Stress Analysis of Thick‐Walled Reinforced Tunnel

Abstract

Analytic solutions are presented for the interaction of a thick‐walled circular cylindrical structure (tunnel) buried deeply underground. The medium is assumed to be homogeneous, isotropic, and linearly elastic so that Michell's formulation of the Airy stress function can be applied. The general expressions for the stresses and displacements in the cylindrically orthotropic structure are formulated using both the elasticity and shell‐theory approaches. Solutions are then obtained by considering the boundary conditions at the structure inner surface and at the tunnel‐medium interface. The shell theory employed is an improved shear‐deformable version of the well‐accepted Sanders shell theory. A technique is also developed to predict the transverse stresses in the structure. The results show a close agreement with those obtained by the theory of elasticity for a shell with an outer radius‐to‐thickness ratio of 5.