# Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China)

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Evaluation Model

#### 2.1. Evaluation Model under the Rainfall Condition

_{i}value of a landslide provided by a certain unit under the combination of P kinds of influencing factors. The specific calculation formula is as follows:

_{i}is the total information quantity of landslide occurrence that objectively reflects the possibility of landslide occurrence, N

_{i}is the number of landslide points or landslide area under the existing index, N is the total number of landslide points or the total landslide area in the study area, S

_{i}is the distribution area under the existing index and S is the total area of the research area.

_{i}, the corresponding grade is determined for the unit. I

_{i}< 0 means that the possibility of a landslide in this unit is less than the possibility of a landslide in the research area; I

_{i}= 0 means that the possibility of a landslide in this unit is equal to the possibility of a landslide in the research area; I

_{i}> 0 means that the possibility of a landslide in this unit is more than the possibility of a landslide in the research area. In short, the larger the unit information value is, the more likely a landslide is to occur [25,26].

_{1}, x

_{2}, …, x

_{n}is the independent variable, and the regression equation is established:

_{n}, b

_{0}, b

_{1}, b

_{2}, …, b

_{n}is the logistic regression coefficient and P represents the probability of landslide occurrence, which has a range of [0, 1].

_{n}is the landslide distribution density factor value after percentage conversion under the nth influence factor and a

_{n}is the component weight value corresponding to the nth impact factor after percentage conversion.

_{i}is the total information quantity of landslide occurrence and objectively reflects the possibility of landslide occurrence, N

_{i}is the number of landslide points or landslide areas under the existing index, N is the total number of landslide points or the total area of landslides in the study area, S

_{i}is the distribution area under the existing index, S is the total area of the research area, b

_{0}, b

_{1}, b

_{2}, …, b

_{n}is the logistic regression coefficient and P

_{LI}represents the probability of landslide occurrence, which has a range of [0,1].

_{i}is the total information quantity of landslide occurrence and it objectively reflects the possibility of landslide occurrence, N

_{i}is the number of landslide points or landslide area under the existing index, N is the total number of landslide points or the total area of landslide in the study area, S

_{i}is the distribution area under the existing index, S is the total area of the research area, I

_{ik}is the information value of the j factor under the ith influence factor and a

_{n}is the component weight value corresponding to the nth impact factor after percentage conversion.

#### 2.2. Evaluation Model under the Earthquake Condition

## 3. Findings

#### 3.1. Overview of the Research Area

#### 3.2. Hazard Assessment

#### 3.2.1. The Rain Condition

#### 3.2.2. The Earthquake Condition

_{s}of the regional slope body was calculated, and then, the corresponding regional critical acceleration distribution was obtained.

_{a}distribution is obtained. Then, Equation (9) is used to obtain the cumulative displacement value of Newmark under the condition of 10% probability of exceedance in 50 years in the research area

