# Comparison of Effects between Different Weight Calculation Methods for Improving Regional Landslide Susceptibility—A Case Study from Xingshan County of China

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## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

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^{2}, mostly belonging to densely populated areas. Therefore, infrastructure and human activities in the region are more frequent, and many natural slopes and landscapes have been affected.

#### 2.2. Influencing Factors

- (1)
- Elevation (Figure 3a): Using the open-source digital elevation model (DEM), the elevation distribution map of the study area is obtained based on ArcGIS. The elevation range of the study area (the following categories) was extracted as 127~2308 m. The study area was divided into five grades according to 127~500 m, 500~1000 m (including 1000 m, the following categories), 100~1500 m, 1500~2000 m and >2000 m, and the development of landslide disasters in each grade was counted. It can be seen from the figure that most landslides in the region are distributed in the elevation range of 500~1000 m, with the most development and the largest distribution density in the elevation range of 1000~1500 m.
- (2)
- Slope (Figure 3b) is also an important factor in landslide, which will affect surface water runoff and slope vegetation. The slope of the study area was extracted to obtain the range of 0~53°, which was divided into five grades of 0~10°, 10~20°, 20~30°, 30~40°, and >40°, and the development of landslide disasters in each grade was counted. It can be seen that the landslide disasters in the region basically occur on the slope below 30°, and the number and density of landslides are large in the range of 10~20°. The reason for this may be that the area with small slope is easily affected by human engineering activities and is not conducive to slope drainage under rainfall conditions. Rainwater aggravates the quality of rock and soil and has a softening effect on rock and soil, reduces its shear strength, and easily leads to landslide disasters. At the same time, this range of slope area accounted for a larger percentage.
- (3)
- Slope direction (Figure 3c): The slope direction is extracted by ArcGIS and its range is 0°~360°, which represents different slope directions. This will affect the specific sunlight and rainwater distribution, thereby affecting the occurrence of landslides. According to the specific meaning represented by each direction, the grading range of this factor is 0°, 0~45°, 45~90°, 90~135°, 135~180°, 180~225°, 225~270°, 270~315°, and 315~360°. It can be seen from Figure 3c that the landslide in the study area is mainly developed on the slope with the orientation of 315~360°. The landslide density is greater than 0.006 individual/km
^{2}, and the development density is relatively average in the orientation. - (4)
- Curvature (Figure 3d): The range of slope curvature in the study area is −1.8~1.9, so it is divided into several intervals of −2~−1, −1~0, 0~1, and 1~2. Statistics of different grades of landslide development are shown in Figure 2d. It can be seen that the landslide in the study area mainly occurs in the curvature of −1~1.
- (5)
- Distance to water (Figure 3e): Rivers and reservoirs in the study area will scour and erode the bank slope, and the immersion softening effect of water on rock and soil mass changes the physical and mechanical properties of rock and soil mass on the bank slope, which affects its stability. Here, the distance from the water system is taken as the classification index. The water system distances are divided into four grades, i.e., <100 m, 100~200 m, 200~300 m, >300 m [49]. It can be seen from the figure that the farther away from the water system in the region, the larger the landslide development density is. This is mainly because the scope of the largest area. However, although the area is small in the buffer distance of 300 m, there are still some landslides gathered here. In particular, in the range of 100~200 m away from the water system, the landslide has a high degree of development. Considering that this range is generally the location of human settlements, it is inevitably affected by human activities. Overall, the water system in the study area has a certain degree of control effect on landslide disasters.
- (6)
- Distance to road (Figure 3f): Based on the highway distribution map of Xingshan area, four grades with the distance of <100 m, 100~200 m, 200~300 m, >300 m are generated [50]. It can be seen from the figure that the analysis result of highway factor is similar to that of water system. Because areas outside the buffer zone occupy the largest area, landslides are mostly distributed in the region. However, in the buffer distance range, the smaller area is still distributed a certain number of landslides, indicating the construction of the highway landslide control.

## 3. Methodology

#### 3.1. Statistically Based Models

#### 3.1.1. Information Value (IV) Model

- (1)
- Calculation of information provided by a single factor on landslides

_{i}is the area of the study area containing the influence factor x

_{i}; N is the total number of landslides in the study area, and N

_{i}is the number of landslides distributed in the influence factor x

_{i}.

