Landslide Risk Assessment Along Railway Lines Using Multi-Source Data: A GameTheory-Based Integrated Weighting Approach for Sustainable Infrastructure Planning

Abstract

Landslides threaten railway safety and operational sustainability. This study developed a game theory-based weighting method that integrates the Entropy Weight Method (EWM) and CRITIC with Analytic Hierarchy Process (AHP) techniques to determine indicator weights, reducing single-method biases. A risk assessment was conducted that coupled hazard likelihood with exposure. These components formed a comprehensive risk index visualized as a landslide risk map. A GIS-integrated assessment of Shandong Province railways incorporated multi-source data to support resilient infrastructure planning. The results show that high-risk zones consistently coincide with mountainous terrain, high-precipitation areas, and concentration of the population/economic activity, identifying critical intervention areas. The integrated weighting method proves effective for multi-criteria risk analysis. Decision-makers can prioritize mitigation measures using these insights, enhancing railway resilience and reducing regional disaster risk.

1. Introduction

According to data from the Railway Bureau, as of the end of December 2022, China’s railway network spanned approximately 155,000 km, traversing regions with highly diverse geological and meteorological conditions. Landslides, debris flows, and collapses along railway corridors can destabilize roadbeds, bury tracks, and cause derailments. Therefore, it is urgent to conduct a comprehensive analysis and prediction of landslide disasters. Landslide risk analysis is a complicated engineering problem, which involves comprehensive analysis of many factors [1]. It constitutes the key technical support for traffic infrastructure safety and sustainable land use.

The existing literature on railway elasticity has formed a certain theoretical framework, such as Bešinović’s definition of resilience-related content [2], but its limitations are gradually becoming apparent. Zhang et al. found that organizational structure and efficiency promote the speed of functional recovery [3]. Jiang et al. emphasized the importance of emergency response and early-warning monitoring capabilities [4]. Di Nardo et al. conducted an elasticity assessment in a high-capacity railway section [5]. Research on railway safety needs to break through the technological optimization of a single dimension to cope with the operating environment of multi-disaster coupling and increased uncertainty.

According to the basic definition of risk as the likelihood and loss of an event, macro-level disaster risk assessment is mainly conducted from two perspectives: the likelihood and the degree of harm of the disaster. Vulnerability assessment refers to obtaining the spatial distribution of potential disasters based on pre-disaster conditions [6]. By combining various landslide factors and their impact degrees, the weight of indicators can be determined [7], which can reveal the spatial likelihood of landslide occurrence [8]. Scholars have combined intelligent methods [9], utilizing multi-source data [10], dynamic characteristics of landslide displacement [11], and other techniques to explore deep features of disasters, and thus achieving the quantification of spatial differences in disaster susceptibility [12]. Many scholars have combined data-driven methods with disaster susceptibility assessment [13], and the combination of deep learning and susceptibility has greatly promoted technological innovation [14]. Deep learning can quantify disaster characteristics [15], fully leveraging the performance advantages of different models [16]. Mohammad et al. applied multiple metaheuristic algorithms to the Adaptive Neuro-fuzzy Inference System (ANFIS) [17]. Zhang et al. constructed a comprehensive explanatory framework for landslide-susceptibility assessment models, analyzing the regional characteristics and spatial heterogeneity of landslide-influencing factors [18]. Hazard assessment refers to the degree of risk after a disaster occurs, such as estimating its potential impact area [19], in order to take corresponding prevention and control measures [20]. The subjective evaluation method is based on a deep understanding of the scene [21], such as Panchal et al.’s analysis of the disaster risk of specific transportation routes through subjective modeling [22]. With the continuous expansion of the field of machine learning, data-driven methods have become a hot research direction [23], including machine learning models [24], such as logistic regression [25] and artificial neural networks [26], as well as horizontal comparisons between various models [27]. Mandal Kanu et al. used multiple machine learning models for landslide sensitivity analysis [28]. Tang et al. utilized five convolutional neural networks to extract ten predictive factors [29]. Wei et al. implemented Bayesian-optimized support vector machines for landslide assessment in Nanping [30]. Chen et al. validated Hoeffding Tree algorithms in susceptibility modeling [31]. Ge Y et al. enhanced rock discontinuity identification through deep learning [32].

