The road transportation infrastructure system (RTIS) provides a network of options that support the movement of people and goods. As a critical lifeline system, the resilience assessment of RTISs under the impact of different natural hazards, particularly earthquakes, has attracted extensive attention. When an earthquake occurs, an assessment of the connectivity reliability and travel time on road networks is necessary for emergency planning. In this study, the road network in the Aba Autonomous Prefecture, Sichuan Province, China, was considered as the study area and divided into 13 traffic analysis zones (TAZs) based on the administrative divisions. To consider the uncertainties related to seismic hazard assessment, random fields of ground motions were generated using a Monte Carlo simulation (MCS), considering the spatial correlation. Additionally, a connectivity reliability assessment model and travel time assessment model for the road networks were proposed. The connectivity reliability between the TAZs and increased travel time on the road networks after an earthquake were evaluated using MCS to evaluate the uncertainties related to the damage state assessment of road assets, such as bridges, tunnels, and road segments. Consequently, the results can be used as a theoretical basis for decisionmaking on the location and number of emergency rescue points after an earthquake and as a functional metric for resilience assessment models.
The road transportation infrastructure system (RTIS) provides a network of options that support the movement of people and goods^{[1]}. As a critical lifeline system, the RTIS has attracted extensive attention owing to its resilience under different natural disasters. Among natural disasters, earthquakes pose a great threat to the RTIS^{[2,3]}. Under the impact of destructive earthquakes, the bridges and tunnels of the RTIS are damaged, which not only leads to the loss in the road traffic capacity but also seriously hinders emergency rescue activities, such as personnel rescue and material delivery. Disruption of the operations of these systems can have cascading effects within the system and on other interconnected critical lifeline systems. In addition to the direct damage to physical transport infrastructure, there may be indirect damage to economic and social systems.
In previous studies, the resilience of an infrastructure system was defined as the joint ability to resist (prevent and withstand) any possible hazards, absorb the initial damage, and recover to normal operation^{[4,5]}. Cimellaro
The componentlevel resilience assessment is mainly used to study the seismic fragility and functional restoration model of important assets, such as bridges^{[9,10]} and tunnels^{[11,12]}. In the United States, a framework was developed using the HAZUS methodology for the fragility assessment of various assets with respect to earthquakes, hurricanes, floods, and tsunamis. Fragility models have been developed for all assets at risk in infrastructure systems, such as utility lifelines and transportation networks^{[13]}. In Europe, the FP7 SYNERG project has led to the development of a method for the systemic analysis of interdependent infrastructures (i.e., systems of systems) exposed to seismic hazards using a scenariobased approach. To this end, various fragility models have been reviewed and implemented for all assets at risk to generate failure events and compute the system performance using connectivity or serviceabilitylevel approaches.
At the network level, different approaches have been adopted for the performance assessment of the RTIS^{[1417]}. Different functional metrics, such as connectivity, capacity, and integrated loss estimation, have been applied, depending on the considered time frame, such as the emergency or economic recovery phases^{[18]}. An overview of the modeling techniques for determining the RTIS performance in disasters is given by Faturechi and MillerHooks^{[1]}. The performance metrics include travel time, flow/capacity, accessibility, topological measures (such as the connectivity), and direct and indirect economic losses. The modeling of possible disasters and associated uncertainties includes specific scenarios, the simulation of a wide range of scenarios, the use of probability distributions, and the identification of the worstcase performance or historical scenarios^{[19]}. Mathematical models of the system performance are classified into analytical, such as the risk matrix, event tree analysis (ETA), fault tree analysis (FTA), analytical hierarchy process (AHP), simulation (such as through Monte Carlo simulations), or optimization using deterministic or stochastic models. MurielVillegas
The third category involves research on the emergency management and seismic hazard mitigation of the RTIS. Postdisaster decisionmaking on recovery management is one of the most promising fields for the application of resilience in engineering practice^{[23]}. Frangopol and Bocchini proposed an optimization model for the postdisaster restoration schedule of transportation networks with respect to the total present cost, using both the total travel time (TTT) and total travel distance (TTD) as network performance metrics^{[24]}. In addition to longterm resilience indicators, Karamlou and Bocchini introduced a connectivitybased resilience indicator to optimize the restoration priorities during mediumphase disaster management^{[25]}. Zhang
Because seismic hazard and risk assessments have shifted from single structures to spatially distributed infrastructure systems, it is important to generate random fields of ground motion that consider spatial correlations during earthquake risk assessment. The excitations of a seismic event are spatially correlated, and this localized spatial correlation may increase the likelihood of the simultaneous damage of many structures during a seismic event. Recently, many researchers have studied the intraevent spatial correlation of ground motion intensity measures (IMs), such as peak ground acceleration (PGA), peak ground velocity (PGV), spectral acceleration (Sa)^{[2837]}, and cumulative absolute velocity (CAV)^{[38]}. Ground motion prediction equations (GMPEs) are important tools used in probabilistic seismic hazard and risk assessments. For a regionally distributed RTIS, a fixed value of the IMs cannot reasonably represent the variation trend in space. Therefore, it is necessary to construct a random field of ground motions with spatial correlations for resilience assessment. Thus, a ground motion influence field was established in this study by considering the spatial correlation of ground motion IMs.