#### 3.3. Data Validation and Comparative Analysis

#### 3.3.1. The Rain Condition

#### 3.3.2. The Earthquake Condition

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lee, S.; Ryu, J.-H.; Kim, I.-S. Landslide susceptibility analysis and its verification using likelihood ratio, logistic regression, and artificial neural network models: Case study of Youngin, Korea. Landslides
**2007**, 4, 327–338. [Google Scholar] [CrossRef] - Nefeslioglu, H.A.; Gokceoglu, C.; Sonmez, H. An assessment on the use of logistic regression and artificial neural networks with different sampling strategies for the preparation of landslide susceptibility maps. Eng. Geol.
**2008**, 97, 171–191. [Google Scholar] [CrossRef] - Yin, K.L. Landslide Disaster Risk Analysis; Science Press: Beijing, China, 2010. [Google Scholar]
- Tang, Y.M.; Zhang, M.S.; Li, L.; Xue, Q. Discrimination to the landslide susceptibility, hazard and risk assessment. Hydrogeol. Eng. Geol.
**2011**, 38, 125–129. [Google Scholar] - Wu, S.R. Landslide Risk Assessment Theory and Technology; Science Press: Beijing, China, 2012. [Google Scholar]
- Tang, Y.M.; Zhang, M.S.; Li, Z.G.; Feng, W. Review and comparison oninland and overseas Geo-hazards risk management. Northwestern Geol.
**2015**, 48, 238–246. [Google Scholar] - Newmark, N.M. Effects of Earthquakes on Dams and Embankments. Geotechnique
**1965**, 15, 139–160. [Google Scholar] [CrossRef] [Green Version] - Wang, H.B.; Wu, S.R. Key theory and method of landslide hazard risk assessments. Geol. Bull. China
**2008**, 27, 1764–1770. [Google Scholar] - Jibson, R.W.; Harp, E.L.; Michael, J.A. A method for producing digital probabilistic seismic landslide hazard maps. Eng. Geol.
**2000**, 58, 271–289. [Google Scholar] [CrossRef] - Rathje, E.M.; Saygili, G. Probabilistic Seismic Hazard Analysis for the Sliding Displacement of Slopes: Scalar and Vector Approaches. J. Geotech. Geoenviron. Eng.
**2008**, 134, 804–814. [Google Scholar] [CrossRef] - Wang, T.; Wu, S.R.; Shi, J.S.; Xin, P. Case study on rapid assessment of regional seismic landslide hazard based on simplified Newmark displacement model: Wenchuan Ms 8.0 earthquake. J. Eng. Geol.
**2013**, 21, 16–24. [Google Scholar] [CrossRef] - Wang, T.; Wu, S.R.; Shi, J.S.; Xin, P. Concepts and mechanical assessment method for seismic landslide hazard: A review. J. Eng. Geol.
**2015**, 23, 93–104. [Google Scholar] - Chen, X.L.; Yuan, R.M.; Yu, L. Applying the Newmark’s model to the assessment of earthquake-triggered landslides during the Lushan earthquake. Seismol. Geol.
**2013**, 35, 661–670. [Google Scholar] - Chen, X.L.; Zhang, L.; Wang, M.M. Study on the distribution pattern of earthquake-triggered landslides based on seismic landslide susceptibility analysis: A case study of landslides triggered by the Ms6.5 Ludian earthquake in 2014. Seismol. Geol.
**2018**, 40, 1129–1139. [Google Scholar] - Chen, X.L.; Shan, X.J.; Zhang, L.; Liu, C.G.; Han, N.N.; Lan, J. Quick assessment of earthquake-triggered landslide hazards: A case study of the 2017 Ms 7.0 Jiuzhaigou earthquake. Earth Sci. Front.
**2018**, 25, 312. [Google Scholar] - Yang, Z.H.; Zhang, Y.S.; Guo, C.B.; Du, G.L. Landslide hazard rapid assessment in the Ms 8.1 nepal earthquake-impacted area, based on Newmark model. J. Geomech.
**2017**, 23, 115–124. [Google Scholar] - Ayalew, L.; Yamagishi, H. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan. Geomorphology
**2005**, 65, 15–31. [Google Scholar] [CrossRef] - Lee, S. Application of logistic regression model and its validation for landslide susceptibility mapping using GIS and remote sensing data. Int. J. Remote Sens.
**2005**, 26, 1477–1491. [Google Scholar] [CrossRef] - Gregory, C.; Ohlmacher; Davis, J.C. Using multiple logistic regression and GIS technology to predict landslide hazard in northeast Kansas, USA. Eng. Geol.
