Pseudo-static analysis method for shield tunnels based on theory of thin-walled cylindrical shell

To simplify the aseismic analysis of deeply-buried shield tunnels, a formula is proposed for solving the additional internal force in the tunnel linings of a deeply-buried shield tunnel under horizontal seismic shear waves based on the acquisition of the shear strain and shear stress of free-field around it and the utilization of the theory of elastic thin-walled cylindrical shell. Then, a model of numerical analysis of equivalent stiffness under the same condition is established for comparison. The research shows that the pseudo-static and numerical results have a good consistency under full slip and no slip conditions. The proposed pseudo-static formula for shield tunnels based on the theory of elastic thin-walled cylindrical shell is reasonable. Meanwhile, under the horizontal seismic shear waves, the additional bending moment and shear under full slip are larger than those under no slip, and the additional axial force under no slip is larger than that under full slip. The additional bending moment and axial force exhibit features of antisymmetric distribution, and their maximum values distribute on radar axis of 45°and 225°or 135°and 315°, and the maximum values of shear distribute on radar axis of 0°and 180°. The research results have certain reference value for the seismic design of shield tunnel engineering.