## 4 Simulation Results of Fully Mechanized Mining with a Large Mining Height and the Analysis
### The Mechanism of the Influence of the Dirt Band on the Morphology of Spalling  
For a long time, it has been generally believed that the support design for multi-seam mining and ordinary mining is not different. However, according to the on-site conditions and simulation results, it is found that the dirt band of the coal seam inhibits spalling to a certain extent. In order to determine the mechanism of the influence of the dirt band on coal wall stability, the force analysis of the coal wall was carried out. The force state of the front end of the coal wall is shown in Figure 13.  
The front end of coal wall is simplified to an elastomer, and the analytic expression of the displacement component is derived from the principle of minimum potential energy as follows [13]:  
\[u_{\rm x}=\frac{6(v^{2}-1)(L\tau-Hqv)}{E[2L^{2}(v-1)+H^{2}(3v^{2}-4)]}xy \tag{1}\]  
\[u_{y}=\frac{-(v^{2}-1)(2L^{2}q-2L^{2}qv+4H^{2}q-3 HL\tau v)}{E[2L^{2}(v-1)+H^{ 2}(3v^{2}-4)]}y \tag{2}\]  
Figure 13: Simplified model of coal wall pressure. In this figure, (**a**) model without dirt band; (**b**) model with dirt band. where \(u_{x}\) and \(u_{y}\) are the displacement functions of the coal wall in the horizontal and vertical directions; \(x\) and \(y\) are the coordinate variables, m; \(E\) is the elastic modulus of coal seam, MPa; \(v\) is Poisson's ratio of the coal seam; \(q\) is the positive stress of roof endured by the coal seam, MPa; \(\tau\) is the shear stress endured by the coal seam, MPa; \(L\) is the depth of the front end of the coal wall, m; and \(H\) is the mining height of the coal seam, m. The constitutive equation and geometric equation under plane strain conditions are introduced into Equations (1) and (2) to obtain the horizontal stress expression under roof pressure:  
\[\sigma_{x}=\frac{(2L^{2}q-2L^{2}qv+4H^{2}q-3 HL\tau v)\
u+6\
u(L\tau-Hqv)}{2L^{ 2}(1-\
u)+H^{2}(4-3v^{2})} \tag{3}\]  
From Equation (3), it can be concluded that the coal seam is only related to Poisson's ratio when under roof pressure. When Poisson's ratio is small, horizontal tensile stress appears on the coal seam. Furthermore, as Poisson's ratio continues to decrease, the tensile stress gradually increases. Figure 13a presents the simplified model of the front-end coal wall under pressure when there is no dirt band in the coal seam. At this time, the coal wall is only affected by the roof pressure and its own mechanical properties. The equation reflects the displacement distribution of the coal wall at this moment. In the simplified model with a dirt band (Figure 13b), due to the different Poisson's ratios of the coal seam and the dirt bands, a horizontal stress gradient difference is formed between the coal seam and the dirt bands, thus generating shear stress between the coal seam and the parting. Hard coal has a small Poisson's ratio, and horizontal tensile stress occurs under the condition of roof pressure. Therefore, the failure of hard coal under roof pressure belongs to tensile-shear failure or splitting failure, which corresponds to the instability of the coal wall during the mining process. According to the analysis, the presence of the dirt band will change the stress-strain state of the coal wall. Since Poisson's ratio of the dirt band is smaller than that of hard coal, under roof pressure, the horizontal strain of the dirt band is smaller than that of the coal seam. Due to the dirt band's tensile strength being greater than coal seam, the dirt band can limit the horizontal displacement caused by the internal tensile stress of the coal wall, producing an anchoring effect, and effectively preventing the fractures from developing obliquely from the boundary points to the plastic zone. This discovery reveals the internal mechanical mechanism of the dirt band inhibiting the spalling of the production coal face.