## 3 Research Methods
### Hazard Index Method  
Geological hazard risk refers to the likelihood of a specific scale and type of geological hazard occurring in a particular area within a certain period under specific triggering factors [27]. The hazard assessment of geological disasters is conducted based on the disaster-susceptibility evaluation, considering three rainfall scenarios: 24-h rainfall of 100 mm, 24-h rainfall of 250 mm, and 72-h effective rainfall of 240 mm. Combined with the developmental characteristics of geological disasters, the hazard assessment classifies the geological disaster risk in Huangshi Town into four levels: extremely high-risk zones, high-risk zones, medium-risk zones, and low-risk zones [28].  
The risk evaluation of geological hazards is conducted using the risk index method, as expressed in Equation (7):  
\[H_{i}=\frac{Y_{i}}{Y_{max}P_{i}} \tag{7}\]  
where \(H_{i}\) represents the risk index (hazard probability) of the \(i\)-th evaluation unit under a specific scenario; \(Y_{i}\) is the susceptibility index of the \(i\)-th evaluation slope unit; \(max\) is the maximum susceptibility index, with \(Y_{max}=5\); and \(P_{i}\) is the instability probability of the \(i\)-th evaluation unit within a given time period under a specific scenario. From Equation (7), it can be seen that the hazard index of an evaluation unit is closely related to its susceptibility index and instability probability. The susceptibility index of each slope unit and the maximum susceptibility index are derived from the geological disaster-susceptibility evaluation indices of the previously surveyed key areas. The instability probability of slope units is typically calculated using two methods: one is based on the extreme rainfall hypothesis, and the other is based on slope stability analysis. In order to assess the regional geological disaster hazard, this investigation uses the calculation method based on the extreme rainfall hypothesis. The specific calculation process is shown in Equation (8):  
\[P_{i}=\frac{L}{L_{max}} \tag{8}\]  
In Equation (8): \(P_{i}\) represents the instability probability of the \(i\)-th evaluation unit under a specific scenario; \(L\) is the rainfall value under a specific scenario; and \(L_{\text{imax}}\) is the 24-h maximum rainfall value at the \(i\)-th evaluation unit.  
This principle is based on the historical occurrence of geological disasters in the evaluation area. It assumes that the maximum rainfall within 24 h, \(L_{\text{imax}}\), has been the main factor triggering disasters since the monitoring records began. Under different rainfall conditions, the probability of instability can be expressed as the ratio of the three rainfall conditions to the 24-h maximum rainfall. When the ratio of rainfall conditions to the 24-h maximum rainfall exceeds 1, the value of \(P_{i}\) is fixed at 1, indicating that as \(P_{i}\) increases from 0 to 1, the slope stability gradually decreases. When \(P_{i}=1\), the slope becomes unstable; thus, the maximum value of the instability probability \(P_{i}\) is 1. After calculating the hazard index \(H_{i}\) for each slope unit, the hazard level is classified into four categories according to the standard recommended geological disaster hazard classification table: extremely high-risk areas, high-risk areas, moderate-risk areas, and low-risk areas.