Game theory, as an emerging weight combination technique, can achieve scientific integration of multi-source information [33] by coordinating the conflict between subjective and objective weighting [34]. Empirical applications demonstrate its effectiveness: Chen et al. combined trapezoidal fuzzy AHP, entropy weighting, and game theory for indicator integration [35], while Ma employed game theory to compute Social Vulnerability Indices [36]. This approach mitigates methodological bias in multi-criteria decision frameworks, enhancing model performance [37]. Contemporary research incorporates remote sensing/GIS systems for multidimensional assessment [38], with multi-source fusion and deep learning emerging as prominent methodologies [39]. For instance, Cao et al. utilized In-SAR and UAV multi-source data to rectify traditional landslide-zoning inaccuracies [40].

The main contribution of this study is that it proposes a weight combination framework based on the correlation between various influencing factors and disaster causation mechanisms in the research area, and constructs an evaluation system consisting of 10 risk indicators.

The rest of this study is organized as follows. Section 2 presents the research framework and methodology. Section 3 describes the research area and data source. Section 4 covers the experiments and discussion, and finally, Section 5 concludes the study.

2. Research Framework and Methodology

The ideological diagram of this paper is shown in Figure 1. This paper evaluates the risk level and distribution of landslide disasters in various regions through game theory combination weight calculation based on multi-source monitoring data.

Subjective weighting methods are susceptible to cognitive bias, introducing decision-making uncertainty. Objective approaches such as EWM and CRITIC eliminate subjective influence, but exhibit strong data dependency. This study integrates both weights through game-theoretic combined weighting to enhance methodological robustness.

2.1. Subjective Weight: Analytic Hierarchy Process

The AHP is a structured decision-making method where experts compare evaluation indicators pairwise to determine their relative importance [41]. By breaking down complex problems into hierarchical levels, the AHP enables systematic comparisons using simple numerical ratings. These comparisons are mathematically synthesized to calculate precise weights for each indicator, reflecting their relative significance. A consistency check ensures logical coherence in expert judgments. By integrating both quantitative data and qualitative expertise into a transparent framework, AHP helps decision-makers to objectively prioritize competing factors in complex evaluations.

2.2. Objective Weight

2.2.1. Entropy Weight

Information entropy quantifies dataset uncertainty by measuring value distribution uniformity across outcomes [42]. High entropy indicates chaotic distributions with greater uncertainty and variability; low entropy reflects ordered uniformity with higher predictability and consistency. The calculation steps of the EWM are as follows:

• Normalize sample data to scale the raw data of each indicator to the 0–1 range and eliminate the influence of dimensionality. For n samples with m indicators, the value of the j-th indicator of the i-th sample is normalized by $m$ to represent the sample data. For $n$ samples with m indicators, the value of the j-th indicator of the i-th sample is represented by $x_{ij}(i=1,\dots ,n;j=1,\dots ,m)$. Among them, $x_{ij}$ represents the indicator of the corresponding order; ${\left(x_j\right)}_{max}$ represents the indicator value corresponding to the sample with the highest indicator value under this indicator, while ${\left(x_j\right)}_{min}$ represents the indicator value with the lowest corresponding indicator value:

  $$x_{ij}^{\prime }={\displaystyle \frac{x_{ij}-{\left(x_j\right)}_{min}}{{\left(x_j\right)}_{max}-{\left(x_j\right)}_{min}}}$$

  (1)

  $$x_{ij}^{\prime }={\displaystyle \frac{{\left(x_j\right)}_{max}-x_{ij}}{{\left(x_j\right)}_{max}-{\left(x_j\right)}_{min}}}$$

  (2)
• Calculate the weight of each sample relative to the total sample under the indicator:

  $$p_{ij}={\displaystyle \frac{x_{ij}^{\prime }}{\sum _{i=1}^n{x}_{ij}^{\prime }}},(i=1,\dots ,n;j=1,\dots ,m)$$

