Study of Phase Transition in Freezing Groundе
УДК 532.546
Abstract
This paper considers the movement of water and air in freezing and thawing soil, based on the equations of non-isothermal two-phase filtration. In order to achieve this, the equations of mass conservation, two-phase filtration, and heat balance are employed. The proposed one-dimensional mathematical model considers the phase transition in the extended region, the varying filtration properties of the soil, and the filtration of water into the phase transition region. This paper presents several empirical relationships for the intensity of the water-ice phase transition and their verification with experimental data from the literature. Numerical experiments have demonstrated the fulfillment of the physical maximum principle for soil porosity and the formation of a layer of lower permeability in the soil. This affects the absorption capacity of the soil and the distribution of surface and subsurface runoff during spring snowmelt. The proposed mathematical model can be used to simulate melting snow on the surface of frozen ground.
Downloads
Metrics
References
Колесников А.Г. К изменению математической формулировки задачи о промерзании грунта // Доклады Академии наук СССР. 1952. Т. 82. № 6. С. 889-891.
Alekseeva S.V., Sazhenkov S.A. Numerical Analysis of a One-dimensional Model of a Melting-freezing Snowpack // Journal of Computational and Engineering Mathematics. 2021. Vol. 8. No 4. P 17-27. DOI: 10.14529/jcem210403
Сибин А.Н., Папин А.А. Тепломассоперенос в тающем снеге // Прикладная механика и техническая физика. 2021. Т. 62. № 1. С. 109-118.
Сибин А.Н., Папин А.А. Моделирование движения растворимой примеси в тающем снеге // Прикладная механика и техническая физика. 2024. Т. 65. № 1. С. 58-69.
Tsypkin G.G. Water - Ice Phase Transition in Unsaturated Soil in the Presence of Capillary Pressure // Fluid Dynamics. 2019. Vol. 5. No 4. P 681-690.
Ершов Э.Д. Влагоперенос и криогенные текстуры в дисперсных породах. М.: МГУ 1979. 214 с.
Waldner P A., Schneebeli M., Schultze-Zimmermann U., Fluhler H. Effect of Snow Structure on Water Flow and Solute Transport // Hydrological processes. 2008. Vol. 18. No 7. P. 1271-1290.
Прохоров А.Е., Желнин М.С., Костина А.А., Пле-хов О.А. Исследование особенностей неравновесного фазового перехода во флюидонасыщенном грунте // Вестник Пермского университета. Физика. 2018. № 4 (42). С. 31-37.
Bronfenbrener L. Non-equilibrium Crystallization in Porous Media: Numerical Solution // Cold Region Science and Technology. 2013. Vol. 85. P. 137-149. DOI: 10.1016/j.coldregions.2012.09.002
Bronfenbrener L. Frost Heave and Ice Lenses Formation in Freezing Soils // Journal of Chemical Engineering Research Updates. 2014. Vol. 1. No 1. P 3-19.
Нерсесова З.А. Изменение льдистости грунтов в зависимости от температуры // Доклады Академии наук СССР. 1950. Т. 75. № 6. С. 845-846.
Шмакин А.Б. Модель снежного покрова с учетом слоистой структуры и ее сезонной эволюции // Криосфера Земли. 2009. Т. 13. № 4. С. 68-79.
Copyright (c) 2025 Антон Николаевич Сибин, Татьяна Андреевна Пекарская
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
