矩形巷道在煤矿井下应用广泛，但其周围应力分布复杂, 其围岩塑性区状态难以进行理论解析。通过数值模拟方法探究不同宽高比矩形巷道在非均匀应力场中围岩塑性区的扩展规律，从塑性区形态、范围、集中位置三个维度与对应外接圆进行映射对照，提出矩形巷道围岩塑性区的等效外接圆理论解析方法。研究表明：①非均匀应力场中矩形与对应外接圆巷道围岩塑性区形态演化规律一致，均呈现圆形、椭圆形、蝶形3种形态；②矩形巷道宽高比ν<2时(已满足现场实际需要)，塑性区最大半径不超过对应外接圆的15 %，ν值越接近1等效外接圆理论解析方法的误差越小，当ν=1时误差趋近于0；③出现蝶形塑性区后矩形与对应外接圆巷道塑性区蝶叶角收敛值均集中在34°~39°，当ν<2时，两者蝶叶角差值在1°~3°；④非均匀应力场中ν<2时塑性区形态、范围、主要集中位置可通过等效外接圆方法进行理论解析。

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.