Towards the issue of the methods of calculating fractal dimension of the disperse pulverescent-clayey soil structure

  • T. P. Mokritska Oles Honchar Dnipro National University
  • K. O. Samoylych graduate student, Oles Honchar Dnipro National University
  • A. O. Stanchev Oles Honchar Dnipro National University
Keywords: loess, porosity, fractal dimension, particle distribution function.


Our study on the structure of pulverescent-clayey loess deposits was conducted at different levels of organization with the purpose of clarifying the characteristics of their deformational behaviour.In our description of the structure and microstructure, the theory of fractals is used in the study ofmacroporosity, inter-aggregate porosity and interparticle porosity of loess loams and sand loams. The calculations of indicators of fractal dimension structure can be made using analysis of electronic images of microstructure, granulometry and dispersity of soils, experimental calculations of penetrability and porosity. Comparison of the results of quantitative fractal dimension indicators obtained using different methods is of interest at the stage of choosing a more efficient and meaningful method. The article analyses the results of calculating the values of the fractal dimension of particle distribution function, which were obtained using different methods. We conducted analysis of discretion of differently formed stratigraphic-genetic horizons. The images were analyzed in the “JmageL” programme, the calculation of the Hurst exponent and fractal dimension of the particle distribution function was made using “Fraktan” software and EXELL electronic tables. The study analyzedimages on different scales. The results of the calculations of the particle sizes were considered as a series of fractal dimension series sufficient for calculation, Hurst exponent, correlational dimension and entropy of length. The results of granulometric examination (pipette method, three methods for preparing the samples) were analyzed using classified data on the fractions. The following fractions were considered: the fractions with particles less than 0.001 mm, 0.002 mm, 0.005 mm, 0.01 mm, 0.05 mm, 0.1 mm, 0.25 mm, 0.5 mm, 1 mm, 2 mm, 5 mm, 10 mm. The values of fractal dimension of particle distribution at the level of inter-aggregate and interparticle porosity were different. When the disperse method for preparing the sample was used, the fractal dimension of particle (fraction) distribution obtains higher values compared to the aggregate and semi-disperse methods. We proved the relation between the values of fractal dimension and the genesis, discretion and method for preparing the soil samples. The dimension values of loess sediments were lower compared to paleosolregardless of the method for the preparation. Comparability of the assessments of fractal dimension of distribution of the solid phase of different topological dimension (flat sections and volumetric particles) was observed during aggregate and semi-disperse methods of preparation. 

Author Biographies

T. P. Mokritska, Oles Honchar Dnipro National University
 Head Department of Geology and Hydrogeology, prof., Dr.  Geol. Sciences, prof.Oles Honchar Dnipro National University
K. O. Samoylych, graduate student, Oles Honchar Dnipro National University
Oles Honchar Dnipro National University
A. O. Stanchev, Oles Honchar Dnipro National University
student, Oles Honchar Dnipro National University


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How to Cite
Mokritska, T., Samoylych, K., & Stanchev, A. (2017). Towards the issue of the methods of calculating fractal dimension of the disperse pulverescent-clayey soil structure. Journal of Geology, Geography and Geoecology, 25(2), 123-128.