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The road network’s transport capacity and traffic function will be directly reduced if urban roads are damaged by earthquakes. To effectively improve the resistance and recovery ability of urban road networks facing earthquake disasters, the establishment of an aseismic resilience evaluation method for the urban road network is the research goal. This paper’s novelty introduces the concept of engineering resilience into the aseismic performance evaluation of urban road networks. It reveals the internal influence principle of nodes and independent pathways on the aseismic resilience of the network. This paper’s significant contribution is to establish a reasonable and comprehensive urban road network aseismic resilience evaluation method. This method can realize the calculation of the aseismic resilience for the existing network, reconstruction network, and new network and propose the optimization, transformation, and layout for the network. The MATLAB program for the whole process calculation of aseismic resilience is developed. The overall network’s aseismic resilience is obtained by the sum of the product of the node importance and the average number of the reliable independent pathways.

With the rapid development of urbanization, cities today are increasingly dependent on water, electricity, gas, transportation, communications, and other crucial urban infrastructures. Lifeline infrastructures are the lifeline of the city. How to ensure that the infrastructure can quickly recover its function when subjected to external shock or damage effect is an important issue facing urban development and the key issue to build a resilient city. Among them, the performance of urban road networks is essential. Under the rapid growth of the economy, information, and logistics, the road network is no longer merely a transfer of persons or goods and extends to all aspects of the whole social and economic life. The urban road system is a multiple-direction and grade separation network composing of multinodes and multilinks. The performance of node and link determines the overall network performance. Earthquake is one of the most severe natural disasters, and it is a potential major threat to urban infrastructure and economic development. The network performance reduction, even partial or total network paralysis caused by seismic actions that directly led to bridges, tunnels, slope structure damage, or buildings damages along the street, indirectly led to road section blocked. How to reasonably evaluate and improve urban road networks’ aseismic resilience is needed to solve.

The influencing factors and management frameworks of disaster resilience for the city and community are studied. Complex urban system resilience to face natural disasters was learned by Katarina Rus in 2018 [

Scholars gave the specific definition and connotation of resilience for urban infrastructure networks. In 2019, six urban critical infrastructure networks, namely, water, drainage, gas, transportation, electric, and communication, were focused. The resilience definitions, hazard categories, methodologies, and enhanced measures for each network were analyzed in detail [

The resilience evaluation index to measure road networks’ performance had been proposed based on network reliability and connectivity in 2016. The independent pathways between two nodes that do not share any road section were selected as the basis for resilience evaluation [

The resilience evaluation system of the transportation network was applied in many ways. As early as 2001, the REDARS shortened by risks from earthquake damage to roadway systems was developed by National Center for Earthquake Engineering Research. The system could simulate the entire performance of the road network to fight the earthquake. The models of seismology, geology, engineering science, economics, and so on were focused on estimating direct losses and indirect losses of systems affected by disasters. But the model relied on detailed seismic observation data. The REDARS had been demonstrated and applied to the road network at Tennessee Shelby County and Los Angeles, California, USA. In 2018, the resilience of large and complex metro networks was assessed by quantitatively analyzing, including vulnerability and recovery rapidity. The network efficiency indicated the network connectivity performance. It was found that the vulnerability of the network depended not only on the node degree of the disrupted station but also on its contribution to the whole network connectivity [

Wang [

To sum up, the resilience network focusing on performance is mainly studied in the existing research of transportation network resilience. In contrast, the actual network resilience should be a complex synthesis integrated into physics, performance, economy, and society. The road network’s static properties, including topological form and road section reliability, need to be considered in the resilience analysis of urban road networks facing earthquake disasters. Simultaneously, the dynamic properties, including the emergency resource distributions, traveler’s itinerary preference, should also be emphatically considered. The resilience for a local or global network of interest can be calculated and compared by the established resilience model. Therefore, this paper aims to address seismic safety for the urban road network based on the concept of “quickly recoverability from disasters.” The seismic safety evaluation system of the urban road network is established to determine the best mitigation strategy and effectively guarantee and improve seismic safety, which can provide a reference method for the aseismic resilience performance evaluation of the urban road network.

