Abstract
Capturing the interrelations among risks is essential to thoroughly understand and promote coal mining safety. From this standpoint, 105 risks and 135 interrelations among risks had been identified from 126 typical accidents, which were also the foundation of constructing coal mine risk network (CMRN). Based on the complex network theory and Pajek, six parameters (i.e., network diameter, network density, average path length, degree, betweenness, and clustering coefficient) were employed to reveal the topological properties of CMRN. As indicated by the results, CMRN possesses scale-free network property because its cumulative degree distribution obeys power-law distribution. This means that CMRN is robust to random hazard and vulnerable to deliberate attack. CMRN is also a small-world network due to its relatively small average path length as well as high clustering coefficient, implying that accident propagation in CMRN is faster than regular network. Furthermore, the effect of risk control is explored. According to the result, it shows that roof collapse, fire, and gas concentration exceeding limit refer to three most valuable targets for risk control among all the risks. This study will help offer recommendations and proposals for making beforehand strategies that can restrain original risks and reduce accidents.
1. Introduction
China is the largest producer and consumer of coal in the world, from which it has derived about 65% of its energy over the past sixty years [1]. In China, more than 90% of fossil energy reserves are coal. That is to say, the energy consumption structure of energy, which relies mainly on coal, cannot be changed within quite a long time. Also, this standpoint can be validated by China’s National Energy Development Strategy Plan (2014–2020) and 13th Five-Year Plan (2016–2020). In 2015, China’s coal output was estimated to be 3.747 billion tons, accounting for 47% of the total in the world (The State Administration of Coal Mine Safety, 2015). According to British Petroleum (BP) Statistical Review of World Energy 2016, the countries whose coal production is larger than 40 million tons can be shown in Figure 1.
Coal mining refers to one of the most hazardous industries worldwide [2–4]. Moreover, coal mine enterprises have to encounter various hazards regarding special geological condition [3]. In the process of coal mining, numerous hazards have the potential to trigger accidents frequently, such as rock stresses, harmful gases, humidity, high temperatures, coal and silica dust, and specialized equipment [5]. Worse still, the intensity and frequency of these hazards could result in extremely serious consequences for human health and life [6]. Coal mine accidents will considerably bring about injuries, casualties, and loss of major assets of enterprise. In China, coal mine accident suffers heavy losses every year. According to statistics, approximately 70% of the coal mine casualties worldwide are estimated to occur in China [7]. 6995 coal workers were killed in various accidents in 2002, which is the maximum record in a single year. Then, it decreased year by year, as shown in Figure 2 (data source: State Administration of Coal Mine Safety). Although the practical situation seemingly gets better and better, still numerous accidents occurred every year in China. All in all, safety management in coal production is still quite critical and serious due to harsh production conditions as well as complicated production processes.
A more valuable process to improve safety performance is to learn from the failure experiences of previous accidents [8]. Accident analysis is a powerful approach for preventing or eliminating similar hazards, risks, and accidents [9, 10]. Indeed, the existing studies often focus on one type of coal mining accident, or statistical analysis of accident in an area or country, while multiple interrelations among verified accidents are usually neglected. In industrial safety research, it is generally acknowledged that the accident is not caused by a single error or fault, but by the confluence of a sequence of hazard, risk, and accident [11]. Moreover, an occurred accident will possibly incur a sequence of the following accidents [12]. Accident chain exists in most of the coal mine accidents, which indicates the actual existence of risk network. These interactions among risks form a coal mine risk network (CMRN) which would bring about a big issue for the coal mine safety. Therefore, capturing the complexity of CMRN is both essential and beneficial to improve safety performance in coal mining.
The structure of this paper can be listed as follows. Section 2 presents a literature review of coal mine safety, and Section 3 elaborates the methodology, including an analytical framework, data collection and analysis, and network modeling. In Section 4, Pajek is employed to help explore CMRN (including network basic quantities metric and network property) and measure the effect of risk control. In Section 5, the potential contributions, limitations, and risk control methods are discussed. Lastly, the conclusions are drawn in Section 6.
