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Lining is gaining acceptance in underground excavations because of its reinforcing and protecting capacities. The purpose of this paper was to derive an analytic expression based on the complex variable method to describe the behaviour of a tunnel with a liner of finite thickness. The stress functions have been expressed as Laurent series where the infinite undetermined coefficients are obtained using force and displacement boundary conditions at the inner face, liner–rock interface and far-field boundaries. The finite element method has been used to verify the proposed solution; a good agreement has been obtained both in the surrounding rock mass and within the liner. In addition, based on the verified solution, the liner effect on the critical position of the interface has been investigated by applying Mohr-Coulomb’s failure criterion. A detailed parametric study shows that the relative liner thickness, relative stiffness and lateral stress coefficient have a great influence on the failure position, while the internal friction angle of the rock has a slight effect on the results. The proposed analytical solution is not restricted to the liner thickness, and the stress distribution within the liner is obtained accordingly; the solution can be generalised to other applications such as backfill analysis by setting the liner thickness equal to the radius of the opening.

The critical behaviour of finite thickness lining systems in tunnels