Analytical algorithm for longitudinal deformation profile of a deep tunnel

Abstract

To investigate the longitudinal deformation profile (LDP) of a deep tunnel in non-hydrostatic condition, an analytical model is proposed in our study. In this model, the problem is considered as a superposition of two partial models, and the displacement field of the second partial model is the same as that of the concerned problem. Therefore, the problem can be solved by a model with simple boundary conditions. We obtain the solutions for the stress and displacement fields of an infinite body caused by arbitrary surface tractions on the boundary of the coming tunnel (zone inside the tunnel before excavation) by integrating the extended Kelvin solution over the boundary. The obtained stress solution is used to solve the specific surface tractions, which can satisfy the boundary conditions of the second partial model, on the boundary of the coming tunnel in an infinite body. Then, the specific surface tractions are substituted into the obtained displacement solution to solve the displacement on the wall and face of the tunnel. Therefore, the LDP can also be calculated. The proposed solution is verified by both numerical simulation and the LDP functions recommended by other researchers. The major advantage of our analytical model is that it can consider the effects of the axial and horizontal lateral pressure coefficients. It is revealed that the horizontal lateral pressure coefficient majorly affects the LDP behind the tunnel face, while the axial lateral pressure coefficient dominates the LDP ahead of the tunnel face. Furthermore, the deformation characteristics of the LDPs ahead of the face and the unexcavated core are investigated. The axial displacements of the excavation face can be used to predict the crown displacements ahead of the face.

Keywords

• Deep tunnel
• Elastic solution
• Longitudinal deformation profile (LDP)
• Tunnel face
• Displacement