## 4 Effect Analysis of Roof Self-Stability Factors  
### Effect Analysis of Roof Self-Stability Factors along Strike  
(1) Preliminary setting of parameters  
The parameters are preliminarily selected in different directions to study the key factor effects of roof self-stability based on the engineering geological conditions of a certain mine [22]. The buried depth of the coal seam is denoted as 700 m along strike; initial rock stress \(q_{0}=\) 17.5 \(\times\) 10\({}^{6}\) N/m; load concentration of overlying roof in goat \(q_{\rm c}=\) 2 \(\times\) 10\({}^{6}\) N/m; immediate roof thickness \(h=\) 3.7 m; elastic modulus of roof \(E=\) 18 GPa; elastic foundation coefficient of coal body \(k_{\rm c}=\) 3 \(\times\) 10\({}^{8}\) N/m\({}^{3}\); elastic foundation coefficient of backfilling body \(k_{\rm g}=\) 9 \(\times\) 10\({}^{6}\) N/m\({}^{3}\); support peak load \(q=\) 1.62 \(\times\) 10\({}^{6}\) N/m; stress concentration coefficient of roof \(k_{1}=k_{2}=\) 2.3; solid-coal length \(L_{1}=L_{6}=\) 50 m; front top beam length \(L_{2}=\) 3.56 m; rear top beam length \(L_{3}=\) 2.81 m, unsupported-roof distance \(L_{4}=\) 1 m; backfilling body \(L_{5}=\) 60 m. The above parameters are used to analyze the effect law of the elastic foundation coefficient of backfill, support peak load, and unsupported-roof distance on roof stability along strike. (2) Effect analysis of elastic foundation coefficient of backfill  
The elastic foundation coefficients of backfill are set to be 8, 9, and 10 MN/m\({}^{3}\), respectively. Figure 3 shows the correlation curves among the elastic foundation coefficient, roof deflection, and bending moment through mechanical calculations. The immediate roof subsidence presents a parabolic curve under the elastic-foundation coefficient of backfill. The roof subsidence decreases with the increased elastic-foundation coefficient. Besides, the position of maximum roof subsidence moves close to the stope coal wall. When the elastic foundation coefficient rises from 8 to 10 MN/m\({}^{3}\), the maximum roof subsidence is decreased by 20.23% (from 0.262 to 0.209 m). A negative correlation exists between the roof bending moment and the elastic-foundation coefficient of backfill. The maximum roof bending moment appears near the stope  
Figure 3: Relationship among elastic foundation coefficients, roof subsidence, and bending moments. maximum roof bending moment shifts to the direction of the goat with the increased elastic-foundation coefficient. When the elastic-foundation coefficient rises from 8 to 10 MN/m\({}^{3}\), the maximum roof bending moment is reduced from 40.9 to 26.06 MN/m, with a change rate of 36.28%. Therefore, the elastic-foundation coefficient of backfill significantly impacts roof self-stability. The elastic foundation coefficient of filling directly affects the strength of filling body and changes the supporting ability of filling body to overlying rock. In order to make the roof reach the self-stable state, the filling elastic foundation coefficient can be improved by increasing the filling rate, optimizing the filling material ratio and optimizing the filling material. Effect analysis of supporting-peak loads  
The peak loads of backfilling hydraulic support are set to be 0.62, 2.62, and 4.62 MPa, respectively. Figure 4 shows the correlation curves among the support peak load, roof deflection, and bending moment through mechanical calculations. A parabolic curve exists between the immediate roof subsidence and the advancing distance of the working face along the strike of coal seams. The roof subsidence reaches the maximum in the middle of the goat, and it decreases with increased supporting-peak loads. When the supporting-peak load rises from 0.62 to 4.62 MPa, the maximum roof subsidence is decreased by 1.3% (from 0.233 to 0.230 m). The roof subsidence is insignificantly impacted by the support peak load.