Forecasting the moisture and thermal conditions of the near-wall and bottom rock masses in the cryolithic zone
E.K. Romanova
N.V. Chersky Mining Institute of the North of the Siberian Branch of the Russian Academy of Sciences, Yakutsk, Russian Federation
Russian Mining Industry №4S / 2025 p. 73-77
Abstract: The objective of this work is to establish the patterns of temperature and moisture conditions in the near-wall and bottom rock masses of an open pit mine in the cryolithic zone depending on the geometric dimensions of the open pit. A computer implementation of the task to forecast the moisture and thermal conditions of the near-wall and bottom rock masses of open pit mines in the cryolithic zone includes the development of a mathematical model of the heat exchange, filtration and moisture transfer, as well as solving the task using numerical methods and computer technologies. A 2D mathematical model of the heat and moisture transfer in the near-wall and bottom rock masses of an open pit mine in the cryolithic zone has been developed with account of moisture ingress, evaporation, migration, and phase transition. An important feature of this model is the absence of a clearly defined boundary between zones of complete and incomplete water saturation, which makes it applicable for analyzing complex geological environments. A computer software based on the developed mathematical model enables long-term forecasting and research into the characteristics of the thermal and moisture conditions in the near-wall and bottom rock masses of an open pit mine in the cryolithic zone depending on various natural and climatic conditions and the design parameters of the open pit mine. Test calculations were performed to assess the impact of the open pit geometric dimensions on the process of forming the moisture and thermal conditions of the near-wall and bottom rock masses of an open pit mine.
Keywords: open pit mine in the cryolithic zone, near-wall rock mass, bottom rock mass, thermal conditions, moisture conditions, moisture transfer
Acknowledgments: The study was carried out within the State Assignment of the Ministry of Science and Higher Education of the Russian Federation (Topic No.0297-2021-0021, EGISU NIOCTR No.122011800083-0) using instruments that belong to the Shared core facilities of the Federal Research Center, Yakutsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences.
For citation: Romanova E.K. Forecasting the moisture and thermal conditions of the near-wall and bottom rock masses in the cryolithic zone. Russian Mining Industry. 2025;(4S):73–77. (In Russ.) https://doi.org/10.30686/1609-9192-2025-4S-73-77
Article info
Received: 08.06.2025
Revised: 13.08.2025
Accepted: 20.08.2025
Information about the author
Elena K. Romanova – Cand. Sci. (Eng.), Researcher, Institute of Mining of the North named after. N.V. Chersky Siberian Branch of the Russian Academy of Sciences, Yakutsk, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
References
1. Изаксон М.В. Управление устойчивостью уступов глубоких карьеров в многолетней мерзлоте теплоизолирующими экранами [автореф. дис. ... канд. техн. наук]. Кемерово; 2006. 22 с.
2. Романова Е.К., Соловьев Д.Е., Киселев В.В., Львов А.С. Выбор оптимальной защиты верхних бровок уступов карьеров криолитозоны от растепления. Горный журнал. 2024;(2):21–25. https://doi.org/10.17580/gzh.2024.02.03Romanova E.K., Soloviev D.E., Kiselev V.V., Lvov A.S. Selection of optimum thawing protection for bench crests in open pit mines in the permafrost zone. Gornyi Zhurnal. 2024;(2):21–25. (In Russ.) https://doi.org/10.17580/gzh.2024.02.03
3. Ткач С.М., Курилко А.С., Романова Е.К. Роль теплофизических исследований в обеспечении эффективности и безопасности эксплуатации глубоких карьеров криолитозоны. Горный информационно-аналитический бюллетень. 2015;(S56):80–85.Tkach S.M., Kurilko A.S., Romanova E.K. Effect of thermophysical research to cryolitezone deep opencast effectiveness and safety exploitation providing. Mining Informational and Analytical Bulletin. 2015;(S56):80–85. (In Russ.)
