An Integrated Risk Assessment of Rockfalls Along Highway Networks in Mountainous Regions: The Case of Guizhou, China

Abstract

Rockfalls, among the most common natural disasters, pose risks such as traffic congestion, casualties, and substantial property damage. Guizhou Province, with China’s fourth-longest highway network, features mountainous terrain prone to frequent rockfall incidents annually. Consequently, assessing highway rockfall risks in Guizhou Province is crucial for safeguarding the lives and travel of residents. This study evaluates highway rockfall risk through three key components: susceptibility, hazard, and vulnerability. Susceptibility was assessed using information content and logistic regression methods, considering factors such as elevation, slope, normalized difference vegetation index (NDVI), aspect, distance from fault, relief amplitude, lithology, and rock weathering index (RWI). Hazard assessment utilized a fuzzy analytic hierarchy process (AHP), focusing on average annual rainfall and daily maximum rainfall. Socioeconomic factors, including GDP, population density, and land use type, were incorporated to gauge vulnerability. Integration of these assessments via a risk matrix yielded comprehensive highway rockfall risk profiles. Results indicate a predominantly high risk across Guizhou Province, with high-risk zones covering 41.19% of the area. Spatially, the western regions exhibit higher risk levels compared to eastern areas. Notably, the Bijie region features over 70% of its highway mileage categorized as high risk or above. Logistic regression identified distance from fault lines as the most negatively correlated factor affecting highway rockfall susceptibility, whereas elevation gradient demonstrated a minimal influence. This research provides valuable insights for decision-makers in formulating highway rockfall prevention and control strategies.

1. Introduction

Rockfall refers to the collapse of rocks on steep cliffs and slopes due to gravity [1,2,3]. Human activities have expanded, leading to increased environmental damage and extreme weather events like heavy rainfall. This has caused a rise in the occurrence of natural disasters such as rockfalls [4,5,6,7] Rockfalls, the most common type of disaster affected by climate, will have a great impact on roads and other infrastructure and result in significant human and economic losses annually [8,9]. In 2015, a passenger train derailed in Northfield, Vermont, after colliding with rockfall debris, resulting in extensive injuries to passengers [10]. On 5 April 2021, a Hongya rockfall avalanche resulted in the deaths of three individuals [11]. The formation of rockfalls is influenced by regional topography, geomorphology, lithology, vegetation, and geological and meteorological conditions [12,13,14]. Predicting and mitigating rockfall risks and conducting risk assessments have become key research areas as rockfall incidents increase [15,16]. Guizhou Province, located in the mountainous region of southwestern China, is characterized by a delicate geological environment that renders it particularly vulnerable to rockfall disasters [17]. As of the end of 2022, the province is projected to encompass approximately 8472 km of highways, positioning it fourth nationally in terms of highway infrastructure. The occurrence of rockfall events on these vital transportation routes can lead to severe traffic congestion, compromise the structural integrity of roadways, and pose significant threats to public safety and property. In light of the escalating frequency of rockfall incidents and their potentially catastrophic consequences, it is imperative to undertake an urgent and comprehensive assessment of rockfall risks along Guizhou’s highways. Immediate action is warranted to devise and implement robust risk mitigation and management strategies, thereby ensuring the safety of travelers and the sustained integrity of the transportation infrastructure. This proactive approach is essential to avert future disasters and safeguard both human lives and economic assets.

Rockfall risk assessment can be categorized into two types: regional-scale assessment through rockfall risk maps and small-scale assessment through rockfall disaster simulations to analyze rockfall movement characteristics and assess risks. Both methods utilize modern computer technology and Geographic Information System (GIS) technology [10,18]. Highway rockfall risk assessment in Guizhou Province is primarily conducted on a large regional scale using a risk mapping approach. The risk mapping methodology includes qualitative and quantitative assessments, with quantitative methods gradually becoming more prevalent as research and technology advance [19,20]. The most common quantitative methods include the analytic hierarchy process (AHP) assessment system [21], expert experience scoring [22], the comprehensive fuzzy evaluation model [23], the information content method [24], logistic regression [25], the frequency ratio method [26], and machine learning models [27,28,29,30,31]. The AHP assessment system, expert experience scoring, and comprehensive fuzzy evaluation model are known for their simplicity and ease of implementation. However, the risk evaluation model constructed using these methods may be heavily influenced by human subjectivity [32]. Machine learning models offer high prediction accuracy but require a large amount of data for learning and training, making the modeling process complex and difficult to understand [33] The information content method involves analyzing the interval area of each rockfall hazard impact indicator and the number of rockfall hazards to determine the probability of a rockfall accident occurrence due to each impact indicator [34]. Logistic regression can analyze the relative importance of each indicator in predicting the probability of rockfall occurrence, allowing for an objective, accurate, and effective rockfall risk assessment [35]. This study introduces the application of the information quantity method, logistic regression, and fuzzy hierarchical analysis for the first time to evaluate rockfall risk. This approach effectively elucidates the impact of specific factors and their corresponding ranges on rockfall incidents, minimizes the influence of human factors, and enables precise and rapid risk assessment over large areas of complex terrain.

