Study on the energy evolution law of asymmetric failure in roadway under principal stress rotation and its support optimization

Understanding energy evolution under principal stress rotation is crucial for controlling asymmetric roadway instability. A combined approach of theoretical analysis and numerical simulation is adopted. Based on the stress tensor transformation, an analytical solution for the strain energy density under principal stress rotation is derived, which reveals how the strain energy evolves under mining-induced disturbance. Taking the 81,209 working face’s main retreating roadway as a case study, numerical simulations reveal the evolution of strain energy and plastic zones under principal stress rotation. The results demonstrate that: (1) Under principal stress rotation, the strain energy density exhibits a centrally symmetric distribution, with high-energy zones rotating counterclockwise and high-risk failure zones migrating from the roadway ribs to the roof and floor; (2) For the main retreating roadway of the 81,209 working face at varying advancement stages of the working face, both strain energy concentration zones and plastic zones display asymmetric expansion trends, with a direct correspondence between them; (3) A support optimization scheme, developed based on the energy migration law, effectively homogenizes high-energy concentration zones, suppresses asymmetric expansion of the plastic zone, and significantly enhances the bearing capacity of the surrounding rock mass. These findings provide a critical theoretical foundation for controlling asymmetric instability in mining-induced roadways.