# Study on the Influence of Water Level on Earth Dam Reinforced by Cut-Off Wall: A Case Study in Wujing Reservoir

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## Abstract

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## 1. Introduction

## 2. Project Overview

## 3. Study on the Influence of Sudden Drawdown on Dam Slope Stability

#### 3.1. Seepage and Slope Stability Analysis Method

_{x}and k

_{y}are the horizontal and vertical permeability coefficients, cm/s or m/d, Q is the flow of water on the boundary, cm

^{3}/s or m

^{3}/d, and $\Theta $ is the volumetric moisture content.

_{se}is the saturated volume water content, u

_{s}is the suction, kPa, c is the soil property parameter of the residual water content function, u

_{r}is the matrix suction corresponding to the water content, kPa, and a and b are the fitting parameters.

_{S}of slope is calculated, and the stability of slope is evaluated according to the equation.

#### 3.2. Numerical Model and Parameters

^{−7}cm/s.

#### 3.3. Stability Analysis of Dam Slope under Sudden Drawdown

## 4. Measuring and Analysis of Dam Deformation under Water Level Rise and Fall

#### 4.1. Arrangement of Measuring Points

#### 4.2. Horizontal Displacement

#### 4.3. Settlements

## 5. Crack Propagation Law Based on Deformation Gradient Method

#### 5.1. Deformation Gradient Method

_{i}on a certain calculation date was Z

_{a}and Z

_{b}, respectively, then the deformation gradient of a and b on the date T

_{i}was defined as $\gamma $, asshown in Equation (5).

_{1}, and the difference in height on a certain calculation date was ∆Z

_{2}, then the modified deformation gradient of points a and b was defined as:

_{1}= 0, i.e., a and b are at the same elevation, the modified deformational gradient agrees with the calculation result of Equation (5).

#### 5.2. Analysis of Crack Width Propagation Law

## 6. Discussion and Conclusions

- Based on the established numerical calculation model of Wujing reservoir, and the geological report parameters, the safety factor of dam slope stability was obtained by the limit equilibrium method, which was about 2.0. When the reservoir encountered a sudden drawdown, the safety factor also decreased sharply. The faster the sudden drawdown was, the faster the safety factor decreased, and the more unfavorable it was to dam slope stability. With the end of the sudden drawdown, the pore water pressure of the dam body soil gradually dissipated, so that the safety factor of stability increased again and finally tended to be stable;
- The horizontal displacement of the dam was affected by the change in the upstream reservoir water level. It was found that the upstream reservoir water level rose and the horizontal displacement of dam shifted to the upstream direction. The upstream reservoir water level dropped, the horizontal displacement of the dam shifted to downstream, and the change of horizontal displacement of downstream slope was significantly larger than that at measuring point of upstream slope;
- The settlement deformation of the dam body was related to the fluctuation of the reservoir water level, in which the water level of upstream reservoir rose, and as surface of the dam body rose, conversely, it tended to sink. The fluctuation of the settlement deformation shows that the upstream side was larger than the downstream side, especially during the period of abrupt change in reservoir water level;
- With the rise in the reservoir water level, the longitudinal cracks on the dam crest showed a tendency of shrinkage, while the cracks showed a tendency of opening when the reservoir water level dropped. The change in the deformation gradient increment was basically consistent with the change in the crack opening, that is, the crack opening decreased with the decrease in the deformation gradient increment and increased with the increase in the gradient increment.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The most dangerous sliding surface of upstream dam slope before sudden drop of water level.

**Figure 4.**The most dangerous sliding surface of upstream dam slope reaches a stable state after sudden drop of water level.

