In this study, using the kinematic approach of limit analysis, a new numerical model was developed to investigate the effect of the coupled flow deformation on tunnel face stability. By incorporating the innovative mesh-dividing optimization technology with the principle of generating a three-dimensional (3D) rotational failure mechanism into a customized program of linear interpolation, the pore-water distribution in the stage of the global failure ahead of the tunnel face determined by FLAC3D was interpolated on the 3D rotational failure mechanism. The support pressures predicted by the developed model improved the existing upper-bound solutions by at least 14.2% for the case of slight cohesion soils but made little difference with the existing upper-bound solutions for high cohesion soils. The support pressures predicted by the developed analytical method were in close agreement with those from numerical simulations and in situ data. The results showed that the critical face pressures increased linearly with increasing water table elevation. Several design charts are provided for parametric analysis, which can be directly used by tunnel engineers in the evaluation of face stability.

The kinematical approach of limit analysis has been historically employed to assess slope stability in the geotechnical community, for which most three-dimensional (3D) failure mechanisms are generally based on a composite of multiple common geometrical bodies. Although these failure mechanisms are straightforward, they may not perform well for slopes that involve multilayered soils with heterogeneous shear strength parameters. This paper aims at proposing a new 3D failure mechanism for steep slopes using a spatial discretization technique. The proposed failure mechanism is composed of a large number of elemental blocks that are generated point by point obeying the kinematically admissible velocity field and the normality condition. The discretization scheme makes it possible to simplify the calculations of internal energy dissipations and external work rates on the failure mechanism when both the soil properties and external loadings are spatially changing. The performance of the proposed method is illustrated to examine the stability of steep slopes in homogeneous soils, multilayer soils, and spatially variable soils, showing good agreements with previously published results and numerical modelings.

Semianalytical or analytical models for calculating active and passive earth pressure coefficients for undrained soil–wall systems subjected to head rotation are rare. To fill this gap, this study proposes a semianalytical theoretical model that describes the real failure features of wall–soil systems with head rotation and under undrained conditions. A continuous velocity field (CVF) that is decomposed into circular and radial velocity components is generated to characterize the movement of undrained soils in the plastic zone. The closed-form solutions of active and passive earth pressure coefficients are formulated based on the upper-bound limit analysis (UBLA) theorem. A comparison with numerical simulations and Rankine’s theory are performed to illustrate the importance of wall movement and the contributions of undrained cohesion. The analysis outcomes demonstrate that (1) the conventional stress-based method that ignores the head rotation of walls leads to an error of earth pressure coefficients up to 15.7%; and (2) the active and passive earth pressure coefficients have linear relationships with undrained cohesion. Finally, an application to shallow excavation is conducted, showing the good performance of the proposed model.