Evaluation of Longitudinal Equivalent Bending Stiffness of Shield Tunnel with Residual Jacking Force

Abstract

Existing tunnels are often subject to longitudinal bending when undercrossing tunnelling. It is of significance to more accurately evaluate the longitudinal equivalent bending stiffness (LEBS) of the existing tunnel within the influential zone. A new analytical method is proposed for the LEBS of tunnel segmental lining joints with consideration of incorporating combined action of residual jacking force and bending moment. The solution can degenerate into a special case with no residual jacking force, which agrees well with other classical solutions and validates the model and solutions. Sensitivity analyses are carried out for the bending moment, tunnel geometry, tensile stiffness of bolts and concrete grade on the LEBS, and effective ratio of the LEBS considering residual jacking force. The LEBS and the effective ratio of LEBS increase nonlinearly as an S-curve with the residual jacking force and decrease with an increasing bending moment. The results show that the LEBS of the shield tunnel is variable stiffness, which exhibits a significant nonlinearity. The maximum increment of the LEBS reaches 80.3% as the ring width increases from 1 m to 2 m, and the LEBS of the shield tunnel increases by approximately 1.3 × 107 kN·m2 for every 4-bolt added. The influential order on the LEBS of shield tunnels is the tunnel diameter > lining thickness > bolts diameter > ring width > the number of bolts > elastic modulus of bolts. When the effective ratio of LEBS is more than 0.85, it does not change with the ring width, lining thickness, tensile stiffness of bolts, and concrete grade. The response characteristics of the tunnel parameters on the LEBS, considering the residual jacking force, could provide a theoretical basis for the design and deformation control of shield tunnels when undercrossing tunnelling.