Calculation method of longitudinal deformation of metro shield tunnel overpassing existing line at short distance

In view of the uneven deformation of the operating subway line caused by the short-distance upward crossing construction of the new subway shield tunnel, the shield segments of the existing line are regarded as a series of short elastic beams connected by the tension spring, compression spring, and shear spring on the Pasternak foundation. The rotation effect and shear effect between segments and the interaction between segments and soil are considered, and a method is developed for calculating the additional stress caused by the construction of new shield tunnel based on Mindlin theory, and the longitudinal deformation of the existing tunnel based on the principle of minimum potential energy. The applicability of this method is verified by comparing with the measured data and the existing methods. According to the engineering example, the proposed method is used to analyze the influence of the segment connection, soil mechanical parameters, relative position parameters between the new line and the existing line and the reinforcement effect on the longitudinal deformation of metro shield tunnel. The results show that the friction force f and grouting pressure p heavily affect the deformation of the existing tunnel when a new tunnel is constructed to the upper crossing part, and that the longitudinal deformation is mainly affected by the unloading additional stress F when the new tunnel passes through the existing tunnel. With increasing shear stiffness k(s) and tensile stiffness k(T), the uplift deformation of the existing line decreases, and k(s) has a relatively greater influence. The tunnel deformation can be controlled by enhancing the values of k(s) and k(T), and the ring support reinforcement measures can effectively control the longitudinal deformation of the existing line, and the ring spacing of 1.5 m and 3-5 rings around the intersection point can achieve good results.