Micromechanical properties and fractal homogenization of coal based on nanoindentation

Distinct from hard rock, coal is relatively soft and fragmented. It is not only challenging to prepare test coal samples that meet the requirements of standard mechanical experiments but also impossible to recycle them for repeated testing. There is an urgent need to explore new mechanical testing methods to enhance the study of the mechanical properties of coal. In this study, the micromechanical parameters of the coal matrix solid phase were acquired through targeted nanoindentation technology. The elemental composition, surface morphology, and pore structure characteristics of each indentation point were determined by energy dispersive spectrometer, optical microscope observation, and high-pressure mercury injection experiments. The fractal homogenization equation is deduced based on fractal geometry and the Mori–Tanaka method. The validity of the fractal homogenization approach is verified by integrating the micromechanical parameters and pore structure characteristics of coal, and the impact of the microstructural parameters on the macroscopic mechanical properties of coal is discussed. The results show that the proportion of clay minerals in the solid phase of the coal is the greatest (81.18%), with the main mineral components being kaolinite and illite. The elastic modulus is 1.974 ± 1.036 GPa, the hardness is 0.131 ± 0.108 GPa, and the ratio of upper and lower pore scales conforms to the fractal calibration rate. The macroscopic equivalent elastic modulus rises along with the increase in the fractal dimension. When the fractal dimension is constant, the macroscopic equivalent elastic modulus decreases with the increase in λmin/λmax and increases with the increase in solid phase elastic modulus.