Studying the Freezing Law of Reinforcement by Using the Artificial Ground Freezing Method in Shallow Buried Tunnels
Abstract
:1. Introduction
2. Project Overview
2.1. Project Profile
2.2. Freeze Pipe Arrangement
3. Numerical Simulation
3.1. Governing Equation
3.1.1. Temperature Field Control Equation
3.1.2. Moisture Field Control Equation
3.1.3. Hydrothermal Coupling PDE Secondary Development Module
3.1.4. Displacement Field Control Equation
3.2. Numerical Modeling Assumptions
- (1)
- The investigation report for this project indicates that powdery clay with high water content produces a large freezing rate during the freezing process. Therefore, this study simplifies the soil body to a homogeneous, continuous, isotropic, and linearly elastic soil layer with the most unfavorable soil parameters. Each parameter is derived from weighted values based on the investigation report, and the soil body has an initial temperature of 18 °C.
- (2)
- Based on existing research [35], it is assumed that the soil body begins to freeze at −1 °C and forms a stable permafrost structure at −10 °C.
- (3)
- Neglecting the loss of cold during the brine circulation process and the influence of heat convection and radiation during heat transfer, the brine temperature is directly applied to the wall of the freezing pipe as a temperature load with heat transferred solely by conduction.
- (4)
- It is assumed that moisture migration in the soil conforms to Darcy’s law.
- (5)
- The migration of salts and other solutes in the soil is not considered. Water migration is assumed to occur primarily in liquid form, ignoring the movement of gaseous water. The soil is considered saturated, containing only liquid water and solid ice in the pore space, with the saturated water content equating to the soil’s porosity.
- (6)
- It is assumed that ice crystals and the solid phase of the soil are incompressible.
3.3. Numerical Modeling
3.3.1. Geometric Modeling, Meshing and Boundary Conditions
3.3.2. Selection of Relevant Parameters
4. Analysis of Simulation Results
4.1. Temperature Field Calculation Results
4.2. Moisture Field Calculation Results
4.3. Displacement Field Calculation Results
4.4. Sensitivity Analysis
5. Conclusions
- (1)
- On the 25th day of freezing, temperature variation cycles from −1 to −10 °C were completed. By the 30th day, a fully frozen curtain had formed, meeting the design requirements for thickness. This indicates that the original cooling plan for the project was relatively conservative. Future optimizations could consider shortening the freezing period and reducing costs, referring to the temperature field analysis for improvements. The soil in the strong freezing zone exhibited a faster cooling rate and greater permafrost thickness than the weak freezing zone. The intervals between the pipe curtains in the strong freezing zone enhance the stability of the gaps and the water-stopping capability, aligning with the project’s requirements.
- (2)
- The influence of the freezing pipes on the soil area resulted in changes in the cooling rate at specific time nodes during the freezing process. Different monitoring points showed varying cooling rates due to differences in the influence of the cold source. Based on monitoring data, specific areas can be targeted for freezing control measures, allowing for adjustments to the freezing program in this project or similar ones.
- (3)
- The ice content in the strong freezing area was higher than that in the weak freezing area. Due to the temperature gradient, moisture in the soil migrated toward the cold area, causing the saturation and water content of the surrounding soil to decline. Near the freezing pipe, moisture migration led to temporary water accumulation and increased saturation. By the 30th day of freezing, saturation within the curtain became uniform and approached zero with higher ice content marking the primary area of freezing and expansion effects. The saturation along the inner and outer edges of the curtain was slightly higher than inside the curtain due to moisture migration. Analyzing the saturation changes during freezing effectively elucidates the relationship between moisture migration and freeze-up.
- (4)
- The soil closer to the freezing pipe experienced a faster rate of water content reduction, eventually reaching a stable water content stage. The soil farther from the freezing pipe initially showed a slight decrease in water content. If later affected by the freezing front’s cold source, a change in the water content reduction rate can be observed; otherwise, only a slight decrease due to water migration occurs. Our analysis of moisture field changes suggests that regions with a rapidly increasing water content decrease, indicating significant moisture phase change to ice, corresponding to strong freezing effects.
- (5)
- In the early-phase change phase, frost heave was observed only near the freezing pipe, with the soil near the surface experiencing a vertical displacement of 0.66 mm. By the 35th day of freezing, upward freezing displacement continued accumulating after forming a stable freezing curtain with the maximum vertical displacement near the surface reaching 320 mm. On the 45th day, maximum freezing displacement reached 358 mm, indicating a decreased freezing heave effect in the later stages. Therefore, in actual projects, the focus should be on controlling the freezing effect before the 35th day. Additionally, dense contour lines near the freezing pipe indicated strong freezing displacement in that area, causing significant surface uplift. The maximum displacement was not centered in the construction soil but in the X-negative direction. The high water content in the powdery clay-based layer resulted in a pronounced frost expansion effect. The analysis in this paper provides a clear understanding of areas with significant frost expansion effects, offering a reference for assessing freezing programs and developing frost expansion control measures in this project or similar ones.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Type of Parameter | Parameter | Value |
---|---|---|
Soil thermophysical parameters | Soil density (kg/m3) | 1930 |
Water density (kg/m3) | 1000 | |
Ice density (kg/m3) | 920 | |
Thermal conductivity of soil (W/(m·°C)) | 1.22 | |
Thermal conductivity of water (W/(m·°C)) | 0.63 | |
Thermal conductivity of ice (W/(m·°C)) | 2.31 | |
Specific heat capacity of soil (J/(kg·°C)) | 1530 | |
Specific heat capacity of water (J/(kg·°C)) | 4200 | |
Specific heat capacity of ice (J/(kg·°C)) | 2100 | |
Latent heat of phase transition (J/kg) | 334,720 | |
Soil mechanical parameters | Elastic modulus of unfrozen soil (MPa) | 40 |
Elastic modulus of frozen soil (MPa) | 120 | |
Unfrozen ground cohesion (kPa) | 30 | |
Angle of internal friction in unfrozen soil (°) | 22 | |
Poisson’s ratio for unfrozen soil | 0.31 | |
Poisson’s ratio for frozen soil | 0.23 |
Time/d | 0 | 10 | 20 | 30 | 45 |
Temperature/°C | 18 | 0 | −20 | −28 | −28 |
Time/d | 0 | 20 | 30 | 45 |
Plan 1/°C | 18 | −20 | −28 | −28 |
Plan 2/°C | 18 | −25 | −33 | −33 |
Plan 3/°C | 18 | −15 | −23 | −23 |
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Liu, P.; Hu, J.; Dong, Q.; Chen, Y. Studying the Freezing Law of Reinforcement by Using the Artificial Ground Freezing Method in Shallow Buried Tunnels. Appl. Sci. 2024, 14, 7106. https://doi.org/10.3390/app14167106
Liu P, Hu J, Dong Q, Chen Y. Studying the Freezing Law of Reinforcement by Using the Artificial Ground Freezing Method in Shallow Buried Tunnels. Applied Sciences. 2024; 14(16):7106. https://doi.org/10.3390/app14167106
Chicago/Turabian StyleLiu, Peng, Jun Hu, Qinxi Dong, and Yongzhan Chen. 2024. "Studying the Freezing Law of Reinforcement by Using the Artificial Ground Freezing Method in Shallow Buried Tunnels" Applied Sciences 14, no. 16: 7106. https://doi.org/10.3390/app14167106