EQResNet: Real-Time Simulation and Resilience Assessment of Post-Earthquake Emergency Highway Transportation Networks

Abstract

Multiple uncertainties in traffic demand fluctuations and infrastructure vulnerability during seismic events pose significant challenges for the resilience assessment of highway transportation networks (HTNs). While Monte Carlo simulation remains the dominant approach for uncertainty propagation, its high computational cost limits its scalability, particularly in metropolitan-scale networks. This study proposes an EQResNet framework for accelerated post-earthquake resilience assessment of HTNs. The model integrates network topology, interregional traffic demand, and roadway characteristics into a streamlined deep neural network architecture. A comprehensive surrogate modeling strategy is developed to replace conventional traffic simulation modules, including highway status realization, shortest path computation, and traffic flow assignment. Combined with seismic fragility models and recovery functions for regional bridges, the framework captures the dynamic evolution of HTN functionality following seismic events. A multi-dimensional resilience evaluation system is also established to quantify network performance from emergency response and recovery perspectives. A case study on the Sioux Falls network under probabilistic earthquake scenarios demonstrates the effectiveness of the proposed method, achieving 95% prediction accuracy while reducing computational time by 90% compared to traditional numerical simulations. The results highlight the framework’s potential as a scalable, efficient, and reliable tool for large-scale post-disaster transportation system analysis.

1. Introduction

Highway transportation networks (HTNs) are typical networked systems where numerous highway segments and bridges work collaboratively and synergistically to deliver essential services. Assessing their resilience and sustainability is becoming an increasingly prominent aspect of pre-disaster preparedness, mitigation, and overall emergency response [1]. These concepts seek to relate seismic hazards to overall system performance, thereby facilitating informed decision-making by stakeholders. Achieving them requires evaluating seismic effects through metrics such as economic losses, functionality reductions, and service disruptions [2,3]. Such efforts are crucial for identifying vulnerabilities [4], prioritizing mitigation efforts [5], and ensuring the continuous functionality [6,7] of transportation systems under adverse conditions.

Earthquakes can inflict widespread injuries and casualties almost instantaneously, along with severe damage to regional infrastructures [8,9,10]. These impacts not only result in substantial capacity losses in highway components but also disrupt the entire HTN system. In the immediate aftermath of a major earthquake, large-scale emergency traffic demand surges due to displaced residents, rescue operations, and medical response efforts [11]. The ability of the HTN to sustain operations under these extreme conditions is critical for effective disaster response. Particularly in the first 72 h following the earthquake—the “golden” window for rescue and relief efforts—ensuring network functionality is paramount [12,13]. During this period, maintaining operational HTNs is essential for the rapid deployment of emergency responders, the delivery of aid, and the evacuation of affected populations. Thus, prioritizing victim rescue and evacuation becomes an urgent necessity [14].

Beyond the immediate impact on mobility and emergency response, disasters can also alter the structural integrity and operational capacity of HTNs in a manner that mirrors the dynamic nature of traffic patterns. These disruptions extend beyond individual highway components, influencing overall network performance. For example, the failure of a single bridge can propagate through the network, triggering cascading disruptions that compromise overall connectivity and mobility [2,15,16,17,18]. As such, the seismic resilience and redundancy of HTNs under emergencies—the capacity of network components to provide alternative routes or services when primary systems fail—deserves particular attention. Generally, seismic resilience assessment generally involves two major steps: (1) Decomposition of the HTN, where the network is divided into interconnected components that can be represented by nodes (e.g., regions) and edges (e.g., highway segments) with certain properties, allowing for seismic damage assessment of highway bridges and traffic demand analysis for emergency response [19,20,21]; and (2) integration of components, which examines their behavior in terms of network topology, statistical dependencies, traffic flow and inherent uncertainties [22,23]. This step evaluates how disruptions propagate through the network and assesses the availability and capacity of alternative routes under various disaster scenarios.

To capture the complex interdependencies among network components, dynamic traffic demands, and post-disaster functional disruption, extensive efforts have been devoted to seismic simulation and analysis of HTNs from various perspectives [24,25,26]. These tools can enable planners and decision-makers to identify potential vulnerabilities and develop strategies to enhance the resilience of HBNs. In these investigations, post-disaster emergency responses have often been investigated by updating the properties of highway links (e.g., traffic capacity, speed) in a manner similar to non-emergency studies. For instance, Dalal and Üster [27] developed an emergency response network design model that integrates relief supply and evacuation demand, as well as the uncertainties in disaster location and intensity. Zhang and Wei [28] proposed a hybrid genetic algorithm to address inspection-routing and restoration-scheduling problems during post-disaster emergencies, emphasizing the inspection–restoration interactions. Liu et al. [29] introduced a multi-scale post-earthquake highway bridge network simulation method considering bridge damage-induced traffic congestion. However, these numerical simulation-based assessments of large-scale infrastructure systems are often computationally intractable or expensive due to the large number of network components, complex network topology, statistical dependence between component failures, and uncertainties in hazards. Real-world HTNs, with their large scale and complex operational dynamics [30], present significant challenges—especially when addressing uncertainties in seismic hazards, structural damage, and dynamic traffic flow using Monte Carlo simulation (MCS). While MCS is widely used for such uncertainty modeling, traditional MCS-based approaches often face substantial computational burdens when applied to large-scale networks.

Recent advances in machine learning, particularly deep neural networks (DNNs), offer promising surrogates to computationally expensive numerical simulations [31]. These methods can significantly accelerate the transportation network analyses, including evaluating the seismic performance of highway components [32,33,34] and capturing the traffic flow characteristics of HTN systems [35]. Liu et al. [36] integrated transformers and graph neural networks (GNNs) for resilience assessment of networked systems using observational data rather than physical models. Wang et al. [37] modeled failure propagation in interdependent networks for multi-perspective resilience analysis, while Nabian and Meidani [38] demonstrated DNN surrogates for rapid network connectivity evaluation. Liu et al. [39] further proposed a GNN-based surrogate for seismic reliability assessment of bridge networks and a heterogeneous GNN for end-to-end traffic assignment, leveraging adaptive attention and virtual OD links to capture spatial interactions [40]. Despite these advances, seismic resilience assessment of HTNs remains challenging due to numerous random variables and highly dynamic traffic conditions, which hinder effective surrogate modeling.

