# Some Considerations for Using Numerical Methods to Simulate Possible Debris Flows: The Case of the 2013 and 2020 Wayao Debris Flows (Sichuan, China)

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## Abstract

**:**

## 1. Introduction

## 2. Study Sample

^{2}, and the main channel length is 2.2 km. The terrain elevation varies between 1191 m and 2973 m, and the slope range is 35–50°. The geological setting consists mostly of Proterozoic magmatic rocks. The Wayao catchment is located southeast of the Wenchuan-Maoxian fault, a thrust fault with a strike of 25° N–45° E [40] that ruptured in the Wenchuan earthquake [41]. Several landslides were triggered by the 2008 Wenchuan earthquake in the Wayao catchment, and most of them were deposited on the slope or along the channel. They provided the main debris source for the debris flow in 2013. The Wayao catchment is in a typically humid subtropical monsoon climate zone, with rainfall mainly concentrated between June and September. Heavy rainfall triggered two debris flow events in the Wayao catchment in 2013 and 2019.

^{5}m

^{3}of debris was transported out, and the average depth of the debris fan was 5 m. The debris flow buried 27 houses and cut national road G213. Then, the local government built a check dam and drainage channel in 2014 to avoid possible debris flows.

## 3. Measuring Debris Flow Volume

## 4. Model Description

#### 4.1. Massflow

^{2}[50,51]. Then the inversion method was used to determine the specific parameter values. A series of numerical simulations were performed to refine the parameter values by comparing the depth distribution of the debris fan. Parameter values for Massflow are summarized in Table 2. The running time was 300 s, with a time step Δt ≤ 1 s.

#### 4.2. Flow-3D

_{i}, additional viscous shear stress due to the presence of solid particles τ

_{v}, and Shear stress in the fluid τ

_{f}.

_{f}is the fluid’s dynamic viscosity. λ is the diameter to the minimum gap ratio. du/dy is the velocity gradient of the mixture. ρ

_{s}is the density of the solid sphere. ρ

_{f}is the density of the fluid sphere. e is the coefficient of restitution of the solid particle, and a typical coefficient of restitution for debris of 0.7 is assumed as a good general value. D is the diameter of spherical particles. ΔR is the gap of a Couette flow. λ is a function of the maximum solid volume fraction ${f}_{s}^{mx}$ divided by the solid volume fraction f

_{s}.

^{3}and 0.01 kg/m/s, respectively. The density of the solid was set to 2700 kg/m

^{3}. The average grain diameter was set to 0.05 m, which was calculated by the measured value of the final deposit [18]. The friction angle (degrees) was between 20 and ~35, as provided by the Sichuan Metallurgical and Geological Exploration Bureau of the Chengdu Geological Survey Institute. The debris flow density was in a range between 1850 and 2030 kg/m

^{3}. The best simulation parameters were obtained through repeated analysis, and the simulation results were satisfactory. Table 2 shows the full set of parameters used in the simulation. The running time was 300 s, with a time step Δt ≤ 0.5 s.

#### 4.3. OpenLISEM_A and OpenLISEM_B

_{s}is the volume fraction of solid phases (-), α

_{f}is the volume fraction of fluid phases (-). δ is the internal friction angle. P

_{b}is the pressure at the surface (Kg/ms

^{2}). b is the basal surface of the flow (m). N

_{R}is the Reynolds number (-). N

_{RA}is the quasi-Reynolds number (-). C

_{DG}is the drag coefficient (-). ρ

_{f}is the density of the fluid (kg/m

^{3}), ρ

_{s}is the density of the solids (kg/m

^{3}), γ is the density ratio between the fluid and solid phase (-). χ is the vertical shearing of fluid velocity (m/s). ε is the aspect ratio of the model (-). ξ is the vertical distribution of α

_{s}(m

^{−1}).

^{3}. The friction angle (degrees) was in a range between 20 and ~35. The debris flow density was in a range between 1850 and 2030 kg/m

^{3}. The value of manning was between 0.02 and 0.1. The porosity was set to 0.38. According to the research results [17], the cohesion was in a range between 0 and 2500 pa.

