Mechanism and early warning of coal mine rockburst accident based on SD-STAMP-DEMATEL

Abstract

As coal mines shift from shallow to deeper excavation, the number of mines facing the risk of rock burst disasters is gradually increasing. Rockburst, with their characteristics of vibration, suddenness, complexity, and unpredictability, make it increasingly difficult to prevent and control these disasters. Therefore, the challenges of preventing and controlling rock burst disasters are becoming more and more severe. This paper, based on the system-theoretic accident model and processes (STAMP) theory, extracts the causal factors affecting coal mine rock burst accidents. Using the interpretative structural modeling (ISM) and decision-making trial and evaluation laboratory (DEMATEL) method, the accident-causing factors are quantitatively assigned. By constructing model equations and drawing causal loop diagrams and stock-flow diagrams, the event is dynamically simulated and early warnings are issued. The results show that the control defects leading to the accident are analyzed from the perspectives of the government level, management level, grassroots level, physical layer, and the dynamic process of the accident. In the short term, safety investment in grassroots operations is the most effective control. In the long run, the most effective measure is for the management level to strengthen its supervisory work. By changing the input ratios of various variables, it can be seen that different variables in the system dynamics (SD) model have different impacts on coal mine rock burst accidents. It is necessary to continuously strengthen the implementation of the safety responsibility system, improve the work efficiency of the government and management level, and enhance the timeliness of emergency decision-making.

1. Introduction

Coal mine rock burst accidents refer to the phenomenon during coal mining where, due to geological conditions and coal mining techniques, the coal seam's roof or floor suddenly fractures, moves, or collapses [1]. This can seriously affect mine production and may even result in casualties and property damage. As early as 1933, China experienced coal mine rock burst accidents. In recent years, the number of rock burst mines in China has shown an increasing trend [2]. Currently, there are 150 rock burst mines nationwide (including 2 managed as rock burst mines) [3]. Due to the vast reserves and wide distribution of coal resources, which are crucial energy resources in China, and given that coal mining is characterized by high risk, high investment, and high efficiency, coal mine rock burst accidents represent not only a significant scientific issue but also one of the severe challenges facing coal mine production safety in China.

Coal mine rock burst accidents are usually not caused by a single factor but result from the interaction and accumulation of multiple factors. Moreover, these interacting factors have varying degrees of importance when leading to rock bursts in coal mines. The key is to quantitatively and qualitatively assess the potential impacts of various influencing factors, assisting mine managers and experts in proposing targeted measures to reduce accident risks. If rock burst accidents in coal mines can be analyzed for early warning from a systematic perspective, it would not only allow for analyzing the multi-level causes of accidents and identifying potential threats in the system, providing a structured framework for decision-making but also help decision-makers better understand the complexity of the issues at hand. By basing decisions on both quantitative and qualitative information, wiser choices can be made. This can enhance the effectiveness of the accident early warning system, reduce risks, and improve mine management efficiency.

Rock burst early warning is an essential link in disaster prevention and mitigation and can provide guidance for the management of rock bursts. In the initial stages of rock burst risk prediction, the danger level of the mining area is typically assessed statically. Commonly used methods include the comprehensive index method [4], likelihood index method [5], and multi-factor coupling method [6]. Starting from the mechanism of rock burst occurrence, it was found that when a rock burst occurs in a mine, there is a phenomenon of stress concentration inside the coal and rock mass. Many scholars have carried out a series of studies on this. For example, Fan Xin et al. [7] based on wavelet theory, we propose using wavelet scattering decomposition to extract features of microseismic events and noise signals. Yao Mingyuan and others [8], using the rock burst initiation theory, classified geoacoustic early warning signals into three types. By analyzing changes in geoacoustic frequency and energy, they provided early warnings for rock bursts. Wang Enyuan and others [9] found that electromagnetic radiation is abnormal in areas with rock burst risks. They developed an electromagnetic radiation monitoring instrument to achieve non-contact prediction. However, due to the limitations of single detection methods, various equipment differ in their monitoring principles, methods, and focus points. This leads to inconsistencies in early warning results using different monitoring equipment, resulting in inefficient use of instrumentation and even occurrences of false negatives or false positives. Therefore, the monitoring and early warning for rock bursts have gradually transitioned to multi-parameter [10], multi-scale comprehensive detection [11], combining both physics-driven and data-driven approaches to dynamically and real-time determine the level, timing, and area of rock bursts in the working face [12]. Currently, many researchers have applied deep learning to the early warning of rock burst accidents. Cao Yali and others [13]built a rock burst early warning model based on convolutional neural networks (CNN), extracting features from time series for predictive warnings; Shi Ce and others [14] combined the PAC method with GRNN to construct a PAC-GRNN model for predicting the risk of mine rock bursts; Chen Jie and others [15]proposed using machine learning to overcome the limitations of traditional methods.

Even so, there are still many pressing issues in this field that need to be addressed, such as the lack of scientific theoretical guidance in choosing early warning methods. Different detection equipment might produce conflicting early warning results, making it difficult for mine managers with limited experience to make the correct decisions. In the context of coal mine rock bursts, where the “mechanisms of occurrence are unclear, prevention measures are ineffective, and the regulatory system is incomplete” [16], literature on coal mine rock burst early warnings indicates that most works focus on the rock bursts themselves. These methods aim to monitor and analyze the stress, strain, and deformation experienced by underground rock layers during mining, as well as the stability of underground spaces. While these methods mainly focus on geological and geopressure physical factors, they often overlook the roles of other elements within the entire system.

