# Deformation Analysis of an Ultra-High Arch Dam under Different Water Level Conditions Based on Optimized Dynamic Panel Clustering

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## Abstract

**:**

## 1. Introduction

## 2. Deformation Zoning Model of Ultra-High Arch Dam

#### 2.1. Panel Data Theory

#### 2.2. Matrix Expression of Spatiotemporal Characteristic Level of Panel Data

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

#### 2.3. Calculating the Objective Weight Coefficient of Comprehensive Distance

#### 2.4. Optimizing Cluster Number

## 3. Deformation Zoning Model of the Ultra-High Arch Dam

## 4. Case Study

#### 4.1. Project Profile

#### 4.2. Characteristics Analysis of the Dam Deformation Zoning

#### 4.2.1. Temporal and Spatial Characteristics Analysis of the Dam Deformation

- (1)
- Deformation characteristics analysis of the first phase

- (2)
- Deformation characteristics analysis of the second phase

- (3)
- Deformation characteristics analysis of the third phase

- (4)
- Deformation characteristics analysis of the different operation phases

#### 4.2.2. Water Level Characteristics Analysis of the Dam Deformation

- Dam deformation is greatly affected by water levels. With the rise of the water level, the deformation of the dam changes obviously, which also proves the rationality of the water pressure component in the statistical model.
- There is an obvious positive correlation between water level and deformation, and the influence of water level on dam deformation is hysteretic. In addition, with the rise of the water level, the cluster center area also rises, indicating that the trend of the expansion and upward movement of the maximum deformation area of the dam body is consistent with the engineering practice.
- The maximum deformation of the dam is the dam section of the middle riverbed. Because the absolute height of the dam body is large and the bearing water pressure is correspondingly larger, the deformation is more obvious. Similarly, due to low water pressure, the deformation of dam sections on both banks is not as significant as that of dam sections in the middle of the riverbed.
- In different elevations of the same dam section, because the water pressure is linearly distributed with the water depth from top to bottom, the water depth pressure in the middle and lower part is large, and the corresponding deformation is more obvious. Although the water depth near the dam bottom is the largest, the dam bottom is equivalent to the constraint of the fixed end due to the existence of the foundation cementation surface, so the deformation is the smallest. For example, the deformation of measuring point IP13-2 is basically unchanged due to its proximity to the dam foundation. However, it can also be seen from the clustering zoning that the gradient of dam bottom zoning changes greatly, and the deformation increases rapidly at the part far away from the dam bottom constraint area.

#### 4.3. Deformation Safety Monitoring of Important Monitoring Points of Dam

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Flow chart of the deformation zoning and monitoring model of an ultra-high arch dam operating at a complex water level.

**Figure 5.**The layout of the inverse plumb line and the displacement monitoring points. (

**A**). The layout of the inverse plumb line (

**B**). Detail drawing of inverse plumb line measuring point (1-oil drum, 2-connecting support, 3-floating ball, 4-connecting rod, 5-floating barrel frame, 6-coordinate instrument base, 7-concrete observation pier, 8-inverse plumb line (stainless steel wire), 9-anchor block, and 10- protection well).

**Figure 11.**Relationship between the deformation of representative monitoring points and variation of reservoir water level.

**Table 1.**Zoning results of deformation measuring points of the ultra-high arch dam during the first phase.

Category | Measuring Point |
---|---|

Ⅰ | PL13-5, PL16-5 |

Ⅱ | PL11-4, PL13-4, PL16-4 |

Ⅲ | PL11-5, PL13-3 |

Ⅳ | PL11-3, PL13-2, PL16-3 |

Ⅴ | PL9-2, PL9-3, PL11-1, PL11-2, PL13-1, PL16-1, PL16-2 |

Ⅵ | PL5-1, PL5-2, PL5-3, PL5-4, PL9-1, PL9-4, PL9-5, IP11-1, IP13-2, IP16-1, PL19-1, PL19-2, PL19-3, PL19-4, PL19-5 |

**Table 2.**Zoning results of deformation measuring points of the ultra-high arch dam during the second phase.

Category | Measuring Point |
---|---|

Ⅰ | PL11-4, PL11-5, PL13-4, PL13-5, PL16-4, PL16-5 |

Ⅱ | PL11-3, PL13-3 |

Ⅲ | PL16-3 |

Ⅳ | PL11-2, PL13-2 |

Ⅴ | PL9-1, PL9-2, PL9-3, PL9-4, PL11-1, PL13-1, PL16-1, PL16-2, PL19-3, PL19-4 |

Ⅵ | PL5-1 PL5-2, PL5-3, PL5-4, PL9-5IP11-1, IP13-2, IP16-1, PL19-1, PL19-2, PL19-5 |

**Table 3.**Zoning results of deformation measuring points of the ultra-high arch dam during the third phase.

Category | Measuring Point |
---|---|

Ⅰ | PL11-4, PL13-4, PL13-5, PL16-4, |

Ⅱ | PL11-3, PL11-5, PL16-5 |

Ⅲ | PL13-3, PL16-3 |

Ⅳ | PL9-2, PL9-3, PL11-2, PL13-2 |

Ⅴ | PL9-1, PL9-4, PL11-1, PL13-1, PL16-1, PL16-2, PL19-3, PL19-4 |

Ⅵ | PL5-1, PL5-2, PL5-3, PL5-4, PL9-5, IP11-1, IP13-2, IP16-1, PL19-1, PL19-2, PL19-5 |

**Table 4.**Zoning results of deformation measuring points of the ultra-high arch dam during the third phase.

Measuring Point | PL13-5 | PL16-4 | PL13-3 | PL13-2 | PL16-2 | PL5-1 | IP13-2 |
---|---|---|---|---|---|---|---|

MIC | 0.596 | 0.595 | 0.632 | 0.426 | 0.500 | 0.417 | 0.429 |

Coefficient | PL11-4 | PL11-5 | PL13-4 | PL13-5 | PL16-4 | PL16-5 |
---|---|---|---|---|---|---|

Multi-correlation coefficient R | 0.998 | 0.982 | 0.983 | 0.978 | 0.971 | 0.969 |

Root mean squared error S | 0.655 | 1.509 | 2.323 | 1.908 | 2.697 | 2.122 |

Mean relative error (predication) | 1.86% | 5.81% | 2.98% | 3.96% | 3.79% | 3.66% |

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**MDPI and ACS Style**

Liu, Y.; Zheng, D.; Georgakis, C.; Kabel, T.; Cao, E.; Wu, X.; Ma, J.
Deformation Analysis of an Ultra-High Arch Dam under Different Water Level Conditions Based on Optimized Dynamic Panel Clustering. *Appl. Sci.* **2022**, *12*, 481.
https://doi.org/10.3390/app12010481

**AMA Style**

Liu Y, Zheng D, Georgakis C, Kabel T, Cao E, Wu X, Ma J.
Deformation Analysis of an Ultra-High Arch Dam under Different Water Level Conditions Based on Optimized Dynamic Panel Clustering. *Applied Sciences*. 2022; 12(1):481.
https://doi.org/10.3390/app12010481

**Chicago/Turabian Style**

Liu, Yongtao, Dongjian Zheng, Christos Georgakis, Thomas Kabel, Enhua Cao, Xin Wu, and Jiajia Ma.
2022. "Deformation Analysis of an Ultra-High Arch Dam under Different Water Level Conditions Based on Optimized Dynamic Panel Clustering" *Applied Sciences* 12, no. 1: 481.
https://doi.org/10.3390/app12010481