Failure mechanisms of rectangular tunnels under coupled geometric and stress variations: insights from DEM and conformal-mapping analysis

Abstract

Stress redistribution around noncircular tunnels is a key mechanism controlling damage and instability in deep underground engineering. However, under constant-area conditions, how geometric ratio, inclination, and confining pressure jointly control crack initiation, spalling evolution, and final failure in rectangular tunnels remains insufficiently understood. This study combined discrete element method (DEM) with an elastic theoretical solution based on conformal mapping to investigate rock specimens containing a rectangular tunnel. A total of 180 cases were analyzed while the tunnel area was kept constant. The varied parameters were geometric ratio R (1.00–2.00), inclination α (0°–90°), and confining pressure q (0–30 MPa). DEM was used to reproduce the full process from crack initiation to specimen-scale instability, whereas the elastic theoretical solution was used to identify boundary local stress extrema and near-field stress-zone partition before failure. Confining pressure was found to be the primary factor controlling both peak strength and failure-mode transition, while inclination and geometric ratio mainly altered crack-initiation position and local spalling extent. Under zero confinement, failure exhibited an X-shaped mixed tensile/shear mode with localized tensile bands. With increasing confinement, the pure tensile zones contracted continuously, tensile cracks disappeared progressively, and the final failure converged toward a more concentrated X-shaped compression-shear mode. The integrated framework provides a mechanical basis for stability assessment and support optimization of rectangular and other noncircular tunnels.