Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the complexity of rock fracture networks and the difficulty in directly applying the limit definition of the fractal dimension, the definition and application of the fractal dimension have become hot topics in related projects. In this paper, the traditional fractal calculation methods were reviewed. Using the traditional fractal theory and the head/tail breaks method, a new fractal dimension quantization model was established as a simple method of fractal calculation. This simple method of fractal calculation was used to calculate the fractal dimensions of three rock fracture networks. Through comparison with the box-counting dimension calculation results, it was verified that the model could calculate the fractal dimension of the fracture length of rock fracture networks, as well as quantify it accurately and effectively. In addition, we found a number of similarities between rock fracture networks and urban road traffic networks in GIS. The application of the space syntax metric to rock fracture networks prevents controversy with respect to the definition of the axis and it showed a good effect. Using the space syntax metric as a parameter can better reflect the space relationship of rock fractures than length. Through the calculation of the fractal dimension of the connection value and control value, it was found that the trend of the length fractal dimension was the same as that of the control value, whereas the fractal dimension of the connection value was the opposite. This further verifies the applicability of the space syntax metric in rock fracture networks.

As a non-homogeneous porous medium, the structural complexity of coal directly affects pore structure parameters and gas percolation characteristics, which in turn determine the fractal dimension of coal samples. Among them, the specific surface area of coal largely determines the complexity of the pore structure and is closely related to coal and gas protrusion hazards. To investigate the relationship between the fractal dimension of coal and its specific surface area, we analyzed the pore structure of coal samples using low-temperature nitrogen adsorption, the mercury pressure method, and X-ray micro-computed tomography (CT) experiments. By calculating the fractal dimension of coal and reconstructing it in three dimensions, the morphological characteristics and distribution of pores can be described qualitatively and quantitatively. The fractal dimension of coal samples was found to increase exponentially with the specific surface area based on measurements of large pores and mesopores via the mercury pressure method and those of small pores and micropores using the nitrogen adsorption method. X-ray micro-CT experiments revealed that the fractal dimension of large pores (i.e., >2 μm) conformed to this pattern.

Studying mining fracture development is vital for geotechnical and mining engineering and geological disaster prevention. This research assesses crack effects on rock mass stress equilibrium during coal mining, potentially causing geological disasters such as land subsidence and landslides. Using fractal geometry theory, the present study investigates the development of horizontal and vertical mining cracks, revealing their propagation patterns. The fractal dimension generally increases as the propulsion distance increases; however, fluctuations vary from 250 to 287.5 m, forming a wavering line chart. The proportion of mining fracture area relative to mining space area increases with greater propulsion distance, indicating expanded upward mining space due to separation layers. The horizontal distribution of mining cracks persists, while the vertical distribution decreases, suggesting ground subsidence results from upward transmission. The fastest increase in fractal dimension occurs at 87.5–100 m. At 250 m, it peaks at 1.4136, indicating complex crack structures. During propulsion, the fractal dimension decreases due to upward mining space expansion through overlying rock layer collapse, forming new cracks. The proportion of mining crack area to mining space area increases gradually throughout the mining process. The present study presents a simulation model for crack identification, noting limitations in identifying tiny cracks.