Gauging the Evolution of Operational Risks for Urban Rail Transit Systems under Rainstorm Disasters

Abstract

With global warming and the frequent occurrence of extreme weather, damage to urban rail transit systems and casualties caused by rainstorm disasters have increased significantly and are becoming more serious. This research developed a network model for the evolution of operational risk in URT systems under rainstorm scenarios that can cause 35 typical accidents. Furthermore, we also investigated the evolution mechanism and devised improvement strategies. Through the network, combined with the complex network theory, the study explored the critical risks and the extent of their impact on the network and proposed optimized strategies to avoid these critical risks. The results show that risk nodes such as R1, R4, R18, and R21 have the most significant impact on the evolution network, both in static and dynamic networks, indicating that station flooding, train stoppage, heavy rainfall, and ponding are the most critical risks to guard against. Gauging the evolution of operational risks in urban rail transit systems and adopting reasonable avoidance measures in this research can effectively improve resilience to rainstorm disasters and the level of operational safety, which can contribute to the sustainable development of transport infrastructure.

1. Introduction

Global warming has increased the frequency and intensity of extreme rainstorm disasters [1,2]. Rainstorms are often sudden and continuous, and their evolution triggers a series of accidents that pose new challenges for the maintenance and emergency management of urban transport infrastructure systems [3,4]. In recent years, with the rapid advancement of urbanization, the urban rail transit (URT) system, as a pillar of the urban transport infrastructure system, has become an essential way for people to travel daily due to its high capacity, speed, convenience, safety, and energy-saving features [5,6,7].

The URT system is an integrated system. It consists of several subsystems such as a vehicle line system, an electromechanical system, and a drainage system. The subsystems interact and influence each other [8]. The geographical location of the URT system is specifical, i.e., it is mostly built below ground level [9,10]. During rainstorm disasters, rainwater will inevitably gather quickly and flow to low-lying areas. The URT system is a structural system that tends to collect water. The inadequate water-retaining system and drainage system of the URT system will lead to problems including inundation of the URT system, damage to the rail network, and failure of station facilities and equipment and will affect the safe operation of URT systems [11,12]. Compared to the growth of prosperity in city development, the operation and maintenance of URT systems are too backward [13]. The design standard of the flood control and drainage system in previous URT systems was low to withstand extreme rainstorms, resulting in failure and significant damage [14,15]. In July 2021, extremely heavy rainstorms caused underground tunnels to back up, resulting in a loss of power and 14 deaths in Zhengzhou, China. In September 2021, a 500-year superstorm flooded 28 underground stations and paralyzed the city’s subways in New York.

There is an urgent need to improve the operational risk control of URT systems. Nevertheless, research on gauging the evolution risks has been limited to date. To address the research gap, the paper aims to employ complex networks to explore the evolutionary process of risk, identify and minimize critical risks, and improve the operational security of URT systems. The objectives of this research are (1) to develop a network model for the evolution of operational risk in URT systems under rainstorm scenarios and to analyze the risk evolution paths, (2) to use complex network theory to calculate the static topological characteristics of the network and select critical risk nodes, and (3) to measure the impact of the failure of critical risk nodes on the network by the principles of a deliberate attack and random failure.

The rest of this article is organized as follows. Section 2 is a literature review of the operational safety of URT systems. The methodology is introduced in Section 3. The research results and analysis are presented in Section 4. The strategies and conclusions are put forward in Section 5 and Section 6, respectively.

2. Literature Review

In the context of frequent natural disasters, the links between different hazards are becoming closer, and the evolutionary relationships between hazards have become a hot issue in the field of disaster research. As research progresses, many related concepts, terms, and corresponding definitions are proposed, such as cascading disasters, disaster chains, disaster clusters, and multi-hazard [16,17,18,19,20]. Among them, the theories of the domino effect [21,22], the cascading effect [23,24], and the disaster causal network [25] have also been applied to explain the course of events in which one hazard leads to a series of hazards. Scholars have offered different insights into the relevant concepts from different perspectives based on their backgrounds in their fields of expertise. Pescaroli defined cascades as sequences of events governed by cause–effect relationships [26]. Zheng defined disaster chains as the secondary and derivative disasters that will occur along with the development of the original one [27]. Scholars have applied these theories and methods to practical problems. Jiang proposed a disaster management system for disaster modeling service chains (DMSCs) to enable interoperable multi-hazard modeling [17]. Qie proposed a cascading disaster scenario modeling approach to support decision-making for complex disaster emergency preparedness and response [28]. Pescaroli investigated how the progress of a cascading disaster can be guided by the vulnerability of critical infrastructure based on the cascading effect theory [26].

