Based on the upper bound limit analysis, the multi-log spiral failure mechanism for earth retaining structures under horizontal seismic loads was constructed, which could introduce the nonlinear strength criterion into stability analysis without any linearization technique. By calculating various external work rates and the internal energy dissipation, the energy balance equation was established, and the active earth pressure formula required for the retaining structure to be in a critical stable state was derived. With the application of a genetic algorithm and particle swarm optimization, the optimal upper bound solutions of active earth pressure coefficients were obtained. The validity of the research results was verified through comparative analysis. This paper provided diagrams of the active earth pressure coefficients required for earth retaining structures to maintain a critical stability state under different parameters. The influences of seismic load, slope inclination angle, soil strength tension cutoff (TC), and the δ/ϕ ratio were investigated. By investigating the design charts, the active earth pressures applicable to practical engineering can be obtained, which provide a theoretical basis for the preliminary design of retaining structures in earthquake-prone areas.

This study investigates the stability of three-dimensional (3D) tunnel roofs with varied burial depth in saturated rock strata following the Hoek–Brown (HB) failure criterion. Within the framework of limit analysis, a 3D kinematic collapse mechanism for tunnel roofs, incorporating the existence of pore water pressure, is developed, and corresponding stability indices are formulated. Numerical methods are utilized to determine the optimal solutions of these indices. A comprehensive parametric study evaluates the influence of 3D geometric characteristics, HB parameters, and burial depth on tunnel stability. Results demonstrate the evolution of tunnel-roof stability as the critical depth-to-span ratio C/R increases from shallow- to deep-buried conditions; for the parameter combinations examined in this study, the critical C/R separating the two mechanisms ranges approximately from 0.15 to 2.0, depending on the rock-mass properties, pore-pressure condition, and tunnel geometry. Furthermore, stability charts correlating supporting pressure and factor of safety (FoS) in saturated strata are proposed to offer practical design guidance. Findings indicate that neglecting pore water pressure may significantly underestimate the structural stability, thereby emphasizing the necessity of incorporating hydrogeological effects in tunnel design. The proposed stability assessment framework provides theoretical support for the safe development of deep underground spaces under complex geological conditions, including deep energy exploitation, underground storage facilities, and related geotechnical engineering applications.