**2003**, 69, 331–343. [Google Scholar] - Akbar, T.; Ha, S. Landslide hazard zoning along Himalayan Kaghan Valley of Pakistan-by integration of GPS, GIS, and remote sensing technology. Landslides
**2011**, 8, 527–540. [Google Scholar] [CrossRef] - Pourghasemi, H.R.; Pradhan, B.; Gokceoglu, C. Application of fuzzy logic and analytical hierarchy process (AHP) to landslide susceptibility mapping at Haraz watershed, Iran. Nat. Hazards
**2012**, 63, 965–996. [Google Scholar] [CrossRef] - Gao, K.C.; Cui, P.; Zhao, C.Y.; Wei, F.Q. Landslide hazard evaluation of Wanzhou based on GIS information value method in the three gorges reservoir. Chin. J. Rock Mech. Eng.
**2006**, 25, 991–996. [Google Scholar] - Tang, Y.; Feng, F.; Guo, Z.; Feng, W.; Li, Z.; Wang, J.; Sun, Q.; Ma, H.; Li, Y. Integrating principal component analysis with statistically-based models for analysis of causal factors and landslide susceptibility mapping: A comparative study from the loess plateau area in Shanxi (China). J. Clean. Prod.
**2020**, 277, 124159. [Google Scholar] [CrossRef] - Zhao, P.D.; Hu, W.L.; Li, Z.J. Statistical Prediction of Mineral Deposits; Geological Press: Beijing, China, 1983. [Google Scholar]
- Falsaperla, S.; Graziani, S.; Nunnari, G.; Spampinato, S. Automatic classification of volcanic earthquakes by using Multi-Layered neural networks. Nat. Hazards
**1996**, 13, 205–228. [Google Scholar] [CrossRef] - Ruan, S.Y.; Huang, R.Q. Application of GIS-based information model on assessment of geological hazards risk. J. Chengdu Univ. Technol.
**2001**, 28, 89–92. [Google Scholar] - Peterson, H.B.; Kleinbaum, D.G. Interpreting the literature in obstetrics and gynecology: II. Logistic regression and related issues. Obstet. Gynecol.
**1991**, 78, 717–720. [Google Scholar] - Cong, W.Q.; Pan, M.; Li, T.F.; Wu, Z.X.; Lv, G.X. Key research on landslide and debris flow hazard zonation based on GIS. Earth Sci. Front.
**2006**, 13, 185–190. [Google Scholar] - Mandelbrot, B. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science
**1967**, 156, 636–638. [Google Scholar] [CrossRef] [Green Version] - Fu, Y.H. Fractal analyses for parameters of wind, wave and current. Port Eng. Technol.
**1996**, 3, 6–9. [Google Scholar] - Xue, T.F.; Yang, Q.; Luan, M.T. Research on fractal characters of spatial distribution of landslide based on GIS. Rock Soil Mech.
**2007**, 28, 347–350. [Google Scholar] - Wilson, R.C.; Keefer, D.K. Dynamic analysis of a slope failure from the 6 August 1979 Coyote Lake, California, earthquake. Bull. Seism. Soc. Am.
**1983**, 73, 863–877. [Google Scholar] [CrossRef] - Fredlund, D.G.; Rahardjo, H. Soil Mechanics for Unsaturated Soils; John Wiley & Sons: New York, NY, USA, 1993. [Google Scholar]
- Yang, X.P.; Feng, X.J.; Huang, X.N.; Song, F.M.; Li, G.Y.; Chen, X.C.; Zhang, L.; Huang, W.L. The late quaternary activity characteristics of the lixian-luojiabu fault: A discussion on the seismogenic mechanism of the lixian M8 earthquake in 1654. Chin. J. Geophys.
**2015**, 58, 504–519. [Google Scholar] - Roberto, R. Seismically induced landslide displacements: A predictive model. Eng. Geol.
**2000**, 58, 337–351. [Google Scholar] - Yang, Z.H.; Guo, C.B.; Wu, R.A.; Zhong, N.; Ren, S.S. Predicting seismic landslide hazard in the Batang fault zone of the Qinghai-Tibet Plateau. Hydrogeol. Eng. Geol.
**2021**, 48, 91–101. [Google Scholar] - Swets, J.A. Measuring the accuracy of diagnostic systems. Science
**1988**, 240, 1285–1293. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Tang, W.; Hu, J.; Zhang, H.; Wu, P.; He, H. Kappa coefficient: A popular measure of rater agreement. Shanghai Arch Psychiatry
**2015**, 27, 62–67. [Google Scholar]

