Elastoplastic Solution for Tunnel Composite Support Structures Based on Mohr–Coulomb Criterion

Abstract

Linings and anchor bolts, as common support structures, play a crucial role in ensuring the stability of tunnel surrounding rock. This study aims to investigate the elastic–plastic behavior of lining-anchor bolt support structures in deep circular tunnels under static water pressure. Based on the Mohr–Coulomb (M-C) criterion and equivalent substitution method, this study derives the solution process for the radius of the plastic zone and the elastic–plastic stress expressions under a given lining internal pressure. Furthermore, through examples, this study analyzes the radius of the plastic zone and the stress evolution curve of the lining-anchor bolt-supported surrounding rock system under three conditions: without anchoring, various elastic moduli, and different anchor bolt support angles. Finally, this study verifies the rationality of the elastic–plastic analytical solution for the lining-anchor bolt-supported surrounding rock structure through numerical simulation methods. The integrated lining-anchor bolt support is notably effective in inhibiting the expansion of the plastic zone, particularly in soft rock. Additionally, the elastic modulus and circumferential spacing of the anchor bolts significantly influence the plastic zone inhibition rate in soft rock.

Keywords

• Mohr–Coulomb criterion
• equivalent substitution method
• elastic–plastic analysis
• plastic zone inhibition