An Improved Failure Model Considering the Arching Effect for Tunnel Face Stability in a Weak and Fractured Rock Mass

Tunneling efforts that use shield machines often encounter weak and fractured rock formations, where the stability of the tunnel face is the principle safety control factor during tunnel construction operations. Within the framework of the limit analysis method, an improved model was proposed. The model consists of two failure modes, effectively addressing the shortcomings that arise from the incomplete contact interface between the traditional model and the tunnel face. Furthermore, the proposed model introduces the nonlinear Hoek–Brown criterion and improves the shape of the sliding failure surface within the cover layer to account for the arching effect. Subsequently, the proposed model was validated by comparison with numerical simulations and results in the literature. Further parameter analysis was conducted to investigate the influence that the Hoek–Brown parameters and tunnel depth have upon the critical support pressure and effectively identify the characteristics of failure mechanisms. The resulting data show that a reduction in the geological strength index (GSI), Hoek–Brown parameter (mi), or uniaxial compressive strength (σci) or an increase in the disturbance coefficient (D) leads to a nonlinear increase in the critical support pressure and an expansion of the failure zone of the tunnel face. Conversely, as the tunnel depth increases, the extent of the failure zone gradually expands, and the stability of the tunnel face exhibits a trend of initially decreasing and then increasing.