Study of Heat–Mass Transfer and Salt–Frost Expansion Mechanism of Sulfate Saline Soil during the Unidirectional Freezing Process
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
The water and salt movement and crystallization deformation of saline soil in cold and arid regions is a complex hydrothermal–salt–mechanical coupling problem. Based on the law of mass conservation, the law of energy conservation, and the theory of permafrost mechanics, the hydrothermal–salt–mechanical coupling mathematical model of unsaturated sodium sulfate saline soil is established. The model takes into account the latent heat of phase transition, crystallization impedance, consumption of crystallization, ice crystal self-cleaning behavior, and temperature as mechanical parameters. Numerical simulations using COMSOL Multiphysics (version 5.5) software were carried out, and the outcomes were analyzed and compared with unidirectional freezing test data. The findings show that the coupled model accurately simulates heat–mass transfer, crystallization, and salt freeze–thaw deformation in unsaturated saline soil. In the unidirectional freezing process, the temperature, salt freezing deformation, and freezing depth within the saline soil showed a three-stage rule of change, and the migration of water and salt to the freezing front made the water and salt content in the freezing zone increase significantly and form a laminar distribution, and the peak of the water and salt content appeared at the freezing front. The migration of water and salt aids in forming ice and salt crystals that rapidly grow within the soil pores of the freezing zone, leading to salt freeze–thaw deformation. Furthermore, the models and results of this study offer crucial insights into the mechanisms of soil salinization, desertification, and salt freeze–thaw deformation in cold and arid regions.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and codes generated or used for the analysis in the paper appear in the published article.
Acknowledgments
This study was supported by the Research Initiation Program for Introducing High-level Talents of Tianshui Normal University (Grant No. KYQ2023-06); the Science and Technology Program of Gansu Province (Grant Nos. 22JR5RA325 and 22JR5RE200); the Project of Innovation Fund for College Teachers of Gansu Provincial Department of Education (2024A-121); and the Qinzhou District, Tianshui City, Gansu Province, Science and Technology Major Special Programs (Grant No. 2023-SHFZG-4741).
References
Ahmadi, S., H. Ghasemzadeh, and F. Changizi. 2021a. “Effects of a low-carbon emission additive on mechanical properties of fine-grained soil under freeze–thaw cycles.” J. Clean. Prod. 304: 127157. https://doi.org/10.1016/j.jclepro.2021.127157.
Ahmadi, S., H. Ghasemzadeh, and F. Changizi. 2021b. “Effects of thermal cycles on microstructural and functional properties of nano treated clayey soil.” Eng. Geol. 280: 105929. https://doi.org/10.1016/j.enggeo.2021.105929.
Alizadeh, A. H., M. Akbarabadi, E. Barsotti, M. Piri, N. Fishman, and N. Nagarajan. 2018. “Salt precipitation in ultratight porous media and its impact on pore connectivity and hydraulic conductivity.” Water Resour. Res. 54 (4): 2768–2780. https://doi.org/10.1029/2017WR021394.
Asadizadeh, M., A. Hedayat, L. Tunstall, J. A. V. Gonzalez, J. W. V. Alvarado, and M. T. Neira. 2024. “The impact of slag on the process of geopolymerization and the mechanical performance of mine-tailings-based alkali-activated lightweight aggregates.” Constr. Build. Mater. 411: 134347. https://doi.org/10.1016/j.conbuildmat.2024.134347.
Bai, Q. B., L. I. Xu, Y. H. Tian, and J. H. Fang. 2015. “Equations and numerical simulation for coupled water and heat transfer in frozen soil.” [In Chinese.] Chin. J. Geotech. Eng. 37 (S2): 131–136. https://doi.org/10.11779/CJGE2015S2026.
Bai, R. Q., Y. M. Lai, W. S. Pei, and M. Y. Zhang. 2020a. “Investigation on frost heave of saturated–unsaturated soils.” Acta Geotech. 15 (3): 3295–3306. https://doi.org/10.1007/s11440-020-00952-6.
Bai, R. Q., Y. M. Lai, M. Y. Zhang, and J. G. Ren. 2020b. “Study on the coupled heat–water–vapor–mechanics process of unsaturated soils.” J. Hydrol. 585: 124784. https://doi.org/10.1016/j.jhydrol.2020.124784.
Benson, C. H., I. Chiang, T. Chalermyanont, and A. Sawangsuriya. 2014. “Estimating van Genuchten parameters α and n for clean sands from particle size distribution data.” In From Soil Behavior Fundamentals to Innovations in Geotechnical Engineering: Honoring Roy E. Olson, edited by M. Iskander, John E. Garlanger, and Mohamad H. Hussein, 410–427. Reston, VA: ASCE.
