Introduction

As the construction of high-speed railways (HSR) in China rapidly progresses, HSR transportation has become a crucial mode of transportation in contemporary Chinese society. According to the “Fourteenth Five-Year Plan”, it is anticipated that by 2025, China’s operational HSR mileage will reach 50,000 kilometers, covering more than 95% of major cities1. However, given the diversity of regional climate and geological conditions, particularly in areas with harsh conditions, HSR subgrades face multiple defects such as settlement, frost damage, uplift deformation, and mud pumping. These issues affect ride comfort and, in severe cases, can even jeopardize traffic safety2. Therefore, an in-depth study of the mechanisms, risk factors, and impacts of HSR subgrade defects is crucial for ensuring the stable operation of HSR.

The key to researching the occurrence mechanisms of HSR subgrade defects lies in identifying and analyzing the main factors affecting subgrade performance within the natural and anthropogenic environments. Historical research has shown that subgrade defects are closely related to environmental factors such as moisture, temperature changes, geological conditions, and railway operational characteristics (such as operational frequency and operating period)3. For example, in cold regions, moisture in the subgrade forms ice crystals during freezing, causing volume expansion as temperatures drop below freezing, thus exerting pressure on subgrade materials and causing frost heave4. In densely populated areas, higher train frequencies often lead to accelerated structural fatigue of the subgrade, resulting in settlement5. Thus, the occurrence of defects results from multiple factors interacting under different environmental conditions. Wang et al.6 field monitoring and laboratory experiments have identified track superelevation and analyzed the causes of HSR subgrade bulging, showing that water infiltration and the action of montmorillonite in the subgrade fill are the primary triggers for the fill’s expansion. Li et al.7 constructed a full-scale track subgrade mud-pumping model test system to analyze the changes in subgrade dynamic water pressure under high-speed train loads, finding that ballastless track subgrades under rainwater infiltration are prone to saturation, leading to mud pumping under high-frequency loads. Wu et al.3 explored how high-frequency railway operations interact with various environmental loads, such as rainwater infiltration, seasonal wet-dry cycles, and freeze-thaw cycles, leading to the degradation of infrastructure performance. Sundell et al.8 examined the increased risk of subgrade settlement in high-speed rail systems due to groundwater extraction around the railway, highlighting the complex environmental factors influencing railway infrastructure stability. While these studies have indicated that climate, geological features, HSR characteristics and economic factors affect subgrade defects, the causal relationships between different factors and the intensities with which they affect defect occurrence are still unclear.

Traditionally, research on HSR subgrade defects has relied on physical model testing and numerical simulation. For example, Huang et al.9 developed a 3D dynamic track model and used discrete element numerical modeling to simulate factors affecting railway subgrades. This shows that increased train frequencies and speeds might lead to subgrade defects. Bian et al.10 physical model testing on the factors influencing HSR subgrade mud pumping showed that permeable rainwater retention above low-permeability subgrades and excessive plastic fine particles in the subgrade provide favorable conditions for mud pumping beneath HSR subgrades. While these methods help understand the nature of the problems, they often rely on certain simplifications and assumptions, making it challenging to capture the complex changes in the natural environment. As technology advances, data-driven methods such as machine learning have been widely used due to their powerful predictive capabilities. For example, Liu et al.11 used machine learning algorithms to calculate the impacts of landslides, debris flows, and floods on railways and to sort and identify critical environmental features affecting railway infrastructure disasters in China, including precipitation, geology, and elevation. However, these methods still need to be improved in explaining complex causal relationships. Structural Equation Modeling (SEM), with its ability to consider interactions between multiple variables and to provide model applicability assessments through various statistical tests, has attracted widespread attention12,13,14. For example, Ji et al.15 used survey data to obtain environmental and workload data, and employed SEM to understand the mechanisms by which various factors affect HSR human safety. Han16 combined SEM with fuzzy element analysis, using survey data to obtain safety data for HSR projects, and built a post-evaluation model for the construction process of HSR projects. In the past, although SEM was applied in the field of railway safety, the analysis was often limited to small-scale studies focusing on local area risk mechanisms. Today, with the accumulation of preliminary data on high-speed railways17, it has become feasible to use SEM for large-scale spatial analysis of HSR subgrade defects. This advancement enables a more accurate reflection of disaster-prone environments’ diversity and spatial heterogeneity.

This study employs SEM to conduct an in-depth analysis of the main factors influencing subgrade defects in China’s HSR system, aiming to reveal and verify the critical drivers of these defects through an actual railway dataset. The primary objectives of the research include (1) exploring the causal relationship between environmental variables, operational characteristics, and subgrade defects; (2) quantitatively analyzing the contribution of different factors to the occurrence and co-occurrence of subgrade defects; (3) Identify key factors and determine priorities, and implement targeted interventions for subgrade defects based on existing railway plans and future climate predictions. The results of this study will provide a scientific basis for the maintenance of the railway system, thereby enhancing the safety and efficiency of HSR.

