# 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

**:**

## 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

## References

- Wang, T.; Chen, J.; Li, P.; Yin, Y.; Shen, C. Natural tracing for concentrated leakage detection in a rockfill dam. Eng. Geol.
**2019**, 249, 1–12. [Google Scholar] [CrossRef] - Chen, S.; Gu, C.; Lin, C.; Wang, Y.; Hariri-Ardebili, M.A. Prediction, monitoring, and interpretation of dam leakage flow via adaptative kernel extreme learning machine. Measurement
**2020**, 166, 108161. [Google Scholar] [CrossRef] - Mozafari, M.; Milanović, P.; Jamei, J. Water leakage problems at the Tangab Dam Reservoir (SW Iran), case study of the complexities of dams on karst. Bull. Eng. Geol. Environ.
**2021**, 80, 7989–8007. [Google Scholar] [CrossRef] - Pan, Y.; Liu, Y.; Chen, E.J. Probabilistic investigation on defective jet-grouted cut-off wall with random geometric imperfections. Géotechnique
**2019**, 69, 420–433. [Google Scholar] [CrossRef] - Wang, K.; Li, Z.; Zheng, H.; Xu, X.; He, H. A theoretical model for estimating the water-tightness of jet-grouted cut-off walls with geometric imperfections. Comput. Geotech.
**2021**, 138, 104316. [Google Scholar] [CrossRef] - Shepherd, D.A.; Kotan, E.; Dehn, F. Plastic concrete for cut-off walls: A review. Constr. Build. Mater.
**2020**, 255, 119248. [Google Scholar] [CrossRef] - Luo, J.; Zhang, Q.; Li, L.; Xiang, W. Monitoring and characterizing the deformation of an earth dam in Guangxi Province, China. Eng. Geol.
**2019**, 248, 50–60. [Google Scholar] [CrossRef] - Yavaşoğlu, H.H.; Kalkan, Y.; Tiryakioğlu, I.; Yigit, C.; Özbey, V.; Alkan, M.N.; Bilgi, S.; Alkan, R.M. Monitoring the deformation and strain analysis on the Ataturk Dam, Turkey. Geomat. Nat. Hazards Risk
**2018**, 9, 94–107. [Google Scholar] [CrossRef][Green Version] - Bestuzheva, A.S.; Anakhaev, K.K. Seepage Through a Homogeneous Earth-Fill Dam with a Cut-Off Wall on a Permeable Foundation. Power Technol. Eng.
**2020**, 54, 147–153. [Google Scholar] [CrossRef] - Barzaghi, R.; Cazzaniga, N.E.; De Gaetani, C.I.; Pinto, L.; Tornatore, V. Estimating and Comparing Dam Deformation Using Classical and GNSS Techniques. Sensors
**2018**, 18, 756. [Google Scholar] [CrossRef] - Lai, J.; Liu, H.; Qiu, J.; Chen, J. Settlement Analysis of Saturated Tailings Dam Treated by CFG Pile Composite Foundation. Adv. Mater. Sci. Eng.
**2016**, 2016, 7383762. [Google Scholar] [CrossRef][Green Version] - Cheng, X.; Li, Q.; Zhou, Z.; Luo, Z.; Liu, M.; Liu, L. Research on a Seepage Monitoring Model of a High Core Rockfill Dam Based on Machine Learning. Sensors
**2018**, 18, 2749. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ri, Y.N.; Han, U.C.; Jang, U.J.; Jong, D.Y.; Kim, C.U. Study on Stability Reduction Characteristics of Earth and Rockfill Dams under Rapid Drawdown Using Fully Coupled Seepage-Stress Analysis. Adv. Civ. Eng.
**2022**, 2022, 7954991. [Google Scholar] [CrossRef] - Azadi, A.; Irani, A.E.; Azarafza, M.; Bonab, M.H.; Sarand, F.B.; Derakhshani, R. Coupled Numerical and Analytical Stability Analysis Charts for an Earth-Fill Dam under Rapid Drawdown Conditions. Appl. Sci.
**2022**, 12, 4550. [Google Scholar] [CrossRef] - Sun, G.; Lin, S.; Jiang, W.; Yang, Y. A Simplified Solution for Calculating the Phreatic Line and Slope Stability during a Sudden Drawdown of the Reservoir Water Level. Geofluids
**2018**, 2018, 1859285. [Google Scholar] [CrossRef][Green Version] - Zhang, Y.; Zhang, Z.; Xue, S.; Wang, R. Stability analysis of a typical landslide mass in the Three Gorges Reservoir under varying reservoir water levels. Environ. Earth Sci.
