# Debris Flow Susceptibility Assessment in the Wudongde Dam Area, China Based on Rock Engineering System and Fuzzy C-Means Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}, which occupies 86% of the Jinsha River. The studied section of Jinsha River is about 210 km long. The area of investigation along the Jinsha River was extended from the alluvial plain to the crest. Based on field investigations, 22 channelized debris flow gullies distributed on both sides of the Jinsha River were identified, as shown in Figure 2. Considering that loose materials from the debris flow gullies could enter the Jinsha River and affect the running of the power station, it is of great significance to carry out a susceptibility analysis for this area.

#### 2.1. Geological and Tectonic Setting

#### 2.2. Geomorphological Setting

#### 2.3. Meteorological Setting

## 3. Influencing Parameters

#### 3.1. Lithology

#### 3.2. Watershed Area

#### 3.3. Slope Angle

#### 3.4. Stream Density

#### 3.5. Length of the Main Stream

#### 3.6. Curvature of the Main Stream

#### 3.7. Distance from Fault

#### 3.8. Vegetation Cover Ratio

_{i}) are shown in Table 1.

## 4. Method

#### 4.1. Rock Engineering System

_{i}represents the influence of other parameters on P

_{i}, while the row through P

_{i}represents the influence of P

_{i}on the remaining parameters. For example, the (i, j)-th element in the matrix represents the influence of parameter i on parameter j.

_{i}) and the ‘‘effect’’ value (E

_{i}), respectively. The coordinate values (C

_{i}, E

_{i}) for each parameter can be plotted in cause and effect space, forming the so-called cause–effect plot, which can help to understand the relative importance of each parameter within the system [43]. The percentage value of (C + E) can be used as the weighting of each parameter, which is given by:

#### 4.2. Fuzzy C-Means Algorithm

**X**

_{j}= (

**X**

_{j}

_{1},

**X**

_{j}

_{2}, …,

**X**

_{jP}), the algorithm is designed to partition the data set into C clusters (i.e., structural domains) by iteratively minimizing the fuzzy objective function which is expressed as follows [29]:

_{ij}represents the degree of membership of observation

**X**

_{j}in cluster i, m is the fuzziness index, which controls the fuzziness of the memberships, and d(

**X**

_{j},

**V**

_{i}) is the distance between observation

**X**

_{j}and the ith cluster center

**V**

_{i}. m = 2 is deemed to be the best for most applications [29]. In this research, the value of P is 6 since there are six parameters that were used for structural domain determination.

**X**

_{j},

**V**

_{i}) is expressed as [45]:

_{ij}can be calculated from [45]:

**V**

_{i}is computed by [45]:

## 5. Results and Discussion

#### 5.1. RES Model for Debris Flow Susceptibility Assessment

_{i}, E

_{i}) of each parameter were calculated (Table 4). A cause–effect plot was drawn with the (C

_{i}, E

_{i}) coordinates, as shown in Figure 7. Each point in the plot represents a particular factor P

_{i}. The cause–effect plot can help to distinguish between “less interactive” and “more interactive” parameters: the “more interactive” parameters are plotted in the upper left region, whereas the “less interactive” parameters are plotted in the lower right region [28]. Figure 7 indicates that P5 (length of the main stream) is more interactive than the other parameters, and it is greatly affected by the system. On the other hand, P1 (lithology) and P7 (distance from fault) have the maximum effect on the system.

_{i}is the weighting of the ith parameter obtained from Table 4, p

_{i}is the rating value of the ith parameter obtained from Table 1, and n is the total number of parameters.

#### 5.2. Debris Flow Susceptibility Assessment

#### 5.3. Validation of the Model

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Location map of the study area [30].

**Figure 3.**Lithology in the study area [31].

**Figure 4.**Regional tectonic framework map [33].

**Figure 5.**General illustration of the interaction matrix with two factors [28].

**Figure 6.**Summation of coding values in the row and column through each parameter to establish the cause and effect coordinates [28].

