Mechanical Model and Mechanical Characteristic Analysis of Isolated Roof in Double‐Layer Goafs

The double‐layer goafs are commonly found in mines that use the open stope mining method. The mechanical characteristics of the isolated roof in the double‐layer goaf column directly affect the safety of the double‐layer goaf and its surrounding goafs and have a greater impact on the safety of mine production. Taking the Bainiuchang Silver Mine as the engineering background, a mechanical model of the ends‐fixed beam of the double‐layer goaf isolation roof with the upper and lower goafs overlapping completely is established. Then, the stress and displacement components of the isolated roof are deduced by using the Airy stress function, which introduces the boundary condition of a fixed end that both considered the restriction of ∂ v / ∂ x and ∂ u / ∂ y on the rotation of the rigid body. The results of three‐dimensional surface and contour show that the maximum stress and displacement of the isolated roof are distributed in different regions of the roof, and the corresponding stress characteristics include shear, compression, and tension. Considering that the thickness of the isolation roof and the overlying load have a great influence on the stress and displacement of the roof, use the controlled variable method to study the influence of both on the maximum stress and displacement of the isolation roof. The results show that the smaller the thickness of the isolated roof depended on the stoping progress of the lower middle, the larger the increase of the stress and displacement components except the maximum vertical stress component. The maximum horizontal stress and the maximum vertical displacement increase greatly when the overburden of the isolated roof depends on the stoping progress of the upper middle. Therefore, in the actual engineering, the thickness of the safety pillars should be reasonably arranged, and at the same time, the stress concentration and vertical displacement changes at both ends of the isolation roof should be paid particular attention.