Numerous research studies have utilized rockfall susceptibility to evaluate the risk associated with it [36,37]. The assessment of highway rockfall risk typically involves three main components: highway rockfall susceptibility, highway rainfall hazard, and highway rockfall vulnerability. Rockfall susceptibility pertains to the probability of rockfall events occurring and is influenced by intrinsic factors such as slope. Consequently, evaluating these elements is crucial for assessing rockfall susceptibility. This study proposes a new method, which adopts logistic regression and a fuzzy analytic hierarchy process to evaluate susceptibility, rainfall hazard, and vulnerability, respectively, and uses the risk matrix to assess the risk of rockfall. This method can assess the risk of rockfalls quickly and accurately, and effectively reduce the risk of rockfall disasters. The normalized difference vegetation index (NDVI), aspect, distance from fault, relief amplitude, lithology, and rock weathering index (RWI) were selected as the evaluation indexes of rockfall susceptibility. Methods like the information content method and logistic regression are commonly used to determine highway rockfall susceptibility. While existing research has explored various individual methods for evaluating rockfall susceptibility, there has been no attempt to combine these methods. Integrating these approaches could enhance the analysis of each factor’s impact and its variability on rockfall occurrences, thereby reducing the reliance on extensive datasets and mitigating potential biases introduced by human subjectivity. The highway rainfall hazard is determined by factors like average annual rainfall and daily maximum rainfall. On the other hand, highway rockfall vulnerability is influenced by variables such as GDP, population, and land use type. By combining highway rockfall vulnerability, highway rainfall hazard, and highway rockfall susceptibility, a risk matrix can be generated to determine the overall highway rockfall risk. The research focused on assessing the highway rockfall risk in Guizhou Province. The accuracy of the risk assessment was verified using the receiver operating characteristic (ROC) curve. This study aims to provide recommendations for the prevention and management of rockfall disasters on highways in Guizhou Province.

The main structure of this article is as follows: Section 2 illustrates the basic situation of Guizhou Province. Section 3 illustrates the risk assessment methods and indicators. Section 4 illustrates the rockfall risk assessment results in Guizhou Province. In Section 5, the accuracy of the model and the key indicators affecting rockfalls are discussed. Conclusions are drawn in Section 6.

2. Study Area

Guizhou Province is located on the Yunnan–Guizhou Plateau in southwestern China and covers an area of 176,000 square km. The study area encompasses nine districts of Guizhou: Guiyang (GY), Zunyi (ZY), Liupanshui (LPS), Anshun (AS), Bijie (BJ), Tongren (TR), Qiandongnan Miao and Dong (QDN), Qiannan Buyei and Miao (QN), and Qianxinan Buyei and Miao (QXN). The average elevation of Guizhou is about 1000 m above sea level, and the terrain is undulating, with the height difference between the highest and the lowest point reaching 2763 m. Guizhou is characterized by mountainous areas, with the mountainous areas accounting for 90% of the province’s area. Guizhou is widely distributed with karst landscapes [38]. Guizhou Province has a plateau-type subtropical climate with abundant rainfall, and the average annual rainfall is mostly between 1100 and 1400 millimeters [39]. The unique topography and climatic conditions of Guizhou Province provide excellent preconditions for the occurrence of natural disasters such as rockfalls and collapses. The study area for the entire Guizhou Province is shown in Figure 1.

The stratigraphy of Guizhou is well developed, and is primarily associated with the Yangtze stratum. This region is predominantly characterized by extensive sedimentary rock formations, with limestone and shale being the most prevalent, along with various clastic rocks [17]. A series of tectonic movements since the Late Triassic has given rise to folded mountain formations, thereby establishing conditions that are highly conducive to rockfall development. Furthermore, coal seams in Guizhou Province are predominantly found within the strata of the Permian Liangshan and Longtan Formations. The rock types in these formations mainly include limestone, mudstone, and sandstone, interspersed with four to six layers of thin mud shale and other soft rocks. Prolonged underground mining activities have created mined-out areas beneath the mountains, which in turn lead to the formation of surface fissures, exacerbating the destruction of the rock mass and causing significant gradient deformation. Figure 2 shows the geological map of the study area. As a result, large-scale rockfalls frequently occur. This geological context highlights the urgent need for comprehensive studies on slope stability and risk management in the region.

Various geological disasters occur in Guizhou every year. According to the Natural Resources Bureau of Guizhou Province statistics, by the end of 2021, there were 28,221 potential geological disasters, including 4812 landslides, 3091 rockfalls, 114 mudslides, and 1377 unstable slopes. According to the statistics of the Guizhou Ministry of Transportation and Communications, by the end of 2021, the length of the roads in Guizhou Province was 188,797.1 km, of which the length of highways was 8368 km. Figure 3 shows some of the rockfall accidents along roads in Guizhou Province. Once a rockfall accident occurs, it will cause traffic congestion in the study area and will even cause many personnel and property losses. Therefore, it is of great significance to evaluate the risk of road networks in the study area and to provide guidance to local governments for their management.

3. Methodology

Rockfall risk can be defined as the harm caused by the occurrence of rockfall. It is usually composed of three parts: rockfall susceptibility, rainfall hazard, and vulnerability. Rockfall susceptibility can be defined as the probability of rockfall occurring; rainfall hazard is defined as rainfall causing rockfall; vulnerability is defined as the impact of rockfall on public safety. The methodology for formulating the risk map associated with highway rockfall was structured in four major phases, as Figure 4 shows. The first step was initial data preparation through field measurements and data collection. The collected data were then categorized by highway rockfall susceptibility, rainfall hazard, and vulnerability. The next step was to map the data according to the information content method, logistic regression, and the fuzzy AHP to create the highway rockfall susceptibility map, the highway rainfall hazard map, and the highway rockfall vulnerability map. The final step was to combine all the above maps with the risk matrix to produce a highway rockfall risk map.

