Semi–analytical solution for ultimate bearing capacity of straight–jointed segmental tunnel lining

•A semi–analytical force–method solution for a straight–jointed tunnel is proposed.•Nonlinear joint stiffness is considered and expressed as a function of M, N and θ.•An incremental iterative algorithm is established for the strong nonlinear system.•The tunnel ultimate bearing capacity under different load distributions is analyzed. The ultimate bearing capacity of a segmental tunnel lining significantly influences its service performance, particularly when the surrounding soil pressure changes. In this study, a semi–analytical force–method solution for a straight–jointed segmental tunnel lining was derived. The nonlinear joint stiffness was considered and expressed as a function of the bending moment, axial force, and rotational angle of the joint. An incremental iterative algorithm and the corresponding convergence criterion of the proposed model were established for the strong nonlinear system. The proposed model was then verified using the full–scale test results for the loading behavior of the joint and the segmental lining. The structural response of the tunnel under different external load distributions was analyzed using the proposed model, and the main conclusions are as follows. As the lateral pressure coefficient increases, the ultimate bearing capacity of the tunnel lining increases and the length of the first yield platform of the convergence deformation decreases. When P3/P1 increases from 0.71 to 0.83, the ultimate bearing capacity of the tunnel lining increases by 20%, but it has no significant effect on the ultimate convergence deformation. For the lining of the shield tunnel of the Shanghai Metro, the recommended convergent deformation limit is 110 mm.