This article first constructs a systematic accident model based on the STAMP theory. It not only focuses on the direct causes of accidents but also considers the complex interactions and hierarchical structure within the system. By deeply understanding the system's functions and structures, potential accident risks can be better identified. Based on the constructed accident model and by extracting causative factors combined with the DEMATEL-ISM method, a structured framework is provided for decision-making. This can help decision-makers better understand the complexity of decision-making issues and make wise decisions based on both quantitative and qualitative information. As for the long-term development and challenges of coal mines, as well as the feedback relationships and interactions between various factors, the system dynamics model can provide a good explanation. Finally, the Hu Jiahe Mining coal mine rockburst accident was selected for case verification. Through an in-depth analysis of the accident in this mine, the main reasons for the formation of rockburst and the key factors leading to the accident were revealed from four perspectives: the government level, management level, grassroots level, and physical level. Overall, this research not only provides systematic technical support for preventing coal mine rockburst accidents but also offers valuable experience and lessons for other mines. It helps mine managers better understand, prevent, and control the risks of rockburst.

2. Methodology

2.1. STAMP theory

STAMP (Systems Theoretic Accident Modeling and Process) was proposed by Professor Nancy Leveson of the Massachusetts Institute of Technology in 2004. In STAMP, a system is seen as interconnected components that maintain a dynamic equilibrium state through information and control feedback loops, transforming safety issues into control problems [17]. The STAMP model views accidents as the result of incomplete control or the absence of safety constraints within a system. Currently, the STAMP model is extensively used across diverse domains, including risk assessment of railway transport for hazardous materials [18], building safety evaluations [19], and identification of safety hazards during emergency evacuation [20].

The STAMP model consists of three fundamental elements: safety constraints, a hierarchical safety control structure, and process models and control loops. Safety constraints refer to the processes that act as safety barriers and prevent the system from reaching hazardous states [21]. In the case of existing coal mine rockburst accidents, accidents are not the result of component failures but rather the violation of safety constraints due to the coupling and interaction among various safety subsystems. The behaviors of individual subsystems, as well as the interactions between these subsystems at various levels, must be confined within safety constraints. The hierarchical control structure divides subsystems from top to bottom based on control relationships, with upper-level subsystems providing constraints for the operations of lower-level subsystems. Lower-level subsystems provide feedback to upper-level subsystems, forming control loops and making decisions. The interaction relationships between subsystems at each level can be represented by process models and control loops, which include safety constraints (i.e., controllers) and controlled processes (Fig. 1).

Fig. 1.

Process model and control defects classification schematic.

Constructing a coal mine safety control structure is the foundation for conducting causal analysis using the STAMP (Systems Theoretic Accident Modeling and Process) model. Based on the actual circumstances of coal mine accidents, the safety control structure can be divided into four levels: government, management, grassroots, and physical layers. (1) Government layer: In the coal mine accident system, the government layer is responsible for formulating policies and regulations, and it needs to establish relevant safety policies and standards to ensure system safety (2) Management layer: The management layer involves coordinating and integrating resources. In the coal mine accident system, safety management and risk prediction are necessary to enable prompt response measures in the event of an accident. The management layer is responsible for coordinating information flow and decision-making among different levels, ensuring the overall system's safety operation. (3) Grassroots layer: The grassroots layer is the operational level where coal mine work is carried out. Grassroots workers need to follow instructions and implement safety measures to ensure the normal operation and safety of the coal mine system. Training and raising awareness among Grassroots employees are crucial for accident prevention. (4) Physical layer: The physical layer consists of specific equipment, processes, and the external environment. In coal mine system safety, the physical layer needs to focus on equipment reliability, construction process safety, and the stability of the external environment to prevent safety risks caused by physical factors. The design, maintenance, and monitoring of the physical layer are all essential for ensuring coal mine system safety.

By analyzing and understanding the interaction among these four levels, a deeper insight into the safety control mechanisms and potential system risks in the coal mine system can be gained. This facilitates the identification of factors contributing to accidents and provides a scientific basis and guidance for accident prevention and safety management.

2.2. Hybrid modeling analysis based on DEMATEL and ISM

The DEMATEL (Decision-Making Trial and Evaluation Laboratory) method was proposed by American scholars in 1971 as a technique for analyzing the relationships among factors in a system [22]. It combines principles from graph theory and matrix theory to construct a direct influence matrix by analyzing the logical relationships between factors in the system. By calculating centrality and causality, the DEMATEL method allows for the hierarchical classification of factors [23]. The DEMATEL model can analyze both the direct and indirect relationships among all factors, providing insights into the causal relationships in complex systems and assisting decision-makers in making informed decisions. The DEMATEL method is applicable to complex problems that require the balancing of multiple factors in decision-making, such as analyzing risk factors in construction safety or studying the influencing factors of urban residents' waste classification.

On the other hand, Interpretive Structural Modeling (ISM) is a technique within the domain of structural modeling. It decomposes complex systems into subsystem elements and then constructs a multi-level hierarchical structure based on practical experience, knowledge, and computer assistance [24]. ISM reveals the influence paths and hierarchical structure among complex factors.

Both the DEMATEL and ISM methods are widely applied as important approaches for analyzing complex systems. The integrated DEMATEL-ISM method combines the principles of both methods. It categorizes factors in complex problems and establishes their interdependencies. By constructing a directed hierarchical structure model for complex decision-making problems, the method achieves problem structuring [25]. The working mechanism of the method is illustrated in Fig. 2.

Fig. 2.

DEMATEL-ISM method working mechanism diagram.

The steps of hybrid modeling are as follows.

