# Uneven Stiffness Coal Seam: A New Structural Factor Prone to Coal Burst Based on Stiffness Theory
## 7 Conclusions  
In this paper, Several often overlooked details of stiffness theory were clarified, and a qualitative evaluation formula for the risk of coal burst was provided. On this basis, a novel structure called uneven stiffness coal seam structure (USCS), which consists of high stiffness zone (HSZ), low stiffness zone (LSZ), and contiguous roof and floor, was proposed to reconcile the contrast between stiffness theory and engineering experience. Comparative analysis of the uneven stiffness coal seam under different roof conditions and examination of the simplified trisection model of the USCS were conducted. The findings revealed that the USCS exhibits two distinct functions, which can facilitate coal burst occurrence and affected by six key parameters. 6 groups of 14 simplified 2D models using COMSOL5.2 software was constructed based on controlled variable method to simulate different responses of the USCS with varying parameters under same working conditions. The main conclusions are as follows. 1. The necessary condition for coal burst based on the stiffness theory include both failure criterion and stiffness criterion. Based on the two criteria of stiffness theory, a qualitative evaluation formula for the risk of coal burst is proposed: the probability of coal burst occurrence (\(r_{\text{CB}}\)) is the product of the probability of failure (\(r_{\text{F}}\)) and the probability of post-peak instability (\(r_{\text{I}}\)). 2. The USCS exhibits pressure concentration function and the stiffness reduction function. The former promote the convergence of normal stress from LSZ to HSZ, thus raising the \(r_{\text{F}}\) of HSZ. The latter decreases the local mine stiffness (LMS), enabling the system to meet the stiffness criterion even with a hard roof, thus reconciling the contrast between the stiffness theory and engineering experience to some extent and increasing the \(r_{\text{I}}\) of HSZ. As a result of these two functions, the HSZ of USCS possesses a higher probability (rCB) of coal burst compared to conventional coal seam. 3. The two functions of USCS are governed by 6 key parameters, such as: the elastic modulus (\(E_{\text{R}}\)) and thickness (\(H_{\text{R}}\)) of the roof, the NSC (\(K_{\text{H}}\)) and area (\(S_{\text{H}}\)) of HSZ,  
Figure 15: Microseismic events distribution before the “9.9” coal burst in Huafeng Coal Mine [41]. the NSC (\(K_{\rm L}\)) and area (\(S_{\rm L}\)) of LSZ. The analysis indicated that \(\sigma_{\rm yH}\) (normal stress in HSZ) is positively correlated with the value of \(E_{\rm R}H_{\rm R}K_{\rm H}S_{\rm L}/K_{\rm L}S_{\rm H}\), the \(\sigma_{\rm yL}\) is positively correlated with the value of \(K_{\rm L}S_{\rm L}/E_{\rm R}H_{\rm R}K_{\rm H}S_{\rm H}\), the LMS (\(k_{\rm p}\)) in HSZ is positively correlated with the value of \(E_{\rm R}K_{\rm L}/K_{\rm H}\). The simulation results validated the analysis results about USCS, and revealed that the variation in stress induced by the USCS is positively correlated with variation gradient of NSC between HSZ and LSZ, while the \(\overline{K}_{\rm pH}\) (average LMS per unit area in HSZ) is negative correlated with \(H_{\rm R}S_{\rm L}S_{\rm H}\). 4. The USCS is associated with many existing theoretical research findings on coal burst. It offers a new way to partially reconcile the contradiction between engineering experience and stiffness theory, and provides a fresh approach to release bending elastic energy without roof breakage for energy theory. It also reveals the presence of a concealed coal pillar embedded within the solid coal, supporting [PERSON]'s proposition regarding \"relatively isolated columnar rock units.\" Additionally, it identifies the HSZ a specific failure position that leads to increased roof subsidence, thereby aligning with [PERSON]'s assertion on the sufficient conditions for coal burst. Moreover, the USCS introduces a novel structural factor into \"three-factors\" mechanism. Consequently, the USCS serves as a valuable tool for integrating and harmonizing various existing theories on coal burst. 5.