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

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