With the rapid development of cities, transport infrastructure is constantly being built and improved, but it is also threatened by natural disasters [29]. Scholars have studied the resilience of transport infrastructure in the face of natural disasters. The main objects of study are external and internal urban transport infrastructures, such as roads [30], railways [31], airlines [32], buses [33], and URT systems [34]. From the existing studies, it can be found that flooding caused by heavy rainfall is the most common natural risk in cities [35]. And URT is the transport infrastructure most vulnerable to flooding [7]. For the phenomena, multiple assessment frameworks for URT systems have been presented, such as a comprehensive multi-stage evaluation framework, a resilience assessment framework, and a cascade damage dynamics model [36,37,38]. The vulnerability of URT systems under rainstorm disasters is increasingly being appreciated by scholars, and some outcomes have been achieved. Zhao et al. used a data-driven ABM simulation model to assess the impact of a flood event [39]. Sun et al. evaluated the complexity and uncertainty of the actual physical environment of metro stations and the flood resilience of metro networks based on the grid hydrodynamic model and the best–worst method [40]. Zhao et al. proposed a root cause analysis method based on fuzzy cognitive maps to simulate the vulnerability of metro systems under heavy rainfall disturbances and revealed the ultimate impact of vulnerability factors on the vulnerability of metro systems [41]. Wang et al. identified the vulnerability factors of metro station engineering and combined project pursuit and particle swarm optimization to evaluate the vulnerability of metro station engineering to stormwater flooding based on the pressure–state–response model [42]. To reduce damage to URT systems from heavy rainfall, the academic community has made a lot of efforts. Chen et al. established a two-layer planning model with the objective of maximizing the global accessibility and global efficiency of the network and proposed a simulation repair strategy to improve the structural resilience of URT networks by optimizing the repair sequence of failed stations [43]. Wang et al. established a two-stage emergency decision-making model based on regret theory and proposed an optimal disaster prevention method and emergency response measures for URT systems under heavy rainfall scenarios [44].

Complex network analysis is a common method to analyze relationships among risks, which has been applied to multiple disciplines, involving urban lifeline networks [45,46,47,48], social networks [49], biological networks [50,51], the Internet of Things [52,53], etc. Among the existing research models of system risk evolution, the complex network model can extract risk factors by means of existing case data in analyzing complex problems of risk evolution, effectively reducing the subjectivity of risk assessment [54]. Complex network analysis has been applied to similar types of research. Qi et al. measured the robustness and vulnerability of actual physical metro networks based on complex networks and network topology features [55]. Ma et al. proposed a metro network robustness and vulnerability measurement method under node interruption and edge failure [56].

Given the above, existing research on the management of operational risks of the URT system is gradually deepening. In recent years, research involving operational risks under extreme natural hazards has also been emerging, whereas previous research has been on linear thinking systems, which is passive. Previous research has focused more on a static assessment and mostly used the actual physical network of URT systems as the subject of study, thereby ignoring the role of risk factors in the dynamic risk network. Therefore, this study is based on the dynamic nature of the network to gauge the evolution of the operational risk of URT systems under rainstorm disasters by complex network theory and offers a different innovative perspective.

3. Methodology

To explore the critical risks and development rules in the evolution of URT systems in rainstorm disasters and clarify the vulnerability of URT systems in rainstorm disasters, this research collects global cases of URT system accidents in rainstorms between 2003 and 2022, selects risk factors, constructs the operational risk evolution network of the URT systems under rainstorms by accident causes, and studies the operational risks of URT systems and their evolutionary relationships by inductive analysis and complex network theory. The research uses Pajek to quantitatively analyze network node characteristics and calculates node importance based on grey relational analysis (GRA) to determine critical risk factors, while it uses the principles of random failure and deliberate attack to simulate the operational risk evolution network of the URT system under rainstorms to explore the changes in the network before and after the failure of critical risk nodes. The results of the research can provide a theoretical basis for the design and layout of safety optimization measures for URT systems and help to improve the resilience of URT systems. The research framework of this paper is shown in Figure 1.

