**UNDERGROUND MINING
**

*Original Paper*

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

ISSN 0041-5790 (Print) • ISSN 2412-8333 (Online) • Ugol’ – Russian Coal Journal, 2023, № 8, pp. 84-96

DOI: http://dx.doi.org/10.18796/0041-5790-2023-8-84-96

**Title **

**MATHEMATICAL MODEL DEVELOPMENT OF THE STRESS FIELD IN THE PILLARS STRATIFIED TEXTURE IN COAL DEPOSITS**

**Authors**

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

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

2Moscow Polytechnic University, Moscow, 105064, Russian Federation

**Authors Information **

**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

**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

**Abstract**

A mathematical model has been developed that makes it possible to determine the stress field in the pillars of a stratified texture in coal deposits. It is assumed that stratums in pillars have a polycrystalline structure. Effective tensors of elastic modulus are used to determine the deformation properties of stratums in pillars. To calculate these elastic characteristics, final expressions are obtained. Calculations based on these expressions give different values of the effective tensors of elastic modulus for stratums in pillars. When such stratums are too close to each other in the pillar, shear stresses arise in them, leading to the formation of a crack. This crack forms an additional stress field, wich are determined with appropriate mathematical expressions. Under the action of rock pressure, an inhomogeneous stress field is induced into the stratums at the structural level. 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 between stratums.

**Keywords**

Mathematical model, Pillar stability, Shearing stress, Main crack, Inhomogeneous medium, Full-crystalline rock, Effective elastic modulus, Superposition of stress fields.

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**For citation**

Khalkechev R.K., Levkin Yu.M. & Khalkechev K.V. Mathematical model development of the stress field in the pillars stratified texture in coal deposits.* Ugol’, *2023, (8), pp. 84-96. (In Russ.). DOI: 10.18796/0041-5790-2023-8-84-96.

**Paper info**

*Received June 6, 2023 *

*Reviewed July 14, 2023*

*Accepted July 26, 2023 *