2D subsidence trough approximation by experimental points

The article discusses algorithms for plotting an analytical function of a preset shape to describe a subsidence trough using the vertical displacements measured at a set of points situated on ground surface at a random fashion. For building and improving calculation algorithms, a one-dimensional problem is examined first, using actual data from base points on ground surface; then, the problem is extended and generalized to a 2D subsidence trough. The shape of the trough is approximated by the preset function in the form of a combination of the Gaussian integrals with three (or five in 2D case) constitutive parameters. The applicability of a random search algorithm in funding parameters of an unknown function is considered. For testing the proposed algorithm applicability, a simulation model is built for a possible subsidence trough formed by means of combination of 1D troughs in the main sections of the model 2D trough. With the help of this model trough, a set of points is generated on ground surface to model a possible real-life ensemble of points. The in situ ensemble of points will be determined using appropriate measurement instrumentation and algorithms being developed these days. Inserted in the algorithm, these points make it possible to find parameters of the approximating functions for the 2D case and to build a relevant analytical expression for ground surface subsidences. This approach can be effective using the satellite technologies and randomly spread natural reflectors in the ground area.

Makeeva T. G., Trofimov V. A. 2D subsidence trough approximation by experimental points. MIAB. Mining Inf. Anal. Bull. 2023;(3):107-123. [In Russ]. DOI: 10.25018/ 0236_1493_2023_3_0_107.

T.G. Makeeva, Cand. Sci. (Geol. Mineral.), Assistant Professor, Moscow State University of Civil Engineering, 129337, Moscow, Russia, e-mail: makeeva13new@yandex.ru,
V.A. Trofimov, Dr. Sci. (Eng.), Head of Laboratory, e-mail: asas_2001@mail.ru, Institute of Problems of Comprehensive Exploitation of Mineral Resources of Russian Academy of Sciences, 111020, Moscow, Russia, ORCID ID: 0000-0001-9010-189X.

V.A. Trofimov, e-mail: asas_2001@mail.ru.

1. Manekar G. G., Shome D., Chaudhari M. P. Prediction of subsidence parameters & 3-D analysis at Balaghat underground manganese mine of MOIL Limited, India. Procedia Engineering. 2017, vol. 191, pp. 1075—1086. DOI: 10.1016/j.proeng.2017.05.281.

2. Ximin Cuia, Xiexing Miaoa, Jin'an Wangb, Shuo Yanga, Huide Liua, Yanqi Songa, Hong Liua, Xikuan Hua Improved prediction of differential subsidence caused by underground mining. International Journal of Rock Mechanics and Mining Sciences. 2000, vol. 37, pp. 615—627.

3. Suchowerska A. M., Merifield R. S., Carter J. P. Vertical stress changes in multi-seam mining under supercritical longwall panels. International Journal of Rock Mechanics & Mining Sciences. 2013, vol. 61, pp. 306—320. DOI: 10.1016/j.ijrmms.2013.02.009.

4. Sheinin V. I., Potapova E. Yu., Kholmyansky M. L., Pushilin A. N., Sarana E. P. Engineering methodology for calculating the settlement of the base above the cavity formed as a result of the dissolution of karst rocks under the hydraulic structure. Vestnik NIC «Stroitel'stvo». 2021, no. 2 (29), pp. 136—148. [In Russ]. DOI: 10.37538/2224-9494-2021-2(29)-136-148.

5. Kozhogulov K. Ch., Takhanov D. K., Kozhas A. K., Imashev A. Zh., Balpanova M. Zh. Methods of forward calculation of ground subsidence above mines. Journal of Mining Science. 2020, vol. 56, pp. 184—195. DOI: 10.1134/S1062739120026637.

6. Hamdi P., Stead D., Elmo D., Töyrä J. Use of an integrated finite/discrete element methoddiscrete fracture network approach to characterize surface subsidence associated with sublevel caving. International Journal of Rock Mechanics and Mining Sciences. 2018, vol. 103, pp. 55—67. DOI: 10.1016/j.ijrmms.2018.01.021.

