Nonlinear Subgrade Modulus for Longitudinal Deformation of Tunnel Considering Mobilized Strength of Undrained Clay

ABSTRACT In view of the limitation that the linear subgrade reaction in the current beam‐spring model is inadequate for scenarios of tunnel embedded in the soft ground condition with large deformation, this paper proposes a novel model to evaluate the nonlinear subgrade reaction. The model incorporated the nonlinear characteristics of the longitudinal subgrade reaction for tunnel lining in undrained clay by considering the mobilized strength design (MSD). Firstly, the energy equilibrium equation correlating the subgrade reaction with the tunnel displacement is established considering the soil displacement field. By solving the energy conservation equation, the nonlinear behavior of the subgrade reaction is obtained and verified against numerical models, confirming its rationality. Finally, the proposed model is applied into a real case for the analysis of tunnel longitudinal deformation under the effect of nearby deep excavation. Compared with traditional linear subgrade reaction, the nonlinear subgrade reaction proposed in this study achieves a mean absolute error of 1.22 mm between the calculated tunnel deformation curve and field observations, with an accuracy improvement exceeding 47.4%. By explicitly incorporating the progressive mobilization of shear strength with displacement into subgrade reaction calculations, this method demonstrates superior performance in predicting large deformations of tunnels in undrained clay.