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On Fractal Dimension Of A Fracture Surface By Volume Covering Method

Author

Listed:
  • H. W. ZHOU

    (State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, P. R. China)

  • D. J. XUE

    (State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, P. R. China)

  • D. Y. JIANG

    (State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P. R. China)

Abstract

An accurate calculation of the fractal dimension of a fracture surface is of prime significance for the quantitative evaluation of mechanical behavior. A laser profilometer is employed to measure a surface roughness of a large sandstone sample. Based on the definition of Minkowski dimension, a new method, referred to as the volume covering method, is proposed to estimate fractal dimension by accurately calculating the number of virtual cell needed to cover prism-like volume. It is indicated that the method can fully use laser scanning-based elevation data of the surface and make an accurate estimation of fractal dimension of a fracture surface. Furthermore, another method related to the opposite corner is adopted to estimate the same rough surface with little error of the fractal dimension. A comparison analysis indicates that the volume covering method has the advantage of high accuracy and good applicability for a real fracture surface.

Suggested Citation

  • H. W. Zhou & D. J. Xue & D. Y. Jiang, 2014. "On Fractal Dimension Of A Fracture Surface By Volume Covering Method," Surface Review and Letters (SRL), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-11.
    • Handle: RePEc:wsi:srlxxx:v:21:y:2014:i:01:n:s0218625x14500152
    DOI: 10.1142/S0218625X14500152
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