Justification of the values of shifting angles in the conditions of mining the reserves of the Verkhnekamskoe deposit of potassium-magnesium salts. Part 1. Theoretical foundations and determination of shift angles under conditions of complete undermining of the earth's surface based on a theoretical-empirical approach

In engineering practice, the use of shift angles has become widespread for assessing the safety of facilities actually located or planned for construction in the immediate vicinity of the boundaries of underground mining of reserves. The values of the latter are not constant and require justification for various mineral deposits. In this paper, the main attention is paid to the Verkhnekamskoye potassium-magnesium salt deposit (VMKMS). In periodically published (since 1960) regulatory documents governing measures to protect mines from flooding and the protection of undermined objects at the VMKMS, the concept of shift angle δ was encountered until 2008. At present, angles δ are not used explicitly – the construction of safety pillars for objects on the earth's surface is carried out according to three fixed values of boundary angles δ0, which contradicts the semantic load of the latter and determines the advisability of returning to the use of shift angles δ. In the pursuit of a balance between the safety of the objects being undermined and the minimization of mineral losses, it is important to be able to estimate the displacement angle δi for the period under consideration depending on the mining and geological conditions at a separate site of mineral reserves development. In the course of the study, an analysis was made of the values of the angles δ previously used in practice under the conditions of the VMKMS and approaches to their determination. The features of the formation of the marginal part of the displacement trough under conditions of complete undermining of the earth's surface were revealed. Based on the theoretical and empirical studies, a dependence was established that allows determining the value of the angle δi for conditions of complete undermining of the earth's surface.

Shchegolkov Y. S. Justification of the values of shifting angles in the conditions of mining the reserves of the Verkhnekamskoe deposit of potassium-magnesium salts. Part 1. Theoretical foundations and determination of shift angles under conditions of complete undermining of the earth's surface based on a theoretical-empirical approach. MIAB. Mining Inf. Anal. Bull. 2026;(2-1):61-84. [In Russ]. DOI: 10.25018/0236_1493_2026_21_0_61.

Yu.S. Shchegolkov, Chief Specialist, PJSC «Uralkali», 618426, Berezniki, Russia, e-mail: rabota.shegolkov@mail.ru.

1. Baryakh A. A., Tenison L. O. Substantiating engineering criteria for safe undermining of water-protective strata at the Verkhnekamsk salt deposit. Gornyi Zhurnal. 2021, no. 4, pp. 57—63. [In Russ].

2. Usanov S. V., Konovalova Yu. P., Usanova A. V. Research into causes of damage to low-rise residential buildings in the zone of influence of underground mining operations. News of the Tula state university. Sciences of Earth. 2023, no. 2, pp. 334—346. [In Russ].

3. Pawluszek-Filipiak K., Borkowski A. Integration of DInSAR and SBAS techniques to determine mining-related deformations using Sentinel-1 data: The case study of rydułtowy mine in Poland. Remote Sensing. 2020, vol. 12, no. 2, article 242. DOI:10.3390/rs12020242.

4. Peng S. S. Surface subsidence engineering: Theory and practice. Boca Raton: CRC Press, 2021. 216 p.

5. Kuznetsov M. A., Akimov L. G., Kuz'min V. I., Panteleev M. G., Chernyshev M. F. Sdvizhenie gornykh porod na rudnykh mestorozhdeniyakh [Rock movement at ore deposits], Moscow, Nedra, 1971, 224 p.

6. Kazakovskiy D. A. Sdvizhenie zemnoy poverkhnosti pod vliyaniem gornykh razrabotok [Movement of the earth's surface under the influence of mining], Moscow-Kharkov, Ugletekhizdat, 1953, 228 p.

7. Bukrinskiy V. A., Orlov G. V. Sdvizhenie gornykh porod i zemnoy poverkhnosti pri podzemnykh razrabotkakh [Rock and ground surface movement during underground mining], Moscow, Nedra, 1984, 247 p.

8. Nesterov M. P. Method for determining ground surface displacement angles for a given period during potash deposit mining. Mekhanika gornykh porod pri razrabotke mestorozhdeniy prirodnykh soley: trudy VNIIG. Vyp. 67 [Mechanics of rocks during the development of natural salt deposits. Proceedings of VNIIG. Vol. 67], Leningrad, 1974, pp. 69—74. [In Russ].

9. Viktorov S. D., Goncharov S. A., Iofis M. A., Zakalinskiy V. M. Mekhanika sdvizheniya i razrusheniya gornykh porod [Mechanics of rock displacement and fracture], Moscow, 2019, 360 p.

