Exploration of the Mountainous Urban Rail Transit Resilience Under Extreme Rainfalls: A Case Study in Chongqing, China

Abstract

Extreme rainfalls could greatly affect operations of urban rail transit systems of mountainous cities, which are prone to have landslides and floods under rainfalls. Therefore, it is essential to assess and enhance the resilience of mountainous urban rail transit networks under heavy rainfalls. Taking the metro network of Chongqing, the largest mountainous city in China, as an example, this study establishes a network topology model to identify the high-risk nodes under rainfalls and find the effective recovery strategies. By introducing the metro ridership and topological shortest distances, a network service efficiency function is developed, and the importance of nodes is quantified using service efficiency index and topological importance index. The resilience assessment model based on service efficiency is constructed using the resilience triangle theory. Additionally, risk levels for landslide and flood-prone areas are classified using the K-means algorithm, based on rainfall, elevation, and slope data, identifying high-risk stations. Finally, the node recovery sequence and strategies for high-risk nodes affected by landslides and floods are examined. The results indicate that in extreme rainfall scenarios, two transfer stations (Daping and Fuhua Road) are among the high-risk landslide stations, while most other nodes have a service efficiency index of less than 0.2. High-risk flood stations are located on non-transfer lines and mostly on metro lines with high traffic flow, with service efficiency index generally high, with some stations, like Bijin Station, exceeding 0.3. When all affected nodes fail, network service efficiency decreases by 84.0% and 75.2% under landslide and flood disasters, respectively. Compared with the random recovery strategy, recovery strategies based on topological importance and service efficiency index, the optimal recovery strategy based on genetic algorithm performs much better.

1. Introduction

With the rapid development of the social economy, as an efficient public transit mode, urban rail transit (URT) has expanded greatly in the world. By the end of 2023, a total of 563 cities in 79 countries and regions had opened URT lines, with a total operating length of 43,400.39 km, and China ranks first in terms of the operating mileage [1]. However, as URT networks continue to expand, the threat from natural hazards has also become increasingly prominent, particularly extreme rainfalls. For example, on 20 July 2021, Zheng’zhou, China, experienced a severe rainstorm, which flooded Metro Line 5, resulting in 14 passenger deaths. Considering the extreme weather is increasingly frequent due to global warming, conducting scientific and well-founded risk assessments before disasters has become crucial for minimizing disaster losses and enhancing a city’s ability to prevent, mitigate, withstand, and respond to disasters effectively.

Scholars have widely focused on this aspect in studies of urban heavy rainfall disaster risk assessment and zoning. Zou et al. [2], using the contribution rate method, found that rainfall and terrain slope had the most significant impact on rain-induced landslides. Further research confirmed that slope was the main influencing factor for landslide disasters [3,4,5]. Meanwhile, Wang et al. [6] applied the XGBoost model to assess the impact of various factors on flood risk, revealing that elevation and rainfall were the most prominent factors affecting flood risk. These studies highlight the potential risk of landslides and floods under the combined influence of rainfall and terrain features. Compared to flatland cities, mountainous cities are more prone to landslides and floods under extreme rainfall conditions due to their unique topographical features [3]. For instance, the frequency of landslides in Chongqing, a mountainous city in China, is the highest in the country [7], with rain-induced landslides accounting for over 90% [8]. Landslides [9] often occur along highways and railways, potentially leading to route blockages or damage, and even causing severe accidents such as train derailments. At the same time, floods caused by heavy rain [7] also can result in drowned trains, infrastructure damage, and even casualties. Therefore, enhancing the resilience of mountainous URT networks under extreme rainfall conditions has become a critical issue in the construction of safe transportation systems.

Resilience is the ability of a system to maintain its basic functions and structures through resistance, mitigation, absorption, and recovery under extreme conditions [10]. Although the definition of resilience varies across different disciplines, its core content includes two aspects: the ability to withstand disruptions and the ability to return to normal after disruptions [11]. Since transportation is essential for the everyday functions of society, the resilience of transportation networks under extreme events has been attracting much attention recently. For example, Testa et al. [12] analyzed the resilience of the New York City highway network faced with extreme storm surges by randomly removing nodes and examining changes in average node degree, clustering coefficient, and redundancy in the network topology. Patriarcap [13] analyzed the relationship between traffic network resilience and efficiency, pointing out that improving network resilience not only improves overall network efficiency but also reduces losses in the event of failures. Resilience is typically quantified through the resilience loss triangle, which is represented by the difference between the normal performance curve and the disrupted performance curve, as well as the durations of the disruption and recovery phases [14]. Li et al. [15] also proposed that transportation network resilience could be evaluated through both total performance loss and recovery speed. Zhou [16] argued that there were significant differences in the resilience performance of different transportation modes, and, therefore, when assessing traffic network resilience, the differences in transportation modes should be fully considered.

