Distribution law and control of the second invariant of deviatoric stress in gob-side entry retaining

Taking the gob-side entry retaining (GER) in the 28,051 panel of Xinzhuang Coal Mine as the engineering background, this study introduces the second invariant of deviatoric stress (J₂) as a quantitative indicator of surrounding rock failure. By constructing mechanical model, performing FLAC^3D numerical simulation, and conducting industrial experiment, the full-cycle failure evolution law of the surrounding rock and its control technology are systematically investigated. A mechanical model of the roadside filling body is established, from which the reasonable filling width beside the roadway is calculated to be 1.0 m. Simulation results indicate that during the early stage of GER, the J₂ of the surrounding rock exhibits a ring-shaped non-uniform distribution with peak values at a depth of 2.5 m in both the roof and the solid coal rib. In the middle stage, under strong mining disturbance, the J₂ peak shifts deeper to 4.5 m in the roof and 3.5 m in the coal rib. In the late stage, as the delayed working face distance increases, the peak value of J₂ show an increasing trend with gradually diminishing increments, stabilizing eventually. However, the peak value of J₂ at the solid coal side rib corner continues to rise. The J₂ distribution of filling body is approximately linear, with stress values increasing from the gob side to the roadway side, and the degree of stress concentration decreases with increasing delayed distance. Based on these findings, a support concept is proposed that requires anchor cables to penetrate through the J₂ peak zones of the solid coal rib and roof. This is integrated with high-density rock bolts and flexible cement slurry walls to form a comprehensive control technology for GER. Industrial practice demonstrates that the maximum roadway deformation is controlled within 294 mm, and the filling body deformation stabilizes around 90 mm, validating the effectiveness of the support design and achieving full-cycle stability control of the surrounding rock in GER.