Study of the Failure Mechanism of a Tunnel Reinforced with a Petal-Shaped Grouting Layer Based on the Upper-Bound Method

During shield tunnel construction, tunnel stability and surface settlement deformation are often improved by backfill grouting; thus, studying the failure mechanisms of grout-reinforced tunnels is significant for evaluating their stability in practical engineering. Previous research has assumed that the grouting layer is homogeneous, which is inconsistent with engineering practice. In this paper, a petal-like grouting layer model is presented. The failure mechanisms of tunnels and surface settlement are investigated using an upper-limit FEM based on second-order cone programming. The results show that, compared with the traditional grouting layer, the ultimate supporting force coefficient σT/c and the plastic failure area of the tunnel are reduced by approximately 14% and 13.4%, respectively. It is thereby shown that the reinforcement effect of a petal-shaped grouting layer is superior to that of a homogeneous grouting layer. For grouting layer eccentricities of d = 0 cm and d = 20 cm, σT/c and the maximum settlement coefficient increase by 16% and 11.7%, respectively, proving that the tunnel stability can be weakened by the eccentricity of the grouting layer. The upper-bound solutions for tunnel stability, which accurately bracket the true collapse load, are summarized in a series of stability charts for use in tunnel design.