Research on Chaos Characteristic of Crack Evolution in Coal-rock Fracturing

Precisely describing the formation and evolution rules of coal-rock fracturing crack have great value on reservoir fracturing improvement and highly efficient mining of coal bed methane well. In this paper, a non-linear dynamic method is used to study crack damage evolution behavior of coal-rock fracturing. Considering distribution characteristics of natural cracks in coal-rock, and based on damage mechanics, a mathematical model on stress around the tip of coal-rock fracturing crack and crack evolution is developed. Micro-crack amounts, circumferential stress, and axial stress at the crack tip of coal-rock fracturing crack evolution process are used as characteristic indicators to describe crack evolutionary. C-C method is chosen to reconstruct the phase space of coal-rock fracturing crack evolution. Correlation dimension, Lyapunov index, and Kolmogorov entropy are introduced as chaos characteristic quantities of crack evolution system, and the process of coal-rock fracturing crack damage evolution could be calculated and described. Coal-rock mass of Zhangchen mining area in Heilongjiang, China was used as a research object, and the results show that as the radial stress increases, the Kolmogorov entropy and the degree of chaos decrease; also, as the circumferential stress increases, the Kolmogorov entropy increases, and a higher degree of chaos is obtained; increasing the number of micro-cracks evolution raises Kolmogorov entropy up to a critical value, and then the Kolmogorov entropy drops, which means the chaotic degree decreases. The results calculated show that crack formation is a damage evolution process which has chaos characteristics. Finally, we provided a new way for further research on coal-rock fracturing crack evolution regularities.