## 3 Roof Structure of DWFs and GSR Load Analysis
### Roof Structure and Stress Calculation of Roadway Surrounding Rock During the IWS  
According to key strata theory [10], an analysis was conducted on the overlying strata exposed in the drilling histogram of No. 18-12 (Figure 2) near an area prone to coal bursts. Medium-grained sandstone (No. 16) and fine-grained sandstone (No. 15) with high strength and large thickness were classified as inferior key strata I (IKS I) and inferior key strata II (IKS II). The key strata fracture structure significantly influences the stress  
Figure 1: The arrangement of the 3\({}^{\text{+}}\)101 and 3\({}^{\text{-}}\)103 working faces and the typical bursting failure characteristics of the GSR [34]. evolution of the surrounding rock. Accurate assessment of the stress state and the loading patterns on the roadway must be evaluated in relation to the fracture structure of the key strata, therefore enabling the analysis of coal burst mechanisms. When the FWF is fully mined and the GSWF reaches its IWS, the roof of the DWFs' gob forms an asymmetrical T-shaped structure (Figure 3). In the FWF area, the IKS I and II fractures give rise to a \"double-inclined voussoir beam\" along the working face. In contrast, the GSWF exhibits a \"single voussoir beam\" structure. Only IKS I fractures, while IKS II remains intact, resulting in an overhanging roof. At this time, the intensity of strata behavior of GSWF is relatively low. The roof load shifts to the strata at the working face ends, inducing localized stress concentration and energy accumulation, which provides conditions for inducing the coal bursts in the GSR. The GSR preceding the GSWF experiences lateral abutment pressure from the FWF gob that is basically the same across various mining stages. Figure 4 illustrates the distribution pattern of this load. Figure 3: Asymmetrical T-shaped roof structure model of DWFs at the IWS of GSWF. Figure 2: The histogram of No.18–12 drillhole (Partial) [1]. According to the literature [1], the lateral static load from the FWF gob on the GSR includes the foundation static load and the mining-induced additional static load:  
\[\sigma_{\text{j}}=\sigma_{\text{y}}+\Delta\sigma_{\text{I}}+\Delta\sigma_{ \text{II}} \tag{1}\]  
where \(\sigma_{\text{j}}\) is the lateral static load from the gob on the GSR throughout the FMS of the FWF; \(\sigma_{\text{y}}\) is the foundation static load due to the self-weight of overlying strata; \(\Delta\sigma_{\text{I}}\) is the mining-induced additional static load formed by the IKS I; and \(\Delta\sigma_{\text{II}}\) is the mining-induced additional static load formed by the IKS II. In Equation (1), \(\sigma_{\text{y}}\), \(\Delta\sigma_{\text{I}}\), and \(\Delta\sigma_{\text{II}}\) are calculated by Equation (2):  
\[\sigma_{\text{y}}= \begin{cases}\frac{\gamma H\tan a}{2(h_{0}+h_{1})+h_{2}}x& \left(0\leqslant x\leqslant\frac{2(h_{0}+h_{1})+h_{2}}{\tan a}\right)\\ \gamma H&\left(x\geqslant\frac{2(h_{0}+h_{1})+h_{2}}{\tan a}\right)\end{cases}  \tag{2}\]  
where \(\gamma\) is the strata bulk density; \(H\) is the mining depth; \(\alpha\) is the strata fracture angle, which can be taken as \(70^{\circ}\)[37]; and \(h_{0}\), \(h_{1}\), and \(h_{2}\) are the respective thicknesses of the immediate roof, IKS I, and IKS II. \[\Delta\sigma_{\text{I}}= \begin{cases}\frac{2\sigma_{\text{Imax}}\tan a}{2(h_{ 0}+h_{1})+h_{2}}x&\left(0\leqslant x\leqslant\frac{2(h_{0}+h_{1})+h_{2}}{2 \tan a}\right)\\ 2\sigma_{\text{Imax}}\Big{(}1-\frac{\tan a}{2(h_{0}+h_{1})+h_{2}}x\Big{)}& \left(\frac{2(h_{0}+h_{1})+h_{2}}{2\tan a}\leqslant x\leqslant\frac{2(h_{0}+h _{1})+h_{2}}{\tan a}\right)\\ 0&\left(x\geqslant\frac{2(h_{0}+h_{1})}{\tan a}\right)\end{cases}  \tag{3}\]  
where \(\sigma_{\text{Imax}}\) is the maximum mining-induced additional static load caused by IKS I.