3.1. Data Sources and Processing

In this paper, the URT system under the rainstorm scenario is taken as the research object. Thirty-five typical accidents caused by a rainstorm in the global URT system between 2003 to 2022 are collected and collated through existing research, global media reports, and accident analysis reports, and the risk chains in each accident are analyzed. Since there may be multiple risk chains for each accident, 47 risk evolution chains are finally obtained, which constitute the research database, as shown in

Table 1. Accident risk chain of URT (Part).

No.	Date	City	Process and Result Description	Risk Chain Analysis
1	July 2007	Chongqing	⮚ There was deep ponding, vehicles were flooded and stalled, landslides caused damage to the overhead lines, and the section was cut off ⮚ The stopping all lines on Line 2 for 9 h 20 min	Heavy rainfall—ponding—train stoppage Heavy rainfall—landslide—overhead line failure—train stoppage
2	July 2012	Beijing	⮚ The rain was not over the subway sensor. ⮚ Train services were suspended for 1 h and passengers were stranded	Heavy rainfall—flood—station flooding Heavy rainfall—flood—line fault—train stoppage—personnel detention
3	September2013	Shanghai	⮚ The train was delayed due to the failure of overhead lines caused by foreign objects, and then external rainwater poured back in. Foreign objects blocked the drainage system and caused ponding. ⮚ Line 2 signal equipment malfunction and passengers stranded	Heavy rainfall—flood—foreign objects—overhead line failure—train delay Heavy rainfall—flood—foreign objects—drainage system failure—ponding Heavy rainfall—flood—station flooding—signal equipment failure—train stoppage—personnel detention
4	July 2021	Zhengzhou	⮚ Heavy rain caused damage to the civil construction system, and the train was forced to stop in the tunnel due to a fault in the train control system. ⮚ 14 dead, personnel detention, passengers panicked	Heavy rainfall—flood—line fault—train stoppage—train flooding—panic Heavy rainfall—flood—water-retaining wall damaged—station flooding—panic Command and dispatch failure—train stoppage—personnel detention—panic
5	July 2021	Guangzhou	⮚ The retaining wall broke down and rain poured back into the station. ⮚ Some stations were closed for 7 h	Heavy rainfall—flood—water-retaining wall damaged—station flooding—train stoppage Heavy rainfall—drainage system failure—ponding
6	September2021	New York	⮚ Some 46 places flooded, inundating 28 stations. ⮚ Subway services were suspended throughout the city	Heavy rainfall—station flooding—train stoppage
7	July 2022	New York	⮚ Rainwater poured into the station, and foreign objects fell onto the tracks. ⮚ Widespread delays and station closures	Heavy rainfall—ponding—roof leak—metro station closed Heavy rainfall—flood—station flooding—foreign objects—train delay

.

To facilitate risk analysis and management, this study identifies 26 accident risk factors for URT system rainstorms based on the 47 accident risk chains extracted, concerning the main impacts and damage caused by rainstorms to URT systems and by consulting safety managers of metro operating companies and industry experts, as shown in

Table 2. Risk factors of rainstorm accidents in URT systems.

Risk Factor	No.	Risk Factor	No.	Risk Factor	No.
Heavy rainfall	R1	Water-retaining wall damaged	R10	Escalator fault	R19
Thunderstroke	R2	Platform collapse	R11	Metro station closed	R20
Flood	R3	Drainage system failure	R12	Train stoppage	R21
Ponding	R4	Overhead line failure	R13	Train delay	R22
Saltwater intrusion	R5	Line fault	R14	Command and dispatchfailure	R23
Foreign objects	R6	Train flooding	R15	Personnel detention	R24
Landslide	R7	Signal equipment failure	R16	Panic	R25
Structural seepage	R8	Power supply equipment failure	R17	Casualties	R26
Roof leak	R9	Station flooding	R18

.

