This study proposed an effective approach to accurately evaluate the three-dimensional (3D) seismic bearing capacity of heterogeneous and anisotropic slopes in the framework of the upper-bound limit analysis theorem. An improved discretized horn mechanism was first developed so that the properties of heterogeneous and anisotropic soils could be involved in the slope stability analysis. To incorporate the impact of seismic forces, the modified pseudo dynamic approach was adopted, which ensured that the complete time-history of the seismic-induced ground movement, the soil-damping properties, and the amplification effect could be considered in this study. The seismic bearing capacity of slopes was then calculated by using a method that integrated the upper-bound limit analysis theorem and the modified pseudo dynamic approach. The proposed method was validated by comparisons with previous analytical solutions for some available cases, showing that the proposed method is an effective approach to determine the 3D seismic bearing capacity of heterogeneous and anisotropic slopes. The effects of model parameters on the ultimate bearing capacity and the critical failure surface are then presented. Finally, the influence of pore–water pressure on the seismic slope stability is discussed.

The aim of this study is to propose an effective approach to evaluate the stability of a shield tunnel face with tensile strength cutoff by using the upper-bound limit analysis method. Based on the discretization and “point by point” techniques, two improved rotational failure mechanisms, namely the improved collapse failure mechanism and the improved blowout failure mechanism, are developed with the tensile cutoff for the first time. Based on these improved failure mechanisms, the critical collapse and blowout pressures of tunnel faces are then determined by using the upper-bound limit analysis method. The proposed method is then validated by comparisons with previous analytical solutions and numerical results, showing that the proposed method is an effective approach to evaluate the stability of shield tunnel faces. The influences of model parameters on the critical support pressures and the failure feature of the proposed mechanisms are finally presented.