Jingshu Xu

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.

Roof stability plays a crucial role in maintaining the overall stability of surrounding rocks to ensure safety of tunnel construction and operation. In this work, tension cut-off (TC) technique is introduced to modify the Hoek–Brown (HB) criterion to describe the tensile failure of rock strata. Thereafter, stability analysis of anchor bolt-reinforced tunnel roofs in rock strata subjected to a hybrid tensile-shear fracture is performed. The work balance equation is established by equating the external work rates of the falling block and the anchor bolts to the internal energy dissipation rate. Two stability indicators, that is the stability number (N) and the factor of safety (FoS) are proposed to quantitatively analyze the stability of tunnel roofs. Optimization algorithms combining genetic algorithm and particle swarm optimization are programmed to capture the optimal upper bound solutions. The influences of TC, strength criterion parameters, and anchor bolt-reinforcement strength on roof stability are explored in this work. It was found that increasing the anchor tension T improves the FoS of reinforced tunnel roofs, with an increase of up to 68% observed for rectangular tunnel roofs under the selected representative case, while the improvement is relatively less pronounced for circular tunnel roofs. Regarding anchor support, as ξ increases, the N for rectangular tunnels nearly doubles. This work provides a theoretical basis for preliminary designing of tunnels in reinforced rock strata.

Saturated‐based approaches relying on shear‐failure assumptions inadequately describe rainfall‐induced active earth pressure in unsaturated soils. This study presents a three‐dimensional (3D) upper‐bound analytical framework for active earth pressure in unsaturated soils by coupling a unified suction‐stress formulation with a composite tensile–shear failure mechanism. Both adsorptive and capillary contributions to suction stress are explicitly incorporated, and hydraulic hysteresis effects are considered through differentiated wetting and drying strength evolution. A two‐segment rotational failure mechanism, consisting of an upper tensile‐dominated zone and a lower shear‐dominated zone, is formulated while maintaining velocity continuity along the entire failure surface. Soil–wall roughness is explicitly included to account for interface friction effects. Closed‐form solutions for the active earth pressure coefficient are derived. A parametric analysis examines the influences of suction‐stress parameters, rainfall intensities and patterns, wall roughness, and 3D geometry. The results demonstrate distinct time‐dependent earth pressure responses governed by adsorption–capillarity partitioning, hysteresis, and interface conditions. This research provides a theoretical framework for evaluating active earth pressure on retaining structures under unsaturated states under rainfall infiltration.

A quantitative stability analysis of a three-dimensional (3D) rectangular cavity crown with limited buried depth in generalized Hoek–Brown (GHB) rock mass is conducted employing the limit analysis approach. A 3D collapse mechanism for a shallow-buried rectangular cavity crown is developed, in which the mechanism for a deep-buried cavity crown represents a special case. The equations for three stability measures—that is, the stability number, the factor of safety (FoS), and the required support pressure—are derived. The feasibility of this study is verified. Consequently, a detailed analysis of the three measures is provided, focusing on the variation trends for the stability measures. An increase in the buried depth ratio C/R and strength index GSI enhances the stability of the cavity crown, while an increase in the 3D characteristics index L/R and strength index m_i weakens it. Additionally, stability charts for both the required support pressure and FoS are presented for practical engineering applications.

Burial depth is one of the most significant factors determining the stability and possible failure patterns of tunnel roofs in rock strata. A tension cut-off (TC) technique​​, based on the Hoek-Brown (HB) criterion, is essential to accurately characterize the strength and failure behavior of rock under low confinement or tensile stress. The synergistic effects of burial depth and TC on tunnel roof stability still pose a challenge, necessitating the present work. Thus, incorporating the modified HB criterion with TC, failure mechanisms for tunnel roofs with varied burial depth are firstly developed. Based on the limit analysis, the energy balance equation is built by equating the work rates and internal energy dissipation to derive the stability indicators. By optimization codes, the optimal upper-bound solutions, that is the minimum results of the stability number ( N) and factor of safety (FoS), and the maximums of the required supporting pressure ( p) are captured. The effects of burial depth and strength criterion parameters with TC on roof stability are investigated. It is found that N for rectangular tunnel roofs initially decreases and then stabilizes, while for circular tunnels, it first increases, then decreases, and finally stabilizes with increasing burial depth. TC has a decisive influence on both the stability and the critical burial depth for tunnel roofs to form a complete collapse arch. Design charts with application examples are plotted for ready reference and application in practical preliminary design scenarios.

Rainfall infiltration is one of the major causes of slope instability. While shear failures were commonly adopted, unsaturated soil slopes are in fact highly susceptible to composite tensile-and-shear failure. To address this problem, a nonlinear Mohr–Coulomb (MC) criterion was modified to capture the time dependent tensile and shear strengths for various soils during rainfall, where the coupled effect between capillary and adsorption pressures in the soils was considered. The results showed that the proportion of adsorption stress in the total suction stress varied greatly across different soil types, with the transitional and saturated gravimetric water contents being the two most sensitive parameters affecting the proportion of adsorption stress. On this basis, energy balance equation was established through a two-stage composite tensile–shear failure mechanism of three-dimensional (3D ) slopes following the modified MC criterion. Based on the upper bound theorem of limit analysis, the factor of safety (FoS) for the slopes was calculated by incorporating the strength reduction technique to systematically investigate the effects of rainfall patterns including intensity and duration and soil types on slope stability. Comparisons by analytical and numerical approaches were conducted to verify the present work. Parametric analysis revealed that a 3D analysis could better reflect the slope stability, and that the falling range of slope FoS was strongly correlated with the rainfall patterns and soil permeability. The present study provides a reference and method for assess the stability of various unsaturated soil slopes under different rainfall conditions.

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.