3.2. Construction of a Rainstorm Risk Network of URT Systems

To be able to quantitatively study the role of operational risk evolution in URT systems, the co-occurrence analysis method was used to analyze the correlation of risk factors. The analysis process was as follows: ① analyze the order and type of risks in the accident case and sort out the risk chain in the accident; ② extract the risk factors in the risk chain and categorize them; ③ standardize the risk factors and convert the risk chain into a co-occurrence matrix with the dimension of 26 × 26; and ④ transform the risk co-occurrence matrix into an adjacency matrix. The adjacency matrix can be expressed as:

$$C_{ij}=\left\{\begin{array}{l}0, i {{\displaystyle }}_{}\mathrm{undirected} {{\displaystyle }}_{}j\\ 1, i {{\displaystyle }}_{}\mathrm{directed} {{\displaystyle }}_{}j\end{array}\right.$$

where $C_{ij}$ represents the ability of risk $i$ to cause risk $j$. If $C_{ij}=0$, it means that risk $i$ will not cause risk $j$. If $C_{ij}=1$, it means that risk $i$ may cause the occurrence of risk $j$.

There is a certain causal relationship between risk factors, and each risk factor exists in multiple risk chains; any risk factor may become the cause or result of other risk factors [57,58]. Therefore, the interactions among risk factors can be abstracted as a complex network model, where the connecting lines in the network represent the interaction relationships between risk factors, and the nodes represent the risk factors. According to the constructed adjacency matrix and accident evolution mechanism of the URT system in rainstorms [59], using the Pajek, the lines and nodes constitute the operational risk evolution network of the URT system under rainstorms, as shown in Figure 2.

The operational risk evolution network of the URT system under rainstorms consists of 26 nodes and 53 edges. The network has a clustering coefficient of 0.119 and an average path distance of 2.291, which meets the characteristics of the small world. The degree distribution probability is shown in Figure 3. It shows a skewed distribution, which is consistent with the characteristic of the scale-free network. This means that the operational risk evolution network of the URT system under rainstorms is a complex network.

3.3. Indicators

3.3.1. The Importance of Network Nodes

In a complex network, the loss of function of one component can lead to a loss of function of the other components connected to it [60]. When analyzing the importance of network nodes, indicators that can reflect the local correlation and global characteristics of the network, such as the node degree, centrality, and clustering coefficient, are usually chosen. Therefore, according to the characteristics of each node indicator, four indicators of a node in a complex network are selected such as the degree, betweenness centrality, closeness centrality, and clustering coefficient to quantify the importance of risk nodes in the operational risk evolution network of the URT system under rainstorms. The definition and the calculation method of the importance calculation parameters for each node are shown in

Table 3. Node importance calculation indicators of the operational risk evolution network of the URT system under rainstorms.

Indicators	Degree	Betweenness Centrality	Closeness Centrality	Clustering Coefficient
Formula	$K_i={\displaystyle \sum _{j\in N}{a}_{ij}}$	$B{C}_i={\displaystyle \sum _{i\ne j\ne k\in V}\frac{n_{jk}^i}{n_{jk}}}$	$C{C}_i=\frac{N-1}{{\displaystyle \sum _{j=1}^N{d}_{ij}}}$	$C_i=\frac{2S_i}{n(n-1)}$
Parameter meaning	$a_{ij}$ is the number of nodes directly associated with $i$ and $j$; $N$ indicates the total number of nodes in the network; $n_{jk}$ is the number of shortest paths connecting nodes $R_j$ and $R_k$; $n_{jk}^i$ is the number of shortest paths passing through node $R_i$ in the shortest path connecting node $R_j$ and node $R_k$; $d_{ij}$ is the shortest path; $S_i$ is the actual correlation number between node $R_i$ and adjacent nodes; and $n$ indicates the number of adjacent nodes of the included node $S_i$.

[61].

Degree (K_i) is an indicator that describes the local characteristics of the network, indicating the number of other nodes in the complex network that are directly connected to node $R_i$. The greater (K_i), the greater the correlation between the risk event and other risk events [62]. In a directed network, the degree is the sum of the out-degree and in-degree. The operational risk evolution network of the URT system under rainstorms is a typical directed network, and the degree of exit and degree of entry of a certain risk event reflect the ability and degree of this risk event to cause other risk events in the process of risk evolution, respectively.

