Analytical solutions for lined circular tunnels in viscoelastic rock considering various interface conditions

The time dependency of ground deformation and stresses in tunneling is mainly due to the rock rheology and tunnel construction process. This study provides an efficient analytical approach to predict the time-dependent displacement and stress fields around deeply buried circular tunnels. The viscoelasticity of host rock, sequential installation of primary and secondary liners, various interface conditions and non-hydrostatic initial stress field are all taken into account in the analysis. The complex variable method, Laplace transformation technique, and extension of correspondence principle are employed in the analytical derivation. Time-dependent potentials expressed as Laurent series are addressed by satisfying all the governing equations in Cases (1)-(4), where all possible conditions at rock-liner and liner-liner interfaces are considered. The time-dependent analytical displacement and stress fields of rock and liners are proposed for the entire tunneling process. As a validation step, the analytical solutions in Case (1) agree well with the results of the FEM numerical simulations. Parametric analyses are then carried out to investigate the influences of installation time of the second liner in Case (1) and (2), and an analytically-based method for design of the second liner is also presented. The proposed solutions in this paper provide a quick and simple alternative method for preliminary tunnel design, any viscoelastic models and any installation time of the first and the second liners can be considered. (C) 2017 Elsevier Inc. All rights reserved.