Abstract: The study of adverse effect of surface surcharge on the longitudinal deformation of existing shield tunnel is of great significance. As a result, an analytical solution for the longitudinal deformation of existing shield tunnel induced by surface surcharge considering the shearing effect of shield tunnel and shearing stiffness of the foundation is presented. This solution assumes that the shield tunnel is a Timoshenko beam resting on Pasternak foundation (defined as T-P Model). The results show that: (1) Compared with other model calculation results, the results of theoretical model proposed in this paper are more consistent with the measured data near the maximum value, which verifies the reliability of T-P model. (2) As for the calculation of the longitudinal deformation of tunnel, the results of T-P model proposed in this paper is larger than that of the Euler Bernoulli beam model, but smaller than that of the T-W model, which shows that the T-P model results are closer to the actual monitoring data; as for the calculation of internal force, the calculation results of Euler Bernoulli beam model are larger, and the maximum bending moment and shearing force of EB-W model are 1.3 times that of T-P model proposed in this paper. (3) With the increase of the horizontal distance from the tunnel axis to the load center, the vertical deformation of tunnel decreases gradually; by increasing the elastic modulus of soil layer and the equivalent bending stiffness of tunnel, the vertical deformation of tunnel can be effectively reduced; when the equivalent shearing stiffness exceeds a certain value, the tunnel deformation tends to be stable.

Key words: shield tunnel, surface surcharge, longitudinal deformation, T-P model, shearing effect, analytical solution