Energy evolution law and differential energy instability model of coal-rock combined body

In order to effectively evaluate the burst liability of coal-rock combination model and reflect the effect of surrounding rock properties on its instability and failure,the energy accumulation characteristics of different types of rocks are first compared. It is found that the elastic energy density of rock at the same stress level mainly depends on its elastic modulus,and there is a negative correlation between them. According to this,the elastic energy evolution laws of coal and rock masses in combination samples are analyzed,indicating that the coal mass is the main body for the accumulation and release of elastic energy. The peak elastic energy density difference between them is further calculated. It is shown that this parameter is closely related to the severity of failure of a combination sample,that is,the greater the peak elastic energy density difference,the more violent the failure of combination samples tends to be. Then, based on a large number of test data,the factors affecting the parameter are discussed. The results indicate that the parameter has a positive correlation with the compressive strength of combination sample, elastic modulus of coal, rock-coal height ratio,and rock-coal elastic modulus ratio,among which the compressive strength is the main factor, while the relationship with the elastic modulus of rock is unclear. After that,based on the viewpoint of nonequilibrium thermodynamics and dissipative structure,a Differential Energy Instability Model (DEIM) for the combined coal-rock system is established from the perspective of elastic energy density difference. When it is in the critical state,the elastic energy density difference of the system is the largest, and the system is in the most unstable state. Accordingly,the ratio of peak elastic energy density difference of coal-rock system to instability duration is proposed as an index to evaluate the bursting liability of coal-rock combination model. The index treats the combined coal⁃rock as a system,taking into account the differences in the mechanical properties and energy accumulation characteristics of the coal and rock masses,and essentially represents the release rate of stored elastic energy during the instability process of coal-rock system,and the rationality of the index is verified by experimental and simulated data. The DEIM of coal-rock combined body can approximately reflect the mechanical phenomenon of coal-rock burst. © 2022 China Coal Society. All rights reserved.