Scholars have also conducted some studies on resilience assessment for metro networks. Zhang et al. [17] used network topology efficiency metrics to evaluate the resilience of the Shanghai metro network. Zhang et al. [18] assessed metro network performance through average network efficiency and used the cumulative loss of network efficiency before and after an attack as a measure of network resilience. To reflect the dynamic resilience of transportation networks, dynamic indicators such as traffic flow and operating speed should be considered. D’Lima et al. [19] analyzed the spatiotemporal characteristics of metro passenger flows and used the recovery speed of passenger flow as an indicator of network resilience. Lu et al. [20] conducted a quantitative analysis of the dynamic changes in metro network resilience under different events, based on network topology and passenger flow data. Xu et al. [21] used a multi-stage resilience framework, combined with historical traffic data, to compare five metro systems—California Bay Area Rapid Transit, the London Underground, Singapore MRT, Queensland Rail, and Washington Metro. They found that the Singapore MRT exhibited the best resilience in the face of both random disruptions and targeted attacks. Ma et al. [22] measured metro network resilience by calculating its absorption, resistance, and recovery capacities, incorporating various data such as passenger flow, train schedules, passenger travel behavior, etc.

The recovery ability after disturbances is also essential for measuring traffic network resilience [23]. Optimizing the recovery process to minimize the recovery time is the key in formulating recovery strategies [24]. To enhance the resilience of transportation networks, Perea et al. [25] proposed that the reasonable allocation of repair resources and the establishment of an effective restoration sequence were crucial for quickly recovering the damaged networks. Lv et al. [26] proposed an optimization model with the goal of maximizing road network service resilience and obtained the optimal recovery strategy based on an optimization algorithm. Zhang et al. [17] used enumeration methods to study the optimal recovery strategy for the Shanghai metro network during emergencies, pointing out that establishing an effective restoration sequence could significantly improve the network’s recovery speed. Additionally, Chen et al. [27], considering factors such as the degree of node failure, the total amount of repair resources, and the number of repair teams, proposed a recovery strategy for damaged metro networks aimed at minimizing resilience loss. Yin et al. [28] simulated the dynamic recovery process of metro networks after failures and proposed a dynamic restoration strategy model.

In summary, although scholars have conducted considerable research on transportation network resilience in recent years, there are still some weaknesses. Firstly, none of the existing studies have explored the resilience of mountainous cities, which, however, are more vulnerable to extreme rainfalls due to their hilly terrains. To account for the influence of terrain, it is necessary to take the topographical factors into account when analyzing the resilience of mountainous cities. Secondly, regarding the disruption of extreme events to transportation networks, most studies randomly select the disrupted nodes. However, nodes should be chosen based on their disaster risk levels to be consistent with the truth and develop effective countermeasures. Lastly, most studies analyze the resilience of transportation networks based only on their physical topological structures, with little consideration given to the impact of passenger flows.

Aiming at these issues, this study focuses on exploring the resilience of the world’s largest mountainous URT network, the Chongqing Metro System, with a solid analysis [29]. It assesses the risk levels of landslides and floods by its geographical characteristics and rainfall data, identifying metro stations at high risk of disaster. Then, a resilience assessment model for the metro network is constructed based on service efficiency indicators. By simulating the failure and recovery processes of the network, this paper proposes an optimal recovery strategy aimed at maximizing resilience, providing theoretical support for mountainous urban rail transit systems in responding to extreme rainfall events. The research work includes five aspects: (1) constructing a rail transit topology network model using the Space L method; (2) analyzing network topology indicators based on complex network theory and developing service efficiency and topological importance indicators; (3) classifying risk levels for disaster-prone areas and identifying nodes in high-risk zones; (4) developing different recovery strategies based on the failed nodes and determining the optimal resilience repair strategy using service resilience evaluation indicators and the resilience loss triangle; (5) applying the analytical framework to real data from Chongqing’s rail transit network, yielding valuable conclusions.

