Fractional creep model of temperature-stress-time coupled damage for deep coal based on temperature-equivalent stress

The effective stress concept of temperature equivalent stress and actual stress acting together is established from the point of view that stress and temperature cause the same strain. The yield failure of coal and rock mass arises from the effective stress formed by the combination of temperature equivalent stress and actual stress. A temperature-stress coupled damage variable is established according to the hypothesis that the strength of coal and rock microunits obeys Weilbull distribution law and meet Drucker-Prager (D-P) yield failure criterion. A temperature-stress-time coupled damage variable is established by introducing a negative exponential function related to temperature and actual stress duration. The temperature-stress coupled damage variable of coal and rock mass is independent of the action time of temperature and time, but only related to the yield function F. The time damage variable is associated with the action time after the effective stress reaches the yield, which is mainly manifested in the viscoplastic deformation. Uniaxial and triaxial fractional creep models considering temperature-stress-time coupled damage are established by using Caputo fractional derivative definition. The parameters of temperature-stress-time coupled damage creep model are obtained by fitting the laboratory test data of deep coal body. The sensitivity of fitting parameters to the model and the goodness of fit analysis show that temperature-stress-time coupled damage model can well demonstrate the creep curves under different temperatures and stresses and the fitting accuracy is high.