ON FRACTAL DIMENSION OF A FRACTURE SURFACE BY VOLUME COVERING METHOD

H. W. Zhou (), D. J. Xue and D. Y. Jiang
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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

Surface Review and Letters (SRL), 2014, vol. 21, issue 01, 1-11

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.

Keywords: Fractal dimension; fracture surface; volume covering method; prism-like volume (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0218625X14500152

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