7. Sepehri M., Apel D. B., Hall R. A. Prediction of mining-induced surface subsidence and ground movements at a Canadian diamond mine using an elastoplastic finite element model. International Journal of Rock Mechanics and Mining Sciences. 2017, vol. 100, pp. 73—82. DOI: 10.1016/j.ijrmms.2017.10.006.

8. Salmi E. F., Nazem M., Karakus M. Numerical analysis of a large landslide induced by coal mining subsidence. Engineering Geology. 2017, vol. 217, pp. 141—152. DOI: 10.1016/j. enggeo.2016.12.021.

9. Lu S., Li L., Cheng Y., Sa Z., Zhang Y., Yang N. Mechanical failure mechanisms and forms of normal and deformed coal combination containing gas: Model development and analysis. Engineering Failure Analysis. 2017, vol. 80, pp. 241—252. DOI: 10.1016/j.engfailanal.2017.06.022.

10. Newman C., Agioutantis Z., Leon G. B. J. Assessment of potential impacts to surface and subsurface water bodies due to longwall mining. International Journal of Mining Science and Technology. 2017, vol. 27, pp. 57—64. DOI: 10.1016/j.ijmst.2016.11.016.

11. Peng S. S. Topical areas of research needs in ground control . A state of the art review on coal mine ground control. International Journal of Mining Science and Technology. 2015, vol. 25, no. 1, pp. 1—6. DOI: 10.1016/j.ijmst.2014.12.006.

12. Liu C., Li H., Mitri H., Jiang D., Li H., Feng J. Voussoir beam model for lower strong roof strata movement in longwall mining — Case study. Journal of Rock Mechanics and Geotechnical Engineering. 2017, vol. 9, pp. 1171—1176. DOI: 10.1016/j.jrmge.2017.07.002.

13. Suchowerska Iwanec A. M., Carter J. P., Hambleton J. P. Geomechanics of subsidence above single and multi-seam coal mining. Journal of Rock Mechanics and Geotechnical Engineering. 2016, vol. 8, pp. 304—313.

14. Kay D. R., McNabb K. E., Carter J. P. Numerical modelling of mine subsidence at Angus Place Colliery. Computer methods and advances in geomechanics. Rotterdam, 1991.

15. Lloyd P. W, Mohammad N., Reddish D. J. Surface subsidence prediction techniques for UK coalfields e an innovative numerical modelling approach. Proceedings of the 15th Mining Conference of Turkey. 1997, pp. 111—124.

16. Coulthard M. A., Holt G. E. Numerical modelling of mining near and beneath tailings Dam. Proceedings of the 1st Southern Hemisphere International Rock Mechanics Symposium. Perth, Australian: Australian Centre for Geomechanics. 2008, pp. 341—154.

17. Zakharov V. N., Shlyapin A. V., Trofimov V. A., Filippov Yu. A. Change in stress–strain behavior of coal-rock mass during coal mining. MIAB. Mining Inf. Anal. Bull. 2020, no. 9, pp. 5—24. [In Russ]. DOI: 10.25018/0236-1493-2020-9-0-5-24.

18. Makeeva T., Trofimov V. Forecast of deformations of the land surface from the separate clearing development, displacement and deformation in the main sections of the trough. E3S Web of Conferences. 2019, vol. 97, article 04016. DOI: 10.1051/e3sconf/20199704016.

19. Kratch G. Sdvizhenie gornykh porod i zashscita podrabatyvaemykh sooruzheniy [Movement of rocks and protection of undermined structures], Moscow, Nedra, 1978, 494 p.

20. Makeeva T., Trofimov V. Regularities of the day surface deformation during layer mining by consecutive lavas. MATEC Web of Conferences. 2018, vol. 251, article 02013. DOI: 10.1051/matecconf/201825102013 IPICSE-2018.

21. Chursin I. N. Satellite monitoring of the displacement of the under-mined earth's surface in Kuzbass using radar interferometry. Mine Surveying Bulletin. 2021, no. 4 (143), pp. 56—60. [In Russ].

22. Trofimov V. A., Makeeva T. G. Forecasting parameters of earth surface subsidence to assess safe operation of engineering structures. MATEC Web of Conferences. 2017, vol. 117, article 00170. DOI: 10.1051/matecconf/201711700170.