• 1)Extract risk factors based on the STAMP model, where n is the number of factors and A is the set of factors.

$${\mathrm{\alpha }}_1{，\alpha }_2，{\alpha }_3\dots \dots {\alpha }_n\in A$$ (1)

• 2)Quantify the influence relationships between factors using the 0–4 scoring method based on expert experience (assign values of 4, 3, 2, 1, or 0 for strong, moderate, weak, no influence) (see Fig. 3). Construct the direct influence matrix B (B = ${\left[{\beta }_{ij}\right]}_{n\times n}$， $\mathrm{i}，\mathrm{j}=1，2，\dots \dots \mathrm{n}$) where ${\beta }_{ij}$ represents the degree of influence of factor ${\alpha }_i$ on factor ${\alpha }_j$. If i = j, ${\beta }_{ij}$ = 0.
• 3)Normalize the original relationship matrix to obtain the normalized influence matrix N ($\mathrm{N}={\left[{\mathrm{n}}_{\text{ij}}\right]}_{\mathrm{n}\times \mathrm{n}}$， $\mathrm{i}，\mathrm{j}=1，2，\dots \dots \mathrm{n}$).

$$\mathrm{N}=\frac{1}{\underset{1\le \mathrm{i}\le \mathrm{n}}{\max }\sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{\beta }}_{\text{ij}}}\mathrm{B}$$ (2)

• 4)Calculate the comprehensive influence matrix T (T = [${t_{ij}]}_{n\times n}，\mathrm{i}，\mathrm{j}=1，2，\dots \dots \mathrm{n}$) based on the normalized direct influence matrix. The normalized direct influence matrix is repeatedly multiplied by itself until all values converge to zero, resulting in a zero matrix. The comprehensive influence matrix represents the sum of indirect influences between elements and can be calculated using the following formula [26]:

$$\mathrm{T}=\mathrm{B}+{\mathrm{B}}^2+{\mathrm{B}}^3+\dots +{\mathrm{B}}^{\mathrm{n}}=\sum _{\mathrm{n}=1}^{\infty }{\mathrm{B}}^{\mathrm{n}}$$ (3)

$$\mathrm{T}=\mathrm{B}{\left(\mathrm{I}-\mathrm{B}\right)}^{-1}$$ (4)

Where I is the identity matrix.

$${\left(\mathrm{I}-\mathrm{B}\right)}^{-1}\text{is}\text{the}\text{inverse}\text{matrix}\text{of}\left(\mathrm{I}-\mathrm{B}\right)$$

• 5)Calculate the influence degree ($f_i$), influenced degree ($e_i$), centrality ($M_i$), and causality ($R_i$)of each causal factor based on the comprehensive influence matrix. The sum of influence degree and influenced degree represents the centrality of the factor, and the difference between influence degree and influenced degree represents the causality. Causality can be used to determine the type of factor. If the causality is greater than zero, the factor is a causal factor; otherwise, it is a result factor.
• 6)Plot the cause-effect diagram based on the calculated causality and centrality, indicating the positions of each causal factor on the coordinate axis. Identify the key causal factors and analyze the problem [27].

$$f_i={\sum }_{j=1}^n{t}_{ij},i=1,2\dots n$$ (5)

$$e_i=\sum _{j=1}^n{t}_{ij},i=1,2,\dots n$$ (6)

$$M_i=f_i+e_i,i=1,2\dots n$$ (7)

$$R_i=f_i-e_i,i=1,2\dots n$$ (8)

• 7)Calculate the overall influence matrix K ($\mathrm{K}={\left[{\mathrm{k}}_{\text{ij}}\right]}_{\mathrm{n}\times \mathrm{n}}，\mathrm{i}，\mathrm{j}=1，2，\dots \dots \mathrm{n}$) based on the comprehensive influence matrix T.

$$\mathrm{K}=\mathrm{T}+\mathrm{I}$$ (9)

• 8)Introduce a threshold λ and calculate the reachable matrix R ($\mathrm{R}={\left[{\mathrm{r}}_{\text{ij}}\right]}_{\mathrm{n}\times \mathrm{n}}，\mathrm{i}，\mathrm{j}=1，2，\dots \dots \mathrm{n}$)

$$r_{ij}=1，if{k}_{ij}>\mathrm{\lambda }$$ (10)

$${\mathrm{r}}_{\text{ij}}=0，\text{if}{\mathrm{k}}_{\text{ij}}<\mathrm{\lambda }$$ (11)

Fig. 3.

Hujiahe coal mine rockburst accident scene map.

The selection of the threshold should consider the specific application requirements. A lower threshold may include non-critical points, while a higher threshold may filter out important points. Therefore, it is necessary to experiment and evaluate to determine an appropriate threshold.

• 9)Determine the reachable ($r_i$)set and antecedent ($s_i$) set of causal factors.

$$R_i=\left\{a_j\right|a_j\in A,R_{ij}\ne 0\}，i=1，2，\dots \dots ，n$$ (12)

$$S_i=\left\{a_j\right|a_j\in A,R_{ij}\ne 0\}，i=1，2，\dots \dots ，n$$ (13)

where A is the set of causal factors.

• 10)Verify the following condition, and if it holds, it indicates that the element is a bottom-level element. Remove the i-th row and column from the R matrix.

$$S_i\cap R_i=R_i，i=1，2，\dots \dots ，n$$ (14)

• 11)Repeat steps 3 and 4 until all factors have been removed.
• 12)According to the order of removed factors, draw a multi-level hierarchical structure diagram.

3. Instance validation

On October 11, 2022, at 13:52, a major rockburst accident occurred in Shaanxi Binchang Mining Group Co., Ltd. The accident took place in the return airway of the 402104 fully-mechanized mining face, specifically in the area 20–124.4 m ahead of the face. A total of 104.4 m of roadway was destroyed. The accident resulted in 4 fatalities, 6 serious injuries, 20 minor injuries, and a direct economic loss of 13.9126 million RMB.

Hu Jiahe Coal Mine Company is one of the five coal mines under Binchang Mining Group. The mining company had twice commissioned Tian Di Technology Co., Ltd. to assess the risk of rockburst and design prevention measures. The assessment identified the 402104 fully-mechanized mining face as having a high risk of rockburst and divided it into 22 rockburst-prone areas. The accident occurred in the return airway of the 402 panel, specifically in the region 20m–124.4 m ahead of the face. At the time of the rockburst, there were no other mining activities within a 500 m radius, with the closest working face being the 401110-transport heading, located 3067 m away.