Building a network map is a critical step in the research of complex urban road networks. The geographically visible road intersection and the route can be abstracted into recognizable symbols and forms in network analysis. Therefore, the generation of the urban road network model is the basis for the network characteristics analysis.

The urban road transportation network is an essential part of the transportation infrastructure, and it has similarities with other modes in terms of transportation functionality. Both classical method and dual method are commonly used in the modeling of the transportation network.

According to intuitive cognition, the network routes are as links, and the intersections or joints between links in the network are as nodes, which is called classical method modeling. This method is the most straightforward mapping of the road network, and all geospatial information of road transportation is retained. The classical method modeling is widely used in urban geography and transportation planning.

In contrast to the classical method, the routes in the network are taken for nodes, and the intersections or joints between nodes in the network are as links, which is called dual method modeling. The dual method is divided into direct duality, road name duality, and continuation duality. The dual method is complicated than the classic method, but it can reflect the road network’s more profound attributes. Different abstract ways of the above two methods are used when mapping road networks, and the characteristics of the two are shown in Table

The characteristics of the modeling method for the transportation network.

Method | Characteristic | |
---|---|---|

Classical method | Simple, intuitive, geographic features of the road network which can be reflected, a large number of nodes, uniform edge distribution, poor profound analysis effect of network | |

Dual method | Direct dual method | Intuitive, simple, large network complexity |

Road name dual method | Historical influence and more subjective factors | |

Continuation dual method | Less network complexity, small correlation of geographic features, but large calculation amount |

Table

The modeling of the urban road network is constructed according to the classical method. The intersections or roundabouts simplify as the nodes, and the routes between nodes simplify as links. The detailed procedures of modeling generation are as follows:

Let

Let _{ij}, and the set is _{11}, _{12}, ……, _{ij}, ……, _{nn}}. When there is no link between node _{ij}

Therefore, a theoretical model of urban road network

According to the theoretical model, the whole urban road networks are visualized. The first step of network visualization is needed to collect specific road information, and then links and nodes are transformed into the network data. The detailed procedures of the simplified network diagram are as follows:

Collecting the basic information of the analyzed network by Google maps, Baidu maps, or other platforms

Screening the nodes in the network and selecting the critical intersection, roundabouts, and interchanges as the road network node

Screening the links in the network and selecting urban expressway and major road as the link of the road network

Using AutoCAD software to draw a visual model of the road network and transforming road model information into the matrix data

Calculating and analyzing the road network data using the prepared MATLAB program

After the above procedures, the aseismic resilience performance of the road network is obtained ultimately.

After generating the abstract model of the urban road network, the network comprises nodes and links. Therefore, the node feature, the network structure, and the link reliability directly affect the road network’s resilience.

Node feature is divided into four aspects considering both the administrative hierarchy and importance degree. The four aspects are degree centrality, betweenness centrality, accessibility, and resource occupy, respectively.

The key node as a hub in the network topology can be represented as its degree centrality. The degree _{i} of node _{i} of each node in the network is obtained firstly, and then degree centrality _{i} of each node is got after normalizations by the formula of _{i} = _{i}/max{_{i}}.

Node importance in the transmission process of the information flow is the node’s degree located in an “intermediate position” in the other pathways. It can be represented as the betweenness centrality of the node. Betweenness centrality is the probability that the network node is located in the shortest pathway between any two nodes. That is, to what extent is a node located in an “intermediate position” between any other nodes. The betweenness centrality _{i} of each node in the network is obtained firstly. The betweenness centrality _{i} of each node is got after normalizations by the formula of _{i} = _{i}/max{_{i}}.

The accessibility from a node to other nodes in the network can be defined as the number of alternative passing ways between nodes. The more the alternative passing ways, the more the number of all pathways and the higher the accessibility. The parameter _{i} represents the number of all pathways between nodes _{i} is obtained after normalizations by the formula of _{i} = _{i}/max{_{i}}.

