## 4 Analysis of Coal Pillar Bearing Structure after Coal Seam Mining  
### Mechanical Analysis of High Bearing Structure of Coal Pillar  
After the coal seam is mined, forming a goaf with a length of x, the immediate roof exhibits an irregular caving shape, creating a cantilever beam structure near the coal pillar side. The fracture line forms a specific angle with the goaf. Due to the mining height, the basic roof fractures within the goaf. As the gangue in the goaf is compacted, a hinged structure forms near the basic roof on the coal pillar side. The stress generated by the movement of the key block gradually transfers to the interior of the coal pillar and the deeper parts of the goaf. At this point, coal pillar L is subjected to the load H of the overlying strata and the forces from the bearing strata breaking onto the coal pillar. The 1513 return airway is also affected by the coal pillar. This establishes the mechanical model of the coal pillar-bearing structure, as illustrated in Figure 5.  
Figure 4: Vertical stress diagram of coal pillars with different widths. Figure 5: Mechanical model of coal pillar bearing structure. Upon completion of the 1512 working face, the mining disturbance causes the basic roof of the goat to fracture, forming a \"masonry beam\" structure. The fracture line and the goat create a specific angle. As key block B rotates and subsides, the key blocks compress against each other, generating horizontal thrust. This interaction creates shear and friction between the blocks, which supports the overlying strata, as illustrated in Figure 6.  
In the diagram, \(P_{1}\) is the load applied by the overlying strata to the key block B, kN/m; \(T\) is horizontal thrust, kN; \(Q_{\rm A}\) is the support force of coal pillar to key block B, kN; \(Q_{\rm B}\) is the support force of the gangue in the goat to the key block C, kN; \(L_{1}\) is the length of key block B, m; \(\theta\) is the rotation angle of the key block B, \({}^{\circ}\); and \(h_{1}\) is the thickness of the block rock beam, m.  
Once mining of the working face is completed, the immediate roof collapses, and the rock stratum undergoes rotation and fracturing, creating a fracture zone. Due to the positioning of the key stratum, the bending subsidence zone experiences minimal damage and functions in supporting the overlying rock stratum. Due to mining disturbance, the overlying strata develop fracture zones and bending subsidence zones, which are distinctly separated. Concurrently, rock blocks fracture, leading to an interruption in force transmission. Consequently, the load exerted on the overlying strata \(P_{1}\) is as follows:  
\[P_{1}\ =\ L_{1}\gamma_{1}h_{1}K_{G} \tag{1}\]  
In the formula, \(\gamma_{1}\) represents the average bulk density (kN/m\({}^{3}\)) of the upper load rock layer of the key block B, \(h_{1}\) denotes the thickness (m) of the upper load rock layer of the key block, and \(K_{\rm G}\) stands for the load transfer coefficient. The internal force key block B comprises \(P_{\rm ZB}\), as follows:  
\[P_{ZB}\ =\ L_{1}\gamma_{2}h_{1} \tag{2}\]  
In the formula, \(\gamma_{2}\) is the average bulk density of the key block B, kN/m\({}^{3}\). The geometric relationship of rock mass after rotation is shown in Figure 6. According to the geometric characteristics of rock mass rotation, the following can be seen:  
\[a\ =\ \frac{1}{2}(h-L\sin\theta) \tag{3}\]  
Due to the plastic hinge relationship between the blocks, the horizontal thrust between the blocks is located at \(a/2\) of the rock block. Figure 6: Mechanical structure of high key stratum breaking “hinged” structure.