Underground Space (Oct 2023)
Analytical and numerical analysis on the torsional performance of elliptically deformed tunnels in the longitudinal direction
Abstract
Segmental lining structures constructed by shields/tunnel boring machines are often subjected to uneven longitudinal cross-section torsion as a result of eccentric external loads, which is extremely adverse to tunnel safety but has not received sufficient attention for a long time. To figure out the torsional performance of segmental tunnels, it is essential to assess the longitudinal torsional stiffness and active-torsion-rejection capability of a segmented tunnel. The aim of the paper is to derive an analytical solution to the longitudinal torsional stiffness of a segmental tunnel with existing elliptical deformation. The longitudinal torsional stiffness under different internal force combinations is deduced considering the longitudinal axial force and bending moment based on the equivalent continuous model and force balance equation. The validity of the analytical solution is verified by comparing it with finite element method results. Then, a parametric analysis, using the new analytical solution, is included to investigate the effect of the key parameters on torsional behaviors, including the segment size, the bolt size and the transverse bending stiffness, etc. It is found that: (1) the longitudinal torsional stiffness efficiency (LTSE) of the segmental tunnel decreases with the rise of segment thickness to diameter ratio but increases with the ring width to diameter ratio; (2) the LTSE reduces with the increase of the effective shear length but rises with the diameter of bolts; (3) the LTSE increases rapidly with the ratio of compression-torsion or bending-torsion. Furthermore, the envelope curve of the critical load (N0, M0) for a tunnel to actively resist a certain internal torque is given. The proposed solution can be easily utilized to determine the longitudinal torsional stiffness of segmental tunnels and is an effective tool for tunnel design and maintenance.