2. Materials

Chongqing is a megacity located in southwestern China, with a population of 31.9 million and a GDP of RMB 3014 billion (about USD 412.9 billion). The Chongqing metro network is one of the largest mountainous URT systems in the world, providing services to the 14 districts of Chongqing. By the end of 2023, it had opened Lines 1, 2, 3, 4, 5, 6, 9, 10, and 18, as well as the Ring Line, International Expo Line, and Jiangtiao Line, totaling 12 lines and 256 stations (Figure 1). The total operating mileage reached up to 538 km, with a peak daily passenger volume of 5.162 million, accounting for 54.28% of public transportation travel in the city [30], which makes a significant contribution to alleviate traffic congestions and promote green travel.

Figure 2 shows the daily ridership of each metro line, which is retrieved from the metro company. Lines 3 and 6 have the highest ridership, reaching 607,000 passengers per day, making them the backbone of the URT network. Following them, Line 1, which connects the east and west sides, and the Ring Line, which encircles the core urban area, exhibit relatively high passenger flows, underscoring their importance. In contrast, Lines 4, 18, the International Expo Line, and the Jiangtiao Line have the lowest ridership, each under 70,000 passengers, mainly due to serving suburban areas with the lower population density. Lines 2, 5, 9, and 10 have moderate ridership, with around 300,000 passengers per day. Overall, passenger volumes across the Chongqing metro lines show a clear hierarchical pattern, closely related to their geographic locations, service areas, and regional development, reflecting the varying capacities of each line to meet urban travel demands.

As a mountainous city, Chongqing is prone to have landslides and floods under rainstorms. Here, landslide risk is determined based on slope and cumulative rainfall, while flood risk is assessed using elevation and the cumulative rainfall. The rainfall data of Chongqing in 2022 is retrieved from the Earth Resource Data Cloud (http://www.gis5g.com, accessed on 15 September 2024), whereas the elevation and slope data are obtained from the Geospatial Data Cloud (https://www.gscloud.cn, accessed on 15 September 2024). The resampling tool in ArcGIS (v.10.8.0) is adopted to adjust the spatial resolution of all raster data to be 1 km × 1 km and then converts them to vector data for clustering. Figure 3 displays spatial distributions of these three indicators.

Here, both landslide risk and flood risk are classified into five levels, i.e., higher, high, medium, low, and lower, with the K-means clustering method. Figure 4 presents the clustering results. As shown in Figure 4a, stations with high landslide risk are predominantly located in the northern part of the city. This region experiences heavy rainfall and features steep slopes due to the presence of several mountains, including Tongluo Mountain, Longwangdong Mountain, and Zhongliang Mountain. Similarly, Figure 4b highlights that high flood risk stations are also concentrated in the northern area, characterized by abundant rainfall and low-lying terrain.

3. Methods

3.1. Network Topology Model

Here, this study adopts the Space L method to construct the URT network, as it more closely resembles the actual railway network [31]. In the Space L model, nodes represent stations, and edges represent segments. Let a network be $G=\left(V,E\right)$, where $V=\left\{v_i,i=1,2,\dots ,N\right\}$ is the set of nodes, $N$ is the number of nodes in the network, and $E=\left\{e_{ij},i,j=1,2,\dots ,N,i\ne j\right\}$ is the set of edges, $e_{ij}=1$ if nodes $i$ and $j$ are adjacent; otherwise $e_{ij}=0$.

In complex networks, the following metrics are commonly used to measure the topological features: average node degree, average clustering coefficient, and average shortest path length. Their definitions and calculation methods are shown in

Table 1. The definitions and calculations of network topological indexes.

Index	Definition	Formula
Average node degree	The average degree of all nodes in the network (the number of connections each node has with other nodes)	$\overline{k}={\displaystyle \sum _i^N{k}_i}/N, k_i={\displaystyle \sum _{j\in V,j\ne i}{e}_{ij}}$
Average clustering coefficient	The average level of clustering among nodes in the network	$C={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{C}_i}, C_i={\displaystyle \frac{2e_i}{k_i\left(k_i-1\right)}}$
Average shortest path length	The average shortest path length between any two nodes in the network	$d={\displaystyle \frac{2}{N\left(N-1\right)}}{\displaystyle \sum _{i,j\in V;i\ne j}{d}_{ij}}$

Note: $k_i$ is the degree of node $i$; $C_i$ is the clustering coefficient of node $i$; $e_i$ is the number of adjacent nodes of node $i$; and $d_{ij}$ denotes the short path distance between node $i$ and node $j$.