Recognizing these limitations, the current research on post-earthquake HTN resilience still faces two major gaps: (i) the lack of a scalable surrogate framework capable of efficiently handling large-scale, uncertainty-driven post-earthquake traffic simulations without incurring prohibitive computational costs, and (ii) limited integration of dynamic traffic demand and multi-stage network disruptions into resilience assessments, reducing the reliability of current decision-support tools for emergency response. To bridge these gaps, this study proposes EQResNet, a real-time deep learning framework that integrates network topology, seismic fragility, and traffic flow dynamics into an end-to-end surrogate model. The framework accelerates resilience evaluation by replacing computationally intensive simulations with high-fidelity predictions, incorporates multi-dimensional and time-varying resilience metrics to capture both emergency accessibility and long-term recovery, and is validated through a realistic case study demonstrating its scalability, efficiency, and applicability for large-scale post-earthquake transportation network analysis. The remainder of this paper is organized as follows: Section 2 reviews the concept of seismic resilience in HTNs and outlines the key analytical framework and influencing factors. Section 3 presents a standardized post-earthquake traffic simulation procedure, emphasizing methods that preserve essential performance metrics while simplifying network complexity. Section 4 introduces a DNN-based surrogate modeling approach, illustrating how it improves both the accuracy and computational efficiency of resilience evaluations. Section 5 applies the proposed methodology to the Sioux Falls transportation network as a case study, demonstrating its practical utility. Finally, Section 6 summarizes the key findings and discusses potential avenues for future research.

2. EQResNet Framework

The proposed EQResNet framework for HTNs is designed to address two primary aspects: emergency-response simulation and resilience assessment. The emergency-response simulation follows a scenario-based approach, starting with the identification of seismic hazards that characterize regional seismic activity and an inventory of spatially distributed HTN configurations derived from geographic information systems (GISs). These datasets provide a fundamental representation of the network and external excitations, forming the basis for subsequent analyses. As exhibited in Figure 1, the emergency-response simulation of HTNs mainly consists of three modules:

(1) Physical properties of links: A typical HTN simulation involves network analysis and traffic flow distribution, where the network is modeled as a graph $\mathbf{G}=\{\mathbf{V},\mathbf{E}\}$ [41]. Here, $\mathbf{V}=\left\{v_i\right\}$ is the node set with $N_{all}$ nodes (e.g., regions or intersections), while $\mathbf{E}=\left\{e_{ij}\right\}$ denotes the edges corresponding to connection links [42]. Traffic flow distribution is determined by assigning origin–destination (OD) demand across available paths, typically following shortest-path or user-equilibrium principles to minimize travel time and congestion. Each node is associated with traffic demands, and each edge possesses physical properties such as travel capacity. In the aftermath of an earthquake, traffic restrictions may be imposed on damaged bridges, leading to a capacity reduction in the affected links. Given that bridges are often the most seismically vulnerable components, this study assumes that post-earthquake network disruptions are primarily caused by bridge damage. Consequently, the network can be dynamically updated by modifying the traffic capacities of affected links to reflect their impaired functionality. This process incorporates seismic fragility curves, which describe the probability of a specific structure reaching different damage states under given ground motion intensities.

(2) OD traffic demand: Traffic demand analysis focuses on estimating the potential vehicle volumes between various OD pairs within the network over a specific time period. This process is typically represented by the derived OD demand matrix $\mathbf{Q}=\left\{q_{ij}\right\}$, which captures the spatial and temporal distribution of travel demand. Given a set of $N_s$ origin nodes ($v_i\in {\mathbf{V}}_s$,) and a set of $N_t$ destination nodes ($v_j\in {\mathbf{V}}_t$), where $N_s+N_t=k\le N_{all}$, the k-node travel volume per unit time represent the network’s function. This analysis is essential for simulating realistic traffic scenarios and understanding how these patterns might shift following an earthquake. In the context of post-earthquake scenarios, the OD demand matrix can be updated to reflect changes in traffic patterns caused by the disaster. These changes include the following:

• Increased demand arising due to emergency response activities, evacuation efforts, and relief supply transportation. For example, heavily damaged areas may experience surges in outbound traffic as residents evacuate, while key emergency facilities such as hospitals and shelters may witness higher inbound traffic.
• Reduced demand resulting from infrastructure destruction that limits accessibility or diminishes economic activity. Severely damaged regions may experience a decline in travel demand due to road closures, collapsed bridges, or restrictions on movement.

Accurately estimating post-disaster traffic demand requires incorporating real-world data, such as population density, evacuation zones, and the locations of critical facilities like hospitals and shelters. By dynamically updating OD demand based on seismic impacts, the proposed model enables a more precise evaluation of network resilience.

(3) Traffic flow distribution: This module simulates the distribution of traffic flow throughout the HTN under various post-earthquake conditions. It accounts for key factors such as infrastructure damage, reduced link capacities, and changes in traffic demand, providing a dynamic and realistic representation of how vehicles navigate the damaged network. In this simulation, vehicles are assumed to follow the path that minimizes travel time (min path($v_i{\to v}_j$)), dynamically adjusting to evolving road conditions. By continuously updating traffic flow distributions as network conditions evolve, this module provides critical insights into post-disaster mobility patterns. This adaptive routing mechanism ensures that emergency response vehicles, evacuees, and supply transports can reach their destinations as efficiently as possible.

By streamlining these methods and extracting key features, they can be effectively integrated into a DNN framework to enable efficient emergency-response simulation and analysis. Specifically, OD demand and link capacity information are embedded into the input layer, serving as the foundation of network state. The post-disaster simulation results, such as the redistributed traffic flow, congestion levels, and the identification of potential bottlenecks across the network, are encoded into the output layer. Furthermore, the aforementioned modules can generate abundant training samples, enabling the development of a DNN model as a powerful alternative for predicting the network’s performance under various disaster scenarios. By dynamically accounting for seismic-induced changes in traffic capacity and demand, the DNN surrogate can comprehensively evaluate HTN’s performance. Finally, the alternative routes and paths that can maintain network functionality despite seismic impacts can be captured for seismic redundancy assessment. This structured approach ensures that both the physical and functional aspects of the HTN are investigated, providing valuable insights into how the HTN responds under seismic stress and guiding effective emergency planning.

3. Post-Earthquake HTN Simulation and Resilience Assessment

3.1. Streamlined Procedures for HTN Simulation

Post-earthquake HTN simulation involves a series of systematic procedures to assess network functionality and resilience under seismic impacts. These procedures integrate seismic hazard analysis, infrastructure damage assessment, traffic demand estimation, and traffic flow modeling to provide a comprehensive representation of the transportation network’s post-disaster performance. The key steps in the simulation process are summarized in Figure 2, while

Table 1. Illustration of post-earthquake HTN analysis methods.