2. Literature Review
Coal mine provides essential energy for supporting high-speed development of Chinese economy and society. Multiple studies have been carried out by worldwide researchers to improve the safety performance. The research topics mainly focus on supervision and regulation, risk management, evaluation, monitoring, and controlling technologies, which is shown in Table 1.
Supervision and regulation refer to two crucial influence factors in the coal mining. Before 2000, ineffective implementation of laws and regulations increases the difficulty for Chinese government to inspect actual situation of coal mine safety [13]. To promote coal mine safety, a variety of effective countermeasures, such as enhancing safety legislation and establishing independent coal mine safety monitoring system, were executed. These improvements in regulatory regime make a great contribution [14]. However, the interrelations between coal mine enterprises and supervision departments are complex and subtle. Rent-seeking exists widely in China’s coal mine supervision, which is a huge obstacle to the further development of coal mining industry. The existing researches on rent-seeking mainly focus on rent-seeking behavior, policy, and tax [15–17]. In the rent-seeking scenario, Chen et al. [18] indicated that each level of the department had an intensity threshold above which coal mine accidents occurred.
The effective risk management is the fundamental guarantee of coal mine safety production based on various theories and methods. Sari et al. [19] developed a stochastic model to predict the number of accidents according to the randomness in the occurrence of accidents. Qing-gui et al. [20] constructed a system to supervise unsafe behavior, release early warning information, and improve controlling measures in coal mine. Based on case studies, Kowalska [21] identified and assessed the risk sources. As suggested by the results, it is necessary to undertake anticipatory activities aiming at reducing environmental and social risks during the colliery liquidation. Badri et al. [22] studied risk management in mining projects based on analytic hierarchy process method, and the results show the importance of considering occupational health and safety (OHS) in the process of coal mining. Wang et al. [23] put forward an analytical framework to analyze human error risk in the emergency evacuation from three perspectives, including organization level, group level, and individual level. Besides, Liu and Li [24] constructed a back propagation (BP) neural network to explore influence factors in coal mine safety.
The evaluation of hazards and risks has attracted much attention of multiple practitioners and researchers due to their serious consequences. These hazards and risks could be divided into three types, including “natural, technical, and human.” Ghasemi et al. [25] developed a risk evaluation model and various possible risks are evaluated in Iran Tabas central mine. Pejic et al. [26] proposed a risk assessment tool to determine the risk of explosion of any work processes or activities in the underground coal mine. Also, the methodology can decide whether the proposal investments are well-justified or not for improving safety. Bahri Najafi et al. [27] proposed an artificial neural network model to predict the out-of-seam dilution. Based on uncertain random variables, Chen et al. [28] developed a practical evaluation model for coal mine safety based on uncertain random variables. According to fuzzy set theory, Petrović et al. [29] presented a risk evaluation model to evaluate the failures of electromechanical equipment. Lokhande et al. [30] came up with a risk evaluation approach based on the identified critical parameters, including depth to height of extraction ratio, rock to soil ratio, brittleness index of rock, and rock density. Spada and Burgherr [31] analyzed the accident data in energy-related severe accidents database and suggested a nonsignificant decreasing tendency for Turkey as well as a significant one for USA.
Some new technologies, which are effective and powerful tools for improving safety performance, have been applied in coal mine. Sun et al. [32] accomplished a monitoring and prealarm system based on cloud computing (CC) and Internet of things (IOT). What is more, Dange and Patil [33] designed a wireless sensor network (WSN) based on MSP430 controller for monitoring smoke, gas, temperature, and humidity in coal mine. Based on wireless sensor network and controller area network (CAN), Bo et al. [34] proposed a remote monitoring system, which was tested in different remote monitoring scenarios. Zhang et al. [35] proposed an integrated environment monitoring system that takes full advantage of cable monitoring system (CMS) in combination with wireless sensor network (WSN). Xu et al. [36] put forward an improved safety management system based on several modern identification and communication techniques, including iris identification, radio frequency identification (RFID), computer network, and database technique.
