Full stress and displacement fields for steel-lined deep pressure tunnels in transversely anisotropic rock

• Solution for deep pressure tunnels with steel lining in transversely anisotropic rock.
• Full displacement and stress fields are derived for the steel liner, concrete, and rock.
• Solution shows uniform pressure on steel lining due to its high flexibility.
• Simplified solutions are presented for flexible support.

An analytical solution is derived that provides closed-form formulations for stresses and displacements for a deep pressure tunnel in a transversely anisotropic rock, with a steel liner, and subjected to a uniform internal pressure. For the derivation, it is assumed that the tunnel support includes a thin steel liner, concrete backfill and that there is an annulus of damaged rock around the concrete. It is also assumed that all materials remain elastic and that the concrete and the damaged rock cannot transmit shear or tangential stresses. The solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. For thin steel liners, it can be assumed that the contact pressure between the different materials is uniform, and thus the bending moments in the liner are negligible. This is due to the low bending stiffness of the steel liner. The paper is inspired by and expands the work by Pachoud and Schleiss (2015) who conducted an extensive numerical parametric analysis to obtain correction factors that, when used with an analytical solution for isotropic materials, approximate the maximum principal stress in the liner and intact rock.