Evaluating the Dynamic Comprehensive Resilience of Urban Road Network: A Case Study of Rainstorm in Xi’an, China

Abstract

Rainstorms and flooding are among the most common natural disasters, which have a number of impacts on the transport system. This reality highlights the importance of understanding resilience—the ability of a system to resist disruptions and quickly recover to operational status after damage. However, current resilience assessments often overlook transport network functions and lack dynamic spatiotemporal analysis, posing challenges for comprehensive disaster impact evaluations. This study proposes an SR-PR-FR comprehensive resilience evaluation model from three dimensions: structure resilience (SR), performance resilience (PR), and function resilience (FR). Moreover, a simulation model based on Geographic Information System (GIS) and Simulation of Urban MObility (SUMO) is developed to analyze the dynamic spatial–temporal effects of a rainstorm on traffic during Xi’an’s evening rush hour. The results reveal that the southwest part of Xi’an is most prone to being congested and slower to recover, while downtown flooding is the deepest, severely affecting emergency services’ efficiency. In addition, the road network resilience returns to 70% of the normal values only before the morning rush the next day. These research results are presented across both temporal and spatial dimensions, which can help managers propose more targeted recommendations for strengthening urban risk management.

1. Introduction

An urban road transportation network is an open network built in an urban space, which includes systematic, dynamic, and complex general network topology and unique social characteristics [1]. As a necessary carrier of people’s daily travel and transportation, the urban road transportation network is essential in promoting the healthy development of the urban economy, society, and civilization. With the acceleration of the urbanization process, urban problems caused by meteorological disasters have gradually become prominent. Sudden local or persistent rainstorms are one of the biggest culprits leading to the destruction of urban infrastructure and national economic losses [2]. The United Kingdom Department for Transport [3] reported that one day of a rainstorm or flooding on the United Kingdom’s motorway network accounts for 2% of the annual delays across the country. Mcdermott [4] estimated that the cost of transport disruption caused by Storm Desmond in Ireland was about EUR 3.8 million. In 2021, extraordinarily heavy rainfall in Zhengzhou, China, caused flooding of several subways, leading to 398 deaths [5]. These studies reinforce the belief that the impact of a rainstorm and flooding on urban transportation systems can be catastrophic. Therefore, it is essential to analyze the resistance and recovery capacity of the transport system during rainstorm disasters. This analysis enables us to identify vulnerable urban areas and assists decision-makers in developing more precise and effective improvement measures within the management and control processes.

In recent years, the concept of resilience has developed rapidly. Resilience originates from the Latin word resilio [2], which indicates the ability to return to the initial state after suffering disturbances. With the development of science, the term “resilience” has been gradually applied to various disciplines. In transportation, resilience means the ability of a transportation network to resist, absorb, adapt, and recover from damage. Transportation is the baseline of any economy. Besides the general topological characteristics common to networks, urban transport networks are characterized by their unique social and dynamic nature [6]. Specifically, in the case of rainstorm disasters, bad weather is likely to lead to complex traffic conditions and increased travel risks. Although various effective methods currently exist for assessing transportation resilience [7,8,9], gaps remain in adequately considering the urban service functions of transportation networks. Moreover, resilience presents multifaceted features encompassing both temporal and spatial dimensions [10]. Consequently, the static nature of previous research on resilience does not adequately address real-world scenarios. It is evident that there is a need to develop a resilience evaluation model that incorporates both urban functions and spatiotemporal dynamics. Such a model would provide a more accurate reflection of the varying performance characteristics of transportation systems under different conditions.

To comprehensively investigate the impact of rainfall on urban resilience, this study selects Xi’an, located in northwestern China, as a case study for several reasons. Firstly, the primary purpose of transportation is to move passengers. According to the seventh national population census [11], Xi’an’s population has increased by 4.49 million over the past five years, ranking third in the country in terms of growth rate, with a total population of 12.95 million. The increase in population will lead to a rise in travel demand, making Xi’an a crucial subject for studying the impact of urban rainfall on the resilience of transportation networks. Secondly, the eastern coastal regions of China have developed extensive flood control measures due to their long-term exposure to typhoons and related disasters [12]. In contrast, Xi’an, being inland, lacks experience in managing disasters like heavy rainfall. Additionally, its economic development in the northwest has been slower than in eastern China [13], making relatively underdeveloped infrastructure more susceptible to problems during heavy rainfall events. Finally, with global warming, northwestern China is increasingly vulnerable to rainstorm disasters, and the severity of these events is rising. For instance, the unprecedented rainfall in Zhengzhou City, Henan Province, in 2021 [5] caused the collapse of the transportation system. That same year, Xi’an, a city in the neighboring province to Zhengzhou, experienced its highest recorded rainfall since 1961, underscoring its vulnerability.

This study combines rainstorm and traffic data to construct a rainstorm–traffic coupling model using microsimulation software. Based on existing research, we introduce an innovative method for quantifying resilience encompassing topological structure, traffic performance, and urban function. This method is applied to the road networks within Xi’an’s main urban area. Urban managers can pinpoint vulnerable areas by analyzing temporal and spatial variations in the resilience indicators of traffic networks during rainstorms. This identification facilitates the provision of targeted improvement recommendations aimed at enhancing the resilience of the transportation system.

The rest of the paper is organized as follows: Section 2 provides a review of the relevant literature. Section 3 first introduces the rainstorm model, traffic model, and their coupling principle. Then, a comprehensive resilience assessment method is proposed to evaluate traffic resilience during disasters. Finally, it outlines the study area, data sources, and preprocessing. Section 4 provides an explanation and analysis of the experimental results. Section 5 discusses the value of the resilience assessment and provides policy recommendations in response to the findings. Section 6 presents the conclusions and limitations of this study, as well as an outlook for future research.

2. Literature Review

2.1. Research on the Impact of Rainstorms on Transportation System

In a study related to the impact of a rainstorm on urban roads, Qiao et al. [14] used SSPG and SWMM models to simulate road runoff and flood depth under different scenarios. They determined the traffic delays and fuel costs caused by rainfall. Ni et al. [15] introduced the VCTM model to analyze the impact of rainfall on traffic speed and flow. The impact of rainfall on traffic is calculated using the formula above, while some researchers obtain research results by importing rainfall information into traffic models. For example, Pyatkova et al. [16] developed software that integrates flood and traffic models, overlaying the flood information simulated by the InfoWork model onto traffic simulation to assess the changes in traffic distance, duration, and cost that may result from transportation disruptions. Similarly, Fang et al. [12] developed a GIS-based storm flooding model and overlaid the resultant flooding data on a road network created using microscopic traffic simulation. This method explored the variations in urban road traffic resilience under different rainfall recurrence intervals and emergency response durations. In addition, some scholars have taken advantage of big data by using RNN and LSTM models to capture correlations between traffic and rainfall to study the impact of rainfall on predicting traffic flow variables for different types of roads [17]. Pregnolato et al. [18] proposed a different approach to extract a series of quantitative data from video and construct a function describing the relationship between flood depth and dynamic vehicle speed. However, the actual depth of the event was not recorded. Therefore, their study did not verify the rationality of the function with actual data.

In summary, previous studies on the impact of heavy rainfall on traffic have mainly focused on temporal changes in indicators such as traffic distribution, pavement performance, and road network accessibility. However, rainfall varies over time and spatially, and urban transportation networks exhibit similar spatial and temporal heterogeneity. Analyzing the spatial and temporal effects of rainfall on transportation can assist decision-makers in more precisely identifying vulnerable areas and formulating more effective optimization strategies.

2.2. Research on the Resilience Evaluation of Transportation Network

Resilience has been a hot topic in all kinds of scientific research into coping with external disturbances in recent years. The aspect of its development history, resilience, was applied in mechanics as early as 1867 [19], and then it was involved in psychology in the 1950s. Holling [20] applied the resilience concept to ecology in 1973. In the 1990s, based on the achievements of economics and geography, the concept of resilience gradually transitioned to the social sciences. Research on the resilience of transportation systems was initially limited to transportation engineering materials. As natural disasters become more severe, resilience in transport networks is becoming more widespread [21].

In resilience assessment, Bruneau et al. [22] introduced a quantitative resilience curve to evaluate system-specific performance metrics. This curve typically depicts a decline followed by a rise during disasters, with the resilience value calculated by comparing system performance under disaster and normal conditions. This methodology has laid the groundwork for resilience evaluation. Researchers have utilized various metrics in transportation to assess resilience, including node degree, betweenness centrality, station capacity, and average traffic speed [23,24]. Despite these advancements, it is crucial to acknowledge that urban transport networks, characterized by their socio-economic attributes, are unique. Pulugurtha and Gouribhatla [25] indicated that the congestion caused by nonrecurring events may lead to four to five times higher energy loss on a weekday and three to four times higher on a weekend than regular traffic. Pyatkova et al. [16] have shown that the impact of flooding on travel near hospitals is more severe than the average in all aspects, with more than 50% of trips to and from hospitals being rescheduled, significantly higher than the 21% road network average. Yang [26] highlighted that a correlation coefficient of 0.536 exists between road emergency rescue demand and rainfall during extreme weather conditions. When the rainfall escalates to the intensity of a rainstorm, the emergency rescue demand may last until the next day. Therefore, post-disaster emergency response is also an important indicator for evaluating resilience. The incorporation of social attributes and the development of a comprehensive evaluation system are crucial for advancing current resilience assessments. Although Chen et al. [27], Zhang and Alipour [28] considered diverse factors like environmental pollution, safety, and economic losses in their evaluations, these assessments remain static, neglecting the dynamic aspects of resilience. To compensate for the overlooked social attributes and dynamic characteristics of resilience in previous studies, it is imperative to develop a methodology for assessing transportation networks’ dynamic and integrated resilience.