3. Methodology
3.1. Analytical Framework
An analytical framework is proposed to conduct the in-depth analysis of coal mine accident, as presented in Figure 3. It is a step-by-step procedure consisting of three main modules. At first, the coal mine accidents are collected from literature and media, such as the website of State Administration of Coal Mine Safety. Then, typical accidents are selected as the data to analyze accident chains. After that, the accident chains will be integrated as a global network. In the second stage, the risk is abstracted as vertex, and meanwhile, the interrelation is abstracted as edge. Also, the software Pajek is employed to establish the coal mine risk network (CMRN). In the third stage, the topology of CMRN is analyzed and network properties are identified according to the network theory. Then, the effect of risk control in CMRN is calculated. According to the research result, the discussions and suggestions are provided to promote safety management in coal mine production.
3.2. Data Collection and Analysis
The data of historical coal mining accidents is used for risk analysis. There are several ways to collect accident cases, such as government, enterprise, literature, and media. In this study, the accidents are collected from literature and media. A coal mine accident database (CMAD), which records the detailed information of accident (including time, position, type, process, death, and losses), is established based on Microsoft Access 2010. Although hundreds of accidents have occurred in China over the past few years, the information of many accidents, especially the process of accident, is unclear. In the end, 176 accidents with exhaustive information are collected. Among these detailed accidents, some accident chains are unobvious, while some happen suddenly and unexpectedly without accident chain. These accidents are not considered in this research. Besides, since some accidents are exactly similar to the rest of the typical accidents, thus there is no need to analyze the repeating accidents. In the end, 126 typical accidents, including all types of coal mining accidents, are recorded in CMAD, and they are selected to conduct accident chain analysis for establishing the risk network model. Two examples of stored accidents can be illustrated in Table 2.
Although these accidents are selective, almost all kinds of accidents have been included. Also, there are no biases in the selection process. From the perspective of person, machine, environment, management, and technology, the accident chains in these accidents are identified and expatiated in Table 3. Most of the accidents have one accident chain, while some have two, such as accidents 41 and 75. As a result, a total of 135 accident chains are obtained from 126 cases.
3.3. Network Modeling
Multiple risks simultaneously appear in different accidents, indicating that the risk is correlated with others. It is essential to identify the risks and interrelations among them so as to establish CMRN. Through statistics, a total of 105 risks and 194 interrelations are obtained from 135 accident chains. Moreover, the vertex number and its type are expatiated in Table 4. After this study abstracts risk as vertex and interrelation as edge, different risks can be connected by these common vertexes into a global network. For a better explanation, accidents 12, 38, and 71 are taken as an example to illustrate the process of network modeling, as depicted in Figure 4. From the risks identification in accidents 12, 38, and 71, it can be seen that there are two same vertexes shown in red color, including R90 and R68. Through this method, the network can be established based on these common risks. Furthermore, software Pajek is employed to establish coal mine risk network (CMRN), as shown in Figure 5.
4. Results
4.1. Network Basic Quantities Metric
With the continuous development of complex network theory, the statistical indexes of network structure have obtained a lot of achievements, which are also the basis of statistical description of various topological characteristics. Compared with visual section, the calculation is much more precise and concise in exploring network [37]. This study uses several typical indexes to explore the properties of CMRN, including network diameter, network density, average path length, degree, betweenness, and clustering coefficient. These topological indexes are calculated by Pajek.
