Analytically-based simplified formulas for circular tunnels with two liners in viscoelastic rock under anisotropic initial stresses

The time-dependency in tunneling is mainly due to the theological properties of the rock and tunnel construction processes. Rock rheology results in tunnel convergence and pressures acting on the liners increase with time, both of which are critical parameters to be determined for tunnel and liner designs. In this study, a general analytical solution was derived and the simplified formulas were suggested based on the analytical results, which allow for the predictions of liner pressures and tunnel convergence. The anisotropic initial stresses and rock viscoelasticity, as well as the primary and secondary liners and their installation times were all accounted for. The derivation procedure for generalized viscoelastic rock models was first provided by considering a circular tunnel under the anisotropic initial stress field supported by two elastic liners which were put in place at different times in plane strain conditions. The time-dependent analytical displacement and stress fields were proposed for the entire time stages, and these were consistent with the results from the numerical simulations and the measured data. Then, based on a large amount of data obtained from analytical solutions, the simplified formulas were suggested by data fitting for the final liner pressures and tunnel convergence, when the rock could be simulated with the generalized Kelvin viscoelastic model. A high fitting precision was found to be evident through a comparison between the results from analytical and simplified formulas. The formulas in succinct form are the function of most of the relevant parameters of the rock and liners; for example, the shear moduli and viscosity of the rock, thicknesses and installation times of the second liner. However, they are only available to the three groups of first liner parameters, which are most commonly adopted in engineering. An application example was then provided to illustrate the application of simplified formulas for the determination of the installation times of the second liner. (C) 2018 Elsevier Ltd. All rights reserved.