3.1. Data Preparation

To analyze the study region, the entire process of calculating and drawing the highway rockfall risk map was done in ArcGIS 10.7 (Esri, Redlands, CA, USA). Highway rockfall susceptibility index data was obtained using the digital elevation model (DEM) with a spatial resolution of 12.5 m and landsat8 OLI remote sensing image data. This is the most accurate data available to researchers at this stage, and it is freely available. The highway rainfall hazard index data was from the Guizhou Provincial Meteorological Bureau. The highway rockfall vulnerability was provided by the Guizhou Provincial Bureau of Statistics. It should be noted that the highways in Guizhou Province are a line element in the GIS. Some scholars have selected a buffer zone of 500 m along the highway as the study area to study the slope hazards along the highway [40]. For this paper, the buffer zone of 500 m along the highway in Guizhou Province was also selected as the research area. All the input data have a uniform reference coordinate format, “WGS_1984_UTM_Zone_48N”, and the causative factors are transformed into raster data with a spatial resolution of 12.5 m for further model calculation.

3.2. Highway Rockfall Susceptibility

The highway rockfall susceptibility index is the internal factor that leads to the occurrence of rockfall. The rockfall may be influenced by a series of factors. The scientific selection of factors is a key step in rockfall susceptibility evaluation studies. Recently, a number of scholars have selected different elements to assess rockfall susceptibility, and we have counted statistics on them, as shown in

Table 1. Statistics of rockfall susceptibility index.

Article	Slope	Elevation	Relief Amplitude	Aspect	NDVI	Lithology	Distance from Fault	RWI
Lin et al. (2021) [41]	√	√		√	√	√	√
Liu et al. (2021) [42]	√		√		√
Wang et al. (2021) [43]	√		√	√
Liu et al. (2022) [13]	√	√		√	√		√
Crawford et al. (2022) [44]	√	√	√	√	√	√
Eitvandi et al. (2022) [45]	√		√	√	√	√	√
Hader et al. (2022) [46]	√	√		√	√		√
Liu et al. (2022) [47]	√	√		√	√	√	√
Chen et al. (2023) [39]	√	√		√	√	√
Wu et al. (2023) [48]	√	√		√	√	√	√
Liu et al. (2023) [49]	√					√	√
Lv et al. (2024) [50]	√	√		√	√	√	√
Meng et al. (2024) [51]	√	√		√	√
Zhang et al. (2024) [52]	√	√		√	√	√	√
Zhang et al. (2024) [53]	√	√		√	√	√
This work	√	√	√	√	√	√	√	√

Note: RWI (rock weathering index); NDVI (normalized difference vegetation index).

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This study posits that the evaluation index for rockfall susceptibility should comprehensively reflect the topographic and geomorphological characteristics, vegetation cover, geological condition, and rock weathering condition. The approach is informed by established evaluation indexes from previous research, emphasizing the scientific rigor, applicability, and accessibility of the data employed. Finally, we selected the indicators shown in the table above. We believe that these elements are the most common and the main internal factors leading to the occurrence of rockfall accidents. Among these 8 evaluation indexes selected for this study, elevation, slope, aspect, and relief amplitude are utilized to characterize the topographic and geomorphological characteristics of the study area, effectively indicating the stability of rock and soil [54]. The NDVI serves to assess vegetation cover, with denser vegetation providing significant protection for slopes and reducing the likelihood of geological disasters [55]. Lithology and distance from fault are employed to represent the geological conditions of the area, with poorer geological conditions correlating with an increased probability of geological disasters [41]. Additionally, the RWI reflects the weathering of rock masses, and a higher probability of landslides, such as rockfall events, is observed with more severe weathering conditions [56,57]. Recently, many studies have used different methods for evaluation, but the most important of them are machine learning methods, such as neural networks, support of random vectors, etc. Although these methods are the mainstream methods, they require a large amount of data for training, and the models built are not very interpretable. We combine the commonly used informative method with logistic regression. The information content method can determine the influence of different intervals of elements on the probability of rockfall accidents, while logistic regression can analyze the influence of each element on rockfall accidents. The combination of these two methods can accurately predict whether a rockfall accident will occur without using a large amount of data.

According to the index of rockfall susceptibility shown in Table 1 and the actual data available to us, we finally chose the following factors for this study: elevation, slope, NDVI, aspect, distance from fault, relief amplitude, lithology, and RWI. The highway rockfall susceptibility index is shown in Figure 5.

(1)

Elevation. Elevation is the absolute distance from a certain point along the vertical direction to a certain point. It is an important factor influencing the occurrence and development of geologic hazards such as rockfall and their morphological characteristics [41]. The greater the elevation, the greater the gravitational potential energy of the rockfall. The terrain of Guizhou Province is high in the west and low in the east, and the average elevation reaches more than 1000 m. At different elevation ranges, there is significant variability in vegetation cover, rainfall, temperature variations, and the intensity of human engineering activities. These factors directly or indirectly affect the occurrence of geologic hazards.

(2)

Slope. Slope reflects the steepness of the surface of the rockfall hazard site, and is generally expressed as the ratio of the vertical distance from a point on the slope surface to the foot of the slope and the horizontal distance from the foot of the slope. Some slopes are potentially hazardous. The steeper the slope, the more water and soluble salts will gradually accumulate down the slope, directly affecting the vegetation distribution on the slope [39]. The movement of water within the slope, the denudation and material distribution of the rock and soil bodies on the slope surface, and the stress characteristics within the slope body will be different for different slope locations, and the probability of a rockfall will vary. The probability of rockfalls will also change accordingly. The greater the slope, the more likely the rocks are to be eroded, leading to the occurrence of rockfall accidents. Moreover, the greater the slope, the greater the kinetic energy of the rockfall.

