# Simulation Feedback of Temperature Field of Super-High Arch Dam during Operation and Its Difference with Design Temperature

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## Abstract

**:**

## 1. Introduction

## 2. Calculation Principles and Methods

#### 2.1. Calculation Principle of Unsteady Temperature Field

^{2}].

^{2}·K], ${T}_{a}$ is the ambient temperature.

#### 2.2. Back Analysis of the Adiabatic Temperature Rise of Concrete

## 3. Analysis of the Temporal-Spatial Evolution Law of Measured Temperature of Arch Dam during the Operation Period

#### 3.1. Outline of the XLD Super-High Arch Dam in China

#### 3.2. Analysis of Surface Temperature

#### 3.3. Analysis of Internal Temperature

## 4. Inversion Analysis on Temperature Field of Dam during Operation

#### 4.1. Computational Model

#### 4.2. Ambient Temperature

#### 4.3. Inversion of Reservoir Water Temperature

#### 4.4. Inversion of Internal Temperature

## 5. Analysis on Temperature Field Difference of Arch Dam under Design Condition and Actual Condition

#### 5.1. Calculation Condition Difference

#### 5.2. Results and Discussions

## 6. Conclusions

- Through the analysis of the monitoring data of temperature at the dam surface measuring points and internal measuring points, it is found that the temporal-spatial evolution law of the overall temperature of the dam accords with conventional knowledge;
- The change process of temperature at the monitoring points calculated by the simulation is in good agreement with that of the monitoring value, which indicates that the adopted simulation analysis method and the thermal parameters obtained by inversion are reasonable and reliable;
- Through simulation calculation, the temperature field of the arch dam under the design and actual conditions were obtained. Under the design condition, the temperature rise inside the dam body is not considered. Due to the influence of low-temperature closure grouting and boundary heat transfer, the temperature of the dam body rises slowly after closure grouting and tends to be stable. In this process, the internal temperature of the dam body is always lower than the stable temperature. Under the actual condition, the temperature of the dam body rises rapidly after closure grouting, by 7.5~9.2 °C. After the arch is sealed, it reaches the highest temperature in about 8~12 years, and then gradually falls back to the final stable temperature in 40~80 years;
- The dam surface temperature is greatly influenced by the air temperature and the reservoir water temperature, but the influence depth is shallow. The internal temperature of the dam body is mainly affected by the temperature recovery in the later period, which changes slightly in January, April, August and November. The internal stable temperature of the dam under the design condition is lower than that under the actual condition. The temperature field inside the dam body has little difference below the 490 m elevation of the deep hole orifice, but a great difference above the 490 m elevation under two conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of the location of temperature monitoring points. (

**a**) Thermometers of No.16 dam section; (

**b**) joint meters of No.15 dam section.

**Figure 3.**Temperature change process line of thermometer measuring points on the upstream surface of cantilever No. 16 dam section. (

**a**) Measuring points above 500 m elevation; (

**b**) Measuring points at 400~500 m elevation; (

**c**) Measuring points below 400 m elevation.

**Figure 4.**Temperature change process line of thermometer measuring points on the downstream surface of cantilever No. 16 dam section.

**Figure 5.**Temperature change process line of measuring points at transverse joints in No.15 dam section. (

**a**) Measuring points below 571.7 m elevation; (

**b**) Measuring points above 571.7 m elevation.

**Figure 10.**The concrete temperature rise process line. (

**a**) C40 concrete; (

**b**) C35 concrete; (

**c**) C30 concrete.

**Figure 11.**Comparison between measured value and calculated value of temperature at dam surface. (

**a**) T16-19; (

**b**) T16-23; (

**c**) T16-27; (

**d**) T16-29; (

**e**) T16-14; (

**f**) T16-28.

**Figure 12.**Comparison between measured value and calculated value of temperature at measuring points inside the dam. (

**a**) J15-11 (358 m, Area A); (

**b**) J15-41 (523.7 m, Area A); (

**c**) J15-20 (403 m, Area B); (

**d**) J15-32 (463 m, Area B); (

**e**) J9-29 (523.7 m, Area C); (

**f**) J15-32 (580.7 m, Area C).

**Figure 14.**Change process line of temperature inside arch dam. (

**a**) Design condition; (

**b**) Actual condition.

**Figure 15.**Cloud map of quasi-stable temperature field distribution of the dam in January (unit: °C). (

**a**) Upstream face; (

**b**) Downstream surface.

**Figure 16.**Cloud map of quasi-stable temperature field distribution of the dam in April (unit: °C). (

**a**) Upstream face; (

**b**) Downstream surface.

**Figure 17.**Cloud map of quasi-stable temperature field distribution of the dam in August (Unit: °C). (

**a**) Upstream face; (

**b**) Downstream surface.

**Figure 18.**Cloud map of quasi-stable temperature field distribution of the dam in November (unit: °C). (

**a**) Upstream face; (

**b**) Downstream surface.

**Figure 19.**Cloud map of quasi-stable temperature field distribution in cross-section of cantilever No. 16 dam section under design reservoir water temperature. (unit: °C). (