Betweenness centrality (BC_i) is an indicator reflecting global characteristics, which represents the proportion of the number of shortest paths through $R_i$ to the number of shortest paths in the whole network [63]. The greater the (BC_i) of a risk event, the stronger its ability to control other risk events through mediation and the more central it is in the risk evolution network.

Closeness centrality (CC_i) measures how easy it is for $R_i$ reach other nodes in the network [64]. The greater (CC_i) of a risk event, the less dependent the risk event is on other risk events in the network, which means that the occurrence of the risk event is less controlled by other risk events.

The clustering coefficient (C_i) is an indicator to describe the degree of node clustering, which represents the ratio between the actual correlation number of nodes and adjacent nodes and the maximum possible correlation number between them and reflects the degree of closeness between nodes. In the operational risk evolution network of the URT system under rainstorms, the greater the clustering coefficient, the higher the degree of clustering among risk events.

3.3.2. Dynamic Evaluation Indicator of the Network

The dynamic simulation of the operational risk evolution network of the URT system under rainstorms was analyzed from the perspective of random failure and deliberate attack. The analysis removed critical risk nodes according to the importance of the nodes to simulate the impact of the failure of critical risk nodes on the network. The effect of the failure risks on the operational safety of the URT system was analyzed through four indicators such as the maximum relative size of connected subgraph, the connectivity, the efficiency, and the rate of change in efficiency. The calculation formulae and parameter meanings of the dynamic evaluation indicators of the operational risk evolution network of the URT system under rainstorms are shown in

Table 4. Dynamic evaluation indicators of the operational risk evolution network of the URT system during rainstorms.

Indicators	Maximum Relative Size of Connected Subgraph	Connectivity	Efficiency	Rate of Change in Efficiency
Formula	$S=\frac{N^{’}}{N}$	$R=\frac{E}{3N-6}$	$e=\frac{1}{N\left(N-1\right)}{\displaystyle {\sum }_{i\ne j}\frac{1}{d_{ij}}}$	$Q=\left|\frac{\left(e-e^{’}\right)}{e}\right|$
Parameter meaning	$N^{’}$ is the number of nodes in the maximum connected subgraph; $E$ is the number of edges in the network; $e$ is the network efficiency of the original network; and $e^{’}$ is the network efficiency after failure simulation.

[65].

4. Research Results

4.1. Analysis of Critical Nodes

In this paper, four indicators describing the static topological characteristics of the network, including the node degree, betweenness centrality, closeness centrality, and clustering coefficient, were selected to measure the importance of nodes in the network. Pajek was used to calculate the indicators of nodes in the network, and the results of the indicators of each node of the rainstorm risk evolution of the URT system were obtained, as shown in

Table 5. The indicator results of the rainstorm risk evolution network of the URT system.

No.	Degree	Betweenness Centrality	Closeness Centrality	Clustering Coefficient
R1	10	0	0.581395	0.077778
R2	2	0.000833	0.384615	0.000000
R3	7	0.005556	0.520833	0.119048
R4	7	0.075972	0.568182	0.133333
R5	2	0.000000	0.384615	0.500000
R6	5	0.030000	0.471698	0.200000
R7	4	0.001667	0.462963	0.083333
R8	2	0.001250	0.446429	0.000000
R9	4	0.017500	0.438596	0.083333
R10	2	0	0.409836	0.500000
R11	3	0	0.462963	0.333333
R12	5	0.058889	0.438596	0.166667
R13	6	0.029583	0.520833	0.066667
R14	3	0.005000	0.446429	0.000000
R15	2	0.008889	0.384615	0.000000
R16	2	0.001667	0.423729	0.000000
R17	3	0.015000	0.409836	0.000000
R18	11	0.073194	0.625000	0.081818
R19	1	0	0.308642	0.000000
R20	2	0	0.416667	0.000000
R21	10	0.072778	0.581395	0.022222
R22	4	0	0.454545	0.333333
R23	1	0	0.373134	0.000000
R24	2	0.008889	0.384615	0.000000
R25	3	0	0.416667	0.000000
R26	3	0	0.423729	0.166667

.