(3)

NDVI. The NDVI is calculated from landsat8 OLI remote sensing satellite bands. The NDVI can separate vegetation from water and soil, can objectively reflect changes in the amount of vegetation cover, and is the best indicator of vegetation growth status and vegetation cover [49]. The vegetation significantly influences the stability of a slope. Studies have shown that vegetation can strengthen the shear capacity of soil through its root system, which has the effect of soil consolidation and slope protection. As the vegetation cover increases, the stability of the slope improves, and the probability of rockfalls decreases.

(4)

Aspect. Aspect is expressed as the angle between the projection of the normal direction of the slope on the plane and the due north direction. Aspect has an effect on both the number of days of sunshine and the total radiation received by the slope [44]. Due to differences in the amount of solar radiation received, the evaporation of water from the slope surface, the distribution of vegetation on the slope surface, the pore water pressure, and the wet–dry cycle of the slope will vary from one slope direction to another, which in turn will lead to rainfall, vegetation cover, erosion, and weathering of the slopes.

(5)

Distance from fault. A fault is a structure in which the earth’s crust is fractured by force, and significant relative displacement of rock masses occurs along both sides of the fracture plane [13]. Faults disrupt the rock and soil structure in the vicinity, and the integrity of the slope is compromised. The closer the fault, the more discontinuous the rock, and the looser the soil, the higher the probability of rockfalls.

(6)

Relief amplitude. Relief amplitude is the difference between the elevation of the highest point and the elevation of the lowest point in a given area. It is a macroscopic indicator that characterizes the topography of a region [58]. Relief amplitude is mainly the result of tectonic movements and surface erosion and represents the degree of regional surface denudation and cutting. As relief amplitude increases, the probability of rockfalls increases.

(7)

Lithology. Lithology refers to some properties that reflect the characteristics of the rock. In different lithologies, shear strength is distinct; permeability is also different; the stability of the slope, destabilization degree, and resistance to stability are different; and the ease of occurrence of geologic disasters is also different [41]. Lithology directly affects the size and extent of rockfalls. In this research, the lithologies are categorized into five categories as very soft rock, soft rock, softer rock, harder rock, and hard rock, and are given the labels 1, 2, 3, 4, and 5.

(8)

RWI. The RWI reflects the degree of rock weathering, which is usually affected by temperature, humidity, sunshine, wind speed, and other factors. When the degree of rock weathering is very high, the rock will be broken, the strength of the rock will be reduced, and rockfall disasters will occur more easily [56,57]. In this research, the wind speed, sunshine duration, daily maximum temperature, and humidity index are taken as the factors to calculate the RWI. The greater the wind speed, the stronger the erosion and weathering effect on rocks, while sunshine and high temperature will accelerate rock weathering, and high humidity will also accelerate rock weathering. These four factors are normalized and superimposed to get the RWI.

After determining the rockfall susceptibility index, rockfall disaster susceptibility in the study area is evaluated according to the information content method. The information model is a quantitative analysis method that describes the degree of correlation between target variables and individual influencing factors. The theory of the information model holds that the occurrence of geological disasters is related to the quantity and quality of the information obtained in the forecasting process, and the probability of geological disasters can be measured by the amount of information, which quantitatively evaluates the susceptibility of rockfall geological disasters in the study area. The greater the amount of information, the greater the possibility of geological disasters. The information content of each index classification interval is determined according to the disaster point of rockfall. The specific calculation formula is as follows:

$$I={\displaystyle \sum _{i=1}^l{I}_{ij}={\displaystyle \sum _{i=1}^l{\log }_2\frac{M_0/M}{N_0/N}}}$$

(1)

where I is the total information content of the evaluation module; I_ij is the amount of information in the jth classification interval in the ith factor; l is the number of evaluation factors; N₀ is the area of the jth grading interval; N is the total area of the study area; M₀ is the number of rockfall hazards occurring in the jth classification interval; M is the total number of rockfall hazard in the study area.

The information content method allows for the determination of the effect of each interval of the highway rockfall susceptibility indicator on susceptibility, but each indicator should be weighted differently for highway rockfall susceptibility. Therefore, we also take the method of logistic regression to determine the influence weight of each susceptibility indicator.

Logistic regression modeling is a generalized linear regression prediction method that can be used to analyze the target variables and multiple influencing factors to analyze the specific numerical relationships between target variables and multiple influencing factors and evaluate the risk of rockfall hazards. This study performed the logistic regression simulation by randomly selecting 500 hazardous and non-hazardous sites and extracting their highway rockfall susceptibility evaluation index parameters. Finally, the simulation results were obtained. The specific calculation formula is as follows:

$$P=1/[1+e^{-(\alpha +{\beta }_1{x}_1+\dots +{\beta }_i{x}_i)}]$$

(2)

where P is the probability of occurrence of rockfall hazards in the evaluation unit; α is the constant term calculated by logistic regression; β_i is the regression weight of the ith factor computed by logistic regression; x_i is the ith independent variable.