4.1.1. Network Diameter
The network diameter is defined as the maximum path length in the network, which can reflect the size of a network. The network diameter in CMRN is 7, which is from poor maintenance (vertex 64) to water leaking (vertex 99). This path is as follows: poor maintenance (vertex 64) causes electrified device failure (vertex 29), electrified device failure (vertex 29) triggers inadequate ventilation (vertex 49), inadequate ventilation (vertex 49) makes gas concentration exceed limit (vertex 38), gas concentration exceeding limit (vertex 38) incurs gas burning (vertex 37), gas burning (vertex 37) sparks off fire (vertex 34), fire (vertex 34) induces roof collapse (vertex 68), roof collapse (vertex 68) leads to penetration into goaf (vertex 61), and penetration into goaf (vertex 61) brings about water leaking (vertex 99). Although these risks may not occur simultaneity in a single accident, it can deeply reflect the process of risk spread. The spread rule of risk is conductive to developing prevention and control strategies for the risk control.
4.1.2. Network Density
Network density is used to describe the degree of affinity between the vertexes in a network from an overall perspective. It specifically refers to the proportion of actual edges to potential edges in a network. Consisting of 105 vertexes, the maximum number of edges in CMRN should be . Since the actual edges in CMRN is 194, thus the network density of CMRN is . In general, the more the vertexes, the smaller the network density. Low density means that CMRN is a relatively sparse network. Moreover, the vertex in CMRN is less connected with all others. That is to say, the degree of a vertex in CMRN directly affected by others is relatively low.
4.1.3. Average Path Length
The transmission efficiency of information or energy is significantly correlated with the average path length. A shorter average path length means higher efficiency. The average path length can be defined as the average number of steps between all possible pairs of vertexes in a network. The value of the average path length in CMRN is 3.0841, indicating that a risk can transmit to another only in three steps on average. For example, cable short circuit (vertex 6) and carbon monoxide poisoning (vertex 8) refer to two correlative risks, which can be connected by electric spark (vertex 26) and fire (vertex 34) in three steps, as shown in accident 31 in Table 3.
4.1.4. Degree
The degree of a vertex is defined as the number of edges connected to the vertex. In a directed network, the degree can be either in-degree (number of incoming edges) or out-degree (number of outgoing edges), with the total degree being the sum of the two. Since there are 105 vertexes in CMRN, it is impossible to show all the vertex degree in a radar graph. Consequently, 30 vertexes with the highest degree are selected as the example to display vertex degree. The values of the in-degree, out-degree, and total degree of these 30 vertexes are presented in Figure 6. Roof collapse (vertex 68) has the highest degree of 17, with an in-degree 10 and out-degree 7. This indicates that the roof collapse is in a relatively central position and plays a critical role in the accident chain. Its in-degree is also the highest in the network, implying that it refers to the biggest “risk recipient” in CMRN and many risks such as poor tunnel support can lead to roof collapse. Multiple paths make it difficult to control for roof collapse, compared to other vertexes with low in-degree. The second is unreasonable blasting (vertex 90) and the third is the management negligence (vertex 51). The in-degree and out-degree of unreasonable blasting are 7 and 9, respectively. It means that 7 risks could give rise to unreasonable blasting, and meanwhile, unreasonable blasting might cause 9 risks in production. Additionally, the management negligence (vertex 51) has the highest out-degree, demonstrating that management negligence is the most serious risk source. If there is something wrong in safety management, many risks might be triggered at any time, such as gas concentration exceeding limit. Controlling these key vertexes can positively influence the safety of coal mine, which is also referential in resource distribution under the condition of limited security resource. Besides, it would greatly help disrupt the connectivity among risks to prevent risks from spreading and propagating in CMRN.
