Algorithm for an Effective Ratio of the Transverse Bending Rigidity Based on the Segment Joint Bending Stiffness

Abstract

An algorithm for calculating the effective ratio of the transverse bending rigidity is established based on the segment longitudinal joint bending stiffness. With the knowledge of this effective ratio, the bending rigidity of a modified uniform rigidity ring is fully defined. To verify this developed algorithm, the effective ratios and convergence deformations of the modified uniform rigidity rings obtained with different methods are compared. Moreover, the responses of the modified uniform rigidity ring model under loading obtained from this algorithm are compared to those obtained with the existing generally accepted beam-spring model. The results show that although the bending moments obtained from these two models are different, the axial forces, horizontal convergent deformations, and vertical convergent deformations are quite consistent with each other. The modified uniform rigidity ring model built on the developed effective ratio algorithm is applicable for the analysis of the tunnel convergence deformation and the interaction between the tunnel structure and the ground during operation. This modified uniform rigidity ring model is simpler and easier to use than the beam-spring model; thus, the significance of the developed algorithm for the effective ratio of the transverse bending rigidity is demonstrated.