3.3. Highway Rainfall Hazard

Rainfall has a significant impact on the occurrence of geological disasters, particularly during intense or prolonged precipitation events. Increased soil moisture can lead to saturation, triggering landslides and debris flows. Additionally, rainfall may compromise the stability of rock formations, heightening the risk of rockfalls. The erosion and surface wash caused by rainfall can further destabilize the landscape, exacerbating the likelihood of geological disasters [11]. Thus, rainfall is a critical factor in the initiation of geological disasters, especially in areas characterized by complex topography and high human activity, necessitating close monitoring of its associated risks. The highway rainfall hazard refers to the occurrence of rockfall accidents through external rainfall. In this research, average annual rainfall and daily maximum rainfall were selected as highway rainfall hazards. The highway rainfall hazard index is shown in Figure 6.

(1)

Average annual rainfall. Guizhou Province has a plateau-type subtropical climate with abundant rainfall, and the average annual rainfall is mostly between 1100 and 1400 mm. It can be seen in Figure 6a that the average annual rainfall distribution of the whole Guizhou Province is higher in the southeast and lower in the northwest. Average annual rainfall can be a good reflection of the climate of the study area; the greater the mean annual rainfall, the greater the surface runoff of the slope, and the greater the probability that the slope will be subjected to rainwater erosion. This can lead to the disruption of slope integrity and vegetation cover, ultimately leading to rockfall accidents.

(2)

Daily maximum rainfall. Daily maximum rainfall is the amount of rainfall in a 24 h period, which can be representative of extreme severe weather. The daily maximum rainfall in Guizhou Province is shown in Figure 6b, which shows that the daily maximum rainfall in Guizhou Province mainly occurs in the central and southern parts of the province. Excessive daily maximum rainfall causes large amounts of surface runoff from slopes, eroding the slopes, washing away the rocks on the slopes’ surface, and reducing vegetation’s protective effect on the slopes. It makes rockfalls much more likely to occur.

After determining the rainfall hazard index, the corresponding weights were given to them through the fuzzy analytic hierarchy process (FAHP). The analytic hierarchy process (AHP) refers to a complex multi-objective decision-making problem as a system, and the objective is decomposed into multiple objectives and then into a number of levels of multi-indicators through the fuzzy quantitative method of qualitative indicators to calculate the hierarchical weights and the total ranking, in order to serve as a systematic method of the target optimization decision-making. The AHP, as one of the most widely used methods, is subject to a great deal of subjectivity, and the introduction of fuzziness can effectively reduce subjectivity. The FAHP is calculated as follows: first, a fuzzy judgment matrix is constructed, then the weights of each element are determined, and finally, a consistency test is performed.

$$A=\left[\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{n1}& \dots & a_{nn}\end{array}\right]$$

(3)

The matrix parameters are selected from 0.1 to 0.9, and the matrix data parameter values are described in

Table 2. Description of matrix data parameter values.

Value	Description
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

.

The weights of the index are calculated as follows:

$$W_i={\displaystyle \frac{{\displaystyle \sum _{j=1}^n}{a}_{ij}+\frac{n}{2}-1}{n(n-1)}}$$

(4)

The weight matrix is calculated as follows:

$$w_{ij}={\displaystyle \frac{W_i}{W_i+W_j}}$$

(5)

Furthermore, fuzzy judgment matrices need to be tested for consistency, usually by means of a compatibility index I (A, W). When I ≤ α (α is the decision-maker’s attitude, usually taken as 0.1), then consistency is considered to be satisfied. The consistency test is calculated as follows:

$$I(A,W)={\displaystyle \frac{1}{n^2}}\sum _{i=1}^n\sum _j^n|a_{ij}+w_{ij}-1|$$

(6)

3.4. 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 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.

After determining the elements of rockfall susceptibility, the same FAHP was used to assign different weights to each of the elements. Then, the highway rockfall vulnerability was calculated for each highway rockfall vulnerability element using a raster calculator in a GIS environment.

3.5. Highway Rockfall Risk

The rockfall risk map is one of the most critical findings of this research, and it can provide effective rockfall prevention and management recommendations to government departments. After determining the three elements of highway rockfall susceptibility, highway rainfall hazard, and vulnerability, as well as highway rockfall, which affect the highway rockfall risk, a map of rockfall risk could be calculated in a GIS environment. The calculation of highway rockfall risk started by dividing the three elements of highway rockfall susceptibility, highway rainfall hazard, and highway rockfall vulnerability into four intervals through the natural discontinuity point method, followed by a risk matrix. The highway rockfall risk for this study was calculated based on the risk matrix shown in Figure 8.

4. Results

4.1. Highway Rockfall Susceptibility Map

After importing all the highway rockfall susceptibility elements into the GIS, the elements were first divided into different zones. In this research, the highway rockfall susceptibility elements were divided into various zones based on the actual situation in Guizhou Province in combination with expert opinions. Then, we calculated the information content in the GIS by counting the area of each interval and the number of hazard points. The information content in each zone is shown in

Table 3. Information content of highway rockfall susceptibility.

