Introduction

Collapse disasters, as one of the most destructive geological hazards worldwide, have long posed severe threats to human society and the natural environment1,2. In recent years, with the acceleration of urbanization and the continuous expansion of mountainous infrastructure, the frequency and severity of collapse disasters have steadily increased, especially in slope areas near mountainous roads, transportation facilities, and residential zones. Meanwhile, the increasing frequency of extreme weather events caused by global climate change, particularly the rise in short-term heavy rainfall events, has significantly exacerbated the stability issues of mountainous slopes3. These weather changes have directly led to frequent rainfall-induced collapse disasters, causing substantial impacts on transportation systems, the safety of human lives and property, as well as the ecological environment4,5. Therefore, accurately analyzing rainfall-induced collapse disasters and deeply understanding their dynamic mechanisms have become hot topics in academic research6. Moreover, constructing effective hazard assessment models for collapses under extreme rainfall conditions can provide a scientific basis for disaster prevention and mitigation in mountainous areas, which holds critical practical significance. Research on this issue is not only at the forefront of scientific exploration but also an urgent need for disaster prevention and mitigation in mountainous areas to ensure transportation safety and protect the lives and property of residents.

In international studies, European and North American scholars have used numerical simulations and climate models to assess the risk of slope instability under different climatic conditions, constructing regional collapse prediction models based on long-term rainfall data7,8. For example, by integrating remote sensing data with meteorological models, they have effectively predicted the impact of rainfall on landslides9,10. Additionally, significant progress has been made in monitoring and early warning systems, which have already been applied to the dynamic early warning of slope displacements11,12,13. In recent years, the application of GIS (Geographic Information System) and remote sensing technology in collapse susceptibility assessments has enhanced the accuracy of multi-factor and spatial analyses, advancing the hazard assessment of collapse disasters in complex terrain conditions14,15.

Researchers have made significant progress in the hazard assessment of regional collapse disasters, gradually integrating UDEC (Universal Distinct Element Code) numerical simulations with geological hazard evaluations for the analysis of collapse hazard along mountainous highways16,17. However, for regions like Changbai County, which are characterized by complex geology and frequent rainfall, traditional qualitative analysis methods and grid-based zoning approaches still have limitations in terms of simulation accuracy and the refinement of hazard zoning18. Particularly under extreme rainfall conditions, the precise prediction of collapse mass deposition ranges and the analysis of their failure mechanisms present significant challenges. These challenges stem from the difficulty of applying more natural unit divisions that align with geomorphological features, such as ridges, faults, and other key terrain elements, which are crucial for understanding the dynamics of collapse events. Furthermore, current models often struggle to effectively capture the dynamic nature of collapse processes under such conditions, requiring more advanced approaches that can better integrate spatial variability and temporal fluctuations. As a result, existing methodologies often fail to provide the level of accuracy and predictive power necessary for addressing the complexities inherent in extreme weather-driven geological hazards.

This study introduces a slope-unit-based zoning approach in the hazard assessment of collapse disasters, replacing the traditional grid-unit method. Compared to grid units, slope units can more naturally capture key geomorphological features such as ridges and faults, while reducing redundant calculations in flat areas, making them more consistent with terrain characteristics and significantly improving the accuracy and computational efficiency of collapse hazard identification19. By integrating the UDEC numerical simulation model with GIS technology, this study achieves high-precision dynamic simulations and mechanism analysis of rock collapses under extreme rainfall conditions. The analysis of case studies on collapse damage helps identify specific indicator factors and define the characteristics of the research area. The application of the UDEC model overcomes the limitations and accuracy bottlenecks of traditional geological evaluations in complex terrain areas, enabling precise prediction of collapse mass falling ranges and deposition locations while revealing the mechanisms of collapses induced by extreme rainfall20,21. Additionally, this study employs a combined weighting method using the AHP and the CV method for the evaluation of collapse susceptibility. Unlike traditional formula-based calculations of CV weights, this study utilizes ArcGIS software to calculate the mean and standard deviation of each indicator, significantly reducing the time and error risks associated with manual calculations. By combining subjective expertise with objective data, the method optimizes the weighting accuracy of different factors under rainfall conditions, balancing adaptability and precision, and providing a more scientific quantification of the impact of various factors on slope stability. This study presents a novel methodological framework for assessing geological hazards, integrating slope-unit zoning with normalized susceptibility metrics to facilitate a more precise analysis of hazard distribution in geologically complex areas. The introduction of slope-unit zoning refines the analytical resolution by aligning with the natural spatial heterogeneity of terrain, including key features such as ridges and fault lines, which traditional grid-based methods often fail to capture effectively. This approach mitigates the limitations posed by inconsistent factor scales and subjective weight assignments inherent in conventional techniques by employing a rigorous normalization process. This significantly bolsters the scientific rigor and accuracy of the hazard evaluation model.Furthermore, by synthesizing multi-source data, including topographical, hydrological, and geological inputs into a unified normalization framework, the method enhances the representation of hazard causation mechanisms within complex geological contexts. The approach ensures both the versatility and scalability of the model, making it adaptable to diverse geographical regions and hazard types. This innovation represents a critical theoretical and methodological advancement in the domain of geological hazard research.The findings of this study not only provide more refined spatial delineation of high-hazard zones but also offer practical, evidence-based insights that inform regional disaster planning and mitigation strategies, thereby setting a new direction in the methodology for geological hazard risk assessment.

By constructing a comprehensive evaluation system that includes rainfall intensity, topographic features, and geological structures, this study delves into the relationship between extreme rainfall and collapse dynamics. Additionally, it provides scientific insights and technical support for the prevention and mitigation of collapses, as well as disaster early warning systems, in Changbai County and regions with similar geological conditions. The specific research process for rock slopes along the highways in Changbai County is shown in Fig. 1.

Fig. 1
figure 1

Flowchart of rock collapse hazard assessment under extreme rainfall conditions. Generated by WPS Office 12.1.0.19770 (https://www.wps.cn).

