Journal of Jilin University(Engineering and Technology Edition) ›› 2026, Vol. 56 ›› Issue (9): 2395-2407.doi: 10.13229/j.cnki.jdxbgxb.20250212

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Theoretical model of water-heat coupling and deformation law of roadbed in cold area

Yong-ming HE(),Peng-fei ZHANG,Jin-yang WANG,Xin TONG,Chen LIANG   

  1. School of Civil and Transportation Engineering，Northeast Forestry University，Harbin 150040，China
  • Received:2025-02-20 Online:2026-09-01 Published:2026-09-07

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Abstract:

To investigate the deformation mechanisms of subgrade in cold regions under hydro-thermal coupling effects， this study focuses on the TQ-Yichun section （62.44 km） of the G1111 He-ha Expressway. A two-dimensional coupled hydro-thermal migration model was developed to analyze the interactions among temperature fields， moisture fields， and deformation fields during freeze-thaw cycles. Based on the theory of phase change heat transfer and non-isothermal moisture migration， Abaqus software was used for simulation and analysis， and nine integrated monitoring points were deployed along the roadway cross-section at a spacing of 1.25 m to quantify the deformation characteristics of the surface layer of the roadway in the freezing and thawing stages. Key findings include： The maximum frost heave displacement at the subgrade surface during freezing periods reached 8.48 mm， with cross-sectional deformation exhibiting a parabolic distribution. The thaw settlement rate in spring （March-May， 0.12 mm/day） was significantly higher than the frost heave rate during freezing periods （0.07 mm/day）， with frost heave rates between November-January surpassing those of January-February by 18.7%. Vertical deformation extremes showed a negative correlation with geothermal gradients. By introducing dynamic ice-water phase-change correction coefficients， the study improves simulation accuracy and proposes a predictive model for subgrade deformation. These results provide critical insights for optimizing frost-resistant designs in cold-region road engineering， particularly in determining interfacial heat transfer coefficients and insulation layer thickness. The research establishes a theoretical foundation for mitigating subgrade deformation and controlling freeze-thaw-induced pavement deterioration in permafrost environments.

Key words: hydro-thermal coupling, deformation law, numerical simulation, permafrost roadbed, finite element

CLC Number: 

  • U416.1

Fig.1

Structure of calculation area"

Fig.2

Grid division of computational area"

Table 1

Thermophysical parameters of the soil"

土壤类型土体状态

导热系数k/

［W·（m·℃）-1］

比热容C/

［J·（kg·℃）-1］

亚黏土冻土1.7471 864
未冻土1.2111 574
砂砾土冻土2.5861 087
未冻土1.9761 516

Table 2

Water movement parameters of the soil"

土壤参数单位亚黏土砂砾土
导水率kucm/s1×10-52×10-6
扩散率Ducm2/s11×10-5

Table 3

Climatological data for Yichun City， 2023"

月份

月平均

气温

/℃

月最高

气温

/℃

月最低

气温

/℃

日太阳辐射量/［（MJ·m-2·d-1）］有效日照时间/（h·d-1）
1-22.242.30-41.305.424.41
2-13.645.80-29.508.416.96
3-1.2518.40-19.6012.327.21
45.3720.90-5.8014.245.92
513.4928.90-2.8017.698.22
618.4534.104.6015.736.89
721.2230.4014.1012.354.87
820.2831.2011.3010.904.76
914.5229.400.1011.497.24
106.1820.90-8.208.706.59
11-9.783.90-26.105.083.31
12-19.503.50-35.204.292.97

Table 4

Calculation model wind speed table at each boundary"

月份阴坡风速阳坡风速路基风速地基风速
12.422.672.842.72
22.783.013.083.06
33.293.373.523.44
43.844.034.204.16
53.783.903.983.94
63.083.113.213.15
72.602.672.812.73
82.542.612.732.68
92.792.883.012.92
103.213.273.443.38
113.083.193.363.27
122.632.722.832.79

Fig.3

Temperature field distribution of roadbed in melting-freezing stage"

Fig.4

Temperature field distribution of roadbed in freezing-thawing stage"

Fig.5

Temperature trend along depth direction at point A over course of a year"

Fig.6

Distribution of moisture field in tundra roadbed"

Fig.7

Distribution of longitudinal moisture saturation of roadbed by month"

Fig.8

Displacement field distribution of frozen roadbed in November"

Fig.9

Vertical displacement map of roadbed surface"

Fig.10

Uneven settlement values of roadbed shady slopes"

Table 5

Average vertical relative displacement extremes of pavements"

路面宽

度/m

路面平均竖向相对变形量/mm
最大值最小值极差
0.004.800.853.95
1.252.23-0.883.11
2.500.86-1.642.50
3.751.19-1.352.54
5.001.37-1.763.13
6.251.23-1.272.50
7.501.15-1.352.50
8.753.02-0.743.76
10.008.480.787.70

Fig.11

Probability plot of extreme distribution of displacement field in road cross-section"

Table 6

Inversion of vertical displacement field model of road cross-section"

月份线性拟合抛物线拟合
公式R2公式R2
1y=0.223d+3.4680.070 3y=-2.388d2+0.261d+7.2760.842 4
2y=0.219d+3.3430.064 4y=-2.487d2+0.271d+7.2890.851 4
3y=0.214d+2.8310.113 1y=-1.761d2+0.198d+5.7110.887 4
4y=0.152d+1.9030.082 2y=-1.272d2+0.142d+3.9790.658 5
5y=0.091d+3.2190.026 5y=-1.689d2+0.178d+5.8160.833 9
6y=0.061d+3.6290.009 9y=-1.921d2+0.198d+6.5190.860 6
7y=0.067d+4.0460.012 4y=-1.865d2+0.193d+6.8630.836 1
8y=-0.032d+3.1500.099 8y=-0.372d2+0.034d+3.6450.990 4
9y=-0.118d+3.4060.151 7y=-1.087d2+0.097d+4.8190.969 9
10y=0.084d+3.0140.113 2y=-0.365d2+0.045d+3.6680.374 9
11y=0.181d+2.3280.130 3y=-1.162d2+0.134d+4.2860.709 9
12y=0.231d+2.5960.107 3y=-1.819d2+0.205d+5.5860.783 6

Fig.12

Validation of surface temperature model"

Fig.13

Verification of settlement model for center of roadbed"

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