The important role of stiffnesses values of circular joints on the stress state developed in the tunnel segmental lining

Under the application of the fluctuating Tunnel Boring Machine (TBM) jack thrust and the non-uniformly distributed total pressure of the slurry around the lining, the bending and the shear deformation occur on the segmental lining along the longitudinal direction, which cause a stress concentration and increase the damage risk of the segmental tunnel lining. The analysis of the circular joint stiffness is a critical step during the evaluation of the stress state of the segmental lining so as to decrease the associated risk of damage. In order to investigate the lining rings and the circular joint separately, an integrated numerical model which is composed of segment elements and joint elements was developed. Furthermore, stiffness equations for describing in the detail the circular joint behaviour of the tunnel segmental lining are derived. The new stiffness equation of the circular joint is also used to analyse the segment lining behaviour based on a well-known indoor test result by the scientific literature, and satisfactory results were obtained. A simplified estimation of the bending stiffness of the circular joint based on the Boltzmann equation is then suggested in order to obtain quickly its calculation. Finally, based on a specific numerical model, the calculated joint stiffnesses are adopted to analyse the vertical displacement of a real case (The Ningbo metro tunnel in China). Through a developed sensitivity analysis, some useful suggestions are proposed to reduce the damage risk of the segmental lining.