## 5. Results

#### 5.1. Application to the Debris Flow Event in 2013

^{3}, most of the debris flow deposits in the channel. When the value of debris flow density is 1850 kg/ m

^{3}, most of the debris flow runs out of the catchment at an abnormal velocity. The friction angle (θ) is another key parameter to the deposition and entrainment of the debris flow. A larger friction angle will cause the debris flow to deposit quickly, while a smaller friction angle will cause the solid particles to be more easily transported. Different simulations were performed to understand the friction angle (θ) influence on the debris flow process. We found that the multiplier in the friction angle significantly impacts the deposition rate of debris flow. The simulation result with θ = 32 is considered to best reproduce the debris flow deposition, and the volume of the simulated debris fan is 67% of the actual debris fan volume. However, the deposition thicknesses in the middle and east of the debris fan are underestimated.

#### 5.2. Prediction to the Debris Flow Event in 2020

#### 5.3. Scenario without Mitigation Structures

## 6. Discussion

- Different models have different predictive capabilities, and this may be due to the different sensitivity to debris flow densities or considering the interactions between the hydrology and the debris flow. Therefore, it should be considered when evaluating model predictive reliability.
- Adopting multiple methods in hazard assessment and early warning systems may achieve ideal results. For example, a model with higher computational efficiency is used for preliminary prediction. Moreover, a model with higher accuracy is used for detailed prediction.
- It is unclear whether a model is always the best performance model for prediction. Therefore, combining various models to form a multi-model real-time risk assessment and early warning system requires further research.

## 7. Conclusions

- All four models provided satisfactory results for the geometry and depth distribution of the debris fan in 2013.
- Combining the simulation results in the scenario without mitigation structures indicates that the mitigation structures played an essential role in reducing the danger of the debris flow event in 2020.
- Considering the prediction of the debris flow event in 2020, including the deposition depth of debris behind the check dam and the runout extent of the debris flow, OpenLISEM_B has the best performance among the four models. However, they are different for both the adopted theoretical rheological model and the numerical scheme. So, it is not easy to understand the different behavior.
- OpenLISEM_B (the model with an entire hydrological catchment) has the advantage of higher prediction accuracy of debris flow deposition depth than OpenLISEM_A (the model without considering). Since the cases in this paper were triggered by runoff, the comparison can only stand for debris flows triggered by runoff.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Overview of the study area. The landslides and deposits along the channel were identified on a satellite image from 15 April 2015.

**Figure 2.**(

**A**) Panoramic view of Wayao debris flow taken on 7 August 2013. The dashed red line indicates the catchment boundary, and the solid red line indicates the extent of the debris fan. (

**B**) The debris deposition along the channel was eroded by the debris flow in 2013. The blue line indicates the debris flow direction, and the red lines indicate the trace of the debris flow. (

**C**) The debris fan of the Wayao debris flow in 2013.

**Figure 3.**(

**A**) The landslides are identified on a satellite image from 27 August 2020. It shows the locations of (

**B**,

**C**). (

**B**) Destroyed drainage channel and debris flow runout on UAV image from 25 October 2020. (

**C**) A drone photo shows that the check dam was filled with debris-flow deposits after the debris flow, and it was taken on 25 October 2020.

**Figure 4.**(

**A**,

**B**) The depth distributions of eroded debris and deposited debris in the 2013 debris flow event and the 2020 debris flow event, respectively. (

**C**,

**D**) The longitudinal profiles along the channel, and their positions are shown in A and B, respectively. The location of profiles a-a’ is shown in (

**A**) and the location of profile b-b’ is shown in (

**B**).

**Figure 5.**Resistivity results and interpretations. (

**A**) Resistivity profile along L1. (

**B**) Resistivity profile along with L2. The white dotted line is the dividing line between the debris fan and the underlying rock layer. L1, L2, and bp1 are shown in Figure 3.

**Figure 6.**Wayao debris flow fan reproduced by four models. (

**A**) Massflow simulations-sensitivity to the Coulomb-type friction μ = 0.4, μ = 0.439, and μ = 0.45. (

**B**) Flow-3D simulations-sensitivity to multiplier in internal friction angle θ = 20, θ = 32, and θ = 35. (

**C**) OpenLISEM_A simulations-sensitivity to internal friction angle θ = 20, θ = 24, and θ = 27. (

**D**) OpenLISEM_B simulations-sensitivity to internal friction angle coefficient θ = 17, θ = 20, and θ = 24.

**Figure 7.**Debris flow fan in 2013: Actual runout (

**A**) and best simulations by Massflow (

**B**), Flow-3D (

**C**), OpenLISEM_A (

**D**), OpenLISEM_B (

**E**). The full sets of model parameters are given in Table 1.

**Figure 8.**Schematic diagram of verification results of debris flow events. A predicted area was measured, and the observed area was from the simulation result. X is the positive accuracy area, Y represents the missing accuracy area, Z is negative.

