hi boy
"Ugol" magazin


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




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


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.


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


1. Qu X., Chen Y. & Yin D. Experimental study on progressive failure characteristics of strip coal pillar models under different roof and floor conditions. Case Studies in Construction Materials, 2023, (18), Article e02147. DOI: 10.1016/j.cscm.2023.e02147.

2. Chen L., Zhang D.S., Yao N., Wang L., Fan G.W., Wang X.F. & Zhang W. Coupling influence of inclination angle and moisture content on mechanical properties and microcrack fracture of coal specimens. Lithosphere, 2021, 2022, (Special 7), Article 6226445. DOI: 10.2113/2022/6226445.

3. Sarfarazi V., Babanouri N., Fattahi S. & Asgari K. Study on failure mechanism of room and pillar with different shapes and configurations under uniaxial compression using experimental test and numerical simulation. Underground Space, 2023, (9), pp. 105–121. DOI: 10.1016/j.undsp.2022.07.002.

4. Levkin Y.M. The usage of remote sensing technology and mathematical modeling for the analysis of emergency mine workings. Ugol’, 2022, (6), pp. 32-34. (In Russ.). DOI: 10.18796/0041-5790-2022-6-32-34.

5. Qiang S., Jialiang G., Feng Y. & Ruhong B. Cooperative mining technology and strata control of close coal seams and overlying coal pillars. Alexandria Engineering Journal, 2023, (73), pp. 473–485. DOI: 10.1016/j.aej.2023.04.071.

6. R?genes, E., Gomes, A.D.S., Farias, M.M.D. & Rasmussen, L.L. Pseudo-discontinuum model to simulate hard-rock mine pillars. Underground Space, 2023, (11), pp. 81–95. DOI: 10.1016/j.undsp.2022.12.002.

7. Khalkechev R.K.Multifractal modeling theory of rock mass deformation and destruction as the basis for automation of drilling and blasting technologies in coal open-pit mines. Ugol’, 2019, (11), pp. 32-34. (In Russ.). DOI: 10.18796/0041-5790-2019-11-32-34.

8. Khalkechev R.K. & Khalkechev K.V. Mathematical modeling of non-uniform elastic stress field of a rock mass with crystalline block structure/ Gornyj zhurnal, 2016, (3), pp. 200-205. (In Russ.). DOI: 10.17580/gzh.2016.03.05.

9. Khalkechev R.K. & Khalkechev K.V. Management of fracture selectivity in crushing and milling of geomaterials based on similarity and dimensional methods in fracture dynamics.Gornyj zhurnal, 2016, (6), pp. 64-66. (In Russ.). DOI: 10.17580/GZH.2016.06.04.

10. Khalkecheva L.K. & Khalkechev R.K. Automated monitoring system of transport berms condition for landslide danger in the form of subsidence. Ugol’, 2022, (4), pp. 50-52. (In Russ.).DOI: 10.18796/0041-5790-2022-4-50-52.

11. Khalkechev R.K. Fuzzy mathematical model of fracture concentration changes in a mineral under external load. Gornyj informacionno-analiticheskij byulleten?, 2019, (6), pp. 97-105. (In Russ.). DOI: 10.25018/0236-1493-2019-06-0-97-105.

12. Cherepanov G.P. Mechanics of brittle fracture. Moscow, Nauka Publ., 1974, 640 p. (In Russ.).

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


Hot from the press