We found that three common subgrade defects, settlement, uplift deformation, and mud pumping, tend to co-occur under similar environmental and operational conditions. Specific land use, geomorphological features, and HSR operational characteristics exacerbate the occurrence of these defects, and the impacts of spatial lag, such as the propagation of defects, should be managed and mitigated. Additionally, we found that settlement and uplift deformation are mainly influenced by bare land, frost damage is primarily affected by the annual freezing days, and mud pumping is mainly influenced by average annual rainfall. Our study suggests that the overall trend of these defects may increase in the future, emphasizing the need for proactive environmental monitoring and risk management strategies.

Results

Socio-environmental causalities underpinning the occurrence of defects

We fitted four types of historical subgrade defects in the subgrade defect measurement model. However, frost damage was not significant in the measurement model (P > 0.1) and was thus excluded, leaving only three defects (settlement, mud pumping, and uplift deformation). Additionally, we fitted all factors within the disaster-prone environment (climate variables, geomorphological variables, spatial lag, land use, geological variables, economic variables) and disaster-causing factors (HSR proximity indicators, HSR operational characteristics), removing non-significant paths (P > 0.05) from the measurement model, with the retained factors listed in the Supplementary Table 1.

In the structural model for subgrade defects, we eliminated the latent variable of geological factors, as they had minimal impact on the occurrence of subgrade defects and showed weak correlations with other variables. Additionally, as shown in Supplementary Table 2, we estimated and tested the hypothesized paths, removing those that did not meet the requirements, such as H3, H4, H5, H9, H12, H14, and H15, while retaining paths H1, H2, H6, H7, H8, H10, H11, H13, and H16 and which all met the significance criterion (P < 0.05). The final results are shown in Fig. 1 and Supplementary Table 3.

Fig. 1: Pathway analysis and standardized effects of multidisciplinary determinants on high-speed rail subgrade defects.
figure 1

a Structural equation modeling of geospatial, operational, and socioeconomic factors impacting subgrade defects. Standardized path coefficients are indicated next to the one-sided directional arrows, representing the hypothesized causal relationships. Significant path coefficients are marked with asterisks, denoting levels of significance (*p < 0.05, **p < 0.01, ***p < 0.001). Gray arrows represent non-significant paths. The small double-sided arrows near the endogenous variables denote the covariance, and the large arrows between latent variables indicate correlation coefficients. b Total, direct, and indirect standardized effect magnitudes for key variables: This subfigure summarizes the total, direct, and indirect effect values for key variables influencing subgrade defects. The total effect value is the sum of the direct and indirect effects. The direct effect is represented by the path coefficients between variables, while the indirect effect is calculated by multiplying the coefficients of multiple paths. Credit: icons, Flaticon.com.

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In path H1, geomorphological variables positively impacted subgrade defects (standardized path coefficient of 0.17); in path H2, land use had a positive effect on subgrade defects (standardized path coefficient of 0.15); and in path H6, HSR operational characteristics had a positive influence on subgrade defects (standardized path coefficient of 0.22). Notably, in path H16, spatial lag factors exhibited a strong positive influence on subgrade defects, with a standardized path coefficient of 0.91. These four paths directly positively influenced subgrade defects. In path H7, geomorphological variables negatively impacted HSR operational characteristics (standardized path coefficient of -0.60); in path H8, climate variables positive influenced land use (standardized path coefficient of 0.21); and in H10, geomorphological variables negatively affected economic factors (standardized path coefficient of -0.07). In path H11, economic factors positively influenced HSR characteristics (standardized path coefficient of 0.09). These pathways indirectly influenced subgrade defects.

As shown in Supplementary Table 4, paths such as H10-H11-H6, H13-H2, H8-H2, and H7-H6 were tested using Bias-corrected and Percentile methods at a 95% confidence interval with 4000 iterations, showing no zeros in the Lower-Upper interval and P values less than 0.05. This confirms the mediation effect of the model. Additional tests with different resample counts (3000, 5000, and 6000), shown in Supplementary Table 5, indicated consistent confidence intervals, confirming that 4000 resamples provided sufficient robustness. The model fit indices are presented in Supplementary Table 6. As shown in Supplementary Fig. 1, the residual covariance values are close to zero, suggesting that the model was well-constructed and that the predicted covariances aligned with the observed data. Through the multi-defect model, we obtained standardized effect values between variables and illustrated them in Fig. 1. The total effect values for spatial lag, economic variables, geomorphological variables, climate variables, land use, and HSR operational characteristics are 0.912, 0.020, 0.056, 0.031, 0.150, and 0.223, respectively. These results indicate that spatial lag, HSR operational characteristics, and land use are the most important factors influencing subgrade defects after considering both direct and indirect impacts. By introducing the spatial lag variable, the model’s R2 increased from 0.205 to 0.914, indicating that the model explains 91.4% of the variance.

