Critical internal pressure for passive failure of shallow pressurized rock caverns/tunnels

The assessment of passive failure of a pressurized storage cavern or tunnel in a rock mass is important for determining the required rock cover thickness (or overburden depth). This study proposes a semi-analytical solution procedure based on the kinematic approach of limit analysis to determine the critical internal storage pressure required to induce passive failure of a long flat-ceiling pressurized cavern or tunnel overlain by a shallow rock mass layer. The analysis is based on a single-wedge failure mechanism with a curved rupture surface, and the rock mass strength is characterized using the generalized Hoek–Brown (GHB) failure criterion. The shape of the rupture surface is governed by the scaled Mohr envelope of the GHB failure criterion expressed in parametric form. Using the work–energy balance expression, the least kinematic solution is obtained through a minimization procedure with respect to a single parameter that defines the complete geometry of the failure mechanism. The results are expressed in terms of the dimensionless critical storage pressure for various dimensionless parameters governing rock mass behavior, the rock cover thickness ratio, and the surcharge pressure ratio. The proposed method yields solutions that are in close agreement with existing studies.