摘要

Stress fields of a lined non-circular tunnel subjected to in situ stress are derived based on the complex variable method and on the assumption that the interface between the liner and surrounding rock is full-slip. The basic equations for solving the stress solutions are obtained according to the stress boundary condition along the inner boundary of the lining and the stress and normal displacement continuity conditions along the rock-lining interface. In the solving process, the support delay is also considered. The basic equations can be solved by the power series method, and the stresses in the surrounding rock mass and lining can be calculated. The distributions of the tangential stresses (also known as the circumferential stresses) along the excavation boundary and the inner boundary of the lining and the contact stresses along the rock-lining interface are analysed. An example demonstrates that the results are significantly affected by the number of terms in the power series. When the number of terms is greater than 100, the boundary conditions can be well satisfied, and the results of the stresses and displacements are highly accurate. The tangential stress results along the inner boundary of the lining for the full-slip condition are compared with those for the perfect bond condition, and the analysis indicates that the maximum value of the tangential stress for the full-slip condition is smaller than that for the perfect bond condition, which gives that the full-slip condition is superior to the perfect bond condition. Thus, the carrying capacity of the lining can be increased if sliding materials are installed between the lining and the surrounding rock mass. The analytic solutions are verified using computer simulation software.