Varying effects of factor categories on different defects

Since removing latent variables, the SEM has shifted to analyzing specific variables subclasses and defects. We fitted models for four types of defects and eliminated non-significant factors (P > 0.05), retaining factors as shown in Fig. 2. The variance inflation factor values for the retained factors are detailed in Supplementary Table 7. Mediation effect tests were conducted for all four defects, with results displayed in the Supplementary Table 8. The results of spatial autocorrelation and spatial lag analysis for the four types of subgrade defects are presented in Supplementary Table 9. After 4000 tests within a 95% confidence interval using Bias-corrected and Percentile methods, mediation effects were confirmed. The model fit indices for the four defects are presented in the Supplementary Table 6, meeting the model evaluation criteria. The standardized total effect values are shown in Fig. 3, where settlement defects are primarily influenced by settlement spatial lag value (total effect value of 0.239), bare land (total effect value of 0.264), bare rock (total effect value of -0.181), construction length (total effect value of 0.166), and operating frequency (total effect value of 0.128). Frost damage is mainly affected by frost damage spatial lag value (total effect value of 0.576), annual freezing days (total effect value of 0.194), and average annual rainfall (total effect value of -0.067). Uplift deformation is significantly influenced by uplift deformation spatial lag value (total effect value of 0.395), bare land (total effect value of 0.213), and construction length (total effect value of 0.094). Mud pumping is primarily impacted by mud pumping spatial lag value (total effect value of 0.415), average annual rainfall (total effect value of 0.110), continuous 5-day rainfall (total effect value of -0.091), and operating frequency (total effect value of 0.077). By incorporating the spatial lag variable, the R2 for the models of settlement, frost damage, uplift deformation, and mud pumping defects increased from 0.091, 0.329, 0.140, and 0.067 to 0.122, 0.496, 0.260, and 0.204, respectively.

Fig. 2: Causal pathways and strength of subgrade defects in high-speed rail.
figure 2

a Subgrade settlement, b Frost damage, c Uplift deformation, and d Mud pumping. Standardized path coefficients are displayed alongside the directional arrows, quantifying the hypothesized influences, where the arrow’s thickness represents the relationship’s strength. Significant path coefficients are marked with asterisks, indicating levels of statistical significance (*p < 0.05, **p < 0.01, ***p < 0.001).

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Fig. 3: Impacts of variable groups on subgrade single-defects.
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a Subgrade settlement, b Frost damage, c Uplift deformation, and d Mud pumping. Color-classified geospatial, operational, and climatic variable impacts across four defect types.

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Furthermore, factors included in SEM were analyzed using RF for 30 sampling analyses, which display the receiver operating characteristic (ROC) curves with average area under the curve (AUC) values of 0.722 (multi-defect), 0.798 (settlement), 0.976 (frost damage), 0.832 (uplift deformation), and 0.894 (mud pumping) (Supplementary Figs. 2 and 3). In the multi-defect RF model, results revealed spatial lag and HSR operational characteristics as the most critical factors driving the co-occurrence of subgrade defects (Supplementary Fig. 4), consistent with SEM findings. In the single-defect model, RF identified spatial lag as the primary driver for all defect types, aligning closely with SEM. Both methods agreed on the importance of individual factors, such as construction length for settlement defects and annual freezing days for frost damage defects. However, RF assigned higher importance to certain variables, such as “Elevate” in uplift deformation defects and operating frequency in mud pumping defects, reflecting its strength in modeling variable interactions (Supplementary Fig. 5). This consistency indicates that the factors identified through SEM not only capture key relationships within the dataset but also serve as reliable inputs for machine learning models, effectively improving the predictive performance and interpretability of these models (Supplementary Results and Discussion).

Discussion

Our research shows that using the Disaster System Theory (DST)18,19,20,21,22 can provide solutions to the complex causality of subgrade defects, offering valuable insights into the main drivers of multi-defects. By analyzing a historical dataset of subgrade defects, our study reveals the direct and indirect impacts of various factors, such as spatial lag, geomorphology, land use, climate change, and HSR operational characteristics, on subgrade defects. Identifying the most important factors chains helps prevent subgrade defects and reduce the overall system risk for HSR. These findings enhance our understanding of the complexity of HSR subgrade defects and underscore the necessity for integrated management strategies.

In the multi-defect analysis, the main latent variables impacting subgrade defects were land use, spatial lag, HSR operational characteristics, and geomorphological variables. We found that three common subgrade defects—settlement, uplift deformation, and mud pumping—tend to co-occur under the same environmental variables and operational stress. The positive impact of HSR operational characteristics on subgrade defects aligns with previous studies’ research23,24, such as increased HSR operating frequencies leading to more subgrade settlements and defects, likely due to increased loads on the subgrade structure.

Spatial lag effects were found to have a particularly significant impact on the co-occurrence of subgrade defects, indicating that the influence of defects is not confined to a single location but is propagated spatially, leading to the expansion and co-occurrence of defects in neighboring areas. Spatial lag refers to the influence of one location’s conditions on its surroundings, highlighting spatial dependencies that can reveal risks and patterns. While spatial lag itself cannot be eliminated, its effects, such as the spread and co-occurrence of defects, should be mitigated through proactive measures like enhanced monitoring, preventive reinforcement, and the integration of digital twin technology. These strategies can effectively manage spatial lag impacts, enhance infrastructure resilience, and reduce the risk of defect expansion.