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Overview of the study area

Changbai County is located in the southeastern part of Jilin Province, on the southern slope of Changbai Mountain and the right bank of the upper reaches of the Yalu River. It borders Linjiang to the west, Fusong to the north, and faces the Democratic People’s Republic of Korea across the Yalu River to the southeast. The county spans 82.9 km from east to west, 30 km from north to south, with a total area of 2,497.6 km2. It has a northern temperate continental humid monsoon climate characterized by long, cold winters, short and rainy summers, and distinct seasons. The multi-year average temperature is 2.1℃, with extreme maximum and minimum temperatures of 34.8℃ and − 36.4℃, respectively. The average frost-free period is 110 days, and the average permafrost depth is 1.5 m. The multi-year average annual precipitation is 694.8 mm, with a maximum daily precipitation of 110.1 mm and an extreme annual maximum of 1,100 mm. The county’s total soil area covers 3,466,587 mu (approximately 231,106 hectares), consisting of 9 main categories, 17 subcategories, 26 soil groups, and 51 soil types, with albic soil and gray-brown soil being the primary types, alongside others such as alluvial soil, paddy soil, and limestone soil. The region has well-developed vegetation with a coverage rate of 81%, featuring typical Changbai Mountain flora, which includes a wide variety of natural species such as woody plants, herbaceous plants, and shrubs, as well as artificial vegetation like plantations and economic tree species.

There are no expressways within Changbai County, and the main roads consist of National Highway G331 and Provincial Highway S203. National Highway G331 follows the border, with most of it running along the Yalu River, while a portion extends north of Malugou Town and continues beyond Changbai County. Provincial Highway S203 is located within Malugou Town, running in a north-south direction, connecting the northern section of G331 in Malugou Town with the riverside sections of G331. The vast majority of roads in Changbai County are rural roads, which are distributed throughout the county, with relatively denser networks in the western and central regions. The following is a location map of National Highway G331 and Provincial Highway S203 (Fig. 2).

Fig. 2
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Location Map. ArcGIS 10.8 (https://www.esri.com) was used for visualization.

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The collapse disasters in this area are relatively small in scale but are concentrated in specific sections, particularly between K648-K726 and K759-K803 of National Highway G331. The slope rocks along both sides of the highway primarily consist of basalt, granite, sandy shale, and sandstone.

During the rainy season each year, rainfall in the study area is concentrated, and collapse events frequently occur, with some areas experiencing 2–3 collapse disasters within a single year. Rainfall acts as a triggering factor for geological collapse disasters; when rainfall infiltrates the rock layers, it softens and lubricates the strata. Simultaneously, changes in water stress alter the internal stress of the rock layers, reducing their strength and ultimately leading to collapse disasters22,23. Additionally, the occurrence of geological disasters is influenced by factors such as rainfall duration and intensity, Previous collapse events were often distributed along highway slopes and in areas significantly affected by human activities24,25.

Data sources and research methods

Data sources

Based on the characteristics of the region, a systematic analysis of the collapse mechanisms and hazard conditions under extreme rainfall was conducted to provide a scientific basis for disaster prevention and control in the area. The data on collapse hazards used in this study are mainly from the comprehensive risk census of geologic hazards and geologic hazard surveys in Changbai Chaoxian Autonomous County, Jilin Province. The data cover all major collapse disaster points within the study area, ensuring temporal and spatial representativeness. In this study, factors such as elevation, slope, and slope direction were selected for the geological hazard assessment (Table 1). These factors were extracted using DEM analysis, which allowed for the precise identification of key topographic features such as slope and aspect. DEM analysis provided high-resolution and highly accurate data, making it suitable for geological hazard assessments and enhancing the overall reliability of the analysis.The maps were generated using ArcGIS 10.8 (ESRI, https://www.esri.com/en-us/home). All maps were created by the authors, using data from public datasets and original calculations.

Table 1 Data sources.
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Prediction of affected areas and mechanism analysis

Case study

This study conducted a detailed analysis of rock collapse geological hazards along highways in Changbai County. To ensure the validity of the numerical simulation results, two typical collapse hazard sites were selected as UDEC simulation objects through field investigations (Fig. 4). These two sites have representative geologic features that reflect the geologic diversity and rainfall characteristics within the study area. Specifically, these sites are located in different geologic and rainfall conditions along the highway in Changbai County, which can effectively reflect the diversity of collapse hazards under complex geologic background and frequent rainfall conditions. Second, these two sites provide sufficient geologic survey data and historical disaster records based on data availability considerations, which provide reliable information support for this study. Through the investigation of these two sites, data with high representativeness and research value can be obtained to provide a scientific basis for disaster assessment and prevention in similar areas. According to the investigation, Collapse Site A was formed by road cutting, with a slope height of 35 m, a slope width of 258 m, and a slope orientation of 185°∠70°. The slope lithology is Sinian limestone. Collapse Site B is located in the northwest within an erosion-structured low mountain area, while the southeast features an alluvial river valley plain. The slope orientation is 270°∠52°, with a slope height of 27 m, a slope width of 52 m, and a slope lithology also consisting of Sinian limestone.

Fig. 3
figure 3

Examples of collapse development characteristics. Sourced from authors Qiuling Lang and Chenglong Yu.

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Through field investigations, UDEC simulation calibration, and empirical formula derivation, the physical and mechanical parameters of the rock mass and the structural surface parameters were obtained, ensuring the scientific validity and accuracy of the parameters (Tables 2 and 3). By inputting the data from these two actual collapse hazard sites into the UDEC model, we can more accurately simulate the collapse process induced by rainfall and analyze the affected areas and collapse mechanisms under different conditions.

Table 2 Physical and mechanical parameters of the rock mass.
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Table 3 Parameters of rock mass structural surface.
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Rainfall condition settings

Through a detailed analysis of rock collapse geological hazards under extreme rainfall in the study area, we collected the maximum daily rainfall data from Changbai County over a nine-year period (2011–2019). The average of these values was used as the extreme rainfall condition input for the model, providing a more scientific and reasonable basis for simulating the collapse process. On this basis, the UDEC model was applied to simulate the dynamic collapse process induced by rainfall, analyzing the movement path, collapse range, and deposition location of the collapse mass. This provides a reliable basis for predicting the affected areas of collapse26,27.

The calculation results show that the average maximum daily rainfall over the nine-year period is 95.6 mm, which is used as the initial extreme rainfall condition and input into the model to analyze the feasibility of collapse. The specific rainfall data are shown in Table 4.