**2020**, 79, 42. [Google Scholar] [CrossRef] - Meng, Q.; Qian, K.; Zhong, L.; Gu, J.; Li, Y.; Fan, K.; Yan, L. Numerical Analysis of Slope Stability under Reservoir Water Level Fluctuations Using a FEM-LEM-Combined Method. Geofluids
**2020**, 2020, 6683311. [Google Scholar] [CrossRef] - Zhang, H.; Jing, Y.; Chen, J.; Gao, Z.; Xu, Y. Characteristics and causes of crest cracking on a high core-wall rockfill dam: A case study. Eng. Geol.
**2022**, 297, 106488. [Google Scholar] [CrossRef] - Wang, Y.; Li, J.; Wu, Z.; Chen, J.; Yin, C.; Bian, K. Dynamic Risk Evaluation and Early Warning of Crest Cracking for High Earth-Rockfill Dams through Bayesian Parameter Updating. Appl. Sci.
**2020**, 10, 7627. [Google Scholar] [CrossRef] - Kaur, A.; Sharma, R. Slope stability analysis techniques: A review. Int. J. Eng. Appl. Sci. Technol.
**2016**, 1, 52–57. [Google Scholar] - Firincioglu, B.S.; Ercanoglu, M. Insights and perspectives into the limit equilibrium method from 2D and 3D analyses. Eng. Geol.
**2021**, 281, 105968. [Google Scholar] [CrossRef] - Arvin, M.R.; Zakeri, A.; Shoorijeh, M.B. Using Finite Element Strength Reduction Method for Stability Analysis of Geocell-Reinforced Slopes. Geotech. Geol. Eng.
**2019**, 37, 1453–1467. [Google Scholar] [CrossRef] - Zhang, K.; Cao, P.; Meng, J.; Li, K.; Fan, W. Modeling the Progressive Failure of Jointed Rock Slope Using Fracture Mechanics and the Strength Reduction Method. Rock Mech. Rock Eng.
**2015**, 48, 771–785. [Google Scholar] [CrossRef] - Dong-Ping, D.; Liang, L.; Jian-Feng, W.; Lian-Heng, Z. Limit equilibrium method for rock slope stability analysis by using the Generalized Hoek–Brown criterion. Int. J. Rock Mech. Min. Sci.
**2016**, 89, 176–184. [Google Scholar] [CrossRef] - Liu, S.; Su, Z.; Li, M.; Shao, L. Slope stability analysis using elastic finite element stress fields. Eng. Geol.
**2020**, 273, 105673. [Google Scholar] [CrossRef] - Siacara, A.; Beck, A.; Futai, M. Reliability analysis of rapid drawdown of an earth dam using direct coupling. Comput. Geotech.
**2020**, 118, 103336. [Google Scholar] [CrossRef] - Duncan, J.; Wright, S. The accuracy of equilibrium methods of slope stability analysis. Eng. Geol.
**1980**, 16, 5–17. [Google Scholar] [CrossRef] - Kong, X.; Cai, G.; Cheng, Y.; Zhao, C. Numerical Implementation of Three-Dimensional Nonlinear Strength Model of Soil and Its Application in Slope Stability Analysis. Sustainability
**2022**, 14, 5127. [Google Scholar] [CrossRef] - Bayrak, T. Modelling the relationship between water level and vertical displacements on the Yamula Dam, Turkey. Nat. Hazards Earth Syst. Sci.
**2007**, 7, 289–297. [Google Scholar] [CrossRef][Green Version] - 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. [Google Scholar] [CrossRef] - Wu, F.; Qi, S.; Lan, H. Mechanism of uplift deformation of the dam foundation of Jiangya Water Power Station, Hunan Province, P.R. China. Hydrogeol. J.
**2005**, 13, 451–466. [Google Scholar] [CrossRef] - Khalilzad, M.; Gabr, M.A.; Hynes, M.E. Deformation-Based Limit State Analysis of Embankment Dams Including Geometry and Water Level Effects. Int. J. Géoméch.
**2015**, 15, 04014086. [Google Scholar] [CrossRef] - Jadid, R.; Montoya, B.; Bennett, V.; Gabr, M. Effect of repeated rise and fall of water level on seepage-induced deformation and related stability analysis of Princeville levee. Eng. Geol.
**2020**, 266, 105458. [Google Scholar] [CrossRef]

**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