Analytical Solution of the Mechanical Response of a Shield Tunnel Crossing an Active Ground Fissure Zone

Abstract

Uneven settlement of the strata induced by ground fissure activity trigger great damage to a shield tunnel crossing a ground fissure zone. It is of great significance for the safe maintenance of tunnels to accurately predict the mechanical response of the tunnel structure under the dislocation of a ground fissure. In this paper, an analytical solution of mechanical behaviors of a shield tunnel crossing an active ground fissure zone is proposed. The shield tunnel-strata interaction in a ground fissure site is simplified as a Timoshenko beam placed on a Vlasov foundation. The governing differential equation and the closed-form solution for an equivalent shield tunnel subjected to additional load induced by the dislocation of ground fissure are derived. The proposed solution is adopted to analyze the mechanical behaviors of a shield tunnel, including tunnel displacement, rotation, bending moment, and shear force. The results of a model test and a numerical model are provided to verify the rationality of the proposed analytical solutions. Finally, a parameter sensitivity analysis about the additional load forms, the compression and shear modulus of the foundation, and the shear stiffness coefficients of the tunnel are conducted. The result shows that the form and value of the additional load has a large impact on the deformation and a slight impact on the internal forces of the tunnel. The foundation compression modulus determines the constraint effect of the strata, and the deformation and internal force response of a tunnel decrease with the increasing foundation shear modulus. In addition, the increase of shear coefficient enhances the shear stiffness of a tunnel, but largely increases the internal force as well.