Table 4 Maximum daily rainfall for each year from 2011 to 2019.
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Calculate the Average Rainfall.

$$\overline{X}=\frac{\sum_{i=1}^{n}x_i}{n}=95.6$$
(1)

However, rainfall data cannot be directly input into the UDEC simulation software. Instead, it is implemented by setting pore water pressure at the surface. Different pore water pressures are applied at the surface, and when the monitored surface flow rate approaches the flow rate calculated by the formula, the corresponding pore water pressure is considered to represent the pore pressure during rainfall infiltration, indicating a successful rainfall simulation. The formula is as follows.

$$\:\text{Q}=\frac{\text{P}}{\text{t}}\cdot\:{\text{l}}_{\text{d}\text{o}\text{m}\text{a}\text{i}\text{n}}\cdot\:\text{d}$$
(2)

where \(\:P\) represents rainfall (mm), \(\:\text{t}\) represents time (1 day), \(\:{\text{l}}_{\text{d}\text{o}\text{m}\text{a}\text{i}\text{n}}\) is the horizontal distance between the 10 m joint domains, and \(\:\text{d}\) represents the unit thickness in the z-direction (1 m).

Modeling analysis

A UDEC model was established based on the collapse development characteristics of the case study. Preliminary rainfall data and rock mass parameters were input to generate the collapse displacement cloud maps, as shown in Figs. 4 and 5. The simulation conditions are as follows:

Fig. 4
figure 4

Displacement cloud maps of collapse under different cumulative rainfall amounts for case A. Generated from UDEC 7.00.22. (https://www.itascacg.com).

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The results of Case A show that, under a cumulative rainfall duration of 24 h, the farthest distance of the collapsed mass from the slope foot is 8.58 m, with an affected collapse area of 2,213.64 m². Analysis of the displacement cloud maps of the rock slope under extreme rainfall conditions reveals a tensile-collapse composite failure mechanism28. Rainfall-induced increases in pore water pressure are identified as the primary triggering factor, leading to a reduction in the shear strength of the joint surfaces and weakening the interlocking forces between rock blocks. In the initial stage (0 h), local loosening occurs at the slope front, accompanied by the appearance of microcracks, indicating that the joint surfaces begin to destabilize due to water infiltration. As rainfall accumulates to 8 h, pore water pressure propagates into the slope body, causing cracks to extend and connect, resulting in significant movement of the front-edge rock blocks, while tensile stress in the rear edge induces initial tensile fractures. In the mid-stage (16 h), the displacement cloud maps show an increased displacement gradient, with large-scale collapse of front-edge rock blocks along joint surfaces, and further crack propagation in the rear edge forming a composite failure plane. Under 24 h of extreme rainfall, the instability of the rock mass accelerates, leading to the overall collapse of the slope. The collapsed blocks accumulate at the slope foot along the collapse direction, while tensile instability in the rear edge forms a distinct tensile failure zone.

Fig. 5
figure 5

Displacement cloud maps of collapse under different cumulative rainfall amounts for case B. Generated from UDEC 7.00.22. (https://www.itascacg.com).

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The results of Case B show that, under a cumulative rainfall duration of 24 h, the farthest distance of the collapsed mass from the slope foot is 5.33 m, with an affected collapse area of 277.26 m². In the initial stage, rainfall infiltrates the rock mass through joint cracks, leading to a localized increase in pore water pressure and weakening the shear strength of the rock mass. Microcracks appear in both the front and rear edges, and localized deformation begins to occur. As rainfall continues, crack extension and connection gradually develop, with rear-edge cracks enlarging and propagating inward, while displacement in the front-edge area accelerates, forming a distinct sliding and collapsing trend. The continued impact of rainfall further reduces the shear strength of the structural surface, causing the front-edge rock mass to gradually become unstable and undergo large-scale sliding and collapse, while the propagation of rear-edge cracks exacerbates the overall instability risk of the slope. During the failure process, the accumulation of pore water pressure, the connection of joint cracks, and the effect of gravity are the key mechanisms triggering the collapse. The collapsed rock mass moves rapidly along the collapse direction and accumulates at the slope foot.

Through an in-depth comparative analysis of the slope collapses in Cases A and B, the differences and commonalities of rock slope collapses under extreme rainfall conditions are revealed. In terms of topographic parameters, the slope in Case A, with a height of 35 m and a steep slope surface, exhibits more significant gravitational effects, resulting in shear forces concentrated at the front edge and triggering large-scale collapse. This leads to an affected collapse area of 2,213.64 m² and a collapse distance of 8.58 m. In contrast, the slope in Case B, with a height of 27 m and a gentler slope surface, experiences smaller-scale collapse, with an affected area of 277.26 m² and a collapse distance of only 5.33 m. In terms of failure mechanisms, both cases exhibit a tensile-collapse composite failure, but Case A, due to its steep terrain and larger displacement gradient, experiences earlier rapid collapse of the front-edge rock mass and earlier rear-edge crack propagation, accelerating the overall slope instability. On the other hand, Case B, influenced by its slope orientation and lower elevation, undergoes slower crack propagation and collapse processes, resulting in relatively limited collapse scale. Additionally, the road-cutting factor exacerbates the instability of both slopes by altering the original in-situ stress distribution, significantly promoting the diffusion and softening effects of pore water pressure along joint surfaces, which becomes the primary triggering condition for the collapses29. Therefore, elevation, slope gradient, slope direction, and distance from the road, as controlling factors, directly influence the slope stability evolution, collapse scale, and dynamic response characteristics. Where the distance from road factor is calculated based on the horizontal distance from points in the study area to the nearest road. This factor is important because roads can alter surface water discharge, increase the risk of soil erosion, affect soil cohesion, and thus slope stability, especially in areas with high traffic or road construction. Considering these factors comprehensively, selecting these four indicators for study not only systematically reveals the instability patterns of rock slopes adjacent to highways under extreme rainfall conditions but also provides scientific and precise decision-making support for slope hazard assessment and protection engineering.

The UDEC model is widely used in the stability analysis of rocky slopes, especially under extreme rainfall conditions, and it can simulate the rainfall-induced changes in pore water pressure, weakening of shear strength, and the process of rock instability. Through this model, we can more accurately analyze the stability of slopes under rainfall, and combine it with the strength discount method to derive the safety coefficients under different rainfall conditions. In this study, the stability of the slope is calculated by establishing a discrete element model, setting the initial stress field and gradually discounting the strength parameters. The current discount factor FOS, which is the slope’s factor of safety, is recorded as 1.18 and 1.25 for Case A and Case B, respectively, when the slope failure occurs under extreme rainfall conditions.The difference between these two values of the factor of safety reflects the difference between the two in terms of the physical parameters of the rock mass and the geological conditions.