**a**) January; (

**b**) April; (

**c**) August; (

**d**) November.

**Figure 20.**Cloud map of quasi-stable temperature field distribution in cross-section of cantilever No. 16 dam section under measured reservoir water temperature. (unit: °C). (

**a**) January; (

**b**) April; (

**c**) August; (

**d**) November.

XLD Arch Dam in China | |
---|---|

Dam type | concrete double-curvature arch dam |

Dam height | 285.5 m |

Crest elevation | 610.0 m |

Normal water elevation | 600.0 m |

Installed capacity | 13,860 MW |

Total reservoir capacity | 124.7 × 10^{8} m^{3} |

Crest thickness | 14 m |

Dam bottom thickness | 60 m |

Thermometers Near the Upstream Surface | Elevation of the Points(m) | Thermometers Near the Downstream Surface | Elevation of the Points(m) | Joint Meters | Elevation of the Points(m) |
---|---|---|---|---|---|

T16-1 | 358.0 | T16-4 | 373.7 | J15-11 | 358.0 |

T16-3 | 373.7 | T16-8 | 403.7 | J15-20 | 403.7 |

T16-5 | 388.7 | T16-14 | 442.7 | J15-26 | 430.7 |

T16-7 | 403.7 | T16-18 | 475.0 | JG15-5 | 481.3 |

T16-17 | 475.0 | T16-20 | 499.7 | JG15-14 | 517.7 |

T16-19 | 499.7 | T16-22 | 523.7 | J15-47 | 544.7 |

T16-21 | 523.7 | T16-24 | 535.7 | J15-53 | 571.7 |

T16-23 | 535.7 | T16-28 | 556.7 | J15-55 | 580.7 |

T16-25 | 544.7 | T16-30 | 571.7 | J15-56 | 577.7 |

T16-27 | 556.7 | ||||

T16-29 | 571.7 | ||||

T16-31 | 580.7 |

Measuring Points | Temperature at the End of Second-Stage Cooling (°C) | Maximum Temperature Recovery (°C) | Temperature Recovery (°C) | Time at the End of Second-Stage Cooling | Time of Maximum Temperature Recovery |
---|---|---|---|---|---|

J15-11 | 11.4 | 19.8 | 8.4 | 2010/9/27 | 2021/4/1 |

J15-20 | 12.4 | 19.5 | 7.1 | 2011/6/20 | 2021/5/2 |

J15-26 | 12.3 | 19.6 | 7.3 | 2011/8/10 | 2021/5/2 |

JG15-5 | 12.1 | 19.5 | 7.4 | 2012/4/4 | 2021/8/29 |

JG15-14 | 10.9 | 20.1 | 9.2 | 2012/9/21 | 2021/8/29 |

J15-47 | 12.1 | 20.9 | 8.8 | 2012/12/20 | 2020/6/16 |

J15-53 | 11.9 | 20.3 | 8.4 | 2013/6/14 | 2021/2/1 |

J15-55 | 13.1 | / | / | 2013/9/27 | / |

J15-56 | 12.8 | / | / | 2013/10/15 | / |

Month | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. | Year |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Average temperature [°C] | 10.6 | 12.4 | 16.2 | 21.1 | 23.9 | 25.8 | 27.1 | 27.1 | 23.9 | 19.6 | 17.0 | 12.2 | 19.7 |

Material | Density (kg/m^{3}) | Thermal Conductivity (W/(m·K)) | Specific Heat (kJ/(kg·K)) |
---|---|---|---|

Foundation | 2750 | 2.302 | 0.990 |

Dam body concrete | 2400 | 1.621 | 0.985 |

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**MDPI and ACS Style**

Hou, C.; Chai, D.; Cheng, H.; Ning, S.; Yang, B.; Zhou, Y.
Simulation Feedback of Temperature Field of Super-High Arch Dam during Operation and Its Difference with Design Temperature. *Water* **2022**, *14*, 4028.
https://doi.org/10.3390/w14244028

**AMA Style**

Hou C, Chai D, Cheng H, Ning S, Yang B, Zhou Y.
Simulation Feedback of Temperature Field of Super-High Arch Dam during Operation and Its Difference with Design Temperature. *Water*. 2022; 14(24):4028.
https://doi.org/10.3390/w14244028

**Chicago/Turabian Style**

Hou, Chunyao, Dong Chai, Heng Cheng, Shaoqing Ning, Bo Yang, and Yi Zhou.
2022. "Simulation Feedback of Temperature Field of Super-High Arch Dam during Operation and Its Difference with Design Temperature" *Water* 14, no. 24: 4028.
https://doi.org/10.3390/w14244028