Nonlinear uplift resistance solution for a buoyant tunnel considering mobilized undrained shear strength under groundwater rise

To quantify the softening of nonlinear uplift resistance around the circular tunnel subjected to groundwater rise, this study develops an analytical framework based on the mobilized strength design (MSD) theory. Tunnel deformation is decomposed into two components: oval deformation and vertical uplift, the latter being induced by a prescribed external load. Using complex variable method, closed form displacement fields are derived that satisfy basic assumptions and displacement boundary conditions. The soil domain is discretized, and the mobilized undrained shear strength and strain energy contribution of each differential element are evaluated from the stress-strain relationship. The MSD‐based energy balance equation is then formulated to back‐calculate the nonlinear uplift resistance acting on the tunnel. Results show that the proposed method can degenerate to the linear elastic solution in the small deformation range but exhibits strong nonlinear behavior as deformation increases. At a convergence ratio of 0.3%, the linear elastic model overestimates the uplift resistance by 45.7%. Furthermore, groundwater rise significantly weakens the uplift resistance. When the convergence ratio is 0.5%, the uplift resistance softens by approximately 19.4%, and the softening becomes more pronounced at larger deformations. A distinct interval sensitivity is observed when tunnel depth exceeds 9 m, indicating that the influence of groundwater table is depth dependent. The proposed framework provides a useful tool for evaluating uplift resistance of circular tunnels under groundwater rise.