Hysteresis characteristics of oxidation-thermodynamic for residual coal in goaf under uniaxial stress

• The characteristics of CSC are mainly affected by particle size and stress. • The change in permeability is the root cause of the thermal hysteresis for CSC. • The stress field could affect the characteristics of CSC during coal mining. During coal-mining processes underground, the coal spontaneous combustion caused by air leakage of narrow coal pillars and residual coal in goaf under pressure not only threatens the safety of mining of coal resources, but also leads to serious casualties. Therefore, the research of multi-field coupling for broken coal could be helpful to reveal the spontaneous combustion law of narrow coal pillars and residual coal in goaf and find the key for coal-fire prevention and control. Therefore, the uniaxial compression equipped with a temperature-programmed device is applied to conduct stress-heating tests on five types of coal particle sizes. Moreover, based on the Hertz contact deformation principle under the three-particle model, the thermodynamic hysteresis characteristics of broken coal under uniaxial stresses are theoretically analyzed. The results are shown as follows: (i) Uniaxial stress leads to significant hysteresis effects on the critical temperature of coal spontaneous combustion, heating rate, Graham’s Ratio-R 2 temperature coefficient and pyrolysis temperature. (ii) As the particle radius increases, the growth rate of the exothermic intensity is suppressed, while it has no inhibitory effect on the critical temperature of the minimum exothermic intensity. (iii) The extreme point for the limit parameter of coal spontaneous combustion and the critical temperature shows the same corresponding hysteresis under uniaxial stress. The particle size ratio changes the limit parameter of coal spontaneous combustion obviously, and coal with a large particle size would reduce the risk of spontaneous combustion. (iv) The stress–strain curves and the stress-porosity curves are divided into stages, and it is found that the critical uniaxial stress of the porosity and strain of each coal sample is up to 4 MPa. Moreover, the temperature is the main reason for the hysteresis of permeability. The stress sensitivity of permeability declines with the effective stress rising, increases with the temperature going up, and decreases with the coal particle size reducing. (v) The hysteresis effect of uniaxial stress on coal spontaneous combustion first increases, then decreases, and finally increases.