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

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.