4. Романова Е.К., Курилко А.С., Киселев В.В. Управление устойчивостью уступов кимберлитовых карьеров криолитозоны с помощью теплоизолированного оградительного сооружения. Горный информационно-аналитический бюллетень. 2017;(S24):264–271. https://doi.org/10.25018/0236-1493-2017-11-24-264-271Romanova E.K., Kurilko A.S., Kiselev V.V. Cryolitezone opencast bench stability controlling with heat insulated protective structures assistance. Mining Informational and Analytical Bulletin. 2017;(S24):264–271. (In Russ.) https://doi.org/10.25018/0236-1493-2017-11-24-264-271
5. Зырянов И.В., Акишев А.Н., Бокий И.Б., Шерстюк Н.М. Общий подход к определению параметров нерабочих бортов сверхглубоких карьеров алмазорудных месторождений. Горный журнал. 2021;(2):48–53. https://doi.org/10.17580/gzh.2021.02.05Zyryanov I.V., Akishev A.N., Bokiy I.B., Sherstyuk N.M. General concept of determining the parameters of non-mining walls of ultra-deep diamond deposits development open pits. Gornyi Zhurnal. 2021;(2):48–53. (In Russ.) https://doi.org/10.17580/gzh.2021.02.05
6. Шполянская Н.А. Особенности открытой разработки месторождений в криолитозоне в условиях континентального климата. Инженерная геология. 2020;15(3):42–52. https://doi.org/10.25296/1993-5056-2020-15-3-42-52Shpolyanskaya N.A. Specific features of opencast mining in the cryolithic zone under continental climate conditions. Engineering Geology World. 2020;15(3):42–52. (In Russ.) https://doi.org/10.25296/1993-5056-2020-15-3-42-52
7. Zairov Sh.Sh., Nomdorov R.U., Ashuraliev U.T. Increasing the stability of the sides of the quarry by forming a concave profile of the slope of a high ledge. Insights in Mining Science & Technology. 2022;3(3):555617. Available at: https://juniperpublishers.com/imst/pdf/IMST.MS.ID.555617.pdf (accessed: 01.07.2025).
8. Равшанов Н., Шадманов И.У., Мирзаева Н.М. Моделирование и визуализация тепловлагопереноса в пористых средах. Проблемы вычислительной и прикладной математики. 2022;(2):72–87. Режим доступа: https://journals.airi.uz/index.php/pvpm/article/view/34 (дата обращения: 01.07.2025).Ravshanov N., Shadmanov I.U., Mirzaeva N.M. Modeling and visualization of heat and moisture transfer in porous media. Problems of Computational and Applied Mathematics. 2022;(2):72–87. (In Russ.) Available at: https://journals.airi.uz/index.php/pvpm/article/view/34 (accessed: 01.07.2025).
9. Шадманов И.У., Шадманова К.У., Фатуллаева М.Ш. Многомерная математическая модель и численный алгоритм решения задач совместного тепловлагопереноса в неоднородных пористых тел. Проблемы вычислительной и прикладной математики. 2022;(S2):254–271. Режим доступа: https://journals.airi.uz/index.php/pvpm/article/view/71 (дата обращения: 01.07.2025).Shadmanov I.U., Shadmanova K.U., Fatullaeva M.Sh. Multidimensional mathematical model and numerical algorithm for solving problems of joint heat and moisture transfer in inhomogeneous porous bodies. Problems of Computational and Applied Mathematics. 2022;(S2):254–271. (In Russ.) Available at: https://journals.airi.uz/index.php/pvpm/article/view/71 (accessed: 01.07.2025).
10. Терлеев В.В., Нарбут М.А., Топаж А.Г., Миршель В. Моделирование гидрофизических свойств почвы как капиллярно-пористого тела и усовершенствование метода Муалема–Ван Генухтена: теория. Агрофизика. 2014;(2):35–44.Terleev V.V., Narbut M.A., Topaj A.G., Mirschel W. Modeling of hydrophysical properties of soil as a capillary-porous medium and modification of the Mualem-Van Genuchten approach: Theory. Agrophysica. 2014;(2):35–44. (In Russ.)
11. van Genuchten M.Th. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal. 1980;44(5):892–898.
12. Самарский А.А., Моисеенко Б.Д. Экономичная схема сквозного счета для многомерной задачи Стефана. Журнал вычислительной математики и математической физики. 1965;5(5):816–827.Samarskii A.A., Moiseyenko B.D. An economic continuous calculation scheme for the Stefan multidimensional problem. USSR Computational Mathematics and Mathematical Physics. 1965;5(5):43–58. https://doi.org/10.1016/0041-5553(65)90004-2
13. Лычман В.В. Численное решение задач фильтрации и влагопереноса в пористых средах [Дис. ... канд. физ.-мат. наук]. Киев; 1984. 156 с.
14. Кучеров А.Б., Николаев Е.С. Попеременно-треугольный итерационный метод решения сеточных эллиптических уравнений в произвольной области. Журнал вычислительной математики и математической физики. 1977;7(3):664–675.Kucherov A.B., Nikolaev E.S. An alternately triangular iterative method for solving mesh elliptic equations in an arbitrary domain. USSR Computational Mathematics and Mathematical Physics. 1977;7(3):664–675. https://doi.org/10.1016/0041-5553(77)90142-2
15. Xiong J.S. Modified upper and lower triangular splitting iterative method for a class of block two-by-two linear systems. Linear and Multilinear Algebra. 2021;71(1):29–40. https://doi.org/10.1080/03081087.2021.2017833
16. Gregoire M. Professional C++. 5th еd. –Birmingham: Wrox; 2021. 1312 р.
17. Stroustrup B. A Tour of C++. 3rd ed. Reading: Addison-Wesley Professional; 2022. 320 p.

