## 4 The Dynamic Changes of Stress and Energy Distributions Induced by Mining Activities
### Energy Density Distribution of GSWF Roof  
A primary factor triggering coal bursts is the abrupt discharge of the substantial energy stored within the surrounding rock of the stop [13; 22; 33; 49; 50; 51]. Multiple factors influence the energy distribution in the surrounding rock of the stop. While the characteristics and magnitude of ground stress are important factors [52; 53] affecting the energy levels in the surrounding rock of the stop, horizontal stress does not significantly impact the overall energy distribution pattern under specific ground stress conditions. By strategically positioning stress monitoring surfaces within the roof to acquire the three principal stress data of the roof layers in the stop with varying coal pillar widths, the energy density value of the roof strata can be computed using Equation (13) [49; 54; 55; 56; 57]. \[u=\frac{1}{2E}\Big{[}\sigma_{1}^{2}+\sigma_{2}^{2}+\sigma_{3}^{2}-2\mu(\sigma _{1}\sigma_{2}+\sigma_{2}\sigma_{3}+\sigma_{3}\sigma_{1})\Big{]} \tag{13}\]  
where \(u\) is the energy density; \(E\) is the elastic modulus; and \(\mu\) is Poisson's ratio. The energy density of different areas in the roof under four typical coal pillar widths of 5, 10, 20, and 40 m is analyzed, and the distribution pattern is illustrated in Figure 16.  
Figure 16 illustrates the varying degrees of energy accumulation in the roof of the gob-side end of the GSWF (the blue \"triangle\" area) for varying coal pillar widths. If the coal pillar width exceeds 20 m, energy accumulation also occurs within the coal pillar behind the working face. This energy accumulation pattern exhibits a notable trend: with the coal pillar width increasing, the amount of energy accumulated within the coal pillar behind the working face gradually decreases. The relationship between the peak values of energy density at the gob-side end of the working face and coal pillar widths demonstrates a linear negative correlation. Within the simulated coal pillar widths range, the peak values of energy density vary from 52.54 to 74.81 MJ/m\({}^{3}\). This relationship is described by \(E_{\text{m}}=-0.67B+78.66\) (\(R^{2}=0.97\)), where \(E_{\text{m}}\) is the maximum energy density and \(B\) is the coal pillar width. The peak energy density decreases at a rate of 0.67 (MJ/m\({}^{3}\))/m corresponding to an increasing coal pillar width (Figure 17). The coefficient of energy accumulation, defined as the ratio of the peak values of energy density in the roof after coal mining to the initial energy density in the roof before coal mining, also exhibits an inverse relationship with coal pillar width. This coefficient ranges from 3.20 to 4.56 and follows \(K_{\text{e}}=-0.04B+4.80\) (\(R^{2}=0.96\)), where \(K_{\text{e}}\) is the coefficient of energy accumulation. The coefficient of energy accumulation decreases at a rate of 0.04/m increase with the coal pillar width (Figure 17). Figure 15: Changes in peak values and concentration coefficient of vertical stress on the roof, influenced by varying coal pillar widths: (**a**) Changes in peak values of vertical stress observed at various points in front of working face; (**b**) Changes in peak values and concentration coefficient of vertical stress. Changes in the peak values of both vertical stress and energy density within the roof, as well as the vertical stress within the coal pillar at the gob-side end of the GSWF, considering the coal pillar widths of 5, 8, 10, 20, 30, and 40 m, are illustrated in Figure 18.  
Figure 16: The energy density distribution at the working face roof under various coal pillar widths: (a) 5 m; (b) 10 m; (c) 20 m; (d) 40 m.  
Figure 17: Changes in peak values of energy density and coefficient of energy accumulation across various coal pillar widths. As illustrated in Figure 18, when the coal pillar width is less than 20 m, reducing the coal pillar width can reduce the overall pressure in the coal pillar and improve stress conditions within the GSR.