Shallow tunnels misaligned with geostatic principal stress directions: Analytical solution and 3D face effects

摘要

Rock masses often present strong stress anisotropy, especially at shallow depths; thus, the alignment of a tunnel with one of the principal stress directions is unlikely. As a result, far-field out-of-plane shear stresses are present and, yet, their effects are often neglected in tunnel design because it is commonly assumed that the tunnel is aligned with one of the principal stress directions. The paper presents an analytical solution to determine the axial displacements and the axial shear stresses around shallow tunnels not aligned with the principal stresses in elastic ground, when subjected to a far-field shear stress. The analytical solution is developed using complex variable analysis and conformal mapping techniques to consider the presence of the ground surface. The analytical solution can be added to the Verruijt and Booker (2000) solution to determine the full 3D stress and displacement fields far-behind the face of unsupported shallow tunnels subjected to a general state of stress. In addition, 3D FEM models are conducted to investigate the effects of the far-field shear stress near the face of the tunnel. The far-field shear stress induces asymmetric ground deformations near the face, which remain far behind the face when the tunnel is supported, and when the ground is elastoplastic.