Abstract：Based on the unified strength theory proposed by Yu Maohong and by considering the behaviors of strength reduction and volume dilatancy for some materials after yielding，that is plastic-softening，the analytical equations for calculating the radius of plastoesidual and plastic-softening zones as well as the displacements around openings are proposed according to the elastic-softening-residual plastic triple linear stress-strain model. At the same time，the equations of stress state for surrounding rocks are also given in the general form. The famous Kastner equation，the Airey equation and the other existing solutions may be taken as special cases of the proposed solution. In the mean time，the influences of shearing dilatancy，softening and different strength models on the results are also analyzed. The results of this paper have an important value in stability analysis of engineering practice and in reinforcement of surrounding rocks.