10. Posyl'niy Yu. V. Geometriya mul'dy sdvizheniya zemnoy poverkhnosti nad gornymi vyrabotkami ugol'nykh shakht [Geometry of the subsidence trough of the earth's surface above mine workings of coal mines], Novocherkassk, 2012, 216 p.

11. Nesterov M. P., Lvova A. V., Anikin N. F. Main features of the patterns of ground surface deformations at potash mines. Stroitel'nye konstruktsii: sbornik nauchnykh trudov NIISK. Vyp. 23 [Building structures. Collection of scientific papers of NIISK. Vol. 23], Kiev, Budivelnik, 1974. [In Russ].

12. Nesterov M. P. Features of the ground surface deformation process at potash deposits and the specifics of their consideration when selecting structural protection measures for undermined facilities. Doklady na mezhdunarodnom Simpoziume po zashchite okruzhayushchey sredy ot posledstviy podzemnoy ekspluatatsii mineral'nogo syr'ya [Reports at the International Symposium on Environmental Protection from the Consequences of Underground Exploitation of Mineral Resources], Tuzla (Yugoslaviya), 1975, pp. 179—183. [In Russ].

13. Anikin N. F., Lvova A. V., Beshentseva E. F. Features of the formation of the marginal parts of subsidence troughs under the conditions of the Verkhnekamsk deposit. Kontrol', prognozirovanie i upravlenie sostoyaniem porod v kaliynykh rudnikakh: sbornik nauchnykh trudov [Monitoring, forecasting and management of rock conditions in potash mines: collection of scientific papers], Leningrad, 1985, pp. 152—160. [In Russ].

14. Shchegolkov Yu. S. Determination of boundary angles of the ground surface displacement process during mining of reserves at the Verkhnekamsk potassium-magnesium salt deposit. Mine Surveying and Subsurface Use. 2024, no. 6, pp. 25—32. [In Russ]. DOI: 10.56195/20793332_2024_6_25_32.

15. Shchegolkov Yu. S. Assessment of full displacement angles and maximum subsidence angles under the conditions of mining reserves at the Verkhnekamsk potassium-magnesium salt deposit. Mine Surveying and Subsurface Use. 2025, no. 1, pp. 61—70. [In Russ]. DOI: 10.56195/2079-3332-2025-25-1-61-70.

16. Kratch G. Sdvizhenie gornykh porod i zashchita podrabatyvaemykh sooruzheniy [Rock movement and protection of undermined structures], Moscow, Nedra, 1978, 496 p.

17. Borisov A. A. Mekhanika gornykh porod i massivov [Mechanics of rocks and rock masses], Moscow, Nedra, 1980, 360 p.

18. Litvinskii G. G. On the theory of displacement of undermined rock mass. Knowledge-intensive technologies and equipment in industry and building. 2024, no. 5(79), pp. 5—20. [In Russ].

19. Jahanmiri S, Noorian-Bidgoli M. Land subsidence prediction in coal mining using machine learning models and optimization techniques. Environmental Science and Pollution Research. 2024, vol. 31, no. 22, pp. 31942—31966. DOI: 10.1007/s11356-024-33300-2.

20. Liya Zhang, Pengfei Gao, Zhengzheng Gan, Wenhao Wu, Yafeng Sun, Chuanguang Zhu, Sichun Long, Maoqi Liu, Hui Peng Surface subsidence monitoring of mining areas in hunan province based on Sentinel-1A and DS-InSAR. Sensors (Basel). 2023, vol. 23, no. 19, article 8146. DOI: 10.3390/s23198146.

21. Chernopazov D. S., Shkuratskii D. N., Sekuntsov A. I. Patterns of specific gravity distribution of rocks overlying the industrial stratum of the Verkhnekamsk salt deposit. Gornyi Zhurnal. 2021, no. 4, pp. 39—45. [In Russ].

22. Sadd M. H. Elasticity: Theory, applications, and numerics. Academic Press, 2025, 648 p.

23. Barashkov V. N., Smolina I. Yu., Puteeva L. E., Pestsov D. N. Osnovy teorii uprugosti: uchebnoe posobie [Fundamentals of elasticity theory: textbook], Tomsk, 2012, 184 p.

24. Timoshenko S. P., Voynovskiy-Kriger S. Plastinki i obolochki [Plates and shells], Moscow, Nauka, 1966, 640 p.

25. Feodos'ev V. I. Soprotivlenie materialov [Strength of materials], Moscow, Nauka, 1986, 514 p.

26. Shchegolkov Yu. S. Substantiating the criteria for the main angular parameters of the displacement process under the conditions of mining reserves at the Verkhnekamsk potassium-magnesium salt deposit. Mine Surveying and Subsurface Use. 2024, no. 3, pp. 42—54. [In Russ]. DOI: 10.56195/20793332_2024_3_42_54.