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Article

# Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric

by 1,*, 3,*, 5, 1 and
1
College of Science, North China University of Technology, Beijing 100144, China
2
College of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China
3
School of Safety Engineering, North China Institute of Science and Technology, Sanhe 065201, China
4
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
5
College of Science, North China Institute of Science and Technology, Beijing 101601, China
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2022, 6(7), 353; https://doi.org/10.3390/fractalfract6070353
Received: 7 April 2022 / Revised: 13 May 2022 / Accepted: 17 May 2022 / Published: 23 June 2022
(This article belongs to the Special Issue Applications of Fractal Geometry Theory in Porous Media)
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. View Full-Text
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MDPI and ACS Style

Sui, L.; Wang, H.; Wu, J.; Zhang, J.; Yu, J.; Ma, X.; Sun, Q. Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric. Fractal Fract. 2022, 6, 353. https://doi.org/10.3390/fractalfract6070353

AMA Style

Sui L, Wang H, Wu J, Zhang J, Yu J, Ma X, Sun Q. Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric. Fractal and Fractional. 2022; 6(7):353. https://doi.org/10.3390/fractalfract6070353

Chicago/Turabian Style

Sui, Lili, Heyuan Wang, Jinsui Wu, Jiwei Zhang, Jian Yu, Xinyu Ma, and Qiji Sun. 2022. "Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric" Fractal and Fractional 6, no. 7: 353. https://doi.org/10.3390/fractalfract6070353

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