Assessment of stress concentration in neighborhood of karst voids during ore mining

The studies on karst are reviewed. The mechanisms of rock failure in neighborhood of karst voids and the procedures of the stability assessment in rock mass enclosing a karst void are discussed. Some investigations using the analytical, numerical and physical simulation methods using equivalent materials consider the interaction between a single roadway and a karst void. This article focuses on the stress–strain behavior of rock mass enclosing karst voids. The problem is formulated so that to assess the influence of karst on the stress–strain behavior of the enclosing rock mass. The karst void under analysis is large and has an irregular surface. The ore and rock mass enclosing the karst void is described using the linearly elastic isotropic model. The physical and mechanical properties of the disturbed rock mass are determined empirically. The analytical domain is a 3D space with a karst void, subjected to the action of the natural stress field. In this investigation, the irregular surface of the karst is simplified to an ellipsoid of the equivalent geometry. The investigation reveals the patterns of stresses from the surface irregularities of the karst void and equivalent ellipsoids in three mutually orthogonal cross-sections.

Protosenya A. G., Veselova A. V., Kotikov D. A. Assessment of stress concentration in neighborhood of karst voids during ore mining. MIAB. Mining Inf. Anal. Bull. 2024;(2): 5-22. [In Russ]. DOI: 10.25018/0236_1493_2024_2_0_5.

A.G. Protosenya¹, Dr. Sci. (Eng.), Professor, e-mail: Protosenya_AG@pers.spmi.ru, ORCID ID: 0000-0001-7829-6743,
A.V. Veselova¹, Graduate Student, e-mail: veselova.nastia2015@yandex.ru, ORCID ID: 0009-0004-6450-183X,
D.A. Kotikov¹, Cand. Sci. (Eng.), Head of Laboratory, e-mail: hromokot@list.ru, ORCID ID: 0009-0006-8445-2689, 
¹ Empress Catherine II Saint-Petersburg Mining University, 199106, Saint-Petersburg, Russia.

A.V. Veselova, e-mail: veselova.nastia2015@yandex.ru.

1. Movchan I., Yakovleva A., Movchan A., Shaygallyamova Z. Early assessment of seismic hazard in terms of Voronezh Massif-Moscow Depression contact. Mining of Mineral Deposits. 2021, vol. 15, no. 3, pp. 62—70. DOI: 10.33271/mining15.03.062.

2. Movchan I. B., Shaygallyamova Z. I., Yakovleva A. A., Movchan A. B. Increasing resolution of seismic hazard mapping on the example of the north of middle russian highland. Applied Sciences. 2021, vol. 11, no. 11, article 5298. DOI: 10.3390/app11115298.

3. Alekseev S. V., Alekseeva L. P., Gladkov A. S., Trifonov N. S., Serebryakov E. V., Pavlov S. S., Il’in A. V. Brines in deep horizons of the Udachnaya kimberlite pipe. Geodynamics and Tectonophysics. 2018, vol. 9, no. 4, pp. 1235—1253. [In Russ]. DOI: 10.5800/GT-2018-9-4-0393.

4. Kuzmin S. B. Natural disasters in the Russian Federation. Issues of risk analysis. 2019, vol. 16, no. 2, pp. 10—35. [In Russ]. DOI: 10.32686/1812-5220-2019-16-2-10-35.

5. Dippenaar M. A., Louis van Rooy J., Diamond R. E. Engineering, hydrogeological and vadose zone hydrological aspects of Proterozoic dolomites (South Africa). Journal of African Earth Sciences. 2019, vol. 150, pp. 511—521. DOI: 10.1016/j.jafrearsci.2018.07.024.

6. Zhang S., Jin Q., Hu M., Han Q., Sun J., Cheng F., Zhang X. Differential structure of Ordovician karst zone and hydrocarbon enrichment in paleogeomorphic units in Tahe area, Tarim Basin, NW China. Petroleum Exploration and Development. 2021, vol. 48, no. 5, pp. 1113—1125. DOI: 10.1016/ S1876-3804(21)60095-2.

7. Strokova L. A., Ezhkova A. V., Leonova A. V. Application of lineament analysis to assess the karst hazard in the design of the main gas pipeline in south Yakutia. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering. 2020, vol. 331, no. 11, pp. 117—126. [In Russ]. DOI: 10.18799/ 24131830/2020/11/2891.

8. Kunitsky V. V. Carbonate karst in permafrost rocks. Nauka i tekhnika v Yakutii. 2008, no. 2(15), pp. 5. [In Russ].

9. Karasev M. A., Petrushin V. V., Rysin A. I. The hybrid finite/discrete element method in description of macrostructural behavior of salt rocks. MIAB. Mining Inf. Anal. Bull. 2023, no. 4, pp. 48—66. [In Russ]. DOI: 10.25018/0236_1493_2023_4_0_48.

