A Theoretical Solution of Deformation and Stress Calculation of the Underlying Tunnel Caused by Foundation Pit Excavation

In the methods for mitigating the effect of foundation pit excavation on underlying tunnel, the conventional analytical calculation method adopted the elastic foundation beam to derive the tunnel deformation and internal forces. However, this traditional approach assumes that the released stress is loaded on the excavation face and subsequently affects the tunnel stress, which can be obtained by Mindlin’s solution. The limitations of this method are analyzed, and the soil deformation caused by excavation is introduced as an external load in the model. A differential equation of the elastic foundation beam is established and used to derive the analytic solution of the deformation and internal force of the tunnel by analysis of the empirical formula of soil deformation under foundation pit. Additionally, the weighted residual solution is introduced due to the difficulty in calculation of analytic solution. Considering that the project in this study is a three-dimensional problem?the torque is derived for a complete elastic foundation beam solution.