The sum of the out-degree and in-degree of a node represents the degree of the node. From Figure 4, the top 3 risks in terms of degree in Figure 2 are R18 (station flooding), R1 (heavy rainfall), and R21 (train stoppage). The out-degree of station flooding is 7; the in-degree is 4. The out-degree of heavy rainfall is 10, and the in-degree is 0. The out-degree of the train stoppage is 2; the in-degree is 8. Heavy rainfall, as the initial node of the network, has the largest out-degree, followed by station flooding, indicating that the risk of station flooding has the strongest outward radiating ability and is most likely to cause other risks during a rainstorm. Train stoppage has the biggest in-degree, which is the easiest factor to cause risks and results. In the operational risk evolution network of the URT system under rainstorms, station flooding is the intermediate node with the largest degree, and its in-degree is smaller than its out-degree, which is more suitable for risk control from the perspective of prevention.

R4 (ponding) has the highest betweenness centrality (0.075972), indicating that R4 has located to a great extent between the other nodes and has strong control over the other nodes. Effective prevention of ponding can cut off the path of disaster evolution and reduce losses to a great extent. From Figure 2, it can be seen that in a rainstorm disaster, ponding may be directly caused by heavy rainfall or indirectly caused by drainage system failure.

R18 (station flooding) has the most significant closeness centrality (0.625000), indicating that the distance from R18 to other nodes is small, and it is in the central position in the geometric sense and least dependent on other nodes for propagation. Therefore, avoiding station flooding can effectively cut off the spread of risk along the evolutionary path and prevent operational accidents in URT systems.

The overall clustering coefficient of the network nodes is small (0.119000), which proves that the degree of a grouping of nodes in the operational risk evolution network of the URT system under rainstorms is low, and the degree of connection among risk events is small. Effective control of critical nodes and connected edges can avoid or reduce the loss of URT system operation by rainstorm disasters. Among them, R5 (saltwater intrusion) and R10 (water-retaining wall damaged) have the most significant clustering coefficient (0.500000), indicating that the degree of connectivity among adjacent nodes of these two nodes is more significant, and they are more likely to influence each other’s evolution. Additionally, saltwater intrusion is an uncontrollable risk following heavy rainfall, so the water-retaining wall damage is the node to focus on in the risk evolution network.

4.2. Dynamic Simulation

Identifying critical risks in the operational risk evolution network of the URT system under rainstorms can help narrow the scope of risk control and improve the targeting, effectiveness, and timeliness of risk control. By carrying out grey relational analysis on the node indicators’ results of the operational risk evolution network of the URT system under rainstorms, the critical nodes of the network were identified, and the dynamic simulation was carried out using the principles of random failure and deliberate attack failure.

4.2.1. Identification of Critical Risk Nodes

GRA is a measurement method to describe the strength, magnitude, and order of the relationship of factors or systems [66]. After the results of the four indicators of each node were analyzed by GRA, the node correlation degree of URT system accidents under rainstorm disasters was obtained, as shown in

Table 6. Accident node correlation degree of the URT system under rainstorm disaster.

Rank	Node	Correlation Degree	Rank	Node	Correlation Degree
1	R18	0.981	14	R9	0.823
2	R21	0.934	15	R26	0.817
3	R1	0.933	16	R14	0.811
4	R4	0.869	17	R17	0.810
5	R3	0.863	18	R25	0.810
6	R13	0.848	19	R8	0.804
7	R6	0.840	20	R16	0.803
8	R12	0.838	21	R20	0.803
9	R22	0.834	22	R24	0.802
10	R11	0.827	23	R15	0.802
11	R10	0.825	24	R2	0.801
12	R5	0.824	25	R23	0.795
13	R7	0.823	26	R19	0.792

. The greater the node correlation degree, the higher the node importance degree. The results show that the importance of station flooding is the largest at 0.981, followed by train stoppage at 0.934. The top ten risk nodes of importance were selected as critical risk nodes for further study in this paper. Therefore, station flooding, train stoppage, heavy rainfall, ponding, flood, overhead line failure, foreign objects, drainage system failure, train delay, and platform collapse are the critical risks of the evolutionary network. And the ten critical risks are the risks that need to be prevented and controlled in URT systems during rainstorm disasters.