**Figure 9.**Comparison of debris fan thickness in 2013 (along two representative cross-sections). Including the actual debris fan and the debris fan of best-fit simulations by Massflow, Flow-3D, OpenLISEM_A, and OpenLISEM_B. (

**A**) shows the debris fan thickness along the cross-section a-a’, and (

**C**) shows the debris fan thickness along the cross-section b-b’. The locations of a-a’ and b-b’ are shown in (

**B**).

**Figure 10.**Snapshots of the debris flow height of Wayao debris flow in 2013 simulated by Massflow (

**A**), Flow-3D (

**B**), OpenLISEM_A (

**C**), and OpenLISEM_B (

**D**). Abbreviations: s means seconds, and m means minutes.

**Figure 11.**Debris flow runout in 2020: actual runout (

**A**) and simulations by Massflow (

**B**), Flow-3D (

**C**), OpenLISEM_A (

**D**), OpenLISEM_B (

**E**).

**Figure 12.**Snapshots of the debris flow height of Wayao debris flow in 2020 simulated by Massflow (

**A**), Flow-3D (

**B**), OpenLISEM_A (

**C**), and OpenLISEM_B (

**D**). Abbreviations: s means seconds, and m means minutes.

**Figure 13.**The prediction results without mitigation structures. Simulations for Massflow (

**A**), Flow-3D (

**B**), OpenLISEM_A (

**C**), and OpenLISEM_B (

**D**).

**Table 1.**The volumes of landslides, eroded debris along the channel, debris fan, and the deposition after the barrier.

Year | 2013 | 2020 |
---|---|---|

Volume of the landslides (m^{3}) | 2.6 × 10^{6} | 1.9 × 10^{4} |

Volume of the eroded debris along the channel (m^{3}) | 5.3 × 10^{6} | 1.1 × 10^{4} |

Volume of the debris fan (m^{3}) | 7.9 × 10^{6} | / ^{1} |

Volume of the deposition after the barrier (m^{3}) | / ^{2} | 0.3 × 10^{4} |

^{1}The debris flow did not form a debris fan in 2020, as it transported into Min River.

^{2}There was no debris deposition after the barrier in 2013, as the barrier was built in 2014.

**Table 2.**Best-fit model parameters used in Massflow, Flow-3D, OpenLISEM_A, and OpenLISEM_B simulations of the Wayao debris flow in 2013. A range of some debris parameters was measured by field measurement and laboratory tests.

Parameter | Massflow | Flow-3D | OpenLISEM_A | OpenLISEM_B |
---|---|---|---|---|

Rheological model | Coulomb frictional | Granular flow | general two-phase debris flow model | |

Topographic mesh resolution | 5 m | 5 m | 5 m | 5 m |

Debris flow density (kg/m^{3}), ρ | 1986 | 1986 | 1986 | - |

Cohesion (pa), c | - | - | 1250 | 1250 |

Friction angle (degrees), θ | — | 32 | 24 | 20 |

Coulomb-type friction, μ | 0.439 | - | - | - |

viscous resistance, ξ | 200 | - | - | - |

Average grain diameter, D | - | 0.05 | 0.05 | 0.05 |

Grain density (kg/m^{3}), ρ_{s} | - | 2700 | 2700 | 2700 |

Fluid density (kg/m^{3}), ρ_{f} | - | 1000 | - | - |

Fluid viscosity (kg/m/s) | - | 0.01 | - | - |

Minimum volume fraction of granular phase | - | 0.001 | - | - |

XY mesh cell size | 5 m | 5 m | 5 m | 5 m |

Z mess cell size | - | 2 m | - | - |

Manning | - | - | 0.1 | 0.1 |

Porosity | - | - | 0.38 | 0.38 |

Initial moisture content | - | - | - | 0.114 |

Rainfall (mm/h) | - | - | - | 18.6 |

**Table 3.**Analysis of the final deposition volume dependence in the debris fan area on the various parameters. When a variable is analyzed, the other parameters are the same as those in Table 1. Vr means the simulated debris fan volume to measured debris fan volume.