Bing, H., P. He, and Y. Zhang. 2015. “Cyclic freeze–thaw as a mechanism for water and salt migration in soil.” Environ. Earth Sci. 74 (1): 675–681. https://doi.org/10.1007/s12665-015-4072-9.
Cameron, D. R., and A. Klute. 1977. “Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model.” Water Resour. Res. 13 (1): 183–188. https://doi.org/ 10.1029/wr013i001p00183.
Cardiff, M., and P. K. Kitanidis. 2008. “Efficient solution of nonlinear, underdetermined inverse problems with a generalized PDE model.” Comput. Geosci. 34 (11): 1480–1491. https://doi.org/10.1016/j.cageo.2008.01.013.
Castellazzi, G., C. Colla, S. D. Miranda, D. Formicac, E. Gabrielli, L. Molari, and F. Ubertini. 2013. “A coupled multiphase model for hygrothermal analysis of masonry structures and prediction of stress induced by salt crystallization.” Constr. Build. Mater. 41: 717–731. https://doi.org/10.1016/j.conbuildmat.2012.12.045.
Fu, Q., R. J. Hou, T. X. Li, M. Wang, and J. W. Yan. 2018. “The functions of soil water and heat transfer to the environment and associated response mechanisms under different snow cover conditions.” Geoderma 325: 9–17. https://doi.org/10.1016/j.geoderma.2018.03.022.
Ghoreishian Amiri, S. A., G. Grimstad, and M. Kadivar. 2022. “An elastic-viscoplastic model for saturated frozen soils.” Eur. J. Environ. Civ. Eng. 26 (7): 2537–2553. https://doi.org/10.1080/19648189.2020.1753797.
Ghoreishian Amiri, S. A., G. Grimstad, M. Kadivar, and S. Nordal. 2016. “Constitutive model for rate-independent behavior of saturated frozen soils.” Can. Geotech. J. 53 (10): 1646–1657. https://doi.org/10.1139/cgj-2015-0459.
Harlan, R. L. 1973. “Analysis of coupled heat–fluid transport in partially frozen soil.” Water Resour. Res. 9 (5): 1314–1323. https://doi.org/10.1029/wr009i005p01314.
Kjelstrup, S., S. A. Ghoreishian Amiri, B. Loranger, H. Gao, and G. Grimstad. 2021. “Transport coefficients and pressure conditions for growth of ice lens in frozen soil.” Acta Geotech. 16: 2231–2239. https://doi.org/10.1007/s11440-021-01158-0.
Koniorczyk, M. 2012. “Salt transport and crystallization in non-isothermal, partially saturated porous materials considering ions interaction model.” Int. J. Heat Mass Transfer 55 (4): 665–679. https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.043.
Konrad, J.-M., and N. R. Morgenstern. 1981. “The segregation potential of a freezing soil.” Can. Geotech. J. 18 (4): 482–491. https://doi.org/10.1139/t81-059.
Lai, Y. M., W. S. Pei, M. Y. Zhang, and Z. J. Zhou. 2014. “Study on theory model of hydro-thermal–mechanical interaction process in saturated freezing silty soil.” Int. J. Heat Mass Transfer 78: 805–819. https://doi.org/10.1016/j.ijheatmasstransfer.2014.07.035.
Li, S. Y., M. Y. Zhang, W. S. Pei, and Y. M. Lai. 2018. “Experimental and numerical simulations on heat–water–mechanics interaction mechanism in a freezing soil.” Appl. Therm. Eng. 132: 209–220. https://doi.org/10.1016/j.applthermaleng.2017.12.061.
Li, S. Y., M. Y. Zhang, Y. B. Tian, W. S. Pei, and H. Zhong. 2015. “Experimental and numerical investigations on frost damage mechanism of a canal in cold regions.” Cold Reg. Sci. Technol. 116: 1–11. https://doi.org/10.1016/j.coldregions.2015.03.013.
Li, Z. M., J. Chen, A. P. Tang, and S. Mitsutaka. 2021. “A novel model of heat–water–air–stress coupling in unsaturated frozen soil.” Int. J. Heat Mass Transfer 175: 121375. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121375.
Luo, C. L. 2023. “Study on water–heat–salt–vapor migration and salt-frost heaving deformation of sulfuric saline soil in Hexi area.” [In Chinese.] Ph.D. Dissertation, School of Civil Engineering, Univ. of Lanzhou Jiaotong.