**Figure 3.**Landslide hazard assessment map under the rainfall condition in the research area (information model).

**Figure 4.**Landslide hazard assessment map under the rainfall condition in the research area (logistic regression model).

**Figure 5.**The cumulative sum fractal sequence diagram of landslide distribution density and various evaluation factors. (

**a**) Slope; (

**b**) Slope height; (

**c**) Slope type; (

**d**) Aspect; (

**e**) Engineering geological rock group; (

**f**) Fracture distance; (

**g**) River distance; (

**h**) Precipitation.

**Figure 6.**Landslide hazard assessment map under the rainfall condition in the research area (fractal theory model).

**Figure 7.**Landslide hazard assessment map under the rainfall condition in the research area (logistic regression–information coupling model).

**Figure 8.**Landslide hazard assessment map under the rainfall condition in the research area (fractal theory–information coupling model).

**Figure 9.**Landslide hazard assessment map under the earthquake conditions in the research area (traditional Newmark model).

**Figure 10.**Soil–water characteristic curve of the research area. (

**a**) Loose rock group; (

**b**) Weak rock group.

**Figure 11.**Landslide hazard assessment map under the earthquake condition in the research area (improved Newmark model).

Evaluation Factor | Grading | This Kind of Area (km^{2}) | The Proportion of Such Area to the Total Area of the Research Area (%) | Number of Landslides in This Category (Point) | Proportion of the Number of Landslides in This Category to Total Number of Landslides (%) | Information Value |
---|---|---|---|---|---|---|

Slope (°) | 0–10 | 380.88 | 19.82 | 54 | 9.18 | −0.7691 |

10–20 | 846.04 | 44.02 | 128 | 21.77 | −0.7041 | |

20–30 | 431.24 | 22.44 | 346 | 58.84 | 0.9642 | |

30–40 | 213.35 | 11.10 | 46 | 7.82 | −0.3499 | |

40–50 | 45.48 | 2.37 | 13 | 2.21 | −0.0679 | |

>50 | 5.06 | 0.26 | 1 | 0.17 | −0.4369 | |

Slope height (m) | 0–20 | 247.74 | 12.87 | 18 | 3.06 | −1.4359 |

20–40 | 801.53 | 41.63 | 272 | 46.26 | 0.1054 | |

40–80 | 740.66 | 38.47 | 275 | 46.77 | 0.1954 | |

80–120 | 109.91 | 5.71 | 18 | 3.06 | −0.6231 | |

>120 | 25.52 | 1.33 | 5 | 0.85 | −0.4439 | |

Aspect (°) | North (337.5–22.5) | 199.39 | 10.40 | 66 | 11.22 | 0.0766 |

North east (22.5–67.5) | 240.93 | 12.56 | 88 | 14.97 | 0.1750 | |

East (67.5–112.5) | 274.67 | 14.32 | 71 | 12.07 | −0.1707 | |

South east (112.5–157.5) | 240.91 | 12.56 | 55 | 9.35 | −0.2949 | |

South (157.5–202.5) | 223.81 | 11.67 | 88 | 14.97 | 0.2487 | |

South west (202.5–247.5) | 250.98 | 13.09 | 83 | 14.12 | 0.0756 | |

West (247.5–292.5) | 264.79 | 13.81 | 92 | 15.65 | 0.1250 | |

North west (292.5–337.5) | 222.23 | 11.59 | 45 | 7.65 | −0.4149 | |

Slope type | Concave shape | 411.40 | 21.40 | 150 | 25.51 | 0.1755 |

Straight slopes and stepped slopes | 1074.03 | 55.88 | 365 | 62.07 | 0.1051 | |

Convex Slope | 436.62 | 22.72 | 73 | 12.41 | −0.6042 | |

Engineering geological rock group | Hardest rock group | 76.39 | 3.97 | 10 | 1.70 | −0.8483 |

Harder rock group | 113.78 | 5.92 | 21 | 3.57 | −0.5048 | |

Softer rock group | 126.14 | 6.56 | 45 | 7.65 | 0.1542 | |

Weak rock group | 504.95 | 26.26 | 221 | 37.59 | 0.3586 | |

Loose rock group | 1101.78 | 57.29 | 291 | 49.49 | −0.1464 | |

Fracture distance (km) | 0–2 | 252.43 | 13.12 | 207 | 35.20 | 0.9874 |

2–4 | 248.12 | 12.89 | 162 | 27.55 | 0.7595 | |

4–6 | 230.90 | 12.00 | 96 | 16.33 | 0.3081 | |

6–8 | 222.04 | 11.54 | 40 | 6.80 | −0.5282 | |

8–10 | 195.00 | 10.13 | 23 | 3.91 | −0.9517 | |

>10 | 776.15 | 40.33 | 60 | 10.20 | −1.3742 | |

River distance (km) | 0–0.5 | 304.48 | 15.83 | 129 | 21.94 | 0.3262 |

0.5–1 | 269.87 | 14.03 | 106 | 18.03 | 0.2505 | |

1–1.5 | 245.85 | 12.78 | 81 | 13.78 | 0.0747 | |

1.5–2 | 220.38 | 11.46 | 65 | 11.05 | −0.0360 | |

2–2.5 | 189.22 | 9.84 | 58 | 9.86 | 0.0025 | |

>2.5 | 693.39 | 36.05 | 149 | 25.34 | −0.3526 | |

Precipitation (mm) | 450–500 | 767.41 | 39.90 | 58 | 9.86 | −1.3976 |

500–550 | 1042.3 | 54.20 | 465 | 79.08 | 0.3779 | |

550–600 | 113.49 | 5.90 | 65 | 11.05 | 0.6277 |

Evaluation Factor | Grading | Normalized Value | B | S.E | Wals | Df | Sig | Exp(B) |
---|---|---|---|---|---|---|---|---|

