underground diaphragm wall construction, a modified three-dimensional (3D) failure mechanism of trench wall is established. By introducing nonlinear characteristic and the nonhomogeneity of soil into the theoretical calculation, the objective function of the safety factor (F_s) of the trench wall in the limit condition is derived, and the upper bound solution of the F_s of the slurry trench is derived by employing the optimization computation. To prove the validity of the presented approach, the solutions derived from the presented method are compared with those previous solutions and the comparing results show a good agreement. Moreover, the parametric analysis is conducted to study the effect of various parameters on the stability of trench wall. The results of parametric analysis show that nonlinear and the nonhomogeneous parameters have significant influence on the safety factors, and the nonlinear failure characteristic of the nonhomogeneity of soil cannot be ignored in the practical engineering.