  (3)
• Calculate entropy value of the calculation indicators $e$ to obtain the degree of difference between the different indicators:

  $$e_j=-{\displaystyle \frac{\sum _{i-1}^n{p}_{ij}\ln \left(p_{ij}\right)}{\ln \left(n\right)}},(i=1,\dots ,n;j=1,\dots ,m)$$

  (4)
• The indicator information entropy reduction $d$ is calculated using the index entropy value:

  $$d_j=1-e_j,(j=1,\dots ,m)$$

  (5)
• The final weights are calculated based on the redundancy of the information entropy of the indicators. The information value scores of each indicator are converted into percentage weights:

  $$o_j={\displaystyle \frac{d_j}{\sum _{j=1}^m{d}_j}},(j=1,\dots ,m)$$

  (6)

2.2.2. CRITIC

The CRITIC method objectively determines indicator weights by evaluating both relative importance and inter-indicator conflict [43]. It quantifies intensity via standard deviation—where higher variability denotes greater discrimination power—and measures conflict through negative correlation coefficients. Strong positive correlations trigger weight reduction to eliminate information redundancy. By synthesizing these mathematically derived metrics, CRITIC produces bias-resistant weights that reflect both the distinguishing capacity of indicators and their unique informational contributions within multivariate systems.

The specific calculation steps of the CRITIC method are as follows:

• Sample data regulation. The calculation process is consistent with Formulas (1) and (2).
• Quantification of the degree of dispersion of sample values within the indicator using standard deviation. If there is a significant difference in the data of a certain indicator, then the indicator has strong discriminative ability.

  $$S_j=\sqrt{{\displaystyle \frac{1}{n-1}}\sum _{i=1}^n{(X_{ij}^{\prime }-\overline{X_j^{\prime }})}^2},(i=1,\dots ,n;j=1,\dots ,m)$$

  (7)
• The degree of contradiction, obtained by the calculation below, reveals the correlation between different evaluation indicators. $R$ is used to indicate the degree of contradiction between the indicator and other indicators. $r_{ij}$ represents the Pearson correlation coefficient between indicators.

  $$R_j=\sum _{i=1}^n(1-r_{ij}),(i=1,\dots ,n;j=1,\dots ,m)$$

  (8)
• Calculation of the information bearer capacity $C$, obtained by the standard deviation of the indicator and the product of the degree of conflict calculation. For $C$ to be a valid metric, the underlying data must exhibit significant variance while simultaneously conveying independent information:

  $$C_j=S_j{R}_j,(j=1,\dots ,m)$$

  (9)
• Calculation of the CRITIC weight of each indicator:

  $$W_j={\displaystyle \frac{C_j}{\sum _{j=1}^m{C}_j}},(j=1,\dots ,m)$$

  (10)

2.3. Calculation of Combination Weight in Game Theory

Landslide risk arises from the complex interactions between various influencing factors. While Bayesian networks depend on expert-derived prior probabilities, and fuzzy logic models face constraints from predefined rule structures, game theory offers a dynamic solution. Through combination weighting, it strategically reconciles subjective and objective weighting approaches, integrating multiple methodologies to achieve more balanced and robust risk assessment outcomes [44]. The calculation method is as follows:

• The weight vector group is computed according to $c_k=\{c_{k1},c_{k2},\dots ,c_{km}\}(k=1, 2\dots , L)$, where ${\mathrm{c}}_{\mathrm{k}}$ is the weight combination calculated by the corresponding method, $L$ is the number of weighted methods, m is the number of indicators, and ${\alpha }_k$ is a linear combination coefficient to be optimized.

  $$c_j=\sum _{k=1}^L{\alpha }_k{c}_k^T,c_k>0$$

  (11)
• Game theory is used to achieve consistency and compromise of different weight vectors. The goal is to minimize the deviation of c and ${\mathrm{c}}_{\mathrm{k}}$ by optimizing the linear combination coefficient ${\mathsf{\alpha }}_{\mathrm{k}}$.

  $$\mathrm{m}\mathrm{i}\mathrm{n}‖\sum _{k=1}^L{\alpha }_k{c}_k^T-c_i^T‖,(i=1,\dots ,L)$$

  (12)