.

In complex networks, degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality are widely used to quantify the connectivity and importance of nodes within the network (

Table 2. The definitions and calculations of node centralities in complex networks.

Index	Definition	Formula
Degree centrality [32]	It is the total number of the connected edges of a node.	$C_D\left(i\right)={\displaystyle \frac{k_i}{N-1}}$
Betweenness centrality [33]	It is the sum of the fractions of all-pairs shortest paths that pass through a node.	$b_q={\displaystyle \sum _{i=1,j=1,i\ne j\ne q}^N\frac{n_{ij}\left(q\right)}{n_{ij}}},C_B\left(q\right)={\displaystyle \frac{2}{\left(N-1\right)\left(N-2\right)}}{b}_q$
Closeness centrality [34]	It is used to measure the ability of a station to affect another node through the network.	$c_i={\displaystyle \frac{1}{{\displaystyle \sum _{i,j\in V;i\ne j}{d}_{ij}}}},C_c\left(i\right)=\left(N-1\right)\times c_i$
Eigenvector centrality [35]	It can identify the different effects of neighbors of a node on it.	$C_E\left(i\right)={\lambda }^{-1}{\displaystyle \sum _{j=1}^N{e}_{ij}{x}_j}$

Note: $b_i$ is the betweenness centrality of node $i$; $n_{ij}$ is the number of shortest paths between node $i$ and node $j$; $n_{ij}\left(q\right)$ is the number of shortest paths between node $i$ and node $j$ that pass through node $q$; $c_i$ is the closeness centrality of node $i$; ${\lambda }^{-1}$ is a proportional constant; and $x_j$ is the centrality score of node $j$.

). This study also utilizes them to evaluate the importance of stations and explore the network’s topological properties here.

3.2. Network Topological Metrics

3.2.1. Service Efficiency Index

Existing studies [17,18] commonly use complex network theory, employing topological efficiency as a performance indicator for road networks. The topological efficiency is the average efficiency of all node pairs within a network, where the efficiency of a node pair reflects their connectivity, which usually uses the inverse of their topological distance. Let $R\left(G\right)$ denote the topological efficiency of network $G$ [36]:

$$R\left(G\right)={\displaystyle \frac{1}{N\left(N-1\right)}}{\displaystyle \sum _{i\ne j,i,j\in V}\frac{1}{d_{ij}}},$$

(1)

where $d_{ij}$ represents the shortest topological distance between node $i$ and node $j$, i.e., the minimum edges required to travel from node $i$ to node $j$.

Equation (1) reflects the physical connectivity of a network. However, when evaluating the performance of transportation networks, the impact of traffic flow should also be taken into account [37,38]. Therefore, this study proposes an URT service efficiency index weighted by traffic flow.

The service efficiency between nodes $i$ and $j$ is defined as the weighted sum of passenger flows of all lines passing through these two nodes, divided by their shortest topological distance.

$$R_{S,ij}={\displaystyle \sum _{l\in L}\left({\delta }_{il}+{\delta }_{jl}\right)}{\displaystyle \frac{f_l}{d_{ij}}},$$

(2)

where $R_{S,ij}$ represents the service efficiency between nodes $i$ and $j$ in the URT network; $L$ represents the line set; $f_l$ represents the average daily ridership on line $l$; ${\delta }_{il}$ is a dummy variable. If node $i$ is on line $l$, then ${\delta }_{il}=1$, otherwise, ${\delta }_{il}=0$. The same applies to ${\delta }_{jl}$.

The service efficiency of a network is defined as the average service efficiency of all node pairs in the network model, and expressed as follows:

$$R_S\left(G\right)={\displaystyle \frac{1}{N\left(N-1\right)}}{\displaystyle \sum _{i\ne j,i,j\in V}{R}_{S,ij}}.$$

(3)

To eliminate the influence of network scale and make the service efficiency comparable across different networks, the service efficiency is further normalized:

$$R_N\left(G\right)={\displaystyle \frac{R_S\left(G\right)}{\underset{i\ne j}{\max }{R}_{S,ij}}}.$$

(4)

In the recovery stage, it is important to determine the restoration sequence of failed nodes. Therefore, to determine the importance of different nodes, we propose a node importance indicator based on the normalized service efficiency by analyzing the relative change in network service efficiency before and after nodes fail.

$${\kappa }_i={\displaystyle \frac{R_N\left(G\right)-R_{N,i}\left(G\right)}{R_N\left(G\right)}},i\in V,$$

(5)

where ${\kappa }_i$ represents the service efficiency importance index for node $i$; $R_{N,i}\left(G\right)$ represents the service efficiency of network $G$ following the failure of node $i$.

