Study on Seasonal Permafrost Roadbed Deformation Based on Water–Heat Coupling Characteristics
Abstract
:1. Introduction
2. The Water–Heat Coupling Model
2.1. Water–Heat Coupling Differential Equations
2.2. Water–Heat Coupling Numerical Model
- (1)
- Modeling of the water field
- (2)
- Modeling of the temperature field
2.3. Validation of Numerical Model
2.3.1. Freezing Simulation Validation and Analysis
2.3.2. Thawing Simulation Validation and Analysis
3. Deformation Analysis of Seasonal Frozen Roadbed
3.1. Project Overview
3.2. Water–Heat Coupling Analysis
3.2.1. Parameters of the Model
3.2.2. Boundary Conditions and Simulation Process
- (1)
- Temperature boundary conditions
- (2)
- Moisture boundary conditions
- (3)
- Initial conditions
3.2.3. Results and Discussion
- (1)
- Temperature field
- (2)
- Moisture field
3.3. Deformation Analysis
3.3.1. Basic Equations for the Stress Field
3.3.2. Numerical Modeling
- (1)
- Calculation parameters
- (2)
- Boundary conditions
- (3)
- Roadbed freezing and thawing coefficient
- (4)
- The deformation analysis steps
3.3.3. Results and Discussion
3.3.4. Discussion and Limitations
- (1)
- A sensitivity analysis of the parameters has not been conducted yet. Initially, identify the dominant variables influencing the frost heave/thaw settlement. Subsequently, develop a multi-source data-driven model for evaluating and predicting the safety of seasonal permafrost roadbeds, with soil-sensitive parameters as controlled independent variables, and frost heave/thaw settlement as the target-controlled variables;
- (2)
- This investigation neglected the stress redistribution caused by external loads and pore water pressure and only analyzed the stress caused by frost heave, thus traffic load was not considered. Hence, it is necessary to incorporate dynamic traffic loads to further develop the water–heat coupling computational model under dynamic load conditions.
4. Conclusions
- (1)
- A water–heat coupling mathematical model is established, of which the calculation is realized by using the secondary development module in the COMSOL software, thereby achieving the fully coupled numerical simulation of the temperature field and the moisture field. The accuracy of the model is verified by the classic freeze–thaw test involving a soil column. The simulation results are in good agreement with the test results, with an error of no more than 10%;
- (2)
- During the freezing and thawing process of the soil, the temperature distribution along the soil column direction is approximately linear, while the water migrates from the positive temperature zone to the negative temperature zone, with the maximum migration amount reaching 20% of the water content. Moreover, the balance of the water field lags behind that of the temperature field;
- (3)
- The duration of the soil freezing period is 4 months, with the maximum freezing depth of the roadbed being 2.5 m and that of the road shoulder being 2 m. After thawing, the water content in the shallow layer of the roadbed increases compared to the initial water content, leading to a decrease in soil strength;
- (4)
- After experiencing multiple freeze–thaw cycles, significant deformation occurs in the roadbed. In the first year, the vertical frost heave deformation of the roadbed is 6 mm, resulting in a concave-shaped road surface; the vertical thaw settlement deformation of the roadbed reaches 1.2 mm, resulting in a convex-shaped road surface. By the seventh year, the maximum frost heave can reach 51 mm, and the maximum thaw settlement can reach 13 mm.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Values | Unit | Definition |
---|---|---|---|
2.59 | 1 | Model parameter | |
0.26 | 1 | Model parameter | |
0.5 | 1 | Ontogenetic coefficient | |
10-7 | m/s | Permeability coefficient | |
0.42 | 1 | Saturated water content | |
0.02 | 1 | Residual water content | |
900 | kg/m3 | Ice density | |
1000 | kg/m3 | Water density | |
2060 | kg/m3 | Soil density | |
334.5 | kJ/kg | Latent heat of phase change in ice and water | |
1.3 | W/(m∙K) | Thermal conductivity of the soil | |
900 | J/(kg∙K) | Specific heat of the soil |
Materials | Density (kg/m3) | Thermal Conductivity (W/(m∙K)) | Specific Heat (J/(kg∙K)) | B |
---|---|---|---|---|
Gravelly soil | 2000 | 1.13 | 1210 | 0.61 |
Powdery clay | 1550 | 1.125 | 1241 | 0.56 |
Ice | 900 | 2.22 | 2090 | — |
Water | 1000 | 0.58 | 4180 | — |
Materials | a0 | m | l | θs | θr | ks |
---|---|---|---|---|---|---|
Gravelly soil | 0.66 | 0.14 | 0.5 | 0.42 | 0.05 | 5 × 10−6 |
Powdery clay | 2.65 | 0.26 | 0.5 | 0.5 | 0.02 | 1 × 10−8 |
Materials | Elastic Modulus E (MPa) | Poisson’s Ratio υ |
---|---|---|
Gravelly soil | 61 | 0.28 |
Powdery clay | 28 | 0.3 |
Ice | - | 0.33 |
Temperature (°C) | −2 | −5.4 | −8 |
Elastic modulus (MPa) | 4910.0 | 6342.0 | 6820.0 |
Soil Types | A | B | C |
---|---|---|---|
Gravelly soil | 0.0684 | 0.0028 | 0.04 |
Powdery clay | 0.08 | 0.0003 | 0.003 |
Soil Types | ωc (%) | K1 |
---|---|---|
Gravelly soil | 14 | 0.6 |
Powdery clay | 18 | 0.7 |
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Share and Cite
Lu, B.; Zhao, W.; Li, S.; Dong, M.; Xia, Z.; Shi, Y. Study on Seasonal Permafrost Roadbed Deformation Based on Water–Heat Coupling Characteristics. Buildings 2024, 14, 2710. https://doi.org/10.3390/buildings14092710
Lu B, Zhao W, Li S, Dong M, Xia Z, Shi Y. Study on Seasonal Permafrost Roadbed Deformation Based on Water–Heat Coupling Characteristics. Buildings. 2024; 14(9):2710. https://doi.org/10.3390/buildings14092710
Chicago/Turabian StyleLu, Bo, Wen Zhao, Shengang Li, Manman Dong, Zhikang Xia, and Yunfang Shi. 2024. "Study on Seasonal Permafrost Roadbed Deformation Based on Water–Heat Coupling Characteristics" Buildings 14, no. 9: 2710. https://doi.org/10.3390/buildings14092710