Transportation networks are vulnerable to extreme events like earthquakes, which can severely damage bridges and disrupt traffic flow. Existing methods often treat bridge damage as independent events, ignoring the spatial correlation of damage caused by geographically widespread hazards. This research addresses this gap by developing a novel stochastic computational framework that explicitly incorporates the spatial correlation of bridge damage into the assessment of transportation network performance. The study's purpose is to provide a more realistic and accurate assessment of network fragility under extreme events, leading to improved infrastructure planning, design, and risk management strategies. The importance of this work lies in its potential to improve the resilience of transportation networks by enabling more informed decision-making regarding infrastructure investments, maintenance schedules, and emergency response planning. Understanding the impact of correlated bridge damage on network-level performance is crucial for minimizing societal and economic disruption following extreme events. This study aims to quantify this impact and provide a framework for incorporating spatial correlation into future network fragility analyses.

Previous research has explored various aspects of infrastructure network performance under extreme events. Studies have focused on life-cycle management, monitoring, maintenance optimization using probabilistic approaches, and the concept of resilience for groups of infrastructure facilities. Researchers have employed methods such as the matrix-based system reliability method and investigated network interactions and systems of networks. While these contributions provide valuable insights, they often overlook the spatial correlation of component failures, particularly in the context of geographically widespread hazards. This research builds upon these existing studies by integrating spatial correlation into the analysis of network fragility, providing a more comprehensive and realistic assessment of network performance.

The proposed methodology integrates five key steps: 1) **Structural fragility analysis:** This involves selecting a region, highway segments, and bridges, computing fragility curves for each bridge, and performing analyses (e.g., using HAZUS) to compute average bridge damage for various scenarios. 2) **Spatial correlation estimation:** This step determines bridge coordinates, computes damage statistics and correlation coefficients, interpolates the correlation coefficient to estimate the spatial correlation length. 3) **Random field simulation:** This involves defining a marginal distribution (e.g., uniform), computing the correlation or spectral density from the estimated correlation coefficient, defining a range for correlation length, and generating damage level samples for each correlation length. 4) **Network analysis:** This stage involves defining the network layout, computing edge characteristics, updating bridge characteristics after an event, and utilizing a combined distribution and assignment algorithm to compute network performance indicators like total travel time and fully connected ratio. 5) **Statistical result analysis:** This final step computes statistics of the performance indicators over multiple simulations, considering the correlation length as a parameter. Bridges are modeled as the most fragile components, and HAZUS is used for structural response assessment. Damage level is represented by a continuous function, and the residual flow capacity of edges is determined by the most damaged bridge on that edge. The network analysis uses an iterative algorithm to solve the combined traffic distribution and assignment problem. Two numerical examples, "bridges in parallel" and "bridges in series," are presented to demonstrate the methodology and assess the influence of correlation distance on network performance.

The numerical examples demonstrate a strong influence of bridge damage correlation on network performance. In the "bridges in parallel" example, the fully connected ratio (FCR), indicating the percentage of samples where all nodes are reachable, and the total travel time (P) are significantly affected by the correlation length (λ). Low correlation (small λ) leads to lower FCR and higher P, while high correlation (large λ) results in improved network connectivity and reduced total travel time. The analysis reveals that disregarding correlation can lead to overly optimistic assessments of network performance. The "bridges in series" example shows a similar trend, but with even more pronounced effects of correlation on network performance, particularly for low values of λ. The analysis demonstrates that the number of bridges and their arrangement significantly affect the network's response to correlated damage. The cumulative distribution function of the residual capacity shows that even with conservative assumptions, damage can disrupt connectivity, especially when correlation is low. The study shows how the correlation distance influences both the mean and variance of the network performance indicator, highlighting the importance of accounting for spatial correlation.

The findings directly address the research question by demonstrating the significant impact of spatial correlation of bridge damage on transportation network performance. The results highlight the limitations of assuming independent damage states in network fragility analyses. The significance lies in the development of a practical framework to quantify this impact, leading to more accurate assessments of network vulnerability. This has implications for infrastructure planning and investment decisions, allowing for more robust and resilient network designs. The research also contributes to the development of improved methods for assessing the spatial correlation of damage using readily available data from sources like HAZUS.

This paper contributes a novel computational framework for integrating structural bridge analysis and traffic flow analysis under extreme events, revealing the significant influence of damage correlation on network performance. A method for assessing this correlation using fragility analyses is presented. The results emphasize the necessity of considering spatial correlation in network performance estimations. Future research could explore more complex correlation models, incorporate other types of extreme events, and extend the framework to include broader considerations of network recovery and resilience.

The study assumes that bridges are the most fragile components of the network. The model simplifies the representation of traffic flow and may not capture all aspects of real-world traffic behavior. The analysis uses specific functional forms for correlation and residual capacity; alternative formulations could be investigated. The numerical examples focus on specific network configurations; further research with a broader range of network topologies and sizes is warranted.