A quantitative description of the permeability of deep coal is of great significance for improving coalbed methane recovery and preventing gas disasters. The Schlumberger–Doll research (SDR) model is often used to predict rock permeability, but it has inherent defects in characterizing the pore structure of deep coal. In this study, a permeability model with fractal characteristics (FCP model) is established for deep coal based on nuclear magnetic resonance (NMR). The constants in the SDR model are theoretically explained by the relevant parameters in the FCP model. Centrifugation and NMR experiments were performed to determine the optimal centrifugal force and dual T₂ cutoff values. The results show that the coal samples are mainly composed of micrometer and nanometer pores. The adsorption pores account for the largest proportion, followed by the percolation pores and migration pores. In addition, the prediction accuracy of the FCP model is significantly higher than that of the other three models, which provides a fast and effective method for the evaluation of deep coal permeability.

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.

The increase in mining depth causes the temperature of the coal seam to rise. Studying the effect of temperature on the mechanical property of coal is very necessary. In this paper, based on the results of conventional triaxial compression experiments of coal samples, the discrete element program PFC^2D was used to conduct a conventional triaxial compression simulation of coal samples to obtain microscopic parameters. On this basis, the conventional triaxial simulation study of coal samples at different temperatures was carried out to explore the influence of temperature on the physical and mechanical properties of coal. In this process, acoustic emission and energy monitoring were carried out. The damage and failure process of coal is divided into three stages: the undamaged stage, the stable damage stage, and the rapid damage stage. The relationship between acoustic emission characteristic law, energy transformation law, and crack evolution in the damage and failure process of coal was analyzed in detail. The results indicate that the fracture evolution is affected by the increase in cross-sectional area and the decrease in distance between particles due to the expansion of particles, which corresponds to the phenomenon that the temperature increase produces new microcracks and the particles expand to fill the original cracks in the experiment. This indicates that PFC^2D can be used as an effective numerical method for a coal mesoscopic study, and the results of these numerical experiments are also helpful to deepen the understanding of the damage mechanism of coal failure under thermo-mechanical coupling.