4.2.2. Individual Node Failure Simulation Analysis

The network efficiency and connectivity are 16.36% and 73.61%, respectively, when the network is static. As a result of the individual node failures, the maximum relative size of the connected subgraph of the network was 96.15%. The network nodes failed in the order of node correlation degree, and the connectivity after a single risk failure is shown in Figure 5. From Figure 5, it can be seen that the network connectivity decreases the fastest after the underground station flooding failure. The reason for this is that the risk of station flooding has a more remarkable ability to trigger and be triggered, and if this risk can be effectively avoided, the safety of the operation of URT systems will be greatly improved.

The rate of change in efficiency after the failure of individual nodes is shown in Figure 6. The most significant difference in the efficiency of the whole network is 23.29% after the failure of the train stoppage risk. In the event of rainstorm disasters, once the train stops in the tunnel, it is very likely to cause significant accidents such as train flooding and tailgating, resulting in severe casualties. The second highest rate of change in efficiency in the network is station flooding, which is one of the more critical risks in the operation of URT systems. If station flooding occurs, it may affect the safety of the facilities and equipment and may also pose a threat to the lives of those who are stranded in the station.

4.2.3. Continuous Node Failure Simulation Analysis

Failure simulation was conducted one by one according to the importance of critical risk nodes. The connectivity, efficiency, and maximum relative size of the connected subgraph of the network are shown in Figure 7. With the increase in the number of failed nodes, the indicators of the network all show a significant downward trend. When the number of failed nodes is six, i.e., when station flooding, train stoppage, heavy rainfall, ponding, flood, and overhead line failure all fail, the ability of risk propagation in the network becomes weaker. Thus, this shows that the failure of the above six risks has the most apparent impact on the whole network in the risk evolution network. Heavy rainfall is unavoidable during rail transit operations. It is of great significance to the safety of rail transit operations under rainstorm disasters if station flooding, train stoppages, ponding, flood, and overhead line failure can be completely avoided.

5. Discussion and Strategies

This research focused on carrying out a systematic exploration of the impacts of URT systems and the evolution of operational risks. By studying the static topological characteristics and dynamic fault simulation of the operational risk evolution network of URT systems under rainstorms, this research contributes to a general awareness of the consequences of the risks to the government and the public, which in turn is a foundation for enacting relevant regulations or policies. Additionally, studying the impacts of such rainstorm disasters can improve risk warning capabilities and the resilience of URT systems and reduce risks; the research can also bridge the gap between theory and practice and complement the emergency management body of knowledge.

Based on the static topological characteristics of the network, it was concluded that station flooding, train stoppage, heavy rainfall, ponding, saltwater intrusion, and water-retaining wall damage have a strong influence on the network. According to the dynamic simulation analysis of the network, it is of great significance for the operational safety of the URT system to avoid the risks of station flooding, train stoppage, heavy rainfall, ponding, flood, and overhead line failure. Whether from the perspective of static or dynamic simulation, risks such as station flooding, train stoppage, heavy rainfall, and ponding have a critical impact on the network. This paper presents some specific mitigation measures for critical risks as follows.

For station flooding, it is one of the most important risks in the network, which has a high ability to trigger and be triggered. Avoiding the risk will significantly reduce network connectivity. It is recommended that three levels of warning steps be set up at station entrances during construction, that flood control facilities be improved, that water retention structures and drainage systems be regularly inspected, and that an optimal rainstorm contingency plan be developed to evacuate people promptly when rainwater is backed up in stations and to reduce the likelihood of other risks arising from station flooding. For train stoppage, it refers to the risks and results of a forced stop due to equipment failure and an active stop due to the prevention of accidents, which is the most easily triggered risk. To control the occurrence of such risks, feed-forward control must be strengthened, i.e., the risk nodes with the ability to cause casualties are examined one by one to reduce the probability of the occurrence of such risks. Control measures include improving the train operation command and dispatch system, strengthening vehicle maintenance and signal system debugging, developing an effective equipment inspection and management system, and formulating plans for extreme weather operations. Heavy rainfall has the greatest out-degree as a causal risk of rainstorm disasters and requires measures in all areas to avoid secondary and derivative disasters. For ponding, it has the strongest intermediary role, and its failure can cut off multiple paths of risk propagation. It is necessary to carry out a comprehensive inspection of the drainage system and regularly clean the foreign objects in drainage inlets, as well as deploy drainage pumps at the tunnel entrances and metro station entrances to eliminate ponding due to system failure of civil or drainage systems.

