# Time History Method of Three-Dimensional Dynamic Stability Analysis for High Earth-Rockfill Dam and Its Application

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## Abstract

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## 1. Introduction

## 2. Finite Element Sliding Surface Stress Method

## 3. Time History Method of Three-Dimensional Dynamic Stability Analysis

#### 3.1. Analysis Method

#### 3.2. Features of Software

#### 3.2.1. Software Framework

#### 3.2.2. The Software Features

#### 3.2.3. Verification and Analysis

## 4. Three-Dimensional Dynamic Stability Analysis of Faced Rockfill Dam

#### 4.1. Numerical Model

#### 4.2. Material Parameters

#### 4.3. Ground Motion Input

#### 4.4. Analysis of Calculation Results

## 5. Conclusions

- Based on the finite element sliding surface stress method and dynamic response analysis, a time history method of three-dimensional stability analysis is presented and realized using in-house software. The developed software is verified to be feasible and efficient by examples. It provides a basis for seismic design and the local reinforcement of high earth-rock dams, helps in the understanding of the time history variation of safety factors and the sliding process and optimizes the efficiency of dynamic stability analysis of high earth-rock dams.
- The stability analysis method based on finite element analysis is more reasonable and has obvious advantages. It is suitable for analyzing earth-rockfill dam slopes with long seismic duration and complicated action forms. In addition, there is a great difference between traditional two-dimensional stability analysis and three-dimensional stability analysis. The two-dimensional analysis assumes that the sliding body extends indefinitely along the dam axis which is not in line with reality. The most dangerous sliding body captured by three-dimensional stability analysis is shallower. The soil body in the sliding surface at the dam crest tends to be pulled apart. The local sliding direction of the sliding surface is symmetrical and the lower and middle sides are inclined outwards.
- The three-dimensional dynamic stability time history analysis not only adopts the 3D finite element dynamic response, which is closer to the real response of the dam, but also reflects the local instability characteristics of the dam slope. It can also reflect and consider the development process of the stress-strain state of the potential sliding surface, as well as the local security of the potential sliding face, time history of safety factor, overall form and space position of the dangerous sliding body, even the sliding process of the failure body and the analysis results are closer to the reality.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) 3D view; (

**b**) 2D view. A typical example of ellipsoid sliding surface is given in this paper.

**Figure 5.**(

**a**) 3D view; (

**b**) 2D view. A typical example of ellipsoid sliding surface obtained by Chen Zuyu.

**Figure 12.**(

**a**) Static stability; (

**b**) Dynamic stability. Schematic diagram of sliding surface of dam slope.

Number of Elements/Piece | Number of Sliding Surfaces/Piece | Number of Seismic Wave Calculation Time/Piece | Serial Calculation Time/h | Parallel Computing Time/h |
---|---|---|---|---|

149,984 | 41,039 | 900 | 3.7 | 0.5 |

${\mathsf{\rho}}_{\mathrm{d}}\text{}(\mathrm{kg}/{\mathrm{m}}^{3})$ | ${\mathsf{\phi}}_{0}\text{}(\xb0)$ | $\Delta \mathsf{\phi}\text{}(\xb0)$ | K | n | Rf | Kb | m |
---|---|---|---|---|---|---|---|

2150 | 52 | 8.5 | 1100 | 0.35 | 0.82 | 600 | 0.1 |

Calculation Example (Year) | Computing Method | Safety Factor |
---|---|---|

Zhang Xing (1988) | Three-dimensional limit equilibrium analysis method | 2.122 |

Chen Zuyu (2003) | Three-dimensional limit equilibrium analysis method | 2.187 |

Fang Jianrui (2007) | Direct Search Method for 3-D Finite Element | 2.386 |

Zhang Changliang (2008) | Three dimensional Sarma method | 2.241 |

Zheng Yingren (2010) | Strength reduction method—(M-C) | 2.150 |

Strength Reduction Method—Inner Corner Point Outer Circle | 2.217 | |

Strength Reduction Method—Outer corner point circumference | 2.489 | |

Wang Ke (2013) | Improved three-dimensional limit equilibrium analysis method | 2.213 |

This Paper | Finite element sliding surface stress method | 2.214 |

K | n | $\mathsf{\upsilon}$ |
---|---|---|

2339 | 0.5 | 0.33 |

Material Type | Modulus of Elasticity (GPa) | Poisson’s Ratio | ρ (kg /m ^{3}) |
---|---|---|---|

Bedrock | 20.0 | 0.250 | 2600 |

Concrete face material | 25.5 | 0.167 | 2400 |

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**MDPI and ACS Style**

Yuan, H.; Yu, X.; Zou, D.; Wang, Y.; Li, M.; Liu, J.
Time History Method of Three-Dimensional Dynamic Stability Analysis for High Earth-Rockfill Dam and Its Application. *Sustainability* **2022**, *14*, 6671.
https://doi.org/10.3390/su14116671

**AMA Style**

Yuan H, Yu X, Zou D, Wang Y, Li M, Liu J.
Time History Method of Three-Dimensional Dynamic Stability Analysis for High Earth-Rockfill Dam and Its Application. *Sustainability*. 2022; 14(11):6671.
https://doi.org/10.3390/su14116671

**Chicago/Turabian Style**

Yuan, Han, Xiang Yu, Degao Zou, Yuke Wang, Minghao Li, and Junchi Liu.
2022. "Time History Method of Three-Dimensional Dynamic Stability Analysis for High Earth-Rockfill Dam and Its Application" *Sustainability* 14, no. 11: 6671.
https://doi.org/10.3390/su14116671