Simple method for supporting pressure determination of double-liner circular tunnels excavated in rheological rock

The time-dependency in tunneling is mainly due to the tunnel construction processes and rheological properties of the rock. By using the complex potential theory and Laplace transform technique, analytical solutions are derived for the double-liner circular tunnels constructed in rheological rock subjected to non-hydrostatic initial stresses. In the derivation, several linear viscoelastic models are adopted to analyze the rheological properties of the host rock, and the first and secondary liners are sequentially installed at any time after the excavation. The solutions are validated by finite element analyses. Based on the analytical solutions, a simple method for determination of supporting pressure provided by the two liners is proposed by using the data fitting method. The result shows that the fitting precision is very high. The formulas for supporting pressure herein are very simple, and very convenient for using in the engineering. This method gives an optional way in the design of the secondary linings. Using this method, the suggested installation time and thickness of the secondary linings corresponding to different values of supporting pressure are provided for a specified example. The solutions in this paper provide a much convenient way for the preliminary design of tunnel construction.