Analytical elastoplastic solutions to supporting rock masses of circular tunnels under asymmetric load

Considering the behaviors of strength reduction and volume dilatancy of rock materials, the approximate analytical solutions to calculating the extent of the plastic zone, stress field and displacement field in rock masses of circular tunnels are proposed. The elastic-softening-residual plastic triple linear stress-strain model and the Mohr-Coulumb failure criterion are involved. The analytical solutions are valid when the plastic zone is comparatively large and the lateral pressure coefficients 1≤λ<3. These solutions are very close to the results calculated by the finite element method, which can be used for the simple elastoplastic analysis of the circular openings instead of the finite element method.