<p>Based on the elastic–plastic theory, the analytical formula of the second invariant <i>J</i>₂ of deviatoric stress at any point around the circular roadway under the non-uniform stress field is derived. The distribution law of <i>J</i>₂ of surrounding rock under the three-dimensional non-isobaric stress field is studied by theoretical analysis and numerical simulation. Combined with the butterfly failure theory of surrounding rock of roadway, the close relationship between the distribution pattern of <i>J</i>₂ and the distribution pattern of plastic zone is found, and the failure mechanism of surrounding rock is revealed. The results show that the distribution form of the second invariant <i>J</i>₂ of deviatoric stress is closely related to the distribution form of plastic zone. When the distribution of <i>J</i>₂ of surrounding rock shows ‘round’, ‘oval’ and ‘butterfly’, the plastic zone shows the corresponding consistent form. When the second invariant <i>J</i>₂ of deviatoric stress produces stress concentration, the surrounding rock of roadway will produce large-scale damage. When the stress concentration is high, it may lead to malignant expansion of surrounding rock of roadway. The distribution of the second invariant <i>J</i>₂ of deviatoric stress is directional. When the principal stress rotates over a certain angle, the second invariant <i>J</i>₂ of deviatoric stress rotates over the same angle as the plastic zone. Under the influence of superimposed mining, the second invariant deviatoric stress <i>J</i>₂ of the wind tunnel of Yangchangwan 160,206 working face presents butterfly distribution, and the stress butterfly leaves present a certain degree of rotation. Based on the failure mode of plastic zone, the corresponding optimization support scheme is proposed, and the engineering effect is good.</p>