Conversely, prior studies had not observed significant impacts from unused land on subgrade defects; however, in this study, this factor emerged as having a significant influence (total effect value of 0.150), suggesting that larger areas of unused land correlate with more HSR subgrade defects. Unused land includes sandy lands, gobi, saline and alkaline lands, bare lands, and bare rocky terrains. Sandy areas, with low vegetation cover, high permeability, and poor structural stability, are more susceptible to subgrade defects under the heavy loads of trains. Gobi surfaces, subjected to intense sunlight and low nighttime temperatures, experience extreme temperature variations that can cause thermal expansion and contraction of subgrade materials, leading to cracks and structural fatigue. In saline and alkaline lands, high salt content rising to the subgrade surface through capillary action accelerates material aging and corrosion, reducing the subgrade’s lifespan and durability. Bare lands, lacking vegetation protection and root consolidation, are prone to displacement or slipping under heavy loads or vibrations. Furthermore, they are susceptible to water infiltration and accumulation, leading to soil liquefaction under load and affecting subgrade performance. Bare rocky terrains may lack sufficient soil cover to absorb and retain rainwater, causing rapid runoff and erosion and affecting the subgrade’s integrity.

Previous studies found that poorer geomorphological conditions lead to more severe HSR subgrade defects25, and our study confirms this viewpoint. However, although geomorphology total impacts subgrade defects positively (standardized total effect values of 0.056), its indirect impact through HSR operational characteristics is negative, suggesting that poor geomorphological conditions can suppress defect occurrence via reduced HSR usage, thus reducing subgrade defects—a scenario often overlooked in previous research26,27. We also found that climatic variables, especially the number of days with maximum temperature exceeding 35 degrees Celsius, can significantly promote the occurrence of subgrade defects (standardized total effect values of 0.031). According to the “Global Climate Change Report 2015–2019” released by the World Meteorological Organization28, the “2022 China Climate Bulletin” published by the China Meteorological Administration29, and the “2016 China Medium and Long-term Railway Network Plan” report by the National Development and Reform Commission30, it is indicated that in the future, temperatures will gradually rise, the frequency of HSR operations in China will increase. Therefore, based on existing climate predictions and HSR operation plans, the overall trend of HSR subgrade settlement, mud pumping, and uplift deformation defects in China may increase in the future. Furthermore, economic variables are also considered drivers of subgrade defects, but they were not significant variables in the subgrade defects tested here. This trend underscores the need for enhanced predictive maintenance strategies and infrastructure resilience planning.

In the single-defect model analysis, our research indicates significant impacts of bare land and bare rock on subgrade settlement and uplift deformation. Bare land, characterized by sparse vegetation and weaker soil structure, tends to facilitate subgrade settlement and uplift deformation, with total effect values of 0.264 and 0.213, respectively. Conversely, bare rock effectively reduces these defects due to their robust load-bearing capacity, with total effect values of -0.181 and -0.063 respectively. These findings are crucial for the planning and construction of HSR foundations. Additionally, the frequency of HSR operations significantly positively affects subgrade settlement, consistent with prior research indicating that increased operational frequency accelerates aging and wear of subgrade materials31,32.

For frost damage, the most significant driver is the annual freezing days, demonstrating that sub-zero temperatures substantially promote the occurrence of frost damage. Average annual rainfall, mediated through freezing days, significantly negatively affects frost damage, indicating that increased rainfall reduces the number of freezing days and directly lowers the risk of frost damage. This effect underscores the complexity and multidimensionality of hydrological conditions on frost damage and highlights the importance of considering climate and weather patterns in subgrade design and maintenance.

Moreover, our research indicates that climatic factors, rather than operational characteristics of HSR, predominantly influence frost damage. Regarding mud pumping, our findings align with previous studies33,34, showing significant effects of HSR operating frequency and rainfall on its occurrence. Rainfall positively impacts mud pumping, while extreme rainfall has a negative effect, likely because areas with extreme rainfall receive more attention to drainage infrastructure, thereby mitigating mud pumping. In regions with regular rainfall, increased moisture content causes subgrade soil particles to move upward under the load of frequent high-speed trains, leading to mud pumping. This trend underscores the need for enhanced predictive maintenance strategies and infrastructure resilience planning.

By comparison, we found that both models emphasize the positive influence of HSR operational characteristics (such as HSR operating frequency) on the occurrence of subgrade defects. Unlike previous studies, our research identified the differentiated effect of bare rock within land use. Previously, bare rock was generally believed to have a high load-bearing capacity and stability, which could mitigate the occurrence of settlement and uplift deformation to some extent. Our single-defect model confirmed this view. However, when bare rock is aggregated with other types of unused land in the same area, the complex environmental stress resulting from the interaction of different land types is more likely to promote the co-occurrence of defects. Additionally, the single-defect model includes many factors not present in the multi-defect model, such as consecutive 5-day rainfall, urban land, and annual freezing days. These factors are not the main contributors to the co-occurrence of defects.