Addressing these gaps, this paper first constructs a rainstorm–traffic coupling model and applies it to a real-world scenario to analyze the spatiotemporal impacts of rainstorms on traffic networks and identify vulnerable areas. Subsequently, a resilience evaluation model is innovatively developed from three dimensions—topology, transportation performance, and urban function—to derive a comprehensive dynamic resilience value. Lastly, incorporating spatial analysis, this study offers targeted improvement suggestions to decision-makers. Such a methodology would allow decision-makers to more accurately understand the resilience traits of transportation systems, with a broader range of parameters improving the precision and efficacy of risk prevention decisions.

3. Methodology

The general outline of the experimental method is shown in Figure 1. Firstly, we need to build a rainstorm model to obtain the flooding information, which will then be integrated into the road network to establish a storm–traffic coupling model. Finally, a resilience evaluation model is established, addressing the problem of quantifying the resilience of urban road networks during rainstorm disasters.

3.1. Rainstorm Model

The disaster field is divided into a disaster-creating surface and a disaster-bearing surface. In the simulation of a disaster-creating surface, it is essential to consider the uneven distribution of rain in time and space due to the heterogeneity of rainfall. Geographic Information System (GIS) is an integrated computer information system designed to process and display data related to geographic distributions [29]. As a technology pivotal for analyzing large volumes of spatial data, GIS is widely used in rainstorm and flood simulation [30,31]. Currently, ArcGIS leads the GIS market due to its comprehensive functionality and stable performance. Therefore, ArcGIS was chosen for this study to calculate and visualize the depth of flooding.

For spatial distribution, historical precipitation data are analyzed and standardized by spatial interpolation function in ArcGIS 10.8 to obtain the differences in spatial rainfall distribution in different regions. As for the temporal distribution, the short-duration design rain patterns encompass methodologies such as the Chicago rain pattern method [32], Huff rain pattern method [33], triangle rain pattern method [34], P&C rain pattern method [35], and others. In contrast, the Chicago rainfall pattern method proves more suitable for extrapolating rainfall conditions in most Chinese regions. This method derives the rainfall pattern using the rainstorm intensity formula and the rainfall peak coefficient, demonstrating low data dependence, simplicity in derivation, and heightened accuracy when designing rainfall duration models spanning approximately 3–5 h. Consequently, this paper uses the Chicago rain pattern method to simulate a rainstorm. Equations (1)–(3) [32] give the formulation of rainstorm intensity and Chicago Rain Pattern.

(1)$i={\displaystyle \frac{167A\left(1+ClgP\right)}{{\left(t+b\right)}^n}}$

where $i$ is average rainstorm intensity, $A$ is the design rainfall with a return period of 1 year, $P$ is the recurrence period, $C$ is the rainfall variation parameter, $n$ is rainstorm attenuation parameter, $t$ is rainfall period, and $b$ is a time correction parameter developed based on rainfall data from a certain region. It is important to note that the parameter $b$ appears in multiple formulas throughout this article but holds different meanings in each context.

(2)$i\left(t_a\right)={\displaystyle \frac{A^{\prime }\left[\frac{\left(1-c\right)t_a}{r}+b\right]}{{\left[\left(\frac{t_a}{r}\right)+b\right]}^{1+c}}}$

(3)$i\left(t_b\right)={\displaystyle \frac{A^{\prime }\left[\frac{\left(1-c\right)t_b}{r}+b\right]}{{\left[\left(\frac{t_b}{1-r}\right)+b\right]}^{1+c}}}$

In Equations (2) and (3), $t_a$ is the pre-peak rainfall period, $t_b$ is after-peak rainfall period, $A^{\prime }$ is the molecular part of Equation (1), $b$ is a decreasing parameter of rainfall intensity over time, and $c$ is a constant. $r$ is the rainstorm peak coefficient, which indicates the location of the rain peak.

Thanks to the development of the Chicago rain pattern generator software, it is possible to obtain the size of rainfall and its trend over time by inputting the rainstorm intensity formula of a city into the application interface and setting the total duration and peak coefficient of rainfall according to the needs. Therefore, this study applies the local rainfall intensity formula of the study area to the Chicago rain pattern to calculate the rainfall changes with time for a given period.

On the disaster-bearing surface, previous research performed rainstorm simulations with professional flood software, such as SWMM 5.1.014 [36], HEC-HMS 4.7.2 [37], and LISFLOOD FP8.0 [38], to calculate the depth of flooding. These methods require large amounts of data and cause high consumption costs. In fact, from a physical point of view, the expression of flooding depth can be presented using Equation (4) [39].

(4)$H{S}_1=R{S}_2-dt$

where $H$ is the flooding depth, $R$ means rainfall, $d$ is the drainage volume per unit of time, $t$ is the duration of rainfall, and $S_1$ and $S_2$ are ponding and confluence areas representing the degree of susceptibility to flooding. This study uses low-lying values to replace ${\displaystyle \frac{S_1}{S_2}}$ [40]. When flooding occurs, the ponding area, confluence area, and drainage per unit of time are relatively fixed so that the formula can be simplified to Equation (5).

(5)$H=f\left(R\right)-c$

where $f\left(R\right)$ is a function related to rainfall, and $c$ is a constant term.

Finally, for the sake of simplicity, the flooding depth throughout the study area is assumed to decrease simultaneously in a linear fashion after the rain stops.

3.2. Traffic Model

In the past, some studies have used traffic detectors in data collection to simulate the changes in traffic volume under rainfall conditions [17]. However, due to the destructive nature of severe weather, traffic data under rainstorm disasters are prone to missing and inaccurate, which leads to biased assessment results. We consider using simulation methods to build the model to avoid this issue.

SUMO 1.12.0 (Simulation of Urban MObility) is an open-source, microscopic traffic simulation software [41]. Compared to other traffic simulation tools, it offers distinct advantages in importing data from external sources, such as easily integrating flooding maps generated from rainstorm simulations. Additionally, SUMO allows for real-time control of vehicle routing based on current road conditions and output dynamic attributes of each vehicle within a large-scale road network simulation. These capabilities enhance our study’s operational precision and accuracy on traffic performance under heavy rain scenarios. Additionally, some scholars [16] have validated the effectiveness of SUMO traffic simulation using Google Maps data. Therefore, we selected SUMO to build our traffic model, and its working principle is as follows:

Initially, the road network data downloaded from OpenStreetMap (OSM) is imported into SUMO, and road speed limits are adjusted according to the actual situation. Subsequently, traffic flow data is entered to generate travel demand information, including departure time, location, destination, and mode of transport. Due to the paucity of transportation data, SUMO’s random trip model [42] is employed to create trips. This model uses a uniform distribution to randomly select departure and destination edges. The routes are then determined based on the demand information and current road conditions. Under free-flow conditions, SUMO aims to minimize travel time by utilizing the Gawron algorithm [43] to efficiently assign routes to users. The specific traffic management and travel behavior rules are shown in Table 1. These models and rules can be set using SUMO’s built-in commands; the relevant parameters are default parameters [44].

3.3. Coupled Model

In this paper, the flooding depth information of the GIS and SUMO traffic networks is superimposed to obtain the rainstorm traffic coupling model. This method is based on previous research and has been recognized and used by many scholars [12,16]. The rationale for coupling rainstorms and transportation is to recognize the impact of flooding on transportation. The impact of flooding on traffic mainly includes: (1) When the flooding depth remains below a specific threshold, there is a reduction in the maximum traffic speed; (2) when the flooding depth surpasses the designated threshold, the road is forced to close, and vehicles will be re-routed [12]. According to previous studies [18], when the flooding depth exceeds 15 cm, it is difficult for ordinary cars to pass through. Therefore, this paper adopts a flooding depth threshold of 15 cm for analytical purposes.

As the road ID serves as the distinctive identifier for each road, this study employs it to correlate the flooded road sections obtained from rainstorm simulation with the corresponding SUMO road segments. Subsequently, the relationship equation between ponding and speed determines the maximum road speed limit. Zhang et al. [49] used the decay model of vehicle travel speed with the flooding depth based on the hyperbolic tangent function in Equation (6).

(6)$v={\displaystyle \frac{v_0}{2}}\mathit{tanh}\left({\displaystyle \frac{-x+a}{b}}\right)+{\displaystyle \frac{v_0}{2}}$

where $v$ is the maximum allowable speed in km/h, $v_0$ is the design speed in km/h, $x$ is the flooding depth in $cm$, $a$ is the median value of flooding depth that leads to the impassability of the vehicle in $cm$, so the value of $a$ in this paper is 7.5 cm. $b$ is the attenuation elasticity coefficient, which generally ranges between 3 and 5, and this research assumes it to be 4.