According to the micro-division nature of the matrix, the first-order guidance conditions optimized above are as follows:

$$\sum _{k=1}^L{\alpha }_k{c}_i{c}_i^T=c_i{c}_i^T$$

(13)

The linear equation corresponding to the above formula is as follows:

$$\left[\begin{array}{ccc}{c}_1{c}_1^T& \dots & c_1{c}_L^T\\ ⋮& \ddots & ⋮\\ c_L{c}_1^T& \dots & c_L{c}_L^T\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ ⋮\\ {\alpha }_L\end{array}\right]=\left[\begin{array}{c}{c}_1{c}_1^T\\ ⋮\\ c_L{c}_L^T\end{array}\right]$$

(14)

3.

The linear combination coefficient is returned.

$${\alpha }_k^{\prime }={\displaystyle \frac{{\alpha }_k}{\sum _{k=1}^L{\alpha }_k}}$$

(15)

4.

The results of the combination of game theory are calculated to ensure that the final weights are neither biased towards one-sidedness of human judgment nor trapped in the mechanical nature of pure data calculation, thus obtaining a more scientific and comprehensive weight result.

$$c^{\prime }=\sum _{k=1}^L{\alpha }_k^{\prime }{c}_k^T$$

(16)

3. Research Area and Data Source

3.1. Research Area Scene Characteristics

Comprehensive monitoring systems for landslide disasters employ specialized equipment to track both internal and external slope dynamics. Various monitoring equipment and their monitoring content are shown in Figure 2 below.

While these methods effectively capture individual landslide deformation and hydrological characteristics, spatial coverage limitations and multi-source data integration constraints impede regional-scale dynamic risk assessment. This study focuses on five cities along the Beijing–Shanghai railway in Shandong Province: Dezhou, Jinan, Jining, Tai’an, and Zaozhuang. Shandong’s coastal location between the Beijing–Tianjin–Hebei and Yangtze River Delta economic zones features a temperate monsoon climate with frequent extreme rainfall in the summer. Sand-rich strata in this region elevate landslide susceptibility on steeper slopes. The study area characteristics are illustrated in Figure 3.

There is a significant amount of critical infrastructure—such as transportation, energy, and communication facilities—along the Beijing–Shanghai corridor. Rainfall-triggered landslides may damage this infrastructure, risking transportation and energy-supply disruptions. The characteristics of the research area are as follows:

• High safety requirements for the railway, which handles substantial passenger and freight traffic and serves as a vital north–south corridor. Its operational stability directly impacts socioeconomic health.
• Diverse disaster exposure along its geographically varied route, including landslides, floods, earthquakes, debris flows, avalanches, windstorms, fires, and explosions.
• Reduced slope stability due to the coastal location and summer rainfall. Precipitation moistens surface soil; subsequent infiltration increases soil water content, accelerates erosion, and promotes loosening.
• Complex disaster-influencing factors spanning geology, topography, climate, and human activities. Factor combinations and intensities vary regionally, creating significant spatial differences in disaster likelihood and impact severity.
• Challenging landslide rescue operations owing to sudden onset, large-scale destruction, and complex post-disaster terrain. In addition, unstable geological conditions after a landslide may also pose a threat to the safety of rescuers, increasing the difficulty and risk of rescue work.

Under the comprehensive influence of the complex surrounding environment, the causes of landslide disasters are complex. Common influencing factor categories, shown in Figure 4, include environmental risk factors predisposing the area to disasters, vulnerability factors governing damage severity in the study area, and internal disaster-reduction capacity. These factors are classified into four aspects based on their respective objects.

This paper selects nine landslide-influencing factors for the five cities along the Beijing–Shanghai corridor in Shandong Province, based on historical research and regional characteristics. These indicators comprehensively quantify four risk dimensions: topography, hydrometeorology, anthropogenic factors, and socioeconomic exposure. The integrated system spans the full risk spectrum, from natural predisposing conditions to human-induced stressors.

3.2. Data Source and Processing

Based on the monitoring data along the railway, this paper combined research results in the field, selected the environmental impact factors that have a great impact on landslide disasters, and evaluated the risk of landslide disasters. The sources of various analysis data is shown in

Table 1. Data source table.