Module	Methods/Algorithms	Parameter Explanation
Traffic demand estimation	OD traffic demand matrix: $\mathbf{Q}=\{q_{ij}\}=\left\{{\kappa }_i\cdot {\kappa }_j{\displaystyle \frac{P_i\cdot A_j}{F(R_{ij})}}+\Delta q_{ij}^e-\Delta q_{ij}^r\right\}$ ($∆q_{ij}^e$ is the additional demand due to evacuation and emergency response, $∆q_{ij}^r$ is the reduction in demand caused by road blockages or economic loss)	$q_{ij}$ denotes the estimated number of trips from $v_i$ to $v_j$; $P_i$ and $A_j$ represent the trip production of $v_i$ and attraction of $v_j$; $F\left(R_{ij}\right)$ is impedance function between $v_i$ and $v_j$; $K_i$ and $K_j$ are calibrated constants.
Traffic flow distribution	Traffic flow on link a: $$\begin{gathered} x_a^{(m+1)}=x_a^{\left(m\right)}+{\displaystyle \sum _{i,j}}{\delta }_{ij}\left(a\right)\times q_{ij}∕N_q \\ {\delta }_{ij}(a)=\left\{\begin{array}{c}1, \mathrm{a}\in \underset{i,j}{\mathrm{path}} \mathrm{m}\mathrm{i}\mathrm{n}{\displaystyle \sum _{ph}}{t}_p\left(x_{ph}\right)\\ 0, \mathrm{otherwise}\end{array}\right. \end{gathered}$$	$N_{\mathrm{q}}$ is the number of divided shares for traffic demand; ${\delta }_{ij}\left(a\right)$ is an indicator function that determines whether link a belongs to the shortest path from $v_i$ to $v_i$.
Link property assessment	Travel time on link p: $t_p(x_p)={\displaystyle \frac{L_p}{v_p}}\left(1+{\beta \left({\displaystyle \frac{x_p}{C_p}}\right)}^{\alpha }\right)$ Traffic capacity of link p: $C_p=C_{\mathrm{B}}·N_{\mathrm{L}}·p_{\mathrm{H}\mathrm{F}}·f_{\mathrm{h}\mathrm{v}}·f_{\mathrm{p}}$	$L_p$ and $v_p$ are the physical length and free-flow velocity of link p, respectively; $\alpha$ and $\beta$ are model parameters; $C_{\mathrm{B}}$ is the basic capacity per lane; $N_{\mathrm{L}}$ is the number of lanes; $p_{\mathrm{H}\mathrm{F}}$, ${\mathrm{f}}_{\mathrm{h}\mathrm{v}}$, and $f_{\mathrm{p}}$ are adjustment factors for peak hour, heavy vehicles and the familiarity of drivers, respectively.
Seismic fragility of bridges	Bridge damage probability: $P_{\mathrm{b}\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{g}\mathrm{e}}[D{S}_k]={\displaystyle \bigcup _{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t}}}{P}_k\left[D{S}_k\right|\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{k}\mathrm{e}]$	The union of component-level damage probabilities $P\left(D{S}_k\right)$ under earthquakes.
Regional seismic hazards	Regional seismic hazard: $$\begin{gathered} \mathrm{l}\mathrm{n}\left(IM\right)=F_{\mathrm{M}}\left(\mathrm{M}\right)+F_{\mathrm{D}}({\mathrm{R}}_{\mathrm{j}\mathrm{b}},\mathrm{M}) \\ +F_{\mathrm{s}}(V_{\mathrm{s}30},R_{\mathrm{j}\mathrm{b}},\mathrm{M})+{\epsilon }_{\mathrm{T}}{\sigma }_{\mathrm{T}} \end{gathered}$$	$F_{\mathrm{M}}$, $F_{\mathrm{D}}$, and $F_{\mathrm{S}}$ are the magnitude scaling, distance, and site amplification, respectively ${\epsilon }_{\mathrm{T}}{\sigma }_{\mathrm{T}}$ is the total standard deviation.

presents the mathematical models and algorithms used in each module.

(1)

Seismic Hazard Analysis: This step focuses on quantifying the seismic intensity measure (IM) distribution across the study region. Ground motion parameters, such as peak ground acceleration (PGA) and spectral acceleration, are typically estimated using Ground Motion Prediction Equations (GMPEs), which incorporate historical earthquake records and probabilistic seismic hazard models. These parameters serve as critical inputs for evaluating the structural vulnerability of transportation infrastructure, forming the basis for subsequent bridge damage assessment and overall network resilience analysis.

(2)

Seismic Damage Assessment of Bridges: As one of the most vulnerable components in HTNs, bridges play a critical role in maintaining network connectivity. Their seismic performance is typically evaluated using fragility curves, which establish the relationship between seismic intensity and the probability of exceeding various damage states. The damage level of each bridge is determined by considering its structural characteristics and the local ground-shaking intensity. Based on this assessment, the functional status of individual bridges—ranging from minor damage with reduced capacity to complete failure—can be identified.

(3)

Evaluation of Physical and Functional Characteristics of Road Links: The physical attributes of roadway links, such as capacity and speed limits, are dynamically updated based on the assessed damage states of bridges. When a bridge sustains moderate to severe damage, the capacity of its corresponding road link is reduced accordingly, while a complete collapse results in a full closure of the link. These modifications are integrated into the updated network topology, forming the foundation for post-earthquake traffic simulations. By reflecting the impaired connectivity and altered traffic conditions, this step ensures a realistic representation of the HTN’s functionality under seismic impacts.

(4)

Traffic Demand Analysis: Post-earthquake OD demand estimation is adjusted based on changes in population distribution, emergency response priorities, and accessibility constraints. The OD demand matrix quantifies traffic demand between OD pairs, capturing how travel patterns evolve after a seismic event. Pre-earthquake traffic demand is typically estimated using a gravity-based model, which considers factors such as population density, land use, and economic activity. Following an earthquake, this model is refined to account for population displacement, road closures, and increased demand for emergency transportation. These shifts significantly influence the operational efficiency and resilience of HTNs, making accurate demand estimation essential for effective disaster response and recovery planning.

(5)

Traffic Flow Assignment and Dynamic Path Selection: Based on the updated network topology and OD demand matrix, traffic flow distribution is performed using the Incremental Traffic Assignment (ITA) approach. This method assigns traffic in small increments, dynamically updating travel times after each step to reflect congestion effects. To simulate realistic vehicle routing behavior, a dynamic path selection model is employed, where vehicles iteratively choose routes that minimize travel time under post-earthquake conditions. Given that critical structures such as bridges are particularly susceptible to seismic damage, their reduced capacity or failure can significantly impact network performance. The system continuously adapts to evolving conditions, ensuring a responsive and accurate representation of post-earthquake traffic flow dynamics.

By integrating these modules into a unified framework, an efficient and realistic post-disaster traffic assessment can be conducted.

