Closed-Form Solution and Reliability Analysis of Deep Tunnel Supported by a Concrete Liner and a Covered Compressible Layer Within the Viscoelastic Burger Rock

Time-dependent rock behavior can significantly affect the design and the construction method of tunnel support lining. As an innovation, a concrete liner covered with a compressible layer is thus of great interest to reduce the underground space project costs. Indeed, the compressible material usually exhibits very high deformability under oedometric loading (30–60% volumetric deformation under a weak variation in axial stress). This helps to absorb the convergence of the excavated wall of the squeezing rock, and thus limit the transmission of stress to the inner concrete lining. This study firstly aims at deriving a closed-form solution for a deep-circular tunnel excavated within the viscoelastic Burger rock and supported by a double-layer concrete/compressible material. The inner concrete layer is assumed to be linear elastic, while the outer compressible layer is described by a tri-linear elastic model. The analytical solution is derived under the integral equation form. Secondly, the effects of uncertainty of time-dependent mechanical properties of host rock on the failure probability of tunnel for a period of 100 years are studied by introducing the closed-form solution into the well-known Kriging-based reliability analysis AK-MCS (Active learning reliability method combining Kriging and Monte Carlo Simulation) method. Notably, the benefit of the compressible layer is highlighted from the reliability analysis.