Data Name	Data Source
Digital elevation	Geographical Space Data Cloud Official Website
Sand content	Resource and environmental science data platform
Land use type	Resource and environmental science data platform
River distribution	Resource and environmental science data platform
Annual rainfall	National Meteorological Science Data Center; WorldClim
Average land GDP	Resource and environmental science data platform
Population density	National Earth System Science Data Center
Railway line data	Railway planning, railway live data, and field survey data
Monthly displacement monitoring data	National Glacier Frozen Earth Desert Science Data Center
Daily rainfall and reservoir water level	National Glacier Frozen Earth Desert Science Data Center

.

According to the occurrence of landslide disasters in the research area, the selected evaluation indicators were divided into two types, as required for risk analysis: possibility and consequences. Among them, precipitation, elevation, slope, land use type, river distance, sand content, and danger of landslide displacement are used as likelihood indicators, and population density, road distance, and average land GDP are used as the consequence indicators. Due to the difficulty of data collection, this paper used 70% of the randomly selected historical landslide points within the region as high-risk landslide risk points for the test set, and the remaining 30% of the landslide points for validation. The density of high-risk landslide risk points in the test set was used as one of the regional risk-influencing factors. A comprehensive analysis framework based on evaluation indicators identifies high-risk areas and formulates effective disaster reduction strategies. This provides a scientific basis for achieving harmonious human–nature coexistence and promoting regional sustainable development. The distribution of the various factors is shown in Figure 5.

Due to the inconsistent accuracy of the original data for each evaluation factor, in order to better analyze the data, data of each evaluation factor was resampled to the same-resolution evaluation unit for data preprocessing and feature extraction. Due to the significantly lower resolution of the population data compared to the other datasets, resampling was performed at a coarser resolution to ensure consistency in spatial analysis. Within ArcMap, the Resampling tool standardized raster datasets to fixed dimensions using nearest-neighbor interpolation, with concurrent spatial-extent alignment.

4. Experiment and Discussion

4.1. Data Processing of Regional Influencing Factors

Through statistical analysis of various data, the data of influencing factors were quantified according to different data dimensions and ranges, historical disaster records, and professional evaluation by experts. Structured data within the study area were classified into five levels using the equal-interval method, while unstructured data such as land use types were categorized into five levels based on expert assessment, as presented in

Table 2. Data quantification table.

Evaluation Indicator	Extremely Low	Low	Medium	High	Extremely High
Elevation (m)	<77	77–174	174–309	309–522	>522
Precipitation (mm/mon)	<4.46	4.46–7.84	7.84–11.23	11.23–14.61	>14.61
Land use	Water body, sandy land, ice and snow coverage	Farmland, urban area, arable land	Wetland, grassland, rare tree grassland	Multi-tree grassland, open shrub forest	Mixed forests, evergreen broad-leaved forests, evergreen needle-leaf forests
Slope (°)	<2.66	2.66–7.02	7.02–14.01	14.01–22.59	>22.59
River distance (km)	>0.74	0.51–0.74	0.32–0.51	0.15–0.32	<0.15
Line distance (km)	>0.76	0.51–0.76	0.32–0.51	0.15–0.32	<0.15
Sand content (%)	<37	37–48	48–53	53–62	>62
Population density (persons/km2)	<931.64	931.64–3566.73	3566.73–9582.43	9582.43–22,146.51	>22,146.51
Average land GDP (10,000 yuan/km2)	<4511	4511–14,098	14,098–39,943	39,943–10,9221	>109,221

.

Correlations among evaluation factors like elevation may introduce analytical bias. To ensure accuracy and reliability, risk indicators should maintain maximum independence. Therefore, this study used the Pearson correlation coefficient to evaluate the correlations, as presented in

Table 3. Each factor’s correlation coefficients.

