The use of circular slot to restore mining displacements

Traditionally, to measure stresses in rocks, slot unloading is used. When unloading, strains are measured in the specified principal directions of the stress tensor, stresses are determined by deformations. Another way to use slot unloading is to set the neighborhood of a point in the shape of a circle, followed by measuring the unloading radial displacements at the boundary points. In addition to unloading radial displacements, it is also proposed to find unloading tangential displacements. With the use of optical and mechanical systems, the authors suggest the way of measuring distances between points lying both on the same diameter and between adjacent points lying on the same circle. The dependences between radial and tangential displacements at the circle boundary are determined, and inside the circular neighborhood there is a homogeneous stress-strain state. For this state, the simplest ways of finding the principal axes of the stress tensor and its principal values are specified. Moreover, to describe the state of plane deformation we considered the generalization of the obtained approach to determining displacements when the investigated circular neighborhood is buried.

Keywords: stress state of rocks, circular slot unloading, normal and tangential displacements, plane-stressed state, plane strain, second boundary value problem, homogeneous state, principal axes and values.
For citation:

Chanyshev A. I., Abdulin I. M., Belousov О. E., Gorodilov L. V., Lukyashko O. A. The use of circular slot to restore mining displacements. MIAB. Mining Inf. Anal. Bull. 2023;(121):141—158. [In Russ]. DOI: 10.25018/0236_1493_2023_122_0_141.


The research was funded by the Russian Science Foundation (project No.2217-00188).

Issue number: 12
Year: 2023
Page number: 141-158
ISBN: 0236-1493
UDK: 539.3
DOI: 10.25018/0236_1493_2023_122_0_141
Article receipt date: 05.10.2023
Date of review receipt: 25.10.2023
Date of the editorial board′s decision on the article′s publishing: 10.11.2023
About authors:

Chanyshev A. I.1,2, Dr. Sci. (Phys. Mathem.), Professor, Chief Researcher, e-mail:;
Abdulin I. M.1, Researcher, e-mail:;
Belousova O. E.1, Dr. Sci. (Eng.), Senior Researcher,;
Gorodilov L. V.1, Dr. Sci. (Eng.), Head of the Laboratory,, Associate Professor;
Luk’yashko O. A.1, Engineer,,
1 Chinakal Institute of Mining Siberian Branch, Russian Academy of Sciences, 630091, Novosibirsk, Russia.
2 Novosibirsk State University of Economics and Management, 630099, Novosibirsk, Russia.


For contacts:

Chanyshev A. I., e-mail:


1. Kuznetsov G. N., Slobodov M. A. Determination by the unloading method of stresses acting in the inter-chamber tselikas of rock salt of Artemovsk mines. Proceedings of VNIMI. 1950, Vol. 22, pp. 151–174. [In Russ].

2. Hast N., Nilson G. Measurement of stresses in rocks and their significance for the construction of dams. Problems of engineering geology. Issue 4, Moscow: Mir, 1967, pp. 94–105. [In Russ].

3. Vlokh N. P., Zubkov A. V., Feklistov Yu. G. Improving the method of slot unloading. Diagnostics of the stressed state of rock massifs: Collection of scientific papers. 1980, pp. 30–35. [In Russ].

4. Mengel D. A. Alteration of initial stress state in the north area of the Sokolov deposit in the course of mining. MIAB. Mining Inf. Anal. Bull. 2020, (3–1), pp. 138–148. [In Russ]. DOI: 10.25018/0236–1493–2020–31–0–138–148.

5. Ai K., Zhang X., Zhou C. Study on the Method for Measuring Stress on Rock Mass Excavation Surface under Extremely High Stress Conditions. Geofluids. 2022, 4509192. DOI:10.1155/2022/4509192.

6. Rebetsky Yu. L., Sim L. A., Marinin A. V. Algorithm for calculating neotectonic stresses in platform areas by the structural-geomorphological method. Geodynamics & Tectonophysics. 2022, 13(1):0577. [In Russ]. DOI: 10.5800/GT-2022–13–1–0577.

7. Ge, X., Hou, M. Principle of in-situ 3D rock stress measurement with borehole wall stress relief method and its preliminary applications to determination of in-situ rock stress orientation and magnitude in Jinping hydropower station. Sci. China Technol. Sci. 2012, vol. 55, pp. 939–949. DOI: 10.1007/s11431–011–4680-x.

8. Sentyabov S. V. Karamnov D. V. Methods for determining the initial stresses of the rock massif by in-situ measurements. Problems of Subsoil Use. 2023. 1 (36). pp. 54–63. [In Russ]. DOI: 10.25635/2313–1586.2023.01.054.

9. Baryshnikov V. D., Kachal’sky V. G. Automated instrumentation to measure rock mass stresses in parallel-drilled holes. Journal of Mining Science. 2010, vol. 46, pp. 338–342. [In Russ]. DOI: 10.1007/s10913–010–0042–5.