The main contributions of this study are as follows: (1) the impact of uncertainties in both the seismic hazard analysis and asset damage assessment on the connectivity reliability and travel time of RTISs after an earthquake are considered. Here, the spatial distribution maps of the peak ground acceleration (PGA) were generated considering the spatial correlation of ground motions; (2) At the component level, models of the seismic fragility of bridges, tunnels, and road segments are established based on earthquake damage data; (3) at the network level, a framework and methodology for the assessment of the connectivity reliability and travel time are proposed; and (4) The framework and methodology were applied to the road network in Aba Autonomous Prefecture, Sichuan Province, China. Thus, the results can provide a basis for decisionmaking during the emergency phase after an earthquake.
The framework of this research study includes five modules, as shown in
The framework used in this study: (A) Road network for the case study; (B) PGA values for the study area; (C) Fragility curves and connectivity probability of the road assets; (D) the connectivity reliability of TAZs; (E) The increased travel time on the road network after an earthquake.
The construction of the road networks was achieved through the following steps:
Step 1: Geographic information data for the bridges, tunnels, and road segments were obtained from the China Geographic Information Resource Directory Service System.
Step 2: To ensure the cities remain interconnected within the study area, the road network was simplified according to the road grade and degree of centrality.
Step 3: The cities and road intersections were abstracted as nodes, and the roads between the nodes were abstracted as edges. Each edge consists of a variable number of bridges, tunnels, and road sections, and the relationship between the edges, bridges, tunnels, and road sections was determined using GIS based on their geographical coordinates. Moreover, the properties of the bridges, tunnels, and roadbeds were added to the edges, and a road network model for the evaluation of the network function was developed.
GMPEs are prediction models used to characterize the variation in the ground motion IMs with factors such as the magnitude, distance, and site. In GMPEs, the randomness of IMs is generally divided into interevent and intraevent residuals to represent the randomness of the seismic motion intensity measures (IMs). In GMPEs, it is generally assumed that the IMs follow a lognormal distribution. For earthquake event
where
The standard deviation of the total residual is expressed as
For the total residual between two random stations
where
where
The station separation distance Δ
where
In the case of a given seismic event
IMs obey not only marginal normal distribution at a given location but also the assumption of multivariate normal distribution at multiple locations. To generate the
where
In summary, the process of generating a spatiallycorrelated random field of the total residual values of ground motion at
In this study, seismic fragility models of bridges^{[39]}, tunnels^{[11]}, and road segments^{[40]} were obtained using the statistics based on the Wenchuan earthquake and other earthquake damage data [
Median and standard deviation of seismic fragility models






Bridge  Median (g)  0.3780  0.5346  0.9502  1.2141 
Log std.  0.6482  0.6482  0.6482  0.6482  
Road segment  Median (g)  0.541  0.655  1.243  1.488 
Log std.  0.774  0.849  0.913  0.501  
Tunnel  Fragility parameters  Slight damage  Moderate damage  Severe damage  
Median (g)  0.75  1.28  1.73  
Log std.  0.53  0.53  0.53 
The connectivity reliability assessment was performed based on six steps:
Step 1: The PGA value of the sites where bridges, tunnels, and road segments are located in the road network was determined based on their positions.