	Digital Elevation	Rainfall	Land Use Type	Slope	River Distance	Line Distance	Sand Content	Population Density	Average Land GDP
Digital elevation	1.00	0.44	−0.24	0.71	0.44	−0.11	0.45	−0.06	0.09
Rainfall	0.44	1.00	−0.12	0.35	−0.15	−0.34	0.12	0.06	0.30
Land use type	−0.24	−0.12	1.00	−0.24	−0.02	0.05	−0.09	0.00	−0.05
Slope	0.71	0.35	−0.24	1.00	0.16	−0.07	0.34	−0.06	0.07
River distance	0.44	−0.15	−0.02	0.16	1.00	0.26	0.24	−0.08	−0.20
Line distance	−0.11	−0.34	0.05	−0.07	0.26	1.00	−0.14	−0.11	−0.35
Sand content	0.45	0.12	−0.09	0.34	0.24	−0.14	1.00	−0.03	0.03
Population density	−0.06	0.06	0.00	−0.06	−0.08	−0.11	−0.03	1.00	0.31
Average land GDP	0.09	0.30	−0.05	0.07	−0.20	−0.35	0.03	0.31	1.00

. Finally, the evaluation indicators of the risk analysis in this study are shown below. Because they are located in the same geographical area, there are special links between certain magnitudes of factors. For example, the land type of areas with high population density is mostly cities, but the correlation between areas with low population density and landslides is different. For example, the probability of landslides in forest areas with low population density is lower, while the probability of landslides in grassland areas with the same low population density is higher. Among them, the correlation coefficient between digital elevation and river distance is the highest. Due to terrain reasons, rivers will converge in low-lying places.

The correlation matrix reveals several key geospatial and economic relationships: digital elevation exhibits a strong positive correlation with slope (r = 0.71), confirming that steeper terrain generally occurs at higher altitudes, while showing moderate positive associations with river distance (r = 0.44) and sand content (r = 0.45). Economically, population density and land GDP show a moderate positive correlation (r = 0.31), whereas land GDP strongly inversely correlates with line distance (r = −0.35), indicating that economic activities cluster near transportation routes. The strongest negative correlation emerges between land GDP and infrastructure proximity (r = −0.35), highlighting how economic development concentrates away from linear transport corridors, while the strongest overall correlation remains the expected elevation–slope relationship. Most variables show weak or negligible correlations with land use types (|r| ≤ 0.24), suggesting that land classification operates independently from other factors in this system. The results were converted into a thermodynamic diagram, as shown in Figure 6.

According to the weights of severity and likelihood, their level distributions can be weighted and divided into five levels. According to the severity and likelihood levels, each level corresponds to a different degree of impact of the disaster. Each level is scored according to the following table, and the product of the severity and likelihood scores is the final risk level score. A detailed classification of the risk level scores and their corresponding levels is shown in the following

Table 4. Severity level division table.

Risk Level Score and Risk Level			Severity Level and Score
			Very Serious	Serious	More Serious	Lighter	Light
			5	4	3	2	1
Possibility level and score	Extremely high	5	25 (extremely high)	20 (extremely high)	15 (high)	10 (high)	5 (middle)
	High	4	20 (extremely high)	16 (high)	12 (high)	8 (middle)	4 (low)
	Middle	3	15 (high)	12 (high)	9 (middle)	6 (low)	3 (low)
	Low	2	10 (middle)	8 (middle)	6 (low)	4 (low)	2 (extremely low)
	Extremely low	1	5 (low)	4 (low)	3 (low)	2 (extremely low)	1 (extremely low)

:

This study counted the distribution of the core density of different factor grades and landslide disaster points. There was a significant correlation between land use type, route distance, and landslide core density. High core density depends on a certain order of magnitude of factors. When these factors reach a specific order of magnitude, an area can be said to have a high landslide core density, indicating that under these conditions, the probability of landslide occurrence would increase significantly. The correlation statistics between each factor and the nuclear density of historical landslide points are shown in Figure 7 below.

The green bars in Figure 7 represent statistical results with an extremely high kernel density. When high kernel density is concentrated at a certain level of a factor, it indicates a certain correlation between landslide disasters and the environment at that specific level of the factor. For “average land GDP” (that refers to Figure 7h), extreme density exclusively occurs in Category 1 (lowest GDP), demonstrating higher landslide frequency in economically disadvantaged areas. This indicates that landslide-prone regions experience constrained economic development, while urban expansion favors stable terrain. For “digital elevation” in Figure 7a, Category 5 (highest altitude) exhibits predominant high-density concentration. Topographically, elevated areas feature steeper slopes where gravitational forces and precipitation infiltration increase pore water pressure, reducing soil shear strength and elevating landslide susceptibility. Overall, the nuclear density-related statistical chart demonstrates a certain correlation between the classification levels of various factors and landslide disasters.

