Imaged based fractal characterization of micro-fracture structure in coal

Hao Wu, Yingfang Zhou* (Corresponding Author), Yanbin Yao, Kejian Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)
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To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, we utilized the improved box counting method to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (Ro from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension and porosity, the size of representative element volume (REV), the relationship between Df2 and Df3 and the relationship between porosity and fractal dimension are investigated extensively. It is noticed that the fractal dimension-based REV of coal is smaller than the porosity-based REV. As the complement of previous theoretical studies, it is proved that porosity has an exponential relationship with fractal dimension. By deducing formulas based on fractal theory, a new way to get the lower self-similar region size from relation between porosity and fractal dimension is provided. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed as
Df3=CDf2+ φ, and the slope of the line, C, depends on the average 2D fractal dimension of the sample. Finally, the reference of the relation between Df2 and C of high rank coal is provided as C= -0.75Df2 +2.75.
Original languageEnglish
Pages (from-to)53-62
Number of pages10
Early online date8 Nov 2018
Publication statusPublished - Mar 2019

Bibliographical note

We acknowledge financial support from the National Natural Science Foundation of China (41830427; 41472137), the Petro China Innovation Foundation (2018D-5007-0101), the Key research and development project of Xinjiang Uygur Autonomous Region (2017B03019-1), the Royal Society Edinburgh and National Natural Science Foundation China (NSFC 41711530129), and the Foreign Experts’ Recruiting Program from the State Administration of Foreign Experts Affairs P.R. China.


  • fractal dimension
  • coal
  • micro-CT images
  • box-counting method
  • REV
  • porosity
  • Micro-CT images
  • Fractal dimension
  • Box-counting method, REV
  • Coal


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