Stress and displacement fields around an arbitrary shape tunnel surrounded by a multilayered elastic medium subjected to harmonic waves under plane strain conditions

Abstract

This study focuses on the propagation of harmonic mechanical waves around both circular and non-circular tunnels. The excavation disturbed zone is explicitly modeled with a multilayered description of the surroundings of the tunnel. The purpose of this paper is thus to establish closed-form solutions for stress and displacement fields for circular and non-circular geometries taking into account the mechanical heterogeneity of the area adjacent to the tunnel. Particularly, the multilayered non-circular shape configuration is a great step not treated previously. The classical approach based on the wave function expansion method is used to determine the expressions of stresses and displacements around circular geometries. To handle non-circular tunnel shapes, the complex variable method based on the Muskhelishvili approach and conformal mapping functions is introduced. Results indicate that the excavation damaged zone strongly modifies the distribution of stress and displacement fields around the tunnel. Geometrical tunnel shapes also affect stress and displacement polar diagrams.