Analysis and Application of Plastic Zone in Roadway Surrounding Rock Considering the Intermediate Principal Stress

Understanding the formation and evolution of plastic zones is fundamental to controlling the deformation and instability of surrounding rock in deep roadways. However, existing plastic zone theories primarily focus on analytical solutions for circular roadway radii under uniform stress fields. To address this limitation, based on the Drucker-Prager strength criterion and butterfly-shaped failure theory, a single-factor analysis method is adopted to investigate the variation trends and sensitivity of the plastic zone in the surrounding rock of the 1201 return airway in a deep mine. Furthermore, numerical simulations based on FLAC3D are conducted to determine the plastic zone expansion morphology, range, and failure characteristics of different roadway cross-sections. The results show that: Under a non-uniform stress field with a lateral pressure coefficient λ = 2.5, the maximum plastic zone depths at the roof, shoulder corners, and floor of a rectangular roadway are 5.3 m, 6.4 m, and 5.0 m, respectively, which are on average 27.5% larger than those of a circular roadway (4.2 m, 5.1 m, 4.0 m). The plastic zone depth in a straight-wall three-centered arch-shaped roadway (4.8 m, 5.7 m, 4.5 m) is 15.2% greater than that of the circular section, demonstrating the significant influence of cross-sectional shape on plastic zone distribution. Field measurements are also employed to validate the numerical results. The study reveals that when the intermediate principal stress coefficient m = 0.7, the plastic zone radius reaches its minimum value. However, for m>0.7, stress redistribution leads to a radius rebound, exhibiting an interval effect. Additionally, increasing the surrounding rock strength parameters can reduce the plastic zone radius by approximately 35% to 48%. Field observations confirm that the measured plastic zone depths at the shoulder corners (5.5 m~5.6 m) have an error margin of less than 10% compared to numerical simulations, and the fracture distribution is highly consistent with the butterfly-shaped failure theory. These findings provide valuable insights for analyzing plastic zones in deep roadways and optimizing excavation cross-section designs.