Three-Dimensional Stability Analysis of a Tunnel Roof at Varying Burial Depths in Saturated Hoek–Brown Rock Masses

Abstract

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.