Although SEM effectively handles relationships among multiple variables, this study still faces several limitations when applying this model. Firstly, the occurrence of subgrade defects is influenced by multiple interacting factors, which are often complex and dynamic. This nonlinear interaction may be difficult to fully capture and quantify through SEM. Secondly, the study primarily relies on statistical significance and model fit indices for hypothesis validation, which may overlook subtle differences that are significant in practical engineering applications. Additionally, the research may underestimate the impact of long-term environmental and climate changes on the subgrade structure. For example, global climate change and the increasing frequency and intensity of extreme weather events could have new, unknown impacts on HSR subgrades, necessitating accurate assessments through long-term and more dynamic studies. Lastly, this study does not explicitly incorporate the effects of dynamic load and vibration, despite their recognized influence on subgrade performance. This omission arises primarily from the scope of this research, which is conducted at a county-scale level and encompasses a large spatial area, whereas dynamic load and vibration effects are typically localized phenomena that require highly detailed and specific data, which are challenging to obtain comprehensively at such a scale.

Future research could address this limitation by focusing on specific local regions, integrating real-time monitoring data of dynamic load characteristics (e.g., train speed and axle load) and vibration features (e.g., frequency and amplitude). Utilizing numerical simulation methods, such as finite element analysis (FEA) and multibody dynamics modeling (MBD), would allow for quantifying the physical impact of dynamic loads and vibrations on subgrade performance. Combined with SEM, this approach could provide a more comprehensive understanding of the effects and causal pathways of multiple factors, including dynamic loads, environmental conditions, and material properties, on subgrade defects. Furthermore, physics-informed neural networks (PINN) could integrate physical laws and monitoring data to compute critical variables such as dynamic stress distribution, which can be incorporated as potential variables in SEM to analyze the complex interactions between dynamic loads and environmental factors affecting subgrade defects. These technologies could eventually be extended into a digital twin framework, enabling real-time monitoring and lifecycle prediction of subgrade performance. This would provide a scientific foundation for optimizing design and maintenance strategies.

While the research focused on China, its findings may be applicable to other regions with similar climates and geographical conditions, such as Southeast Asia and parts of Europe. The methods used can contribute to infrastructure maintenance and operational strategies globally. Moreover, as climate change was predicted to lead to more frequent extreme weather events35,36,37, the study’s insights on the impact of climate variables on subgrade defects offer valuable guidance for future infrastructure planning. In addition to HSR, these methods could also be adapted to assess other types of infrastructure, such as highways, bridges, and tunnels, under various environmental pressures. However, regional differences in geological and economic conditions may limit the direct applicability of these findings, indicating a need for further testing in diverse contexts. This study provides a theoretical foundation for improving global infrastructure resilience and informs strategies for managing the challenges posed by climate change.

The findings of this study provide key insights that can inform policy recommendations for improving the stability and resilience of high-speed rail infrastructure. One approach is to optimize railway route planning based on land use patterns and geomorphological characteristics. Our study shows that adverse land use and geomorphological variables have standardized direct impact values of 0.150 and 0.056, respectively, on the co-occurrence of HSR subgrade defects. Therefore, when planning new railway routes, areas prone to subgrade problems, such as low-coverage grasslands, gobi deserts, saline-alkaline lands, and bare lands should be avoided. During the planning and construction phases, comprehensive geological and environmental assessments should be conducted to identify high-risk areas, such as high-altitude lines like the Lanzhou-Xinjiang HSR. In areas with unfavorable land use, climate-appropriate vegetation and soil improvement techniques can enhance stability. For Gobi or saline-alkaline areas, geotextiles and windbreaks can be used to mitigate the effects of weathering and salinization. For example, a study in Old Dalby, United Kingdom, using Electrical Resistivity Tomography (ERT), showed that grass cover can improve the stability of railway embankments38.

Beyond land use and geomorphology, extreme temperatures also pose a major challenge to subgrade stability. Our study shows that extreme temperatures have a significant impact on the stability of high-speed rail subgrades during operation. Specifically, the number of days with maximum temperature exceeding 35°C leads to the co-occurrence of subgrade defects, such as settlement, uplift, and mud pumping. Therefore, it is recommended to reduce train frequency during high-temperature periods by strengthening monitoring and early warning systems, in order to alleviate the load on the subgrade and track. Additionally, a high-temperature emergency response mechanism should be established to ensure that timely measures can be taken under extreme weather conditions to maintain railway safety. Based on long-term climate change forecasts, it is suggested that localized modifications be implemented in high-risk areas (with extended periods of high temperatures) to reduce subgrade deformation and structural fatigue under high-temperature conditions. Furthermore, our research indicates that an increase in the annual freezing days significantly raises the risk of subgrade frost damage (standardized total effect value of 0.194). Therefore, it is recommended to use materials with stronger anti-frost heave properties in permafrost regions (such as the Harbin-Dalian HSR) to ensure the long-term stability and safety of infrastructure in cold climates. For example, the Madrid-Cádiz railway line in Spain uses platforms to monitor foundation degradation in extreme climate conditions39, with alarm thresholds were set trigger speed and frequency adjustments39.

