Abstract: Surface subsidence will be induced by rock-soil mass being disturbed in the process of excavation and long-term operation of tunnels. At present, there is no mature analytical model based on the theory of mechanics. In this research, the surface subsidence above tunnel is approximated to boundary deformation in the elastic semi-infinite space containing a horizontally cylindrical cavern with shrinkage force. By solving the symmetrically plan-strain problem in elastic infinite space, the elastic analytical solution of the surface subsidence in integral form is derived with the principle of superposition. Subsequently, the viscoelastic analytical solution in integral form in space-time domain is obtained by Laplace transformation of elastic analytical solution with volume deformation regarded as elasticity and distortion as Maxwell viscoelasticity. The proposed model reveals that the width coefficient of settlement troughs above tunnels is 0.6, in good agreement with the monitoring data in many other regions. The method in this article offers a theoretical approach for surface subsidence prediction in the process of excavation and long-term operation of tunnels.

Key words: tunnel, surface subsidence, mechanical analytical solution, viscoelastic model, dimensionless