As the rainfall and flooding depth are continuously updated over time, we can obtain the dynamic change of the road speed limit based on Equation (6). Then we use the “VariableSpeedSign” command of SUMO to modify the road speed limit in real-time during the traffic simulation and through the “Rerouter” command based on the re-routing algorithm shown in Table 1 to enable vehicles to automatically find new alternative routes when they encounter roads interrupted or congested by the rainstorm. This approach establishes a dynamic connection between rainstorm disasters and traffic simulation, providing the groundwork for analyzing traffic safety and resilience in extreme weather conditions.

3.4. Resilience Evaluation Model

In this paper, the urban road network is divided into three levels: topology structure network, traffic performance network, and urban function network. This section provides a new resilience evaluation model for the urban road network. The following section introduces the indicators used in this paper and the establishment of the comprehensive evaluation model. Equations (7)–(13) in Table 2 show the calculation formula for all indicators.

Table 2

The indicator calculation method.

Indicator	Formulation	Order	Variable
Network Efficiency	$e={\displaystyle \frac{1}{N\left(N-1\right)}}{\displaystyle \sum _{i\in s,j\in t}}{\displaystyle \frac{1}{d_{ij}}}$	$\left(7\right)$	$N$: the number of nodes$d_{ij}:$ the shortest path distance from node $i$ to node $j$
Clustering Coefficient	$c={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{\displaystyle \frac{2R_i}{k_i\left(k_i-1\right)}}$	(8)	$N:$ the number of nodes$k_i$: the number of neighboring nodes for node $i$$R_i:$ the number of triangles that actually contain node $i$
Relative Speed	$\overline{v_i}={\displaystyle \frac{KL}{\sum _{k=1}^K{t}_k}}$	(9)	$t_k:$ the travel time for the $k^{th}$ vehicle$KL:$ the total distance traveled by all vehicles on a given road$\overline{v_i:}$ the road’s mean space speed.
	$s={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i\in n}}{\displaystyle \frac{\overline{v_i}}{v_{i-max}}}$	(10)	$v_{i-max}:$ the maximum allowable road speed$n:$ the number of all roads$s:$ the average relative network speed
Time Delay	$\overline{t}={\displaystyle \frac{\sum _{i=1}^n{t}_i}{n}}$	(11)	$n:$ the number of all roads,$t_i:$ the time delay of road $i$$\overline{t}:$ the average time delay in the network
Functionality Loss	$FL={\displaystyle \frac{1}{\mu }}{\displaystyle \sum _{j=1}^{\mu }}{\displaystyle \frac{n_j}{N_j}}\left(1-{\omega }_i\right)$	(12)	$\mu :$ the number of all public service facilities selected$N:$ the number of public service facilities of the $j^{th}$ type under normal conditions$n_j:$ the number of destroyed public service facilities of the $j^{th}$ type under heavy rain conditions${\omega }_i:$ the functional reduction coefficient for the flooding depth of each destroyed facility
Emergency Services	$ES={\displaystyle \frac{C_t^s}{C_t}}$	(13)	$C_t^s:$ the number of accident points within 8 min of medical emergency services$C_t:$ the number of all accident points at time t.

3.4.1. Structure Resilience (SR) Indicators

Like any network’s topology, a transportation network can be regarded as a set of intersections and road connections between them, identifying the network as an undirected graph, the intersections as nodes, and the roads as edges. This study selects the network efficiency and clustering coefficient to measure the resilience of the topology structure after being damaged by a rainstorm.

(1) Network Efficiency (NE).

In rainstorm conditions, some of the shortest paths may change, causing people to spend more time going around to reach their destinations. Network efficiency is commonly employed to quantify the connectivity of a topological network. It is defined as the ratio of the sum of the reciprocals of the shortest paths to the maximum number of edges between all points in the network [50], as detailed in Equation (7) of Table 2.

(2) Clustering Coefficient (CC).

The clustering coefficient is a concept essential to the study of graph theory, and it indicates the degree of aggregation of all nodes in the network. As shown in Equation (8) of Table 2, the calculation of the clustering coefficient is based on the number of triangles, which is simply the ratio of the actual number of triangles formed by neighboring nodes to the maximum possible number of triangles [51]. Because the triangle represents a stable structure, high clustering coefficients result in better network stability.

3.4.2. Performance Resilience (PR) Indicators

(1) Relative Speed (RS).

The urban roads studied in this paper include urban expressways, primary roads, secondary roads, and branch roads, each with different speed limits. Consequently, this paper introduces an indicator known as ‘relative speed’, defined as the ratio of the road’s spatial average speed to the maximum allowable speed for the corresponding road type [52,53]. This indicator is employed to represent the congestion situation, as illustrated in Equations (9) and (10) of Table 2.

(2) Time Delay (TD).

Travel time is a common indicator of network performance. As shown in Equation (11) of Table 2, the delay is calculated based on the total time lost when the vehicle’s speed is lower than expected [12]. Therefore, the delay can indicate the effect’s severity and measure the service level of the transportation system.

3.4.3. Function Resilience (FR) Indicators

(1) Functionality Loss (FL).

The transportation network is a vital link connecting all corners of the city. When it is disrupted, in addition to travel restrictions, the operation of urban functions is also seriously affected. Song [54] indicated that from the perspective of resilient cities, the relevant national standards pay more attention to the construction of land for public management and public service facilities because the better the public service, the stronger the convenience of life, and the higher the happiness index of the residents in the city. Therefore, this study provides a Function Loss indicator to represent the damage to public service facilities adjacent to roads under heavy rainfall. This indicator is one of the measures of road functional resilience.

As the flooding considered in this paper is mainly on the road, the affected facility can be assumed to be within 500 m of flooded roads. Thereafter, the grading of the flooding depth impact on roadside building facilities can be obtained based on the related standards [55,56,57], as shown in Table 3. The value representing optimal functionality is set to 1 for ease of indicator normalization. The functionality reduction coefficient is assigned a range of 0 to 1, quantifying the impact’s magnitude, as detailed in Table 3. Referring to the resilience loss from Liu et al. [23], we calculate the actual value by subtracting the loss value from the optimal value. Subsequently, the ratio of the damaged to undamaged quantity for each type of facility is used as a weight to derive the weighted sum of the actual values for each facility type. The average functional loss value of the road network is then determined by dividing this sum by the total number of facilities, as detailed in Equation (12) of Table 2.

(2) Emergency Services (ES).

During rainstorms, traffic accidents such as slips, scratches, and collisions frequently occur, underscoring the critical importance of efficient post-disaster rescue operations for the safety of the injured. The accessibility of emergency medical facilities plays a pivotal role in enhancing traffic resilience in such situations [58]. Wu and Chen [59] introduced an elasticity index, considering traffic efficiency and disaster uncertainty in patient travel, to assess transportation network resilience during the emergency response phase quantitatively. Taghizadeh et al. [60] utilized probability distributions of hospital accessibility to evaluate the seismic resistance of roads. It can be seen that emergency efficiency is also one of the critical indicators for evaluating resilience.

Recognizing the international health agency’s established golden rescue time of 8 min [61], this study employed ArcGIS to delineate the emergency response range of hospitals in the study area reachable within 8 min. Subsequently, this study calculated the temporal changes in the emergency response area size and the number of accidents covered. If an accident occurs within the emergency response area, timely rescue operations are assumed to be feasible. Ultimately, the emergency services efficiency of the transportation network is assessed by the proportion of accidents that occur within the emergency response area. The formula references the form of calculation of the accident rate [62], as detailed in Equation (13) of Table 2.

3.4.4. SR-PR-FR Comprehensive Resilience Evaluation Model

A robust transportation network can mitigate damages from hazards and maintain normal city functions as much as possible. As mentioned above, this study proposes six indicators from three dimensions of structure resilience (SR), performance resilience (PR), and function resilience (FR) to build a comprehensive transportation network resilience evaluation system.

Normalization is generally required to obtain parameter values of the same magnitude. For network efficiency, clustering coefficient, and relative speed, normalization is calculated using Equations (14)–(16) by dividing their values by the values under normal conditions without rainstorms [23]. The prime superscript reflects the occurrence of floods, and the zero superscript reflects normal transportation operations. Equation (17) defines the normalization of time loss, where $t_{worst}$ represents the time delay exceeding 50% of the average delay time under normal conditions [28], considered the worst case. As both indicators in functional resilience belong to an abstract concept, they already have a value between 0 and 1. Then values of all indicators were normalized, and the closer to 1, the better.

(14)$NE={\displaystyle \frac{e^{\prime }}{e^0}}$

(15)$CC={\displaystyle \frac{c^{\prime }}{c^0}}$

(16)$RS={\displaystyle \frac{s^{\prime }}{s^0}}$

(17)$TD=1-\left({\displaystyle \frac{\overline{t}}{t_{worst}}}\right)$

Finally, the comprehensive resilience evaluation value can be defined as the ratio of the flooded value divided by the normal value. Combined with the resilience curve [22], the theoretical basis of the comprehensive resilience evaluation method is shown in Figure 2.