10. Lavrova N. V. Revisiting the evolution of deformation zones under platform conditions in the case study of the Kungur Ice Cave (Cis–Urals). Journal of Mining Institute. 2020, vol. 243, pp. 279—284. [In Russ]. DOI: 10.31897/PMI.2020.3.279.

11. Potekhin D. V., Galkin S. V. Use of machine learning technology to model the distribution of lithotypes in the Permo-Carboniferous oil deposit of the Usinskoye field. Journal of Mining Institute. 2023, vol. 259, pp. 41—51. [In Russ]. DOI: 10.31897/PMI.2022.101.

12. Putilov I. S., Vinokurova E. E., Guliaeva A. A., Yuzhakov A. L., Popov N. A. Creation of a conceptual geological model based on lithological-petrographic research on the example of the PermoCarboniferous deposit of the Usinskoe deposit. Perm Journal of Petroleum and Mining Engineering. 2020, vol. 20, no. 3, pp. 214—222. [In Russ]. DOI: 10.15593/2712-8008/2020.3.2.

13. Belyakov N. A., Belikov A. A. Prediction of the integrity of the water-protective stratum at the Verkhnekamskoye potash ore deposit. MIAB. Mining Inf. Anal. Bull. 2022, no. 6-2, pp. 33—46. [In Russ]. DOI: 10.25018/0236_1493_2022_62_0_33.

14. Evdokimov A. N., Pharoe B. L. Features of the mineral and chemical composition of the Northwest manganese ore occurrence in the Highveld region, South Africa. Journal of Mining Institute. 2021, vol. 248, pp. 195—208. [In Russ]. DOI: 10.31897/PMI.2021.2.4.

15. Anisimov K. A., Nikiforov A. V. Modern technologies of the development of diamondiferous deposits. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering. 2023, vol. 334, no. 1, pp. 196—208. [In Russ]. DOI: 10.18799/24131830/2023/1/3837.

16. Melnik V. V., Harisov T. F., Zamyatin A. L. Methodological bases of complex geomechanical studies for selecting optimal parameters of drainage of waterlogged areas felds. MIAB. Mining Inf. Anal. Bull. 2020, no. 3-1, pp. 127—137. [In Russ]. DOI: 10.25018/0236-1493-2020-31-0-127-137.

17. Dalatkazin T. Sh., Kayumova A. N. Ensuring safe mining operations in the development of Sokolovskoye iron ore deposit. Problems of Subsoil Use. 2019, no. 4, pp. 113—121. [In Russ]. DOI: 10.25635/2313-1586.2019.04.113.

18. Melnik V. V., Zamyatin A. L. Draining of orebodis in conditions of high watering and cavernous porosity of superincumbent rock stratum. Problems of Subsoil Use. 2018, no. 1, pp. 101—111. [In Russ]. DOI: 10.25635/2313-1586.2018.01.105.

19. Melnik V. V. Diagnostics of karst manifestations during engineering and geological surveys. MIAB. Mining Inf. Anal. Bull. 2010, no. 7, pp. 275—278. [In Russ].

20. Guo J., Wu W., Liu X., Huang X., Zhu Z. Theoretical analysis on safety thickness of the waterresistant rock mass of karst tunnel face taking into account seepage effect. Geotechnical and Geological Engineering. 2022, vol. 40, pp. 697—709. DOI: 10.1007/s10706-021-01916-7.

21. Wang I. Lithological composition and reservoir properties of the Lower Ordovician deposits of the Modyagou suite at the Tabamiao field (Ordos basin, China). Moscow State University Bulletin. Series 4. Geology. 2016, no. 5, pp. 81—86. [In Russ].

22. Huang F., Zhao L., Ling T., Yang X. Rock mass collapse mechanism of concealed karst cave beneath deep tunnel. International Journal of Rock Mechanics and Mining Sciences. 2017, vol. 91, pp. 133—138. DOI: 10.1016/j.ijrmms.2016.11.017.

23. Lyu C., Yu L., Wang M., Xia P, Sun Y. Upper bound analysis of collapse failure of deep tunnel under karst cave considering seismic force. Soil Dynamics and Earthquake Engineering. 2020, vol. 132, article 106003. DOI: 10.1016/j.soildyn.2019.106003.

24. Yang Z., Zhang R., Xu J., Yang X. Energy analysis of rock plug thickness in karst tunnels based on non-associated flow rule and nonlinear failure criterion. Journal of Central South University. 2017, vol. 24, pp. 2940—2950. DOI: 10.1007/s11771-017-3708-1.

25. Yu L., Lyu C., Wang M., Xu T. Three-dimensional upper bound limit analysis of a deep soiltunnel subjected to pore pressure based on the nonlinear Mohr-Coulomb criterion. Computers and Geotechnics. 2019, vol. 112, pp. 293—301. DOI: 10.1016/j.compgeo.2019.04.025.

