Geotechnical and Geological Engineering

, Volume 36, Issue 2, pp 737–745 | Cite as

Research on the Fractal Dimension of the Orientation Pole Distribution for Rock Mass Joint

  • Yuanjing Mao
  • Bin HuEmail author
  • Lu Wang
  • Yao Li
Original paper


The spatial distribution of joint orientations features self-similarity. Based on the fractal theory, a new method for meshing of Schmidt pole diagram has been established to study the fractal dimension of the orientation pole distribution of joint. Meshing of Schmidt pole diagram by equal area is performed in both circumferential and radial directions. When the cycle number n is set, the circle is evenly divided with n diameter lines to obtain 2n sectors of equal area; meanwhile the radius R is divided n times to obtain n rings, and specific ring radii are set to perform meshing of Schmidt pole diagram by equal area, thus obtaining different side lengths of cells and corresponding number of cells occupied by poles; on this basis the fractal dimension of joints was calculated. This method is applied to the research on the fractal dimension of joints in rock mass of mine. The results of the research showed that the method with fewer parameters made the process in which the fractal dimension of the orientation pole distribution of joint was solved simply and easy to operate, and calculating the fractal dimension of the orientation pole distribution for joint by this method could better describe the dispersity and complexity of the orientation distribution of joint.


Rock mass joint Equal area stereonet Orientation pole distribution Fractal dimension Fractal features 



This study is supported by the National Natural Science Foundation of China (Grant No. 41672317). We express our deep appreciation to the reviewers for their helpful comments and suggestions.


  1. Carr JR, Warriner JB (1989) Relationship between the fractal dimension and joint roughness coefficient. Bull Assoc Eng Geol 26(2):253–263Google Scholar
  2. Chen JP, Xiao SF, Wang Q (1995) A principle of random discontinuities 3-D network numerical modeling. Publication House of Northeast Normal University, ChangchunGoogle Scholar
  3. Chen JP, Shang XC, Lu B et al (2001) A delineation of orientation data randomly distributed in rock mass. J Chengdu Univ Sci Technol 28(S):86–92Google Scholar
  4. Chen JP, Wang Q, Gu XM et al (2007) Fractal dimension of orientation pole distribution for rock mass joints. Chin J Rock Mech Eng 26(3):501–508Google Scholar
  5. Chen W, Jian WB, Dong YS et al (2015) Influence of weak structural surface on stability of granite residual soil slopes. Chin J Geol Hazard Control 26(1):23–30Google Scholar
  6. Ding DW (1993) Study on the fractal of structure of rock mass and its application. Rock Soil Mech 14(3):67–71Google Scholar
  7. Ghosh A, Daemem JK (1993) Fractal characteristics of rock discontinuities. Eng Geol 34:1–9CrossRefGoogle Scholar
  8. Jin AB, Li B, Deng FG (2012) Effect of intermittent joints on the mechanical properties of rock mass. J Univ Sci Technol Beijing 34(12):1359–1363Google Scholar
  9. Liu YZ, Sheng JL, Ge RX et al (2007) Study on fractal character of rock mass discontinuity distribution and evaluation of rock mass quality. Rock Soil Mech 28(5):971–975Google Scholar
  10. Liu B, Jin AB, Gao YT et al (2016) Construction method research on DFN model based on fractal geometry theory. Rock Soil Mech 37(S1):625–631Google Scholar
  11. Lu HF, Yao DX (2014) Stress distribution and failure depths of layered jointed rock mass of mining floor. Chin J Rock Mech Eng 33(10):2030–2039Google Scholar
  12. Mahtab MA, Yegulalp TM (1984) A similarity test for grouping orientation data in rock mechanics. In: Proceedings of the 25th US symposium on rock mechanics. Plenum, New York, pp 495–502Google Scholar
  13. Shanley RJ, Mahtab MA (1976) Delineation and analysis of clusters in orientation data. Math Geol 8(1):9–23CrossRefGoogle Scholar
  14. Song LJ, Xu M, Lu SQ et al (2013) Fractal dimension improved algorithm of orientation pole distribution for joints. Chin J Rock Mech Eng 32(S2):3303–3308Google Scholar
  15. Sun GZ (1988) Rock mass structural mechanics. Science Press, BeijingGoogle Scholar
  16. Wang Q (1992) Study on statistical methods of joint. Site Investig Sci Technol 4:27–31Google Scholar
  17. Wang LS, Li TB, Zhao QH (1994) Near epigenetic time-dependent structure and human engineering. Geological Publishing House, BeijingGoogle Scholar
  18. Xie HP (1994) Estimation on rock joint roughness coefficient (JRC) by fractal feature. Sci China Ser B 24(5):524–530Google Scholar
  19. Yuan BY, Yang ZF, Xiao SF (1998) Fractal geometry of essential elements of rock mass structure. J Eng Geol 6(4):355–361Google Scholar
  20. Zhang XR (1989) Joint angle statistic method. J Guilin Coll Geol 9(2):219–222Google Scholar
  21. Zhu ZC, Wei BZ, Zhang WS et al (1999) Structural geology. China University of Geosciences Press, Wuhan, pp 219–231Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of EngineeringChina University of GeosciencesWuhanChina

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