Abstract:Subway tunnels built in longitudinal inhomogeneous formations will inevitably cause the differential settlement of the underlying soil because of the cyclic loading of trains. Differential soil settlement, in turn, adversely affects the safety of existing tunnels. An analytical solution for the effect of differential foundation settlement on the vertical deformation of existing tunnels and that considers the tunnel shear effect was proposed. The existing tunnel was assumed as a Timoshenko beam resting on a Winkler foundation. The two-stage approach was used to analyze the tunnel response caused by differential soil settlement. First, the dynamic deviator stress caused by the cyclic loading of trains was determined, and static deviator stress and failure deviator stress were calculated by using soil mechanical indexes. Second, the cumulative settlement of the soil underlying the tunnel was calculated by using the empirical equation of cumulative plastic strain and then transformed into the force imposed on the underlying shield tunnel. Finally, the differential equations for tunnel vertical deformation accounting for the shear effect of tunnel were established on the basis of Timoshenko beam theory. Then, the analytical solution was obtained through calculation, and the tunnel internal forces, including tunnel bending moment, shear force, rotation angle, and dislocation between adjacent rings, were further obtained in accordance with the proposed analytical method.