The criticality of nodes on the administrative level and the emergency resource supply can be expressed by the relative distance from the nearest administrative center, fire center, or rescue center, and so on. The shortest distance from node _{i} listed in equation (_{i} value is multiplied by 0.9 on the result from

The hub degree, center degree, accessibility, and resources occupy degree are considered in node importance named _{i}, which is calculated according to_{1}, _{2}, _{3}, and _{4} are the weighting factor of _{i}, _{i}, _{i}, and _{i}, respectively.

The relationship between the four weighting factors is _{1} + _{2} + _{3} + _{4} = 1. The network’s working status is divided into three: the daily operation phase, the emergency recovery phase, and the comprehensive recovery phase. The daily operation phase refers to the network’s functional state before the disaster, at which time, the nodes and links have high reliability. The emergency recovery phase refers to the golden rescue time from the moment of the disaster to 72 hours after the disaster. After the disaster, the comprehensive recovery phase refers to the period from 72 hours after the disaster to one month. After the recovery of this period, the link’s function in the network is restored, and it is close to the daily operation phase after one month. Network resilience performances of different phases have different requirements and metrics, so the values of weighting factors are different in the model. When the connectivity performance of the daily operation phase of the network is stressed, _{1}, _{2}, and _{3} have preferred a larger value. When the emergency rescue capability of the emergency recovery phase is emphasized, _{3} and _{4} are taken a larger value. The suggested values of node weighting factor

The suggested values of weighting factor

Phase | _{1} | _{2} | _{3} | _{4} |
---|---|---|---|---|

Daily operation phase | 0.30 | 0.30 | 0.30 | 0.10 |

Emergency recovery phase | 0.10 | 0.10 | 0.20 | 0.60 |

Comprehensive recovery phase | 0.20 | 0.20 | 0.30 | 0.30 |

The structure morphology of the road network is usually manifested in a topology structure, which reflects the physical characteristics of the road network. The network connectivity, travel time, traffic capacity, and so on are dependent on the performance and the number of the pathways between nodes. According to the different connection statuses, the pathways between nodes can be divided into the shortest pathways, all pathways, and independent pathways.

The shortest pathway is the shortest distance connecting between two nodes. The shortest pathways for postdisaster emergency rescue, evacuation, and transfer have great significance. The network reliability regarded as the shortest pathway has been extensively studied. Generally speaking, the number of the shortest pathways between two nodes is limited, and the minimum quantity is one.

All possible connections between two nodes compose all pathways, which are divided into the shortest pathway, the shorter pathway, the longer pathway, and the longest path according to the pathway length division. Most of all pathways share some of the same links. When the share link’s reliability decreases, the reliability of the pathways, including shared links, is directly affected. The more the number of pathways between two nodes, the more the passing ways between two nodes and the greater the reliability between two nodes. The number of all pathways between nodes in the complex network is typically huge. The number of all pathways between node

The independent pathway refers to the pathway without any shared link between node _{ij} between two nodes is found ⟶ remove the pathways shared with the shortest pathway from the all pathways database, and then the intermediate pathways database is obtained ⟶ remove the pathways with shared links in the intermediate pathways database according to the shortest path principle ⟶ the independent pathways database including one shortest pathway between the node

According to the above analyses, the specific relationships of three aspects for network structure are shown in Figure

Characteristics of network structure.

The resilience performance of the network is directly determined by the reliability of the pathway. The _{l} of links

The pathway’s average daily traffic reflects this pathway’s relative influence on personal life activities and local economic development. The pathway between the origin-destination (O-D) pairs with a shorter length and a greater traffic flow has a big contribution to the network function, which should be taken into account the network’s resilience performance. The average daily traffic volume can be estimated from the monitoring data of actual traffic flow or traffic assignment models. It is considered that the minimum average daily traffic volume of each link in an independent pathway can determine the traffic volume of this pathway. Let vl represent the traffic volume of the link l, and let

The total length of the pathway can portray the ease or complexity of that a node arrives through the network at the other nodes in the complex network, which is the sum of the length _{l} for each link