3.2.2. Topological Importance Index

In Equation (5), a service efficiency importance index is proposed to determine the recovery priority of failed nodes. To compare the effects under different recovery sequences, a composite topological importance index is constructed as a reference. It adopts 4 metrics, i.e., degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality, to measure the importance of each node. The topological importance index is calculated based on the entropy weight method to more accurately assess the relative importance of each node in the network.

The entropy weight method is an objective weighting approach that determines the weights based on the amount of information provided by the data itself. In this paper, the entropy weight method is used to calculate the weights of degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality for each node in the network. First, these centrality indicators are normalized to convert the different dimensions into comparable standard forms. Then, the variation value of each node in each centrality indicator is calculated to derive the information entropy. Information entropy reflects the degree of uncertainty of the information in each indicator. The smaller the entropy, the more information the indicator provides and the larger its weight. Based on the information entropy, the weights of each centrality indicator are calculated, as shown in

Table 3. The weights of centrality indicators.

Degree Centrality	Betweenness Centrality	Closeness Centrality	Eigenvector Centrality
0.353	0.277	0.297	0.073

, and the final topology importance index for each node is obtained. This process ensures that the importance of each indicator is objectively determined based on the distribution of the data itself, thereby reasonably evaluating the role and influence of nodes in the network.

3.3. Resilience Evaluation and Network Repair

3.3.1. Network Resilience Assessment Model

The metro network performance under disruptions is shown in Figure 5. It can be divided into four stages: the normal stage (before $t_1$), in which $t_1$ is the moment of node failures; the disturbed stage (from $t_1$ to $t_2$), in which $t_2$ is the moment when the network service efficiency decreases to the minimum and also the repair plan is initiated; the restoration stage (from $t_2$ to $t_3$), in which $t_3$ is the moment when the network service efficiency returns to normal after nodes are repaired; and the return-to-normal stage (after $t_3$). The area enclosed by points A, B, and C is the performance loss of the metro network under repair strategy.

Here, service resilience is defined as the ratio of the accumulated performance retained by the network from the moment of node failure to the moment of returning to normal, to the accumulated performance of the network over an equivalent duration under normal conditions. That is, service resilience is the ratio of the green area to the sum of the blue and green areas in Figure 5.

$${\psi }_e={\displaystyle \frac{{\displaystyle {\int }_{t_2}^{t_3}{R}_N\left(t\right)dt}}{R_N\left(t_1\right)\left(t_3-t_2\right)}},$$

(6)

where ${\psi }_s$ represents the service resilience of the metro network; $R_N\left(t\right)$ denotes the network service efficiency at time $t$; and $R_N\left(t_1\right)$ represents the network service efficiency under normal conditions.

3.3.2. Repair Strategies

Under heavy rains, it is assumed that when all the top-10 high-risk nodes for both landslide and flood scenario fail, the repairment of transfer stations requires 2 days and other stations require 1 day [26]. Here, we consider four recovery strategies: random repair, priority recovery based on the topological importance index, service efficiency index, and optimal recovery using a genetic algorithm. Each strategy offers a distinct approach to restoring system performance. Random repair involves selecting nodes for recovery in a random sequence, providing a baseline for comparison. Priority recovery based on the topological importance index targets nodes with the highest topological importance in the network, aiming to quickly restore connectivity and robustness. Similarly, the service efficiency index prioritizes nodes that play a critical role in maintaining service performance. The final strategy identifies the optimal recovery sequence by simulating and evaluating multiple strategies, ensuring the most efficient and effective restoration process.

To optimize the recovery strategy, the Genetic Algorithm (GA) was employed. The genetic algorithm is an optimization technique based on natural selection and genetic mechanisms, simulating the biological evolution process to find the global optimal solution through multiple iterations. In this algorithm, the population consists of several individuals, each representing a possible solution, with the population size being 50. The solution is continuously optimized through selections, crossovers, and mutations. This study’s genetic algorithm represents the repair sequence using a permutation encoding scheme, with each individual corresponding to a permutation of nodes. The crossover operator employs Partially Mapped Crossover (PMX), where two crossover points are randomly selected. Genes within the interval are exchanged between parents, and external conflicting genes are adjusted without explicit parameters. The mutation operator utilizes random swap mutation, randomly swapping the positions of two genes with a mutation probability of 0.15, enhancing the exploration capability of the solution space. The maximum number of generations is 50. As the number of iterations increases, the genetic algorithm progressively optimizes the priority of node recovery to enhance the overall network recovery efficiency, ultimately achieving the optimal resilience value.