3.2. Mathematical Representation and Functionality of HTNs

To facilitate the integration of deep learning models for post-earthquake transportation analysis, it is essential to establish a structured mathematical representation of the HTN. This representation should accurately reflect both the physical state of the infrastructure and the dynamic behavioral response of traffic systems following seismic events. However, predicting the precise temporal evolution of traffic flow immediately after an earthquake is extremely challenging due to high uncertainty regarding driver behavior, rapid changes in demand patterns, incomplete information on infrastructure conditions, and possible emergency interventions such as road closures and contraflow operations. In practical emergency response, decision-makers often need an instant estimation of traffic states under a given set of disrupted network conditions and assumed demand levels, rather than a long-term dynamic traffic evolution forecast.

In this context, the proposed framework is designed as a scenario-based surrogate model that provides rapid predictions of post-earthquake traffic flows once the OD demand matrix and residual link functionality are defined. At its core, the HTN model ingests two primary inputs: (1) Traffic demand—The OD matrix, representing the number of vehicles traveling between all OD pairs, and (2) residual link functionality—the remaining operational capacity of highway segments after accounting for earthquake-induced damage, especially due to bridge failures or capacity degradation. The model outputs include the redistributed traffic flow across the network, reflecting detours and congestion effects.

As illustrated in Figure 3, the HTN state is characterized by a state matrix ${\mathbf{H}}_{\mathrm{T}}$, which integrates essential network properties, and a functionality matrix ${\mathbf{F}}_{\mathrm{T}}$, which captures post-earthquake traffic conditions.

$${\mathbf{H}}_{\mathbf{T}}=[\mathbf{Q},\mathbf{C}({\mathbf{D}}_{\mathbf{s}}),{\mathbf{T}}_{\mathbf{0}}({\mathbf{D}}_{\mathbf{s}}\left)\right],\hspace{1em}{\mathbf{F}}_{\mathbf{T}}=[{\mathbf{X}}_{\mathbf{p}},{\mathbf{T}}_{\mathbf{p}}]$$

(1)

where $\mathbf{Q}=\left\{q_{ij}\right\}$ refers to the OD demand in terms of the volume of vehicles traveling between different OD pairs; $\mathbf{C}\left({\mathbf{D}}_{\mathrm{s}}\right)=\left\{C_p\right|{\mathbf{D}}_{\mathrm{s}}\left\}{\mathbf{V}}_0\right({\mathbf{D}}_{\mathrm{s}})=\{v_0\left|{\mathbf{D}}_{\mathrm{s}}\right\}$, and ${\mathbf{T}}_0\left({\mathbf{D}}_{\mathrm{s}}\right)=\left\{t_0\right|{\mathbf{D}}_{\mathrm{s}}\}$ denote the post-disaster traffic capacity, free-flow speed, and travel time of highway segments under the condition of seismic-induced damage to bridges; ${\mathbf{X}}_{\mathrm{p}}=\left\{x_a\right\}$ stores the assigned traffic volume on each link under post-earthquake conditions; and ${\mathbf{T}}_{\mathrm{p}}=\left\{t_a\right\}$ represents the updated travel times, considering congestion and network disruptions.

By integrating state matrix ${\mathbf{H}}_{\mathrm{T}}$ and functionality matrix ${\mathbf{F}}_{\mathrm{T}}$, the HTN model provides a standardized mathematical foundation for further data-driven learning and predictive modeling. It enables rapid, scenario-specific predictions of system-wide performance to support urgent post-disaster decision-making, even in the absence of reliable temporal traffic evolution forecasts.

4. EQResNet Development for HTNs

4.1. DNN Description

Traditional MCS based on numerical modeling provides a robust approach for assessing the seismic resilience of HTNs. This approach typically employs three nested iterative loops to comprehensively capture uncertainties in seismic hazard, structural damage, and transportation network performance. As illustrated in Figure 4, while MCS provides a thorough probabilistic assessment of HTN resilience, its computational demands are extremely high, often requiring thousands or even millions of iterations to achieve statistical convergence. This high computational burden makes it impractical for real-time emergency response and rapid decision-making.

To address the limitations of MCS, DNNs are introduced as surrogate models to approximate the complex nonlinear relationships between ${\mathbf{H}}_{\mathrm{T}}$(inputs) and ${\mathbf{F}}_{\mathrm{T}}$(outputs). A typical DNN can be mathematically expressed as follows:

$${\mathbf{F}}_{\mathrm{T}}=f_{\mathrm{D}\mathrm{N}\mathrm{N}}({\mathbf{H}}_{\mathrm{T}};\mathsf{\theta }={\sigma }^h({\mathbf{W}}^h{\sigma }^{h-1}({\mathbf{W}}^{h-1}\cdots {\sigma }^1({\mathbf{W}}^1{\mathbf{H}}_{\mathrm{T}}+{\mathbf{b}}^1)\cdots +{\mathbf{b}}^{h-1})+{\mathbf{b}}^h)$$

(2)

where $\mathsf{\theta }=\{{\mathbf{W}}^{hi},{\mathbf{b}}^{hi}\}$ (hi = 1, 2,…, h) represents all trainable parameters, including weight matrices ${\mathbf{W}}^{hi}$ and bias vector ${\mathbf{b}}^{hi}$; h is the total number of layers; ${\sigma }^{hi}(·)$ is the activation function of the hi-th layer, and common ReLU activation functions $(\sigma (z)=\mathrm{m}\mathrm{a}\mathrm{x}(0,z\left)\right)$ are used herein.

By leveraging large-scale datasets generated from MCS, DNN architecture is trained and validated to capture the intricate mappings between seismic inputs and network resilience metrics. To enhance model stability and generalization, several key techniques are incorporated into the training process: batch normalization is applied to normalize layer inputs, accelerating convergence and mitigating internal covariate shifts; dropout regularization randomly deactivates neurons during training to prevent overfitting and improve robustness; and early stopping monitors validation loss, halting training when performance begins to degrade to avoid overfitting. Once trained, the DNN-based surrogate model enables real-time predictions of HTN emergency functionality and probabilistic resilience assessment, significantly enhancing computational efficiency while maintaining high predictive accuracy.

4.2. Surrogate Model Training and Testing

Figure 5 outlines the structured development procedure, encompassing dataset preparation, model training, validation, and testing to ensure accuracy, generalizability, and computational efficiency. The DNN surrogate model for seismic emergency simulation of HTNs combines MCS-based traffic demand data and link properties with numerical simulation outputs (traffic flow volumes and travel times) to generate training datasets. These input–output pairs serve as the foundation for training the DNN model. To enhance generalization and predictive performance, the dataset should be split into training, validation, and test sets (e.g., 70%-20%-10%). The validation set is leveraged to fine-tune hyperparameters. The surrogate model is constructed as a multi-layer feedforward DNN. The input layer integrates critical features of the HTN, including traffic demand patterns, road characteristics, and network topology. The hidden layers, comprising fully connected neurons, capture complex spatial–temporal relationships between traffic conditions and network disruptions. The architecture is designed to balance model complexity and computational efficiency while capturing nonlinear dependencies within the HTN.