Based on on-site exploration and historical records of the accident area, it was found that the advance section of the return airway of the 402104 fully-mechanized mining face had experienced floor heave, roof subsidence, and rib spalling in early September 2021. The floor heave reached 1 m towards the outbye roadway, causing difficulties in retracting the advancing supports and installing additional rockburst prevention supports. The mining team arranged dedicated personnel for maintenance operations, and the mine management held coordination meetings to discuss the progress of repairs and address any issues. On September 27, 2021, the amount of roadway repair work increased, and on October 1, a 40-ton scraper conveyor was installed within the range of 76 m ahead of the return airway. Starting from October 3, the scraper conveyor was used to transport the bottom coal, which was then loaded onto rubber-tired haulage trucks and transported along the return airway to the belt conveyor transfer point in the main roadway. The direct cause of this accident was determined to be coal instability caused by extensive hard roof strata cutting and caving due to mining-induced disturbances. Fig.3 And Fig.4 depict the scene of the rockburst accident in Hu Jiahe Coal Mine and the distribution of equipment at the site.

Fig. 4.

Equipment distribution diagram.

3.1. Construction of safety control structure of rockburst accident in Hujiahe mining coal mine

To analyze the various causes of the rockburst accident at Hu Jiahe Coal Mine in a more specific manner, it is important to consider the actual operational conditions of the coal mine (see Fig. 4). Based on the STAMP model, the safety of the system can be evaluated by identifying safety constraints at the system level. The accident occurred due to inappropriate implementation of safety constraints [28].To analyze the reasons for inappropriate control measures, we need to establish an accident safety control structure and pinpoint the inappropriate controls. This will help refine the safety constraints. The safety control structure for the rockburst accident at Hu Jiahe Coal Mine is illustrated in Fig. 5.

Fig. 5.

Safety control structure model of rockburst accident in Hujiahe mining mine.

3.2. Screening of rockburst accident in Hujiahe mining coal mine

According to the security control structure and accident analysis report mentioned above, factors leading to the accident can be extracted from two aspects: management hierarchy and time sequence. Specifically, improper behaviors of the government level, management level, grassroots level, and physical level should be analyzed in terms of pre-incident, during-incident, and post-incident phases to identify the hazardous factors that caused the accident. Based on the STAMP layered security control structure, each level should be analyzed sequentially to identify the hazardous behaviors, associated hazards, safety requirements and constraints, implemented controls, and external environmental factors related to control deficiencies.

Improper control behaviors at the government level: The Xianyang Coal Industry Bureau, as the highest-level institution in the entire hierarchical control structure, failed to take measures to rectify the daily violations of workers by mine safety supervisors, ultimately leading to the occurrence of the accident. Typically, the coal industry bureau is responsible for supervising and implementing the safety production responsibility system for coal resource extraction. However, in practice, the mine safety supervisors did not effectively supervise the work, indicating loopholes in the safety supervision of the Hujiahe Coal Mine.

Improper control behaviors at the management level: Based on the accident investigation report and actual circumstances, there were many improper behaviors at the management level in this accident. Firstly, the direct supervisory department did not promptly stop and punish the underground workers' violations. Even in the case of severe deformation and floor heaving in the back-above-section of the 402104 fully-mechanized face, they did not implement measures such as production limitation, personnel limitation, and time limitation. The fact that they not only arranged personnel to work in the stress concentration area but also allowed over-limit repair operations in the back-above-section of the working face indicates weak safety awareness both in the supervisory department and among the workers. This also reflects the inadequate safety awareness training for the workers by the supervisory department. Secondly, the Hu Jiahe Mining Company had inadequate rockburst prevention and control measures and did not focus on cultivating top technical talents, resulting in insufficient understanding of the dangers related to rockburst mechanics and disturbance hazards in roadway repair operations under complex conditions. This also led to inadequate analysis and judgment of the impact hazards. From September 27th until the accident occurred, the floor heaving was severe within a 100-m range of the return airway of the 402104 fully-mechanized face, and the energy frequency of microseismic monitoring increased. At this point, relevant departments should have recognized the problem and proposed corresponding measures. However, due to the insufficient understanding and lack of attention, the conclusion of the impact hazard analysis and judgment remained “moderate risk".

Improper control behaviors at the grassroots level: In this accident, there were multiple occurrences of workers' violations, such as the loss of control at the workface anti-impact limit management station, cross-sectional and cross-working operations for roadway reinforcement and floor lifting, and the failure of on-site management personnel to take measures against violations. This indicates that workers' violations are not exceptional and that higher-level supervisory departments are lax in management or even unable to directly manage. However, a more important factor is the inadequate qualifications of the workers. In order to obtain greater benefits, the construction team chose to hire idle labor from rural areas surrounding the mine who had not received professional training but were willing to accept lower wages. This led to workers making incorrect decisions or engaging in improper control behaviors without proper professional and safety training.

Improper control behaviors at the physical level: Scholars and experts in the field of rockburst prevention and control at scientific research institutes identified the 402104 fully-mechanized face as having a high risk of rockburst. The face was divided into 22 rockburst hazard zones, including 10 zones with moderate impact hazards and 12 zones with strong impact hazards. According to regulations, it is strictly prohibited to conduct parallel operations for roadway expansion and backfilling within the affected area of mining. However, in reality, during the maintenance of the roadway, a 40-ton scraper conveyor and control switch were installed within 200 m of the working face, with only pillars installed at the head and tail of the scraper conveyor, while other areas lacked proper fixation measures. For development driveways with moderate and higher impact hazards, active support methods with strong deformation resistance and strata protection capabilities should be adopted, such as high pre-stressed fully-grouted anchor cables, yielding anchor rods, high-strength protective steel straps, high-strength protective nets, and large-diameter trays. These should be combined with reinforcing support methods that still provide a safe space after being subjected to impact, such as retractable U-shaped steel sheds, hydraulic unit supports, or gantry supports. However, in the accident area, the roadways were supported using anchor cables with mesh and grouting, as well as unit supports for reinforcement. Under strong impact loads, these support measures partially failed, leading to casualties.

