Seismic events are an active factor in causing slope instability, and the existing pseudo-dynamic method ignores some practical engineering conditions. In this paper, the seismic stability of three-dimensional (3D) two-step slopes is evaluated utilizing the modified pseudo-dynamic method based on the kinematical approach of limit analysis, in which the nonlinear characteristics of soil are considered using the generalized tangent technique. A 3D horn-like rotational failure mechanism is established to solve internal energy dissipation and external force work, in which the seismic work is considered in addition to the soil weight work and obtained by the layer-wise summation method. Based on the force-increase technique, the analytical expression for the safety factor (FS) of 3D two-step slopes is derived more readily. To verify the reliability of the new expression, the present results are compared with already posted solutions and the original pseudo-dynamic solutions. Ultimately, the sensitivity discussions are carried out to investigate the impacts of various factors on slope stability. This has some significance for the design and safety of 3D two-step slopes.

Currently, the study of analytical solutions for the seismic stability of slopes under anchorage conditions is one of the hottest subjects in engineering. In this paper, an analytical solution for the seismic safety of the three-dimensional (3D) two-stage rock slope reinforced with prestressed anchor cables governed by the nonlinear Hoek–Brown criterion was deduced, in which the analyses of seismicity were performed by the latest modified pseudo-dynamic method. This method supplements the consideration of the damping effect of the rock medium on seismic waves, which is more in line with the real seismic situation. A mathematical geometric model was developed for calculating the external forces work and internal energy dissipation acting on 3D rotating rock masses reinforced with prestressed anchor cables, in which the seismic work rate was calculated using a new layer-by-layer superposition summation method. The analytical solution of the safety factor could be collated as an explicit function of several variables, and then, the optimal value was obtained by the Particle Swarm Optimization (PSO) algorithm. To corroborate the accuracy of new analytical solutions, the results were contrasted with those of the pertinent literature. The results of the two comparisons were very close. Ultimately, the sensitivity analyses and coupling effects of seismic pseudo-dynamic factors and prestressing anchorage factors were carried out. It was found that even small seismic intensities had a large effect on the stability of rock slopes with developed joints. Increasing the number of steps and prestressing anchors can effectively improve the stability of rock slopes under seismic effects. The conclusions have significant implications for the anchorage design of the 3D two-stage rock slope as seismic events occur.

The shear strength of unsaturated soils exhibits significant nonlinearity, while previous studies often simplified it with linear strength models. The objective of this paper is to investigate the distinctions in the stability of three-dimensional (3D) tunnel faces when using linear and nonlinear strength models. A new 3D rotational failure mechanism and an extended form of the Mohr–Coulomb (M-C) failure criterion were integrated into the kinematically limited analysis (KLA) framework to describe the failure characteristics of tunnel faces. Subsequently, the factor of safety (FS) of the 3D tunnel faces was calculated using the strength reduction method (SRM). In the discussion section, the impacts of nonlinear shear strength, matric suction in the unsaturated soils, and the 3D geometric parameters of the tunnel on the stability of the tunnel face were analyzed. The outcomes indicate that, in unsaturated soil conditions, diverse nonlinear strength calculation models and soil types exert disparate influences on the FS of 3D tunnel faces. The main novelty of this study lies in establishing an effective method for assessing the stability of tunnel faces in unsaturated soils.