Distribution characteristics and expansion law of butterfly plastic zone of circular hole in polar coordinates

As for surrounding rock of roadway or chamber of big buried depth,near mining engineering or tectonic zone will appear butterfly plastic zone,the paper uses theoretical calculation and computer programming based on formation and development of plastic zone of circular hole surrounding rock in polar coordinates.It expounds formation mechanical mechanism of plastic zone of circular hole surrounding rock,analyzes different geometry and scope of plastic zone of circular hole surrounding rock,mainly studies formation,development and spatial evolution law of boundary expansion of butterfly plastic zone,and discusses key factors influencing distribution of butterfly plastic zone and influence extent and engineering harm of variation characteristics between the various factors on butterfly plastic zone.The research shows that after hole surrounding rock formed butterfly plastic zone,when the parameters of buried depth,hole radius,angle of internal friction and cohesion of is unchanged,the boundary of butterfly plastic zone increases from 1.43 m to 3.22 m with lateral pressure coefficient decreases from 0.4 to 0.3.With lateral pressure coefficient continue decreasing from 0.3 to 0.2,butterfly plastic zone boundary is diagonally multiplied from 3.22 to 12.27 m,butterfly leaf disappears after expansion to infinity.According to the degree,influencing factors of butterfly leaf expansion is divided into lateral pressure coefficient,buried depth,hole radius,angle of internal friction and cohesion.It provides theoretical basis for stability analysis and control of deep engineering such as mining,water conservancy and hydropower,tunnel,and oil and gas exploration.