Slope (°) | 0–10 | 0.0918 | 0.328 | 0.841 | 5.578 | 1 | 0.008 | 0.501 |

10–20 | 0.2177 | |||||||

20–30 | 0.5884 | |||||||

30–40 | 0.0782 | |||||||

40–50 | 0.0221 | |||||||

>50 | 0.0017 | |||||||

Slope height (m) | 0–20 | 0.0306 | 1.647 | 0.476 | 5.921 | 1 | 0.000 | 3.132 |

20–40 | 0.4626 | |||||||

40–80 | 0.4677 | |||||||

80–120 | 0.0306 | |||||||

>120 | 0.0085 | |||||||

Aspect (°) | Flat(−1) | 0.0000 | 1.442 | 0.383 | 3.875 | 1 | 0.000 | 2.206 |

North (337.5–22.5) | 0.1122 | |||||||

North east (22.5–67.5) | 0.1497 | |||||||

East (67.5–112.5) | 0.1207 | |||||||

South east (112.5–157.5) | 0.0935 | |||||||

South (157.5–202.5) | 0.1497 | |||||||

South west (202.5–247.5) | 0.1412 | |||||||

West (247.5–292.5) | 0.1565 | |||||||

North west (292.5–337.5) | 0.0765 | |||||||

Slope type | Concave shape | 0.2551 | 0.358 | 0.325 | 2.961 | 1 | 0.035 | 0.448 |

Straight slopes and stepped slopes | 0.6207 | |||||||

Convex Slope | 0.1241 | |||||||

engineering geological rock group | Hardest rock group | 0.0170 | 0.122 | 0.461 | 5.110 | 1 | 0.024 | 0.353 |

Harder rock group | 0.0357 | |||||||

Softer rock group | 0.0765 | |||||||

Weak rock group | 0.3759 | |||||||

Loose rock group | 0.4949 | |||||||

Fracture distance (km) | 0–2 | 0.3520 | 2.072 | 0.279 | 15.346 | 1 | 0.000 | 7.941 |

2–4 | 0.2755 | |||||||

4–6 | 0.1633 | |||||||

6–8 | 0.0680 | |||||||

8–10 | 0.0391 | |||||||

>10 | 0.1020 | |||||||

River distance (km) | 0–0.5 | 0.2194 | 0.876 | 0.504 | 1.753 | 1 | 0.000 | 1.014 |

0.5–1 | 0.1803 | |||||||

1–1.5 | 0.1378 | |||||||

1.5–2 | 0.1105 | |||||||

2–2.5 | 0.0986 | |||||||

>2.5 | 0.2534 | |||||||

Precipitation (mm) | 450–500 | 0.0986 | 0.546 | 0.302 | 0.890 | 1 | 0.006 | 0.846 |

500–550 | 0.7908 | |||||||

550–600 | 0.1105 | |||||||

Constant | — | — | −4.611 | 0.553 | 1.286 | 1 | 0.005 | 0.012 |

Evaluation Factor | Grading | Number of Landslides (Point) | Partition Area (km^{2}) | Landslide Distribution Density (Point/km^{2}) | Converted Landslide Distribution Density Factor Value | Fractal Value | Converted Fractal Weight Value |
---|---|---|---|---|---|---|---|

