Numerical calculation of lateral pressure on frozen wall envelope

Mine shaft construction in difficult hydrogeological conditions is carried out under protection of a frozen wall. The frozen wall is a critical geoengineering structure, and its strength governs efficiency of shaft sinking. The common method of the frozen wall thickness optimization is using analytical formulas with limiting state criteria. However, the result found this way essentially depends on the value of lateral pressure which affects the frozen wall envelope. This study is a theoretical research of the lateral pressure exerted on the frozen wall envelope by the adjacent unfrozen rock mass based on the numerical modeling of the stress–strain behavior of a rock mass layer with an opening made under protection of the frozen wall. The scope of the modeling embraces both the condition of rigid cohesion at the frozen and unfrozen rock interface and the smooth outer boundary of the frozen wall. For analyzing influence of plastic deformation on the lateral pressure, the modeling includes the cases of the elastic and elastoplastic deformation. The influence of high hydrostatic pressure on the frozen wall is investigated individually. The modeling results offer an inference that the value of the lateral pressure applied to an unsupported section of the frozen wall depends on the ductibility of the frozen rocks. The hydrostatic pressure distributes the lateral pressure over the frozen wall envelope more evenly. The comparison of the numerical modeling results and the lateral pressure estimates from the analytical formulas used in the engineering practices shows that the formulas always predict the higher lateral pressure values as against the numerical modeling.

Keywords: frozen wall, artificial freezing, vertical mine shaft, rock pressure, physical and mechanical properties of rocks, inelastic deformation of rocks, hydrostatic pressure, numerical modeling.
For citation:

Zhelnin M. S., Kostina A. A., Plekhov O. A., Semin M. A., Brovka G. P. Numerical calculation of lateral pressure on frozen wall envelope. MIAB. Mining Inf. Anal. Bull. 2022;(10):62-77. [In Russ]. DOI: 10.25018/0236_1493_2022_10_0_62.

Acknowledgements:

The study was supported by the Ministry of Science and Higher Education of the Russian Federation, Project No. S-26/563.

Issue number: 10
Year: 2022
Page number: 62-77
ISBN: 0236-1493
UDK: 622.253
DOI: 10.25018/0236_1493_2022_10_0_62
Article receipt date: 12.04.2022
Date of review receipt: 08.08.2022
Date of the editorial board′s decision on the article′s publishing: 10.09.2022
About authors:

M.S. Zhelnin1, Cand. Sci. (Phys. Mathem.), Junior Researcher, e-mail: zhelnin.m@icmm.ru, ORCID ID: 0000-0003-4498-450X,
A.A. Kostina1, Cand. Sci. (Phys. Mathem.), Researcher, e-mail: kostina@icmm.ru, ORCID ID: 0000-0002-5721-3301,
O.A. Plekhov1, Dr. Sci. (Phys. Mathem.), Deputy Director for Science, e-mail: poa@icmm.ru, ORCID ID: 0000-0002-0378-8249,
M.A. Semin, Candidate of Technical Sciences, Researcher, Mining Institute of Ural Branch of Russian Academy of Sciences, 614007, Perm, Russia, e-mail: seminma@inbox.ru, ORCID ID: 0000-0001-5200-7931,
G.P. Brovka, Dr. Sci. (Eng.), Assistant Professor, Head of Laboratory, e-mail: brovka_gp@rambler.ru, Institute of Nature Management of National Academy of Sciences, Minsk, 220076, Belarus,
1 Institute of Continuous Media Mechanics of Ural Branch of Russian Academy of Sciences, 614013, Perm, Russia.

 

For contacts:

M.A. Semin, e-mail: seminma@inbox.

Bibliography:

1. Bulychev N. S., Komarov D. S., Lukashin S. B. Calculation of the necessary parameters of the ice barrier in the castle part. Izvestiya Tula State University. Natural sciences. 2012, no. 1-2, pp. 54—60. [In Russ].

2. Vakulenko I. S. Nikolaev P. V. Analysis and outlook for development of artificial freezing of rocks in underground construction. MIAB. Mining Inf. Anal. Bull. 2015, no. 3, pp. 338—346. [In Russ].

3. Levin L. Y., Semin M. A., Parshakov O. S. Improving methods of frozen wall state prediction for mine shafts under construction using distributed temperature measurements in test wells. Journal of Mining Institute. 2019, vol. 237, pp. 268—274. [In Russ]. DOI: 10.31897/ pmi.2019.3.274.

4. Kaimonov M. V., Kiselev V. V. Designs, technologies and temperature conditions of frozen structures in placer mines in the North. MIAB. Mining Inf. Anal. Bull. 2020, no. 8, pp. 118— 129. [In Russ]. DOI: 10.25018/0236-1493-2020-8-0-118-129.

5. Hu J., Wang X. B., Jiang B. R. Numerical analysis of temperature field of vertical frozen soil wall reinforcement at shield shaft. Advanced Materials Research. 2014, vol. 918, pp. 218—223. DOI: 10.4028/www.scientific.net/AMR.918.218.

6. Parshakov O. S. Review of emergency situations during the construction of mine shafts by a special method of artificial freezing of rocks. Gornoe ekho. 2019, no. 2, pp. 89—92. [In Russ].

7. Lai Y., Xu X., Dong Y., Li S. Present situation and prospect of mechanical research on frozen soils in China. Cold Regions Science and Technology. 2013, vol. 87, pp. 6—18. DOI: 10.1016/j.coldregions.2012.12.001.

8. Qi J., Ma W. A new criterion for strength of frozen sand under quick triaxial compression considering effect of confining pressure. Acta Geotechnica. 2007, vol. 2, no. 3, pp. 221—226. DOI: 10.1007/s11440-007-0034-z.