3.5. Data Collection and Collation

Xi’an is located in the central region of China and has a warm temperate continental monsoon climate. Therefore, the rainfall of Xi’an is concentrated in summer and autumn, when it often suffers from a threat of rainstorms. This paper applies the proposed method to the road network in the central urban area of Xi’an, as shown in Figure 3, including Beilin District, Lianhu District, Yanta District, and Xincheng District. The four districts above are located in the central part of Xi’an, with a dense population and complex transportation conditions, where traffic problems caused by natural disasters are particularly prominent. Furthermore, it is essential to note that while heavy rain complicates travel, it is an inevitable challenge for commuters. Additionally, congestion during the evening rush hour in Xi’an is significantly more severe than during the morning [63], making it more susceptible to the impacts of disasters. Therefore, this study selects the evening rush period of Xi’an for the experiment.

3.6. Data Sources and Pre-Processing

The data used in this study comes from publicly available sources, has a certain level of reliability, and has been validated by several researchers [12,16]. The specific data sources and descriptions are given in Table 4.

The road network utilized for rain and traffic simulations consists of 14,387 edges and 9566 nodes. In this study, focusing solely on private cars for traffic simulation, it is necessary to filter the road network to retain only expressways, primary, secondary, and branch roads. According to the Code for Design of Urban Road Engineering [64], the corresponding speeds for the four types of roads mentioned above are adjusted to 120 km/h, 80 km/h, 60 km/h, and 40 km/h, respectively.

For calculating flooding depth, DEM data is processed in ArcGIS by filling depressions to identify low-lying areas. Utilizing Equations (4) and (5), a multiple linear regression model (Equation (18)) is developed based on 30 real rainstorm cases in Xi’an. The detailed derivation of Equation (18) is provided in Appendix A.

(18)$H=0.782R+0.138RL+0.04$

where $H$ is flooding depth, $R$ represents the rainfall, and $L$ represents the low-lying value of one point.

The statistical significance and the p-values for each variable of Equation (18) are shown in Table 5.

All variables and the overall regression equation passed the test of significance, where the variables R and R*L were significant at the 0.001 level (2-tailed). The adjusted R² of the regression equation is 0.932, demonstrating that the model accounts for 93.2% of the variance in the data, indicating a robust fit.

Finally, in the Functionality Loss indicator of the resilience assessment model, the POI data of public service facilities mainly includes the POI data of hospitals, schools, government agencies, and shopping malls. We import it into ArcGIS and use spatial connectivity tools to calculate the number of service facilities adjacent to each road.

3.7. Simulation

To explore Xi’an’s traffic situation from the rainstorm in the evening rush hour to its recovery, this study sets the period from half an hour before the start of the evening rush (16:30) to 30 min before the start of the morning rush the next day (6:30) as the total simulation time.

For the calculation of traffic flow, first, according to the 2021 Xi’an Urban Transport Development Annual Report, the proportion of car travel structure is multiplied by the average daily total traffic volume of the study area to obtain the total traffic volume. Then, according to the general traffic volume hourly variation graph in the Introduction to Traffic Engineering [65], the hourly traffic volume distribution from 16:30 to 20:30 accounts for 3%, 9%, 13%, and 10% of the total traffic volume, respectively, while the rest of the time is set at 1% of the total traffic volume, thus obtaining the hourly traffic volume. Finally, the SUMO loaded the volume in real-time (see Table 6). It should be noted that the traffic volume in this article is calculated based on the average daily traffic in Xi’an city throughout the year. This method may overlook the influence of factors such as holidays, weather, and seasons, but as it is an average, it has an excellent overall universality.

According to the flood control standard of Xi’an City and the previous research on rainfall disasters [66,67], we set the recurrence period of rainfall intensity as once in 20 years and the duration of rainfall as 4 h. As the rainfall peak coefficient, it ranges from 0 to 1 with no fixed value. To improve the general applicability of the model, a symmetric rainfall pattern with a peak coefficient of 0.5 is used. Furthermore, this study assumes that all standing water recedes within 1 h upon ending the rainfall [12]. The rainfall changes obtained from the rainstorm model are shown in Table 6. For simple calculation, the maximum allowable speed of each road was updated every 1800 s.

4. Results and Analysis

The most apparent network damage from a rainstorm is the closure of transportation infrastructures owing to inundation. This study considers the roads with more than 15 cm of flooding as closed sections. The result of temporal variation in the rainstorm, average flooding depth, and road closures is shown in Figure 4.

Figure 4 illustrates that rainfall and flooding depth peaked at 28 mm and 70 cm at 19:00 and 21:00, respectively. This indicates that flooding was most severe, approximately two hours following the peak rainfall. Concurrently, the number of road closures reached a maximum during the heaviest rainfall, with 876 roads closed until the flooding had fully drained. According to the characteristics of flooding depth and road closures over time, this study divides the results into six key stages: $t_1$ is the normal conditions without rainstorms (17:30), $t_2$ is the last moment of the flat phase of rainfall (18:30), $t_3$ is the moment of the heaviest rainfall (19:00), $t_4$ is the moment when the average flooding depth is deepest (21:00), $t_5$ is the time when the stagnant water has just completely receded (22:00), $t_6$ is the end of the experiment (6:30 the next day).

4.1. Spatial Distribution

To identify vulnerabilities in the transportation network, Table 7 lists the spatial distribution features of flooding depth, relative speed, and emergency services at six key time points.

Floods result from rainfall disasters and contribute to transportation damage. This section first explores flood depths’ spatial and temporal variability, as illustrated in Figure 4 and the leftmost column of Table 7. Between time points $t_2$ and $t_3$, the extent of flooding increases sharply with rising rainfall levels, with Beilin District being the first to experience flooding depths exceeding 150 mm. The peak of the flooding occurs at $t_4$, where there is a significant rise in the number of locations with flooding depths over 150 mm, though the spatial distribution of flooded areas shows slight expansion. These areas are still mainly concentrated in and around the center of the Beilin district, which the urban heat island effect and the old drainage facilities in the city center may cause. This also indicates a certain regularity in the distribution of flooding, which can help city managers identify critical areas for intervention.

As previously discussed, heavy rainfall disasters often lead to road closures, subsequently diminishing traffic operation efficiency. In Table 7, relative speed is used to indicate road congestion. This indicator and corresponding congestion classes are derived from the Specification for Urban Traffic Performance Evaluation [68]. From $t_2$ to $t_3$, severe congestion initially appears in the southwestern part of Yanta District, an area that does not completely align with the spatial distribution of flooding depth. However, the peak of congestion across the entire road network also occurs at $t_4$. Comparisons between $t_5$, $t_6$, and $t_1$, periods devoid of standing water, reveal varied congestion levels. At $t_1$, slight congestion results from typical traffic flow—a normal occurrence. Conversely, the congestion at $t_5$ and $t_6$ is notably more severe than at $t_1$, likely due to road closures during periods of flooding, which cause traffic jams. Persistent congestion post-flooding suggests that the road network’s resilience requires enhancement.

In the context of urban functionality, the right-hand column of Table 7 illustrates the emergency response capacity of the road network. Red crosses mark hospitals, highlighting that in Xi’an, hospital distribution features a dense center and a sparse peripheral. The zones are reachable within 8 min from any hospital, which defines the emergency response area, with black dots representing accident locations. The effectiveness of emergency services is measured by the ratio of accident points within the emergency service area to the total number of accident points. From $t_1$ to $t_6$, the emergency service efficiencies are recorded at 100%, 85.7%, 73.3%, 62.9%, 66.7%, and 92.3%, respectively. Notably, the service area in the southwestern part of Yanta District shows a significant reduction at $t_3$ and $t_4$, coinciding with areas of severe congestion. This pattern suggests that emergency accessibility is strongly linked to road efficiency and is not directly influenced by the depth of flooding.

To provide more effective decision-making guidance for urban managers, we identified the top ten roads with the highest levels of flooding depth, severe congestion, and accident-prone conditions based on the spatial damage distribution detailed in Table 7. The results are shown in Table 8.

From the roads listed in Table 8, it is clear that the most heavily congested roads often coincide with those experiencing deep flooding. In contrast, roads prone to accidents appear more randomly distributed. This observation supports the earlier conclusion that the depth of water accumulation significantly impacts congestion.

Table 7 and Table 8 offer valuable insights for identifying areas particularly vulnerable to disaster impacts. City managers should focus more on these areas and roads to develop targeted strategies for enhancing urban resilience.

4.2. Temporal Distribution

The various resilience evaluation indicators were reported over time to quantify the dynamic resilience of the transportation network, according to the simulation results.

The classical resilience curve shows an initially decreasing and increasing trend (Figure 2). Looking at Figure 5, it can be seen that the changes in network efficiency and clustering coefficients are consistent with the classic resilience curve, indicating that the changes in topological structure follow the resilience law and reflect the process from disaster affected to disaster resistance. Network efficiency and clustering coefficient represent all nodes’ connectivity efficiency and the degree of clustering, respectively. The maximum value is 1; the higher the value, the better the topology resilience. Nevertheless, as shown in Figure 5, the initial network efficiency and clustering coefficient values are both low. This may be because the road network is limited by space, construction costs, and other factors; it is different from a regular network, and a node generally only connects two or three edges. It is noteworthy that heavy rainfall diminishes topology attribute values, although the reduction is not substantial. This observation suggests that the primary issue resides within the network topology rather than the meteorological conditions alone. This shows that there is still much room for improvement in the connectivity of the road network in Xi’an.