**Figure 10.**Geological and environmental conditions of the Shenyuhe debris flow gully. (

**a**) loose materials deposited along the main channel; (

**b**) unstable slopes composed of sediments of the Madianhe Group and a small mudflow.

**Figure 11.**Landslides occurred in the study area. (

**a**) landslides on the Quaternary deposits; (

**b**) landslides on the fine sand layer.

Description | Rating | Description | Rating |
---|---|---|---|

1. Lithology | 5. Length of the main stream (km) | ||

Magmatic rocks, and limestones | 0 | <1 | 0 |

Phyllite, slate and schist | 1 | 1–5 | 1 |

Sandstones, mudstones, and shale | 2 | 5–10 | 2 |

Quaternary deposits | 3 | >10 | 3 |

2. Watershed area (km^{2}) | 6. Curvature of the main stream | ||

<0.5 or >50 | 0 | <1.1 | 0 |

0.5–10 | 1 | 1.1–1.25 | 1 |

10–35 | 2 | 1.25–1.4 | 2 |

35–50 | 3 | >1.4 | 3 |

3. Slope angle (°) | 7. Distance from fault (km) | ||

<15 | 0 | >0.6 | 0 |

15–25 | 1 | 0.4–0.6 | 1 |

25–32 | 2 | 0.2–0.4 | 2 |

>32 | 3 | <0.2 | 3 |

4. Stream density (km/km^{2}) | 8. Vegetation cover ratio | ||

<5 | 0 | >0.75 | 0 |

5–10 | 1 | 0.5–0.75 | 1 |

10–20 | 2 | 0.25–0.5 | 2 |

>20 | 3 | <0.25 | 3 |

**Table 2.**ESQ interaction matrix coding [28].

Coding | Description |
---|---|

0 | No interaction |

1 | Weak interaction |

2 | Medium interaction |

3 | Strong interaction |

4 | Critical interaction |

P1 | 2 | 4 | 3 | 3 | 3 | 2 | 3 |
---|---|---|---|---|---|---|---|

0 | P2 | 2 | 1 | 2 | 1 | 2 | 1 |

0 | 1 | P3 | 2 | 3 | 2 | 0 | 2 |

1 | 0 | 3 | P4 | 2 | 3 | 0 | 2 |

1 | 0 | 2 | 2 | P5 | 2 | 0 | 1 |

1 | 0 | 1 | 2 | 4 | P6 | 0 | 1 |

3 | 3 | 3 | 3 | 2 | 3 | P7 | 2 |

2 | 0 | 1 | 3 | 2 | 2 | 0 | P8 |

Parameter | C_{i} | E_{i} | w_{i} (%) |
---|---|---|---|

Lithology | 20 | 8 | 14.58 |

Watershed area | 9 | 6 | 7.81 |

Slope angle | 10 | 16 | 13.54 |

Stream density | 11 | 16 | 14.06 |

Length of the main stream | 8 | 18 | 13.54 |

Curvature of the main stream | 9 | 16 | 13.02 |

Distance from fault | 19 | 4 | 11.98 |

Vegetation cover | 10 | 12 | 11.46 |

Gullies | Influencing Parameters | SI | RES_KM | RES_FCM | Actual Condition | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | |||||

Xiabaitan | T–K | 3.1 | 36.1 | 5.51 | 3.08 | 1.19 | 0 | 10 | 188.53 | High | High | High |

Shangbaitan | T–K | 0.91 | 28.5 | 10.29 | 1.87 | 1.08 | 0 | 10 | 176.03 | Moderate | Moderate | Moderate |

Menggugou | P_{t2} | 37.1 | 41.37 | 6.73 | 10.52 | 1.13 | 0 | 40 | 205.19 | High | High | High |

Aibagou | P_{t2} | 6.66 | 42.13 | 8.43 | 5.09 | 1.19 | 0 | 20 | 187.49 | High | High | High |

Nuozhacun | γ_{2} + Z_{2} | 32.61 | 40 | 4.96 | 10.5 | 1.17 | 0 | 10 | 194.78 | High | High | High |

Zhugongdi | T–K | 6.5 | 41.8 | 6.24 | 4.98 | 1.15 | 0 | 15 | 176.55 | Moderate | Moderate | Moderate |