4.2. Weight Combination Risk Analysis

This study used the method of combining weights in game theory to combine the AHP with the EWM and CRITIC, respectively. The weight calculation results of each indicator are summarized as follows:

Figure 8 indicates that factors are categorized as likelihood or consequence, with each category summing to a unit weight. The likelihood index assigns higher weighting to historical landslide kernel density, reflecting persistent predisposing factors. Most of the predisposing factors have little variation over a long period of time, and areas with a history of frequent landslide disasters often have long-term fragile geological conditions, such as frequent hydrological activities, which persist as inherent factors. Historical landslides may damage the original structure of the slope, forming unstable residual bodies or loose-material accumulations, which are more prone to instability under external triggering conditions. Among the consequence factors, economic level has a higher weight; the population and facilities are concentrated in prosperous areas, and the vulnerability to disasters is also stronger.

According to the natural-fracture method, the landslide risk level was divided into five levels. The final risk assessment results are shown in Figure 9.

The risk level distributions remain consistent across weighting methods, with high-risk areas concentrated in the eastern study region. The specific distribution of historical disasters was used to calculate the AUC, precision, recall, and the F1-score. The AUC measures the ranking capability of a binary classification model. A higher value indicates stronger model performance in distinguishing positive and negative samples. Precision quantifies the proportion of correctly identified positive instances among all samples predicted as positive. High precision reduces misclassification costs. Recall measures the proportion of actual positive samples correctly identified by the model. The F1-score is the harmonic mean of precision and recall, providing a balanced assessment of both metrics. The comparison results of the various analysis methods are shown in Figure 10.

The calculation results of the AHP-EWM method show that low-risk areas have a high probability of being misreported as high-risk using this method. In contrast, the CRI-AHP method achieved a higher F1-score. Overall, the CRI-AHP model exhibits superior comprehensive performance. The weight distribution of factors is as follows, with an area of 1 under each factor curve in Figure 11.

The weights of possibility indicators generally remain below 0.25, with land use distribution demonstrating concentrated patterns and higher stability of weight values. The distribution of river distance and kernel density is relatively scattered and low. Consequence indicators display concentrated distribution characteristics, necessitating coordinated management and multidimensional control strategies in disaster risk prevention efforts. According to the weight allocation results, landslide disasters are more affected by elevation, river distance, and economic level.

According to the CRI-AHP results, high-risk areas are mainly distributed in Jinan and Jining Cities. The high-risk and medium-risk areas are mainly distributed in Jining City, the southern part of Jinan City, and the eastern area of Zaozhuang City in Tai’an City; the low-risk and extremely low-risk areas are mainly distributed around lakes and in the northern region of the study area.

The main reason for the high risk of landslide disasters in the high-risk distribution areas of Jining City and the southern part of Jinan City is the large difference in altitude, and sufficient precipitation provides environmental conditions for the occurrence of landslide disasters. The two locations are situated in the low mountainous and hilly regions of central and southern Shandong Province, characterized by significant variations in elevation. For example, the topography of the Mount Taishan Mountains ranges from 200 to 500 m, and there is generally a large amount of slope in the area. In addition, the prosperous economy at the intersection of railway lines has also led to an increase in regional vulnerability. At the intersection of transportation arteries such as the Beijing Shanghai and Jiaozhou Jinan railways, vegetation cover has been damaged by human activities such as slope cutting, road construction, mining, and urban expansion, resulting in an imbalance in slope load. The eastern part of Jinan City and the eastern part of Jining City are mainly affected by factors such as slope, rainfall, and sand content. The size of the slope will affect the stability of the soil, and an increase in rainfall will also increase the saturation of the soil. Areas with high sediment content are more prone to soil erosion during heavy rainfall, thereby increasing the risk of landslides. The annual precipitation in this region is concentrated in summer, and heavy rainfall seeps into the slopes through cracks, increasing pore water pressure, softening the rock and soil structure, and accelerating soil erosion. In the eastern part of Jining, with a high proportion of sandy soil, concentrated heavy rainfall can easily cause seepage instability, and the comprehensive impact increases the risk of landslides. The results of multi-source data show that the landslide disaster risk is affected by a variety of factors. After in-depth understanding has been obtained and comprehensive consideration has been taken of the influencing factors, preventive measures can be taken more efficiently to reduce the impact of landslide disasters.