Step 2: The probability of different road asserts earthquake damage states was simulated based on the seismic fragility models and PGA values.
Step 3: The connectivity probability of each edge was calculated using the following equation:
where
When calculating the connectivity reliability of the edges based on Equation 9, it was necessary to convert the damage state probability of the assets obtained from the fragility curves into a single connectivity probability value. According to the total probability formula, the connectivity probability of assets was obtained as
where
Step 4: The edge connectivity probabilities were sampled. A
where
Step 5: The road network topology of the
Step 6: The simulated average connectivity reliability (ACR) among the TAZs was calculated using the following equation:
where
The travel time assessment was achieved using the following steps:
Step 1: The same as step 1 in the connectivity reliability assessment module.
Step 2: The same as step 2 in the connectivity reliability assessment module.
Step 3:
Step 4: Based on
Reduction factors for the postearthquake traffic capacity and free flow speed of bridges, tunnels, and road segments







Bridge & road segment  1.00  0.90  0.60  0.30  0.00  
1.00  0.80  0.60  0.40  0.00  
Tunnel  Coefficient  Intact  Slight damage  Moderate damage  Severe damage  
1.00  0.90  0.50  0.30  
1.00  0.80  0.50  0.40 
Step 5: The simulated mean value of the traffic capacity reduction coefficients (
Based on the
Step 6: To analyze the road network before and after the earthquake, the travel time was calculated according to the static traffic assignment method. The increase in the travel time on the road network after the earthquake was calculated using the following equation:
where Δ
The simplified road network in the Aba Autonomous Prefecture, Sichuan Province, is shown in
Road network for the case study: (A) location of the bridges, tunnels, and road segments; and (B) division of the TAZs
The study area was divided into 1 km × 1 km grids. It was assumed that the faults in this area were normal faults and that the average site condition of the area was bedrock. Additionally, the shear wave velocity was assumed to obey a normal distribution with a mean of 600 m/s and a standard deviation of 50 m/s. There was only one potential focal fault in this area, which only produces earthquakes with a magnitude of
PGA values for the study area.
The PGA values were extracted according to the positions of the bridges and tunnels and the midpoints of the road segments. As shown in
Fragility curves of the road assets: (A) bridges, (B) tunnels, and (C) road segments.
After calculating the probabilities of different road asset damage states, the connectivity probabilities of the bridge tunnels and road segments were calculated according to Equation 11, as shown in
Connectivity probability of the road assets: (A) bridges, (B) tunnels, and (C) road segments.
The visualization of connectivity probability of road assets in GIS.
The connectivity reliability of the edges can be obtained from the results of the asset connectivity probability. In this study, the centroids 1, 2, and 3 of the TAZs were selected as the source points for analyzing the connectivity reliability between the centroids of the 13 TAZs in the study area. We calculated all the combinations of these three source points. Moreover, for the determination of the connectivity between the source points and other centroids when two or three TAZs are selected as source points, we consider other centroids to be connected when they were connected to one of the source points.
For all combinations, which comprise one, two, and three TAZs, we conducted 10^{4} MCS, and the average connectivity reliability (ACR) was calculated. The nodes and names of TAZs are shown in
Connectivity reliability of the TAZs.
The nodes and names of TAZs







Maerkang  Wenchuan  Lixian  Maoxian  Songpan 







Jiuzhaigou  Jinchuan  Xiaojin  Heishui  Rangtang 






Aba  Ruoergai  Hongyuan 
Regarding the simulation of the travel time, this study was based on the following assumptions.
1. Owing to the lack of OD matrices in the 13 TAZs, the OD matrices used in this study were based on the population proportion of the TAZs.
2. The traffic demand before and after the earthquake remains the same.
The traffic flow and travel time of each edge were simulated according to the road network OD matrices and traffic capacity of the edge before and after the earthquake. We conducted 10^{4} MCS and calculated the increased travel time according to Equation 16, and the results are shown in
The increased travel time of the road network after an earthquake.