To further enhance subgrade management, integrating causal analysis into predictive maintenance strategies is essential. Our research shows that causal analysis can identify key factor chains influencing subgrade defects (e.g., geomorphology affecting HSR operational characteristics, which in turn impact subgrade defects). Therefore, it is recommended to combine causal analysis with data-driven management by regularly collecting data on high-speed rail operations, environmental conditions, and infrastructure. By integrating these datasets with the key factors identified through causal analysis, data-driven methods (such as machine learning) can be applied to more accurately identify and predict potential subgrade defect risks. This integration not only improves the understanding of the interactions between various factors through causal chains, but also enhances the transparency and interpretability of data-driven management, avoiding the “black box” issue often associated with models. Additionally, optimizing predictions can enhance subgrade predictive maintenance, improving the efficiency and safety of railway infrastructure management while reducing unnecessary costs. For example, on the Zamudio railway bridge in the Basque region of Spain, machine learning algorithms were used to monitor railway infrastructure. Compared to traditional monitoring methods, this approach reduced costs and improved the efficiency of detecting structural defects40.

Finally, digital twin technology offers a promising approach for real-time monitoring and decision-making in railway operations. This study reveals that spatial lag variables significantly impact subgrade defects, with their spatial propagation characteristics potentially leading to the expansion of defects in neighboring areas. Building on this finding, we recommend the deployment of sensors in high-risk zones to monitor key data in real time, such as train operations (e.g., speed and axle load), subgrade deformation, and environmental conditions. The collected data can then be integrated into a digital twin platform. This platform aligns with the United Nations Sustainable Development Goals (SDGs), particularly the Sustainable Development Goal 9 (Industry, Innovation, and Infrastructure) and the Sustainable Development Goal 11 (Sustainable Cities and Communities), by improving the reliability of high-speed rail operations, minimizing disruptions caused by subgrade defects, and enhancing connectivity in remote and underdeveloped areas. While this study focuses on the theoretical aspects of defect spatial propagation, the proposed digital twin platform provides a practical framework for future research and intelligent high-speed rail management. For example, a digital twin system was established on the Varzea Bridge in the Aveiro district of Portugal, improving the efficiency of fatigue assessment during operations41.

Conclusion

Based on disaster system theory, this study utilizes SEM and historical defect datasets to analyze the comprehensive factors affecting China’s HSR infrastructure. The results indicate that three common subgrade defects—settlement, uplift deformation, and mud pumping—tend to co-occur under the same environmental and operational stress. Specific land use composition, geomorphological characteristics, and HSR operational characteristics exacerbate the occurrence of these defects. The impacts of spatial lag, such as the propagation of defects, should be managed and mitigated. Additionally, the important factors for each defect were identified: settlement and uplift deformation are mainly influenced by bare land, frost damage is primarily affected by the annual freezing days, and mud pumping is mainly influenced by average annual rainfall. Based on existing climate predictions and HSR operation plans, the overall trend of HSR subgrade settlement, mud pumping, and uplift deformation defects in China may increase in the future. Therefore, proactive measures in environmental monitoring and risk assessment are necessary to mitigate the increasing trend of these defects. Nevertheless, the study has limitations in capturing the nonlinear interactions among various influencing factors, as well as the effects of long-term environmental changes and dynamic loads. Future research should address these limitations by incorporating real-time monitoring data and advanced simulation techniques, such as finite element analysis, to better understand subgrade behavior under complex conditions.

Methods

Theoretical framework

In this study, we have drawn on the DST18,19,20,21,22 to analyze the factors influencing HSR subgrade defects in China. DST provides a theoretical framework designed to systematically analyze and manage complex disasters. It seeks to explain the mechanisms of disaster occurrence, the pathways of disaster impact, and how systematic management can mitigate the negative impacts of disasters. The theory views disasters as the result of complex interactions among the natural environment, engineering structures, and human activities19. It posits that different disaster-causing factors arise from different environmental systems, allowing these factors to serve as mediating variables between the disaster-prone environment and the disaster-bearing body (i.e., the HSR subgrade). Additionally, due to the Earth’s inherent self-regulating abilities, internal factors within the disaster-prone environment may influence each other through mediating effects. This study aims to analyze the degree of association between these factors, reveal the main conditions for forming HSR subgrade defects, and develop effective mitigation strategies20,21,22.

We compiled an extensive georeferenced dataset of historical HSR subgrade defects, selecting 661 event records that span various administrative levels and involve elements of the track structure, roadbed, and foundation. This dataset includes defects directly related to track unevenness, enabling us to analyze the influence of track structure on subgrade defects. The distribution of HSR subgrade defect records and land use is illustrated in Fig. 4. Based on the analysis of these records, the causes of the defects were categorized according to different attributes and associations into factors such as land use, climate, geology, geomorphology, proximity to HSR, HSR operational characteristics, spatial lag, and economic factors. As DST defines the disaster-prone environment as encompassing both natural and human environments, factors related to the natural environment, such as land use, climate, geology, spatial lag, and geomorphology, along with those related to the human environment, like economic factors, can be integrated into the disaster-prone environment category. According to DST, disaster-causing factors can be classified into natural and human-induced categories. In this study, HSR operational characteristics (human-induced) and proximity to HSR (natural-induced) are identified as disaster-causing factors18.

