The analytical predictions on displacement and stress around shallow tunnels subjected to surcharge loadings

Tunnels in urban areas inevitably lie near the ground surface, and will be affected significantly by the loads on the surface. In this study, a new analytical solution is presented for the first time, by means of which the ground responses around circular shallow tunnels subjected to surcharge loadings can be quickly predicted. The ground is approximately assumed as an elastic or viscoelastic medium, and arbitrary distribution of surcharge loads, as well as any viscoelastic models, are accounted for. Case (A) is modelled with surcharge loads applied before the tunnel excavation. The incremental elastic displacements and stresses which occur after the tunnel excavation are provided by Verruijt's method, combined with a Fourier expansion of the tractions. Case (B) represents the model in which the surcharge loads are applied after the tunnel excavation, and the elastic ground responses due to the presence of surcharge load are proposed by the superposition of modified Flamant's solutions and the solution of Case (A). The solutions for the viscoelastic problem of the two cases are also proposed by an extended corresponding principle, taking into account the time-dependence of the rock/soil with any types of the linear viscoelastic model. All of these analytical solutions are verified by good agreements of the comparison between the analytical solutions and FEM results. Furthermore, they are consistent with measured data qualitatively. Finally, a parametric study is carried out to investigate the influence of the uniform surcharge load on the stresses and displacements of the ground in the two cases. The proposed new solutions potentially provide an alternative approach in the preliminary designs of future shallow tunnels.