Luo, C.-L., Y.-Y. Yu, J. Zhang, J.-Y. Tao, Q.-J. Ou, and W.-H. Cui. 2023. “Thermal–water–salt coupling process of unsaturated saline soil under unidirectional freezing.” J. Mountain Sci. 20 (2): 557–569. https://doi.org/10.1007/s11629-022-7652-7.
Ministry of Transport of the People's Republic of China. 2020. Test methods of soils for highway engineering. [In Chinese.] Beijing: P.R. Ministry of Communications Press.
Mokni, N., S. Olivella, and E. E. Alonso. 2010. “Swelling in clayey soils induced by the presence of salt crystals.” Appl. Clay Sci. 47 (1–2): 105–112. https://doi.org/10.1016/j.clay.2009.01.005.
Naillon, A., P. Joseph, and M. Prat. 2018. “Ion transport and precipitation kinetics as key aspects of stress generation on pore walls induced by salt crystallization.” Phys. Rev. Lett. 120 (3): 034502. https://doi.org/10.1103/PhysRevLett.120.034502.
Panday, S., and M. Y. Corapcioglu. 1991. “Solute rejection in freezing soils.” Water Resour. Res. 27 (1): 99–108. https://doi.org/10.1029/90WR01785.
Richards, L. A. 1931. “Capillary conduction of liquids in porous mediums.” Physics 1: 318–333. https://doi.org/10.1063/1.1745010.
Shao, X., B. Qin, Q. Shi, Y. Yang, Z. Ma, Y. Li, Z. Jiang, and W. Jiang. 2024. “The impacts of CO2 mineralization reaction on the physicochemical characteristics of fly ash: A study under different reaction conditions of the water-to-solid ratio and the pressure of CO2.” Energy 287: 129676. https://doi.org/10.1016/j.energy.2023.129676.
Shen, M., and B. Ladanyi. 1987. “Modelling of coupled heat, moisture and stress field in freezing soil.” Cold Reg. Sci. Technol. 14 (3): 237–246. https://doi.org/10.1016/0165-232X(87)90016-4.
Steiger, M., and S. Asmussen. 2008. “Crystallization of sodium sulfate phases in porous materials: The phase diagram Na2SO4-H2O and the generation of stress.” Geochim. Cosmochim. Acta 72 (17): 4291–4306. https://doi.org/10.1016/j.gca.2008.05.053.
van Genuchten, M. T. 1980. “Closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Wang, D. Y., J. K. Liu, and X. Li. 2016. “Numerical simulation of coupled water and salt transfer in soil and a case study of the expansion of subgrade composed by saline soil.” Procedia Eng. 143: 315–322. https://doi.org/10.1016/j.proeng.2016.06.040.
Wei, M. D., and F. Dai. 2021. “Laboratory-scale mixed-mode I/II fracture tests on columnar saline ice.” Theor. Appl. Fract. Mech. 114: 102982. https://doi.org/10.1016/j.tafmec.2021.102982.
Wei, M. D., A. Polojärvi, D. M. Cole, and M. Prasanna. 2020. “Strain response and energy dissipation of floating saline ice under cyclic compressive stress.” Cryosphere 14 (9): 2849–2867. https://doi.org/10.5194/tc-14-2849-2020.
Wei, M. D., M. Prasanna, D. M. Cole, and A. Polojärvi. 2022. “Response of dry and floating saline ice to cyclic compression.” Geophys. Res. Lett. 49 (15): e2022GL099457. https://doi.org/10.1029/2022GL099457.
Wu, D. Y., Y. M. Lai, and M. Y. Zhang. 2015a. “Heat and mass transfer effects of ice growth mechanisms in a fully saturated soil.” Int. J. Heat Mass Transfer. 86: 699–709. https://doi.org/10.1016/j.ijheatmasstransfer.2015.03.044.
Wu, D. Y., X. Y. Zhou, and X. Y. Jiang. 2018. “Water and salt migration with phase change in saline soil during freezing and thawing processes.” Groundwater 56 (5): 742–752. https://doi.org/10.1111/gwat.12605.
Wu, M. S., X. Tan, J. S. Huang, J. W. Wu, and P.-K. Jansson. 2015b. “Solute and water effects on soil freezing characteristics based on laboratory experiments.” Cold Reg. Sci. Technol. 115: 22–29. https://doi.org/10.1016/j.coldregions.2015.03.007.
Xiao, Z. A., and Y. M. Lai. 2018. “Study on water and salt transfer mechanism in saline soil under freezing–thawing and dry–wet conditions.” Chin. J. Rock Mech. Eng. 37 (S1): 3738–3746. https://doi.org/10.13722/j.cnki.jrme.2016.1250.