Fig. 4: Spatial distribution of high-speed rail subgrade defects in China.
figure 4

Map boundaries comply with China’s “Regulations on Public Map Content Representation”60.

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Hypotheses on impact pathways

Researchers have proposed a conceptual model of the causal relationships between HSR subgrade defects and their driving factors, as shown in Supplementary Fig. 6. They have tested it using SEM to examine its statistical significance.

From a perspective of direct impact, the disaster-prone environment (including climate variables, geomorphological variables, land use, spatial lag, geological variables) and disaster-causing factors (such as HSR proximity index, HSR operational characteristics) may all potentially have direct effects on HSR subgrade defects. In previous studies, a range of factors was considered essential, such as geomorphological variables (H1), land use (H2), climate variables (H3), geological variables (H4), and HSR proximity index (H5) respectively42,43,44,45. Data on HSR operational characteristics mainly include the operating period, design speed, operating frequency, and mileage within a district or county. Longer operational periods might face more severe aging issues, thereby increasing the likelihood of defect occurrence46; different design speeds set different standards for subgrade resilience, generally, the higher the design speed, the stronger the resistance to subgrade defects47; the operating frequency directly affects the cumulative stress on the subgrade, continually increasing fatigue and wear in subgrade materials, and when design and construction standards do not fully consider high-frequency use, continuous dynamic loads can exacerbate defect occurrence48; districts or counties with longer stretches of HSR might be more susceptible to defects, also likely passing through more diverse geographical and geological regions49. Thus, the direct impact of HSR operational characteristics on defect pathways corresponds to hypothesis H6. Moreover, it is important to recognize that spatial lag effects, as subgrade defects in regions with similar environmental, geological, and operational conditions, may potentially impact neighboring areas, thereby amplifying the overall risk of defect occurrence and exacerbating defect propagation50. Therefore, the potential impact of spatial lag on defect pathways corresponds to hypothesis H16.

From an indirect perspective, geomorphological variables may influence HSR characteristics, such as complex terrain, which could extend the construction period of HSR (H7). Climate variables might affect land use, such as in arid and semi-arid areas where extreme rainfall could trigger sudden floods, causing soil erosion and affecting subgrade stability (H8). Climate variables could also impact HSR characteristics, as extreme rainfall and the number of freezing days might affect the frequency of HSR operations (H9). Geomorphological variables can affect economic variables. For example, elevation and mountains determine the layout of transportation networks and transportation costs, thereby influencing regional economic output (H10). Economic variables might influence HSR characteristics, as regions with larger populations and higher economic activity typically demand more HSR services, which could lead to increased operating frequencies to meet travel needs (H11). HSR proximity indices could affect HSR characteristics; for example, areas close to water bodies might require exceptional design standards due to geological conditions and terrain complexity, which could influence the design speed of HSR corresponding (H12). Geomorphological variables may influence land use, as residential areas in high-altitude regions often require more resources (H13). Land use may influence HSR operational characteristics; different land use types can affect population density and the distribution of industrial and commercial activities along the rail line, directly impacting the demand for and frequency of HSR operations (H14). Land use can further impact economic factors; larger urban areas typically have higher populations and Gross Domestic Product (H15). Supplementary Table 2 provides detailed explanations for each path (H1-H16).

Data preparation and processing steps

Due to the factors involved having different measurement units and ranges—for example, economic data are typically in the thousands or tens of thousands, whereas climate data may be in decimal values—we adopted Moon’s min-max normalization method to standardize the factors, thereby minimizing the impact of differing magnitudes on analysis results51,52. Min-max normalization was chosen over other methods because it scales all variables to a [0,1] range, ensuring equal contribution to the analysis without introducing biases due to differences in units or magnitudes. This approach is particularly suitable for the SEM analysis conducted in this study, as it better preserves the intrinsic relationships between variables. Definitions and units for the driving factors are provided in Table 1.

Table 1 Categorized variables for high-speed rail subgrade defect analysis
Full size table

Gross Domestic Product data were sourced from the National Earth System Science Data Center (http://www.geodata.cn) for 2015. Additionally, we utilized the zonal statistics function in ArcGIS to aggregate data within specified regions and displayed it in tabular form. Population data were directly obtained from the China National Bureau of Statistics, which conducted the sixth national census 2010. The area of districts and counties was sourced from the 2015 administrative division boundary data of districts and counties in China, provided by the Institute of Geographic Sciences and Natural Resources Research of the Chinese Academy of Sciences (https://www.resdc.cn). The operational start date for HSR was sourced from official websites such as the Chinese Government Network and People’s Railway Network up to January 1, 2023. If a district or county contains more than one HSR line, the comprehensive operational time is calculated based on the proportion of the line lengths. HSR design speed was also sourced from official websites such as the Chinese Government Network, People’s Railway Network, and China Economic Network. The distribution of design speeds for China’s HSR system is shown in Supplementary Fig. 7. HSR operational frequency was obtained from Lulutong software (http://www.lltskb.com/view/32.html). The mileage of HSR within a district or county represents the total length of HSR within that area, calculated using the split intersecting lines function in ArcGIS to break the HSR lines and obtain the length within each district or county. The spatial lag variables were obtained through the application of Moran’s I measurement in ArcGIS to determine whether defects exhibited spatial autocorrelation. If spatial autocorrelation was confirmed, a spatial weight matrix was constructed, and the spatial lag values for each defect were calculated, as detailed in the Supplementary Methods.

