A Coupling Model for Rock–Lining Interaction Considering Hardening Performance of Shotcrete Lining and Intermediate Principal Stress

Abstract

The interactive mechanism between the surrounding rock and lining system is a central issue in tunnel-support design. Previous studies have seldom considered both the hardening characteristics of the shotcrete lining and the intermediate principal stress effect simultaneously, resulting in inaccurate predictions of tunnel convergence and support pressure. To address this, a coupled analytical model for rock–lining interaction is developed based on the Kelvin–Voigt model and unified strength theory. This model characterizes the shotcrete hardening process through its time-evolving stiffness and represents the tunnel-face confinement effect using the concept of fictitious support pressure. The accuracy and reliability of the coupled analytical solutions are verified by comparing them with field-monitoring data. Furthermore, the effects of relevant parameters on the mechanical performance of tunnel structures are analyzed through a case study. The results show that neglecting the hardening characteristics of the shotcrete lining leads to an underestimation of tunnel convergence but an overestimation of the pressure borne by the shotcrete lining. Accounting for the intermediate principal stress unlocks the self-supporting potential of the rock, resulting in optimized support parameters and lower construction costs. An increase in the creep modulus parameter ( G 2 ) leads to a reduction in tunnel wall deformation; consequently, the support pressure also decreases. As the excavation speed increases, the stress release rate increases, leading to greater tunnel wall deformation and higher support pressure. With increases in the creep modulus parameter ( G 2 ) and excavation speed, the development of the viscoplastic zone in the surrounding rock accelerates. These findings provide a theoretical foundation for support design and construction in similar tunnel projects.