Case A has a rock mass with an internal friction angle (φ) of 45° and a cohesion (C) of 2.0 kPa, indicating that the rock mass has a high shear strength, which contributes to the stability of the slope. However, the steeper slope (185°∠70°) in Case A resulted in a more significant gravity effect under rainfall, which increased the risk of instability. Despite the higher strength of the rock mass, the factor of safety for Case A is still lower, indicating that the slope has a more significant effect on stability. Rainfall increased the pore water pressure, which exacerbated the damage to the rock mass. Therefore, the factor of safety of 1.18 reflects that the slope is close to a critical stable state and suggests that under similar geological conditions, steeply sloping areas are particularly susceptible to failure or collapses under the action of rainfall. In contrast, Case B, with an angle of internal friction (φ) of 38° and cohesion (C) of 1.5 kPa, has a lower rock strength, but it has a gentler slope (270°∠52°). The slower slope makes the gravitational force in Case B relatively small, and the infiltration of water and the accumulation of pore water pressure during rainfall are slower, which enhances the stability of the slope, resulting in a factor of safety of 1.25, which shows a stronger resistance to instability. Although the rock mass is weaker, the slope and relatively better stability of Case B result in a higher factor of safety, indicating that the slope is less susceptible to extreme rainfall.

Establishment of the evaluation index system

Selection of evaluation factors

Based on the collapse-affected areas obtained from simulations and field investigations, and to better avoid the dangers posed by collapses and reduce casualties and property losses along the roadsides, we established a 2.5 km buffer zone on both sides of the potential study area using GIS technology. This expanded the scope of the identified affected areas, allowing us to describe the hazards associated with collapse disasters over a larger region and conduct a comprehensive hazard assessment. After excluding the territorial parts outside of China, the final evaluation area for this study was determined. We carried out a detailed analysis of the various environmental factors in the study area, and in addition to the four selected indicators, we learnt that factors such as vegetation cover (NDVI) and Lithology also have a serious impact on slope stability (Table 5)303132 , NDVI is derived from remotely sensed data in 2023, which represents typical vegetation conditions in the study area, with little change in land use during this period. Ultimately, it is then determined which factors are most critical to slope stability, after which each indicator is quantified as a means of analysing the extent of the spatial distribution of these influencing factors (Fig. 6).

Table 5 Impact of indicator factors on collapse disasters.
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Fig. 6
figure 6figure 6

(a) Elevation, (b) Slope, (c) Slope direction, (d) NDVI, (e) Distance from road, (f) Distance from fault, (g) Distance from river, (h) Lithology, (i) Curvature. ArcGIS 10.8 (https://www.esri.com) was used for visualization.

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Correlation analysis

Correlation analysis is a statistical method used to analyze the degree of correlation between variables pairwise. Compared to traditional correlation analysis, this study employs a more advanced approach by utilizing the multivariate analysis and band statistics tool in ArcGIS software to perform statistical analysis on the raster data of indicator factors, simultaneously calculating the covariance and correlation matrices33. Subsequently, the data were visualized using Origin software to generate a heatmap (Fig. 7), illustrating the correlation relationships. The results indicate that the nine factors exhibit low correlations with each other, suggesting minimal mutual influence, thereby supporting the feasibility of subsequent model calculations. This method not only evaluates the strength of relationships between variables but also identifies independent variables with low correlations, providing a scientific basis and higher analytical precision for subsequent modeling efforts. As a result, the practicality and applicability of the research are significantly enhanced.

Fig. 7
figure 7

Heatmap of correlation among evaluation factors.

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Comprehensive evaluation model

Analytic hierarchy process

The Analytic Hierarchy Process (AHP), proposed by Thomas L. Saaty, is a multi-criteria decision-making method that breaks down complex decision problems into hierarchical levels, making it possible to assess the risk of collapse hazards in regions like Changbai County, which features complex geological and climatic conditions34,35. Through the application of AHP, the key factors contributing to collapses in the study area can be systematically evaluated and quantified, allowing for the determination of their relative significance. This process facilitates the creation of a collapse susceptibility map, which serves as a scientific foundation for regional disaster mitigation and resource distribution36,37. This method effectively compensates for the shortcomings of traditional qualitative analysis under complex geological conditions and demonstrates significant value in addressing slope collapses triggered by extreme rainfall.

  1. (1)

    Establishing a hierarchical structure model.

The evaluation indicators are categorized into three levels: the goal level, the criterion level, and the indicator level.

  1. (2)

    Constructing the judgment matrix.

This study incorporates the expertise of six experts from different fields, including climate change, geohazards, slope stability, environmental science, disaster risk assessment and emergency management. To ensure comprehensiveness, a pairwise comparison method was used to assess the relative importance of each indicator at different levels. The experts, who were selected for their extensive experience in their respective fields, participated in a structured discussion to assess and assign weights to the factors, ensuring the robustness and accuracy of the results of the assessment. The 1–9 scale method (Table 6) was applied to quantify the relative importance between evaluation factors (Table 7). To enhance the objectivity of the evaluation results, expert scoring was conducted, and pairwise comparisons of the evaluation factors were performed to construct the judgment matrix D.

$$\begin{aligned} D = \begin{bmatrix} D_{11} & D_{12} & \cdots & D_{1n} \\ D_{21} & D_{22} & \cdots & D_{2n} \\ \cdots & \cdots & \cdots & \cdots \\D_{n1} & D_{n2} & \cdots & D_{nn} \end{bmatrix} \end{aligned}$$
(3)

Here, Dij represents the relative importance of the i-th element compared to the j-th element.

Table 6 Average random consistency index (RI).
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Table 7 Pairwise comparison judgment matrix.
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  1. (3)

    Consistency test.