**Figure 5.**Duration curve of dam slope stability safety factor under different sudden drawdown speeds.

Material | Permeability Coefficient/cm/s | Density/kg/m^{3} | Cohesion/kPa | Friction Angle |
---|---|---|---|---|

Silty sand of dam body | 5.0 × 10^{−5} | 1700 | 20 | 20 |

Dam foundation overburden | 5.0 × 10^{−4} | 1800 | 15 | 28 |

Strongly weathered rock mass of dam foundation | 1.0 × 10^{−4} | 2400 | 15 | 30 |

Weakly weathered rock mass of dam foundation | 1.0 × 10^{−5} | 2600 | 20 | 33 |

Basement rock | 1.0 × 10^{−6} | 2700 | 30 | 35 |

Monitoring Time | 1# Section | 2# Section | 3# Section | |||
---|---|---|---|---|---|---|

S11 | S12 | S21 | S22 | S31 | S32 | |

5 March 2020 | 0.00 | / | 0.00 | 0.00 | 0.00 | 0.00 |

23 March 2020 | −2.75 | 3.07 | 1.17 | −0.99 | −0.67 | |

7 April 2020 | −2.66 | 0.38 | 32.05 | −0.97 | 13.70 | |

6 May 2020 | 0.84 | 1.31 | −31.72 | 0.69 | −12.90 | |

21 May 2020 | 0.53 | 0.62 | −1.33 | 2.58 | 0.55 | |

15 June 2020 | −5.46 | −2.93 | 3.22 | −1.31 | 1.03 | |

28 June 2020 | 8.95 | −3.04 | −2.01 | −1.23 | −0.96 | |

3 August 2020 | −17.46 | −9.96 | −4.01 | −11.80 | −6.05 | |

17 August 2020 | 3.13 | −0.02 | 0.32 | 0.99 | 0.06 | |

4 September 2020 | 0.41 | −5.00 | 0.71 | −2.37 | 1.26 | |

12 October 2020 | −3.88 | 5.52 | −0.21 | 0.10 | −0.28 | |

4 December 2020 | 11.93 | 4.90 | 1.83 | 4.90 | 1.91 | |

28 December 2020 | 1.57 | −0.46 | 4.81 | 1.36 | 0.07 | |

18 March 2021 | 4.04 | 7.98 | −1.01 | 6.04 | 0.76 | |

26 March 2021 | −2.17 | −2.50 | 0.98 | 1.94 | 2.25 | |

2 April 2021 | −1.54 | 0.54 | −1.95 | −3.96 | −1.54 |

Monitoring Time | 1# Section | 2# Section | 3# Section | |||
---|---|---|---|---|---|---|

S11 | S12 | S21 | S22 | S31 | S32 | |

5 March 2020 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

23 March 2020 | −34.50 | −38.30 | −34.20 | −25.19 | −32.40 | −28.60 |

7 April 2020 | 15.50 | 4.40 | 7.70 | 4.79 | 4.10 | 7.90 |

21 May 2020 | −9.30 | −1.70 | −3.50 | −2.90 | 1.70 | −6.60 |

15 June 2020 | −4.80 | −9.80 | −9.00 | −16.00 | −8.20 | −5.30 |

28 June 2020 | −5.90 | 6.80 | −0.10 | 9.50 | 1.10 | 1.60 |

3 August 2020 | −6.20 | −11.20 | −4.40 | −4.10 | −4.70 | −1.90 |

17 August 2020 | 6.80 | 5.40 | −1.50 | 0.80 | 2.60 | 1.80 |

4 September 2020 | −2.30 | 8.70 | 4.30 | 6.70 | −4.20 | 0.50 |

12 October 2020 | 3.10 | −9.90 | −2.50 | −8.90 | 3.20 | −3.00 |

4 December 2020 | 6.90 | 6.30 | 2.60 | 4.70 | 4.60 | 1.70 |

28 December 2020 | 4.00 | −0.10 | 5.90 | 3.50 | 2.60 | 2.30 |

18 March 2021 | −3.70 | 3.50 | −3.10 | −0.70 | −4.30 | −1.00 |

26 March 2021 | −5.20 | −1.60 | −1.90 | −2.50 | 1.70 | −0.30 |

2 April 2021 | 8.60 | −1.00 | 6.00 | −3.10 | 2.20 | 1.90 |

Monitoring Time | Settlement Z/mm | Horizontal Distance of Observation Points on the Same Section/m | Deformation Gradient/% | |||||||
---|---|---|---|---|---|---|---|---|---|---|

