Analytical Solution for Segmental-Tunnel Lining Incorporating Interaction between Adjacent Rings

The different joint arrangements resulting from different segmental assemblies between adjacent rings may inevitably give rise to the interaction for staggered jointed lining, which is crucial for the structural analysis of segmental-tunnel lining. However, most existing analytical solutions only consider the straight jointed lining and are not applicable to the staggered jointed lining. By using the state-space method, a unified analytical solution is obtained for the circular segmental-tunnel lining irrespective of the layout of segmental assemblies between adjacent rings, and the interaction effect between adjacent rings is explicitly addressed. The segments were treated as curved Euler beams, while the longitudinal joints between the segments were modeled by a set of springs with three-directional resistances, and the circumferential joints between the adjacent rings were modeled by shear springs with both radial and circumferential resistances. A rigorous theoretical proof is implicitly embedded to eliminate the rigid-body displacements of the proposed method as a self-balancing condition of external loads acting on the lining. Finally, the solutions are verified through comparisons with both the experimental and analytical results in the literature. The results show that the present method exhibits high efficiency and suitability for both linings with straight joints and those with staggered joints.