Кафедра вищої математики

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Відповідальний за розділ: доцент кафедри Вищої математики Глухов Олександр Дмитрович. E-mail: glukhov@nau.edu.ua

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Browsing Кафедра вищої математики by Author "Balashova, Yuliia"

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    Consideration the rheological properties when investigating the heterogeneous behavior of a rock mass in time
    (National Transport University, 2023) Liashenko, Yana; Bondarenko, Liudmyla; Balashova, Yuliia; Ляшенко, Яна Григорівна; Бондаренко, Людмила Петрівна; Балашова, Юлія Борисівна
    The paper is devoted to the solution of nowadays relevant issue regarding the scientific substantiation of the most effective methods of mining rocks for various needs of the national economy, including for the construction of highways. The research was carried out on the basis of mathematical modeling methods, taking into account the rheological properties of rocks, heterogeneity of their structure, microdamage and behavior of the rock massif over time. As part of the work, geological material consisting of an isotropic viscoelastic matrix with stochastically placed inclusions in different directions was considered. The change in the stress-strain state of rocks with viscoelastic properties and containing randomly placed inclusions is determined. Provided that the size of the body is much greater than the size of the microinhomogeneities, the area containing the environment is considered infinite. The mathematical model is constructed on the basis of the fact that when homogeneous loads interact on a statistically homogeneous body, the random fields of stresses and strains that arise are also statistically homogeneous, and therefore, volume averaging can be performed as statistical averaging. The derivation of the calculation formulas is connected with the setting of an explicit form of density distribution of inclusions by direction. Based on the constructed mathematical model, microstructural stresses were investigated, effective parameters were calculated, and their dependence on the shape, orientation, and volume concentration of inclusions was determined. In addition, as a particular case, a fractured environment is considered. Taking into account such a significant heterogeneity of the geological rock and the presence of microdamages, the dependence of viscoelastic deformations on time and degree of damage was obtained. The obtained results make it possible to further evaluate the geomechanical situation, as well as to obtain the parameters of development systems for underground or open mining operations, which in turn will allow efficient mining of useful material.