# Efficient and Accurate 3-D Numerical Modelling of Landslide Tsunami

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

^{3}is used here).

## 3. Model Validation and Scale Effect

#### 3.1. Validation: Subaerial and Submarine Landslide

#### 3.2. Model Scale Effect

## 4. Mesh Strategy and Application

#### 4.1. Numerical Cases

#### 4.2. Numerical Result and Mesh-Generation Scheme

## 5. Real-Word Application: Landslide Tsunami in Laxiwa Reservoir

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Water surface elevation $\eta $ at different time. (

**a**) t = 1.5 s; (

**b**) t = 3 s: experimental data (circle), current solution (black), and Nasa-vof2D results (red) of Heinrich [7].

**Figure 3.**Water surface elevation $\eta $ varying with time at different positions. (

**a**) x = 1.2 m and (

**b**) x = 1.8 m correspond to the relative positions x/h = 5.0 and 7.5 in Heller et al. [5]: experimental data (circle), current solution (black), ISPH results (ISPH(a), blue; ISPH(b), red) of Yeylaghi et al. [29], DEM-SPH results (green) [49], and DualSHPysics results (DualSPHysics(a), orange; DualSPHysics(b), purple) of Heller et al. [5]. DualSPHysics(a) results are obtained using a reduced slide front-impact velocity of 1.32 m/s, and DualSPHysics(b) results are obtained using an unreduced slide front-impact velocity of 2.43 m/s; ISPH(a) results are obtained with particle resolution of 0.01 m, and ISPH(b) results are obtained with particle resolution of 0.005 m. The particle resolution in DualSPHysics is 0.01 m.

**Figure 4.**Comparison between numerical and experimental wave profiles in the near field: (

**a**) t = 0.5 s; (

**b**) t = 1.5 s; and (

**c**) t = 3 s.

**Figure 5.**Wave gauges: Comparison between experimental and computed waves in the propagation field: (

**a**) x = 4 m; (

**b**) x = 8 m; and (

**c**) x = 12 m.

**Figure 6.**Calculation results of uniform mesh of different sizes in the near field: (

**a**) t = 5 s; (

**b**) t = 10 s.

**Figure 7.**Calculation results of uniform mesh of different sizes in the propagation field: (

**a**) t = 15 s; (

**b**) t = 20 s; (

**c**) t = 50 s; and (

**d**) t = 60 s.

**Figure 8.**Computational results of different mesh schemes compared with that of original global uniform mesh calculation: (

**a**) t = 15 s; (

**b**) t = 20 s; (

**c**) t = 50 s; and (

**d**) t = 60 s.

**Figure 9.**Large-scale numerical model of Laxiwa Reservoir, China. (

**a**) Laxiwa terrain. (

**b**) Geometric model.

**Figure 10.**Mesh scheme application for engineering. The size of block 1: 130 m × 170 m × 150 m; the size of block 2: 1000 m × 750 m × 400 m; the size of block 3: 750 m × 1100 m × 300 m; the size of block 4: 800 m × 1500 m × 300 m.