Factor	Class	Information Value	Factor	Class	Information Value
Elevation Slope NDVI Relief amplitude Distance from fault	<500 m 500~1000 m 1000~1500 m >1500 m <10° 10–25° 25–40° >40° <0.2 0.2–0.4 0.4–0.6 0.6–0.8 >0.8 <150 m 150~300 m 300~450 m >450 m <1.5 km 1.5–3 km 3–4.5 km >4.5 km	−0.004715 −0.052104 0.011811 0.073626 −0.254924 0.146219 0.266531 −0.094343 0.863558 0.215351 0.196962 −0.127839 −0.455454 −0.419209 0.152283 0.163818 0.267191 0.158946 −0.096210 −0.074668 0.051317	Lithology Aspect RWI	1 2 3 4 5 Flat North Northeast East Southeast South Southwest West Northwest <0.2 0.2–0.4 0.4–0.6 0.6–0.8 >0.8	0.255183 −0.110352 −0.004681 0.1611609 −0.058467 0 0.012289 −0.034320 −0.036404 −0.002801 0.078364 −0.018094 −0.035378 0.045654 −0.11986 −0.065318 −0.28685 0.60475 0.35773

Note: RWI (rock weathering index); NDVI (normalized difference vegetation index).

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After determining the influence of each zone on highway rockfall susceptibility through the information content method, it was still necessary to use logistic regression to assign different weights. The specific steps are as follows: First, 250 rockfall hazard sites were randomly selected, and the same number of non-rockfall hazard sites were determined. Then the parameters of the highway rockfall susceptibility index corresponding to these random points were extracted. The data were then analyzed by logistic regression to derive the appropriate weights. Finally, the highway rockfall susceptibility map was created using the GIS. The results of logistic regression modeling are shown in

Table 4. Logistic regression of highway rockfall susceptibility.

Factors	Parameters
Elevation	0.237
Slope	0.458
NDVI	−2.125
Aspect	1.154
Distance from fault	−2.621
Relief amplitude	0.375
Lithology	−1.848
RWI	2.293
α (constant term)	1.974

Note: RWI (rock weathering index); NDVI (normalized difference vegetation index).

. After calculating the highway rockfall susceptibility, the susceptibility was categorized into four levels of low, medium, high, and very high by the natural discontinuity method. The highway rockfall susceptibility map is shown in Figure 9.

Based on the highway rockfall susceptibility map, it can be found that most of the study area is of high rockfall susceptibility and above. The percentage of high susceptibility regions reached 20%, while very high susceptibility regions reached 45%. This means that the entire study area may face rockfall accidents at any time, and the rockfall accident distribution map of Guizhou Province also shows that there have been a large number of rockfall accidents in the entire study area. According to the statistics, QDN and QN have the longest mileage of very high rockfall susceptibility. In addition, BJ and LPS have the highest percentage of low and medium rockfall susceptibility road mileage. The results of the highway rockfall susceptibility statistics for the entire study are shown in Figure 10.

4.2. Highway Rainfall Hazard Map

Highway rainfall hazards are a factor affecting highway rockfall risk. This study considers annual average rainfall and daily maximum rainfall. Annual average rainfall and daily maximum rainfall data were obtained from the Guizhou Meteorological Bureau and imported into the GIS. The two datasets were then normalized, and different weights were assigned based on the FAHP. The assignment and weighting of highway rainfall hazards is shown in

Table 5. Assignments and weights of highway rainfall hazard.

Index	Annual Average Rainfall	Daily Maximum Rainfall	Weight
Annual average rainfall	0.5	0.3	0.4
Daily maximum rainfall	0.7	0.5	0.6
Consistency		I (A, W) = 0.075 < 0.1

.

The calculation of highway rainfall hazard results is based on weights calculated by the FAHP. The highway rainfall hazard map is shown in Figure 11.

The highway rainfall hazard results are categorized into four classes by the natural discontinuity method. It can be seen that rainfall hazards in Guizhou Province are mainly concentrated in the central and southern parts of the province. The entire province of Guizhou has an abundance of rainfall due to its climate, making the province one with a considerable highway rainfall hazard. The highway rainfall hazard in the entire Guizhou Province is above the high-risk level in AS, GY, and QDN, with QN having the highest highway rainfall hazard mileage. BJ, as the only district with a low rainfall hazard, suffers the least rainfall hazard. The results of the highway rainfall hazard statistics for the entire study are shown in Figure 12.

4.3. Highway Rockfall Vulnerability Map

Highway rockfall vulnerability refers to the magnitude of damage after a rockfall occurs. Data on population, GDP, and land use types in highway rockfall vulnerability are from the Guizhou Provincial Bureau of Statistics. These data were not processed in the same way as before, but with the following steps: First, the population and GDP of Guizhou Province were directly inputted according to each county and city; then land use types were assigned different values according to type, with values ranging from 5 to 1 for built-up areas, clearings, crops, flooded vegetation, and trees, respectively. All three indicators were then normalized, and different weights were assigned by the FAHP. The assignments and weighting of highway rockfall vulnerability are shown in

Table 6. Assignments and weights of highway rockfall vulnerability.

Index	Population	GDP	Land Use Type	Weight
Population	0.5	0.4	0.8	0.40
GDP	0.6	0.5	0.7	0.43
Land use types	0.2	0.3	0.5	0.17
Consistency			I (A, W) = 0.044 < 0.1

.

The calculation of highway rockfall vulnerability results is based on weights calculated by the FAHP. The highway rockfall vulnerability map is shown in Figure 13.

Highway rockfall vulnerability results are categorized into four classes by the natural discontinuity method. The high highway rockfall susceptibility of the entire Guizhou Province is mainly concentrated in the northwest and central parts of the province. BJ and LPS are the two districts with the longest mileage and very high highway rockfall vulnerability. QDN and QN are the two districts with the longest mileage of low highway rockfall vulnerability. The results of the highway rockfall vulnerability statistics for the entire study are shown in Figure 14.