To verify the rationality of the weight determination method used in this study, a consistency test is required.

$$\:\text{C}\text{I}=\frac{{{\uplambda\:}}_{\text{m}\text{a}\text{x}}-\text{n}}{\text{n}-1}$$
(4)
$$\:\text{C}\text{R}=\frac{\text{C}\text{I}}{\text{R}\text{I}}$$
(5)

Here, \(\:{{\uplambda\:}}_{\text{m}\text{a}\text{x}}\) represents the maximum eigenvalue of the judgment matrix, \(\:\text{n}\) indicates the total number of indicators involved in the comparison, \(\:\text{C}\text{I}\) is the consistency test index, and \(\:\text{C}\text{R}\) is the consistency ratio. \(\:\text{R}\text{I}\) denotes the average value of the consistency test index. When \(\:\text{C}\text{R}\) < 0.1, the result is considered to meet the consistency requirement; when \(\:\text{C}\text{R}\) > 0.1, the values of the evaluation indicators in the judgment matrix are adjusted and recalculated until the consistency test is satisfied.

  1. (4)

    Weight calculation.

$$\:{\text{w}}_{\text{j}}=\frac{1}{\text{n}}\sum\:_{\text{i}=1}^{\text{n}}\frac{{\text{D}}_{\text{i}\text{j}}}{\sum\:_{\text{i}=1}^{\text{n}}{\text{D}}_{\text{i}\text{j}}}$$
(6)

Coefficient of variation method

The Coefficient of Variation method (CV) is a statistical approach used to evaluate the degree of variation in evaluation indicators. This method is particularly useful in multi-criteria decision-making as it objectively assigns different weights to indicators based on their variability, thereby effectively reducing the influence of subjective judgment38,39.

  1. (1)

    Coefficient of variation calculation.

$$\:{\text{V}}_{\text{i}}=\frac{{\text{S}}_{\text{i}}}{{\text{X}}_{\text{i}}}$$
(7)

Here, \(\:{\text{S}}_{\text{i}}\) represents the standard deviation of the i-th indicator, and \(\:{\text{X}}_{\text{i}}\)represents the mean value of the i-th indicator. Both evaluation factors are calculated using the multivariate analysis-band statistics tool in ArcGIS software.This method not only generates correlation hotspot maps to visualize the spatial relationship between indicators, but also calculates statistics such as mean and standard deviation more efficiently and accurately. Previous studies have fully demonstrated the use of GIS to generate correlation hotspot maps, and this study extends this method by including the calculation of the mean and standard deviation of each indicator in the same analytical framework33.

  1. (2)

    Weight calculation.

$$\:{\text{w}}_{\text{i}}=\frac{{\text{V}}_{\text{i}}}{\sum\:_{\text{i}=1}^{\text{n}}{\text{V}}_{\text{i}}}$$
(8)

Combined weight calculation

The single AHP is significantly influenced by subjective factors, and the resulting subjective weights cannot accurately evaluate the impact of each indicator factor on the hazard of rock slopes under extreme rainfall conditions (Table 8). Therefore, the Coefficient of Variation method is integrated to perform objective weighting (Table 9).

$$\:{\text{w}}_{\:}={{\upalpha\:}\text{w}}_{\text{i}}+{{\upbeta\:}\text{w}}_{\text{j}}$$
(9)

Since the single AHP relies on expert subjective judgments, subjective factors may carry significant weight in the allocation process, leading to less accurate evaluations of the impact of each indicator on the hazard of rock slopes under extreme rainfall conditions. Therefore, this study integrates the CV to perform objective weighting, compensating for the subjectivity bias in expert scoring within the AHP method and further enhancing the scientific validity and objectivity of the evaluation results38.

In the specific weight allocation process, this study adopts a linear weighting method that combines the subjective weight \(\:{\upbeta\:}\) and the objective weight \(\:{\upalpha\:}\) to balance their influences, thereby better assessing the collapse hazard of rock slopes along highways in Changbai County under extreme rainfall conditions. In this weighting formula, the subjective weight is primarily based on expert judgments regarding the influence of indicator factors, particularly their understanding of rock slope stability under extreme rainfall conditions. To emphasize the importance of expert opinions, the coefficient for subjective weights is set to 0.6. Meanwhile, the objective weight, derived using the Coefficient of Variation method, reflects the variability and inherent characteristics of the data for each factor and is assigned a coefficient of 0.4.

This weighting approach not only effectively integrates expert experience and judgment but also fully reflects the objective characteristics of the data. By using the combined AHP-CV weighting method (Table 10), it provides a more scientific and accurate evaluation of the collapse hazard of rock slopes along highways in Changbai County under extreme rainfall conditions compared to traditional single-weight allocation methods. This method offers a reliable scientific basis for disaster warning and prevention.

Table 8 AHP index factor weight table.
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Table 9 CV index factor weight table.
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Table 10 Combined weight table.
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Through the final combined weight table, it is evident that elevation and slope have the highest weight proportions, at 0.1652 and 0.1793, respectively, followed by direction and distance from road, at 0.1421 and 0.1029, respectively. This indicates that elevation and slope are the main intrinsic factors contributing to the collapse and damage within the study area.

Susceptibility assessment of collapse disasters

This study combines the results of field investigations with a comprehensive analysis of the geographical and geological environment, as well as external disaster-inducing factors. A hybrid approach, utilizing both subjective and objective methods, was applied to calculate the combined weight of each evaluation index. The Raster Calculator in ArcGIS was then used to assign values to these indices, and the natural break method was applied to categorize the susceptibility into five levels: very low, low, medium, high, and very high. This process resulted in a susceptibility zoning map (Fig. 8a). By integrating the strengths of DEM analysis and the AHP-GIS method, the study is able to accurately identify high-hazard areas under extreme rainfall conditions. DEM analysis provides key terrain features and slope units, while the AHP-GIS method enhances the model’s scientific rigor and accuracy by assigning appropriate weights to the influencing factors, ensuring reliable results even in complex terrain and geological conditions.

Fig. 8
figure 8

Susceptibility map of collapses along highways in Changbai County (a. Spatial distribution of collapse susceptibility, b. Area Proportion of Different Susceptibility Levels.) ArcGIS 10.8 (https://www.esri.com) was used for visualization.

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According to statistics (Fig. 8b), the area of very high susceptibility zones within the study area is approximately 124.39 km². These zones are mainly distributed on steep slopes with well-developed geological faults and sparse vegetation coverage, which are prone to the effects of heavy rainfall and road excavation. The high susceptibility zone covers an area of approximately 160.53 km2 and is mainly located in areas of softer rock and closer to roads. These areas have complex geological conditions, and hydrological factors during the rainy season can easily trigger slope instability. The moderate susceptibility zones have the largest area, approximately 185.09 km², and are mainly distributed in mid-altitude regions. Although these areas generally have better geological conditions, their gentle slopes are occasionally affected by water accumulation and debris flows. The low susceptibility and very low susceptibility zones cover areas of approximately 95.30 km² and 64.79 km², respectively. These zones are primarily distributed in regions with gentle slopes, dense vegetation, low annual rainfall, stable geological conditions, and minimal external influence.

