Expansion patterns of plastic zone in surrounding rock of rectangular roadway in non-uniform stress field and equivalent circumcirble analytical method

Rectangular roadway is widely used in coal mine as a type of roadway section with easy excavation, simple support and high space utilization. Yet it is difficult to analyze the state of its plastic zone in the surrounding rock because of complex stress distribution. This study conducted numerical simulation to investigate the expansion patterns of plastic zone in surrounding rock of the rectangular roadway with different width-to-height ratio in the non-uniform stress field. The mapping between the plastic zone shape, range and concentration position was compared with the corresponding circumcirble, based on which we proposed a analytical method for the equivalent circumscribed circle of the plastic zone in the surrounding rock of the rectangular roadway. The result show that: ① In the non-uniform stress field, the shape evolution of the plastic zone in the surrounding rock of the rectangular roadyway is consistent with that of the corresponding circumcircle roadway, exhibiting a round, oval and butterfly shape. ② When the width-height ratio ν of a rectangular roadway is less than 2 (which has met the actual needs of the field), the maximum radius of the plastic zone is less than 15 % of the corresponding circumcircle roadway. Smaller ν value leads to lower error between the two, and the error approximates 0 when the ν =1. ③ The butterfly leaf angle in the plastic zone of the rectangle and the corresponding circumcircle roadway exhibits convergence values between 34° and 39°, and the difference between their butterfly leaf angles is between 1° and 3° when ν is less than 2. ④ When the width-height ratio ν of a rectangular roadway is less than 2 in the non-uniform stress field, the shape, range and main concentration position of the plastic zone can be quantified using the equivalent circumscribed circle method.