Figure 6 depicts the variations in performance resilience indicators, where the average relative speed follows the same trend as the classic resilience curve (Figure 2). However, the trend of the average time delay is the opposite. This is because the delay time is negatively correlated with performance resilience, and the longer the delay time, the lower the resilience. Combining the data in Table 6, it can be concluded that rainfall and traffic volumes peak between 18:30 and 19:30, yet delay time reaches its apex at 22:00, aligning with the peak in flooding depth. This timing suggests that delay time is more heavily influenced by flooding depth than rainfall or traffic. Furthermore, the average relative speed begins at 0.7 rather than 1, indicating that vehicles typically do not operate at the road’s maximum speed limit under normal conditions, likely due to safety and comfort considerations. While the trend in average relative speed is inversely related to delay time, its peak corresponds with the highest flooding depth, reinforcing the notion that flooding depth is a critical determinant of traffic performance.

For the functional elasticity index (Figure 7), the change in functional loss value is consistent with the classic resilience curve (Figure 2), showing an initial decreasing and then increasing trend. However, the rate of increase in the emergency service curve is relatively slow. Specifically, functional loss value decreases sharply during periods of maximum rainfall and reaches its nadir concurrently with the peak in flooding depth. However, the indicator of emergency services shows substantial volatility. This is due to the significant uncertainty caused by the rainstorm, especially during the evening rush hour, which makes traffic conditions more complicated. The frequency and locations of accidents exhibit temporal variations. Moreover, with the change in average relative speed, the 8-min reach range of hospital emergencies is also constantly changing. Hence, the emergency service indicators are continuously fluctuating for a long time.

The analysis in this section shows that the changes in each of the six resilience indicators presented in this paper strongly correlate with the flooding depth. This suggests that the flooding depth leads to forced road closures, which have a range of impacts on road topological structure, traffic performance, and urban function.

5. Discussion

In this section, the six indicators of “SR-PR-FR” are combined into a radar chart, where the blue part represents the values under normal conditions and the red part represents the values after disasters, corresponding to the normal and flooded values in Figure 2. Therefore, the ratio of the area of the blue and red parts is the comprehensive toughness value (CRV). Six key points in time were then selected, as shown in Figure 4, to measure the variation in the CRV over time.

According to statistics, the average delay time in Xi’an evening rush is 8 min under normal conditions. This value is substituted into Equation (17) to calculate the normalization for the time delay. All indicators are normalized and integrated into a comprehensive resilience evaluation model, as shown in Figure 8.

Figure 8 indicates that ES, RS, and TD are the first to decrease among all indicators. TD decreases significantly, and until the end of the simulation, it does not recover well. This is followed by RS, which drops sharply at $t_4$ but recovers well at $t_6$. The indicator with the shortest duration of value decline is FL, which starts to fall only at $t_3$ and ultimately returns to its normal value at $t_6$. In addition, CC and NE decreased the least and gradually returned to normal values after $t_5$.

In general, the CRV shows a general trend of first decreasing and then increasing throughout the experiment. It drops to a minimum value of 0.49 at the maximum depth of flooding ($t_4$), and then gradually increases. However, at the end of the experiment ($t_6$), the CRV is only 0.7, 30% lower than the value under normal conditions. It can be seen that if a rainstorm disaster hits Xi’an during the evening rush period without regard to any evacuation measures, the normal performance of the road network will be affected for more than 14 h. This means that it will negatively influence normal travel the next day.

Based on the resilience assessment results and the microanalysis of spatiotemporal changes in resilience indicators outlined and discussed previously, this paper proposes precise policy recommendations aimed at enhancing the urban road network’s resilience to rainfall disasters from the perspective of government managers:

(1) The first column of Table 7 reveals that the center of the city, particularly the Beilin District, is most susceptible to flooding during rainfall disasters. To address this critical issue, city managers should address low-lying road surfaces in vulnerable areas like the Beilin District. Additionally, they should regularly inspect drainage facilities in Beilin District and promptly repair or upgrade the drainage network to enhance drainage capacity while mitigating flooding risks.

(2) Figure 5 shows Xi’an’s road network has low structural resilience. Statistically, only two of Xi’an’s 17 administrative districts meet the national road density standard of 8 km/km² [69], and closed blocks in the city center contribute to poor network connectivity. Figure 4, Figure 5, Figure 6 and Figure 7 indicate that the performance resilience indicators, Relative Speed and Travel Delay, are the poorest in the evaluation, highlighting the need to boost traffic performance to improve resilience. The second column of Table 7 shows that the southwest of Yanta District is prone to traffic congestion, giving urban managers a clear area to target. Given the circumstances above, the city government should first focus on enhancing road infrastructure, particularly by addressing incomplete roads and increasing road network density. Secondly, they should prioritize improving traffic management in high-congestion areas such as Yanta District, facilitating timely traffic evacuation, and alleviating congestion in vulnerable areas.

(3) Table 7 reveals that the distribution of medical facilities in Xi’an exhibits a pattern of “dense in the middle and sparse around.” During heavy rainfall, emergency services efficiency in the southwestern part of the city is notably reduced due to congestion. City management should focus on rationalizing the distribution of medical facilities, increasing their presence in the southwestern part of the city, bolstering the reserve of emergency resources in vulnerable areas, and establishing an information-sharing platform with road congestion data to enhance emergency service efficiency on time.

The method proposed in this article can be applied to other cities besides Xi’an, but some details may need to be adapted according to the actual situation. We provide the following guidance for research in other regions:

(1) The rainfall–traffic coupling model used in this paper is universal. However, researchers need to use the local road network data, traffic flow data, historical rainfall data, DEM data, etc., in the study area for simulation and query the local rainfall intensity calculation formula on the local meteorological bureau website.

(2) Regarding parameter settings, researchers can set road speed limits directly based on the “Code for Design of Urban Road Engineering” or adjust them according to the actual speed limits of local roads. Researchers can directly refer to the data in this article to set the simulation total duration, rainfall duration, rainfall recurrence interval, rainfall peak coefficient, water accumulation subsidence time, and related models used in SUMO traffic simulation or adjust them according to local actual conditions or research needs.

(3) The equations in Table 2 can be used directly to calculate resilience indicators. The depth of accumulated water can be calculated using the derivation procedure in Appendix A after collecting relevant local data.

6. Conclusions

The transportation system plays a crucial role in daily life, linking all areas of a city and safeguarding the quality of life for its residents. However, road damage from disasters can lead to significant direct and indirect losses, potentially threatening lives. Since rainstorms are among the most frequent natural disasters, this paper outlines several rainstorm scenarios based on different return periods. While various researchers have developed methods to assess transportation resilience from topological, performance, or socio-economic perspectives, these often capture only partial aspects and lack a comprehensive, dynamic portrayal of resilience changes. This paper introduces a comprehensive resilience evaluation method encompassing structural, performance, and functional resilience. Utilizing a rainstorm–traffic coupling simulation, this approach is applied to Xi’an to fully reproduce the changes in the road network’s topological structure, operational performance, urban functions, and integrated resilience values during heavy rainfall events. Finally, this paper presents recommendations from the perspective of government administrators to bolster transportation resilience against urban disasters.

The main findings and implications of this research are as follows: (1) Spatiotemporal impact analysis of the results indicates significant road flooding in Beilin District’s central area and pronounced congestion in the southwestern part of Yanta District, with a marked reduction in emergency response range corresponding closely with congested areas. This enables urban managers to target risk management strategies effectively in these vulnerable zones. (2) When aggregating the six indicators that represent topological resilience, performance resilience, and functional resilience into a polygon graph, it becomes clear that performance resilience indicators exert the most significant negative impact on the overall resilience value. This underscores the critical need to enhance road capacity to bolster transportation resilience. (3) The experiment concluded that the comprehensive resilience value had recovered to only 70% of the normal level. This outcome indicates that after rainfall disasters during the evening peak, the system cannot fully revert to its normal state autonomously before the early peak of the following day. This situation emphasizes the Xi’an municipal government’s need to implement emergency measures in response to 20-year rainstorm disasters.

This paper’s primary contributions relative to existing literature are threefold. First, it undertakes a spatial and temporal analysis of the impact of heavy rainfall to identify correlations between vulnerable areas and their outcomes and to examine the underlying causes of these impacts. Second, it integrates urban functional indicators to develop a comprehensive resilience assessment model that encapsulates the road network’s topological, performance, and functional attributes. Finally, it calculates the results of the comprehensive resilience assessments at crucial time points, providing a thorough, process-wide dynamic evaluation of resilience. These micro-simulation-based findings furnish decision-makers with more precise management recommendations.

Despite its contributions, this study has several limitations that could be addressed in future research:

(1) For traffic analysis, the scope of this paper is confined to ordinary private cars and lacks the integration of multiple transportation modes. As a result, the resilience of the transportation system may be underestimated. Future studies could expand the resilience evaluation model to include multiple transportation modes such as subways, buses, and light rails, allowing for a comprehensive comparison of resilience across different modes.

