Abstract
The possibility of using a multifractal approach to study the tectonic disturbance of coals has been investigated. The relationship between the coal disturbance and the asymmetry of fractal spectra of coal images obtained by means of scanning electron microscopy (SEM) is revealed: it has been established that undisturbed coals are characterized, as a rule, by a symmetric fractal dimension spectrum, and the disturbed coals are described by a fractal spectrum with some degree of asymmetry. It is shown that if fractal spectra of images have a symmetric appearance, then brightness distributions of these images are well fitted by a lognormal curves and parameters of these fittings can be estimated through characteristics of the fractal spectra. By using multifractal analysis of images for more than 140 test coal specimens from the quiet zone of a seam and the outburst zone, differences in the brightness distributions for images of coals with various degrees of disturbance were revealed. The basis of the research is the assumption that differences in the structure of disturbed and undisturbed coals are reflected in histograms of the brightness distributions for images of coal specimens. According to the results of multifractal analysis of images for the test coal specimens, it was established that the brightness distributions for images of the surface of undisturbed coal specimens are lognormal, while the brightness distributions for images of the surface of highly disturbed coal specimens, in most cases, deviate from the lognormal one. The conducted studies allow us to conclude about the applicability of the multifractal approach for assessing the degree of coal disturbance using digital images of coal specimens.
Highlights
The causes of methane explosions and many other accidents in coal mines are, as a rule, sudden and rapid destruction of coal seam in mines
To characterize the structure of coals with various degrees of disturbance, it seems appropriate to use a multifractal approach, which is a natural generalization of the fractal approach and allows us to move from studying scale–invariant properties of defects cascades to studying a measure, reflecting the spatial distribution of various kinds of defects in coals
Based on the results of the analysis of calculated asymmetry coefficient values, it was established that undisturbed coals are characterized, as a rule, by a symmetric spectrum of fractal dimensions, and the disturbed coals are described by a spectrum having a certain degree of asymmetry (Fig. 1)
Summary
The causes of methane explosions and many other accidents in coal mines are, as a rule, sudden and rapid destruction of coal seam (rocks) in mines In this regard, we can conclude that the prediction of the destruction of rocks and rock masses requires a more in–depth study of the destruction process, taking into account large–scale heterogeneities and structural features of the geological environment. The non–uniform nature of the distribution of defects in coal entails a heterogeneous distribution of loads: some structural blocks of coal are overloaded, while others remain underloaded or do not any load at all In this regard, to characterize the structure of coals with various degrees of disturbance, it seems appropriate to use a multifractal approach, which is a natural generalization of the fractal approach and allows us to move from studying scale–invariant properties of defects cascades to studying a measure, reflecting the spatial distribution of various kinds of defects in coals. The aim of this work is to demonstrate a progress in developments and experimental verification of a multifractal approach to assessing the degree of coal disturbance from SEM–images of coal specimens
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