Elasto-plastic analysis of a circular tunnel including the effect of the axial in situ stress

Analytical solutions are derived for the elastic–plastic stresses and strains around a circular tunnel subjected to an axial in situ stress, in a rock mass governed by the Mohr–Coulomb failure criterion. The calculation results show that the stresses, strains, and failure zones in the surrounding rock depend not only on the transverse in situ stress p   but also on the axial in situ stress pzpz. The pattern of failure zones vary with different combinations of p   and pzpz, which is different from the results produced by earlier plane strain analyses. If pzpz is less than some critical value, the radius of the plastic zones are the same as give by the plane strain analysis, and depends only on p  . If pzpz exceeds the critical value, the radius of the plastic zone increases with increasing pzpz. The analytical solutions are verified by three-dimensional numerical analyses using FLAC3D software.