In this study, the area under the curve (AUC) of the receiver operating characteristic curve (ROC) was used to assess the accuracy of the susceptibility mapping results (Fig. 9)40. The AUC values were obtained by SPSS software. Based on the fundamentals of the subject’s work characteristic curve, an equal number of collapse and non-collapse points were randomly selected from the results of the collapse susceptibility mapping to produce the ROC curve for this model and to determine the area under the curve AUC value. Figure 2 also shows the locations of these collapse sites to clearly illustrate the data used for the analysis, which were obtained from the Geological Hazards Investigation Bureau of Changbai Korean Autonomous County, Jilin Province.

The ROC curve is a common tool for evaluating binary classification models, which can clearly reflect the classification performance of the model under different thresholds.The area under the ROC curve (AUC value) is used to measure the overall accuracy of the model, and the closer the AUC value is to 1, the higher the accuracy of the model. From the ROC results in the figure, the AUC value is 0.908, which is a very good precision, indicating that the results of this susceptibility zoning have a high degree of accuracy and can be used in the evaluation of geological hazard.

Fig. 9
figure 9

ROC curve chart.

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Hazard assessment of collapse disasters

Rainfall return period

Hazard assessment is conducted based on susceptibility evaluation. Susceptibility only reflects the spatial hazard of geological disasters without involving temporal probability or triggering factors. Hazard assessment, on the other hand, focuses more on the probability of geological disasters occurring within a specific timeframe, incorporating both temporal probability and triggering factors such as rainfall and earthquakes41. Changbai County, located in a mountainous region, experiences rainfall as the primary triggering factor for geological disasters such as landslides and collapses. The intensity and frequency of rainfall directly affect slope stability, especially during heavy rainfall events, when water infiltrates the rock layers, leading to structural softening and inducing collapses42,43. In order to more accurately predict the probability of disaster occurrence, it becomes crucial to study the rainfall return period. In this study, rainfall data from 2011 to 2019 were selected, which can reflect the dynamic characteristics of climate change more effectively.Due to the fluctuating rainfall patterns in the study area, the use of data from these years can better capture the trends in recent years, especially the extreme rainfall events.In view of the increasing frequency of extreme weather events related to climate change, the time period is useful for assessing the rainfall-induced collapse hazard. The recent trends are representative of the recent trends, and by applying the Pearson Type III frequency curve formula, the rainfall amounts under different recurrence periods were calculated and the rainfall induced geohazards were assessed44. This method provides a quantitative analytical approach to the relationship between rainfall and geological disasters in Changbai County, offering a scientific basis for geological disaster early warning and risk management in the region.

Therefore, this study selects rainfall as an evaluation factor. By collecting the maximum daily rainfall over a consecutive nine-year period and calculating the mean value, the K-values for each year were subsequently derived based on the mean (Table 11).

Table 11 Maximum daily rainfall from 2011 to 2019.
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$$\:{\text{C}}_{\text{v}}=\sqrt{\frac{{{\Sigma\:}}_{\text{i}=1}^{\text{n}}{\left({\text{k}}_{\text{i}}-1\right)}^{2}}{\text{n}-1}}= 0.2678$$
(10)
$$\:{C}_{s}=\frac{\sum\:_{i=1}^{n}{\left({K}_{i}-1\right)}^{3}}{\left(n-3\right){C}_{v}^{3}}= 0.9929$$
(11)

Referring to the pearson type III frequency curve skewness coefficient (ϕ) table, the rainfall intensity for each probability in Changbai County was calculated (Table 12).

Table 12 Maximum daily rainfall under different probabilities in Changbai County.
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From the calculated rainfall intensities under different probabilities, the maximum daily rainfall for 10-year, 50-year, and 100-year return periods is 129.9 mm, 159.6 mm, and 171.4 mm, respectively, all reaching the intensity of extreme rainfall events. Under these conditions, highway rock slopes are subjected to significant rainwater erosion, leading to a notable increase in rock layer saturation, further weakening of weak structural planes, and a substantial reduction in slope stability. This significantly increases the probability of collapse-related geological disasters. This indicates that under extreme rainfall conditions, protective measures for highway slopes in the region need to be strengthened to mitigate potential hazards.

Evaluation methods and results

The hazard assessment method in this study utilizes the hazard index under different rainfall conditions caused by the rainfall intensities predicted for 10-year, 50-year, and 100-year return periods based on the Pearson Type III curve.

$$\:{\text{H}}_{\text{i}}=\frac{{\text{Y}}_{\text{i}}}{{\text{Y}}_{\text{m}\text{a}\text{x}}}{\text{P}}_{\text{i}}$$
(12)
$$\:{\text{P}}_{\text{i}}=\text{L}/{\text{L}}_{\text{m}\text{a}\text{x}}$$
(13)

In the formula, \(\:{\text{H}}_{\text{i}}\) represents the hazard index of the i-th evaluation unit under a specific condition, \(\:{\text{Y}}_{\text{i}}\) represents the susceptibility index of the i-th evaluation unit, \(\:{\text{Y}}_{\text{m}\text{a}\text{x}}\) represents the maximum susceptibility index, \(\:{\text{P}}_{\text{i}}\) represents the instability probability under a specific condition, \(\:\text{L}\) represents the rainfall amount under different conditions (10-year, 50-year, and 100-year return periods), and \(\:{\text{L}}_{\text{m}\text{a}\text{x}}\) represents the maximum daily rainfall recorded in the study area over the past nine years. This evaluation method differs from traditional approaches by effectively integrating the collapse susceptibility assessment of slope units with the rainfall probability formula for Changbai County, demonstrating strong scientific rigor and practical applicability.

Based on the susceptibility index within the study area, combined with rainfall probabilities, the hazard index of evaluation units under different rainfall conditions was analyzed and overlaid using GIS. The natural break method was then applied to divide the results into five hazard levels, resulting in the final hazard zoning map (Fig. 10).

