# Numerical Simulation of Frost Heave Deformation of Concrete-Lined Canal Considering Thermal-Hydro-Mechanical Coupling Effect

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## Abstract

**:**

## 1. Introduction

## 2. Multi-Physics Coupling Equations of Soil

#### 2.1. Seepage Field

#### 2.2. Temperature Field

#### 2.3. Dynamic Equilibrium Relationship of Ice-Water Phase Transition

#### 2.4. Stress Field

## 3. Multi-Physics Coupling Equations of Concrete

#### 3.1. Stress Field

#### 3.2. Seepage Field

#### 3.3. Temperature Field

## 4. Computational Model and Results Analysis

#### 4.1. Computational Model

#### 4.1.1. Geometry Modeling and Mesh Generation

#### 4.1.2. Initial and Boundary Conditions

#### 4.1.3. Calculation Parameters

^{−6}, ${a}_{2}=$ 9.366 × 10

^{−4}, ${a}_{3}=$ 9.580986 × 10, ${a}_{4}=$ 2.27832.

#### 4.2. Calculation Results and Analysis

#### 4.2.1. Evolution of Temperature Distribution

#### 4.2.2. Evolution of ice Content and Frost Depth

#### 4.2.3. Evolution of Frost heave Deformation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Composition | $\mathit{\rho}$ (kg/m ^{3})
| $\mathit{\lambda}$ (W/m·k) | $\mathit{C}$ (J/kg·K) | $\mathit{\alpha}$ (GPa) | $\mathit{K}$ (GPa) | $\mathit{E}$ (GPa) | $\mathit{D}$ (m ^{2})
| $\mathit{b}$ | $\mathit{n}$ |
---|---|---|---|---|---|---|---|---|---|

Concrete | 2400 | — | — | — | 11.1 | 35 | 8.3 × 10^{−12} | 0.657 | 0.155 |

Skeleton | — | 1.80 | 950 | 2.0 × 10^{−5} | 32.4 | — | — | — | — |

Water | 1000 | 0.54 | 4200 | −9.2 × 10^{−5} | 2.0 | — | — | — | — |

Ice | 900 | 2.22 | 2100 | 1.2 × 10^{−4} | 8.0 | — | — | — | — |

Composition | $\mathit{\rho}$ (kg/m ^{3})
| $\mathit{C}$ (J/kg·°C) | $\mathit{\lambda}$ (W/m·k) | T_{f}(°C) | $\mathit{E}$ (GPa) | $\mathit{A}$ |
---|---|---|---|---|---|---|

Soil | 1940 | 1680 | 1.22 | −0.15 | 0.30 | 0.56 |

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**MDPI and ACS Style**

Teng, R.; Gu, X.; Xia, X.; Zhang, Q.
Numerical Simulation of Frost Heave Deformation of Concrete-Lined Canal Considering Thermal-Hydro-Mechanical Coupling Effect. *Water* **2023**, *15*, 1412.
https://doi.org/10.3390/w15071412

**AMA Style**

Teng R, Gu X, Xia X, Zhang Q.
Numerical Simulation of Frost Heave Deformation of Concrete-Lined Canal Considering Thermal-Hydro-Mechanical Coupling Effect. *Water*. 2023; 15(7):1412.
https://doi.org/10.3390/w15071412

**Chicago/Turabian Style**

Teng, Renjie, Xin Gu, Xiaozhou Xia, and Qing Zhang.
2023. "Numerical Simulation of Frost Heave Deformation of Concrete-Lined Canal Considering Thermal-Hydro-Mechanical Coupling Effect" *Water* 15, no. 7: 1412.
https://doi.org/10.3390/w15071412