Theoretical solutions of a circular tunnel with the influence of axial in situ stress in elastic–brittle–plastic rock

Theoretical solutions are presented for the prediction of stresses and displacements around a circular tunnel in Mohr–Coulomb (M–C) rock mass, which is subject to a hydrostatic stress field in the cross section of the tunnel and out-of-plane stress in the axis of it. Elastic–brittle–plastic constitutive model with a non-associated flow rule is used in the analysis. After the axial in situ stress is taken into account, the out-of-plane stress is not always the intermediate one in principle stress space. Therefore, solutions are different from those in the normal plane strain problem where the out-of-plane stress is supposed to be the intermediate principle stress. Moreover, different patterns of plastic zones are formed with the various combinations of hydrostatic stress in the cross section and out-of-plane stress in the axis of the tunnel. Numerical examples illustrate that the distribution of stresses and displacements in the surrounding rock mass of the tunnel is significantly influenced by the axial stress in the case where there is a large drop in strength at yield or a big difference between the uniform in-plan stress and the out-of-plane stress.

► Theoretical solutions are obtained for circular tunnel with axial stress included.
► Different types of plastic zone are formed when the axial in situ stress varies.
► Stress and displacement are affected by the axial stress.
► Deformation increases for the same dilatancy angle if in situ stress is considered.
► The results are influenced by different constitutive models.