The training process follows a supervised learning paradigm, where the DNN surrogate model learns to map input features to output predictions through forward propagation and backpropagation. The model parameters are optimized using gradient-based algorithms, such as Adam or stochastic gradient descent (SGD), ensuring efficient convergence. Hyperparameter tuning—including network depth, the number of neurons per layer, activation functions, and learning rate selection—is performed through cross-validation to achieve an optimal balance between prediction accuracy and computational efficiency. To mitigate overfitting, regularization techniques such as dropout and batch normalization are implemented, enhancing model robustness and generalization. The loss function (e.g., mean squared error) quantifies the discrepancy between the predicted metrics and the true values. By iteratively refining the model, the surrogate achieves high-fidelity approximations of complex HTN responses.

After training, the model undergoes validation using independent datasets to assess generalizability. Performance metrics, including root mean squared error (RMSE) and coefficient of determination (R²), are used to evaluate predictive accuracy:

$$RMSE=\sqrt{{\displaystyle \frac{\sum _{i=1}^{N_y}\sum _{j=1}^{M_y}{(y_{ij}-{\widehat{y}}_{ij})}^2}{M_y{N}_y}}}, R^2=1-{\displaystyle \frac{\sum _{i=1}^{N_y}\sum _{j=1}^{M_y}{(y_{ij}-{\widehat{y}}_{ij})}^2}{\sum _{i=1}^{N_y}\sum _{j=1}^{M_y}{(y_{ij}-{\overline{y}}_j)}^2}}$$

(3)

where $y_{ij}$ and ${\widehat{y}}_{ij}$ are the true value from numerical simulations and DNN predicted value, respectively. $M_y$ is the number of output variables and $N_y$ is the number of samples.

Through this structured training and development procedure, the DNN-based surrogate model efficiently replaces computationally intensive numerical simulations, enabling rapid emergency traffic assessment and response planning in post-earthquake scenarios.

4.3. Seismic Resilience Formulation During Emergencies

As illustrated in Figure 6, the HTN’s functionality evolves through four stages following an earthquake: pre-disaster preparedness, emergency response, long-term recovery, and post-disaster operations. While previous studies have extensively examined overall resilience across these stages [2,6,42], each phase serves unique operational objectives, necessitating a specialized framework for assessing emergency resilience. The pre-disaster phase primarily focuses on monitoring, mitigation, and preparedness, aiming to minimize potential damage and enhance response capabilities. In contrast, the recovery phase is dedicated to rehabilitation and reconstruction, restoring infrastructure and normalizing operations. However, it is during the emergency response phase that resilience is very critical, directly influencing the effectiveness of rescue and medical operations, evacuation procedures, critical infrastructure functionality, shelter accessibility, and relief distribution. This phase demands a rapid, adaptive, and coordinated response to minimize casualties and maintain essential services amid the immediate aftermath of a seismic event.

To quantitatively evaluate HTN resilience during emergencies, this framework integrates traffic flow distribution and travel time metrics, establishing five emergency resilience indicators to assess network performance under seismic disruptions:

(1)

Rescue support resilience ($R_{\mathrm{T}}^{\mathrm{r}}$) evaluates the HTN’s ability to facilitate timely deployment of rescue teams and emergency personnel to affected areas. It measures how efficiently the transportation network supports search-and-rescue operations by ensuring adequate traffic flow to critical rescue sites, as follows:

$$R_{\mathrm{T}}^{\mathrm{r}}={\int }_{t_0}^{t_0+t_E}{\displaystyle \frac{1}{N_{\mathrm{v}\mathrm{r}}}}{\sum }_{v_i\in {\mathrm{V}}^{\mathrm{r}}}\mathrm{m}\mathrm{i}\mathrm{n}({\displaystyle \frac{min{ t}_0\left(path\right(v_r\to v_i\left|x_{ph}\right))}{min t_p\left(path\right(v_r\to v_i\left|x_{ph}\right))}},100\%)dt$$

(4)

where $t_E$ denotes the time duration (set to post-disaster 72 h, based on standard emergency response guidelines, emphasizing the critical window for life-saving operations and immediate relief efforts); ${\mathrm{V}}^{\mathrm{r}}$ represents the set of nodes waiting for rescue; $N_{\mathrm{v}\mathrm{r}}$ denotes their total number. $min{ t}_0\left(path\right(v_r\to v_i\left|x_{ph}\right))$ and $min t_p\left(path\right(v_r\to v_i\left|x_{ph}\right))$ is shortest travel time from a rescue unit node vr to a distressed node vi under pre- and post-earthquake traffic conditions, respectively.

(2)

Medical assistance resilience ($R_{\mathrm{T}}^{\mathrm{m}}$): The ability to transport injured individuals to medical facilities is paramount in minimizing casualties. This metric assesses the efficiency of routes leading to hospitals, medical centers, and triage points under post-earthquake conditions, as follows:

$$R_{\mathrm{T}}^{\mathrm{m}}={\int }_{t_0}^{t_0+t_E}{\displaystyle \frac{1}{N_{\mathrm{v}\mathrm{m}}}}{\sum }_{v_i\in {\mathrm{V}}^{\mathrm{m}}}\mathrm{m}\mathrm{i}\mathrm{n}({\displaystyle \frac{1}{t_p\left(path\right(v_m\leftrightarrow v_i\left|x_{ph}\right))}},100\%)dt$$

(5)

where ${\mathrm{V}}^{\mathrm{m}}$ represents the set of nodes waiting for medical assistance; $N_{\mathrm{v}\mathrm{m}}$ denotes their total number. $t_p\left(path\right(v_m\leftrightarrow v_i\left|x_{ph}\right))$ denotes the shortest travel time between the hospital node $v_m$ and the affected node v_i. In this context, medical intervention within 1 h is deemed to fully meet the functional requirement (100% efficiency). Delays beyond one hour impede the network’s ability to provide effective medical assistance, diminishing overall resilience. Extended travel times after an earthquake increase medical risks and decrease survival rates.