10. Kuznetsov S. V., Savostyanov E. V. Method of measuring mechanical stresses in an array of rocks: No. 2830448: application 09.10.1979: publ. 15.07.1981; Copyright certificate No. 846730 A1 USSR, IPC E21C 39/00. applicant Institute of Problems of Integrated Development of Subsurface AH CCCP. [In Russ].

11. Schwab A. A. Experimental analytical method for quasi-homogeneous material characteristics determination based on elasto-plastic analysis of experimental data. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2012, vol. 16(2), pp: 65–71. [In Russ].

12. Chanyshev A. I., Abdulin I. M. Stress-strain behavior of rocks from the measurements of vectors of the Cauchy stresses and displacements at the boundary of an underground excavation. Journal of Mining Science. 2021, Vol. 57. no. 1. pp. 10–17. [In Russ]. DOI:10.1134/ S1062739121010026.

13. Chanyshev A. I., Abdulin I. M. Study of elastic, elastoplastic and post-limiting states of rock mass in the vicinity of openings using the measurement data at their boundaries. Journal of Mining Science. 2019, Vol. 55. no. 4. pp. 538–546. [In Russ]. DOI: 10.1134/ S1062739119045880.

14. Feklistov Yu. G. Deformation method of complex determination of the stress state and elastic characteristics of mining and construction objects. Problems of subsoil use. 2017, vol. 4 (15), pp. 28–32. [In Russ]. DOI: 10.18454/2313–1586.2017.04.028.

15. Zubkov A. V., Feklistov Yu. G., Lipin Ya. I., Khudyakov S. V., Krinitsyn R. V. Deformation methods for determining the stress state of rocks at subsurface use facilities. Problems of subsurface use. 2016. No. 4(11). pp. 41–49. [In Russ]. DOI: 10.18454/2313–1586.2016.04.041

16. Korsunsky A. M. A teaching essay on residual stresses and eigenstrains. ButterworthHeinemann, 2017. 197 р.

17. Uzun F., Korsunsky A. M. On the identification of eigenstrain sources of welding residual stress in bead-on-plate inconel 740H specimens. International Journal of Mechanical Sciences. 2018, vol. 145, pp. 231–245. DOI: 10.1016/j.ijmecsci. 2018.07.007.

18. Salvati, E., Korsunsky A. M. A simplified FEM eigenstrain residual stress reconstruction for surface treatments in arbitrary 3D geometries. International Journal of Mechanical Sciences. 2018, vol. 138–139. pp. 457–466. DOI: 10.1016/j.ijmecsci. 2018.02.016.

19. Valentine M. D., Dhokia V., Flynn J., McNair S. A., Lunt A. J. Characterisation of residual stresses and oxides in titanium, nickel, and aluminium alloy additive manufacturing powders via synchrotron X-ray diffraction. Materials Today Communications. 2023, vol. 35, pp. 105900. DOI: 10.1016/j.mtcomm.2023.105900.

20. McNair S. A., Srisuriyachot J., Omole S., Connolley T., Rhead A., Lunt, A. J. The effect of porosity on strain evolution and failure of soldered, small-diameter, thin-walled metallic pipes. Journal of Materials Research and Technology. 2023, vol. 22. pp. 2409–2424. DOI: 10.1016/j.jmrt.2022.12.088.

21. Petukhov D., Keller I. Exact reconstruction formulas for plastic strain distribution in the surface-treated plate and their applications. Acta Mechanica. 2020, vol. 231. pp. 1849–1866. DOI: 10.1007/s00707–020–02625–7.

22. Muskhelishvili N. I. Some basic problems of the mathematical theory of elasticity: Basic equations: Plane theory of elasticity: Torsion and bending. Moscow: USSR Academy of Sciences, 1966, 708 p. [In Russ].

23. Protosenya A. G., Belyakov N. A., Bouslova M. A. Modelling of the stress-strain state of block rock mass of ore deposits during development by caving mining systems. Journal of Mining Institute. 2023, Vol. 262, pp. 619–627. [In Russ].

24. Protosenya A. G., Katerov A. M. Justification of the parameters of the rheological model of the salt massif. MIAB. Mining Inf. Anal. Bull. 2023, No. 3. pp. 16–28. [In Russ]. DOI: 10.25018/0236_1493_2023_3_0_16.

25. Zuev B. Yu., Zubov V. P., Smychnik A. D. Determination of static and dynamic stresses in physical models of layered and block rock masses. Gornyi Zhurnal. 2019, No. 7, pp. 61–66. [In Russ]. DOI: 10.17580/gzh.2019.07.02.

26. Shemyakin E. I. On complex loading. Elasticity and inelasticity. Moscow: Publishing House of Moscow State University. 2001, pp. 124–132. [In Russ].

27. Khristianovich S. A. Problems of the theory of plasticity and geomechanics. M.: Nauka. 2008, 391 p. [In Russ].

28. Ilyushin A. A. Plasticity Ch. 1. Elastic-plastic deformations. Logos. 2004, 388 p. [In Russ].

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