Roads are exposed to various degradation mechanisms during their lifetime. The pavement deterioration caused by the surrounding environment is particularly severe in winter when the humidity and subfreezing temperatures prevail. Frost heave-induced damage is one of the winter-related pavement deterioration. It occurs when the porewater in the soil is exposed to freezing temperatures. The study of frost heave requires conducting a multiphysics analysis, considering the thermal, mechanical, and hydraulic fields. This paper presents the use of a coupled thermo-mechanical approach to simulate frost heave in saturated soils. A function predicting porosity evolution is implemented to couple the thermal and mechanical field analyses. This function indirectly considers the effect of the water seepage inside the soil. Different frost heave scenarios with uniform and non-uniform boundary conditions are considered to demonstrate the capabilities of the method. The results of the simulations indicate that the thermo-mechanical model captures various processes involved in the frost heave phenomenon, such as water fusion, porosity variation, cryogenic suction force generation, and soil expansion. The characteristics and consequences of each process are determined and discussed separately. Furthermore, the results show that non-uniform thermal boundaries and presence of a culvert inside the soil result in uneven ground surface deformations.
thermal conductivity of soil particles, (W·m–1·K–1)
1.95
thermal conductivity of water, (W·m–1·K–1)
0.56
thermal conductivity of ice, (W·m–1·K–1)
2.24
volumetric heat capacity of soil particles, (MJ·m–3·K–1)
2.358
volumetric heat capacity of water, (MJ·m–3·K–1)
4.18
volumetric heat capacity of ice, (MJ·m–3·K–1)
1.834
specific latent heat of fusion of water, (J·kg–1)
333 × 103
Poisson’s ratio,
0.3
mass density of soil particles, (kg·m–3)
2620
mass density of water, (kg·m–3)
1000
mass density of ice, (kg·m–3)
917
Tab.1
Fig.7
parameter
value
(s?1)
6.02 × 10?5
(°C)
?0.87
(°C·m?1)
100
(MPa)
0.56
Tab.2
parameter
value
(MPa?1)
0.26
1.85
0.43
0.01
Tab.3
Fig.8
Fig.9
Fig.10
Fig.11
Fig.12
Fig.13
Fig.14
Fig.15
Fig.16
Fig.17
Fig.18
Fig.19
Fig.20
Fig.21
1
X Chen, D Shi. Influence of freeze–thaw cycles on apparent dynamic tensile strength, apparent dynamic fracture toughness and microstructure of concrete under impact loading. European Journal of Environmental and Civil Engineering, 2019, 25(11): 1977–2001
2
O Sylvestre, J P Bilodeau, G Doré. Effect of frost heave on long-term roughness deterioration of flexible pavement structures. International Journal of Pavement Engineering, 2019, 20(6): 704–713 https://doi.org/10.1080/10298436.2017.1326598
3
B Sun, Y Yang, X Li, M Yan, M Xie, Y Bao. Full-scale investigation of post-tensioned prestressed concrete bridge girders subjected to frost heaving in cold regions. Engineering Structures, 2022, 250: 113413 https://doi.org/10.1016/j.engstruct.2021.113413
J K Mitchell. Fundamentals of the Soil Behavior. New York: John Wiley & Sons, 1976
6
S Takagi. Segregation freezing as the cause of suction force for ice lens formation. Engineering Geology, 1979, 13(1−4): 93−100
7
L A Wilen, J G Dash. Frost heave dynamics at a single crystal interface. Physical Review Letters, 1995, 74(25): 5076–5079
8
A W Rempel, J S Wettlaufer, M G Worster. Interfacial premelting and the thermomolecular force: Thermodynamic buoyancy. Physical Review Letters, 2001, 87(8): 088501 https://doi.org/10.1103/PhysRevLett.87.088501
9
D Dagli. Laboratory Investigations of Frost Action Mechanisms in Soils. Luleå: Luleå University of Technology, 2017
10
E J Chamberlain. Frost Susceptibility of Soil, Review of Index Tests. Hanover: Cold Regions Research and Engineering Lab, 1981
11
T TakashiH YamamotoT OhraiM Masuda. Effect of penetration rate of freezing and confining stress on the frost heave ratio of soil. In: Proceedings of the 3rd International Conference on Permafrost. Proceedings of the 3rd International Conference on Permafrost, 1978
12
H Zheng, S Kanie. Combined thermal-hydraulic-mechanical frost heave model based on Takashi’s equation. Journal of Cold Regions Engineering, 2015, 29(4): 04014019 https://doi.org/10.1061/(ASCE)CR.1943-5495.0000089
13
J M Konrad, N R Morgenstern. The segregation potential of a freezing soil. Canadian Geotechnical Journal, 1981, 18(4): 482–491 https://doi.org/10.1139/t81-059
14
J M Konrad, N R Morgenstern. Frost heave prediction of chilled pipelines buried in unfrozen soils. Canadian Geotechnical Journal, 1984, 21(1): 100–115 https://doi.org/10.1139/t84-008
15
K O’Neill, R D Miller. Exploration of a rigid ice model of frost heave. Water Resources Research, 1985, 21(3): 281–296 https://doi.org/10.1029/WR021i003p00281
16