Fig. 10
figure 10

Collapse hazard maps under different rainfall probabilities along highways in Changbai County: (a) Once in 10 years, (b) Area proportion of different hazard levels for a 10-year return period, (c) Once in 50 years, (d) Area proportion of different hazard levels for a 50-year return period, (e) Once in 100 years, (f) Area proportion of different hazard levels for a 100-year return period. ArcGIS 10.8 (https://www.esri.com) was used for visualization.

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This study analyzes the collapse hazard zoning areas under different rainfall conditions (Fig. 10). The results show that as the rainfall return period increases, the proportion of very high hazard areas rises significantly, reaching 38.68% for a 100-year return period. Conversely, the proportion of low hazard areas decreases from 6.7% for a 10-year return period to 1.56% for a 100-year return period, reflecting the significant impact of heavy rainfall on regional geological stability. The proportion of medium hazard areas remains relatively stable, indicating that these areas possess a certain degree of stability under rainfall conditions but still carry a potential hazard of collapse. The table below (Table 13) shows the area distribution for different zones under various rainfall probabilities.

Table 13 Area statistics of each hazard level under different rainfall probabilities (km2).
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This study examines the susceptibility of rocky slopes along highways in Changbai County to failure under different rainfall scenarios and return periods, focusing on the significant expansion of high-hazard zones from the 10-year return period to the 100-year return period. As the return period increases, the intensity and frequency of rainfall rise, leading to more extreme weather events. Rainfall intensity during a 100-year return period is typically much higher than during a 10-year return period, resulting in increased soil saturation, higher runoff volumes, and a greater potential for slope instability. The analysis shows that very high and high hazard zones are primarily concentrated in areas with steeper slopes and more complex geological conditions, which closely align with the susceptibility zoning. These areas are often characterized by low elevations, steep slopes, and intense human engineering activities. Consequently, areas that might not have been considered at hazard under a 10-year return period become highly susceptible under the extreme conditions of a 100-year event, illustrating a direct correlation between the severity of extreme rainfall events and the expansion of slope failure-prone areas. This highlights the importance of incorporating longer return periods into hazard assessments for effective disaster preparedness, risk management, and strengthening slope protection measures in regions with frequent rainfall to prevent collapse disasters.

Rainfall analysis and model validation

Rainfall analysis

Through statistical analysis of daily rainfall from 2011 to June 2020, the rainfall characteristics in the study area exhibit seasonal fluctuations and extreme rainfall events (Fig. 11). Notably, in 2013 and 2014, the maximum rainfall reached 120.2 mm and 147.0 mm, respectively. Both rainfall amounts and the number of rainy days significantly increased during these years, indicating higher rainfall intensity and frequent extreme rainfall events. These heavy rainfall events directly affect slope stability, increasing pore water pressure and reducing the shear strength of soil and rock masses, thereby significantly increasing the hazard of collapse. Once rainfall exceeds a certain threshold, it can rapidly trigger collapse-related geological disasters45.

The analysis indicates that, under the context of climate change, the frequency of extreme rainfall events may further increase in the future, exacerbating the probability of slope instability. By analyzing daily rainfall data, high-risk periods can be identified, especially during consecutive days of heavy rainfall, when the potential hazard of collapse is particularly pronounced. Taking proactive measures for slope monitoring and protection is therefore crucial.

In addition, the statistical analysis of daily rainfall helps identify the critical rainfall threshold that triggers collapses, verifying the model’s ability to predict slope stability under different rainfall conditions. This result provides technical support for developing accurate rainfall early warning mechanisms in the future, facilitating the timely issuance of warning signals and reducing the occurrence of potential disasters.

Fig. 11
figure 11

10-Year daily rainfall statistics for Changbai County.

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Model validation

To further determine the reliability of the model, this section conducts a validation analysis using 291 collapse hazard points surveyed in 2015 and 2022 around the highway. By utilizing ArcGIS software, the spatial distribution of collapse points was overlaid with the hazard zoning maps under different rainfall scenarios from this study (Fig. 12). The results show that the collapse points are primarily concentrated within the very high hazard zones of the study area, with a small portion located in high hazard zones and medium hazard zones, while almost no collapse points are found in low hazard zones and very low hazard zones.

Fig. 12
figure 12

Collapse points along highways in Changbai County. ArcGIS 10.8 (https://www.esri.com) was used for visualization.

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By comparing the number of collapse points contained in the geological hazard zoning of highway slopes in Changbai County under different rainfall scenarios (Fig. 13), it was found that as rainfall intensity increases within the study area, the number of collapse points in low hazard zones remains small and shows no significant change. In medium hazard zones, the number of collapse points eventually decreases considerably, while in high hazard zones and very high hazard zones, the number of collapse points gradually increases. This phenomenon occurs because rainfall significantly weakens slope stability by increasing pore water pressure, reducing the shear strength and cohesion of rock layers. Under extreme rainfall conditions, combined with intense human engineering activities on both sides of the highway, slopes are more likely to become unstable and collapse46. Heavy rainfall not only triggers surface water erosion but also softens rock layers through water infiltration, further exacerbating the structural damage to slopes. When rainfall exceeds a critical threshold, the sliding surface and fracture water pressure within slopes increase significantly, and the probability of collapse rises rapidly. Therefore, rainfall is one of the main triggering factors for slope collapses, particularly under conditions of prolonged rainfall or short-term heavy rainfall, posing a severe threat to slope stability.

Fig. 13
figure 13

Collapse point statistics under different rainfall probabilities.

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Through further validation analysis, not only was the effectiveness of the model used in this study confirmed, but it also demonstrated that slope units can effectively represent the comprehensive geomorphological characteristics of different slopes, significantly enhancing the reliability and validity of the hazard assessment results.

Discussion

This study has achieved three key innovations and contributions in the field of research on rock collapses induced by extreme rainfall. First, a slope unit zoning model was introduced to replace the traditional grid cell method. This model allows for a more natural capture of complex geomorphological features such as ridges and faults, reduces redundant calculations in flat areas, and significantly improves the spatial accuracy and computational efficiency of collapse hazard zoning. Second, the study adopted the AHP-CV combined weighting method, integrating the subjectivity of expert judgment with the objectivity of data variability. This method quantitatively evaluated the weights of key indicators such as elevation, slope, aspect, and NDVI, optimizing the scientific and rational basis of factor weights and addressing the limitations of single weighting methods. Lastly, through the integration of UDEC numerical simulation and GIS technology, this study accurately simulated the instability process of rock slopes under extreme rainfall conditions, revealing the dynamic mechanisms of tensile failure and collapse as well as the movement paths of collapse masses. This provides new methods and insights for understanding the mechanisms of collapses induced by extreme rainfall.

