Abstract: Based on the studies of conventional longitudinal equivalent rigidity ratio, the tunnel’s displacement and deformation are calculated using a variable rigidity beam elasticity calculation method. A simplified expression of the tunnel’s longitudinal equivalent rigidity ratio is obtained. The analysis shows that the longitudinal equivalent rigidity ratio is linearly proportional to the number of bolts. At the same time, the longitudinal equivalent rigidity ratio nearly parabolically increases with the increasing of the bolt radius. However, with the increase of segment ring thickness and the segment modulus of elasticity, the longitudinal equivalent rigidity ratio is reducing. Because of the stress concentration caused by the tunnel’s rigidity change, the tunnel longitudinal equivalent bending rigidity and effectiveness of the rigidity reduce with the increasing of depth. The proposed model is more widely applicable and is of reference value for longitudinal stability design of shield tunnels.

Key words: equivalent bending rigidity, rigidity mutation, rigidity ratio, stress concentration