- (2)
- Usually, the information value of each evaluation unit is the result of the interaction of multiple influencing factors, and various factors exist in various different states. The following formula is used to calculate the total information I
_{i}under the condition of the combination of various influencing factors in the evaluation unit:

_{i}can be used as the vulnerability evaluation index of the study area. The probability of landslide in the evaluation unit increases with the increase of its value. By dividing the range of the obtained total information content, the vulnerability zoning evaluation of the study area can be carried out.

#### 3.1.2. Weighted Information Value Model

#### 3.2. Weight Calculation Method

#### 3.2.1. Fuzzy Analytical Hierarchy Process (FAHP)

- (1)
- According to the importance of each factor, the complementary fuzzy judgment matrix A = a
_{ij}(n × n) is established, where A is the judgment matrix, n is the number of evaluation indexes, a_{ij}is the relative membership value, which indicates the importance relationship between the first index and the j index. If i is more important than j, the value of a_{ij}is 1, otherwise 0, and if the two are equally important, then a_{ij}is 0.5. - (2)
- According to the following formula, the above matrix is transformed into fuzzy consistency judgment matrix E = e
_{ij}(n × n):

_{i}and r

_{j}represent the sum of relative membership values for line i and line j, respectively.

- (3)
- Based on the above matrix, the ranking vectors among the factors are iteratively calculated.
- (4)
- When the calculation error is less than the initial set value, the iterative calculation stops, and the final ranking vector can be used as the index weight of the factor.

#### 3.2.2. Principal Component Analysis (PCA)

_{nm}represents the value of a landslide factor, and then the average and variance of each factor can be calculated. For this matrix, its eigenvalues and eigenvectors can be calculated by:

_{i}and l

_{i}are eigenvalues and eigenvectors, respectively. The influence of each eigenvalue can be given by the contribution rate. The greater the eigenvalue is, the greater the contribution rate is. The maximum eigenvalue corresponds to the principal components related to most variability in observed data. For a specific feature vector, its cumulative contribution rate can be calculated by the following equation:

#### 3.3. Modeling

#### 3.3.1. Modeling of IV-Only

#### 3.3.2. Modeling of FAHP-IV Model

#### 3.3.3. Modeling of PCA-IV Model

#### 3.4. Model Performance Evaluation

_{i}is the number of landslides in a certain susceptibility grade, N is the total number of landslides in the whole area, S

_{i}is the area of this grade, and S is the total area of the whole region. The final calculated HAR index is a relative value. The larger the HAR value is, the greater the actual number of landslides is in the same range, and the greater the probability of landslides is. Therefore, the reliability of the susceptibility assessment results is determined.

## 4. Result

#### 4.1. Landslide Susceptibility Prediction

- (1)
- The very high susceptibility area is 310.18 km
^{2}, accounting for 13.33% of the total area of the study area, and 49 landslides are developed in the subregion. Most of these areas belong to structurally eroded hills and low mountainous areas, which provide favorable topographic conditions for the occurrence of landslides. At the same time, it is easy to cause landslides under the strong effects of water erosion, human construction and slope cutting, mining and other engineering activities. - (2)
- The high susceptibility area is 386.56 km
^{2}, accounting for 16.61% of the total area of the study area, and 10 landslides developed in the sub-region. - (3)
- The moderate susceptibility area is 581.78 km
^{2}, accounting for 25.0% of the total area of the study area. There are five landslides in the study area, the most widely distributed in the study area, mostly located in the structural denudation hilly area. Compared with the high-risk areas from the water system, highway and residential areas have a certain distance, but the impact is still strong, easy to cause landslides. - (4)
- The low susceptibility area is 400.84 km
^{2}, accounting for 17.23% of the total area of the study area. There are three landslides in the study area. The distribution in the study area is not continuous, most of which are scattered in the erosion area around the middle prone area. This is area is at low altitude. Although the topography is not conducive to the occurrence of landslides, with the existence of water systems and human engineering activities, there will be a small number of landslides. - (5)
- The very low susceptibility area is 647.64 km
^{2}, accounting for 27.83% of the total area of the study area, and there is one landslide point in the partition. Most of these areas are located in the low mountain areas of structural erosion far away from the water system, highways and residential areas. There is almost no human activity, the mountains are relatively intact, the vegetation coverage rate is high, and the probability of landslide disasters is low.

