## 3 Roof Movement Mechanical Model of GERRC
### Relationship between Roadway Roof Deformation and Support Stiffness  
Based on engineering test conditions, the roadway roof load during mining retention is approximately \(q_{1}=2.2\) MPa, \(q=4.1\) MPa, and other measured parameters are \(E=2.5\) GPa, \(\gamma=250\) kN/m\({}^{3}\), \(h=3\) m, \(a=4.0\) m, \(\lambda=2.0\), \(x_{0}=8.3\) m (roadway width 4.3 m), \(k=6.62\times 10^{6}\) N/m. From Equation (3), it is known that during mining retention, the location and stiffness of temporary support (stacking support) within the roadway are crucial for roof control. When the additional stiffness of the temporary support is \(6.2\times 10^{6}\) N/m, the roof subsidence increases towards the gob side, generally in a parabolic form, with the subsidence increasing as it moves closer to the cutting side. The closer the support position is to the cutting side, the smaller the roof subsidence. In line with the test roadway, the limit equilibrium zone is 4 m away from the roadway wall. When the support position is at 6.3 m, the roof subsidence on the solid coal side is 100 mm, and the roof subsidence at the cutting side increases to 345 mm, an increase of 70.1%, indicating that during roadway retention, the roadway roof will rotate and subside towards the gob side. During roadway retention along the roadway roof dip direction, as the support position moves from the  
Figure 10: Mechanical model of immediate roof and main roof. solid coal to the cutting side of the roadway wall, the deformation of the roof at different positions shows a decreasing trend, as shown in Figure 11a. By statistically analyzing the maximum deformation of the roadway roof at different support positions, as shown in Figure 11b, the maximum deformation occurs when the support position is at the solid coal roadway wall side. As the support position moves closer to the solid coal side, the maximum deformation decreases. Therefore, in engineering practice, it is recommended to place temporary support bodies close to the cutting side of the roof to control roof subsidence deformation. As the support stiffness increases from 4.2 \(\times\) 10\({}^{6}\) N/m to 8.2 \(\times\) 10\({}^{6}\) N/m, the roadway roof subsidence gradually decreases. The deformation of the roof near the cutting side becomes larger. When the support stiffness is 4.2 \(\times\) 10\({}^{6}\) N/m, the maximum roof subsidence is 338 mm. When the support stiffness increases to 8.2 \(\times\) 10\({}^{6}\) N/m, the maximum roof subsidence decreases to 235 mm, a reduction of 30.5%, as shown in Figure 12. In engineering practice, the stiffness of the support system is the ability of the support system to resist deformation under force. The roof deformation of GERRC is loaded onto the support body, and the deformation of the immediate floor is also loaded onto the support system. An increase in the number of temporary support bodies can be used to increase the stiffness of the support system and control the subsidence and deformation of the roof. Similarly, it can also suppress the deformation of the floor drum. From the above analysis, it is clear that increasing the stiffness of the temporary reinforcement support for the roadway roof during retention can reduce the roof deformation. Additionally, the closer the support position is to the cutting side of the roadway wall, the more it can control the roof deformation. During GERRC, using a single high-stiffness support body can control roof deformation, but it also causes the support body and the roof to accumulate elastic energy, which may lead to impact accidents during the retreat. Therefore, to control roof subsidence, it is necessary to fully utilize the matching of the support stiffness and roof subsidence. In the dip direction of the roadway roof, parallel support can be adopted, increasing the number of support bodies to enhance the stiffness of the support system, and the support position should be as close as possible to the cutting side of the roadway wall.