## 3 Methodology
### Highway Rockfall Vulnerability  
Vulnerability, a common concept in natural hazard risk assessment, refers to differences in social, cultural, economic, and other factors in response to natural hazards [59]. Highway rockfall vulnerability is the main consideration of the affected body at the time of the rockfall. It usually refers to the magnitude of damage caused to various social elements when rockfall occurs. Once rockfall occurs, it can cause varying degrees of damage to transportation, the economy, and populations. In this study area, vulnerability research is critical for disaster risk management and serves as a fundamental basis for natural disaster prevention and mitigation and sustainable development. This research not only identifies and assesses potential risks but also provides theoretical support for developing effective response strategies, thereby enhancing study area's sustainability [60]. In this research, GDP, population, and land use type were chosen for the highway rockfall vulnerability index, and all data were from the Guizhou Bureau of Statistics. The highway rockfall vulnerability index is shown in Figure 7.  
1. Population. Population is an important social indicator that reflects the size of a city's development. The greater the population, the greater the likelihood of injury or death from rockfall accidents and the greater the susceptibility of the highway rockfall. The population of the entire Guizhou Province is mainly concentrated in the northwestern part of the province, while the eastern and southern parts of the province have a smaller population distribution since they are areas where ethnic minorities gather. The population distribution of the entire Guizhou Province is shown in Figure 7a. In this study, the population distribution of the whole Guizhou Province was mapped by the GIS and extracted through the previously established buffer zone of 500 m \begin{table}
\begin{tabular}{c c} \hline
**Value** & **Description** \\ \hline
0.5 & Two factors are of equal importance \\
0.6 & One factor is slightly more important than the other \\
0.7 & One factor is significantly more important than the other \\
0.8 & One factor is much more important than the other \\
0.9 & One factor is extremely more important than the other \\
0.1–0.4 & In contrast to comparisons with a value of 0.6–0.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Description of matrix data parameter values. range as the number of people that might be affected by the rockfall hazard along the study area. (2) GDP. GDP is an important indicator that reflects the social economy and can well reflect the level of urban development. The higher the city's GDP, the higher the damage caused by rockfall. In this study, the GDP was obtained from the data released by the Guizhou Provincial Government. Population increases will also promote economic growth, so the economic situation and population distribution of Guizhou Province are similar. Both are high in the northwest and low in the east, as well as in the south. The GDP distribution of the entire Guizhou Province is shown in Figure 7b. (3) Land use type. The land use type is also a reflection of how well a city has been developed and constructed. In this research, land use types in Guizhou Province were categorized into trees, flooded vegetation, crops, built-up areas, and clearings. The impact of highway rockfall vulnerability varies by land use type. Once rockfall accidents occur, the built-up area will be more affected, but the vegetation cover area will be less affected. The land use type distribution of the entire Guizhou Province is shown in Figure 7c. The land use types in this study have an accuracy of 10 m, which can accurately reflect the land use types along the study area, and different land types are affected differently by rockfall hazards; for example, they will have a large impact on built-up areas and a small impact on land types such as clearings.