According to the analysis of unsafe behaviors in the previous text, after classification and summarization, a total of 24 causal factors for the Hu Jiahe coal mine rockburst accident were identified. The system hierarchy of each causal factor is shown in the table below.

3.3. Quantitative analysis of the factors caused by rockburst accident in Hujiahe mining coal mine

• 1)Select 24 causal factors that lead to the occurrence of accidents based on the STAMP model. Set this set of factors as A.
• 2)Experts rate the degree of influence between causal factors and create a direct influence matrix B. To visually represent the relationships between factors, use a Cartesian heatmap instead of the direct influence matrix, as shown in Fig. 6.

• 3)Normalize the direct influence matrix B to obtain the normalized direct influence matrix N using MATLAB, according to Eq. (2). Then, process the normalized influence matrix N using Eq. (4) to obtain the comprehensive influence matrix T. Quantify the centrality, causality, impact, and affectedness of each causal factor based on the comprehensive influence matrix (as shown in Fig. 7). This quantification can be depicted in Fig. 8 and Fig. 9.

• 4)The overall influence matrix is calculated based on equation (9). To eliminate relationships with minimal influence between factors, a threshold value λ is introduced. Based on expert advice, λ values of 0.02, 0.05, and 0.1 are selected. By performing calculations, it is determined that λ = 0.02 best matches the actual situation. Combining the selected threshold value, the reachable matrix is calculated using equations (10), (11), as shown in Fig. 10.

• 5)Based on equation (14), the reachable matrix is used for hierarchical partitioning, resulting in the construction of a hierarchical structure model for the causal factors of the Hu Jiahe Mine rockburst accident. as shown in Fig. 11.

Fig. 6.

Direct influence matrix.

Fig. 7.

Comprehensive influence matrix.

Fig. 8.

Influence degree - Influenced degree.

Fig. 9.

Centrality-causality.

Fig. 10.

Reachable matrix.

Fig. 11.

Hierarchical structure model.

3.4. Results for discussion and analysis

• 1)According to the distribution of inappropriate behaviors in Fig. 5, it can be observed that the rescue activities carried out by various levels of units during the accident were relatively timely, and the post-accident handling was also compliant and reasonable. However, it also exposed the inadequate performance of various levels of work before the accident, weak awareness of safety red lines, and the problem of prioritizing production over safety. Therefore, efforts should be made to strengthen the management at various levels in order to prevent and control rockburst accidents in coal mines. Mine safety inspectors should strictly and conscientiously fulfill their responsibilities. Meanwhile, leaders and safety production management personnel should firmly implement the safety responsibility system. Violations such as multiple concentrated cross-repairs in the same area, exceeding the permitted number of workers, and allowing workers to enter high-risk impact areas without positioning cards should be avoided.
• 2)From Figs. 8 and 9, it can be seen that issues such as inadequate implementation of the safety responsibility system (S1), workers not following rules and regulations (S4), insufficient implementation of rockburst prevention measures (S3), and inadequate establishment of rockburst prevention systems (S2) have higher centrality and influence within the entire complex system structure. This requires government departments to effectively carry out safety supervision work, including conducting comprehensive inspections and checks on coal mines, implementing special supervision at all stages of the system, and county-level leadership oversight. After the government departments issue requirements, mining companies should immediately rectify the identified problems and provide timely feedback on the rectification progress.
• 3)According to Fig. 11, factors such as poor physical and mental conditions of workers (S24), inadequate risk analysis and judgment (S19), and equipment malfunctions in mining (S18) are direct influencing factors, while chaotic rockburst management in the mine (S8) and inadequate support resistance design (S9) are transitional factors, and inadequate implementation of the safety responsibility system (S1) and imperfect rockburst prevention systems (S2) are deep-layer factors. In the short term, taking measures to strengthen the control of these direct influencing factors can rapidly and significantly reduce the occurrence rate of rockburst accidents in coal mines, as well as minimize casualties and property losses during accidents. For example, in the case of workers' violations, mining-related departments should define the criteria for unauthorized operations and strengthen the investigation and accountability of responsible individuals, while also closely monitoring the physical and mental conditions of grassroots workers, especially those who have experienced mining accidents. Prompt treatment and psychological counseling should be provided, and cases of workers with illnesses entering the mine should be strictly prohibited.

4. 4 Early warning analysis of rockburst accident in Hujiahe mining coal mine

4.1. 1 Analysis of subsystems and key influencing factors

The coal mine rockburst accident is a dynamic and evolving process that requires considering the influences of multiple factors. System Dynamics (SD) is a method that can measure the long-term dynamic changes in complex systems [29]. Therefore, based on the System Dynamics approach combined with the factors identified through the STAMP method and the specific circumstances of the Hu Jiahe coal mine, the system can be divided into four subsystems: the government subsystem, management subsystem, grassroots subsystem, and physical subsystem. These subsystems interact and influence each other, forming an organic whole. Safety investment, which encompasses human resources, material resources, and financial resources, directly affects the level of safety in the system [30].