4.1.5. Betweenness
Betweenness is used to describe the extent to which a vertex plays an intermediary role in the interaction between all possible pairs of vertexes in a network [38]. Two types of betweenness, vertex betweenness and edge betweenness, are used extensively in the network analysis [39, 40]. According to the research object, only vertex betweenness is utilized in this study. High betweenness indicates greater importance in the whole network. The vertex betweenness in the CMRN ranges from 0 to 0.059852, as shown in Table 5. Only 47 vertexes are invisible because their vertex betweenness is zero, which indicates that they do not play the role of intermediary among interactions between other vertexes. The roof collapse (vertex 68) has the highest value of vertex betweenness, meaning that the maximum number of the shortest paths passes through roof collapse (vertex 68). It is a key link in the process of risk spread. The stagnant water (vertex 78) has the lowest value of vertex betweenness, meaning that the minimum number of the shortest paths passes through stagnant water (vertex 78). It is not a key link in the process of risk spread. According to the value of betweenness, the impact of roof collapse (vertex 68) is much larger than stagnant water (vertex 78) in the process of risk spread. Furthermore, fire (vertex 34) and spark (vertex 75) are 0.048486 and 0.020668, respectively. The cumulative vertex betweenness of the five highest vertex betweenness is equal to 0.542701, which indicates that about 55% shortest paths pass through these five vertexes. These vertexes should be focused in the safety management. It seems that effectively controlling these few key vertexes can slow down the risk diffusion and decrease the chain reaction in CMRN.
4.1.6. Clustering Coefficient
The clustering coefficient is used to describe which vertexes in a network tend to cluster together from a local perspective [41]. The clustering coefficient of a vertex is defined as the probability of two randomly selected neighbors of the vertex being connected. It can be found that 33 vertexes get the missing value of 999999998 because the degrees of these vertexes are equal to 1, and 34 vertexes have the value of 0. The clustering coefficients of other 38 vertexes are presented from high to low in Table 6. The clustering coefficient of vertex in CMRN ranges from 0 to 0.5. The vertexes with the highest clustering coefficient are vertex 25 and vertex 80. The network clustering coefficient can be defined as the average value of all vertexes in the network, and it is 0.0623 in CMRN which is larger than a random network with the same network scale. The large clustering coefficient denotes that CMRN has a high degree of cliquishness.
4.2. Network Property
With the development of network theory, it can be found that small-world property and scale-free property are the most obvious distinction between real network and random network. To obtain greater insight into the nature of CMRN, this section explores these two properties.
4.2.1. Small-World Property
A small-world network is a special kind of graph, in which most vertexes can be reached from every other vertex by a short path. In general, small-world network is associated with the possession of relatively high value of clustering coefficient and small average path length [42, 43]. For comparison, three random networks with 105 vertexes and 194 edges are created by Pajek, which are the same scale as CMRN. The clustering coefficient and average path length of CMRN and random networks are presented in Table 7. Obviously, CMRN is a relatively small-world network according to its clustering coefficient and average path length, indicating that the risk propagation in CMRN is much faster than a random network. To avoid a worse consequence under the condition of an occurred accident, controlling the catenation among accidents is of great significance.
4.2.2. Scale-Free Property
A scale-free network is a network whose degree distribution satisfies power-law decay. In such network, numerous vertexes are poorly connected and relatively few vertexes are linked to many other vertexes [44]. Due to rare vertexes with high degree, analyzing statistic data in the tail of the degree distribution is meaningless. The degree distribution is defined as the proportion of vertexes with degree , while the cumulative is defined as the proportion of vertexes equaling to or greater than [45]. In practice, the cumulative is preferred in statistical analysis using double logarithmic coordinate system, with the purpose of reducing statistical errors caused by finite network size [46]. The cumulative of CMRN is depicted in Figure 7 with approximate fit , which basically follows the power-law. This indicates that the CMRN has scale-free property according to complex network theory. The property means that CMRN is robust to random risks to some extent. The vertex with degree equaling to or less than 4 accounts for 75%, and the influence of these vertexes on the network is relatively small. However, CMRN is vulnerable to simultaneous attacks aiming at vertexes with high degree. In other words, only targeted actions can greatly prevent the cascading effects in CMRN.