#### 4.2. Accuracy Analysis

## 5. Discussion

## 6. Conclusions

- (1)
- In this paper, the landslide disaster in Xingshan County of Hubei Province is taken as the research object. Based on the ArcGIS platform, the information model and two weighted information models are used to evaluate the regional landslide susceptibility. The final accuracy shows that the accuracy of the three models is between 0.7 and 0.8, indicating that the information method is an effective method to predict the spatial susceptibility of landslides.
- (2)
- Compared with the IV-only model, FAHP and PCA were used to calculate the weight of index factors, and it was found that water system, slope, and highway were the main factors affecting the occurrence of landslides in the region.
- (3)
- Compared with IV-only model, FAHP and PCA can effectively calculate the weight of index factors, and the accuracy of principal component analysis-information model is higher, which can provide certain scientific basis for future landslide susceptibility research.
- (4)
- The outcome results represent an important direction to improve the LSA model and provide a reference for subsequent researchers to improve the accuracy of LSA by increasing the indicator weights, thereby obtaining a high quality landslide susceptibility map.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The influencing factors used for landslide susceptibility assessment: (

**a**) elevation, (

**b**) slope, (

**c**) aspect, (

**d**) curvature, (

**e**) distance to river, (

**f**) distance to road.

**Figure 3.**The relationship between influencing factors and landslides in the study area: (

**a**) elevation, (

**b**) slope, (

**c**) aspect, (

**d**) curvature, (

**e**) distance to river, (

**f**) distance to road.

Factor | Category | IV | Rank | Factor | Category | IV | Rank |
---|---|---|---|---|---|---|---|

Elevation (m) | 0~500 | −0.4085 | 22 | Distance to river (m) | 200~300 | 0.593 | 4 |

500~1000 | 0.7572 | 2 | >300 | −0.2991 | 20 | ||

1000~1500 | 0.1774 | 8 | Aspect (°) | −1~0 | 0.2519 | 7 | |

1500~2000 | −0.4014 | 21 | 0~45 | −0.7586 | 26 | ||

>2000 | −0.286 | 18 | 45~90 | −0.4426 | 23 | ||

Slope (°) | 0~10 | −0.4869 | 24 | 90~135 | −0.7244 | 25 | |

10~20 | −0.0018 | 14 | 135~180 | −1.607 | 31 | ||

20~30 | 0.0537 | 12 | 180~225 | −0.9708 | 27 | ||

30~40 | 0.6404 | 3 | 225~270 | −0.2503 | 17 | ||

>40 | 0.0249 | 13 | 270~315 | −0.2085 | 16 | ||

Curvature | −2~−1 | −1.1587 | 28 | 315~360 | −0.1562 | 15 | |

−1~0 | −1.294 | 30 | Distance to road (m) | <100 | 1.0182 | 1 | |

0~1 | −1.2154 | 29 | 100~200 | 0.352 | 5 | ||

1~2 | 0.1601 | 9 | 200~300 | 0.0971 | 10 | ||

Distance to river(m) | <100 | 0.348 | 6 | >300 | −0.2871 | 19 | |

100~200 | 0.082 | 11 |

Weight of Factor | Elevation | Slope | Aspect | Distance to River | Curvature | Distance to Road |
---|---|---|---|---|---|---|

FAHP | 0.0443 | 0.3168 | 0.0288 | 0.1792 | 0.0833 | 0.2500 |

PCA | 0.0308 | 0.2987 | 0.0265 | 0.2563 | 0.0769 | 0.2010 |

Classification | IV-Only | FAHP-IV | PCA-IV |
---|---|---|---|

Very low | 0.003 | 0.003 | 0.007 |

Low | 0.280 | 0.177 | 0.256 |

Moderate | 0.855 | 0.806 | 0.813 |

High | 2.825 | 3.226 | 3.098 |

Very high | 3.146 | 3.537 | 3.292 |

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## Share and Cite

**MDPI and ACS Style**

Cao, B.; Li, Q.; Zhu, Y.
Comparison of Effects between Different Weight Calculation Methods for Improving Regional Landslide Susceptibility—A Case Study from Xingshan County of China. *Sustainability* **2022**, *14*, 11092.
https://doi.org/10.3390/su141711092

**AMA Style**

Cao B, Li Q, Zhu Y.
Comparison of Effects between Different Weight Calculation Methods for Improving Regional Landslide Susceptibility—A Case Study from Xingshan County of China. *Sustainability*. 2022; 14(17):11092.
https://doi.org/10.3390/su141711092

**Chicago/Turabian Style**

Cao, Bo, Qingyi Li, and Yuhang Zhu.
2022. "Comparison of Effects between Different Weight Calculation Methods for Improving Regional Landslide Susceptibility—A Case Study from Xingshan County of China" *Sustainability* 14, no. 17: 11092.
https://doi.org/10.3390/su141711092