# Uneven Stiffness Coal Seam: A New Structural Factor Prone to Coal Burst Based on Stiffness Theory
## 3 Uneven Stiffness Coal Seam Structure (USCS)  
### Structure Composition, Functions, and Typical Examples of USCS  
[PERSON] modified the flexible testing machine by adding a copper pipe parallel connection with the crossbeam to reduce its bending deformation and increase its stiffness, enabling the testing machine measure the post-peak curve of the rock for the first time [31; 32]. If a special structure similar to a flexible testing machine exists within the coal measure strata, the key parts responsible for reducing the LMS through bending, similar to the flexible testing machine's crossbeam, would be the roof or the floor. To achieve bending in either the roof or the floor, it is necessary for varying compression deformations to occur at different positions along the coal seam, which implies that the normal stiffness of the coal seam is uneven. Hence, this unique structure within the coal measure strata can be termed as the Uneven Stiffness Coal seam Structure (USCS). USCS is composed of continuous roof and floor that sandwich coal seam with uneven stiffness distribution. The uneven distribution of stiffness is quantified using the Normal Stiffness Coefficient (NSC), which represents the normal stiffness per unit area and is measured in N/m3. Within the USCS, sections of the coal seam with higher NSC values are identified as high stiffness zone (HSZ), whereas regions with lower NSC values are classified as low stiffness zone (LSZ). On the other hand, the Even Stiffness Coal seam Structure (ESBS) represents the contrasting counterpart of USCS, comprising continuous roof and floor along with a coal seam exhibiting an even distribution of stiffness. Figure 2 provides a visual comparison between USCS and two types of ESCS. The uneven distribution of normal stiffness enable USBS to have pressure concentration function which make the HSZ bears a higher static pressure under evenly distributed overlying loads. This function results in the coal mass of HSZ reaching the failure criterion more easily. Once the failure criterion is reached, the coal mass of HSZ would serves as a pressure bearer and undergoes failure, while the surrounding rock, including the roof, floor, and coal seam of LSZ in series, serves as a pressure provider and releases stored energy. Due to the overall stiffness of the series structure being lower than the stiffness of any constituent unit, the LMS of HSZ is in a state lower than the normal stiffness of LSZ. Therefore, the HSZ can exhibits lower LMS even when the roof and floor are hard,thus reconciling the contradiction between stiffness theory and engineering common sense. USCS exhibits both the pressure concentration function and the stiffness reduction function. The former enables stress to concentrate from the LSZ to the HSZ, thereby increasing the risk (\(r_{\text{F}}\)) of failure. The latter reduces the LMS of HSZ, making it easier to meet the stiffness criterion and leading to post-peak instability, thus elevating the risk (\(r_{\text{I}}\)) of instability. In contrast, ESBS lacks any pressure concentration or stiffness reduction function, regardless of the normal stiffness of the coal seam. Equation (3) supports the conclusion that the risk (\(r_{\text{CB}}\)) of coal burst in HSZ of USCS surpasses that in ESBS. Therefore, USCS is a structural factor prone to coal burst incidents. In the case of a uniform rock stratum with an elastic modulus represented by \(E\) and a thickness denoted by \(H\), Equation (4) can be employed to calculate the NSC. \[K=k/S=E/H \tag{4}\]  
Equation (4) states that altering the elastic modulus of coal or the thickness of the coal seam can both modify the NSC of the coal seam. Thinning the thickness of coal seam in certain areas or replacing certain sections of the local coal seam by rock with higher elastic modulus can both increase NSC, leading to the formation of USCS.