**UNDERGROUND MINING
**

*Original Paper*

UDC 622.272:658.012.122:51.001.57© Khalkechev K.V., Khalkechev R.K., Levkin Yu.M., 2023

ISSN 0041-5790 (Print) • ISSN 2412-8333 (Online) • Ugol’ – Russian Coal Journal, 2023, № 7, pp. 56-58

DOI: http://dx.doi.org/10.18796/0041-5790-2023-7-56-58

**Title **

**MATHEMATICAL MODEL OF THE STRESS FIELD IN THE PILLARS WITH DUE ACCOUNT TAKEN OF THE MAIN CRACK IN COAL FIELDS**

**Authors**

Khalkechev K.V. 1, Khalkechev R.K.1, Levkin Yu.M.2

1National University of Science and Technology “MISIS” (NUST “MISIS”), Moscow, 119049, Russian Federation

2Moscow Polytechnic University, Moscow, 105064, Russian Federation

**Authors Information **

**Khalkechev K.V.,**Doctor of Physico-Mathematical Science, Doctor of Engineering Sciences, Professor at subdepartment: “Geology and mine surveying”, e-mail: h_kemal@mail.ru

**Khalkechev R.K.,** Doctor of Engineering Sciences, Professor at subdepartment: “Infocommunication technologies”, e-mail: syrus@list.ru

**Levkin Yu.M.,** Doctor of Engineering Sciences, Professor, Member of the Russian Union of Surveyors, e-mail:* *lev5353@bk.ru

**Abstract**

In order to determine the stress-strain state in the pillars represented by full-crystalline rocks, a mathematical model of the stress field with due account taken of the main crack was constructed. It is assumed that the analyzed pillar has a full-crystalline structure, in which there is a horizontally oriented crack. The dimensions of this crack exceed the characteristic size of the elementary volume. The main horizontally oriented open crack in the pillar has technogenic origin and induces an additional internal stress field. On the other hand, the internal stress field, due to the structural features of full-crystalline rocks, contributes to the formation of vertically oriented cracks. Moreover, if they formed a main crack, then the pillar will lose stability, which can lead to an emergency. As a result, the stress state in the pillars is formed by a superposition of stresses induced by the external field and the field induced by the main crack.

**Keywords**

Mathematical model, Pillar stability, Stress state, Fracture, Full-crystalline rock, Inhomogeneous medium, Effective elastic modulus, Superposition of stress fields.

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**For citation**

Khalkechev K.V., Khalkechev R.K. & Levkin Yu.M. Mathematical model of the stress field in the pillars with due account taken of the main crack in coal fields.* Ugol’, *2023, (7), pp. 56-58. (In Russ.). DOI: 10.18796/0041-5790-2023-7-56-58.

**Paper info**

*Received June 6, 2023 *

*Reviewed June 14, 2023*

*Accepted June 26, 2023 *