Based on the critical risks and their mitigation measure, this paper proposes enhancement strategies to improve the operational safety of URT systems under rainstorm disasters from the perspective of risk response, as shown in Figure 8.

(1)

Improving risk preventive mechanisms of URT systems under rainstorm disasters. The emergency management to establish an emergency expert committee composed of multidisciplinary experts. The committee can organize cross-departmental, cross-regional, and cross-system collaboration with information coordination networks, big data analysis, and blockchain technology. The government can establish a multi-organizational framework of emergency coordination that includes government management departments, operating companies of URT, and residents. The government will try to explore the collaborative mechanism of multi-organization participation in risk warning and emergency response and optimize the path of emergency response to avoid significant damage in the URT systems.

(2)

Optimizing the risk warning mechanism and the design standards for flood and drainage in URT systems under rainstorm disasters. At present, the standard of red rainstorm warnings issued by the Chinese meteorological department is on the low side for URT systems, which makes it difficult to alert grassroots management and greatly weakens the effectiveness of meteorological warnings. When constructing an early warning system for URT systems, the meteorological department should take crucial factors into full consideration such as the carrying standards and linkages of URT systems. The design and construction of disaster prevention engineering for URT systems should strictly implement relevant design and construction specifications to work sufficiently for URT systems according to local conditions. At the same time, big data monitoring technology should be upgraded and intelligently transform URT systems to enhance the capability of meteorological disaster detection and reduce the hazards and losses of URT systems caused by rainstorm disasters.

(3)

Standardizing the daily patrol and inspection institutions and reducing the probability of risk. Operating companies of URT should organize regular safety training to enhance awareness of the emergency safety of staff. Operating companies should also improve inspection rules and implement safety responsibilities to ensure that they can deal with all kinds of emergencies. Staff should take relevant accident cases as a wake-up call and check carefully on easily overlooked facilities and components, focus on safety hazards in water-retaining structures and drainage systems, and promptly identify sources of danger and deal with them accordingly.

(4)

Perfecting engineering laws and formulating insurance regulations for the operation of projects. For damage caused by force majeure factors, the URT operating company will receive a reimbursement fee for obstacle removal, inspection, reconstruction, and compensation for some passengers. This system could reduce the financial losses of the government and the operating company.

6. Conclusions

This research investigates the evolutionary network of operational risks of the URT system in rainstorm disasters. In total, 47 accident risk evolution chains and 26 risk factors were identified based on 35 worldwide accidents in URT systems during rainstorm events from 2003 to 2022, and the operational risk evolution network of the URT systems under rainstorms was constructed to conduct simulation studies. The contributions of this study are as follows:

(1)

Perfecting the safety system of URT systems. This research establishes the operational risk evolution network of URT systems under rainstorms, and the evolutionary path of risk can be visually seen from the network. And the research helps urban transport management to manage the risk to URT under rainstorm disasters.

(2)

Identifying the critical risks based on the static network. The research determined that station flooding is the risk that is most associated with other risks and least dependent on other risks for propagation. Ponding has the strongest control over other risks. Saltwater intrusion and water-retaining wall damage are the most grouped clusters, and water-retaining wall damaged is a precursor risk to station flooding, which can be interrupted in time to avoid more serious events. The above risks are among the critical risks and vulnerabilities of the network and are the focus of rainstorm disaster management for URT systems.

(3)

Clarifying the role of the critical risks based on the dynamic network. The failure of train stoppage has the greatest impact on the efficiency of the overall network, and the network connectivity drops the fastest after the failure of station flooding. Strict avoidance of train stoppage and station flooding will significantly reduce the connectivity and efficiency of the overall network. Moreover, taking the necessary risk prevention measures for station flooding, train stoppage, heavy rainfall, ponding, flooding, and overhead line failure will effectively improve the operational safety of URT systems under rainstorm disasters.

There are still some limitations to this research. Due to the increasing complexity of URT systems in practice, the indicators will continue to evolve and change. Therefore, in subsequent research, our group will continue to keep track of these dynamic changes and design adaptive network models and provide more methods and bases for enhancing the ability of URT systems to operate safely. Furthermore, scholars can study the operational risks of URT systems under compound hazards such as rainstorm–earthquake and earthquake–tsunami events.