26. Guo J., Chen J., Chen F., Huang S., Wang H. Using the Schwarz alternating method to identify critical water-resistant thickness between tunnel and concealed cavity. Advances in Civil Engineering. 2018, vol. 2018, article 8401482. DOI: 10.1155/2018/8401482.

27. Jiang H., Li L., Rong X., Wang M., Xia Y., Zhang Z. Model test to investigate waterproofresistant slab minimum safety thickness for water inrush geohazards. Tunnelling and Underground Space Technology. 2017, vol. 62, pp. 35—42. DOI: 10.1016/j.tust.2016.11.004.

28. Pan D., Li S., Xu Z., Lin P., Huang X. Experimental and numerical study of the water inrush mechanisms of underground tunnels due to the proximity of a water-filled karst cavern. Bulletin of Engineering Geology and the Environment. 2019, vol. 78, pp. 6207—6219. DOI: 10.1007/s10064019-01491-5.

29. Wang L., Huang P., Chen L., Wang J., Zheng Z., Ma J. Study of the mechanism of water inrush in karst tunnel based on transparent rock mass physical model test. IOP Conference Series: Earth and Environmental Science. 2021, vol. 861, article 052091. DOI: 10.1088/1755-1315/861/5/052091.

30. Yin Q., Jing H., Zhu T., Wu L., Su H., Yu L. Spatiotemporal evolution characteristics of fluid flow through large-scale 3D rock mass containing filling joints: an experimental and numerical study. Geofluids. 2021, vol. 2021, article 8883861. DOI: 10.1155/2021/8883861.

31. Zhang Q., Wang J., Feng L. Mechanical mechanism of hydraulic fracturing effect caused by water inrush in tunnel excavation by blasting. Mathematical Problems in Engineering. 2021, vol. 2021, article 9919260. DOI: 10.1155/2021/9919260.

32. Guo J., Qian Y., Chen J., Chen F. The minimum safe thickness and catastrophe process for water inrush of a karst tunnel face with multi fractures. Processes. 2019, vol. 7, article 686. DOI: 10.3390/ pr7100686.

33. Wang J., Li S., Li L., Shi S., Zhou Z., Song S. Mechanism of water inrush in fractures and block collapse under hydraulic pressure. Mathematics and Computers in Simulation. 2020, vol. 177, pp. 625—642. DOI: 10.1016/j.matcom.2020.05.028.

34. Demenkov P. A., Komolov V. V. Study of influence of the deep pit construction on soil mass in flat and spatial formulation. MIAB. Mining Inf. Anal. Bull. 2023, no. 6, pp. 97—110. DOI: 10.25018/ 0236_1493_2023_6_0_97.

35. Fazioa N. L., Perrottia M., Lollinoa P., Pariseb M., Vattanoc M., Madoniac G., Di Maggio C. A three-dimensional back-analysis of the collapse of an underground cavity in soft rocks. Engineering Geology. 2017, vol. 228, pp. 301—311. DOI: 10.1016/j.enggeo.2017.08.014.

36. Patskevich P. G. On the possibility of using elastic problem solving for modeling the stressstrain state of the rock mass and structural elements of the development system during the development of kimberlite pipes of the M.V. Lomonosov. MIAB. Mining Inf. Anal. Bull. 2003, no. 4, pp. 25—28. [In Russ].

37. Serebryakov E. V., Gladkov A. S. Geological and structural characteristics of deep-level rock mass of the Udachnaya pipe deposit. Journal of Mining Institute. 2021, vol. 250, pp. 512—525. [In Russ]. DOI: 10.31897/PMI.2021.4.4.

38. Vásárhelyi B., Kovács D. Empirical methods of calculating the mechanical parameters of the rock mass. Periodica Polytechnica Civil Engineering. 2017, vol. 61, no. 1, pp. 39—50. DOI: 10.3311/ PPci.10095.

39. Pavlovich A. A., Korshunov V. A., Bazhukov A. A., Melnikov N. Y. Estimation of rock mass strength in open-pit mining. Journal of Mining Institute. 2019, vol. 239, pp. 502—509. [In Russ]. DOI: 10.31897/PMI.2019.5.502.

40. Protosenya A. G., Katerov A. M. Substantiation of rheological model parameters for salt rock mass. MIAB. Mining Inf. Anal. Bull. 2023, no. 3, pp. 16—28. [In Russ]. DOI: 10.25018/0236_1493_ 2023_3_0_16.

41. Trushko V. L., Protosenya A. G., Matveev P. F., Sovmen Kh. M. Geomekhanika massivov i dinamika vyrabotok glubokikh rudnikov [Geomechanics of rock masses and dynamics of workings in deep mines], Saint-Petersburg, SPGGI, 2000, 395 p.