Multi-defect model for relationships between factors and defect co-occurrence

This paper employs a multi-defect model to analyze the causal relationships, influencing variables, and pathways among the disaster-prone environment, disaster-causing factors, and subgrade defects. To achieve this, we use SEM as the primary analytical tool. SEM combines confirmatory variables analysis and multiple regression to test predefined hypothesis models. This model is suitable for handling continuous and binary variables, allowing direct incorporation of actual defect data to reveal complex causal relationships between variables53,54.

Using SEM, we can considerably enhance the understanding of defect formation mechanisms, accurately identify key influencing variables, and effectively support disaster risk assessment and management decisions. Before applying the SEM model, certain assumptions must be met: the data used should have no outliers, the causal relationship between endogenous and exogenous variables must adhere to a time sequence, the sample size should be sufficient, and the error terms in the model should be independent of one other. SEM consists of a measurement model and a structural model. The measurement model associates observed variables (such as average annual rainfall, consecutive 5-day rainfall) with latent theoretical variables (such as climate variables), representing relationships between endogenous and exogenous variables. The structural model investigates the causal relationships among these latent variables (such as paths H1-H16), analyzing their interactions55,56. Thus, SEM synthesizes theory and data to analyze the direct and indirect effects between variables systematically. It is calculated according to Eqs. (1)-(3).

$$x={{{\Lambda }}}_{x}\xi +\delta$$
(1)
$$y={{{\Lambda }}}_{y}\eta +\varepsilon$$
(2)
$$\eta ={{{\bf{B}}}}\eta +\Gamma \xi +\zeta$$
(3)

Equations (1) and (2) represent the measurement model, which links observed variables with latent variables. This process helps identify measurement errors and explains how the data reflect the underlying theoretical constructs. Specifically, ξ and η represent the exogenous and the endogenous latent variable, respectively. \({{{\Lambda }}}_{x}\) and \({{{\Lambda }}}_{y}\) denote the relationships between observed exogenous variables and exogenous latent variables, and between observed endogenous variables and endogenous latent variables, respectively. \(\delta\) and \(\varepsilon\) represent the errors in the measurement model for x and y, respectively. Equation (3) is the structural model, which analyzes the causal relationships among latent variables and assess their impact on the overall model. In this model, B is the coefficient matrix representing the impact of endogenous latent variables on exogenous latent variables, \(\Gamma\) denotes the coefficient matrix for the direct effects of exogenous latent variables on endogenous latent variables, and \(\zeta\) is the error vector for the structural equations.

We utilized AMOS (version 23) software to construct an integrated multi-defect model, as shown in the Supplementary Fig. 6. This model includes the disaster-prone environment (climate variables, geomorphological variables, spatial lag, land use data, geological variables, economic variables), disaster-causing factors (HSR proximity indices, HSR operational characteristics), and historical defect investigations. Initially, we fit these factors within the measurement model, during which we will eliminate non-significant paths (P > 0.05) and correlate factors that exhibit associations. Subsequently, we will use the fitted measurement model to compose the structural model according to disaster system theory and refit to exclude non-significant paths (Supplementary Methods). Finally, we use various indicators such as RMSEA (Root Mean Square Error of Approximation) and SRMR (Standardized Root Mean Square Residual) to evaluate the overall fit of the model57,58.

Single-defect model to distinguish the driving mechanisms of each defect

Since each type of subgrade defect is affected differently by the disaster-prone environment and disaster-causing factors, we have also established single-defect models for each type of HSR subgrade defect (settlement, frost damage, uplift deformation, and mud pumping). These models remove latent variables to display the relationships between defects and variable subclasses directly. By deleting non-significant paths and correlating associated variables, we fit each type of subgrade defect to meet model requirements59. Given the absence of latent variables in the single-defect models, we conducted collinearity checks to ensure model stability, excluding variables with a variance inflation factor greater than 10.

To enhance the reliability of the path hypotheses, we conducted mediation effect tests on the pathways indirectly affecting subgrade defects. This paper uses Visual Basic programming within AMOS software to write mediation effect testing code, testing all mediation variables across the SEM (multi-defect, settlement, frost damage, mud pumping, and uplift deformation). Initially, the mediation effect code is tested; subsequently, the Bootstrap method is employed to perform 4000 resamples. The Bias-corrected method and the Percentile method are used to test the mediation variables at a 95% confidence level. If both methods show that the Lower-Upper interval does not include zero and the path significance P < 0.05, then a mediation effect exists, supporting the hypothesis of indirect effects. Additionally, since the SEM relies on linear fitting methods, it may overlook nonlinear relationships and complex interaction effects between variables. Therefore, we further employed Random Forest (RF) to validate variable importance and explore potential nonlinear relationships.