{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:48Z","timestamp":1760060268612,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"research project of Gansu Hengtong Road &amp; Bridge Engineering Co., Ltd.","award":["2024-THTJ3-QT68"],"award-info":[{"award-number":["2024-THTJ3-QT68"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Infrastructure development in permafrost regions continues to face growing challenges from frost heaves and thaw settlement. The traditional frost heave theory considers that soil freezing is caused by the migration of liquid water in the soil; however, existing engineering practice shows that the migration of water vapor during the freezing process cannot be neglected. Based on the hydrothermal\u2013air migration theory of unsaturated soils and their frost heave mechanism, this study established a coupled hydrothermal\u2013air frost heave model for unsaturated silty clay under unidirectional freezing conditions. The computational model was verified through indoor modelling tests. The entire process of water vapor migration, moisture accumulation, and condensation-induced ice formation in unsaturated silty clay was comprehensively reproduced by numerical simulation. The results showed that the moisture field is redistributed during the freezing process of unsaturated soil. The increase in volumetric ice content in the frozen zone is due mainly to the migration of water vapor. Liquid water and water vapor in the unfrozen zone migrate towards the freezing edge driven by the temperature gradient, where they accumulate, leading to a decrease in the unsaturated pore space and a decrease in the equivalent vapor content. This study\u2019s results can provide theoretical support for frost damage prevention in unsaturated silty clay in permafrost regions.<\/jats:p>","DOI":"10.3390\/sym17081357","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T10:59:01Z","timestamp":1755601141000},"page":"1357","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process"],"prefix":"10.3390","volume":"17","author":[{"given":"Dengzhou","family":"Li","sequence":"first","affiliation":[{"name":"Gansu Hengtong Road & Bridge Engineering Co., Ltd., Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanghang","family":"Wang","sequence":"additional","affiliation":[{"name":"Gansu Hengtong Road & Bridge Engineering Co., Ltd., Lanzhou 730070, China"},{"name":"School of Chemistry and Chemical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"ref_1","unstructured":"Xu, X.Z., Wang, J.C., and Zhang, L.X. (2001). Physics of Permafrost, Science Press."},{"key":"ref_2","unstructured":"Ma, W., and Wang, D.Y. (2014). Permafrost Mechanics. Science Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1016\/j.applthermaleng.2017.04.128","article-title":"Deformation mechanism of an expressway embankment in warm and high ice content permafrost regions","volume":"121","author":"Chang","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10064-020-01919-3","article-title":"Monitoring of permafrost degradation along the Bei\u2019an Heihe Expressway in China","volume":"80","author":"Guo","year":"2021","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7652371","DOI":"10.1155\/2022\/7652371","article-title":"Analysis of necessity and feasibility for ground improvement in warm and ice-rich permafrost regions","volume":"2022","author":"Wang","year":"2022","journal-title":"Adv. Civil. Eng."},{"key":"ref_6","first-page":"2329","article-title":"Experimental study on hydrothermal distribution and frost heave characteristics of coarse-grained graded soil under unidirectional freezing condition","volume":"42","author":"Liu","year":"2023","journal-title":"Chin. J. Rock. Mech. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"100390","DOI":"10.1016\/j.trgeo.2020.100390","article-title":"Study on the heat and deformation characteristics of an expressway embankment with shady and sunny slopes in warm and ice-rich permafrost regions","volume":"24","author":"Luo","year":"2020","journal-title":"Transp. Geotech."},{"key":"ref_8","first-page":"1373","article-title":"Influence factors for the pot-cover effect","volume":"40","author":"Yao","year":"2018","journal-title":"Chin. J. Geotech. Eng."},{"key":"ref_9","first-page":"68","article-title":"Pot-cover effect of soil","volume":"44","author":"Li","year":"2014","journal-title":"Ind. Construction."},{"key":"ref_10","first-page":"1813","article-title":"Moisture transfer and phase change in unsaturated soils: Physical mechanism and numerical model for two types of \u201ccanopy effect\u201d","volume":"38","author":"Teng","year":"2016","journal-title":"Chin. J. Geotech. Eng."},{"key":"ref_11","first-page":"1190","article-title":"Vapour transfer and its effects on water content in freezing soil","volume":"40","author":"He","year":"2018","journal-title":"Chin. J. Geotech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1680\/geot.13.P.042","article-title":"A potential new frost heave mechanism in high-speed railway embankments","volume":"64","author":"Sheng","year":"2014","journal-title":"G\u00e9otechnique"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1680\/jgeot.16.P.016","article-title":"Canopy effect caused by vapour transfer in covered freezing soils","volume":"66","author":"Zhang","year":"2016","journal-title":"G\u00e9otechnique"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1139\/cgj-2014-0456","article-title":"Analysis of frost heave mechanisms in a high-speed railway embankment","volume":"53","author":"Zhang","year":"2016","journal-title":"Can. Geotech. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.coldregions.2016.02.011","article-title":"Importance of vapor flow in unsaturated freezing soil: A numerical study","volume":"126","author":"Zhang","year":"2016","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.coldregions.2016.10.007","article-title":"Soil moisture, ground temperatures, and deformation of a high-speed railway embankment in Northeast China","volume":"133","author":"Niu","year":"2017","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s11440-018-0740-8","article-title":"The study of frost heave mechanism of high-speed railway foundation by field-monitored data and indoor verification experiment","volume":"15","author":"Niu","year":"2020","journal-title":"Acta Geotech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"784","DOI":"10.2136\/vzj2006.0007","article-title":"Numerical analysis of coupled water, vapor, and heat transport in the vadose zone","volume":"5","author":"Saito","year":"2006","journal-title":"Vadose Zone J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"707","DOI":"10.2136\/sssaj2008.0094","article-title":"Water and vapor movement with condensation and evaporation in a sandy column","volume":"73","author":"Sakai","year":"2009","journal-title":"Soil. Sci. Soc. Am. J."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chen, W., Liu, B., Wu, Q., Zhao, Y., Wan, W., Liu, J., and Peng, W. (2025). Experimental Investigation of Acidic Dry\u2013wet Cycles on Coal-rock Combination: Mechanical Performance and Microstructural Analysis. Rock Mech. Rock Eng.","DOI":"10.1007\/s00603-025-04617-2"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103182","DOI":"10.1016\/j.coldregions.2020.103182","article-title":"Assessing frost heave susceptibility of gravelly soils based on multivariate adaptive regression splines model","volume":"181","author":"Wang","year":"2021","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102914","DOI":"10.1016\/j.coldregions.2019.102914","article-title":"An analysis of vapour transfer in unsaturated freezing soils","volume":"169","author":"He","year":"2020","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"892","DOI":"10.2136\/sssaj1980.03615995004400050002x","article-title":"A closed-form equation for predicting the hydraulic conductivity of unsaturated soils","volume":"44","year":"1980","journal-title":"Soil. Sci. Soc. Am. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1016\/j.applthermaleng.2017.10.121","article-title":"Theory and application of a novel soil freezing characteristic curve","volume":"129","author":"Bai","year":"2018","journal-title":"Appl. Therm. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1029\/WR012i003p00513","article-title":"A new model for predicting the hydraulic conductivity of unsaturated porous media","volume":"12","author":"Mualem","year":"1976","journal-title":"Water Resour. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.2136\/sssaj1996.03615995006000040008x","article-title":"Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: II. Field evaluation","volume":"60","author":"Noborio","year":"1996","journal-title":"Soil. Sci. Soc. Am. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1139\/t78-058","article-title":"A model for coupled heat and moisture transfer during soil freezing","volume":"15","author":"Taylor","year":"1978","journal-title":"Can. Geotech. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10596-010-9197-z","article-title":"Three-phase numerical model of water migration in partially frozen geological media: Model formulation, validation, and applications","volume":"15","author":"Painter","year":"2011","journal-title":"Comput. Geosci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.2136\/sssaj1984.03615995004800010005x","article-title":"Enhancement of thermal water vapor diffusion in soil","volume":"48","author":"Cass","year":"1984","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_30","first-page":"131","article-title":"Equations and numerical simulation for coupled water and heat transfer in frozen soil","volume":"37","author":"Bai","year":"2015","journal-title":"Chin. J. Geotech. Eng."},{"key":"ref_31","unstructured":"Wu, J.C., Lu, Y., Zhang, Y.Y., Wang, J., and Liu, S. (2025). A mathematical model describing the frozen deformation of unsaturated clayey soils in a closed system. Chin. J. Geotech. Eng., 1\u201310. Available online: https:\/\/kns.cnki.net\/kcms2\/article\/abstract?v=RK2PMiCRJa1ApeouRAnTfNSzqYlS9OsIiEbBIDzO1YViT3qf7ZI7RxCGxk8Pvikm68CX9e1rIdacVLZ4rY0jxJWdGj6V7NIBMODEKTpgMum9RJyMW-wEuEngPrVVUPPWxVhAObFJEY12KqA_A_nM06jz1bDJc5kRpjdlkb4gwzI=&uniplatform=NZKPT."},{"key":"ref_32","first-page":"1677","article-title":"Temperature and deformation analysis on slope subgrade with rich moisture of Qinghai-Tibet railway in permafrost regions","volume":"35","author":"Zhang","year":"2016","journal-title":"Chin. J. Rock Mech. Eng."},{"key":"ref_33","unstructured":"Li, Z.M. (2021). Research on Coupling of Multifield in Frozen Soil Based on Hybrid Mixture. [Ph.D. Thesis, Harbin Institute of Technology]."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1357\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:30:44Z","timestamp":1760034644000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":33,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081357"],"URL":"https:\/\/doi.org\/10.3390\/sym17081357","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,8,19]]}}}