Mechanical and energy characteristics of coal–rock composite sample with different height ratios: a numerical study based on particle flow code

To explore the differences in mechanical and energy evolution characteristics of coal–rock composite samples with different coal–rock height ratios, uniaxial compression tests of coal–rock composite samples with height ratios ranging from 4:1 to 1:4 were conducted by PFC software. A total of 7 PFC models were built and calculated. Results show that the smaller coal–rock height ratios lead to the higher elastic modulus and higher peak strength, both following exponential relationships with coal–rock height ratios, while the peak strain decreases linearly with the decrease of coal–rock height ratios. When the coal–rock height ratios decrease from 4:1 to 1:3, the fragmentation degree of coal body decreases gradually, and the failure modes are mainly of “V” type. And when the ratio is reduced to 1:4, failure mode is no longer of “V” type, the degree of coal body breaking becomes larger, and the part of rock body in the composites is also damaged. With the decrease of coal–rock height ratios, number of acoustic emission events of the composites increase first and then decrease. And U, $$U_{e}$$ and $$U_{d}$$ at different coal–rock height ratios exhibited similar trends, all of which increase slowly first, fast afterwards and very sharply at the peak stress points. At the peak stress point, the values of total input energy ( $$U_{A}$$ ) and dissipative energy ( $$U_{A} {d}$$ ) decrease firstly then increase as the coal-rock height ratios decreases and the value of elastic strain energy ( $$U_{A} {e}$$ ) decrease as coal-rock height ratios decreases. While the decrease of both $$U_{A}$$ and $$U_{A} {d}$$ are larger than $$U_{A} {e}$$ . These results can provide a useful reference for safe and efficient exploitation of coal resources.