Roof stability of tunnels with varied burial depth in rock strata following a modified HB criterion

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.