4.4. Highway Rockfall Risk Map

In this research, highway rockfall risk consists of three components: highway rockfall susceptibility, highway rainfall hazard, and highway rockfall vulnerability. These three components were superimposed in the GIS, and the highway rockfall risk results were calculated based on the risk matrix from the previous section. The highway rockfall risk map is shown in Figure 15.

Calculations show that most highways in the entire Guizhou Province are at medium and high risk, with very few at low and very high risk. The proportion of highway rockfall risk in the entire Guizhou Province is shown in

Table 7. The proportion of highway rockfall risk.

Rockfall Risk	Percentage
Low	18.87%
Medium	28.09%
High	41.19%
Very high	11.84%

.

The highway rockfall risk in Guizhou Province is characterized by a high spatial distribution in the west and a low spatial distribution in the east. BJ has the highest very high risk highway ratio of 22.1%. The proportion of high-risk highway ratios in the districts of BJ, LPS, QXN, QN, and ZY exceeds 50 percent. QDN has a low-to-medium risk ratio of over 70 percent. The results of the highway rockfall risk statistics for the entire study are shown in Figure 16.

5. Discussion

The accuracy of a model usually needs to be verified after the model has been built to calculate the risk results. The receiver operating characteristic (ROC) curve provides a simple and intuitive validation of model accuracy by analyzing the sensitivity and specificity of continuous variables. Moreover, the ROC curve avoids the interference of excessive human factors in the accuracy verification of the results, with good objectivity. Nowadays, ROC curves are widely used to verify the accuracy of geological risk assessments. In this research, 250 random disaster points with an equal number of non-disaster points at intervals of more than 1 km apart were selected, and their probability values were extracted. The data was then imported into SPSS Statistics 26.0 (IBM Corp., Armonk, NY, USA) to verify the accuracy of the risk assessment. The ROC curve for the highway rockfall risk assessment of Guizhou Province is shown in Figure 17. The precision–recall (PR) curve was used to better evaluate the model’s performance under class imbalance. The average precision (AP) was 0.765, indicating a good capability to identify very high-risk zones despite their relatively low proportion. The precision–recall curve for the highway rockfall risk assessment of Guizhou Province is shown in Figure 18. The area under the ROC curve in Guizhou Province is 0.827, which indicates that the result of the highway rockfall risk assessment in this area is accurate and reliable.

In order to further validate the accuracy of the model, this paper compares it to the report on the trend prediction of sudden geologic disasters in Guizhou Province issued by the Guizhou Provincial Government in 2023. In this report, the geologic disasters that occurred in 2022 in each district of Guizhou Province were counted, and the specific statistical results are shown in

Table 8. Statistics of geologic disasters in each district of Guizhou Province in 2022.

District	Rockfall Number	Economic Loss (Thousands)
LPS	5	29,000
BJ	2	21,100
QXN	3	4902
TR	2	2600
GR	2	1700
QN	1	1100
AS	1	900
ZY	3	720
QDN	2	400

. According to Table 8, LPS had the highest number of rockfall accidents, which caused much higher economic losses than experienced by the other districts. Although the number of rockfalls in BJ was not as high, the economic loss caused by it was second only to that of LPS, which may be due to the fact that BJ and LPS have the largest proportion of very high-risk and high-risk areas, and their risk level is much higher than that of the other districts. Moreover, QDN has a large proportion of low- and medium-risk areas, so its economic losses were small. Thus, the accuracy of the evaluation model developed in this paper is further demonstrated.

Rockfall is one of the most common natural disasters. Once it occurs, it will cause a huge hazard. In recent years, the issue of how to assess the risk of rockfalls and manage and prevent them has become a hot topic. A number of studies have selected and analyzed some of the elements that influence the occurrence of rockfalls to obtain the results of rockfall risk. In this study, the highway rockfall risk is considered to be composed of three components: highway rockfall susceptibility, highway rainfall hazard, and highway rockfall vulnerability. Highway rockfall susceptibility is the probability that internal factors influence the occurrence of rockfalls; highway rainfall hazard is the size of the hazard posed by the occurrence of rockfall due to rainfall; and highway rockfall vulnerability is the size of the hazard brought about by the occurrence of rockfalls. With the further development of the research, many methods for rockfall risk assessment have emerged, which are mainly categorized into two types: qualitative methods and quantitative methods. The qualitative methods include the expert empirical method, fuzzy comprehensive evaluation method, and spatial principal component analysis method. Quantitative analysis methods include the AHP method, information content method, frequency ratio method, and machine learning method. The present methodology for evaluating rockfall risk faces the following challenges: Firstly, the weighted combination of various evaluation indicators is greatly influenced by human subjectivity and cannot objectively reflect the impact of different indicators on geological disasters (as is the case with the AHP method and expert empirical method). Furthermore, a large amount of accurate data is required for modeling and analysis, and insufficient and inaccurate data can have a significant impact on the accuracy of the overall assessment model (as is the case with the machine learning method). In comparison, the information content method analyzes the area of the interval of each rockfall hazard impact indicator and the number of rockfall hazards to get the information content of the probability of the occurrence of a rockfall accident due to each rockfall impact indicator. In this research, we first used the information content method to assign information content to each indicator zone, then used logistic regression to assign different weights to different indicators, and finally combined them to obtain the results of highway rockfall susceptibility. This research method fully considers the objective influence of evaluation indexes on rockfall disasters and effectively avoids the influence of human subjectivity, and its evaluation results are more scientific and reasonable.

