Mechanical mechanism of roof instability in gob-side entry retaining and side reinforcement principles for roof control

<title>Abstract</title> <p>To reveal the mechanical mechanism of roof instability under roadside backfilling in gob-side entry retaining, the evolution law of roof abutment pressure was analyzed, and an model of the immediate roof as an elastic foundation beam was established under conditions of different support stiffness on the two ribs. The distribution characteristics of roof deflection and internal force, as well as the loading mode of the main roof, were systematically clarified, and the catastrophic failure modes of the roof were summarized from the perspective of material mechanics. Based on the imbalance in support stiffness between the two ribs, the theory of “strong rib for roof control” was proposed. It was pointed out that by increasing the support stiffness of the solid coal rib and the backfilling wall, the internal force distribution of the roof can be actively regulated, thereby effectively restraining roof instability. The results show that the evolution of roof internal force is mainly governed by the “preset deformation” of the main roof, and the distributions of deflection and internal force exhibit obvious asymmetry. The position of the main-roof fracture line and its rotation angle significantly affect the distribution of roof internal force: the former determines the range of the applied deformation, while the later determines its intensity. The resulting instability modes include oblique shear failure of the roof, roof cutting at the wall edge, roof crushing in the backfilling zone, and roof bed separation and collapse. Increasing the support stiffness of both ribs can effectively reduce roof displacement and bending moment. Both numerical simulations and engineering practice verify that strengthening the support of the solid coal rib and increasing the stiffness of the backfilling wall are effective engineering measures for controlling roof instability in gob-side entry retaining.</p>