Massflow | Flow-3D | |||||
---|---|---|---|---|---|---|

ID | ξ | μ | Vr | ρ | θ | Vr |

1 | 200 | 0.4 | 76% | 1986 | 20 | 49% |

2 | 200 | 0.439 | 85% | 1986 | 32 | 67% |

3 | 200 | 0.45 | 66% | 1986 | 35 | 39% |

4 | 100 | 0.439 | 57% | 1850 | 32 | 32% |

5 | 300 | 0.439 | 71% | 2030 | 32 | 1% |

Common parameters | OpenLISEM_A | OpenLISEM_B | ||||

ID | D | c | θ | ρ | Vr | Vr |

1 | 0.04 | 1250 | 24 | 1986 | 0.43 | - |

2 | 0.05 | 0 | 24 | 1986 | 0.68 | - |

3 | 0.05 | 1250 | 20 | 1986 | 0.7 | 0.59 |

4 | 0.05 | 1250 | 24 | 1850 | 0.52 | - |

5 | 0.05 | 1250 | 24 | 1986 | 0.73 | 0.53 |

6 | 0.05 | 1250 | 24 | 2030 | 0.65 | - |

7 | 0.05 | 1250 | 27 | 1986 | 0.65 | - |

8 | 0.05 | 1250 | 35 | 1986 | 0.52 | 0.49 |

9 | 0.05 | 2500 | 24 | 1986 | 0.59 | - |

10 | 0.06 | 1250 | 24 | 1986 | 0.5 | - |

11 | 0.04 | 1250 | 20 | - | - | 0.36 |

12 | 0.05 | 0 | 20 | - | - | 0.58 |

13 | 0.05 | 1250 | 17 | - | - | 0.56 |

14 | 0.05 | 2500 | 20 | - | - | 0.54 |

**Table 4.**Comparison of the simulation accuracy of four models. Ap means the positive accuracy area. An means the negative accuracy area. Am means the missing accuracy area. Vp means the positive accuracy volume. Mean depth means the mean depth of the debris fan.

Models | Area (×10^{4} m^{2}) | Volume (×10^{5} m^{3}) | Mean Depth (m) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Ap | % | An | % | Am | % | Vp | % | H | % | |

Actual | 2.9 | 100% | 0 | 0% | 0 | 0% | 1.4 | 100% | 4.8 | 100% |

Massflow | 2.1 | 71% | 1.0 | 33% | 0.9 | 29% | 1.2 | 86% | 7.3 | 152% |

Flow-3D | 2.0 | 69% | 2.1 | 73% | 0.9 | 31% | 0.9 | 67% | 4.7 | 97% |

OpenLISEM_A | 2.2 | 75% | 2.7 | 94% | 0.7 | 25% | 1.0 | 73% | 4.7 | 97% |

OpenLISEM_B | 1.6 | 55% | 0.04 | 1% | 1.3 | 45% | 0.8 | 58% | 5.1 | 106% |

**Table 5.**With different mesh resolutions, the computational times required to simulate the debris flow event in 2013.

Model | Topographic Mesh Resolution | Time for Computation |
---|---|---|

Massflow | 5 m | ~4 min |

10 m | ~2 min | |

Flow-3D | 5 m | ~2 h |

10 m | ~14 min | |

OpenLISEM_A | 5 m | ~28 min |

10 m | ~16 min | |

OpenLISEM_B | 5 m | ~2.5 h |

10 m | ~1.3 h |

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**MDPI and ACS Style**

Zhang, X.; Tang, C.; Yu, Y.; Tang, C.; Li, N.; Xiong, J.; Chen, M.
Some Considerations for Using Numerical Methods to Simulate Possible Debris Flows: The Case of the 2013 and 2020 Wayao Debris Flows (Sichuan, China). *Water* **2022**, *14*, 1050.
https://doi.org/10.3390/w14071050

**AMA Style**

Zhang X, Tang C, Yu Y, Tang C, Li N, Xiong J, Chen M.
Some Considerations for Using Numerical Methods to Simulate Possible Debris Flows: The Case of the 2013 and 2020 Wayao Debris Flows (Sichuan, China). *Water*. 2022; 14(7):1050.
https://doi.org/10.3390/w14071050

**Chicago/Turabian Style**

Zhang, Xianzheng, Chenxiao Tang, Yajie Yu, Chuan Tang, Ning Li, Jiang Xiong, and Ming Chen.
2022. "Some Considerations for Using Numerical Methods to Simulate Possible Debris Flows: The Case of the 2013 and 2020 Wayao Debris Flows (Sichuan, China)" *Water* 14, no. 7: 1050.
https://doi.org/10.3390/w14071050