The impact of each rockfall susceptibility indicator zone could be determined for the entire study area based on the information content values, and a combination of the highest risk zones for highway rockfall susceptibility could be identified. The dominant influencing factors that can easily induce highway rockfall hazards in Guizhou Province include elevation > 1500 m, slope of 25–40°, NDVI < 0.2, aspect of south, distance from fault <1.5 km, relief amplitude > 450 m, lithology being 1 (very soft rock), and RWI of 0.6–0.8. The information content can only reflect the effect on the probability of rockfall occurrence within a single indicator of highway rockfall susceptibility, whereas logistic regression can analyze the ranked size of the effect of each indicator on the probability of rockfall occurrence. The results of the logistic regression ranking of rockfall susceptibility are shown in Figure 19. The RWI is the most important factor influencing the probability of rockfall. The distance from the fault is the most negatively correlated indicator of the probability of rockfall. The greater the distance from the fault, the lower the probability of rockfall.

According to the above conditions, the probability of rockfall can be effectively determined, and the probability of rockfall accidents is the highest when there is an area where most of the evaluation indexes belong to the zone of the main impact indexes. The relevant departments can enhance the protection and management of rockfalls in the area to minimize the hazards caused by rockfall accidents. In this research, highway rockfall susceptibility, highway rainfall hazards, and highway rockfall vulnerability were considered when evaluating the highway rockfall risk results for the whole research. This can provide scientific and reasonable protection management advice to the relevant authorities for decision-making and management of highway rockfall risks. For areas with high rockfall risks, such as Bijie, regular monitoring and the establishment of rockfall protection nets can be implemented to reduce the damage caused by rockfalls.

Research findings indicate that natural geologic hazards, such as rockfalls, are influenced by a variety of factors, including the natural environment and human activities. Considering the natural environment, rainfall, temperature, sunshine, vegetation, etc., can have an impact on the slope, potentially leading to rockfall accidents. Human activities have an impact on the entire ecosystem, resulting in the overall destruction of slopes, reduced vegetation cover, and more frequent rockfall accidents. In the process of future urban development and construction, ecological protection should be the guiding principle to minimize the damage to the stability of the original ecosystem and to achieve a harmonious coexistence between human beings and nature. Land development and utilization should try to avoid areas with high ecological vulnerability and a high risk of rockfall disasters. Necessary ecological restoration can also be appropriately implemented in areas with a high risk of geohazards to restore and rebuild the stability of regional ecosystems.

There are some limitations in this study; first of all, in the selection of evaluation indexes. The selection of indexes of rockfall susceptibility can also consider the influence of climatic factors such as the terrain humidity index and distance from rivers, etc. The terrain humidity index is a physical indicator of the influence of regional topography on runoff flow and accumulation, and the larger the terrain humidity index is, the closer the distance from rivers is, which will result in the increase in water content and softening of slopes, leading to the reduction in slope stability, thus leading to the occurrence of rockfall accidents Sun et al., 2024 [61]. Therefore, these are also important indexes to consider in the evaluation of rockfall susceptibility elements, and the influence of these indicators can be further considered. The evaluation indexes of rockfall vulnerability elements can additionally consider transportation elements, such as highway traffic flow and other indexes, which can further reflect the size of the impact on the highway when rockfall accidents occur. Furthermore, the 12.5 m DEM data still has certain limitations. A higher-precision DEM can identify rockfall accidents in a smaller range more accurately because the higher the precision of the DEM, the more accurately it can reflect the real terrain conditions, and the occurrence of rockfall accidents can also be judged more accurately. In addition, the accuracy of the evaluation model established in this study can be further improved. It was found that the AUC value of this model reached 0.827 through the ROC curve, but now there are quite a number of research models of the ROC curve of the AUC value that can reach 0.85. It can be considered to select more rockfall accident disaster points, as more data will improve the accuracy of the model described in this research.

6. Conclusions

Mountainous areas significantly heighten the risk of rockfalls along highways due to their unique geological and topographical conditions. This increased risk poses a serious threat to traffic safety and infrastructure. Consequently, conducting a comprehensive assessment of rockfall risks in these terrains is essential to effectively mitigate hazards and enhance safety measures. In this research, the risk matrix combining highway rockfall susceptibility, highway rainfall hazard, and highway rockfall vulnerability was used to assess the highway rockfall risk in Guizhou Province and to characterize the distribution and influencing elements of rockfall risks in Guizhou Province. This research aims to provide valuable insights for local authorities and stakeholders, informing risk management strategies, enhancing safety protocols, and supporting infrastructure planning in areas prone to rockfalls. The main conclusions are as follows:

(1)

The total highway rockfall risk in the whole of Guizhou Province is high. High-risk areas dominate, making up 41.19% of the total risk area. Medium-risk and low-risk areas account for 28.09% and 18.87%, respectively, while very high-risk areas represent just 11.84%.

(2)

The highway rockfall risk in Guizhou Province is characterized by a high spatial distribution in the west and a low spatial distribution in the east. BJ has the largest percentage of highway mileage that is above the high-risk level, over 70%, while QDN has the largest percentage of road mileage that is below the medium-risk level, over 75%.

(3)

A logistic regression analysis revealed that the RWI is the most important factor influencing highway rockfall susceptibility. The distance from the fault is the most negatively correlated indicator of highway rockfall susceptibility. The elevation has the least effect on the susceptibility to highway rockfalls.

(4)

By extracting the risk probabilities of disaster and non-disaster points and plotting the ROC curve, its AUC value reached 0.827. This proves that the model of this study is highly accurate.