Difference solution of passive bolts reinforcement around a circular opening in elastoplastic rock mass

• Strain and stress of circular opening by convergence–confinement method.
• Passive bolts reinforcement in elastoplastic rock mass.
• Passive bolts reinforcement solved by finite difference solution.

This paper presents the solution based on Finite Difference Method for the analysis of passive bolts reinforcement around a circular opening. Linked to the classical convergence–confinement method, the solution provides a framework to the ground and passive bolts responses and can be applied to the elastoplastic models such as Mohr–Coulomb and Generalized form of Hoek–Brown failure criterions. The passive bolt and rock mass interaction is incorporated through the results of pullout tests and the reinforcement mechanism is illustrated through parameters studies. The proposed solution is validated with known analytical results for the unbolted case. Numerical examples of bolted tunnels are also provided to demonstrate significant advantage and efficacy of the proposed solution for practical applications.