A variational approach to the analysis of excavation-induced vertical deformation in a segmental tunnel

Abstract

This paper aims to provide an analytical solution for evaluating the deformation of a segmental tunnel induced by upper basement excavation. To this end, a model considering shear dislocation and rotation of a segmental tunnel is proposed and the interaction between tunnel and ground is modeled using a two-parameter Pasternak foundation model. The vertical displacement of the tunnel is then approximated by the finite Fourier series. Energy balance equations for the tunnel and soil are obtained via energy method and then the governing equation is derived based on the principle of minimum potential energy. With the variational approach, expressions for the tunnel heave, relative vertical deformation, rotational angle and shear force between two tunnel rings are derived. The feasibility of the proposed model is validated against the field data and the results obtained using Euler-Bernoulli beam and Winkler beam, indicating that the proposed method can be used to effectively estimate the responses of a segmental tunnel to upper excavation. Finally, a parametric analysis is performed to examine the effects of different factors on the responses of existing shield tunnel to upper deep excavation.