The travel time of a link is related to the length and the traffic volume, but also the width of the link. In order to directly reflect traffic jams and travel efficiency, the index of travel time is selected as an evaluation criterion. Let _{l} represent the average speed of the link _{l} be the average travel time for vehicles of the link _{l} = _{l}/_{l} exists. The total travel time of the

Pathway importance named _{1}, _{2}, and _{3} are the weighting factor of

The relationship between the three weighting factors is _{1} + _{2} + _{3} = 1. The way to assume values of the weighting factor for the independent pathway is the same as to node weighting factor, and the values of weighting factors can be assigned by urban transport managers or government decision-makers according to the actual situation. When the network usage function is stressed, _{1} and _{2} have preferred a larger value. When the network traffic efficiency is emphasized, _{2} and _{3} are taken a larger value. When the postearthquake quick emergency repair and resource configuration are emphasized, _{2} is chosen a larger value. The suggested values of weighting factor

The suggested values of weighting factor

Phase | _{1} | _{2} | _{3} |
---|---|---|---|

Daily operation phase | 0.20 | 0.30 | 0.50 |

Emergency recovery phase | 0.10 | 0.50 | 0.40 |

Comprehensive recovery phase | 0.5 | 0.25 | 0.25 |

The differences in topography and hydrology in the cities lead to different types of links in urban road networks. The complicated resilience calculation model is taken into account herein. The types of link include bridges, tunnels, slopes, and ordinary road sections, which is referred to as the network components. The reliabilities of the network components are the securities of links in the network. The component performance indexes refer to the reliability of bridges, the reliability of tunnels, the reliability of the slopes, and the reliability of the ordinary road sections [

Bridge reliability: from the view of seismic performance for the bridge, the bridge damage index is selected as the indicator of bridge reliability refers to [

Tunnel reliability: the tunnel damage index is selected as the indicator of bridge reliability, which can be calculated by the seismic damage evaluation method of tunnels proposed by Lin [

Slope reliability: many road sections in the mountainous city are built down the mountains. The secondary disaster such as slope failure and landslide caused by the earthquake is the main cause of road sections damages in the mountainous city based on historical damage experience. The slope stability index is selected as an indicator reflecting the slope reliability, which can be calculated by the slope damage prediction method proposed by Wang [

Reliability of ordinary road section: the road structure itself is damaged to some extent when suffered earthquake disaster. The major failure modes of the ordinary road section have cracks, bumps, spraying of the pavement and roadbed collapse, and so on. A strong earthquake usually does not cause damage to the road structure itself, according to earthquake damage investigations, so the damage of the road structure itself is not considered in this paper. But when a strong earthquake occurs, a lot of debris from buildings of collapse or serious damage along the street has a major influence on the traffic capacity of the road section. Therefore, the amount of debris is the decisive factor for the connectivity of the ordinary road section. The reliability of the road section proposed by Du [

Comprehensive Evaluation Method of resilience performance is built based on node-link diagram from Section

The road network’s resilience performance metric referred to as

The meaning and role of parameters in the equations.

Parameter | Meaning and role |
---|---|

The resilience performance metric of the road network | |

The number of all nodes in the network | |

A node in the network, | |

A node in the network, | |

_{i} | |

_{i} | The average number of reliable independent pathways considering pathway importance between node |

The total number of independent pathways between node | |

Counting the number of independent pathways | |

_{k} ( | The |

The resilience performance of an existing network with topological structure and functional status is evaluated. For the network with less resilience, the ways of changing network topology, enhancing the importance of key nodes, or the reliability of links can be employed to improve the network’s resilience performance. The resilience performances of changed networks are calculated repeatedly, then the degrees of network resilience improvement are compared, and optimal risk control measures are identified based on the above analyses.

The established comprehensive evaluation method of network aseismic resilience performance in Section

The network’s resilience performance is divided into two aspects of node and pathway in the Zhang model. The node aspect mainly considers the ability to supply emergency resources. The value of the node importance is the reciprocal of the shortest distance from the nearest emergency response facilities, which reflects the importance of node

The whole thought of Zhang model.