**Figure 11.**Highest initial wave in the near field at t = 10 s: (

**a**) 6-m global uniform mesh; (

**b**) 3-m global uniform mesh; and (

**c**) mesh-scheme solution.

**Figure 12.**Wave height in the propagation field at t = 30 s: (

**a**) 6-m global uniform mesh; (

**b**) 3-m global uniform mesh; and (

**c**) mesh scheme solution.

Parameter | Value |
---|---|

slide length (two right angle sides) | 0.5 m |

slide width | 0.55 m |

slide mass | 140 kg |

still water depth (h${}_{0}$) | 1 m |

water density ($\rho $) | 1000 kg/m${}^{3}$ |

initial slide position | 1 cm below the undisturbed free surface |

slope inclination | ${45}^{\circ}$ |

channel width | 0.55 m |

channel length | 20 m |

wave gauges position | x = 4 m, x = 8 m, x = 12 m |

Parameter | Value |
---|---|

slide length (${l}_{s}$) | 0.599 m |

slide width (w) | 0.577 m |

slide thickness (s) | 0.12 m |

slide density (${\rho}_{s}$) | 1540 kg/m${}^{3}$ |

slide mass (${m}_{s}$) | 60.14 kg |

still water depth (h${}_{0}$) | 0.24 m |

slide front initial position (${x}_{s}$) | −0.55 m |

water density ($\rho $) | 1000 kg/m${}^{3}$ |

channel width | 0.6 m |

channel length | 24 m |

channel height | 1.5 m |

relative wave probe distances ($x/{h}_{0}$) | 3.0, 5.0, 7.5, 10.0, 15.0, 22.5, 35.0 |

Mesh Size (m) | $\mathbf{r}({\mathbf{s}}_{1}/{\mathbf{s}}_{2})$ | $\mathbf{MATKE}\left({\mathbf{m}}^{2}\xb7{\mathbf{kg}}^{-1}/{\mathbf{s}}^{2}\right)$ | $\mathbf{Relative}\phantom{\rule{4pt}{0ex}}\mathbf{Error}\left(\mathit{\epsilon}\right)$ | GCI (%) |
---|---|---|---|---|

3.0 | — | 0.003621 | — | — |

2.5 | 1.2 | 0.003854 | 0.06046 | 17.18 |

2 | 1.25 | 0.003976 | 0.03068 | 6.82 |

1.5 | 1.33 | 0.004024 | 0.01193 | 1.94 |

Case | Mesh Size (m) | Number of Mesh |
---|---|---|

1 | 1.5 | 2,960,000 |

2 | 2 | 1,260,000 |

3 | 2.5 | 633,600 |

4 | 3 | 360,000 |

5 | 3.5 | 233,376 |

6 | 4 | 157,500 |

7 | 4.5 | 107,892 |

8 | 5 | 79,200 |

9 | 5.5 | 60,060 |

10 | 6 | 45,000 |

11 | 6.5 | 33,264 |

12 | 7 | 29,104 |

13 | 7.5 | 22,400 |

14 | 8 | 19,740 |

Mesh Schemes | Mesh Number | Calculation Time (Hour) |
---|---|---|

1.5 m global uniform mesh | 2,960,000 | 5.9 |

Mesh scheme 1 | 960,000 | 1.45 |

Mesh scheme 2 | 490,000 | 0.27 |

Parameter | Value |
---|---|

landslide type | rigid block |

landslide volume | 86,960 m${}^{3}$ |

landslide density | 2650 kg/m${}^{3}$ |

dam height | 250 m |

still water surface height | 230 m |

water density ($\rho $) | 1000 kg/m${}^{3}$ |

calculation region in x,y,z direction | 3045 m $\times 2340$ m $\times 805$ m |

Mesh Schemes | Mesh Number | Calculation Time (Hour) |
---|---|---|

3-m global uniform mesh | 16,297,154 | 22.3 |

6-m global uniform mesh | 2,238,731 | 2.5 |

Mesh scheme | 7,427,669 | 4.8 |

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## Share and Cite

**MDPI and ACS Style**

Li, G.; Chen, G.; Li, P.; Jing, H. Efficient and Accurate 3-D Numerical Modelling of Landslide Tsunami. *Water* **2019**, *11*, 2033.
https://doi.org/10.3390/w11102033

**AMA Style**

Li G, Chen G, Li P, Jing H. Efficient and Accurate 3-D Numerical Modelling of Landslide Tsunami. *Water*. 2019; 11(10):2033.
https://doi.org/10.3390/w11102033

**Chicago/Turabian Style**

Li, Guodong, Guoding Chen, Pengfeng Li, and Haixiao Jing. 2019. "Efficient and Accurate 3-D Numerical Modelling of Landslide Tsunami" *Water* 11, no. 10: 2033.
https://doi.org/10.3390/w11102033