A constitutive model of coal and rock mass compaction in goaf areas considering particle re-fragmentation

Given the lack of effective characterization of the compaction-fragmentation multi-scale coupling effect in broken rock of the goaf caving zone by the existing constitutive models, this paper establishes a compaction constitutive model for goaf materials that integrates linear and nonlinear mechanical features. Based on the series spring theory, a stress-strain relationship expression is constructed by introducing the fractional calculus theory. Reliability analysis is conducted using compaction tests on broken coal-rock specimens with different strengths and moisture conditions. The results showed that the compaction of specimens under different conditions experienced three stages: rapid compaction, stable compaction and complete compaction. Saturated specimens were significantly affected by water-rock softening, and their stress thresholds at each stage were higher than those of dry specimens. The strain values were larger under the same stress, and the compaction characteristics of the three stages were more prominent. The proposed compaction constitutive model was in good agreement with the experimental stress-strain curves. The model parameter α was sensitive to specimen strain, and the α value of saturated specimens was higher than that of dry specimens. The root mean square error of the model in describing the compaction behavior of broken specimens ranged from 0.005 to 0.008, and the coefficient of determination ranged from 0.885 to 0.970, which verified the rationality and reliability of the model.