In this study, the functional metrics of road networks during earthquakes were investigated. To account for the impact of uncertainty in seismic hazard analysis and highway asset damage assessment, a distribution map of the seismic intensity parameters was generated considering the spatial correlation of ground motions. An assessment framework and methodology of the connectivity reliability and travel time using MCS were also proposed. The framework and methodology were then applied to the road network in Aba Autonomous Prefecture, Sichuan Province, China. Consequently, the following were the main conclusions:
(1) In a largescale distribution area, the intensity of ground motions has a significant effect on the spatial correlation changes. Considering the spatial correlation, the PGA distribution changes more uniformly, which is more in line with the spatial distribution characteristics of real IMs.
(2) When two TAZs were selected as source points, the Hongyuan and Maoxian TAZs had the highest ACR, and the highest ACR of the two TAZs was 11.7% higher than that of a single TAZ. When three TAZs were selected as source points, the Hongyuan, Maoxian, and Rangtang TAZs had the highest ACR, and the highest ACR of the three TAZs was only 2% higher than that of the two TAZs. In the earthquake scenario assumed in this study, two emergency rescue points were set up in the study area after the earthquake, at Hongyuan and Maoxian. Therefore, the connectivity reliability model proposed in this study can provide a theoretical basis for decisions on the number and location of emergency rescue points after an earthquake.
(3) The increased travel time of the edges is distributed between 1 h and 63 h, and edges exceeding 12 h are widely distributed in the study area. This shows that earthquakes have a significant impact on the road network travel time. Moreover, the total travel time (TTT) and travel time delay (TTD) are important functional metrics for road network resilience assessment. Therefore, the proposed travel time assessment model based on the MCS method can be used as a foundation for the development of road network resilience assessments.
Resilience assessment is probabilistic in nature; therefore, uncertainty needs to be integrated into all the steps of resilience evaluation, including the modeling of hazard events, response of exposed road infrastructures, and evaluation of functional losses.
The spatial correlation of the ground motion field generated by the GMPEs was built using a correlation distance and intraevent variability. It is an essential component of the seismic risk analysis of RTISs. In contrast to the GMPE used in most current studies to construct earthquake scenarios, the spatial correlation of the ground motion was considered in this study. Compared with the PGA ShakeMap without spatial correlation, the intensity distribution of the PGA ShakeMap with spatial correlation is more uniform and consistent with the attenuation characteristics of the real spatial distribution of the ground shaking intensity parameters. In future research, more uncertainty issues should be considered in seismic hazard assessment, such as the estimation of design earthquake events, occurrence of earthquake events, choice of GMPEs, and estimation of the site amplification factor for a specific site.
Once various sources of uncertainty have been identified, they must be associated with a set of probabilistic distributions. The variability of uncertain sources can be expressed in several ways. An MCS method consists of the sampling of random realizations of various input variables, and the estimation of the final risk metric for each run can be used. After many runs, a stable estimation of the probabilistic distribution of the outcome can be constructed. Even though it is straightforward in principle, the MCS method may require an almost intractable number of runs to achieve convergence, especially when extreme risk values (low probability outcomes) have to be sampled. However, robustness to the number of input variables (high dimensionality) is one of the main merits of MCS methods. In this study, the sampling of the damage states of bridges, tunnels, and road segments was implemented based on the MCS method. Subsequently, the connectivity reliability and travel time were analyzed based on the simulation results and were found to be closer to the actual damage scenario.
This study can be further improved by using a more accurate OD matrix and a dynamic traffic assignment (DTA) model. Moreover, the change in the traffic demand before and after the earthquake and the uncertainty of the division of bridges, tunnels, and subgrade damage states can also be considered.
Substantial contributions to conception and design of the study and performed data analysis and interpretation: Lu DG, Dou Q, Zhang BY
Software, investigation, data curation, methodology, writingoriginal draft, visualization: Dou Q, Ding JW
Performed technical support: Ding JW, Zhao H
Some or all data and materials that support the findings of this study are available from the corresponding author upon reasonable request.
This work was supported by the National Key R&D Program of China (Grant No. 2021YFB2600500) and the Natural Science Foundation of Chongqing CSTC (Grant No. 2022NSCQMSX4037).
All authors have declared that there are no conflicts of interest.
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© The Author(s) 2023.