# Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China

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## Abstract

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## 1. Introduction

## 2. Effect Mechanisms of Solar Radiation, Valley Contraction, and Dam Overhanging on a Super-High Arch Dam’s Deformation

#### 2.1. Numerical Analysis of a Super-High Arch Dam’s Deformation Considering the Effects of Solar Radiation

#### 2.1.1. Numerical Analysis of a Super-High Arch Dam Temperature Field Considering the Effects of Solar Radiation

- (1)
- The first type of boundary condition:

- (2)
- The second type of boundary condition:

- (3)
- The third type of boundary condition:

- (1)
- Below the water surface of dam face S1:

- (2)
- The dam face in contact with air S2:

- (3)
- The foundation base surface S3:

- (4)
- The foundation sidewall surface S4:

#### 2.1.2. Method for Numerical Analysis of a Super-High Arch Dam’s Temperature Deformation Considering the Influence of Solar Radiation

#### 2.2. Numerical Analysis of a Super-High Arch Dam’s Deformation Characteristics in the Alpine and Gorge Regions of Southwest China

#### 2.2.1. Analysis of the Causes of Valley Contraction in the Alpine and Gorge Regions of Southwest China for Super-High Arch Dams

#### 2.2.2. Numerical Analysis of a Super-High Arch Dam’s Deformation Characteristics Considering the Effect of Valley Contraction

#### 2.3. Numerical Analysis of a Super-High Arch Dam’s Deformation Considering the Effects of the Dam-Overhanging Effect

#### 2.3.1. Analysis of the Overhanging Effects of Super-High Arch Dams

#### 2.3.2. Numerical Analysis of a Super-High Arch Dam’s Deformation Characteristics by Considering the Effects of Dam Overhanging

## 3. Case Study

#### 3.1. Analysis of the Influences of Solar Radiation on the Arch Dam Deformation Characteristics

#### 3.1.1. 3D Finite Element Model of Jinping I Arch Dam

#### 3.1.2. Numerical Calculation Results of Temperature and Deformation Fields of the Jinping I Super-High Arch Dam

#### 3.2. Analysis of the Influence of Valley Contraction on a Super-High Arch Dam’s Deformation in the Alpine and Gorge Regions in Southwest China

#### 3.2.1. 3D Finite Element Model of Jinping I Arch Dam

#### 3.2.2. Analysis of the Pore Pressure of a Super-High Arch Dam under Normal Storage Conditions

#### 3.2.3. Numerical Calculation Results of Rock Saturation Degree for the Jinping I Arch Dam

#### 3.2.4. Analysis of the Influence of Valley Contraction on a Super-High Arch Dam’s Deformation

#### 3.3. Analysis of the Influence of Dam-Overhanging Effect on a Super-High Arch Dam’s Deformation in the Alpine and Gorge regions of Southwest China

#### 3.3.1. 3D Finite Element Model of the Jinping I Arch Dam

#### 3.3.2. Numerical Calculation Results of the Influence of the Overhanging Effect on the Super-High Arch Dam’s Deformation

- (1)
- Radial deformation was mainly upward in the upstream direction. The maximal deformation occurred near the arch beam elevation on the dam’s upstream surface, reaching 12.22 mm. The dam’s downstream surface near the spillway orifice had deformation in the downstream direction with a maximum value of 2.47 mm.
- (2)
- Tangential deformation of the super-high arch dam was relatively small. Due to the compressive effect, the lower-left-bank dam deformed towards the left bank, and the right-bank dam deformed towards the right bank. The deformation directions in the upper dam were opposite to those of the lower dam: the left-bank dam deformed towards the right bank, and the right-bank dam deformed towards the left bank.
- (3)
- Due to the self-weight load, the deformation direction was downwards. The vertical deformation near the arch beam’s elevation on the dam’s upstream surface and the spillway orifice on the dam’s downstream surface was relatively large, reaching nearly 20 mm.

## 4. Conclusions

- (1)
- Based on the consideration of the influences of solar radiation on dam temperature and reservoir water temperature, the numerical analysis method of a super-high arch dam’s temperature fields and deformation fields considering the influence of solar radiation was proposed.
- (2)
- After analyzing the genesis mechanism of valley contraction from the perspective of the coupling of seepage-stress fields, the numerical analysis method of super-high arch dam deformation characteristics under the influence of valley contraction was studied.
- (3)
- This study analyzed the overhanging effect on the super-high arch dam and proposed a numerical calculation method for the influence of the overhanging effect on the super-high arch dam’s deformation behavior. The calculation results show that the overhanging effect will have a certain impact on the deformation of the arch dam.
- (4)
- The finite element models which were used to analyze the effects of solar radiation, valley contraction, and overhanging effect on the dam deformation characteristics were established. After taking Jinping I super-high arch dam as an example, we concluded that all of the above factors have an impact on the dam deformation to some extent. The research results are supposed to provide a new way to analyze the causes of super-high arch dam special deformation in the alpine and gorge regions of Southwest China.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Finite element model of the dam body and mountains near the Jinping I super-high arch dam. (

**a**) Dam upstream surface. (

**b**) Dam downstream surface.

**Figure 9.**The temperature fields of the arch crown beam on a summer solstice day. (

**a**) Consideration of solar radiation. (

**b**) Without consideration of solar radiation.

**Figure 10.**Temperature field of the arch dam influenced by the solar radiation during one day in summer.

**Figure 12.**The impact of summer water temperature correction on the temperature field of the arch dam. (

**a**) Without consideration of solar radiation. (

**b**) Consideration of solar radiation.

**Figure 13.**Radial deformation field of the dam caused by solar radiation during a whole day in summer.

**Figure 15.**Radial deformation field of the dam caused by summer air temperature, water temperature, and solar radiation.

**Figure 16.**The finite element model of the super-high arch dam. (

**a**) The finite element model of the mountain in the vicinity of the dam and the dam body. (

**b**) The finite element model of the dam and its foundation.

**Figure 23.**Numerical calculation results of the saturation degree of the first stage of the arch dam’s spillway section (water level: 1707 m).

**Figure 24.**Numerical calculation results of the saturation degree of the second stage of the arch dam’s spillway section (water level: 1800 m).

**Figure 25.**Numerical calculation results of the saturation degree of the third stage of the arch dam’s spillway section (water level: 1880 m).

**Figure 28.**Numerical calculation results of radial deformation field of the dam influenced by valley contraction.

**Figure 29.**Numerical calculation results of arch crown beam radial deformation influenced by valley contraction.

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**MDPI and ACS Style**

Shao, C.; Zhao, E.; Xu, Y.; Zheng, S.; Tian, S.
Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China. *Mathematics* **2023**, *11*, 1753.
https://doi.org/10.3390/math11071753

**AMA Style**

Shao C, Zhao E, Xu Y, Zheng S, Tian S.
Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China. *Mathematics*. 2023; 11(7):1753.
https://doi.org/10.3390/math11071753

**Chicago/Turabian Style**

Shao, Chenfei, Erfeng Zhao, Yanxin Xu, Sen Zheng, and Shiguang Tian.
2023. "Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China" *Mathematics* 11, no. 7: 1753.
https://doi.org/10.3390/math11071753