# Numerical Analyses of Slope Stability Considering Grading and Seepage Prevention

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## Abstract

**:**

## 1. Introduction

## 2. Method and Theory

#### 2.1. Theoretical Model Construction

#### 2.2. The Numerical Calculation Model

#### 2.3. Calculation Parameters

#### 2.4. Model Boundary Conditions

## 3. Simulation Analysis

#### 3.1. Simulation Analysis 1

#### 3.2. Simulation Analysis 2

#### 3.3. Simulation Analysis 3

## 4. Conclusions

- Under the combined effects of two reservoir water levels and three different rising and falling speeds, the change in the bank slope FS occurs later than the water level change. Such a lag expands as the water level rises faster and higher, and slower water level declines occur. Meanwhile, the PFS of the three water level modes increases when the water level rises faster and higher.
- When there is rainfall, the FS decreases faster with higher rainfall intensity. In addition, the FS increases after the rainfall stops. The initial stability of the bank slope under different conditions was improved after the GSP measures, but the main slope was more sensitive to the changes in rainfall and water level.
- Under the coupling effects of real rainfall infiltration and reservoir water fluctuation from 1 to 27 July 2019, the PWP changed. The farther the monitoring point from the highest water level, the lower the PWP, and vice versa. The displacement is positively correlated with the rainfall intensity and concentration.
- Simulations for all three conditions indicate that GSP improves the FS of the slopes with no significant improvement to the main slopes but a significant improvement to their total displacement.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the study site in the northwestern Yunnan Province, China. (

**b**) Google Earth image of the study site. (

**c**) Topographical map of the bank slopes near the dam.

**Figure 2.**The numerical simulation models of the slopes. (

**a**) Grid model of the main slope before GSP. (

**b**) Grid model of the main slope after GSP. (

**c**) Grid model of the side slope before GSP. (

**d**) Grid model of the side slope after GSP.

**Figure 6.**The FS of the main slope under different reservoir water level modes (

**a**) before and (

**b**) after GSP.

**Figure 7.**The side slope FS under different reservoir water level modes (

**a**) before and (

**b**) after GSP.

**Figure 9.**Variation of the horizontal displacement of the main slope (

**a**–

**d**) before GSP and (

**e**–

**h**) after GSP.

**Figure 10.**Variation of the main slope FS under different reservoir water level modes (

**a**) before and (

**b**) after GSP.

**Figure 11.**Variation of the FS of the side slope under different reservoir water level modes (

**a**) before GSP and (

**b**) after GSP.

**Figure 12.**Saturation of the main slope under a rainfall intensity of 17 mm/h (

**a**–

**d**) before and (

**e**–

**h**) after GSP.

**Figure 13.**Horizontal displacement of the main slope under a rainfall intensity of 17 mm/h (

**a**–

**d**) before and (

**e**–

**h**) after GSP.

**Figure 14.**The PWP of (

**a**) the 59 monitoring points of the main slope before GSP. (

**b**) the 59 monitoring points of the main slope after GSP, (

**c**) the 66 monitoring points on the side slope before GSP and (

**d**) at the 66 monitoring points on the side slope after GSP.

**Figure 15.**Variation of the FS and displacement under condition 3 for (

**a**) main slope before GSP, (

**b**) main slope after GSP, (

**c**) side slope before GSP, and (

**d**) side slope after GSP.

Materials | Elastic Modulus (MPa) | Poisson Ratio | Unit Weight (kN/m^{3}) | Cohesion (kPa) | Friction Angle (°) |
---|---|---|---|---|---|

Gravel soil | 261.6 | 0.4 | 20.5 | 15 | 32 |

Strongly weathered carbonaceous slate | 2644.9 | 0.38 | 22.4 | 93.6 | 33.3 |

Moderately weathered carbonaceous slate | 5561 | 0.35 | 26.5 | 120 | 35 |

Silty clay soil | 179.8 | 0.42 | 18.5 | 35 | 15 |

Breccia | 222.7 | 0.42 | 20 | 15 | 30 |

Materials | SWCC Parameters | Hydraulic Conduction Coefficient | ||||
---|---|---|---|---|---|---|

a/kPa | m | n | θ_{s} | θ_{r} | kx (m/s) | |

Gravel soil | 100 | 0.5 | 2 | 0.346 | 0.005 | 3.14 × 10^{−3} |

Strongly weathered carbonaceous slate | 10 | 0.31 | 1.45 | 0.242 | 0.001 | 8.08 × 10^{−5} |

Moderately weathered carbonaceous slate | 10 | 0.31 | 1.45 | 0.021 | 0.001 | 2.47 × 10^{−6} |

Silty clay soil | 100 | 0.145 | 1.17 | 0.476 | 0.001 | 6.51 × 10^{−6} |

Breccia | 100 | 0.5 | 2 | 0.39 | 0.005 | 1.28 × 10^{−2} |

HDPE geomembrane | 1 × 10^{−15} |

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**MDPI and ACS Style**

Feng, Y.; Yan, F.; Wu, L.; Lu, G.; Liu, T.
Numerical Analyses of Slope Stability Considering Grading and Seepage Prevention. *Water* **2023**, *15*, 1745.
https://doi.org/10.3390/w15091745

**AMA Style**

Feng Y, Yan F, Wu L, Lu G, Liu T.
Numerical Analyses of Slope Stability Considering Grading and Seepage Prevention. *Water*. 2023; 15(9):1745.
https://doi.org/10.3390/w15091745

**Chicago/Turabian Style**

Feng, Yuting, Fuyu Yan, Lianrong Wu, Guangyin Lu, and Taoying Liu.
2023. "Numerical Analyses of Slope Stability Considering Grading and Seepage Prevention" *Water* 15, no. 9: 1745.
https://doi.org/10.3390/w15091745