Analytical Model for Tunnel Face Stability in Equivalent Homogeneous Rock Masses with Persistent Joint Sets

Reliable assessment of tunnel face stability in rock masses containing persistent joints remains challenging because existing analytical methods generally neglect the influence of joint orientation. This study develops an equivalent analytical model that incorporates joint orientation into the limit analysis framework by modifying rock mass parameters. The proposed model explicitly considers joint orientations from 0° to 90°, enabling anisotropic joint effects to be efficiently represented within the analytical solution. Validation against numerical simulations demonstrates high prediction accuracy with substantially improved computational efficiency. Parametric analyses reveal that joint orientation is the primary factor controlling tunnel face stability, producing a symmetric M-shaped variation in stability and identifying the most unfavorable joint orientations. Rock mass quality, tunnel buried depth, and excavation-induced disturbance also significantly influence stability. The proposed model provides a rapid and practical approach for tunnel face stability evaluation in jointed rock masses, offering valuable support for tunnel design and construction.