Solutions for lined circular tunnels sequentially constructed in rheological rock subjected to non-hydrostatic initial stresses

The time dependency of tunnelling results mainly from the rheological properties of the rock mass, the sequential excavation and the construction process of liner. This study focuses on the construction of lined circular tunnels in viscoelastic rock mass subjected to non-hydrostatic far-field stresses. The analytical solutions of stress and displacement for both rock mass and liner are developed. In the derivation, several linear viscoelastic models are adopted to analyse the rheological properties of the host rock, and the tunnel radius is regarded as time-dependent to simulate the excavation process of tunnel cross-section. Two time-dependent potentials with undetermined coefficients are first introduced to express the displacements and stresses of the rock mass by using the complex potential theory and the Laplace transform technique. According to the boundary and compatibility conditions, a set of equations can be built in the Laplace space for these undetermined coefficients, where no-slip and full-slip rock-liner interface conditions are both considered. The time-dependent displacements and stresses for the rock mass and liner are finally achieved by solving these equations. The proposed solutions are verified by comprising with the results of finite element method. A comprehensive parametrical analysis is then conducted to investigate the influence of the lateral pressure coefficient, the installation time and stiffness of the lilner on the resulting displacements and stresses.