Topographic factors constitute the fundamental material basis for landslides, where high-elevation zones frequently feature steep slopes that facilitate the accumulation of gravitational potential energy. When precipitation intensifies, hydrological processes dangerously couple with the terrain: rainfall rapidly infiltrates steep inclines, generating transient pore pressures within coarse-grained soils that substantially reduce geotechnical shear strength. These compounding effects drive a sharp increase in landslide probability. Concurrently, human activities amplify risk through engineering disturbances and vegetation removal—an anthropogenic–natural feedback loop that elevates landslide susceptibility in high-GDP-density areas. This coupling necessitates multidimensional risk-reduction strategies beyond single-factor interventions.

Along the Beijing–Shanghai railway, high-risk zones manifest through subgrade instability and track deformation risks. Sudden landslides may cause derailments or line interruptions, with disaster chains likely following extreme weather. Railway authorities should prioritize slope reinforcement and sensor networks in high-risk areas, pre-position emergency resources, and collaborate with local governments on graded response plans. The railway department can simulate disaster chain scenarios based on actual situations to improve collaborative disposal efficiency and minimize operational interruption time and secondary disaster losses.

5. Conclusions

This study comprehensively analyzed nine key landslide-influencing factors across topography, geomorphology, meteorology, and hydrology. Multi-source data acquisition and transformation enabled quantification through historical data distributions. The landslide risk assessment for five Beijing–Shanghai corridor cities, utilizing multi-source monitoring data and game-theoretic combined weighting, identified Jining and southern Jinan as having elevated landslide risk levels. In terms of comprehensive indicators, the F1-score of the CRI-AHP method was 0.34 higher than that of EWM-AHP.

The high risk in the results is mainly the result of the slope effect caused by concentrated rainfall and significant altitude difference. The economic prosperity brought by the convenient transportation at the intersection of railway lines in Jinan makes the damage consequences of landslide disasters in this area more serious. Consequently, these regions require enhanced landslide monitoring and early-warning systems, alongside effective disaster-prevention measures, to mitigate losses and help the region to realize a virtuous cycle of economy, society, and environment. Precise risk classification enables optimized resource allocation and strengthens climate-adaptation capabilities. Railway authorities can strategically deploy monitoring equipment in high-risk zones while reducing redundant investments in low-risk areas. Collaborative efforts with local governments to improve resident disaster awareness will further reduce casualty risks.

Limitations remain regarding spatial data bias, as historical records concentrate in accessible and populated areas, with gaps in remote regions. Temporal dynamics pose challenges, since historical data cannot capture evolving impacts from new infrastructure or extreme weather that alter geological stability. Low-resolution resampling reduces computational loads, but sacrifices detail, causing small-scale, high-risk zones to be overlooked. Limited historical landslide datasets yield incomplete spatial coverage and feature representation, while rare-event omissions may lead to underestimation of critical triggering mechanisms and reduced prediction reliability for novel scenarios.

Future research will focus on multidimensional data fusion and dynamic assessment of disaster risks, with a focus on breaking through the bottleneck of existing models in fine analysis at the micro scale. Integration of high-precision remote sensing, IoT sensors, and geological drilling data will establish a comprehensive database spanning from macro-terrain evolution to micro-geotechnical parameters. Climate change projections will be incorporated to quantify time-varying impacts of extreme weather on landslide processes. This will facilitate the development of machine learning-based real-time risk inference models, advancing from static assessment to dynamic early-warning systems to support disaster resilience and sustainable development along the Beijing–Shanghai corridor and similar high-risk regions.