A Fractional Creep Model for Deep Coal Based on Conformable Derivative Considering Thermo-Mechanical Damage

Abstract

In deep high-geostress and high-temperature environments, understanding the creep deformation of deep coal is of great significance for effectively controlling coal deformation and improving gas control efficiency. In this paper, the Abel dashpot is defined based on the conformable derivative, and a damage variable is introduced into the conformable derivative order, thereby constructing a damaged Abel dashpot. Combining the Weibull distribution and the Drucker–Prager yield criterion, the thermo-mechanical coupling damage variable is defined, and the coupling damage variable is introduced into the damaged Abel dashpot to establish a thermo-mechanical coupling damaged Abel dashpot. Based on the traditional framework of the Burgers creep model, a three-dimensional fractional creep model of deep coal considering the influence of thermo-mechanical coupling damage is proposed. Experimental data on coal creep under different temperatures and stress conditions are utilized to validate the effectiveness and applicability of the proposed three-dimensional fractional creep model and to determine the model parameters. A comparison between experimental data and model results reveals that the creep model effectively characterizes the time-dependent deformation of coal samples under varying temperature and stress influences. Additionally, an in-depth analysis is carried out on the influence mechanism of key parameters in the creep model, particularly focusing on the effects of stress levels and temperature on creep deformation.