Analytical method for predicting tunnel heave due to overlying excavation considering spatial effect

Deep excavations have significant influence on existing metro tunnels. Currently, there is still a lack of practical and simple assessment approaches for predicting this influence. In this paper, a new analytical method is developed that uses a continuous Euler-Bernoulli beam to simulate shield tunnel behavior due to overlying basement excavation. Firstly, the excavation-induced greenfield displacement at the tunnel axis is obtained with the application of Mindlin’s solution. Secondly, the longitudinal response of the tunnel due to the ground movement induced by excavation is computed using a finite difference method. The effectiveness and applicability of the proposed method are validated by three high-quality case histories, including field measurement, FEM method, and semi-analytical method. Different from previous studies, the tunnel-soil interaction behavior is studied based on the displacement coupling condition in the proposed method, capable of accurately considering tunnel-soil interaction behavior. Subsequently, with the verified proposed analytical solution, further parametric studies are performed to investigate the spatial factors affecting tunnel behavior including tunnel buried depth, excavation-tunnel relative distance, excavation geometry, skew angle between tunnel axis, short side of the excavation, and excavation depth, yielding abundant artificial data. Then, a semi-empirical formula considering spatial effect is established for directly predicting the maximum vertical displacement of the tunnel with adequate engineering accuracy and applicability. The proposed analytical method can be applied to predict the potential risk of existing tunnel due to nearby excavation.