Ze-Hang Qian

Tunnels are commonly constructed in water-bearing zones, which necessitates stability analyses of saturated tunnels based on the upper bound of the plastic theory. Previous kinematical approaches have the following drawbacks: (1) using an empirical approach to estimate pore-water pressure distributions; (2) using failure mechanisms that are not rigorously kinematically admissible. To overcome these shortcomings, we proposed a rigorously kinematically admissible translational–rotational failure mechanism for an underwater shallow square tunnel where velocity discontinuity surfaces were derived. Then, the pore-water pressure field surrounding the tunnel under the boundary of constant water pressure is analytically generated based on the complex variable method and imported into the kinematically admissible velocity field. Work rates performed by external forces and the internal dissipation rate are numerically computed to formulate the power balance equation, followed by a mixed optimization algorithm to capture the critical states of the surrounding soils of tunnels. The outcomes of pore-water pressure distributions, safety factors, and failure mechanisms are in tandem with those given by the numerical simulation but show higher computational efficiency than the numerical simulation. In the end, we highlight the advantages of the proposed model over the empirical approach, where soil properties and water table elevation effects are analyzed.

Stability analysis of slopes subjected to steady infiltration is a hot topic in geotechnical engineering. However, the existing three-dimensional (3D) upper-bound limit analyses of unsaturated rotational slopes failed to take variable strength parameters and hydraulic parameters in space into account. To fill this gap, a semianalytical model is developed to capture the factor of safety (FS) and the critical failure region of unsaturated slopes based on the kinematical approach of limit analysis (KALA). A 3D rotational failure mechanism of unsaturated slopes subjected to steady vertical infiltrations is generated by a “point-by-point” technique, which can readily incorporate spatially variable strength parameters and hydraulic parameters. The work rates are calculated to formulate the objective function of FS, and the critical FS are optimized. The proposed model is validated through comparisons with the existing solutions and numerical solutions in terms of both the FSs and the failure patterns. The combined effects of hydraulic parameters and the size of slopes are investigated. An application to the stability analyses of unsaturated slopes with spatially variable physical parameters demonstrates that the proposed model has the potential to serve as a benchmark for the KALA of unsaturated slopes under complex geological conditions. Generally, the described framework can help geotechnical designers quickly evaluate the stability of unsaturated slopes in the preliminary design phase if the water table elevation is available and the hydraulic and strength parameters have been calibrated.

In the existing upper bound limit analyses (UBLA) of rotational slopes reinforced with prestressed anchor cables, the mobilized axial forces of all cables are assumed to be equal to the ultimate pullout force. However, such an assumption overestimates the mechanical contribution of prestressed anchor cables, resulting in excessively high safety factors. In this technical note, we aim to tackle this issue by proposing a pseudo-plastic design concept, in which soil masses and prestressed cables are treated as plastic and elastic-plastic, respectively, when slopes collapse. A pseudo-plastic failure model of prestressed anchor cables is proposed, where the variation of tension forces and movement of anchor heads are accounted for. Several interesting conclusions are drawn as follows: (1) Contrary to the conventional plastic failure mode of cables, upper bound solutions obtained by the proposed model are much closer to the exact solutions. (2) Variation of factors of safety (FSs) against the accumulated rotational displacement can be explained by the force-displacement curve obtained in the pullout test of prestressed anchor cables. (3) The sliding slope reinforced with cables may turn out to be stable after a slight rotational movement, which can be utilized in the economical design.

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.

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.

Geotechnical structures often have position-dependent soil strength parameters as a consequence of stress history, deposition process, mineralogical composition, and weathering effect. However, most available theoretical models for estimating active earth pressures focus only on homogeneous cases. By a point by point technique, this work develops a friction-angle-dependent discretized failure mechanism to evaluate the active earth pressure on backfills in the framework of the limit-equilibrium slice method. The generated failure mechanism is composed of a series of horizontal elements. Compared with previous theoretical models, the benefits of the proposed method are twofold: (1) the friction-angle-dependent failure mechanism agrees well with the actual failure surface for heterogeneous backfills; (2) not only the multilayer frictional backfill but also the backfill with a position-dependent friction angle can be accounted for. The total active earth pressure coefficient, the earth pressure distributions, and the failure mechanisms are obtained, all showing excellent agreement with the available experimental data and the existing analytical solutions. For practical use, applications to backfills with a weathered zone and spatially variable frictional angles are then conducted. Finally, the proposed model is degraded into a two-layer case in which the active earth pressure coefficients under various mechanical and geometrical parameters are tabulated.