Xiao, Z. A., L. Z. Zhu, Z. R. Hou, and X. Q. Dong. 2021. “Study on water/salt phase transition temperature of saline soil containing sodium chloride and sodium sulfate.” J. Glaciol. Geocryol. 43 (4): 1121–1129. https://doi.org/10.7522/j.issn.1000-0240.2021.0064.
Xu, J., W. Lan, Y. F. Li, S. H. Wang, W.-C. Cheng, and X. L. Yao. 2020. “Heat, water and solute transfer in saline loess under uniaxial freezing condition.” Comput. Geotech. 118: 103319. https://doi.org/10.1016/j.compgeo.2019.103319.
Xu, J., W. Lan, C. Ren, X. G. Zhou, S. H. Wang, and J. Yuan. 2021. “Modeling of coupled transfer of water, heat and solute in saline loess considering sodium sulfate crystallization.” Cold Reg. Sci. Technol. 189: 103335. https://doi.org/10.1016/j.coldregions.2021.103335.
Xu, X. Z., J. C. Wang, and L. X. Zhang. 2001. Frozen soil physics. [In Chinese.] Beijing: Science Press.
Yuanming, L., Z. Xuefu, X. Jianzhang, Z. Shujuan, and L. Zhiqiang. 2005. “Nonlinear analysis for frost-heaving force of land bridges on Qing–Tibet Railway in cold regions.” J. Therm. Stresses 28 (3): 317–331. https://doi.org/10.1080/01495730590909531.
Zhang, J., Y. Lai, Y. Zhao, and S. Y. Li. 2020a. “Study on the mechanism of crystallization deformation of sulfate saline soil during the unidirectional freezing process.” Permafrost Periglacial Process. 32 (1): 102–118. https://doi.org/10.1002/ppp.2080.
Zhang, J., Y. M. Lai, J. F. Li, and Y. H. Zhao. 2020b. “Study on the influence of hydro-thermal–salt–mechanical interaction in saturated frozen sulfate saline soil based on crystallization kinetics.” Int. J. Heat Mass Transfer 146: 118868. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118868.
Zhang, X. D., Q. Wang, G. Wang, W. H. Wang, H. Chen, and Z. Q. Zhang. 2017. “A study on the coupled model of hydrothermal–salt for saturated freezing salinized soil.” Math. Probl. Eng. 2017: 1–12. https://doi.org/10.1155/2017/4918461.
Zhang, X. D., Q. Wang, T. W. Yu, and G. Wang. 2018. “Numerical study on the multifield mathematical coupled model of hydraulic-thermal–salt–mechanical in saturated freezing saline soil.” Int. J. Geomech. 18 (7): 04018064. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001173.
Zhang, X. D., E. C. Zhai, Y. J. Wu, D. A. Sun, and Y. T. Lu. 2021. “Theoretical and numerical analyses on hydro-thermal–salt–mechanical interaction of unsaturated salinized soil subjected to typical unidirectional freezing process.” Int. J. Geomech. 21 (7): 04021104. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002036.
Zhang, Y., R.-Z. Tian, and T.-L. Wang. 2023. “Study on salt expansion mechanism of subgrade-culvert transition section in saline soils and cold regions.” Cold Reg. Sci. Technol. 205: 103701. https://doi.org/10.1016/j.coldregions.2022.103701.
Zhou, J. Z., and D. Q. Li. 2012. “Numerical analysis of coupled water, heat and stress in saturated freezing soil.” Cold Reg. Sci. Technol. 72: 43–49. https://doi.org/10.1016/j.coldregions.11:006.
Zhou, L. Z., F. X. Zhou, Y. Sai, and S. Y. Li. 2021. “Study on water and salt migration and deformation properties of unsaturated saline soil under a temperature gradient considering salt adsorption: Numerical simulation and experimental verification.” Comput. Geotech. 134: 104094. https://doi.org/10.1016/j.compgeo.2021.104094.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Sep 30, 2023
Accepted: May 3, 2024
Published online: Aug 6, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 6, 2025
ASCE Technical Topics:
- Chemical compounds
- Chemical properties
- Chemicals
- Chemistry
- Cold regions engineering
- Continuum mechanics
- Deformation (mechanics)
- Engineering mechanics
- Environmental engineering
- Freeze and thaw
- Freezing
- Frozen soils
- Geomechanics
- Geotechnical engineering
- Pollutants
- Salinity
- Salt water
- Salts
- Soil deformation
- Soil dynamics
- Soil mechanics
- Soil properties
- Soil water
- Soils (by type)
- Solid mechanics
- Structural mechanics
- Sulfates
- Water (by type)
- Water and water resources
- Water management
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.