A full-plane strain complex variable analytical model considering three-dimensional principal stress rotation and its engineering applications

Abstract To explore the influence of stress space rotation on roadway stability, this study establishes Cartesian and principal stress axes, obtains principal stress characteristic parameters and direction cosine matrix, and determines the conversion process between coordinate axes. By breaking through the traditional plane strain mechanics model, a full plane strain model of rectangular roadway considering the deflection effect of principal stress axis is established. The analytical solution of stress complex variation of any element around the roadway is derived, and the calculation method of plastic zone is given. The influence of stress deflection on the stress of roadway and the shape distribution of plastic zone is discussed and the control system of roadway under the action of principal stress deflection in spatial region is established. The research results show that: (1) the shear stress and normal stress formed in the remote of the roadway during the stress rotation are in the same order of magnitude, and the plastic quantitative calculation of the roadway cannot simply consider the normal stress. (2) Stress deflection causes the distribution of stress and plastic zone around the roadway to show ‘asymmetric’ failure characteristics, and the transient deflection of stress may cause the rapid expansion of the plastic zone of the roadway. (3) The distribution characteristics of plastic zone calculated by this study are compared with the deformation and failure feature and peep results of the return air roadway in Cuncaota Mine, and the comparison results are good. The supporting system and technology of roadway under the action of principal stress deflection in space area are put forward, and the field application effect is good.