Incremental analytical solution for failure history of a single ring of segmented tunnel lining

As one important and fundamental research part in exploring the failure history of segmented tunnel lining, the analytical solution in incremental mode for the single segment ring is developed to trace and understand the behavior of the segment ring especially at failure. The relative stiffness method (RSM) and bending-moment search method (BSM) are proposed and utilized to scan and snap the ultimate bending moment capacities and real-time safeties of the segment and segment joint in the whole linear and nonlinear loading histories of a single segment ring. The finite element model based on one full-scale-test is revised by neglecting the interaction between the rings and the reinforcements in the segment in order to provide one benchmark test for the analytical solutions of RSM and BSM. The bending moments in the segment and segment joint of the analytical solutions are compared to FE calculations based on the same validation model, and a very good agreement is found. It is concluded that the proposed incremental analytical methods (RSM and BSM) are applicable.