(3)

Evacuation operation resilience ($R_{\mathrm{T}}^{\mathrm{e}}$): Evacuation operations depend on efficient egress routes to move displaced populations toward safety. Populations require quick access to emergency shelters and relief centers. $R_{\mathrm{Y}}^{\mathrm{e}}$ evaluates the HTN’s capacity to maintain traffic flow on designated evacuation corridors, ensuring safe, timely, and organized evacuations, as follows:

$$R_{\mathrm{T}}^{\mathrm{e}}={\int }_{t_0}^{t_0+t_E}{\displaystyle \frac{{\sum }_{v_i\in {\mathbf{V}}^e}{q}_{ei}\times \mathrm{m}\mathrm{i}\mathrm{n}\left({\sum }_{ph}\mathrm{m}\mathrm{i}\mathrm{n}{ t}_0\left(path\right(v_i\to v_e\left)\right|x_{ph})\right)}{{\sum }_{v_i\in {\mathbf{V}}^e}{q}_{ei}\times \mathrm{m}\mathrm{i}\mathrm{n}\left({\sum }_{ph}\mathrm{m}\mathrm{i}\mathrm{n}{ t}_p\left(path\right(v_i\to v_e\left)\right|x_{ph})\right)}}dt$$

(6)

where $q_{ei}\times \mathrm{m}\mathrm{i}\mathrm{n}\left({\sum }_{ph}\mathrm{m}\mathrm{i}\mathrm{n} t_0\left(path\right(v_i\to v_e\left)\right|x_{ph})\right)$ and $q_{ei}\times \mathrm{m}\mathrm{i}\mathrm{n}\left({\sum }_{ph}\mathrm{m}\mathrm{i}\mathrm{n} t_p\left(path\right(v_i\to v_e\left)\right|x_{ph})\right)$ denote the total travel time from node ${\mathrm{v}}_{\mathrm{i}}$ to shelter node $v_e$ before and after the earthquake, respectively; ${\mathbf{V}}^{\mathrm{e}}$ represents the set of nodes in evacuation areas.

(4)

Critical infrastructure interaction ($R_{\mathrm{T}}^{\mathrm{c}}$): Post-disaster resilience is highly dependent on access to lifeline infrastructure, including power plants, water stations, emergency warehouses, and command centers. This indicator measures the efficiency of the HTN in maintaining connectivity between critical nodes, as follows:

$$R_{\mathrm{T}}^{\mathrm{c}}={\int }_{t_0}^{t_0+t_E}{\displaystyle \frac{{\sum }_{v_i\in {\mathbf{V}}^{\mathrm{c}}}{\sum }_{v_c\in {\mathbf{V}}^{\mathrm{c}}}\mathrm{m}\mathrm{i}\mathrm{n}({\sum }_{ph}{q}_{ci}\times \mathrm{m}\mathrm{i}\mathrm{n}{ t}_0(path(v_c\leftrightarrow v_i)\left|x_{ph}\right))}{{\sum }_{v_i\in {\mathbf{V}}^{\mathrm{c}}}{\sum }_{v_c\in {\mathbf{V}}^{\mathrm{c}}}\mathrm{m}\mathrm{i}\mathrm{n}({\sum }_{ph}{q}_{ci}\times \mathrm{m}\mathrm{i}\mathrm{n}{ t}_p(path(v_c\leftrightarrow v_i)\left|x_{ph}\right))}}dt$$

(7)

where ${\mathbf{V}}^{\mathbf{c}}$ represents the set of critical infrastructure nodes essential for maintaining urban operations.

(5)

Normal support resilience ($R_{\mathrm{T}}^{\mathrm{n}}$): Beyond emergency logistics, the network must also support essential daily mobility (e.g., supply chains, business continuity). This metric evaluates how well general-purpose traffic recovers over time, as follows:

$$R_{\mathrm{T}}^{\mathrm{n}}={\int }_{t_0}^{t_0+t_E}{\displaystyle \frac{\sum x_a^0\times t_a^0}{\sum x_a^p\times t_a^p}}dt$$

(8)

where ${ x}_a^0\times t_a^0$ and $x_a^p\times t_a^p$ represent the total travel times on link a before and after the earthquake, respectively.

These indicators provide a structured basis for measuring the network’s ability to sustain critical operations, minimize disruptions, and facilitate effective emergency response efforts. By studying the impact of repairing road segments on network resilience, the repair priority of bridges in the post-earthquake region can be quickly determined to maximize network resilience.

5. Case Study for Sioux Falls Transportation Network

5.1. HTN Overview

The Sioux Falls transportation network is a widely studied benchmark in transportation research, consisting of 24 nodes and 76 directed links [43,44,45], as illustrated in Figure 7. This network represents a mid-sized urban road system, making it a suitable testbed for evaluating the applicability of the proposed DNN-based surrogate modeling approach for emergency simulation and seismic resilience assessment. To better reflect real-world emergency scenarios and demonstrate the algorithm’s adaptability, several modifications were introduced to the original network structure:

(1) Bridge Infrastructure: A total of 62 road segments are assumed to contain at least one bridge, making them particularly vulnerable to seismic damage and associated traffic disruptions. The seismic fragility of these bridges is explicitly incorporated into the resilience assessment to reflect varying structural vulnerabilities under different earthquake intensities.

(2) Heterogeneous roadway capacities: The network consists of three hierarchical road classifications to reflect realistic variations in road design and usage.

• Expressways (Highways): Six-lane roads with a free-flow speed of 120 km/h, primarily serving as major transportation corridors.
• Arterial roads (Major Roads): Four-lane roads with a free-flow speed of 100 km/h, connecting key urban areas and critical facilities.
• Local roads: Two-lane roads with a free-flow speed of 80 km/h, providing access to residential and commercial zones.

(3) Critical facility representation: Several key nodes in the network represent essential urban infrastructure:

• Node 4 and 19: Node 4 contains a school contains a, contributing to local community support and emergency response efforts. Node 19 includes a stadium, which can function as an evacuation shelter for displaced populations.
• Nodes 5 and 12: Locations with hazardous facilities, including flammable and explosive materials, posing additional risks in seismic events.
• Node 15: A regional hospital serving as the primary medical response center in post-disaster scenarios.
• Node 22: A major commercial district, influencing post-earthquake economic recovery and business continuity.
• Node 23: The site of fire and police departments, critical for emergency response coordination

(4) Pre-earthquake OD traffic demand: Significant variations exist in traffic generation and attraction across nodes before the earthquake. For instance, Nodes 3 and 4 generate approximately 2300 pcu/h, whereas Node 22 exhibits the highest traffic demand and generation at around 5500 pcu/h. Post-earthquake, traffic flow patterns across different nodes may increase or decrease depending on the severity of disruptions and emergency response demands.