1# Section | 2# Section | 3# Section | γ_{1} | γ_{2} | γ_{3} | |||||

S31 | S32 | S21 | S22 | S11 | S12 | |||||

5 March 2020 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 9.00 | 0 | 0 | 0 |

23 March 2020 | −32.4 | −28.6 | −34.2 | −25.19 | −34.5 | −38.3 | 0.0422 | 0.1001 | 0.0422 | |

7 April 2020 | 4.1 | 7.9 | 7.7 | 4.79 | 15.5 | 4.4 | 0.0422 | 0.0323 | 0.1233 | |

21 May 2020 | 1.7 | −6.6 | −3.5 | −2.9 | −9.3 | −1.7 | 0.0922 | 0.0067 | 0.0844 | |

15 June 2020 | −8.2 | −5.3 | −9 | −16 | −4.8 | −9.8 | 0.0322 | 0.0778 | 0.0556 | |

28 June 2020 | 1.1 | 1.6 | −0.1 | 9.5 | −5.9 | 6.8 | 0.0056 | 0.1067 | 0.1411 | |

3 August 2020 | −4.7 | −1.9 | −4.4 | −4.1 | −6.2 | −11.2 | 0.0311 | 0.0033 | 0.0556 | |

17 August 2020 | 2.6 | 1.8 | −1.5 | 0.8 | 6.8 | 5.4 | 0.0089 | 0.0256 | 0.0156 | |

4 September 2020 | −4.2 | 0.5 | 4.3 | 6.7 | −2.3 | 8.7 | 0.0522 | 0.0267 | 0.1222 | |

12 October 2020 | 3.2 | −3 | −2.5 | −8.9 | 3.1 | −9.9 | 0.0689 | 0.0711 | 0.1444 | |

4 December 2020 | 4.6 | 1.7 | 2.6 | 4.7 | 6.9 | 6.3 | 0.0322 | 0.0233 | 0.0067 | |

28 December 2020 | 2.6 | 2.3 | 5.9 | 3.5 | 4.0 | −0.1 | 0.0033 | 0.0267 | 0.0456 | |

18 March 2021 | −4.3 | −1.0 | −3.1 | −0.7 | −3.7 | 3.5 | 0.0367 | 0.0267 | 0.0800 |

Dam | Dam Type | Research Method | Whether the Water Level Fluctuation Affects the Dam Deformation | How Water Level Fluctuation Affects Dam Deformation |
---|---|---|---|---|

Chengbihe [7] | Earth dam | In situ measurements | Yes | Settlement on the dam’s upstream side |

Yamula [29] | Earth dam | In situ measurements | Yes | Vertical deformation. The rising water level increases the subsidence velocity |

An ultra-high arch dam [30] | Concrete arch dam | In situ measurements | Yes, but the influence of water level on dam deformation is hysteretic. | 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 |

Jiangya [31] | Gravity dam | In situ measurements | Yes | The reservoir impoundment is the predominant cause of the uplift of dam foundation. |

An earth embankments of dams [32] | Earth dam. | Numerical simulation | Yes | The horizontal deformation of the dam toe is higher for a higher rising rate |

Princeville [33] | Earth levee | Numerical simulation | Yes | The Factor of safety is affected by rate of rise/drawdown of the water level |

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## Share and Cite

**MDPI and ACS Style**

Liu, D.; Lin, T.; Gao, J.; Xue, B.; Yang, J.; Chen, C.; Zhang, W.; Sun, W.
Study on the Influence of Water Level on Earth Dam Reinforced by Cut-Off Wall: A Case Study in Wujing Reservoir. *Water* **2023**, *15*, 140.
https://doi.org/10.3390/w15010140

**AMA Style**

Liu D, Lin T, Gao J, Xue B, Yang J, Chen C, Zhang W, Sun W.
Study on the Influence of Water Level on Earth Dam Reinforced by Cut-Off Wall: A Case Study in Wujing Reservoir. *Water*. 2023; 15(1):140.
https://doi.org/10.3390/w15010140

**Chicago/Turabian Style**

Liu, Da, Taiqing Lin, Jianglin Gao, Binghan Xue, Jianhua Yang, Congxin Chen, Weipeng Zhang, and Wenbin Sun.
2023. "Study on the Influence of Water Level on Earth Dam Reinforced by Cut-Off Wall: A Case Study in Wujing Reservoir" *Water* 15, no. 1: 140.
https://doi.org/10.3390/w15010140