4.2. Causality analysis between the influencing factors

Vensim software is a modeling, analysis, and visualization tool designed by Ventana Corporation in the United States [31]. It is used for modeling various complex systems to help businesses, researchers, and others better understand and control these systems, Causal loop diagrams consist of multiple orthogonal factors and describe the causal relationships that contribute to the occurrence of a particular system behavior. The causal relationships are represented by directed arrows, with the cause pointing to the effect. Each causal link can have positive or negative polarity. Positive feedback loops, denoted by "+", indicate that system elements increase as the influence increases. For example, enhancing the knowledge and skills of underground workers in preventing coal mine accidents can lead to a greater emphasis on individual protection and a reduction in casualties during accidents. Strengthening the implementation of corporate responsibility and holding the primary individuals accountable for violations related to coal mine accidents can improve the safety level of the management team. All these variables affect the overall safety level of the coal mining system. On the other hand, negative feedback loops, denoted by "-", indicate that system elements decrease as the influence increases. The causal loop diagram for coal mine rockburst accidents is represented in Fig. 12.

Fig. 12.

Cause and effect loop diagram.

4.3. Quantitative analysis of the influencing factors

A stock and flow diagram is used to describe the changes and evolution trends among variables within a system. It consists of elements such as stock variables, flow variables, auxiliary variables, and functions. Stock variables represent accumulative quantities within the system, flow variables represent dynamic changes, and constants are important parameters that determine the system's structure. The design of stock and flow diagrams is based on research hypotheses and causal loop diagrams. They help researchers delve into the causes and effects within the system, enabling the formulation of more reasonable policies and measures. Each variable can reflect the actual safety status of the enterprise-government-management-grassroots-physical subsystems, accurately representing the logical and dynamic relationships among the indicator variables. The stock and flow diagram for the safety level of coal mine rockburst accidents is shown in Fig. 13 below.

Fig. 13.

Stock and flow diagram.

Combined with the actual situation of the coal mine accident site, the influencing factors of the accident are analyzed, and the following equation is constructed according to the system dynamic principle [32].

$$\mathrm{Z}=\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{W}}_{\mathrm{i}}\bullet {\mathrm{Y}}_{\mathrm{i}}$$ (15)

$$Y_i=INTEG\left(R_i,0\right)$$ (16)

$$R_i=W_{ij}\bullet P_{ij}$$ (17)

$$S_{ij}=WITHLOOKUP\left(TIME,\left(\left[\left(a，b\right)-\left(c，d\right)\right],\left(e，f\right)\cdots \right)\right)$$ (18)

In the equation:

Z represents the level value of the coal mine safety system.

W represents the weight value ($W_i$ represents the weight value of the i-th subsystem or $W_{ij}$ the weight value of the j-th influencing factor in the i-th subsystem).

$Y_i$ represents the level value of the i-th subsystem.

$R_i$ represents the level increment of the i-th subsystem.

$P_{ij}$ represents the evaluation value of the j-th influencing factor in the i-th subsystem.

$S_{ij}$ represents the conversion rate of the input on the j-th influencing factor in the i-th subsystem.

DT represents the time step length.

Other variables are initial values or constants (see Table 1).

Table 1.

Hierarchy of causal factors.

System hierarchy	No.	Casual factor
Government level	S1	Incomplete implementation of safety responsibility systema
	S2	Incomplete institutional constructionb
	S15	Inadequate regulatory and supervisory workc
Management level	S3	Inadequate implementation of measure
	S5	Security awareness level
	S6	Penalties for non-compliant behavior
	S7	Failure to prepare contingency plans
	S8	Mining management chaosd
	S10	Lack of meticulous work on hidden danger inspection
	S17	Deviations in mine hazard prediction and warning
	S22	Early warning system anomaly
	S23	The degree of perfection of the strategy feedback system
Grassroots level	S4	Staff did not work in accordance with the rules and regulations
	S12	Not wearing the required personal protective equipment
	S14	Coal mine working face advance speede
	S16	Improper equipment settingsf
	S19	Insufficient analysis and judgment of risksg
	S24	Poor psycho-physical condition of staff
Physical level	S9	Unreasonable design of coal seam support resistanceh
	S11	Decreased coal seam stability
	S13	Irrational mining sequencei
	S18	Mining equipment failure
	S20	Irrational layout of mining area roadwayj
	S21	Substandard quality of mining equipment

^aThe safety responsibility system is a management measure, primarily aimed at ensuring that leaders and employees at all levels of a company or organization clearly understand their responsibilities and obligations in safe production.

^bIt typically refers to a system or organization that lacks adequate systems or measures for preventing unexpected events or responding to crises.

^cIt suggests inadequate supervision and inspection of certain risk factors or potential issues, which could lead to an increased potential risk and even possible accidents or incidents.

^dFor example, the mine safety inspector did not supervise as required, and multiple violations by workers went unmanaged.

^eThe advancement speed of the coal mine working face refers to the rate at which the working face progresses during the coal mining process, typically used to measure the production efficiency of the coal mine.

^fThe placement of equipment needs to consider factors such as location, spacing between devices, and coverage area.

^gWhen assessing and managing the risks related to rockburst, the analysis and judgment are not sufficiently thorough or accurate.

^hThe design of support resistance needs to take into account the type of support, ground pressure, and support materials.

ⁱFirstly, consider safety risks such as mine pressure, rockburst, and toxic and harmful gases, and then formulate the corresponding mining sequence.

^jThe mining area tunnel refers to the underground passage excavated in the mining area of the mine for the purpose of extracting the ore body. The layout of the tunnel should be based on geological conditions, ore body shape, mining methods, and equipment requirements.

4.4. Evolutionary early warning

According to the characteristics of coal mine rockburst accidents, the simulation is conducted using Vensim software. The simulation unit is set as months, and the simulation period is 12 months with a time step of 1 month. Based on the research data and expert scoring results, the initial values of the sub-variables in the government, management, grassroots, and physical subsystems are assigned. The initial values for the level variables are set as (C1, C2, C3, C4) = (70, 80, 60, 60) (dimensionless). Then, the relative weights of each influence factor are obtained by summing and normalizing the influence and influenced degrees calculated by the DEMATEL method [33], their weights are shown in Table 2 below. Finally, by substituting the values of the variables into the SD equations, the model is run to obtain the results shown in Fig. 14.

