Most adverse geometry of structural discontinuity on roof collapse in circular rock tunnels

Structural discontinuities are common in rock masses around underground structures. Their influence on tunnel stability has been investigated extensively. However, previous studies focused on the given geometry of a structural plane subjected to a high in situ stress state. The motivation of this study was to determine the most critical location and orientation of an individual discontinuity against a gravity-driven collapse of roof detached from the surrounding stationary rock. A circular tunnel in a Hoek–Brown rock mass with potential discontinuity was considered based on a semi-analytical approach incorporating a nature-inspired optimization algorithm. The most adverse discontinuity was identified to be a vertical open crack initiated from the springline of the circular tunnel. The inclusion of a critical crack resulted in a significant increase in the stability number and a decrease in the factor of safety. This indicated significantly less stable tunnel roofs. Assuming the worst-case scenario associated with the most unfavorable crack geometry, the relative increase in the stability number was approximately 1,600% on an average. A comprehensive sensitivity analysis in the presence of cracks was conducted to understand the influence of the rock properties and crack geometries on the tunnel roof safety.