Through UDEC numerical simulations and comparisons with real cases, the mechanisms of rock slide occurrence, the safety coefficient at critical damage, and the spatial distribution pattern are discussed in depth. The simulation results show that the accumulation of pore water pressure and the reduction of shear strength along joint planes are the primary causes of rock slope instability. In the early stages, water infiltration softens the joint planes, leading to the formation of microcracks in the frontal area. As rainfall continues, these cracks gradually expand and connect, resulting in tensile failure and a compound collapse mechanism, ultimately causing large-scale collapse masses to accumulate at the slope base. In terms of spatial distribution, the results indicate that very high hazard zones are mainly concentrated in areas with steep slopes, sparse vegetation, and proximity to faults, particularly along the G331 National Highway. As the rainfall return period increases, the proportion of very high hazard zones rises significantly, from 118.43 km² for a 10-year return period to 243.85 km² for a 100-year return period. This demonstrates that rainfall intensity has a significant impact on slope stability, and collapse hazards intensify further under high-intensity rainfall conditions.

To validate the effectiveness and reliability of the model, this study conducted verification analysis through two methods. First, the ROC curve was used to validate the collapse susceptibility model, and the results showed that the model’s AUC value was 0.908, indicating high accuracy and reliability. The model effectively identifies very high susceptibility zones and high susceptibility zones. Second, a spatial comparison was conducted between the model’s zoning results and 291 collapse hazard points obtained from field surveys in 2015 and 2022. It was found that the collapse points were primarily distributed in very high hazard zones and high hazard zones, with a small number in medium hazard zones, and almost none in low hazard zones. This result further confirmed the model’s accuracy in identifying spatial distributions. Additionally, the validation results demonstrated that the slope unit zoning method effectively represents the comprehensive geomorphological characteristics of different slopes, improving the accuracy and applicability of hazard assessment.

Despite achieving certain breakthroughs in methods and results, this study still faces some limitations and challenges. First, in terms of data limitations, the rainfall data used in this study is based on the maximum daily rainfall and does not account for the dynamic impacts of rainfall duration and cumulative rainfall on slope stability, which may underestimate the potential risks of collapse triggered by short-term intense rainfall. Additionally, the results of the UDEC numerical simulation rely on initial parameter settings, particularly the selection of rock mass physical and mechanical parameters and pore water pressure, which affects the generalizability of the results to some extent. Second, in terms of methodological limitations, the study focuses primarily on rainfall as the sole triggering factor and does not incorporate a coupled analysis framework that includes multiple factors such as earthquakes, temperature changes, and human engineering disturbances, leading to a less comprehensive analysis of the disaster causes. Furthermore, the slope unit zoning method requires significant memory and time during the computation process, making it difficult to apply to larger areas or higher-resolution hazard assessments. Further optimization of computational methods is needed to improve efficiency47.

To address the limitations of this study, future research can be optimized and expanded in the following aspects. First, a multi-factor coupling model can be further integrated by incorporating multiple disaster-triggering factors such as rainfall, earthquakes, temperature changes, and human engineering disturbances into the evaluation system to investigate the collapse mechanisms and hazard distribution patterns under the interaction of these factors. Second, data precision can be improved by introducing higher-resolution remote sensing images and real-time monitoring data to analyze the rainfall-collapse response mechanisms at different temporal scales, accurately obtain the physical and mechanical parameters of rock masses, and enhance the accuracy and stability of numerical simulation results. Additionally, the evaluation framework proposed in this study can be applied to other regions with complex terrain and geological conditions to validate the model’s generalizability and reliability. Meanwhile, by integrating machine learning and big data technologies, the model can achieve more efficient and broader-scale automatic identification and evaluation of collapse hazards, enhancing its practicality and applicability.

In conclusion, this study, through the introduction of slope unit zoning, the AHP-CV combined weighting method, and UDEC numerical simulation, revealed the mechanisms of rock collapses induced by extreme rainfall and quantified the hazard distribution patterns under different rainfall scenarios. The results indicate that very high hazard zones expand significantly with increasing rainfall intensity, primarily distributed in areas with steep slopes and low vegetation coverage. Field validation further confirmed the high accuracy and applicability of the model. Future research will focus on multi-factor coupling analysis, data precision optimization, and method expansion to enhance the scientific rigor and generalizability of the model, providing more comprehensive technical support and theoretical basis for the prevention and control of geological hazards along mountainous highways.

Conclusion

This study, based on the slope unit zoning model, UDEC numerical simulation, and GIS technology, conducted a systematic mechanism analysis and hazard assessment of rock collapses induced by extreme rainfall along highways in Changbai County. The main conclusions are as follows:

(1) The study introduced the slope unit zoning model to replace the traditional grid cell method, enabling more accurate capture of geomorphological features such as ridges and faults, thereby improving the spatial accuracy of collapse hazard assessments. Very high susceptibility zones are mainly distributed in areas with well-developed faults, steep slopes, and sparse vegetation, accounting for 19.74% of the total area and exhibiting significant spatial clustering.

(2) Using the Pearson Type III frequency curve, rainfall intensities for different return periods were calculated, and collapse hazards under various rainfall scenarios were assessed. The results indicate that as rainfall intensity increases, the proportion of very high hazard zones rises significantly, reaching 38.68% under 100-year return period rainfall conditions, reflecting a positive correlation between rainfall intensity and collapse hazard.

(3) Elevation, slope, aspect, and distance to roads are the main factors influencing slope stability, with slope and elevation weights being 0.1793 and 0.1652, respectively. Under the impact of heavy rainfall, the increase in pore water pressure and the reduction in the shear strength of joint planes are the primary mechanisms of rock slope instability, further intensifying the tensile failure-collapse compound failure process.

(4) The hazard assessment model proposed in this study was validated using the AUC value, achieving an accuracy of 0.908, which indicates high reliability and applicability of the model. The distribution of actual collapse points is highly consistent with the model results, further confirming the effectiveness of the model.

(5) The research results provide a scientific basis for geological disaster warning and prevention in Changbai County and similar regions. For areas with extremely high hazard, real-time monitoring and slope protection measures should be strengthened to prevent collapse disasters induced by extreme rainfall.