An analytical approach for the sequential excavation of axisymmetric lined tunnels in viscoelastic rock

The main factors for the observed time dependency in tunnel construction are due to the sequence of excavation, the number of liners and their times of installation and the rheological properties of the host rock. A generalized derivation procedure for any viscoelastic model is presented accounting for the sequential excavation of a circular tunnel supported by any number of liners of different thicknesses and stiffnesses installed at different times in a viscoelastic surrounding rock under a hydrostatic stress field under plane strain axisymmetric conditions. Sequential excavation was accounted for assuming the radius of the tunnel growing from an initial value to a final one according to a time-dependent function to be prescribed by the designer. The effect of tunnel advancement was also considered. For the generalized Kelvin viscoelastic model, explicit analytical closed form solutions were presented, which can be reduced to the solutions for the Maxwell and Kelvin models