(2) Due to data limitations, the OD points in this study are randomly distributed, resulting in a possible deviation of the simulation scenarios from the actual situation. Future research should aim to collect actual OD distribution data for each traffic cell to enhance the realism of the traffic flow settings.

(3) Optimizing resource allocation has a significant impact on improving resilience. While this paper evaluates emergency response efficiency, it does not address optimizing emergency resource allocation. This area requires expertise in operations research and deserves further exploration within resilience research.

Author Contributions

Y.H.: writing—original draft preparation, writing—review and editing, conceptualization, methodology, software, validation, visualization, formal analysis, investigation, and data curation. Z.Z.: writing—review and editing, conceptualization, methodology, software, supervision, project administration, validation, and visualization. X.F.: writing—review and editing, visualization, data curation, software, and formal analysis. L.L.: writing—review and editing, project administration, software, visualization, methodology, data curation, formal analysis, and investigation. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data will be made available on request.

Acknowledgments

The author wants to acknowledge the hardware and software support from the Transportation Research Center of Shanghai Jiao Tong University and partial data from the AMAP.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. The general outline of the experimental method.

Figure 2. The theoretical basis of the comprehensive resilience evaluation method.

Figure 3. Administrative division map of the research area.

Figure 4. Temporal variation in the rainstorm, network average flooding depth, and road closures.

Figure 5. Topological resilience indicators over time.

Figure 6. Performance resilience indicators over time.

Figure 7. Function resilience indicators over time.

Figure 8. The comprehensive resilience value over time. (a) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (b) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (c) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (d) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (e) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (f) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]

Figure 8. The comprehensive resilience value over time. (a) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (b) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (c) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (d) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (e) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]. (f) [Forumla omitted. See PDF.]: [Forumla omitted. See PDF.]

Table 1

Model and rule settings of traffic simulation.

Model/Algorithm	Rule/Description
Initial route-choice algorithm	Gawron [43] algorithm
Re-routing algorithm	Dijkstra [45] algorithm
Car-following model	Krauss [46]
Lane-change model	LC2013 [47]
Trip distribution	Choosing the origin and destination edges uniformly at random.
Signal light model	Webster [48] algorithm

Table 3

Flooding depth and risk classification.

Flooding Depth (cm)	Risk Level	Functionality Reduction Coefficient
0–5	No Risk	0
5–15	Slightly Lower Risk	0.2
15–27	Low Risk	0.4
27–40	Medium Risk	0.6
40–60	Slightly Higher Risk	0.8
Above 60	High Risk	1

Table 4

Data source and data description.

Data Name	Data Source	Description
Road Network	OpenStreetMap (http://www.openstreetmap.org/ accessed on 5 August 2022)	An OSM-type file that can be imported into SUMO and ArcGIS
Traffic volume	The 2021 Xi’an Urban Traffic Development Annual Report (http://zygh.xa.gov.cn/zwgk/ghjh/64a3d59af8fd1c1a703495a5.html accessed on 10 December 2022)	Statistics on daily average motor vehicle travel volume of residents
Historical precipitation data	China Meteorological Data Service Centre (https://data.cma.cn/ accessed on 7 September 2022)	Statistics on the precipitation of various districts and counties in China between 2000 and 2019
Digital Elevation Model (DEM)	Geospatial Data Cloud (https://www.gscloud.cn/ accessed on 11 October 2022)	Grid type files with 12.5 m resolution
Rainstorm intensity formula	Xi’an Municipal Meteorological Bureau (http://sn.cma.gov.cn/dsqx/xaqx/ accessed on 13 September 2022)	A calculation formula for rainstorm intensity in Xi’an
Points of interest (POIs) of public service facilities	AMAP (https://ditu.amap.com/ accessed on 30 December 2022)	Point shapefile type files for POIs that can be imported into ArcGIS

Table 5

Significance test results.

Variable	H				Adj. R2	p-Value	F-Value	VIF
	Coef.	β	t	p-Value
R	0.782	0.361	7.12 ***	0.000	0.932	0.000	193.63	1.165
R*L	0.138	0.814	16.03 ***	0.000
Constant	−0.04	-	3.67 *	0.04

* Correlation is significant at the 0.05 level (2-tailed). *** Correlation is significant at the 0.001 level (2-tailed).

Table 6

Rainfall and travel condition settings.

Time	Rainfall (mm)	Traffic Volume (No. of Vehicles)
16:30–17:00	0	15,500
17:00–17:30	1.1436
17:30–18:00	1.9782	46,500
18:00–18:30	4.5479
18:30–19:00	27.5941	71,500
19:00–19:30	24.7027
19:30–20:00	4.3883	54,250
20:00–20:30	1.936
20:30–21:00	1.261	5000
21:00 to 6:30 the next day	0

Table 7

Spatial and temporal variation in flooding depth, relative speed, and emergency services.

	Flooding Depth	Relative Speed	Emergency Services
$t_1$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
$t_2$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
$t_3$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
$t_4$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
$t_5$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
$t_6$	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]
	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]	[Image omitted. Please see PDF.]

Table 8

Name of the ten most severely affected roads.

with a Deep Flooding Depth	with Severe Congestion	with an Accident-Prone
Zhuque Road South Section	Zaoyuan West Road	Fuyuan Third Road
Tangyan Road	Changrong North Road	Hongguang Road
Xingqing Road	Xingqing Road	Jinye Road
Zhangjiacun Street	Zhangjiacun Street	Keji Eighth Road
Middle section of Tuanjie North Road	Middle section of Tuanjie North Road	Xiaobeimen underpass tunnel
Shapo Road	Shapo Road	Keji Second Road
Youyi Road	Youyi Road	Zhangjiacun Street
Baimiao Road	Lianhu Road, North Street	Cuihua Road
Chang’an North Road, Zhongmao Street	Chang’an North Road, Zhongmao Street	Yucai Road
Lianhu Road, North Street	Keji Fifth Road	Beihuo Street

Appendix A

According to Equation (4) in the text, the calculation of flooding depth (H) is related to rainfall (R), drainage (d), ponding area ($S_1$), and confluence area ($S_2$). Therefore, we compiled 30 real cases of flooding events in Xi’an from social media, such as news reports and microblogs, and extracted the flooding point’s location, the flooding depth, and the maximum hourly rainfall for each event. However, since there is no specific documented record for $S_1$ and $S_2$, with reference to Huang et al., who mentioned in their study that low-lying topography is an essential cause of ponding and catchment [40], we use the low-lying values (L) obtained from the DEM data processing instead of the values of ${\displaystyle \frac{S_1}{S_2}}$, and thus obtain the depth of ponding as a function of R*L. In order to perform regression analysis, we first use H as the dependent variable and R, L, and R*L as the independent variables for correlation analysis, and the results are shown in Table A1.

Table A1

Correlation analysis.

Variables		H	R	L	R*L
H	Pearson’s correlation	1	0.662 **	0.830 **	0.903 **
	Sig. (2-tailed)		0.002	0.000	0.000
R	Pearson’s correlation	0.662 **	1	0.122	0.246
	Sig. (2-tailed)	0.002		0.528	0.198
L	Pearson’s correlation	0.830 **	0.122	1	0.973 **
	Sig. (2-tailed)	0.000	0.528		0.000
R*L	Pearson’s correlation	0.903 **	0.246	0.973 **	1
	Sig. (2-tailed)	0.000	0.198	0.000

** Correlation is significant at the 0.01 level (2-tailed).

It can be concluded that H is strongly correlated with R, L, and R*L, which is suitable for linear regression analysis. Next, we conducted several sets of experiments to obtain the best-fitting model with the best results. We fitted linear regression with H as the dependent variable, R alone, L alone, R*L alone, R and L, R and R*L as the independent variables. We obtained five regression models; the results are shown in Models 1 to 5 in Table A2.

Table A2

Significance test results for each model.

	Variable	H				Adj. R2	p	F	VIF
		Coef.	β	t	p
Model 1	R	0.931	0.562	3.53 **	0.002	0.290	0.002	12.43	1.000
	Constant	6.165	-	0.61	0.547
Model 2	L	6.924	0.830	7.74 ***	0.000	0.678	0.000	59.89	1.007
	Constant	23.714	-	6.92 ***	0.000
Model 3	R*L	0.172	0.903	9.70 ***	0.000	0.808	0.000	118.56	1.005
	Constant	24.656	-	10.89 ***	0.000
Model 4	R	0.774	0.467	7.63 ***	0.000	0.897	0.000	122.56	1.115
	L	6.448	0.773	12.64 ***	0.000
	Constant	−2.178	-	−0.56	0.582
Model 5	R	0.782	0.361	7.12 ***	0.000	0.932	0.000	193.63	1.165
	R*L	0.138	0.814	16.03 ***	0.000
	Constant	−0.04	-	3.67 *	0.04

* Correlation is significant at the 0.05 level (2-tailed). ** Correlation is significant at the 0.01 level (2-tailed). *** Correlation is significant at the 0.001 level (2-tailed).

Except for Model 1, the p-value of the remaining four models is less than 0.001, which passes the significance test. However, regarding the adjusted R-squared values of the whole model, the independent variable of Model 5 has the best explanatory effect on the dependent variable, which can explain 93.2% of the variation in the data and has the highest degree of fit among all the models. Therefore, Model 5 is selected as the formula for calculating the flooding depth. Finally, in conjunction with the theoretically derived form of Equation (5), we need to subtract the constant value from the function containing R to obtain Equation (18).