9. Yang Y., Lai Y., Chang X. Laboratory and theoretical investigations on the deformation and strength behaviors of artificial frozen soil. Cold Regions Science and Technology. 2010, vol. 64, no. 1, pp. 39—45. DOI: 10.1016/j.coldregions.2010.07.003.

10. Li D., Zhang C., Ding G., Zhang H., Chen J., Cui H., Pei W., Wang S., An L., Yuan C. Fractional derivative-based creep constitutive model of deep artificial frozen soil. Cold Regions Science and Technology. 2020, vol. 170, article 102942. DOI: 10.1016/j.coldregions. 2019.102942.

11. Li S., Zhang M., Tian Y., Pei W., Zhong H. Experimental and numerical investigations on frost damage mechanism of a canal in cold regions. Cold Regions Science and Technology. 2015, vol. 116, pp. 1—11. DOI: 10.1016/j.coldregions.2015.03.013.

12. Levin L. Y., Semin М. А., Plekhov О. А. Comparative analysis of existing methods for calculating frozen wall thickness for mine shafts under construction. Architecture and Construction of Russia. 2018, vol. 9, no. 4, pp. 93—103. [In Russ]. DOI: 10.15593/2224-9826/2018.4.09.

13. Kostina A., Zelnin M., Plekhov O., Panteleev I., Levin L., Semin M. Applicability of Vyalov’s equations to ice wall strength estimation. Frattura ed Integrità Strutturale. 2020, vol. 14, no. 53, pp. 394—405. DOI: 10.3221/IGF-ESIS.53.30.

14. Zhelnin M., Kostina A., Plekhov O., Panteleev I., Levin L. Numerical analysis of application limits of Vyalov’s formula for an ice-soil thickness. Frattura ed Integrità Strutturale. 2019, vol. 13, no. 49, pp. 156—166. DOI: 10.3221/IGF-ESIS.49.17.

15. Semin M. A., Brovka G. P., Pugin A. V., Bublik S. A., Zhelnin M. S. Effects of temperature field nonuniformity on strength of frozen wall in mine shafts. MIAB. Mining Inf. Anal. Bull. 2021, no. 9, pp. 79—93. [In Russ]. DOI: 10.25018/0236_1493_2021_9_0_79.

16. Ignatiev S. А., Sudarikov А. Е., Imashev А. Z. Modern mathematical forecast methods of maintenance and support conditions for mining tunnel. Journal of Mining Institute. 2019, vol. 238, pp. 371—375. [In Russ]. DOI: 10.31897/PMI.2019.4.371.

17. Protosenia А. G., Semenov V. I. Forecast of the stress-strain state of an ore massif around the working of the vaulted cross-section in the area of influence of sewage works. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2015, no. 3, pp. 31—36. [In Russ].

18. Wang X., Kulatilake P., Song W. Stability investigations around a mine tunnel through three-dimensional discontinuum and continuum stress analyses. Tunnelling and Underground Space Technology. 2012, vol. 32, pp. 98—112. DOI: 10.1016/j.tust.2012.06.003.

19. Schwamb T., Soga K. Numerical modelling of a deep circular excavation at Abbey Mills in London. Geotechnique. 2015, vol. 65, no. 7, pp. 604—619. DOI: 10.1680/geot.14.P.251.

20. Shao J. F. Hydromechanical modelling of shaft excavation in Meuse/Haute-Marne laboratory. Physics and Chemistry of the Earth, Parts A/B/C. 2008, vol. 33, pp. S422—S435. DOI: 10.1016/j.pce.2008.10.030.

21. Igolka D. A. Igolka Е. Y., Luksha Е. М., Kologrivenko А. А. Influence of an ice wall temperature at calculation of the shafts lining system. Gornaya mekhanika i mashinostroenie. 2014, no. 3, pp. 36—41. [In Russ].

22. Sentyabov S. V. Analysis of the current status of construction vertical mine shafts. MIAB. Mining Inf. Anal. Bull. 2014, no. 7, pp. 415—419. [In Russ].

23. Oreste P., Spagnoli G., Bianco L. L. A combined analytical and numerical approach for the evaluation of radial loads on the lining of vertical shafts. Geotechnical and Geological Engineering. 2016, vol. 34, no. 4, pp. 1057—1065. DOI: 10.1007/s10706-016-0026-6.

24. Michalowski R. L. Coefficient of earth pressure at rest. Journal of Geotechnical and Geoenviron-mental Engineering. 2005, vol. 131, no. 11, pp. 1429—1433. DOI: 10.1061/ (ASCE)1090-0241(2005)131:11(1429).

25. Brooker E. W., Ireland H. O. Earth pressures at rest related to stress history. Canadian Geotechnical Journal. 1965, vol. 2, no. 1, pp. 1—15.

26. Ghoreishian Amiri S. A., Grimstad G., Kadivar M., Nordal S. Constitutive model for rateindependent behavior of saturated frozen soils. Canadian Geotechnical Journal. 2016, vol. 53, no. 10, pp. 1646—1657. DOI: 10.1139/cgj-2015-0467.

27. Igosheva L. A., Grishina A. S. Review of the basic methods of the ground improvement. Vestnik Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo universiteta. Stroitel'stvo i arkhitektura. 2016, vol. 7, no. 2, pp. 5—21. [In Russ].

28. VSN 189-78 «Instruktsiya po proektirovaniyu i proizvodstvu rabot po iskusstvennomu zamorazhivaniyu gruntov pri stroitel'stve metropolitenov i tonneley» [VSN 189-78 «Instructions for the design and production of works on artificial freezing of soils during the construction of subways and tunnels»], Moscow, Mintransstroy, 1978, 68 p.

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