5.2. DNN-Based Surrogate Development for Emergency-Response

5.2.1. Data Preparation Based on Numerical Simulations

A robust DNN-based surrogate model requires a representative and diverse dataset that captures the complex dynamics of transportation networks under post-earthquake conditions. This study generates such a dataset through conventional numerical simulations, which are designed to reflect variations in both traffic demand and infrastructure functionality following seismic events.

In the aftermath of an earthquake, travel demand is subject to considerable fluctuation, driven by population displacement, urgent medical needs, relocation to emergency shelters, and logistics activities. To represent this variability, traffic demand levels are modeled within a broad range—spanning from 20% to 200% of normal pre-earthquake values. Demand surges are concentrated around critical facilities such as hospitals, emergency shelters, and supply hubs, while depopulated or isolated areas experience pronounced demand reductions. Meanwhile, roadway capacity is degraded due to structural damage. Each segment is assigned a residual functionality ratio ranging from 10% to 100%, depending on the severity of the damage. Fully intact roads retain 100% capacity, partially damaged but passable roads operate at 50%, and severely impaired or obstructed segments are reduced to 10%, reflecting limited accessibility via detours or alternative paths.

To capture the full spectrum of post-disaster network behaviors, 105 simulation scenarios are developed. These scenarios incorporate variations in earthquake magnitude, bridge damage patterns, and demand redistribution. Figure 8 presents the statistical distribution of key features in the dataset, illustrating the variability in residual link functionality, network-wide travel time changes, and accessibility disruptions under different earthquake scenarios. This dataset serves as the foundation for training a predictive model capable of estimating network performance under different seismic impact scenarios.

5.2.2. Model Training and Validation

To ensure the reliability and predictive accuracy of the DNN-based surrogate model, a systematic training and validation strategy is implemented. The dataset is divided into training (80%) and test (20%) subsets. Within the training set, K-fold cross-validation is employed to improve model robustness, where the data is iteratively split into K subsets, with one subset used for validation in each iteration while the rest are used for training. This approach ensures comprehensive utilization of the dataset and mitigates overfitting risks.

The model adopts a multi-layer feedforward neural network architecture. The input layer consists of two matrices: a 24 × 24 OD traffic demand matrix, representing traffic demand between different nodes, and a 76 × 2 link attribute matrix, encoding basic traffic capacity and free-flow velocity properties of road segments. The output layer produces a 76 × 1 vector, estimating post-earthquake traffic flow for each road segment. Multiple hidden layers with nonlinear activation functions capture the intricate relationships between seismic impact, network damage, and transportation performance. To prevent overfitting and enhance generalization, batch normalization, dropout regularization, and early stopping are applied. The Adam optimizer is used to minimize the mean squared error between the predicted and simulated outcomes. Hyperparameter tuning is conducted using Bayesian optimization, searching over the number of layers, neurons per layer, learning rate, dropout rate, and batch size.

Figure 9 compares the post-earthquake traffic flow and travel time predicted by the DNN-based surrogate model with those obtained from high-fidelity numerical simulations. The results indicate that the DNN model effectively captures the complex nonlinear behavior of the transportation network under seismic disruption, producing predictions that closely match the simulation results across all 76 road segments. For traffic flow prediction, the model achieves a MSE of 0.1015 and 0.1038 on the training and test sets, respectively, with corresponding R² values of 0.9465 and 0.9250, demonstrating strong generalization capability. Similarly, travel time estimation yields comparable accuracy, further confirming the model’s robustness across varying network configurations and seismic damage scenarios.

Overall, the DNN-based surrogate model achieved about 95% prediction accuracy while requiring only about 10% of the computational cost compared to conventional numerical simulations. These results demonstrate that the model maintains high prediction fidelity across diverse post-earthquake scenarios. Comparative evaluations further indicate that the proposed framework achieves similar or better accuracy than traditional traffic simulation methods while significantly reducing runtime, particularly under Monte Carlo sampling with large scenario sets. This computational advantage becomes increasingly pronounced as the network scale expands, suggesting that the approach is inherently scalable to larger or real-world transportation networks once representative datasets and feature inputs are prepared for training. These findings validate the proposed DNN-based surrogate as a computationally efficient, reliable, and adaptable tool for post-earthquake traffic state prediction and resilience assessment, supporting rapid emergency decision-making in disaster-prone transportation systems.

5.2.3. Post-Earthquake HTN Simulation

To simulate the emergency functionality of the HTN following a seismic event, a representative earthquake scenario is applied, characterized by a magnitude 7.0, strike-slip fault event with epicenters located near Nodes 15 and 19. Ground motion IMs are generated based on the regionally calibrated attenuation relationship developed by Boore and Atkinson [46]. This model ensures accurate spatial variation of seismic shaking across the network. Bridge-level seismic damage is then probabilistically estimated using fragility curves proposed by Nielson and Desroches [47], which provide a component-specific mapping between seismic demand and limit states.

These simulations are well-recognized for their detailed classification of seismic demand and structural capacity in transportation infrastructure. Following the damage assessment, residual roadway capacities and travel speeds are computed based on empirical post-earthquake performance models [48,49], reflecting degradation and progressive recovery. These attributes serve as input to a trained DNN surrogate model, which efficiently approximates network-level performance metrics under diverse seismic scenarios. The time-dependent network functionality ${\mathbf{F}}_{\mathrm{T}}\left(t\right)$ is represented as a conditional probability function:

$$\mathrm{P}\left({\mathbf{F}}_{\mathrm{T}}\right(t\left)\right|\mathbf{M},R_{\mathrm{j}\mathrm{b}},V_{\mathrm{s}30})=P(f_{\mathrm{D}\mathrm{N}\mathrm{N}}\left({\mathbf{H}}_{\mathrm{T}}\right(t\left)\right|\left\{{\gamma }_{\mathrm{B}}\right(t\left|DS\right({\mathrm{B}}_k\left)\right)\left\}\right|\left\{I{M}_k\right\}|F_{\mathrm{M}},F_{\mathrm{D}},F_{\mathrm{S}}))$$

(9)

To operationalize this framework,

Table 2. Pseudocode for MCS of post-earthquake HTN simulation using the DNN surrogate.

