Physically based method for determining the Hausdorff’s topological dimension of capillary-porous media

¹ Agrophysical Research Institute, St. Petersburg, Russia
² St. Petersburg State University, St. Petersburg, Russia
³ Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia
⁴ St. Petersburg State Agrarian University, St. Petersburg-Pushkin, Russia
⁵ Research Institute of Agriculture of Crimea, Simferopol, Russia
⁶ AdGuard Software Limited, Nicosia, Cyprus

^* Corresponding author: kir_moiseev@mail.ru

Abstract

The soil structure the solid phase and pore space of the soils are a set of self-similar parts of each other at different levels ( for example, on level aggregates, micro-aggregates or elementary particles of soil). Fractal models of the soil structure best describe this spatial composition of soils. For a quantitative description of the soil structure, the dimension Hausdorff (D) is adopted, based on the premise different of scales in the soil structure. The existing methodology for determining the Hausdorff dimension using computational methods represents a series of labor- intensive operations including either special analysis of images or tomograms, or production of analyzes such as dry sieving and soil granulometric analysis. The development of less labor-intensive algorithms for determining the Hausdorff dimension is relevant. The direct, physical method for determining the parameters of the structure of the object of study presented in the work is preferable to the calculation method. The testing of the method proposed in the work consists in comparing the results of determining the values of the Hausdorff dimension obtained by the generally accepted methodology and the method for determining D by moisture filtration. The research results are summarized in a table and show almost complete convergence of the Hausdorff dimension values obtained on the different methodologies basis.