Slope (°) | 0–10 | 54 | 380.88 | 0.1418 | 0.0790 | 1.3894 | 0.119 |

10–20 | 128 | 846.04 | 0.1513 | 0.0843 | |||

20–30 | 346 | 431.24 | 0.8023 | 0.4471 | |||

30–40 | 46 | 213.35 | 0.2156 | 0.1202 | |||

40–50 | 13 | 45.48 | 0.2858 | 0.1593 | |||

>50 | 1 | 5.06 | 0.1976 | 0.1101 | |||

Slope height (m) | 0–20 | 18 | 247.74 | 0.0727 | 0.0636 | 1.5105 | 0.129 |

20–40 | 272 | 801.53 | 0.3394 | 0.2969 | |||

40–80 | 275 | 740.66 | 0.3713 | 0.3248 | |||

80–120 | 18 | 109.91 | 0.1638 | 0.1433 | |||

>120 | 5 | 25.52 | 0.1959 | 0.1714 | |||

Aspect (°) | Flat (−1) | 0 | 4.35 | 0 | 0.0000 | 0.8440 | 0.072 |

North (337.5–22.5) | 66 | 199.39 | 0.3310 | 0.1347 | |||

North east (22.5–67.5) | 88 | 240.93 | 0.3653 | 0.1487 | |||

East (67.5–112.5) | 71 | 274.67 | 0.2585 | 0.1052 | |||

South east (112.5–157.5) | 55 | 240.91 | 0.2283 | 0.0929 | |||

South (157.5–202.5) | 88 | 223.81 | 0.3932 | 0.1600 | |||

South west (202.5–247.5) | 83 | 250.98 | 0.3307 | 0.1346 | |||

West (247.5–292.5) | 92 | 264.79 | 0.3474 | 0.1414 | |||

North west (292.5–337.5) | 45 | 222.23 | 0.2025 | 0.0824 | |||

Slope type | Concave shape | 150 | 411.40 | 0.3646 | 0.4183 | 1.5251 | 0.131 |

Straight slopes and stepped slopes | 365 | 1074.03 | 0.3398 | 0.3899 | |||

Convex Slope | 73 | 436.62 | 0.1672 | 0.1918 | |||

engineering geological rock group | Hardest rock group | 10 | 76.39 | 0.1309 | 0.0953 | 1.5050 | 0.129 |

Harder rock group | 21 | 113.78 | 0.1846 | 0.1344 | |||

Softer rock group | 45 | 126.14 | 0.3567 | 0.2596 | |||

Weak rock group | 221 | 504.95 | 0.4377 | 0.3186 | |||

Loose rock group | 291 | 1101.78 | 0.2641 | 0.1922 | |||

Fracture distance (km) | 0–2 | 207 | 252.43 | 0.8200 | 0.3622 | 1.9782 | 0.169 |

2–4 | 162 | 248.12 | 0.6529 | 0.2884 | |||

4–6 | 96 | 230.90 | 0.4158 | 0.1837 | |||

6–8 | 40 | 222.04 | 0.1801 | 0.0795 | |||

8–10 | 23 | 195.00 | 0.1179 | 0.0521 | |||

>10 | 60 | 776.15 | 0.0773 | 0.0341 | |||

River distance (km) | 0–0.5 | 129 | 304.48 | 0.4237 | 0.2159 | 1.6097 | 0.138 |

0.5–1 | 106 | 269.87 | 0.3928 | 0.2002 | |||

1–1.5 | 81 | 245.85 | 0.3295 | 0.1679 | |||

1.5–2 | 65 | 220.38 | 0.2949 | 0.1503 | |||

2–2.5 | 58 | 189.22 | 0.3065 | 0.1562 | |||

>2.5 | 149 | 693.39 | 0.2149 | 0.1095 | |||

Precipitation (mm) | 450–500 | 58 | 767.41 | 0.0756 | 0.0691 | 1.3172 | 0.113 |

500–550 | 465 | 1042.3 | 0.4461 | 0.4076 | |||

550–600 | 65 | 113.49 | 0.5727 | 0.5233 |

Evaluation Factor | Grading | Information Value | B | S.E | Wals | Df | Sig | Exp(B) |
---|---|---|---|---|---|---|---|---|

Slope (°) | 0–10 | −0.7691 | 0.805 | 0.516 | 6.457 | 1 | 0.005 | 0.667 |

10–20 | −0.7041 | |||||||

20–30 | 0.9642 | |||||||

30–40 | −0.3499 | |||||||

40–50 | −0.0679 | |||||||

>50 | −0.4369 | |||||||

Slope height (m) | 0–20 | −1.4359 | 1.539 | 0.249 | 6.048 | 1 | 0.000 | 3.885 |

20–40 | 0.1054 | |||||||

40–80 | 0.1954 | |||||||

80–120 | −0.6231 | |||||||

>120 | −0.4439 | |||||||

Aspect (°) | Flat(−1) | 0.0000 | 1.307 | 0.546 | 3.045 | 1 | 0.000 | 1.897 |

North (337.5–22.5) | 0.0766 | |||||||

North east (22.5–67.5) | 0.1750 | |||||||

East (67.5–112.5) | −0.1707 | |||||||

South east (112.5–157.5) | −0.2949 | |||||||

South (157.5–202.5) | 0.2487 | |||||||

South west (202.5–247.5) | 0.0756 | |||||||

West (247.5–292.5) | 0.1250 | |||||||

North west (292.5–337.5) | −0.4149 | |||||||

Slope type | Concave shape | 0.1755 | 0.441 | 0.509 | 3.594 | 1 | 0.045 | 0.554 |

Straight slopes and stepped slopes | 0.1051 | |||||||

Convex Slope | −0.6042 | |||||||

engineering geological rock group | Hardest rock group | −0.8483 | 0.189 | 0.587 | 6.208 | 1 | 0.035 | 0.407 |

