Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process
Abstract
1. Introduction
2. Theoretical Model
2.1. Computational Modelling of Water–Heat–Vapor Migration in Unsaturated Soils Under Unidirectional Freezing Action
- Soil is a continuous, isotropic, and porous medium.
- Water migration in unsaturated soil encompasses only the migration of liquid water and water vapor, disregarding ice migration.
- Unsaturated frozen soil pores have connectivity, and the pressure borne by each point is atmospheric.
- In the calculation of frost heave deformation, the soil is in a long-term static equilibrium state, and all stress and strain is caused by frost heaving.
2.1.1. Water and Vapor Migration Control Equations
2.1.2. Temperature Control Equations
2.2. Calculation of Frost Heave Volume Change of Unsaturated Silty Clay
3. Model Test and Validation
3.1. Model Test
3.2. Model Validation
4. Analysis of Simulation Results
4.1. Analysis of the Results of the Hydrothermal Field of the Freezing Process
4.2. Analysis of Freezing Deformation Results of the Freezing Process
5. Conclusions and Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Unit | Value | Parameters | Unit | Value |
---|---|---|---|---|---|
Volumetric heat capacity of soil particles Cn | kJ∙m−3∙K−1 | 2160 | Residual moisture content θr | m3∙m−3 | 0.05 |
Ice volume heat capacity Ci | kJ∙m−3∙K−1 | 1874 | Saturated water content θs | m3∙m−3 | 0.55 |
Volumetric heat capacity of water Cl | kJ∙m−3∙K−1 | 4180 | VG model parameters α | m−1 | 0.149 |
Volumetric heat capacity of air Cv | kJ∙m−3∙K−1 | 1.21 | VG model parameters m | 1 | 0.267 |
Thermal conductivity of soil particles λn | W∙m−1∙K−1 | 1.2 | Shape factor | °C−1 | 0.522 |
Ice thermal conductivity λi | W∙m−1∙K−1 | 2.22 | Coefficient of ice–water ratio b | 1 | 0.47 |
Thermal conductivity of water λl | W∙m−1∙K−1 | 0.58 | Clay mass fraction fc | 1 | 0.7 |
Air thermal conductivity λv | W∙m−1∙K−1 | 0.025 | Saturated permeability coefficient Ks | m∙s−1 | 10−7 |
Soil particle density ρs | kg∙m−3 | 2700 | Modulus calculation factor a1 | MPa | 28 |
Ice density ρi | kg∙m−3 | 917 | Modulus calculation factor b1 | 1 | 26 |
Density of water ρl | kg∙m−3 | 1000 | Poisson’s ratio calculation factor a2 | 1 | 0.4 |
Freezing temperature Tf | K | 272.85 | Poisson’s ratio calculation factor b2 | 1 | −0.0080 |
Latent heat of phase transition of ice and water Lf | kJ∙kg−1 | 334.5 | Cohesion calculation factor a3 | MPa | 0.150 |
Gravity acceleration g | m∙s−2 | 9.8 | Cohesion calculation factor b3 | 1 | 0.090 |
Molar mass of water M | kg∙mol−1 | 0.018 | Calculation factor for angle of internal friction a4 | 1 | 22.0 |
Vapor constant R | J∙mol−1∙K−1 | 8.341 | Calculation factor for angle of internal friction b4 | 1 | 8.00 |
25 °C surface tension γ0 | g∙K−2 | 71.89 |
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Li, D.; Wang, H. Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process. Symmetry 2025, 17, 1357. https://doi.org/10.3390/sym17081357
Li D, Wang H. Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process. Symmetry. 2025; 17(8):1357. https://doi.org/10.3390/sym17081357
Chicago/Turabian StyleLi, Dengzhou, and Hanghang Wang. 2025. "Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process" Symmetry 17, no. 8: 1357. https://doi.org/10.3390/sym17081357
APA StyleLi, D., & Wang, H. (2025). Water, Heat, Vapor Migration, and Frost Heaving Mechanism of Unsaturated Silty Clay During a Unidirectional Freezing Process. Symmetry, 17(8), 1357. https://doi.org/10.3390/sym17081357