Discrete-element analysis and constitutive model for coal with predefined voids

Internal voids and other defects in coal-rock readily trigger local or global failure, causing dynamic hazards such as roadway collapse and rock bursts. To quantify the effects of voids on mechanical behavior and failure, displacement-controlled uniaxial compression simulations were performed on coal specimens with five void counts and eight distribution patterns. Key findings are: (1) Compressive strength, Elastic modulus, Pre-peak strain energy decreases monotonically with increasing number of voids and is approximately linear. Void distribution also affects strength, with a maximum reduction of 14.7 %. (2) The impact energy index decreases with increasing void count. Void distribution has a pronounced effect: the index spans 6.40–11.09 across the eight distribution patterns, indicating strong impact propensity in all cases. (3) As the number of voids increases, the crack-initiation stress first decreases and then increases, while the cumulative impact count decreases monotonically. The vertical three-void layout yields the highest cumulative impact count. (4) As void count increases, cracking progressively localizes toward the specimen's lower region. (5) A damage constitutive model for voided coal was developed by coupling statistical distribution theory with the Drucker-Prager (D-P) criterion and subsequently validated. The model achieves greater than 90 % accuracy and reliably reproduces the stress-strain response of voided coal. (6) An energy-migration model for instability in voided coal was established, and energy accumulation, redistribution, and release under loading were analyzed to elucidate the associated instability mechanism. These findings offer theoretical guidance for roadway support design, stability assessment in mining engineering, and the prevention and control of coal-rock dynamic hazards.