Analytical Approach to Evaluating the Influence of the Compressible Layer on the Time-Dependent Response of Deep Soft-Rock Tunnels

The application of the compressible layer in linings provides a feasible and safe solution to addressing the problems of the excessive deformations of surrounding rocks and support failure in the deep soft-rock tunnels. However, there still has not been a well-constructed method to report the mechanical responses of the tunnels supported by such a support system. The objective of this study is to provide an analytical approach to estimating the influence of the compressible layer on the tunnel performance. The mechanical model of the tunnel supported by the compressible layer and concrete lining within the viscoelastic-plastic geomaterial was established. The corresponding analytical solutions for the tunnel displacement and lining pressure are provided, where the influences of the stress path, tunnel face advancement, and installation delay of supports are considered. The effectiveness and reliability of the proposed model are validated by using the numerical calculation, and a good agreement between the analytical and numerical results are obtained. Finally, a comprehensive parametric investigation is carried out, including the influences of the yielding stress, yielding length and elastic modulus of the compressible layer and the lining installation time. The important findings are provided and several useful recommendations are proposed for the design of this supporting system.