Deformation Analysis of Circular Tunnels Based on a Viscoelastic–Plastic Rheological Model

Geomaterials experience time-dependent deformation resulting from underground excavation. Herein, we propose a novel six-parameter creep constitutive model incorporating a Hookean elastomer, Kelvin body, and plastic element (HKP) model to characterize the nonlinear rheological behavior of rocks. The plastic component of the conventional Ramberg–Osgood mechanical model is adapted into the plastic element of the HKP model. The proposed viscoelastic–plastic model is validated using uniaxial creep tests conducted on sandstones. Based on the Mohr–Coulomb criterion and the nonassociative flow rule for geotechnical materials, a time-dependent deformation solution for tunnels is derived using the HKP model. The analytical solution for surrounding rock deformation is then examined through parameter analysis. The solution is applied to analyze the displacement of an actual tunnel. Results show that the HKP model effectively captures the mechanical behavior of rocks across all three creep stages. Additionally, the calculated results from the analytical solution closely match the tunnel monitoring data. The findings of this study offer a reliable tool for early warning of tunnel deformation during excavation and operation.