Harder rock group | −0.5048 | |||||||

Softer rock group | 0.1542 | |||||||

Weak rock group | 0.3586 | |||||||

Loose rock group | −0.1464 | |||||||

Fracture distance (km) | 0–2 | 0.9874 | 1.905 | 0.322 | 10.346 | 1 | 0.000 | 6.127 |

2–4 | 0.7595 | |||||||

4–6 | 0.3081 | |||||||

6–8 | −0.5282 | |||||||

8–10 | −0.9517 | |||||||

>10 | −1.3742 | |||||||

River distance (km) | 0–0.5 | 0.3262 | 1.116 | 0.408 | 2.458 | 1 | 0.000 | 1.129 |

0.5–1 | 0.2505 | |||||||

1–1.5 | 0.0747 | |||||||

1.5–2 | −0.0360 | |||||||

2–2.5 | 0.0025 | |||||||

>2.5 | −0.3526 | |||||||

Precipitation (mm) | 450–500 | −1.3976 | 0.598 | 0.552 | 0.985 | 1 | 0.008 | 0.741 |

500–550 | 0.3779 | |||||||

550–600 | 0.6277 | |||||||

Constant | — | — | −3.947 | 0.435 | 2.845 | 1 | 0.003 | 0.027 |

**Table 5.**Statistical table of landslide risk calculation based on the fractal theory–information coupling model.

Evaluation Factor | Grading | This Kind of Area (km^{2}) | The Proportion of Such Area to the Total Area of the Research Area (%) | Number of Landslides in This Category (Point) | Proportion of the Number of Landslides in This Category to Total Number of Landslides (%) | Information Value | Converted Fractal Weight Value |
---|---|---|---|---|---|---|---|

Slope (°) | 0–10 | 380.88 | 19.82 | 54 | 9.18 | −0.7691 | 0.119 |

10–20 | 846.04 | 44.02 | 128 | 21.77 | −0.7041 | ||

20–30 | 431.24 | 22.44 | 346 | 58.84 | 0.9642 | ||

30–40 | 213.35 | 11.10 | 46 | 7.82 | −0.3499 | ||

40–50 | 45.48 | 2.37 | 13 | 2.21 | −0.0679 | ||

>50 | 5.06 | 0.26 | 1 | 0.17 | −0.4369 | ||

Slope height (m) | 0–20 | 247.74 | 12.87 | 18 | 3.06 | −1.4359 | 0.129 |

20–40 | 801.53 | 41.63 | 272 | 46.26 | 0.1054 | ||

40–80 | 740.66 | 38.47 | 275 | 46.77 | 0.1954 | ||

80–120 | 109.91 | 5.71 | 18 | 3.06 | −0.6231 | ||

>120 | 25.52 | 1.33 | 5 | 0.85 | −0.4439 | ||

Aspect (°) | Flat (−1) | 4.35 | 0.00 | 0 | 0.00 | 0.0000 | 0.072 |

North (337.5–22.5) | 199.39 | 10.40 | 66 | 11.22 | 0.0766 | ||

North east (22.5–67.5) | 240.93 | 12.56 | 88 | 14.97 | 0.1750 | ||

East (67.5–112.5) | 274.67 | 14.32 | 71 | 12.07 | −0.1707 | ||

South east (112.5–157.5) | 240.91 | 12.56 | 55 | 9.35 | −0.2949 | ||

South (157.5–202.5) | 223.81 | 11.67 | 88 | 14.97 | 0.2487 | ||

South west (202.5–247.5) | 250.98 | 13.09 | 83 | 14.12 | 0.0756 | ||

West (247.5–292.5) | 264.79 | 13.81 | 92 | 15.65 | 0.1250 | ||

North west (292.5–337.5) | 222.23 | 11.59 | 45 | 7.65 | −0.4149 | ||

Slope type | Concave shape | 411.40 | 21.40 | 150 | 25.51 | 0.1755 | 0.131 |

Straight slopes and stepped slopes | 1074.03 | 55.88 | 365 | 62.07 | 0.1051 | ||

Convex Slope | 436.62 | 22.72 | 73 | 12.41 | −0.6042 | ||

Engineering geological rock group | Hardest rock group | 76.39 | 3.97 | 10 | 1.70 | −0.8483 | 0.129 |

