## 3 Roof Structure of DWFs and GSR Load Analysis
### Roof Structure and Stress Calculation of Roadway Surrounding Rock During the FMS  
The GSWF undergoes several stages as the working face progresses: the IWS, PWS, and FMS. During the PWS, the IKS II fractures and forms a \"double-inclined voussoir beam\" structure along the working face. This fracture creates a symmetrical T-shaped structure in the roof of the DWFs' gob (Figure 7). The IKS II failure generates dynamic loads on IKS I and the working face. These dynamic loads elevate the potential of coal bursts in the GSR, particularly in areas where the coal and rock mass already experience high-stress concentrations or significant elastic energy accumulation. Figure 6: Schematic diagram of dynamic and static loads combined in front of working face at the IWS. Throughout the FMS of the GSWF, the roof of the DWFs' gob forms a symmetrical T-shaped structure, as depicted in Figure 8. Meanwhile, this triggers large-scale movement in the overlying high-position thick and hard strata, leading to energy release within the roof, thereby intensifying the dynamic disturbance exerted by the IKS II on the underlying strata. This intensified disturbance could induce coal bursts in the GSR when the total stress or energy exceeds the critical threshold for burst failure of the coal and rock mass. Therefore, the FMS presents a higher propensity for coal bursts in the GSR compared to the PWS. This increased risk stems from the more intense dynamic loading effect due to the large-scale movement of the overlying strata at the DWFs. Figure 9 illustrates a three-dimensional model of the DWFs' roof during the IWS of the GSWF. It also shows the patterns of different load distributions: the lateral static load \(\sigma_{\rm j}\) of the FWF gob, the advanced static load \(\sigma_{\rm jz}\) of the GSWF, and the dynamic load \(\sigma_{\rm dz}\) caused by the fracturing of thick and hard roofs. Analysis reveals a higher likelihood of coal bursts in the GSR throughout the FMS compared to the PWS. Consequently, we focus on the load status of the GSR in front of the working face at the FMS of the GSWF. Figure 10 exhibits the roof structure and the dynamic and static loads combined along the mining direction as the GSWF reaches the FMS. At this stage, the static load on the GSR surrounding rock remains comparable to that in the IWS. However, the primary dynamic load source stems from the fracture-induced dynamic load of IKS I and II (Figure 10). Research indicates that the maximum disturbance dynamic load occurs when these two sets of inferior key strata break simultaneously [16]. The stress estimation should take into account the most adverse stress conditions for the surrounding rock, which is determined by the strong disturbance dynamic load generated during the simultaneous fracture of two sets of inferior key strata. Figure 7: Symmetrical T-shaped roof structure model of the DWFs during the PWS of the GSWF. (**a**) UDEC numerical simulation results of the roof structure form of the DWFs; (**b**) symmetrical T-shaped roof structure model of the DWFs. According to the literature [41], the approach of determining the disturbance dynamic load generated by the synchronous fracture of IKS I and II is presented as follows:  
\[ \begin{split}&\sigma_{\text{dz}}=0.0645\rho V_{\text{s}}[\eta(U_{ \text{zwz1}}+U_{\text{wzz1}})]^{0.3566}L^{-\beta}\\ &=0.0645\rho V_{\text{s}}\left[\eta\frac{(q_{\text{zz1}}l_{\text{z 1}}^{3}+q_{\text{zz1}}l_{\text{z1}})}{8E_{\text{z1}}}\right]^{0.3566}L^{- \beta}\end{split}  \tag{10}\]  
where \(q_{\text{zz1}}\) and \(q_{\text{zz1}}\) are the overlying strata load of IKS I and II; and \(l_{\text{z1}}\) and \(l_{\text{zz1}}\) are the periodic breaking intervals of IKS I and II. Figure 8: Symmetrical T-shaped roof structure model of the DWFs during the FMS of the GSWF. (**a**) UDEC numerical simulation results of roof structure form of the DWFs; (**b**) symmetrical T-shaped roof structure model of the DWFs. Figure 9: 3D model of the DWFs’ roof and “three-load” superposition combined on the GSR at the FMS of the GSWF.