Table 2.

Element weighting table.

Fig. 14.

Evolutionary results.

The safety evaluation indicators for coal mines are highly complex, consisting of both qualitative and quantitative measures that are difficult to directly compare in terms of superiority or inferiority. To achieve the transformation from qualitative to quantitative evaluation, we refer to the safety grade evaluation criteria established in fuzzy comprehensive safety assessment research for coal mines and make necessary modifications. The safety grade evaluation criteria are defined as follows: “Light Alert” (≥90 points), “Low Alert” (80–89 points), “Medium Alert” (70–79 points), “Heavy Alert” (60–69 points), and “Critical Alert” (<60 points). By establishing these evaluation criteria, the smooth conversion from qualitative evaluation to quantitative scores can be achieved. Using the simulation model, dynamic simulation analysis is conducted on the influencing factors at various levels of the coal mine safety level. The simulation results are compared with the predetermined reference values for the warning zones. Based on different alert levels, different signals, namely warning signals, are issued. The division of rockburst accident warning level zones and the setting of warning lights are shown in Fig. 15.

• (1)Green: Safety level value S ∈ (100, 90]. At this stage, the coal mine system is in a safe state, with the lowest possibility of accidents and the highest overall safety level.
• (2)Yellow: Safety level value S ∈ (90, 80]. At this stage, the coal mine system is in a relatively safe state, but there are certain risk factors in the system. The interaction and coupling of these factors lead to a decrease in safety level.
• (3)Orange: Safety level value S ∈ (80, 70]. At this stage, the coal mine system is in a relatively dangerous state, with a large number of risk factors present. The likelihood of accidents is high, and there may be some sudden incidents. Corresponding measures must be taken to further strengthen prevention and control.
• (4)Red: Safety level value S ∈ (70, 60]. At this stage, the coal mine system is in a dangerous state, with significant hidden risks. The possibility of accidents occurring is very high, and immediate hazard investigation work must be conducted, along with measures to control the situation.
• (5)Dark red: Safety level value S ∈ (60, 0). At this stage, the coal mine is in an extremely dangerous state, with the possibility of accidents occurring at any time. Immediate production suspension and rectification measures must be taken.

Fig. 15.

Accident warning level regional division and the setting of police lights.

Based on the coal mine safety system level curve in Fig. 14, it can be observed that the increase in investment gradually leads to an increase in the coal mine safety system level. From months 0–5, the coal mine safety system level increases at a relatively slow pace. This indicates that the improvement of the coal mine safety system level is not an instantaneous process but rather a cumulative one over time. From months 5–9, there is a rapid increase in the coal mine safety system level, indicating that increased safety investment has an impact on coal mine safety. From months 9–12, the increase becomes more moderate, which can be attributed to a higher coal production emphasis and lower safety considerations during the winter heating period. Therefore, it is important to focus on the changing trends of the influencing factors, study the main reasons for the coal mine system being in a dangerous state, analyze them step by step, and identify the fundamental causes leading to a dangerous state. This will help determine the key areas of risk prevention and control and prevent rockburst accidents.

The upward trend of the coal mine safety system level indicates an improvement in coal mine safety conditions. It is important to analyze the influencing factors with high impact levels and study the conversion rates of those factors' inputs. Corresponding control measures should be formulated and implemented to ensure the continuous growth of the overall coal mine system level.

Based on the simulation and analysis of the SD model, adjustments are made to the government-level factors, management-level factors, grassroots-level factors, and physical-level factors proportionally, in order to further analyze the coal mine rockburst accident model. In this study, the inputs of the four influencing factors are reduced by 40%, and the differences in emergency management effectiveness are compared among the five scenarios. The results are shown in Fig. 16. From the figure, it can be seen that compared to the initial value of the coal mine safety system level, when the management-level factors are reduced by 40% while other factors remain unchanged, the safety level decreases by 0.5393 from months 0–6 and decreases by 1.0023 from months 6–12. This indicates that the management-level factors have a significant impact on coal mine safety, and their influence becomes more significant over time. The management-level factors include the implementation of rockburst prevention measures, reinforcement of rockburst awareness, punishment for violations related to rockburst, development of emergency response plans, management of rockburst prevention, hazard inspections in mines, rockburst risk predictions, and feedback and revision of rockburst prevention strategies. However, due to the time required for policy adjustments and implementation, changes in safety investment in management-level factors do not have an immediate impact on the coal mine safety system in the short term. Nevertheless, the reduction in safety investment in the later stages leads to a significant decrease in the coal mine safety system level, highlighting the long-term nature of management issues. In daily management, relevant departments should strictly enforce workers' compliance with regulations and impose severe penalties for violations. Additionally, management departments should educate workers about safety awareness and improve policies to ensure worker safety.

Fig. 16.

Simulation results of evolution under different scenarios.

When the government-level factors are reduced by 40% while other factors remain unchanged, the safety level decreases by 1.4939 from months 5–12. The government-level factors include the implementation of safety responsibility systems, the establishment of rockburst prevention regulations, and the supervision of rockburst prevention. This indicates that government regulation plays an important role in ensuring coal mine safety. However, the lack of communication and coordination feedback loops between the coal industry bureau and coal mines results in delayed problem-solving and policy formulation, causing a lagged effect of safety investment on government-level factors. Therefore, it is necessary to strengthen the close relationship between the government and coal mines. Relevant government departments should strictly supervise coal mines and effectively implement safety responsibility systems.

