Estimation of fractal dimension of rock samples fracture surface

№1 (2021)

УДК 539.421: 539.38: 004.932.2
DOI: 10.47148/1609-364X-2021-1-36-44

S.A. Imashev, M.E. Cheshev

AbstractAbout the AuthorsReferences
An approach to estimate fractal dimension of a microphotograph of rock sample fracture surface using the Differential Box Counting (DBC) method is presented. The difference between this algorithm and the classical method for fractal dimension calculation is in that the grayscale levels of pixels of analyzed image are taken into account. This approach does not require initial binarization of the image, which is poorly applicable for estimation of fractal dimension of real objects, such as microphotographs of rock sample surface, which in turn does not lead to the loss of useful information. Testing the method on a set of images generated with different content of pixels of gray levels showed that there is a steady increase in fractal dimension values ​​with increase in the number of added pixels. It is shown that fractal dimension for a set of images simulating crack propagation also demonstrates growth with increasing of fracturing. From a geometric point of view, this feature is a consequence of increase of roughness of the surface, which is a set of rectangles, the height of which corresponds to gray level of pixels of analyzed image. This approach can be used to quantify changes in sample surface structure before and after load action, as well as in real time using high-speed photography of the sample surface or radioscopy of internal cracks.
Imashev Sanjar Abylbekovich, Candidate of Science in Physics and Mathematics, Senior Researcher Laboratory of Integrated Studies of Dynamic Processes in Geophysical Fields, Research Station of the Russian Academy of Sciences in Bishkek. Bishkek, 720049. Kyrgyzstan. E-mail:

Cheshev Mikhail Evgenevich, Junior Researcher, Laboratory of Integrated Studies of Dynamic Processes in Geophysical Fields, Research Station of the Russian Academy of Sciences in Bishkek. Bishkek, 720049, Kyrgyzstan. E-mail:

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Keywords: fractal analysis, fractal dimension, differential box-counting, fracture surface.

Section: Modeling geo objects and geo-processes