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Direct Estimation of the Fractal Dimensions of a Fracture Surface of Rock

Author

Listed:
  • H. W. Zhou

    (Institute of Rock Mechanics and Fractals, China University of Mining and Technology, Xueyuan Road D11, Beijing 100083, P R China)

  • H. Xie

    (Institute of Rock Mechanics and Fractals, China University of Mining and Technology, Xueyuan Road D11, Beijing 100083, P R China)

Abstract

A direct determination of the fractal dimensions of a fracture surface is essential for a better understanding of its complete topographic characteristics. In this paper, a laser profilometer is employed to measure the topography of a rock's fracture surface. With the use of the triangular prism surface area and projective covering methods, the resultant data set enables us to directly determine the fractal dimensions of a rock's fracture surface. Moreover, a new method, referred to as the cubic covering method, is proposed. The theoretical issues of fractal dimension estimation are also discussed.

Suggested Citation

  • H. W. Zhou & H. Xie, 2003. "Direct Estimation of the Fractal Dimensions of a Fracture Surface of Rock," Surface Review and Letters (SRL), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 751-762.
    • Handle: RePEc:wsi:srlxxx:v:10:y:2003:i:05:n:s0218625x03005591
    DOI: 10.1142/S0218625X03005591
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    Cited by:

    1. Guosheng Ding & Hejuan Liu & Debin Xia & Duocai Wang & Famu Huang & Haitao Guo & Lihuan Xie & Yintong Guo & Mingyang Wu & Haijun Mao, 2023. "Experimental Study of the Shear Characteristics of Fault Filled with Different Types of Gouge in Underground Gas Storage," Energies, MDPI, vol. 16(7), pages 1-16, March.
    2. Zou, Mingqing & Yu, Boming & Feng, Yongjin & Xu, Peng, 2007. "A Monte Carlo method for simulating fractal surfaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 176-186.
    3. Yongjun Chen & Tubing Yin, 2024. "Digital Fracture Surface Morphology and Statistical Characteristics of Granite Brazilian Tests after Non-Steady-State Thermal Disturbance," Mathematics, MDPI, vol. 12(5), pages 1-27, February.
    4. Xiaolong Li & Chen Cao & Xin Lin, 2021. "Improved Image Analysis Method to Evaluate Tracking Property under Successive Flashover Based on Fractal Theory," Energies, MDPI, vol. 14(24), pages 1-13, December.

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