# Forecasting Landslides via Three-Dimensional Discrete Element Modeling: Helong Landslide Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Study Area

#### 2.2. Helong Landslide

## 3. Methodology

_{1,2}is the equivalent mass of particle P

_{1}and P

_{2}; I

_{1,2}is the equivalent moment of inertia of the particle; S is the rotation radius; u

_{n}and u

_{s}are the normal and tangential relative displacements of the particles, respectively; $\theta $ is the rotation angle of the particle; F

_{n}and F

_{s}are the normal and tangential components of the external force on the particle, respectively; M is the external torque received by the particle; K

_{n}and K

_{s}are the normal and tangential elastic coefficients in the contact model, respectively; and c

_{n}and c

_{s}are the normal and tangential damping coefficients in the contact model, respectively. For contact points, the magnitude of the force is determined by the magnitude of the overlap. The displacement and velocity are calculated using the original location and force, which are updated according to Newton’s second law of movement in every time step (Figure 7b). The macroscopic physical-mechanical behavior of material is reflected by the microscopic granular interaction using this method.

## 4. Results and Discussions

#### 4.1. Stability Analysis

#### 4.2. Post-Failure Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Visual interpretation of historical deformation of the rockslide from Google Earth images (the date is shown using the YYYY.MM.DD format). (

**a**) 2008.12.26, (b) 2011.09.02, (c) 2011.09.25, (d) 2013.09.22, (e) 2015.10.16, (f) 2018.05.31.

**Figure 4.**Photographs of the Helong landslide in April 2018: (

**a**) collapsed area of the landslide, (

**b**) composition of the sources, (

**c**) consolidation pressure test of the material, (

**d**) terrain bulged phenomenon at the front part of potential failure mass, (

**e**) cracks and trop head at the trilling edge, and (

**f**) infiltration at the bottom of the source area.

**Figure 5.**ERT inverse models for the investigated (

**a**) longitudinal and (

**b**) transverse profiles. The positioning of ERT profiles is shown in Figure 3a.

**Figure 7.**Principle of a digital elevation model (DEM): (

**a**) schematic of the force–displacement model between two particles and a (

**b**) calculation flow chart.

**Figure 9.**Parameter calibration of the DEM: (

**a**) flow chart, (

**b**) numerical direct shear test, and (

**c**) comparison of the shear test between the numerical model and the laboratory experiment.

**Figure 11.**Simulation results with friction coefficients of (

**a**) 0.35, (

**b**) 0.3, (

**c**) 0.25, and (

**d**) 0.2 to illustrate the final deposition areas.

**Figure 12.**Dynamic process of the Helong landslide (friction coefficient = 0.25) with snapshots at different times: (

**a**) T = 2 s, (

**b**) T = 10 s, (

**c**) T = 18 s, and (

**d**) T = 25 s.

**Figure 13.**Run-out behavior in different parts of the sliding mass: (

**a**) position of the monitoring balls and corresponding traces, and (

**b**) velocity of the monitoring balls in the whole sliding process.

Soil Type | Natural State | Saturated State | ||||
---|---|---|---|---|---|---|

Weight (kN/m ^{3}) | Cohesion C (kPa) | Friction φ (°) | Weight (kN/m ^{3}) | Cohesion C (kPa) | Friction φ (°) | |

Soil aggregate | 18.2 | 16.5 | 21 | 19.1 | 9.5 | 18 |

Gravel and silt | 18.5 | 18.5 | 19 | 19.0 | 11.0 | 15 |

Granite | 27.2 | \ | \ | 29.7 | \ | \ |

Parameters | Values from the Shear Test | Values from the Landslide Modeling |
---|---|---|

Number of particles | 3788 | 30872 |

Radius (m) | 0.0025–0.01 | 0.5–2 |

Particle density (kg/m^{3}) | 2500 | 2500 |

Friction between balls | 0.5 | 0.25 |

Friction between balls and slip surface | 0.5 | 0.2–0.35 |

E (MPa) | 20 | 20 |

ν | 0.4 | 0.4 |

${\overline{\sigma}}_{c}$(Pa) | 2 × 10^{6} | 2 × 10^{6} |

${\overline{\tau}}_{c}$(Pa) | 1 × 10^{6} | 1 × 10^{6} |

${\overline{k}}_{n}$(N/m^{3}) | 8 × 10^{10} | 2 × 10^{8} |

${\overline{k}}_{s}$(N/m^{3}) | 4 × 10^{10} | 1 × 10^{8} |

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**MDPI and ACS Style**

Peng, W.; Song, S.; Yu, C.; Bao, Y.; Sui, J.; Hu, Y.
Forecasting Landslides via Three-Dimensional Discrete Element Modeling: Helong Landslide Case Study. *Appl. Sci.* **2019**, *9*, 5242.
https://doi.org/10.3390/app9235242

**AMA Style**

Peng W, Song S, Yu C, Bao Y, Sui J, Hu Y.
Forecasting Landslides via Three-Dimensional Discrete Element Modeling: Helong Landslide Case Study. *Applied Sciences*. 2019; 9(23):5242.
https://doi.org/10.3390/app9235242

**Chicago/Turabian Style**

Peng, Wei, Shengyuan Song, Chongjia Yu, Yiding Bao, Jiaxuan Sui, and Ying Hu.
2019. "Forecasting Landslides via Three-Dimensional Discrete Element Modeling: Helong Landslide Case Study" *Applied Sciences* 9, no. 23: 5242.
https://doi.org/10.3390/app9235242