4. Results and Discussion

4.1. Network Topology Analysis

The constructed Space L model of the Chongqing metro network contains 256 nodes and 288 edges.

Table 4. Characteristics of Chongqing metro network.

Network Parameters	Values
Nodes	256
Edges	288
Average node degree	2.25
Average shortest path length	15.4

presents its main topological features. The average node degree is 2.25. The average shortest path length is 15.4, indicating that the commuting distance for passengers within the Chongqing rail transit system is approximately 15.4 stations.

4.2. Topological Analysis of Affected Nodes

Based on the classification results in Section 2, 10 stations in high-risk areas were selected as high-risk ones as shown in Figure 6. The high-landslide-risk stations are pretty scattered, primarily along Lines 5, 1, and 9. Among them, Daping Station is a representative station for landslide disasters. Daping Station has the highest passenger flow and topological importance index, indicating its significance within the network.

In contrast, the high-flood-risk stations are more concentrated, especially near the intersection of Lines 3 and 10, as well as along Lines 6 and 1. Bijin Station is a typical high-risk station, with a daily passenger flow of 607,000, and it has the highest topological importance index and service efficiency index, indicating that a failure at this station during flood disasters would significantly impact the service capacity of the entire metro network.

By analyzing attributes of high-risk stations for landslide and flood disasters in

Table 5. Attributes of high-risk disaster-affected stations.

Disturbance Scenario	Station Name	Line(s)	Line Traffic (10,000 Passeengers)	Topological Importance Index	Service Efficiency Index	Transfer Available
Landslide disaster	Daping	Line 1, Line 2	87.7	0.564	0.245	1
	Fuhua Road	Line 9, Line 18	30.9	0.453	0.245	1
	Gailanxi	Line 9	25.6	0.422	0.165	0
	Huanshan Park	Line 10	27.5	0.324	0.16	0
	Huxia Street	Line 5	26.3	0.294	0.165	0
	Ciqikou	Line 1	51.9	0.284	0.107	0
	Zhongliang Mountain	Line 5	26.3	0.24	0.165	0
	Gaopu Lake	Line 3	60.7	0.18	0.331	0
	Sanbanxi	Line 4	6.5	0.159	0.055	0
	Yuegang North Road	Line 5	26.3	0.0915	0.165	0
Flood disaster	Bijin	Line 3	60.7	0.325	0.331	0
	Baosheng Lake	Line 9	25.6	0.289	0.206	0
	Liujiaping	Line 6	60.7	0.282	0.181	0
	Xingke Avenue	Line 9	25.6	0.271	0.206	0
	Luxi	Line 4	6.5	0.255	0.055	0
	Shuangbei	Line 1	51.9	0.236	0.107	0
	Shuangfeng Bridge	Line 3	60.7	0.22	0.331	0
	Lushan	Line 10	27.5	0.215	0.16	0
	Xiangjiagang	Line 6	60.7	0.208	0.181	0
	Jiandingpo	Line 1	51.9	0.141	0.107	0

, it can be observed that among the high-risk landslide stations, two are interchange nodes, which have a higher overall topological importance index. In contrast, most other nodes have a service efficiency index below 0.2, indicating that their failure would have a relatively limited impact on the overall network. In comparison, although the high-risk flood disaster stations are all non-interchange nodes, the majority are located on important metro lines with high traffic volumes, and they generally have higher service efficiency indexes. Some stations, such as Bijin Station, have a service efficiency index exceeding 0.3, highlighting their vulnerability during flood disasters and their critical impact on network service.

