Explicit Analysis for the Ground Reaction of a Circular Tunnel Excavated in Anisotropic Stress Fields Based on Hoek–Brown Failure Criterion

Abstract

The study aims to utilize the convergence–confinement method (CCM) by considering non-hydrostatic stress assumptions in the analysis of the surrounding rock in a circular tunnel. The rock mass properties should adhere to the criteria of the non-linear Hoek–Brown failure criterion. Through a thorough theoretical analysis approach, an analytical solution was derived to determine the stress and displacement induced by tunnel excavation, particularly in the elastic and plastic zones. This solution, applicable under anisotropic stress conditions, involves accounting for confinement loss incrementally for computational feasibility. The implementation of this analytical solution, facilitated by a straightforward spreadsheet, was validated against existing data to evaluate the impact of non-linear failure criteria on ground reaction behavior. The study scrutinizes the mechanical response at the tunnel’s inner curve and assesses stress–displacement distribution across the tunnel cross-section. A comparison between the proposed solution and published results demonstrates a consistent and promising correlation.

Keywords

• tunnel analysis
• non-linear failure criterion
• closed-form solution
• incremental procedure
• anisotropic stress fields
• convergence–confinement method