R L Michalowski. A constitutive model of saturated soils for frost heave simulations. Cold Regions Science and Technology, 1993, 22(1): 47–63 https://doi.org/10.1016/0165-232X(93)90045-A
17
R L Michalowski, M Zhu. Frost heave modeling using porosity rate function. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(8): 703–722 https://doi.org/10.1002/nag.497
18
N Li, B Chen, F Chen, X Xu. The coupled heat−moisture−mechanic model of the frozen soil. Cold Regions Science and Technology, 2000, 31(3): 199–205 https://doi.org/10.1016/S0165-232X(00)00013-6
19
N Li, F Chen, B Su, G Cheng. Theoretical frame of the saturated freezing soil. Cold Regions Science and Technology, 2002, 35(2): 73–80 https://doi.org/10.1016/S0165-232X(02)00029-0
20
N Li, F Chen, B Xu, G Swoboda. Theoretical modeling framework for an unsaturated freezing soil. Cold Regions Science and Technology, 2008, 54(1): 19–35 https://doi.org/10.1016/j.coldregions.2007.12.001
21
S Nishimura, A Gens, S Olivella, R J Jardine. THM-coupled finite element analysis of frozen soil: Formulation and application. Geotechnique, 2009, 59(3): 159–171 https://doi.org/10.1680/geot.2009.59.3.159
22
Z Liu, X Yu. Coupled thermo-hydro-mechanical model for porous materials under frost action. Acta Geotechnica, 2011, 6(2): 51–65 https://doi.org/10.1007/s11440-011-0135-6
23
J Zhou, D Li. Numerical analysis of coupled water, heat and stress in saturated freezing soil. Cold Regions Science and Technology, 2012, 72: 43–49 https://doi.org/10.1016/j.coldregions.2011.11.006
24
X Yin, E Liu, B Song, D Zhang. Numerical analysis of coupled liquid water, vapor, stress and heat transport in unsaturated freezing soil. Cold Regions Science and Technology, 2018, 155: 20–28 https://doi.org/10.1016/j.coldregions.2018.07.008
25
X Weng, Y Sun, Z Yang, D Wang, H Yu. A thermal-hydromechanical coupled model for poro-viscoplastic saturated freezing soil. European Journal of Environmental and Civil Engineering, 2020, 26(9): 4220–4236
26
Y Lai, W Pei, M Zhang, J Zhou. Study on theory model of hydro-thermal-mechanical interaction process in saturated freezing silty soil. International Journal of Heat and Mass Transfer, 2014, 78: 805–819 https://doi.org/10.1016/j.ijheatmasstransfer.2014.07.035
27
Y Zhang, R L Michalowski. Thermal-hydro-mechanical analysis of frost heave and thaw settlement. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(7): 04015027 https://doi.org/10.1061/(ASCE)GT.1943-5606.0001305
28
Y A Çengel. Heat and Mass Transfer: A Practical Approach. New York: McGraw-Hill, 2007
29
M Hohmann. Soil freezing—The concept of soil water potential. State of the art. Cold Regions Science and Technology, 1997, 25(2): 101–110 https://doi.org/10.1016/S0165-232X(96)00019-5
30
A Bower. Applied Mechanics of Solids. Boca Raton: CRC Press, 2009
31
N Vu-Bac, T X Duong, T Lahmer, P Areias, R A Sauer, H S Park, T Rabczuk. A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 480–510 https://doi.org/10.1016/j.cma.2019.03.011
32
N Vu-Bac, T Rabczuk, H S Park, X Fu, X Zhuang. A NURBS-based inverse analysis of swelling induced morphing of thin stimuli-responsive polymer gels. Computer Methods in Applied Mechanics and Engineering, 2022, 397: 115049 https://doi.org/10.1016/j.cma.2022.115049
33
P Areias, N Vu-Bac, T Rabczuk. A multisurface constitutive model for highly cross-linked polymers with yield data obtained from molecular dynamics simulations. International Journal of Mechanics and Materials in Design, 2018, 14(1): 21–36 https://doi.org/10.1007/s10999-016-9358-x
34
J Ren, S K Vanapalli, Z Han. Soil freezing process and different expressions for the soil-freezing characteristic curve. Sciences in Cold and Arid Regions, 2018, 9(3): 221–228
B L Kurylyk, K Watanabe. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Advances in Water Resources, 2013, 60: 160–177 https://doi.org/10.1016/j.advwatres.2013.07.016
37
M T van Genuchten. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, 44(5): 892–898 https://doi.org/10.2136/sssaj1980.03615995004400050002x
38
A Moberg. Stockholm Historical Weather Observations—Daily Mean Air Temperatures Since 1756. Stockholm: Bolin Centre Database, 2020
39
P J WilliamsM V Smith. The Frozen Earth, Fundamentals of Geocryology. Cambridge: Cambridge University Press, 1989
40
A P S Selvadurai, J Hu, I Konuk. Computational modeling of frost heave induced soil–pipeline interaction: I. Modeling of frost heave. Cold Regions Science and Technology, 1999, 29: 215–228 https://doi.org/10.1016/S0165-232X(99)00028-2
41
B LadanyiM Shen. Freezing pressure development on a buried chilled pipeline. In: Proceedings of International Symposium on Frost Geotechnical Engineering. Rotterdam: A.A. Balkema, 1993
42
M FukudaH KimY Kim. Preliminary results of frost heave experiments using standard test sample provided by TC8. In: Proceedings of Ground Freezing 97: Frost Action in Soils. Boca Raton: CRC Press, 1997