4.3. Analysis of Repair Strategies

4.3.1. Resilience Assessment Under Multiple Strategies

The optimization process is illustrated in Figure 7. It shows the optimization process of the network recovery strategy as the number of iterations increases. In the landslide disaster scenario (Figure 7a), the genetic algorithm converged to the optimal solution after the 12th iteration, demonstrating good convergence and suitability for the metro network topology model constructed in this paper. The maximum network resilience value was 0.628, with the corresponding optimal recovery node sequence being Gaofeng Lake, Huanshan Park, Daping, Gailan Creek, Fuhua Road, Ciqikou, Yuegang North Road, Huxia Street, Zhongliang Mountain, and Sanban Creek. In the flood disaster scenario (Figure 7b), the genetic algorithm converged to the optimal solution after the 10th iteration, with a maximum network resilience value of 0.646. The corresponding optimal recovery node sequence was Bijin, Baosheng Lake, Liujiaping, Xingke Avenue, Luqi, Shuangbei, Shuangfeng Bridge, Lushan, Xiangjiagang, and Jiandingpo.

Table 6. Metro node recovery order table under four recovery strategies.

Disturbance Scenario	Recovery Strategy	Node Recovery Order	Resilience Value
Landslide disaster	Random Recovery	Yuegang North Road—Sanbanxi—Huanshan Park—Ciqikou—Gailanxi—Gaopu Lake—Huxia Street—Fuhua Road—Zhongliang Mountain—Daping	0.440
	Priority Recovery Based on Topological Importance Index	Daping—Fuhua Road—Gailanxi—Huanshan Park—Huxia Street—Ciqikou—Zhongliang Mountain—Gaopu Lake—Sanbanxi—Yuegang North Road	0.441
	Priority Recovery Based on Service Efficiency index	Gaopu Lake—Daping—Fuhua Road—Gailanxi—Huxia Street—Zhongliang Mountain—Yuegang North Road—Huanshan Park—Ciqikou—Sanbanxi	0.570
	Optimal Recovery Based on Genetic Algorithm	Gaopu Lake—Huanshan Park—Daping—Gailanxi—Fuhua Road—Ciqikou—Yuegang North Road—Huxia Street—Zhongliang Mountain—Sanbanxi	0.628
Flood disaster	Random Recovery	Shuangbei—Jiandingpo—Luxi—Xiangjiagang—Lushan—Shuangfeng Bridge—Xingke Avenue—Liujiaping—Baosheng Lake—Bijin	0.470
	Priority Recovery Based on Topological Importance Index	Bijin—Baosheng Lake—Liujiaping—Xingke Avenue—Luxi—Shuangbei—Shuangfeng Bridge—Lushan—Xiangjiagang—Jiandingpo	0.474
	Priority Recovery Based on Service Efficiency index	Bijin—Shuangfeng Bridge—Baosheng Lake—Xingke Avenue—Xiangjiagang—Liujiaping—Lushan—Shuangbei—Jiandingpo—Luxi	0.617
	Optimal Recovery Based on Genetic Algorithm	Lushan—Shuangfeng Bridge—Bijin—Xiangjiagang—Liujiaping—Xingke Avenue—Baosheng Lake—Luxi—Shuangbei—Jiandingpo	0.646

lists the node recovery order and their network resilience values under each recovery strategy.

In the landslide disaster scenario, the optimal recovery strategy using the genetic algorithm performs exceptionally well. Specifically, the network resilience values under random repair, importance, service efficiency index, and the optimal recovery strategy from the genetic algorithm are 0.440, 0.441, 0.570, and 0.628, respectively. The optimal recovery strategy from the genetic algorithm improves resilience by approximately 42.9%, 42.4%, and 10.3% compared to random repair, topological importance, and service efficiency index, respectively. This optimal recovery strategy not only significantly enhances network resilience but also better ensures the stability and reliability of the network during node failures. By comprehensively considering the overall topological performance of the network and the service efficiency of nodes, it achieves the ultimate optimization of resilience.

In the flood disaster scenario, the network resilience values under random repair, topological importance, service efficiency index, and the optimal recovery strategy from the genetic algorithm are 0.470, 0.474, 0.617, and 0.646, respectively. The optimal recovery strategy from the genetic algorithm improves resilience by 37.5% compared to random repair, by 36.2% compared to the strategy based on topological importance, and by 4.6% compared to the strategy based on service efficiency index. These results further validate the significant enhancement effect of the genetic algorithm’s optimal strategy on network resilience in the context of flood disasters, providing the best recovery plan for the network in the case of multiple node failures.

4.3.2. Temporal Analysis of Network Service Efficiency

Based on the established recovery time relationships and the recovery order in Table 3, the temporal variation curves of network service efficiency under four recovery strategies—random repair, topology-based importance, service efficiency index, and resilience optimization—were calculated. Figure 8 illustrates the dynamic changes in the service efficiency temporal variation curves under the impacts of landslide and flood disasters.