4.3. Measuring the Effect of Risk Control
The analysis on effect of risk control is conductive to providing recommendations and proposal for safety management in coal mine. To measure the effect of risk control, an assumption is made. Namely, a risk would be supposed not to occur if it is completely controlled in coal mine production. Furthermore, if a risk will not happen, it can be deleted from CMRN. Then, the effect of risk control can be measured by network global efficiency. Although many definitions on network global efficiency are currently created and studied, they all have different limitations. The generally accepted measure method is average reciprocal shortest path lengths of networks, in which network global efficiency of a network G could be calculated by (1) [47, 48], where refers to the number of vertexes and refers to the distance between two vertexes.
The effect of risk control of every risk in CMRN can be measured according to the degree of network global efficiency declined. For example, if the network global efficiency decreases by 0.1 after deletion of vertex 8, it means that the effect of risk control of vertex 8 is 0.1. The better the effect is, the greater the risk will be. The 30 most serious risks in CMRN are identified through calculation, and the risk control effects can be shown in Figure 8. It is observed that roof collapse is the most serious risk and controlling roof collapse could help decrease 32.63% of network global efficiency of CMRN, followed by fire (25.96%) and gas concentration exceeding limit (11.22%). However, due to the interaction between roof collapse and gas concentration exceeding limit, the effect of controlling “roof collapse” and “gas concentration exceeding limit” is not equal to 32.63% plus 25.96%, but 44.03% by calculation. Obviously, measuring the effect of risk control can suggest and designate the directions and key points to further safety management. Anyway, controlling several most serious risks is the most appropriate and most effective approach for preventing accident and further promoting the safety management level in the coal mine production.
5. Discussion
Based on the network theory, an analytical framework has been put forward to promote coal mine production safety, which turns out to be feasible and effective. The proposed network modeling method is a powerful and promising tool to analyze risk in various disciplines. It is envisaged that this study can help managerial personnel deeply understand coal mine risk for the sake of developing necessary strategies that can improve safety management in a dynamic operating environment, especially in emergency.
The potential contributions of this study include four aspects. First, it is beneficial to understand the complexity and transitivity of risks in coal mine. The main topology properties and network properties of CMRN are captured and analyzed. Second, it is conductive to enhance the safety performance by controlling original risks and avoiding derivative accidents. Third, this study has the potential benefits in coal mine emergency and relief, which can help managers make decisions in emergency rescue for lightening the casualties and losses. Additionally, network modeling technique is employed in this study, which may offer a promising approach for the analysis of the accident. Also, the application range of network theory will be enlarged.
The main limitation of this research is that the established network model fails to take the vertex weight into consideration. Moreover, the frequency of risks in Table 3 cannot reflect the vertex weight in current study, and it is very difficult to discern and distinguish the different importance for different risks. Therefore, assigning the weight is quite difficult. That may explain why the network model in this study is unweighted. In the future study, more attention should be paid to improve the network model based on more precise understanding of risks in coal mine. Also, how to reduce the risks in coal mine is a significant direction that deserves further research. Meanwhile, a particular failure knowledge database (FKD) would be significant in studying the coal mine accidents, which is the foundation of case based reasoning (CBR) for analyzing hazard and risk.
What is more, several identified risks seem to be general, rather than specific. There are two reasons for this result. First, the risk identification is carried out on the basis of accident data collected from literature and media. If some detailed information is ignored and not recorded during the investigation of these accidents, the unavailable information may affect the accuracy of risk identification. Second, this research is implemented from a holistic perspective. If the identified risks are too specific, finding the common vertex and constructing the coal mine risk network will be difficult. Hence, the similar risks are divided into the same category for the sake of convenience.
Safety researchers assiduously aim to lower the prevalence of accident and raise the safety level. Accident precursor is studied in various industries, and many studies indicate that a series of precursors always occur before the accident [8, 11, 49]. Therefore, lowering precursor frequency is an effective approach to reduce the accident probability [50]. An accident precursor is broadly defined as the “conditions, events, and sequences that precede and lead up to an accident” by the National Academy of Engineering [51]. Even though it is impossible to completely prevent coal mine accident, monitoring and controlling precursory information is a useful and effective approach for safety managers to identify hazards or risks in advance. Also, this can reduce the possibility of accident or alleviate their consequence. Hence, precursor analysis seemingly has huge potential to promote safety management of coal mine production.