The established evaluation method in Section

The diagram of the instance network.

The aseismic resilience at some particular states of the network in the literature of Zhang [

Resilience recovery of improving the reliability of the key links after the disaster.

Serial number | Network state | Increment percentage | Zhang model | Increment percentage | |
---|---|---|---|---|---|

1 | After disasters, that is the result in Section 7.2 | 3.73 | — | 0.61 | — |

2 | Using 28 unit costs, repairing a total of seven links including links 5, 17, 8, 32, 10, 4, and 33, and making the reliability of seven links resume to 0.999 | 4.36 | 16.9↑ | 0.76 | 24.6↑ |

3 | Using 65 unit costs, repairing a total of sixteen links including links 22, 5, 28, 17, 20, 14, 12, 19, 27, 15, 24, 16, 36, 21, 37, and 31, and making the reliability of sixteen links resume to 0.999 | 5.67 | 52.0↑ | 1.07 | 75.4↑ |

4 | Using 86 unit costs, repairing a total of twenty-two links including links 27, 11, 19, 16, 10, 31, 5, 17, 18, 37, 23, 30, 28, 14, 12, 24, 21, 22, 29, 36, 15, and 20, and making the reliability of twenty-two links resume to 0.999 | 6.42 | 72.1↑ | 1.24 | 103.3↑ |

5 | Using 105 unit costs, repairing a total of twenty-seven links including links 7, 6, 11, 19, 27, 31, 1, 5, 17, 8, 18, 37, 25, 26, 23, 30, 28, 14, 2, 24, 21, 35, 22, 29, 36, 20, and 13, and making the reliability of twenty-seven links resume to 0.999 | 7.15 | 91.7↑ | 1.51 | 147.5↑ |

Resilience recovery of changing the original network topology before the disaster.

Serial number | Network state | Increment percentage | |
---|---|---|---|

1 | The reliability of all links is 0.999 before disasters, and network topology is still shown in Figure | 8.33 | — |

2 | Only adding S1 link and S4 link | 9.94 | 19.3↑ |

3 | Only adding S1 link and S5 link | 9.73 | 16.8↑ |

4 | Only adding S2 link and S4 link | 9.78 | 17.4↑ |

5 | Only adding S2 link and S5 link | 9.88 | 18.6↑ |

6 | Only adding S3 link and S4 link | 10.07 | 20.9↑ |

7 | Only adding S3 link and S5 link | 10.21 | 22.6↑ |

There are two main means of promoting network resilience to resist seismic hazard: improving the reliability of key links and changing the network topology. Four kinds of maintenance plans under available total restoration costs are provided, and the reliability of the link resumes to 0.999 after repairing. There are a total of 37 links in the original network shown in Figure

The network resilience is increased by means of adding new links before the disaster. Based on the calculation results in Table

The resilience results obtained from the model proposed by this paper and Zhang have big differences presented in Table

The research on the evaluation method of resilience performance for urban road networks facing an earthquake disaster is carried out in this study. Based on the urban road network’s structural hierarchy and functional characteristics, the independent pathways without any shared links between nodes are the core of aseismic resilience performance. The aseismic resilience named

The result data used to support the findings of this study are included within the supplementary information file.

The authors declare that they have no conflicts of interest.

This research was funded by the Chongqing Natural Science Foundation (CSTC2019jcyj-msxmX0781), the Youth Project of Science and Technology Research Program of Chongqing Education Commission of China (KJQN201901332), and the National Natural Science Foundation of China (51678544).

In the supplemental file of this paper, Table S1 lists the data of reliability, average daily traffic, and restoration cost for each road section in the network of Figure 3. Table S2 calculates node importance in the emergency recovery phase by using the model proposed in this paper. Figure S1 shows the results of Table S2 graphically. Table S3 takes the independent pathway calculation of node 1 to other 29 nodes as an example. Node connection sequences of pathways, ADT, ADT index, total length, length index, pathway importance, and pathway reliability are given in Table S3.