References

1. Yin, K.; Wu, J.J.; Wang, W.P.; Lee, D.H.; Wei, Y. An integrated resilience assessment model of urban transportation network: A case study of 40 cities in China. Transp. Res. Part A Policy Pract.; 2023; 173, 24. [DOI: https://dx.doi.org/10.1016/j.tra.2023.103687]

2. Maranzoni, A.; D’Oria, M.; Rizzo, C. Quantitative flood hazard assessment methods: A review. J. Flood Risk Manag.; 2023; 16, 31. [DOI: https://dx.doi.org/10.1111/jfr3.12855]

3. Parliament, P.T. Transport Resilience Review A Review of the Resilience of the Transport Network to Extreme Weather Events. Forecasting. 2014; Available online: https://www.gov.uk/government/publications/transport-resilience-review-recommendations (accessed on 24 May 2022).

4. Mcdermott, T.; Kilgarriff, P.; Vega, A.; O’donoghue, C.; Morrissey, K. The Indirect Economic Costs of Flooding: Evidence from Transport Disruptions during Storm Desmond. Proceedings of the Irish Economic Association Annual Conference 2017; Dublin, Ireland, 4–5 May 2017.

5. Yin, L.; Ping, F.; Mao, J.H.; Jin, S.G. Analysis on Precipitation Efficiency of the "21.7" Henan Extremely Heavy Rainfall Event. Adv. Atmos. Sci.; 2023; 40, pp. 374-392. [DOI: https://dx.doi.org/10.1007/s00376-022-2054-x]

6. He, Y.Y.; Thies, S.; Avner, P.; Rentschler, J. Flood impacts on urban transit and accessibility—A case study of Kinshasa. Transp. Res. Part D Transp. Environ.; 2021; 96, 102889. [DOI: https://dx.doi.org/10.1016/j.trd.2021.102889]

7. Gonçalves, L.; Ribeiro, P.J.G. Resilience of urban transportation systems. Concept, characteristics, and methods. J. Transp. Geogr.; 2020; 85, 102727. [DOI: https://dx.doi.org/10.1016/j.jtrangeo.2020.102727]

8. Wei, M.; Xu, J.; Wang, Y. Resilience Assessment of Traffic Networks in Coastal Cities under Climate Change: A Case Study of One City with Unique Land Use Characteristics. Land; 2022; 11, 1834. [DOI: https://dx.doi.org/10.3390/land11101834]

9. Ding, J.; Wang, Y.; Li, C. A Dual-Layer Complex Network-Based Quantitative Flood Vulnerability Assessment Method of Transportation Systems. Land; 2024; 13, 753. [DOI: https://dx.doi.org/10.3390/land13060753]

10. Wei, Y.; Kidokoro, T.; Seta, F.; Shu, B. Spatial-Temporal Assessment of Urban Resilience to Disasters: A Case Study in Chengdu, China. Land; 2024; 13, 506. [DOI: https://dx.doi.org/10.3390/land13040506]

11. National Bureau of Statistics of China. 2021; Available online: https://www.gov.cn/guoqing/2021-05/13/content_5606149.htm (accessed on 10 December 2022).

12. Fang, X.; Lu, L.; Li, Y.; Hong, Y. A Driver-Pressure-State-Impact-Response study for urban transport resilience under extreme rainfall-flood conditions. Transp. Res. Part D Transp. Environ.; 2023; 121, 103819. [DOI: https://dx.doi.org/10.1016/j.trd.2023.103819]

13. Qin, H. Research on the Unbalanced Development of Regional Economy in China. Mod. Bus.; 2020; 12, pp. 55-56. [DOI: https://dx.doi.org/10.14097/j.cnki.5392/2020.12.024]

14. Qiao, Y.N.; Wang, Y.X.; Jin, N.; Zhang, S.Y.; Giustozzi, F.; Ma, T. Assessing flood risk to urban road users based on rainfall scenario simulations. Transp. Res. Part D Transp. Environ.; 2023; 123, 103919. [DOI: https://dx.doi.org/10.1016/j.trd.2023.103919]

15. Ni, X.Y.; Huang, H.; Liu, Y.; Liu, K.; Wang, M.; Hu, J. Study of Local Traffic Flow Fluctuation under Rainfall and Waterlogging with Characteristics of Dynamic Spatiotemporal Changes. J. Transp. Eng. Part A Syst.; 2022; 148, 17. [DOI: https://dx.doi.org/10.1061/JTEPBS.0000670]

16. Pyatkova, K.; Chen, A.S.; Butler, D.; Vojinovic, Z.; Djordjevic, S. Assessing the knock-on effects of flooding on road transportation. J. Environ. Manag.; 2019; 244, pp. 48-60. [DOI: https://dx.doi.org/10.1016/j.jenvman.2019.05.013] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/31108310]

17. Nigam, A.; Srivastava, S. Weather impact on macroscopic traffic stream variables prediction using recurrent learning approach. J. Intell. Transp. Syst.; 2023; 27, pp. 19-35. [DOI: https://dx.doi.org/10.1080/15472450.2021.1983809]

18. Pregnolato, M.; Ford, A.; Wilkinson, S.M.; Dawson, R.J. The impact of flooding on road transport: A depth-disruption function. Transp. Res. Part D Transp. Environ.; 2017; 55, pp. 67-81. [DOI: https://dx.doi.org/10.1016/j.trd.2017.06.020]

19. Alexander, D.E. Resilience and disaster risk reduction: An etymological journey. Nat. Hazards Earth Syst. Sci.; 2013; 13, pp. 2707-2716. [DOI: https://dx.doi.org/10.5194/nhess-13-2707-2013]

20. Holling, C.S. Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst.; 1973; 4, pp. 1-23. [DOI: https://dx.doi.org/10.1146/annurev.es.04.110173.000245]

21. Zhang, X.W.; Mao, F.; Gong, Z.Y.; Hannah, D.M.; Cai, Y.N.; Wu, J.S. A disaster-damage-based framework for assessing urban resilience to intense rainfall-induced flooding. Urban Clim.; 2023; 48, 101402. [DOI: https://dx.doi.org/10.1016/j.uclim.2022.101402]

22. Bruneau, M.; Chang, S.E.; Eguchi, R.T.; Lee, G.C.; O’Rourke, T.D.; Reinhorn, A.M.; Shinozuka, M.; Tierney, K.; Wallace, W.A.; Winterfeldt, D.V. A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities. Earthq. Spectra; 2003; 19, [DOI: https://dx.doi.org/10.1193/1.1623497]

23. Liu, Z.Z.; Chen, H.; Liu, E.Z.; Zhang, Q. Evaluating the dynamic resilience of the multi-mode public transit network for sustainable transport. J. Clean. Prod.; 2022; 348, 131350. [DOI: https://dx.doi.org/10.1016/j.jclepro.2022.131350]

24. Lu, Y.D.; Zhang, Z.; Fang, X.Y.; Gao, L.J.; Lu, L.J. Resilience of Urban Road Network to Malignant Traffic Accidents. J. Adv. Transp.; 2022; 2022, 3682472. [DOI: https://dx.doi.org/10.1155/2022/3682472]

25. Pulugurtha, S.S.; Gouribhatla, R.P. Spatio-temporal variations in energy loss due to traffic congestion. Transp. Lett.-Int. J. Transp. Res.; 2020; 12, pp. 9-17. [DOI: https://dx.doi.org/10.1080/19427867.2018.1501963]

26. Yang, Z.Z. Road Rescue Demand Prediction for the Improvement of Traffic System Resilience. J. Adv. Transp.; 2023; 2023, 6648740. [DOI: https://dx.doi.org/10.1155/2023/6648740]

27. Chen, H.R.; Zhou, R.Y.; Chen, H.; Lau, A. Static and dynamic resilience assessment for sustainable urban transportation systems: A case study of Xi’an, China. J. Clean. Prod.; 2022; 368, 133237. [DOI: https://dx.doi.org/10.1016/j.jclepro.2022.133237]

28. Zhang, N.; Alipour, A. Multi-scale robustness model for highway networks under flood events. Transp. Res. Part D Transp. Environ.; 2020; 83, 102281. [DOI: https://dx.doi.org/10.1016/j.trd.2020.102281]

29. Demers, M.N. Fundamentals of Geographic Information Systems; 4th ed. John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2008.

