Constitutive model of coal considering temperature under cyclic loading and unloading conditions

As the deep coal mining tends to be “normal”, it is of great significance to understand the mechanical properties and damage evolution of coal under high ground stress and high ground temperature environment in deep coal mining. The coal body of the Ji16-17-31030 working face in the Pingmei 12th Coal Mine was selected as the research object. The triaxial cyclic loading and unloading tests on the coal samples were carried out under different temperature conditions to examine the impact of temperature on their fundamental mechanical parameters, including peak strength, deformation modulus, and Poisson’s ratio. The stress-strain problems associated with different loading and unloading rates were reformulated into time-stress-strain problems, and a fractional viscoelastic-plastic constitutive equation considering the coupling effect of thermal and force was proposed by introducing the fractional derivative theory and the continuum damage theory. The results show that the deformation modulus of coal decreases linearly with the increase of cycle times, while the Poisson ratio of coal shows a deceleration increase, reaches the extreme value at the peak stress, and then decreases, indicating that the cyclic loading and unloading has a deterioration effect on the basic mechanical properties of the coal. With the increase of temperature, the peak strength of coal decreases nonlinearly, the damage accumulation slows down, and the corresponding strain increases gradually, which indicates that heating could enhance the ductile deformation ability of coal and accelerate the development of coal damage. In the process of cyclic loading and unloading, the input energy density, elastic energy density and dissipated energy density decay obviously decay with the increase of temperature in the stage of coal failure and instability, indicating that high temperature intensifies the damage inside the coal, reduces the coal strength, and reduces the external input energy required for failure. The fractional viscoelastic-plastic model considering the effect of temperature can better describe the mechanical behavior of deep coal body under cyclic loading and unloading conditions. The model is suitable for the complex stress state of deep coal body under a thermal-mechanical coupling, and provides an important reference for the research on the deformation and stability of deep coal body.