# Uneven Stiffness Coal Seam: A New Structural Factor Prone to Coal Burst Based on Stiffness Theory
## 4 Simple Numerical Simulation of Uneven Stiffness Coal seam Structure (USCS)
When \(E_{\text{R}}\), \(H_{\text{R}}\), \(K_{\text{H}}\), and \(S_{\text{L}}\) increase, or \(K_{\text{L}}\) and \(S_{\text{H}}\) decrease, the pressure concentration function of the USCS becomes stronger, resulting in a higher concentration of stress and an increased risk (\(r_{\text{F}}\)) of failure in HSZ. When \(H_{\text{R}}\), \(K_{\text{H}}\), \(S_{\text{L}}\), and \(S_{\text{H}}\) increase, or \(E_{\text{R}}\) and \(K_{\text{L}}\) decrease, the stiffness reduction function of the USCS becomes stronger, leading to lower LMS and an increased risk (\(r_{\text{I}}\)) of instability in HSZ. 2. The analysis results and simulation results are in agreement with engineering experience in many cases, affirming the suitability of utilizing uneven stiffness coal seam structure for investigating coal burst phenomena. 3. Reduce \(K_{\text{H}}\), \(S_{\text{L}}\) (\(S_{\text{R}}\)), or increase \(K_{\text{L}}\) of USCS can simultaneously decrease the \(r_{\text{F}}\) and \(r_{\text{I}}\), thus decrease \(r_{\text{CB}}\). The majority of existing engineering measures for coal  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & **Controlled** & **Controlled** & **Variable** & **Normal** & **Stress** & **Con-** & **Compression** & **Bending** & **Total** & **NSC of** & **NSC of** & **Pressure** \\  & **Variable** & **Value** & **Stress** & **Factor** & **Bygail/mm** & **DESgail/mm** & **DESgail/mm** & **DESgail/mm** & **DESgail/mm** & **Root/K\({}_{\text{R}}\)/N-mm\({}^{-3}\)** & **Provider** \\ \hline \(1\) & & & 4 & 23.837 & 1.589 & 4.065 & 8.569 & 12.635 & 4.000 & 0.322 & 1.287 \\ \(2\) & \(S_{\text{H}}/\text{m}\) & \(10\) & 19.576 & 1.305 & 3.798 & 13.471 & 17.269 & 4.000 & 0.220 & 0.880 \\ \(3\) & & 20 & 17.442 & 1.163 & 3.602 & 13.638 & 17.241 & 4.000 & 0.209 & 0.836 \\ \hline \(1\) & & & 20 & 23.847 & 1.589 & 4.065 & 8.569 & 12.635 & 4.000 & 0.322 & 1.287 \\ \(4\) & \(E_{\text{R}}/\text{GPa}\) & \(15\) & 23.469 & 1.564 & 5.346 & 8.978 & 14.324 & 3.000 & 0.373 & 1.120 \\  
burst preventing involve modifying one of these 3 key parameters to achieve their intended effect. For ESCS systems consisting of a continuous roof and floor that sandwich a coal seam with even stiffness, the LMS (\(k_{\rm p}\)) is equivalent to normal stiffness of the roof (\(k_{\rm R}\)). In cases where the roof is considered \"hard,\" indicating a higher elastic modulus (\(E_{\rm R}\)), the \(k_{\rm R}\) is elevated, resulting in a higher \(k_{\rm p}\). Consequently, meeting the required stiffness criterion becomes a challenge. This dash between stiffness theory and practical engineering experience remains unresolved within ESCS arrangements. In contrast, for USCS systems consisting of a continuous roof and floor that sandwich a coal seam with an uneven stiffness distribution, the stiffness reduction function allows for a decrease in \(k_{\rm p}\), making it easier to meet the stiffness criterion. Although an increase in \(E_{\rm R}\) results in a higher \(k_{\rm p}\), the increment in \(k_{\rm p}\) for USCS is considerably smaller compared to ESBS. Simulation results indicate that parameters such as \(H_{\rm R}\), \(S_{\rm R}\), and \(K_{\rm H}/K_{\rm L}\), in addition to \(E_{\rm R}\), can affect the value of \(k_{\rm p}\). Certain USCSs have \(H_{\rm R}\)S\({}_{\rm R}\)K\({}_{\rm H}/K_{\rm L}\) values that are sufficiently large, effectively reducing \(k_{\rm p}\) below the threshold stated in Equation (1). Even with an increase in \(E_{\rm R}\) within a specific range, these USCSs continue to satisfy the stiffness criterion, thereby maintaining a high risk (\(r_{\rm I}\)) of instability. In accordance with Equation (3), raising the \(E_{\rm R}\) of specific USCSs with sufficiently larger \(H_{\rm R}\)S\({}_{\rm R}\)K\({}_{\rm H}/K_{\rm L}\) values can lead to an increase in \(r_{\rm F}\) while keeping the \(r_{\rm I}\) constant, thereby resulting in an increase in the \(r_{\rm CB}\).