An Analytical Coupling Framework for the Synergistic Interaction between Strain-Softening Rock and Prestressed Yielding Anchorage System Considering Tunnel-Face Spatial Effects

Abstract Accurately characterizing the three-dimensional interaction between anchorage systems and strain-softening surrounding rock remains a significant challenge in tunnel engineering due to the complex nonlinear mechanical processes involved. This study develops a comprehensive analytical framework by integrating two-dimensional (2D) elastoplastic solutions with the longitudinal deformation profile (LDP) to rigorously account for the spatial effect of the tunnel face. The 2D mechanical foundation is established using the unified strength theory and a nonassociated flow rule, specifically considering the strengthening effect of the intermediate principal stress on rock bearing capacity. A 2D + LDP mapping methodology is then proposed, in which the longitudinal installation position of the support is precisely correlated with a virtual support force in the cross-sectional plane. This integrated approach facilitates a robust quantitative analysis of the synergistic mechanism between the rock mass and a prestressed yielding anchorage system. Research findings indicate that the application of prestress provides immediate active reinforcement, manifesting as a characteristic step effect on the deformation profile, while the yielding segment functions as a mechanical safety valve to accommodate large squeezing deformations without risking structural failure. Furthermore, sensitivity analysis reveals that while strength-related parameters significantly influence the spatial constraint evolution, elastic properties exhibit a notable decoupling effect in the normalized deformation domain, explaining the physical nature of overlapping LDP curves. Finally, a dynamic delay–compensation design framework is formulated, providing a computationally efficient tool for the iterative design and on-site calibration of tunnel supports in high-geostress environments.