Soil-tunnel interaction modelling for shield tunnels considering shearing dislocation in longitudinal joints

The existing longitudinal structural model of shield tunnels usually simplify the tunnel as a Euler-Bernoulli beam on elastic foundation, which ignores the shearing dislocation between rings. To model the dislocation between rings, this paper proposed a soil-tunnel interaction model based on the Timoshenko beam simplified model (TBSM) of tunnel on Vlasov foundation. The governing differential equation and the closed-form solution for TBSM on Vlasov foundation subjected to any given pressure are derived with consideration of two types of boundary conditions. The proposed model was adopted to analyze the behaviors of a shield tunnel subjected to external forces transferred from surcharge load on the ground surface. Factors influencing the longitudinal behavior of shield tunnels are discussed. The factors include the equivalent of shear stiffness, location of load application, and the rotational stiffness of the joint between tunnel and station. The results indicated that Euler-Bernoulli beam model underestimates deformation and overestimates the internal forces in the tunnel structure. When the load application is close to the station, with the decrease of the distance between the load and the station will lead to a slightly decrease of the maximum settlement of the tunnel, and an increase of the maximum internal forces and the maximum joint deformation. A stiffer joint between tunnel and station will cause greater internal forces at the location of joint.