Step	Pseudocode	Description
Initialize Simulation	Set HTN features (e.g., road segments, bridge locations, and network topology) Set earthquake characteristics (e.g., magnitude, fault mechanism) Define simulation parameters (e.g., number of iterations, MCS size)	Define transportation network features, earthquake parameters (Mw = 7.0, strike-slip), and simulation settings (iterations, sampling size).
2. For each iteration Mi, Di, ri, and Qi in MCS	Sample seismic hazard (IMs: PGA, Sa) based on earthquake scenario Estimate bridge damage states DS(Bk) using fragility curves Calculate residual capacity for each link using damage state DS(Bk): RC_l(t) ← f_recovery(DS(Bk), t) d. Evaluate the traffic demand among all OD sets	Loop over N_sim MCS iterations for probabilistic seismic hazard Loop over DS_sim MCS iterations for seismic fragilities of regional bridges Loop over rs_sim MCS iterations for potential recovery process of regional bridges Update link functionality based on recovery process models Loop over Qn_sim MCS iterations for potential OD traffic demand
3. Use DNN Surrogate Model to estimate network functionality	Input: Residual link capacities, bridge damage states, and seismic hazard data Input ← [H(t), Q(t)] Output: Estimated functionality of each road segment at time t [F_T(i,t)] ← f_DNN(Input)	Build input feature matrix, formulate HT(t) and Q of the HTN Use the DNN model to predict the functionality of each road segment at a given time t.
4. Aggregate the results	Compute overall network functionality based on individual link functionalities	Track how network performance changes over time until the end of MCS loops

outlines the MCS procedure using the DNN-based surrogate model. Each iteration involves seismic hazard sampling, bridge damage assessment, residual capacity estimation, and network functionality prediction. By leveraging the efficiency of the DNN model, this approach offers a robust, data-driven solution for post-earthquake recovery, capturing the entire seismic impact chain—from ground motion to network-level degradation—while significantly reducing computational time compared to traditional simulations, thereby enabling rapid, scalable, and resilience-informed emergency response planning.

5.3. Multi-Dimensional Seismic Resilience Assessment

Building on the predictive capabilities of the DNN-based surrogate model, the functional status of each roadway segment after an earthquake can be rapidly estimated under a wide range of uncertain input conditions, including variable traffic demand and stochastic roadway damage states. These uncertainties are propagated through MCS of demand levels of baseline values and residual link functionality ratios, generating multiple post-earthquake network realizations. The surrogate model then replaces computationally expensive traffic assignment simulations, providing high-fidelity predictions of traffic states for each scenario. These outputs form the basis for a multi-dimensional resilience assessment of the transportation network, capturing the variability in emergency accessibility, detour efficiency, and overall recovery performance under different seismic impact scenarios.

Figure 10 presents the spatial distribution of five key resilience indicators under a representative M7.0 earthquake scenario. The results reveal significant spatial heterogeneity in resilience performance, with certain regions exhibiting marked reductions in accessibility to critical services such as hospitals, emergency shelters, and intermodal infrastructure hubs. This variation reflects the combined influence of seismic intensity, bridge vulnerability, and network topology. From a probabilistic perspective, the five resilience indicators exhibit the following statistical characteristics (mean ± standard deviation): rescue support resilience $R_{\mathrm{T}}^{\mathrm{r}}$ = 0.7886 ± 0.0813, medical assistance resilience $R_{\mathrm{T}}^{\mathrm{m}}$ = 0.9564 ± 0.0219, evacuation operation resilience $R_{\mathrm{T}}^{\mathrm{e}}$ = 0.9103 ± 0.0438, critical infrastructure interaction $R_{\mathrm{T}}^{\mathrm{c}}$ = 0.9818 ± 0.0122, and normal support resilience $R_{\mathrm{T}}^{\mathrm{n}}$ = 0.8804 ± 0.0282. Assuming approximate normality of these distributions, over 95% of observed resilience values for each indicator are expected to lie within their respective mean ± 2σ intervals. Among the indicators, rescue support resilience $R_{\mathrm{T}}^{\mathrm{r}}$ generally ranges between 0.62 and 0.95, indicating that access to search-and-rescue routes is moderately-to-severely affected in epicentral areas. Medical assistance resilience $R_{\mathrm{T}}^{\mathrm{m}}$ falls between 0.87 and 0.99, suggesting that while access to hospitals is mostly retained, certain regions still suffer from limited medical connectivity. Evacuation operation resilience ${ R}_{\mathrm{T}}^{\mathrm{e}}$ and critical infrastructure interaction $R_{\mathrm{T}}^{\mathrm{c}}$ display values between 0.68 and 0.96 and 0.90–0.99, respectively, reflecting the overall robustness of evacuation routes and inter-facility linkages, though localized disruptions remain evident. Normal support resilience $R_{\mathrm{T}}^{\mathrm{n}}$ performs best, with values largely above 0.85, highlighting the network’s capacity to support daily mobility and logistics even under stress.

By incorporating both predicted traffic flow and travel time into resilience evaluation, the proposed framework offers a granular and dynamic perspective on network performance degradation. This multi-dimensional approach moves beyond traditional binary functional assessments and allows for differentiated resilience diagnostics across space and function. Such insights enable decision-makers to formulate more effective mitigation and response strategies. For example, the identification of critical corridors with disproportionate influence on system-wide accessibility can guide investment in seismic retrofitting or prioritize emergency repair operations. Ultimately, this facilitates the design of transportation networks that are not only more robust against disruption but also better equipped to support emergency response and recovery efforts.

Although the proposed framework is validated on a small-scale Sioux Falls network as a benchmark, its methodology is inherently scalable to larger highway transportation systems. Applying the model to large-scale networks would require additional feature engineering to represent complex topologies, heterogeneous traffic demand patterns, and high-dimensional output variables. By expanding the input layer to capture broader network characteristics, preparing a representative dataset, and adapting the surrogate architecture accordingly, the proposed approach can be trained for larger systems following the same procedures. Once trained, the model is expected to deliver fast and reliable post-earthquake traffic state predictions and resilience assessments, making it a promising tool for metropolitan-scale emergency decision support.

6. Conclusions

This study presents a holistic methodology, EQResNet, to simulate the emergency response of HTNs and conduct resilience assessment under seismic events. The framework integrates probabilistic seismic hazards, regional bridge fragilities, and traffic flow distribution, etc., to comprehensively evaluate network performance during emergencies. By employing a DNN-based surrogate model, it significantly improves computational efficiency while maintaining high prediction accuracy compared to traditional simulation methods.

The proposed resilience assessment framework quantifies the emergency functionality of HTNs affected by earthquakes by incorporating key resilience indicators, including emergency rescue accessibility, evacuation efficiency, and critical infrastructure support. A case study on the modified Sioux Falls transportation network demonstrates the model’s applicability, highlighting its ability to rapidly estimate network functionality and support emergency response operations. Importantly, the proposed approach is designed to be readily extendable to real-world networks once appropriate data is available, enabling practical, data-driven resilience assessment and decision support. Future work will focus on integrating real-time traffic and infrastructure data, refining surrogate modeling techniques, and addressing cascading failures and multi-hazard scenarios to further enhance emergency response capabilities.