When the disaster causes all 10 key nodes to fail, the network service efficiency significantly decreases. Under the landslide disaster, the service efficiency drops to 0.00627; under the flood disaster, it decreases to 0.00975. Compared to the network service efficiency in normal conditions (0.0393), the service efficiency after node failure declines by 84.0% and 75.2%, respectively.

In the landslide disaster (Figure 8a), the resilience optimization and service efficiency index recovery strategies based on the genetic algorithm show that, after one day in the first recovery phase, the network service efficiency rebounds to 0.0137, representing an improvement of 19.0% compared to the failure state of 0.00627. In contrast, the random repair strategy shows no improvement during the first recovery phase. During the second recovery phase, the resilience optimization strategy surpasses the service efficiency index strategy, demonstrating better recovery performance.

In the case of the flood disaster (Figure 8b), the resilience optimization repair strategy recovers the network service efficiency to 0.0146 after one day in the first recovery phase, marking a 12.4% improvement, while the other three strategies do not see any increase in network service efficiency after the first recovery phase. As the recovery enters the second phase, the network service efficiencies of these three repair strategies begin to gradually improve. This indicates that the genetic algorithm-based network resilience optimization recovery strategy outperforms the random repair, topology importance, and service efficiency index strategies in terms of overall network performance.

5. Conclusions

This study analyzes the functional characteristics of the Chongqing metro network, establishes a topological model of the metro network, and investigates its network properties. By constructing a service efficiency function and resilience recovery model, it explores recovery strategies for metro nodes in high-risk areas of landslide and flood disasters when key nodes fail. The main conclusions are shown as follows.

(1) Using the K-means algorithm, the study analyzes the impacts of elevation, rainfall, and slope on disaster risk, dividing the research area into five risk levels. The northern districts of Chongqing, such as Yuzhong, Yubei, and Jiangbei, are at higher risk of landslides and floods due to heavy rainfall, complex terrain, and low elevation. Among the high-risk landslide disaster nodes, there are two transfer stations (Daping and Fuhua Road), while most other nodes have a service efficiency index generally below 0.2. Conversely, the high-risk flood disaster nodes are non-transfer stations and are mostly located along metro lines with high traffic flow, demonstrating generally high service efficiency index; some stations, like Bijin Station, even exceed 0.3.

(2) When disasters cause the complete failure of key nodes, the network service efficiency significantly declines. In the case of landslide disasters, service efficiency drops to 0.00627, and in the case of flood disasters, it decreases to 0.00975. Compared to the normal state of network service efficiency (0.0393), the efficiency after node failure decreases by 84.0% and 75.2%, respectively. Among different recovery strategies, the resilience optimization recovery strategy based on genetic algorithms outperforms random repair, topology importance-based, and service efficiency importance-based strategies. In the case of key node failures during landslide disasters, the resilience values for the three strategies are 0.440, 0.441, and 0.570, while the resilience value for the optimal recovery strategy is 0.628, representing improvements of 42.9%, 42.4%, and 10.3%, respectively. A similar trend is observed in flood disasters, further confirming the significant enhancement of network resilience by the genetic algorithm optimization strategy in both disaster scenarios.

Although this study focuses on exploring the resilience of the metro network of Chongqing, it also provides many new insights for other cities faced with similar challenges. Firstly, the study confirms that when assessing the resilience of transportation networks, it is important to consider both their topological structures and passenger flows. Secondly, the study shows that transportation networks might have very different resilience performance for different disasters, such as landslides and floods. Therefore, it is important to explore the resilience of transportation networks under different disasters separately to develop the corresponding countermeasures, rather than produce some fixed ones. Thirdly, the study demonstrates the superiority of optimal recovery strategies in improving the resilience of transportation networks. Considering that transportation networks vary greatly between cities, it is also essential for them to develop customized optimal recovery strategies based on their transportation features.

Nevertheless, this study does have its limitation. Firstly, regarding the impact of landslides and floods on the metro network, it only considers the failure of metro stations. However, both disasters might also strike metro segments, which are expected to be more destructive, as trains usually run faster on segments. Future studies might further explore the resilience of the metro network in the event of metro segment failures. Secondly, recovery strategies do not consider resource constraints. However, the repair time of metro stations after disasters is greatly influenced by the available resources, including workers, devices, costs, etc. In practice, these resources are often limited to increase the repair time. Therefore, future researchers might focus on further optimizing the recovery strategies under resource constraints.