Support provided to rock excavations by a system of two liners

The support provided by a system of two liners to a cylindrical excavation which is subjected to a shear stress at infinity is considered. The tensile, shear and normal stresses and the rotation of a material element at the surface of the excavation before and after the liners are applied are calculated to second order in the thickness parameter ɛɛ using the theory of plane strain in elasticity. Stress is transferred from the rock mass to the liners. To first order in the thickness parameter ɛɛ the changes in the stresses and the rotation do not depend on the order in which the liners are bonded to the surface of the excavation. A small dependence on the order in which the liners are attached was found at second order in ɛɛ. Effective boundary conditions on the shear and normal stress at the surface of the excavation which could replace the liner system were obtained.