According to the results of network analysis, it can be known that some key vertexes play an important role in accident prevention. In practice, precursor can be used to reduce the frequency and probability of these key risks. For example, the precursor of water leaking mainly includes the following: air turns cold; mist appears on the roadway; and coal wall has water seepage. If the coal miner can pay more attention to these precursors, the water leaking will be reduced to a large extent. Therefore, an organization structure should be proposed to manage and control precursors, as depicted in Figure 9. The real executors of precursor management include general staff, safety manager, and safety expert. General staff should report precursor to the safety officer, and then safety officer submits precursor reports to the safety manager. Furthermore, safety expert assists safety manager to analyze risk as well as factor and propose processing measures. The proposed measures or solutions are executed by general staff and safety officer, and meanwhile, the evaluation of them is implemented by safety manager and safety expert. The coal mine enterprise can set up a committee, mainly including safety manager and safety expert, to deal with precursor management.
6. Conclusion
The accidents in the coal industry have been widely analyzed to promote safety production. By changing the original method of analyzing a single accident, this research aims to develop an innovative approach of fusing various risks that can explore the full complexity of CMRN based on network theory.
The CMRN is constructed by software Pajek based on 135 typical accident chains, which are obtained from 126 typical accidents in coal mine accident database (CMAD). As an unweighted directed network model, CMRN includes 105 vertexes and 194 edges. The network diameter in the CMRN is 7 and the network density of CMRN is 0.178, which indicates that CMRN refers to a relatively sparse network. The value of the average path length in CMRN is 3.0841, suggesting that a risk can transmit to another only in three steps on average. Roof collapse (vertex 68) has the highest degree of 17, which indicates that roof collapse plays a critical role in the accident chain. In general, this type of vertex is regarded as a key point. The vertex betweenness in the CMRN ranges from 0 to 0.059852. Additionally, the roof collapse (vertex 68) has the highest value of vertex betweenness, which means that the maximum number of shortest paths passes through roof collapse (vertex 68). It is a key link in the process of risk spread. Next, fire (vertex 34) and spark (vertex 75) are 0.048486 and 0.020668, respectively. About 55% shortest paths pass through these five highest betweenness vertexes. Effectively controlling roof collapse, fire, spark, gas concentration exceeding limit, and collision could not only increase the network diameter and average path length but also slow down the efficiency of accident propagation and weaken the chain reaction. The vertex clustering coefficient in CMRN ranges from 0 to 0.5. Moreover, the clustering coefficient of CMRN is 0.0623 in CMRN, which denotes that CMRN has a high degree of cliquishness. Besides, CMRN is a relatively small-world network according to its clustering coefficient and average path length, demonstrating that the risk propagation in CMRN is much faster than a random network. CMRN also has the scale-free property because cumulative follows the power-law. The property indicates that CMRN is robust to random risks to some extent. Furthermore, the effect of risk control is calculated precisely. Overall, roof collapse, fire, and gas concentration exceeding limit are not only three most valuable targets in safety management but also the three most dangerous risks in coal mine production.
Precise calculation of these six parameters and effective risk control are beneficial to capture the complexity and nature of coal mine accident and designate the targets for risk control. Also, the results can help promote coal mine safety management in controlling original risks and preventing derivative accidents. In view of the sequential interrelations among accidents in CMRN, this research may also positive influence the early warning of accidents. In practice, the safety managers should focus more on the identified and valuable targets of risk control and put more resources to help promote safety performance in coal mine production.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The authors also gratefully acknowledge those who provided data and suggestions. The research described in this paper is supported by National Natural Science Foundation of China (51323004), the Humanities and Social Sciences Youth Foundation of China’s Education Ministry (17YJCZH035), the Fundamental Research Funds for the Central Universities (2017QNB13), and Jiangsu Planned Projects for Postdoctoral Research Funds (1701143C).