Longitudinal deflection of existing shield tunnels due to deep excavation

In the area of infrastructure construction,increasing attention has been paid to the deflection of existing shield tunnels due to deep excavation unloading. The simple two-stage method is adopted to study this problem. The existing shield tunnel is simplified as an infinite beam on a Kerr-type three-parameter elastic foundation. Its governing differential equations are formulated and analytically solved. The parameters of the Kerr model from the simplified elastic continuum method are adjusted by comparing the results with those of finite element models, and comparisons are carried out among Winkler, Pasternak and Kerr models. To obtain more reasonable results, the effects of the lateral soil beside the tunnel are considered and the governing equations are modified and solved accordingly. A good agreement is achieved between the analytical results and finite element ones after considering the lateral effects. The study indicates the superiority of the Kerr foundation model. The effects from the lateral soil are remarkable and should be considered in the analysis.