30. Hinge, G.; Hamouda, M.A.; Mohamed, M.M. Flash Flood Susceptibility Modelling Using Soft Computing-Based Approaches: From Bibliometric to Meta-Data Analysis and Future Research Directions. Water; 2024; 16, 26. [DOI: https://dx.doi.org/10.3390/w16010173]

31. Escandón-Panchana, P.; Herrera-Franco, G.; Jaya-Montalvo, M.; Martínez-Cuevas, S. Geomatic tools used in the management of agricultural activities: A systematic review. Environ. Dev. Sustain.; 2024; 35, [DOI: https://dx.doi.org/10.1007/s10668-024-04576-8]

32. Keifer, C.J.; Chu, H.H. Synthetic storm pattern for drainage design. J. Hydraul. Div.; 1957; 83, pp. 1331-1332. [DOI: https://dx.doi.org/10.1061/JYCEAJ.0000104]

33. Huff, F.A. Time distribution of rainfall in heavy storms. Water Resour. Res.; 1967; 3, pp. 1007-1019. [DOI: https://dx.doi.org/10.1029/WR003i004p01007]

34. Yen, B.C.; Chow, V.T. Design hyetographs for small drainage structures. J. Hydraul. Div.; 1980; 106, pp. 1055-1076. [DOI: https://dx.doi.org/10.1061/JYCEAJ.0005442]

35. Pilgrim, D.H.; Cordery, I. Rainfall Temporal Patterns for Design Floods. J. Hydraul. Div.; 1975; 101, pp. 81-95. [DOI: https://dx.doi.org/10.1061/JYCEAJ.0004197]

36. Zhang, X.Q.; Qiao, W.B.; Huang, J.F.; Li, H.Y.; Wang, X. Impact and analysis of urban water system connectivity project on regional water environment based on Storm Water Management Model (SWMM). J. Clean. Prod.; 2023; 423, 138840. [DOI: https://dx.doi.org/10.1016/j.jclepro.2023.138840]

37. Sahu, M.K.; Shwetha, H.R.; Dwarakish, G.S. State-of-the-art hydrological models and application of the HEC-HMS model: A review. Model. Earth Syst. Environ.; 2023; 9, pp. 3029-3051. [DOI: https://dx.doi.org/10.1007/s40808-023-01704-7]

38. Ramirez, J.A.; Zischg, A.P.; Schürmann, S.; Zimmermann, M.; Weingartner, R.; Coulthard, T.; Keiler, M. Modeling the geomorphic response to early river engineering works using CAESAR-Lisflood. Anthropocene; 2020; 32, 100266. [DOI: https://dx.doi.org/10.1016/j.ancene.2020.100266]

39. Linta, Y.; Yunfan, S.; Yingqing, Z.; Ling, L.; Jingan, L.; Shaojun, L.; Bureau, F.M. Error Analysis of Waterlogging Depth Using Maximum Precipitation fitting in Fuzhou City. Meteorology and Disaster Reduction Research; 2018; Available online: https://sc.panda985.com/scholar?cluster=13764574080725881305&hl=zh-CN&as_sdt=0,5 (accessed on 11 December 2022). (In Chinese)

40. Huang, H.; Wang, X.; Liu, L. A review on urban pluvial floods: Characteristics, mechanisms, data, and research methods. Prog. Geogr.; 2021; 40, pp. 1048-1059. [DOI: https://dx.doi.org/10.18306/dlkxjz.2021.06.014]

41. Krajzewicz, D. Traffic simulation with SUMO–simulation of urban mobility. Fundamentals of Traffic Simulation; Springer: New York, NY, USA, 2010; pp. 269-293.

42. German Aerospace Center. 2022; Available online: https://sumo.dlr.de/docs/Tools/Trip.html (accessed on 2 September 2022).

43. Gawron, C. Simulation-Based Traffic Assignment. Computing User Equilibria in Large Street Networks. Ph.D. Thesis; Universität zu Köln: Cologne, Germany, 1998.

44. German Aerospace Center. 2022; Available online: https://sumo.dlr.de/docs/ (accessed on 5 September 2022).

45. Dijkstra, E.W. A note on two problems in connexion with graphs. Numer. Math.; 1959; 1, pp. 269-271. [DOI: https://dx.doi.org/10.1007/BF01386390]

46. Krau, S. Microscopic Modeling of Traffic Flow: Investigation of Collision Free Vehicle Dynamics. 1998; Available online: https://www.osti.gov/etdeweb/biblio/627062 (accessed on 5 September 2022).

47. Erdmann, J. SUMO’s Lane-changing model. Modeling Mobility with Open Data; Springer: Cham, Switzerland, 2015; [DOI: https://dx.doi.org/10.1007/978-3-319-15024-6_7]

48. Webster, F.V. Traffic Signal Settings. Road Research Technical Paper. 1958; Available online: https://www.semanticscholar.org/paper/TRAFFIC-SIGNAL-SETTINGS-Webster/1515023f6bb213d7f106d57b270917ba30016a8b (accessed on 5 September 2022).

49. Zhang, M.; Xu, M.; Wang, Z.; Lai, C. Assessment of the vulnerability of road networks to urban waterlogging based on a coupled hydrodynamic model. J. Hydrol.; 2021; 603, 127105. [DOI: https://dx.doi.org/10.1016/j.jhydrol.2021.127105]

50. Latora, V.; Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett.; 2001; 87, 198701. [DOI: https://dx.doi.org/10.1103/PhysRevLett.87.198701]

51. Luce, R.D.; Perry, A.D. A method of matrix analysis of group structure. Psychometrika; 1949; 14, pp. 95-116. [DOI: https://dx.doi.org/10.1007/BF02289146]

52. Lee, J.; Roh, S.; Shin, J.; Sohn, K. Image-Based Learning to Measure the Space Mean Speed on a Stretch of Road without the Need to Tag Images with Labels. Sensors; 2019; 19, 1227. [DOI: https://dx.doi.org/10.3390/s19051227]

53. German Aerospace Center. 2022; Available online: https://sumo.dlr.de/docs/Simulation/Output/Lane-_or_Edge-based_Traffic_Measures.html (accessed on 15 October 2022).

54. Song, D. Research on Land Use Mode of Guilin City Under the Perspective of Toughness. Master’s Thesis; Guilin University of Technology: Guilin, China, 2020; [DOI: https://dx.doi.org/10.27050/d.cnki.gglgc.2021.000469]

55. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Code for Design of Metro. 2014; Available online: https://www.mohurd.gov.cn/gongkai/zhengce/zhengcefilelib/201308/20130820_224416.html (accessed on 10 October 2022).

56. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Technical Specification for Urban Local Flooding Prevention and Control. 2017; Available online: https://www.mohurd.gov.cn/gongkai/zhengce/zhengcefilelib/201703/20170302_231224.html (accessed on 11 October 2022).

57. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Uniform Standard for Design of Civil Buildings. 2019; Available online: https://www.mohurd.gov.cn/gongkai/zhengce/zhengcefilelib/201905/20190530_240715.html (accessed on 8 October 2022).

58. Hsieh, C.H.; Feng, C.M. The highway resilience and vulnerability in Taiwan. Transp. Policy; 2020; 87, pp. 1-9. [DOI: https://dx.doi.org/10.1016/j.tranpol.2018.08.010]

59. Wu, Y.Y.; Chen, S.R. Traffic resilience modeling for post-earthquake emergency medical response and planning considering disrupted infrastructure and dislocated residents. Int. J. Disaster Risk Reduct.; 2023; 93, 103754. [DOI: https://dx.doi.org/10.1016/j.ijdrr.2023.103754]

60. Taghizadeh, M.; Mahsuli, M.; Poorzahedy, H. Probabilistic framework for evaluating the seismic resilience of transportation systems during emergency medical response. Reliab. Eng. Syst. Saf.; 2023; 236, 109255. [DOI: https://dx.doi.org/10.1016/j.ress.2023.109255]

61. Li, M. The Impact of Urban Pluvial Flooding on Emergency Medical Services for Highly Vulnerable Populations. Master’s Thesis; East China Normal University: Shanghai, China, 2022; [DOI: https://dx.doi.org/10.27149/d.cnki.ghdsu.2022.003616]

62. Hauer, E. On exposure and accident rate. Traffic Eng. Control; 1995; 36, pp. 134-138.

63. Wang, F.Z.; Zhong, J. 2022. Available online: https://tech.chinadaily.com.cn/a/202206/08/WS62a0674ea3101c3ee7ad986a.html (accessed on 11 September 2022).

64. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Code for Design of Urban Road Engineering. 2012; Available online: https://www.mohurd.gov.cn/gongkai/zhengce/zhengcefilelib/201607/20160713_228082.html (accessed on 22 September 2022).

65. Xu, J. Introduction to Traffic Engineering; China Communications Press: Beijing, China, 2010; (In Chinese)

66. Xi’an Bureau of Emergency Management. 2024; Available online: https://yjglj.xa.gov.cn/xw/mtbd/1798158169678053377.html (accessed on 7 August 2024).

67. Hu, R.; Wang, S.; Wang, P. Study on short duration rainstorm rainfall pattern based on cluster analysis. Hydroelectr. Energy Sci.; 2021; 39, pp. 8-10. (In Chinese) [DOI: https://dx.doi.org/10.11648/j.sjee.20210901.12]

68. Administration of Quality Supervision and Inspection and Quarantine of the People’s Republic of China. Specification for Urban Traffic Performance Evaluation. 2016; Available online: https://www.nssi.org.cn/cssn/js/pdfjs/web/preview.jsp?a100=GB/T%2033171-2016 (accessed on 10 October 2022).

69. Ren, H.; Sun, Y. Analysis of Road Network Patterns in Xi’an and Exploration of ‘Narrow Roads, Dense Road Network’ in Xi’an. 2019; Available online: https://xueshu.baidu.com/usercenter/paper/show?paperid=190602c05e3j0gb0j16x0m50m4459197 (accessed on 10 October 2022).