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

A tension cut-off (TC) technique becomes essential to account for the strength and failure characteristics of rock in low and tensile stress ranges, since that the generalized Hoek-Brown (GHB) criterion emphasizing shear failure. The synergistic effects of burial depth and TC on tunnel roof stability still poses a challenge, necessitates the present work. Thus, incorporation 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 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, the ones first increase, then decrease, and finally stabilize 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.