# Uneven Stiffness Coal Seam: A New Structural Factor Prone to Coal Burst Based on Stiffness Theory
## 1 Introduction  
Coal burst, also known as coal bump or rock burst, is a dynamic phenomenon arising from the rapid release of stored elastic energy within the coal and rock mass around the mining space [1; 2; 3]. This phenomenon manifests suddenly, accompanied by fragments ejection or rapid deformation of roadway, generating load noise and air blasts, and often resulting in significant damage [4; 5; 6]. Undoubtedly, coal burst is a paramount dynamic hazard, posing a serious threat to the safety of coal mine production. Researchers proposed many kinds of theory, such as strength theory [7], energy theory [8], stiffness theory [9; 10; 11; 12], bursting liability theory [13], instability theory [14],catastrophe theory [15; 16; 17], the \"three-factors\" mechanism [18], the rock burst start-up mechanism [19], the dynamic and static combined load-induced mechanism [20], and the disturbance response instability mechanism [21], to clarify the mechanism underlying coal burst. Although so many progress have been made in understanding coal burst mechanisms, there is still no universally accepted theory within the academia [22]. The stiffness theory merits particular attention among the various mechanisms of coal burst due to its evident advantages and disadvantages. The stiffness theory originated from the research on the influence of testing machine stiffness on the bursting intensity of rock specimen failure. [PERSON] emphasized the resemblance between the unstable failure of specimens on low-stiffness test machines and rock burst incidents, and proposed that the necessary condition for unstable failure of specimens is also a prerequisite for rock burst or coal burst [9; 10]. In 1970, [PERSON] introduced the concept of local mine stiffness (LMS) and noted that if the LMS is \"softer\" than the post-peak stiffness of a coal pillar, the pillar would fail in an unstable and violent manner [11; 23]. In the analysis of the The Galena Mine, [PERSON] highlighted that the stiffness of the mine pillar exceeds that of the surrounding rock, a necessary condition for rock burst [12]. [PERSON] proposed a method for calculating the LMS based on numerical simulation results before and after coal pillar excavation [24]. [PERSON] demonstrated through numerical simulation that as the working face advances, the LMS decreases, leading to an increased probability of instability of coal pillars and coal walls [25]. In addition to the vast amount of data documenting the occurrence of unstable failure in specimens tested on low-stiffness machines, there are also many results of experimental research that can empirically support the stiffness theory. [PERSON], [PERSON], and [PERSON] individually conducted experiments on series-connected combined coal and rock samples, uniformly showed that a decrease in loading stiffness correlates with an increase in the bursting intensity of coal sample failure [26; 27; 28]. Furthermore, [PERSON] et al. successfully reproduced ejective rock burst in indoor experiments by reducing the loading stiffness through the addition of series spring [29]. [PERSON] proposed that the the involvement of the surrounding rock in energy release is a necessary condition of coal burst, and deduced, based on the principle of minimum potential energy, that this prerequisite is equivalent to the LMS being smaller than the post-peak equivalent stiffness of the coal mass [14]. [PERSON]. [15], [PERSON]. [16], and [PERSON] [17] derived, using the cusp-type catastrophe theory, that the instability failure or coal burst requires a stiffness ratio between the surrounding rock and the coal mass of less than 1. Although the theoretical basis of these studies differs, their conclusions align with the stiffness theory. These theoretical research findings have further enhanced the credibility of the stiffness theory. While the stiffness theory has garnered significant experimental support and aligns with numerous theoretical research findings, it is not without its shortcomings.