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.

In the process of drilling, the drilling fluid will invade into the bedding plane of shale under the action of pressure difference that will cause hydration collapse and wellbore instability. In order to ensure the wellbore stability during shale oil and gas drilling, it is necessary to clarify the invasion law of drilling fluid along bedding fractures during the drilling process. The immersion experiment method is often used to study the invasion law of drilling fluid, which is quite different from the actual invasion process of drilling fluid underground. In this paper, the depth of drilling fluid invasion into shale under different confining pressures and displacement times is intuitively and accurately determined by the displacement experiment and NMR scanning first. Also, then the mathematical relationships between drilling fluid invasion depth and invasion time, invasion pressure difference, confining pressure, bedding angle, and drilling fluid viscosity were established. The errors between the calculated values of the drilling fluid invasion depth and the experimental values were less than 15%, and the calculation accuracy was high. In addition to the influence of invasion time, formation pressure difference and confining pressure on invasion depth were researched through the method of numerical simulation. The results showed that the liquid invasion depth increased logarithmically with the increase of invasion time and formation pressure difference, but it grew slowly in the later period and tended to be stable; the invasion depth decreased exponentially with the increase of confining pressure, bedding plane angle, and drilling fluid viscosity. The results in the paper provide a basis for the subsequent determination of the collapse pressure and collapse period of bedding shale.