When the grassroots-level factors are reduced by 40% while other factors remain unchanged, the coal mine safety system level decreases by 1.7805. This indicates that changes in safety investment have a significant impact on grassroots-level factors in the short term. The grassroots-level factors include whether workers follow regulations and procedures, whether they wear proper personal protective equipment, whether the advancement speed of coal mining faces is reasonable, whether rockburst prevention equipment is appropriately installed, whether risk analysis and judgment are accurate, and the psychological and physical conditions of workers. Since these factors are outcome-oriented, they are greatly influenced by safety investment. Therefore, to improve the coal mine system safety level in the short term, attention should be given to the mentioned factors. For example, hiring experts to assess mining risks, strictly supervising workers to wear appropriate personal protective equipment, and closely monitoring the psychological condition of miners. However, the underlying issue is ultimately a matter of inadequate management. Strengthening management is essential to address the root causes of problems.

When the physical-level factors are reduced by 40% while other factors remain unchanged, the coal mine system safety level decreases by 1.2309. The physical-level factors include coal seam support design, coal seam stability, mining sequence, mining equipment, layout of mining areas and tunnels, quality of mining equipment, and rockburst early warning systems. Since the physical-level factors involve external environmental factors and other uncontrollable forces, the impact of reduced safety investment on these factors is not very apparent. The influence of safety investment on physical-level factors is primarily reflected in the operation of machinery and equipment and the actions of personnel. Therefore, management should strengthen skills training for frontline workers, improve their overall capabilities, and ensure that only those who have received qualified safety training can be deployed to work.

5. Discussion

Based on the STAMP theory, a safety control structure is constructed to analyze and extract causal factors from four levels: government, management, grassroots, and physical levels. The extracted causal factors, combined with the DEMATEL-ISM method, are used to build a hierarchical structure model, which analyzes the impact degree and causal relationships of the causal factors of coal mine rockburst incidents, revealing deeper connections between accidents and factors.

Reviewing the complete accident chain of the Hu Jiahe Mining Company's rockburst accident, the STAMP model based on systems theory shows a high degree of compatibility with rockburst accidents. The constructed safety control structure efficiently identifies unsafe control behaviors, highlighting the significant impact of pre-accident unsafe behaviors. The analysis results align with accident investigation reports and provide a more comprehensive understanding of the interactions between different hierarchical structures.

To control and prevent coal mine rockburst accidents, it is necessary to identify the root causes by considering the causal relationships between different levels and the results of SD simulation. While grassroots factors are the outcome factors contributing to accidents, the focus should be on organizational causes that can prevent accidents. This not only requires government supervision and management but also effective implementation of measures, early warning systems, and other aspects by mining companies. Therefore, the government should urge coal mining enterprises to rectify hidden problems and firmly implement safety responsibility systems to fundamentally ensure the level of safety management in coal mines. The management should strictly supervise rockburst prevention measures and conduct effective supervision and inspections of coal mine safety production, thereby preventing accidents at the source.

6. Conclusions

The occurrence of coal mine rockburst accidents results from the interaction of factors at various levels. Based on the causal relationships of each level and the simulation results of SD (System Dynamics), it is found that in the short term, increasing the investment in grassroots-level management shows apparent effects. However, from the perspective of the long-term development of the mine, only by strengthening the investment in the management level can the mine develop sustainably. The management level acts as a pivot connecting the government level and the grassroots level. Through the management layer, the government communicates policies and delegates tasks, ensuring directives are executed by the grassroots personnel. Subsequent feedback from the grassroots is channeled back up through management, allowing adjustments based on real-time situations. Inadequate communication or disrupted feedback loops among these tiers can culminate in flawed decisions and mismanagement. At first glance, workers' violations appear to be the direct cause of the accident, but the management lapses behind them should be the focal point for accident prevention. Issues like insufficient worker qualifications due to a lack of professional skill and safety training (with mixed outsourced team members), a dearth of safety supervision and penalties (management ignoring policy regulations, prioritizing personal relationships over policies), neglect of workers' physical and psychological conditions (pushing production limits, valuing production over safety), and flaws in mine design (designers not placing support equipment as prescribed) arise. By using the STAMP method to extract factors leading to the accident layer by layer and constructing a system dynamics model to analyze the causality among these factors, we can obtain a more detailed understanding and explanation. The goal is not to place blame but to help personnel at all levels identify and resolve issues, preventing the recurrence of similar accidents in the future.

This article primarily delves into the management aspects of rockburst accidents but touches less upon the inherent mechanisms behind their occurrence. To comprehensively understand the causes and impacts of rockbursts, future research should delve deeper into their genesis mechanisms and integrate them with causative factors at all levels, thereby providing a more accurate reference for decision-making. Moreover, although the article introduces a preliminary system theory model, this model still requires further validation and refinement in actual applications. Especially in terms of early warnings, the article doesn't describe corresponding emergency response measures in detail. Therefore, in practical operations, mining professionals need to continuously adjust the model based on specific situations, ensuring its effectiveness and practicality within the rockburst early warning system. Concurrently, it's vital to supplement and refine related response measures, ensuring that early warning information is promptly and effectively translated into safe operational practices.

Additional information

No additional information is available for this paper.

Funding statement

This research was supported by the Ministry of Education's Humanities and Social Sciences Research Youth Fund Project (21YJCZH135): Research on the evaluation mechanism and control system of major disaster risk in coal mine based on complex system theory.

Data availability statement

The data related to this study has not been deposited in a publicly available repository. Data included in article/supp. material/referenced in article.

Ethics declarations

Review and/or approval by an ethics committee was not needed for this study because it is a non-medical research and does not involve human or animal subjects.

CRediT authorship contribution statement

Junwei Shi: Methodology. Shiqi Wang: Writing – review & editing, Writing – original draft, Software. Jianli Shao: Writing – original draft, Resources, Data curation.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Junwei shi reports financial support was provided by the Ministry of Education's Humanities and Social Sciences Research Youth Fund Project.