Stability for Anchor Bolt-Reinforced Tunnel Roofs in Rock Strata with Modified HB Criterion

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.