Physical similarity principles of coal-rock dynamics simulation for coal burst

Coal burst is a sudden dynamic disaster that occurs under the superposition of dynamic and static loads, characterized by a violent failure process, concentrated energy release, and complex occurrence mechanism, posing a serious threat to mine safety. To reproduce the failure process of coal burst and reveal its dynamic essence in laboratory conditions, conventional physical simulation methods based on static similarity principles are inadequate to fully capture its dynamic characteristics. Therefore, with the dynamic disaster mechanism of coal burst as the research focus, a coal-rock dynamic similarity criterion system centered on the acceleration similarity ratio is proposed, aiming to establish a theoretical framework for physical simulation that can realistically reflect the dynamic response characteristics of coal burst. Through dimensional analysis, the key parameters involved in the coal burst process were systematically analyzed. Using the acceleration similarity ratio as the primary control parameter, a theoretical equation set of dynamic similarity criteria for coal burst was derived, and a system of dynamic similarity coefficients was constructed, including the stress similarity ratio, elastic modulus similarity ratio, time similarity ratio, and strain rate similarity ratio. By introducing the dynamic similarity coefficient, the coupling relationships and constraint conditions among various similarity ratios were analyzed, and a similarity criterion system describing the impact tendency of physical models was established. Furthermore, based on the derived theoretical relationships, the evolution laws of model strength curves under different geometric similarity ratios were summarized, and the applicable range and parameter intervals of the dynamic similarity criteria were clarified. The results show that the dynamic similarity coefficient is the key parameter governing dynamic similarity relationships, and its value directly determines the similarity of inertia response and energy transfer between the model and the prototype. The optimal geometric similarity ratio and wave velocity similarity ratio for the dynamic similarity criteria were determined. The proposed coal-rock dynamic similarity principle for coal burst breaks through the limitations of traditional static similarity theory, achieves quantitative characterization of inertia effects and energy release behavior, and provides an operable theoretical basis for dynamic physical simulation experiments of coal burst.