Permeability in porous media has an important role in many engineering applications, which depends mainly on the pore size, distribution, and connectivity of porous media. As the pore structure distribution of coal has a multi-scale fractal dimension characteristic, this study aimed to propose a multi-scale fractal dimension characteristics units model (MFU) to describe the pore structure distribution by analyzing the multi-scale fractal dimension characteristics of coal pore media. Then, a multi-scale fractal permeability model was established based on MFU. The pore structure distribution was obtained by mercury injection porosimetry (MIP) and nuclear magnetic resonance (NMR) experiments. Based on MIP and NMR experimental data, the permeability contribution of different pore diameters were calculated. The results show that the permeability contribution of the micropore was minimal and can be ignored. The permeability contribution of mesopores was about 1–5%, and the permeability contribution of macropores was about 95–99%, which plays a decisive role in the seepage process. The calculated results, based on multi-scale fractal permeability model and the experimental permeability data, are in the same order of magnitude. The permeability prediction based on proposed model is better than classical single fractal permeability model.

Dynamic failure of surrounding rock often causes many casualties and financial losses. Predicting the precursory characteristics of rock failure is of great significance in preventing and controlling the dynamic failure of surrounding rock. In this paper, a triaxial test of granite is carried out, and the acoustic emission events are monitored during the test. The fractal characteristics of acoustic emission events’ energy distribution and time sequence are analyzed. The correlation dimension and the b value are used to study the size distribution and sequential characteristics. Furthermore, a rock failure prediction method is proposed. The correlation dimension is chosen as the main index and the b value is chosen as a secondary index for the precursor of granite failure. The study shows that: (1) The failure process can be divided into an initial stage, active stage, quiet stage, and failure stage. (2) The b value and correlation dimension both can describe the process of rock failure. There is a continuous decline before failure. Because of the complexity of the field, it is difficult to accurately estimate the stability of surrounding rock using a single index. (3) The combination of the b value and correlation dimension to establish a new method, which can accurately represent the stability of the surrounding rock. When the correlation dimension is increasing, the surrounding rock is stable with stress adjusting. When the correlation dimension is decreasing and the b value remains unchanged after briefly rising, the surrounding rock is stable, and stress is finished adjusting. When the correlation dimension and b value are both decreasing, the surrounding rock will be destroyed.

To study the mechanical behavior and energy evolution law of gas-filled deep coal, conventional triaxial compression experiments under different confining pressure and gas pressure conditions and cyclic loading and unloading experiments under different gas pressures were carried out. The failure characteristics and mechanical parameters evolution of two loading modes were analyzed. In addition, the energy density and ratio evolution law under cyclic loading was revealed, and based on these findings, an attempt was made to depict the relation of cumulative dissipated energy density and volumetric strain by fitting the experimental data. The results indicated that failure of coal is expressed as a single shear surface under conventional compression, while under cyclic loading mode, coal behaves with multi-fracture crushing failure. Mechanical parameters showed a trend of decay with increasing gas pressure, and that cyclic loading and unloading increases the bearing capacity of coal by 8–38%. The dissipated energy density and ratio grew significantly when coal entered the yield stage. In the compaction stage, the cumulative dissipated energy density rose with volumetric strain in the form of an exponential function, and it increased with relative volumetric strain as a power function.