Elastoplastic solution for surrounding rock of circular roadway based on D-P criterion by considering post-peak strain softening and dilatancy

In this paper, the circular roadway surrounding rock was divided into plastic residual zone, plastic softening zone and elastic zone, and the softening modulus of strength parameters, coefficients of dilatancy and shear dilatancy angle were introduced by considering the rock post-peak strain softening and dilatancy. Meanwhile, based on Drucker-Prager criterion and its generalized non-associated flow rule, the relationship between dilatancy angle and softening zone coefficient of dilatancy was established. By using Lode parameter to describe intermediate principal stress, the analytical solutions of elastoplastic stress, displacement and plastic zone radius were obtained. In addition, an example was analyzed to study the effect of different factors on plastic zone radius and displacement of surrounding rock. The results show that the intermediate principal stress has significant effect on plastic zone radius and displacement, and presents the interval characteristic. The larger the residual value cohesive force and internal friction angle are, the smaller the plastic zone radius and displacement are. Meanwhile, the selection of dilatancy angle has great influence for analysising dilatancy, and softening modulus decreasing and supporting resistance increasing can control the surrounding rock deformation in different drgree, while softening mainly has effect on plastic residual zone radius and dilatancy mainly has affect on displacement of surrounding rock.The study in this paper can provide theoretical basis for surrounding rock stability evaluation and supporting quantitative design.