TREND ANALYSIS OF THE ROCK MASS PROPERTIES ON THE BASIS OF FRACTAL REPRESENTATION OF SPATIAL RANGESO. G. Latyshev, O. O. Kazak |
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DOI http://dx.doi.org/10.21440/2307-2091-2018-2-79-84
O. G. Latyshev, O. O. Kazak / News of the Ural State Mining University 2 (2018) 79-84
Evaluation of rock mass characteristics is the basis for designing the technology of mineral deposits development, which indicates the relevance of the work.
The purpose of the present work is to establish the laws of spatial distribution of rock mass properties. Their establishment requires the solution of the following problems: determination of the probability of a trend; identification and elimination of emissions (local component) and construction of a trend line.
The research methodology consists of using the tools of fractal geometry to determine the properties of a random spatial series. The use of the apparatus of classical trend analysis, based on purely statistical analysis, in relation to the specifics of research data does not provide an adequate solution to these problems. This paper discusses the results of implementing the fractal representation of the spatial series in case of the rock mass strength distribution in the Yubileynoye deposit (Bashkortostan). The quantitative estimation of the trend line as a fractal object is to determine its fractal dimension by the method of “fractal lengths”. Step-by-step implementation of this method allowed identifying areas of the rock mass with natural variability of properties by depth. The variation of the values of a number (the random component) obeys an equation of the fractal Brownian motion (FBM). Determination of the parameters of this equation makes it possible to predict the characteristics of the rock mass in those areas where engineering-geological testing was not carried out. For this purpose, a statistical model of variability of the characteristics of the array, based on the Monte Carlo method was developed. Implementation of the model allows us to add the spatial series (replicate sample), i.e., to predict the properties of the array between the points of sampling.
Summary. The proposed techniques and software that forms the methodology of fractal analysis of variability of a rock mass at depth and along strike of the deposit. The methodology provides additional information for engineering and geological studies of deposits, especially with a limited amount of sample data. It allows increasing the reliability of the forecast of mining conditions for the construction of mines and mining operations.
Keywords: rocks; rock mass strength; fractal trend analysis.
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