Harder rock group | 113.78 | 5.92 | 21 | 3.57 | −0.5048 | ||

Softer rock group | 126.14 | 6.56 | 45 | 7.65 | 0.1542 | ||

Weak rock group | 504.95 | 26.26 | 221 | 37.59 | 0.3586 | ||

Loose rock group | 1101.78 | 57.29 | 291 | 49.49 | −0.1464 | ||

Fracture distance (km) | 0–2 | 252.43 | 13.12 | 207 | 35.20 | 0.9874 | 0.169 |

2–4 | 248.12 | 12.89 | 162 | 27.55 | 0.7595 | ||

4–6 | 230.90 | 12.00 | 96 | 16.33 | 0.3081 | ||

6–8 | 222.04 | 11.54 | 40 | 6.80 | −0.5282 | ||

8–10 | 195.00 | 10.13 | 23 | 3.91 | −0.9517 | ||

>10 | 776.15 | 40.33 | 60 | 10.20 | −1.3742 | ||

River distance (km) | 0–0.5 | 304.48 | 15.83 | 129 | 21.94 | 0.3262 | 0.138 |

0.5–1 | 269.87 | 14.03 | 106 | 18.03 | 0.2505 | ||

1–1.5 | 245.85 | 12.78 | 81 | 13.78 | 0.0747 | ||

1.5–2 | 220.38 | 11.46 | 65 | 11.05 | −0.0360 | ||

2–2.5 | 189.22 | 9.84 | 58 | 9.86 | 0.0025 | ||

>2.5 | 693.39 | 36.05 | 149 | 25.34 | −0.3526 | ||

Precipitation (mm) | 450–500 | 767.41 | 39.90 | 58 | 9.86 | −1.3976 | 0.113 |

500–550 | 1042.3 | 54.20 | 465 | 79.08 | 0.3779 | ||

550–600 | 113.49 | 5.90 | 65 | 11.05 | 0.6277 |

Serial Number | Rock Group Type | $\mathbf{c}\u2019/\mathbf{Pa}$ | ${\mathit{\phi}}^{\prime}/(\xb0)$ | $\mathit{\gamma}/(\mathbf{N}\xb7{\mathbf{m}}^{3})$ |
---|---|---|---|---|

I | Hardest rock group | 130,000 | 38 | 26,000 |

II | Harder rock group | 70,000 | 32 | 23,000 |

III | Softer rock group | 50,000 | 28 | 22,000 |

IV | Weak rock group | 20,000 | 19 | 19,000 |

V | Loose rock group | 16,000 | 15 | 17,000 |

**Table 7.**Value table of mechanical parameters of engineering geology rock group (improved Newmark model).

Serial Number | Rock Group Type | $\mathbf{c}\u2019/\mathbf{Pa}$ | ${\mathit{\phi}}^{\prime}/\left(\text{\xb0}\right)$ | $\mathit{\gamma}/(\mathbf{N}\xb7{\mathbf{m}}^{3})$ | ${\mathit{\phi}}^{\mathit{b}}/\left(\text{\xb0}\right)$ |
---|---|---|---|---|---|

I | Hardest rock group | 130,000 | 38 | 26,000 | - |

II | Harder rock group | 70,000 | 32 | 23,000 | - |

III | Softer rock group | 50,000 | 28 | 22,000 | - |

IV | Weak rock group | 20,000 | 19 | 19,000 | 11 |

V | Loose rock group | 16,000 | 15 | 17,000 | 10 |

**Table 8.**Summary table of accuracy of test results of different model evaluation methods under the rainfall condition.

Testing Method | Information Model | Logistic Regression Model | Fractal Theory Model | Logistic Regression–Information Coupling Model | Fractal Theory–Information Coupling Model |
---|---|---|---|---|---|

ROC curve method | 0.788 | 0.754 | 0.793 | 0.845 | 0.856 |

Kappa coefficient method | 0.764 | 0.737 | 0.755 | 0.801 | 0.807 |

**Table 9.**Summary table of accuracy test results of different model evaluation methods under the earthquake condition.

Testing Method | Traditional Newmark Model | Improved Newmark Model |
---|---|---|

ROC curve method | 0.748 | 0.805 |

Kappa coefficient method | 0.722 | 0.794 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Feng, W.; Tang, Y.; Hong, B.
Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China). *Sustainability* **2022**, *14*, 8098.
https://doi.org/10.3390/su14138098

**AMA Style**

Feng W, Tang Y, Hong B.
Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China). *Sustainability*. 2022; 14(13):8098.
https://doi.org/10.3390/su14138098

**Chicago/Turabian Style**

Feng, Wei, Yaming Tang, and Bo Hong.
2022. "Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China)" *Sustainability* 14, no. 13: 8098.
https://doi.org/10.3390/su14138098