Experimental Study on the Longitudinal Equivalent Shearing Stiffness of Shield Tunnel by Considering Axial Force

Due to the presence of a large number of joints between the segments of shield tunnel, the overall stiffness of the structure was significantly reduced. Consequently, the tunnel lining becomes highly susceptible to surrounding stratum. In addition to bending deformation, shear deformation could not be ignored either. Therefore, aiming at a 6.2 m diameter shield tunnel as the prototype, the model segments fabricated by 3D printing were stagger-assembled by curved bolts to form the shield tunnel lining model with 3 rings. The experimental apparatus was developed to test the inter-ring joints with increasing shear force under different axial forces. Based on the physical significance of longitudinal equivalent shearing stiffness, the full nonlinear characteristics of longitudinal equivalent shear stiffness with shear force were established. The influencing mechanism and law of axial force on the longitudinal equivalent shear stiffness were also investigated. The test results show that the longitudinal equivalent shearing stiffness varied nonlinearly with the shear force, which could be divided into the static friction stage, the elastic shear stage and the plastic shear stage. In the static friction stage, the shear force was mainly carried by the static friction, and the inter-ring dislocation was minimal. The inter-ring joints could be regarded as a homogeneous cylinder, exhibiting a horizontal line with increasing shear force. In the elastic shear stage, the shear force was carried by the static friction and bolts jointly; the longitudinal equivalent shearing stiffness decreased rapidly with the shear force. In the plastic shear stage, the longitudinal equivalent shearing stiffness decreased slowly with shear force and converged to its steady value. The axial force significantly suppressed deformation development by increasing inter-ring friction, thereby considerably enhancing the longitudinal equivalent shear stiffness of the shield tunnel. Furthermore, the three-dimensional surface relationship between the longitudinal equivalent shear stiffness, axial force, and shear force was fitted using a logistic function.