Yindigou | T–K | 60.5 | 43.26 | 5.08 | 20.17 | 1.23 | 166 | 18 | 207.8 | High | High | Moderate |

Fujiahe | P_{t2} | 8.62 | 42.7 | 6.34 | 5.16 | 1.26 | 0 | 17 | 176.55 | Moderate | Moderate | Moderate |

Zhangmuhe | Pt_{2} | 4.62 | 29.1 | 9.7 | 5.39 | 1.42 | 0 | 10 | 199.99 | High | High | Moderate |

Hepiao | J + K | 9.1 | 29.6 | 9.9 | 6.83 | 1.32 | 0 | 30 | 175.51 | Moderate | Moderate | Moderate |

Hongmenchang | P_{t2} | 46.9 | 30 | 6.6 | 12.9 | 1.29 | 0 | 15 | 216.13 | High | High | High |

Tianfanghe | P_{t2} | 13.1 | 34 | 9.3 | 5.6 | 1.17 | 0 | 16 | 195.3 | High | High | High |

Zhiligou | T–K | 120.6 | 24 | 6.3 | 15.8 | 1.28 | 0 | 25 | 181.76 | Moderate | Moderate | Moderate |

Pingdicun | T–K | 24.2 | 17 | 5.9 | 9.9 | 1.14 | 3000 | 40 | 171.34 | Moderate | Moderate | Moderate |

Fangshanguo | T–K | 98 | 28 | 4.63 | 20.2 | 1.38 | 6662 | 10 | 193.22 | High | High | High |

Daqiangou | T–K | 18.9 | 29 | 10.95 | 5.1 | 1.11 | 18 | 17 | 174.46 | Moderate | Moderate | Moderate |

Shenyuhe | T–K | 256 | 21 | 2.26 | 29.63 | 1.47 | 0 | 50 | 169.26 | Low | Moderate | Moderate |

Zhuzhahe | T–K | 152.6 | 26.6 | 4.32 | 26.3 | 1.7 | 378 | 20 | 170.3 | Moderate | Moderate | Moderate |

Heizhe | T–K | 51.7 | 13.5 | 5.12 | 13.9 | 1.15 | 3485 | 20 | 167.18 | Low | Low | Low |

Yanshuijing | P_{t1} | 48.58 | 22.6 | 9.25 | 14.43 | 1.22 | 0 | 5 | 153.63 | Low | Low | Low |

Yajiede | T–K | 22.3 | 12 | 4.7 | 9.3 | 1.31 | 0 | 70 | 145.3 | Low | Low | Low |

Daqinggou | T–K | 31.8 | 32 | 6.02 | 7.32 | 1.1 | 378 | 15 | 147.38 | Low | Low | Low |

Level | Susceptibility Degree | Description |
---|---|---|

1 | High | Abundance of loose materials accumulated on slopes, steep channels, inventory of debris flows |

2 | Moderate | Between levels 1 and 3 |

3 | Low | Absence of loose materials, smooth terrains , no debris flow record |

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**MDPI and ACS Style**

Li, Y.; Wang, H.; Chen, J.; Shang, Y.
Debris Flow Susceptibility Assessment in the Wudongde Dam Area, China Based on Rock Engineering System and Fuzzy *C*-Means Algorithm. *Water* **2017**, *9*, 669.
https://doi.org/10.3390/w9090669

**AMA Style**

Li Y, Wang H, Chen J, Shang Y.
Debris Flow Susceptibility Assessment in the Wudongde Dam Area, China Based on Rock Engineering System and Fuzzy *C*-Means Algorithm. *Water*. 2017; 9(9):669.
https://doi.org/10.3390/w9090669

**Chicago/Turabian Style**

Li, Yanyan, Honggang Wang, Jianping Chen, and Yanjun Shang.
2017. "Debris Flow Susceptibility Assessment in the Wudongde Dam Area, China Based on Rock Engineering System and Fuzzy *C*-Means Algorithm" *Water* 9, no. 9: 669.
https://doi.org/10.3390/w9090669