1. Introduction
During urbanization and globalization, a substantial number of transportation infrastructures have been constructed worldwide [
1]. Among them, highway bridges play a critical role [
2]. For example, by the end of 2022, there are a total of 1.03 million highway bridges and 92 thousand railway bridges in China. Situated in regions prone to seismic activity of the Eurasian Plate and the Circum-Pacific Seismic Belt, these bridges are at risk of seismic damages. Regrettably, the effects of moderate and small-scale earthquakes tend to be underestimated due to their lower immediate damage. However, given their higher frequency—numbering in the hundreds annually—and the necessity for cities to promptly return to normalcy after such events, it is crucial for emergency response measures and regular operations to seamlessly coexist.
In fact, the advancements in modern seismic design standards considerably decrease the collapse probability of bridges, even under strong earthquakes with magnitudes (
Mw) larger than 7.0. However, recent earthquakes underscore that bridges remain vulnerable under moderate earthquakes. For instance, the Lushan earthquake (
Mw = 6.6) in 2013 [
3] and Luding earthquake (
Mw = 6.8) in 2022 [
4] caused damage to 440 bridges and 103 bridges, respectively, not only resulting in enormous economic losses, but also impeding restoration efforts. To make informed decisions on emergency response, it is imperative to (1) capture the seismic damages and (2) understand the related outcomes of bridges, especially within the critical post-earthquake “Golden 72 h” [
5]. Generally, regional bridges can only fulfill transportation functions when cooperating with highway segments into a highway bridge network (HBN) [
6]. They exhibit significant variations in site conditions, structural types, construction ages, service environments, etc. Coupled with inherent uncertainties, it is extremely difficult to account for all the influencing factors, making it intricate to predict the seismic responses of regional bridges [
7,
8].
Traditional seismic analysis methods were primarily developed for individual structures, relying on post-disaster investigations, experts’ opinions, numerical simulations, or structural health monitoring (SHM), etc. While these approaches provide valuable insights into the seismic performance of structures, their complexity and computational demands limit their effectiveness or accuracy when directly applied to region-scale bridges, each with unique characteristics and conditions [
9]. For instance, the current SHM techniques require numerous sensors and data acquisition devices [
10]. Numerical simulations based on finite element models (FEMs) cannot be easily conducted due to the enormous computational cost, especially when it comes to large-scale structures [
11]. To address these defects, several simplified methods based on statistics or intelligent algorithms have been specifically custom designed for regional bridges [
12,
13,
14]. They can quantify the probability in certain damage states of structures in terms of fragility curves, based on experts’ opinions, test data, or numerical results, etc. [
15,
16,
17,
18]. For example, HAZUS generated fragility curves for bridges across various groups. With the advancement of intelligent algorithms, artificial neural networks (ANNs), decision trees (DTs), etc., have exhibited superior nonlinear learning performance over traditional methods. In the case of available sufficient data, ANNs can model complex relationships between input parameters and structural behaviors (e.g., dynamic response [
19] and hysteresis [
20]) with high accuracy. DTs, on the other hand, can identify key influencing factors through segmenting data into subsets, such as to predict the seismic behaviors like damage states of structures [
17,
21]. Compared with traditional methods based on predefined equations and models, these machine learning-based methods are data driven, and require no prior knowledge, making them more promising for region-scale seismic analysis.
On the other hand, for safety, preventive traffic restrictions will be imposed on damaged bridges, potentially obstructing rescue and evacuation efforts over the HBN [
22]. Upon becoming aware of an emergency, the situation needs to be quickly assessed to determine the type and scope of the emergency. To capture updated disaster information, various emergency response systems have been developed worldwide, such as the Global Disaster Alert and Coordination System (GDACS,
www.gdacs.org accessed on 1 June 2016). However, most of the existing emergency responses lack explicit decisions based on historical emergency response events, which is necessary for realistic emergency response modeling [
23]. This is because earthquakes occur without warning, leaving little time for comprehensive planning [
24]. Limited information leads to decision making under incomplete knowledge, increasing the risk of errors. Processing and synthesizing this vast amount of information in real time poses a significant challenge. Moreover, large-scale bridge maintenance and repairing efforts are bound to impede highway traffic and economic development [
25].
Resilience has become increasingly popular owing to its ability to comprehensively account for a system’s robustness, rapidity, vulnerability, etc., in the recovery process [
26,
27]. Currently, resilience studies mainly focus on the holistic functionality and unexpected societal events under extreme disasters. Hosseini et al. [
28] proposed a probabilistic model to evaluate the network resilience of urban road networks. Kiremidjian et al. [
29] evaluated the seismic risk of transportation networks in terms of direct economic losses of bridges and indirect travel delays. The results demonstrated that the rare earthquakes with
Mw of 7.0 contribute more to seismic loss than the frequent earthquakes with smaller magnitudes (less than 6.0) in the SFBR. Nevertheless, post-earthquake investigations indicated that moderate earthquakes also tend to incur serviceability deterioration of HBNs [
30]. Even if structural damage may not be substantial, the lack of coordinated action of highway administrators may increase drivers’ insecurity and distress [
31,
32]. This will impede the operation of the HBN, further resulting in additional injuries and losses. In spite of these facts, to the best of the authors’ knowledge, there is limited literature on the emergency resilience of HBNs.
Recognizing the gap in current studies, this study aims to devise a rapid emergency response resilience assessment methodology for HBNs under moderate earthquakes. It applies an inter-disciplinary approach, combining FEM, intelligent algorithms, and traffic flow simulations. In the following sections,
Section 2 describes the flowchart of the proposed methodologies.
Section 3 provides an ANN-based method for a real-time seismic assessment of regional bridges, which is employed to capture their recovery processes. Additionally, in
Section 4, a DT-based approach is to determine potential responses using historical emergency data after extreme events. A comprehensive resilience vector is proposed for evaluating the emergency response of HBNs in
Section 5. Finally, the seismic emergency response resilience of the Sioux Falls HBN is investigated using the developed ANN and DT models, demonstrating their effectiveness.
3. Rapid Seismic Assessment of Regional Bridges
A comprehensive seismic assessment of bridges should indeed incorporate diverse characteristics that significantly impact their seismic behaviors. Traditional FEM-based techniques simulate their mechanical behaviors through a series of interconnected component elements. However, the identification of parameters for various structural components and dynamic analysis processes causes an enormous computational cost, especially when applied to regional bridges with large inherent uncertainties. It is not readily available in the immediate aftermath of an earthquake. To address that, simplified methods need to consider these characteristics and ensure that their effects are adequately captured.
3.1. Data-Driven Seismic Fragility
Fragility curves in the context of bridges typically refer to the condition probability of their components
ci being in a certain damage state given a specific intensity measure (
IM) of the ground motion excitation, i.e.,
[
7]. They can be determined by whether the seismic demands
exceed a certain limit state
, namely
[
33]. The pre-defined limit state of
describes the extent of damage that a bridge can withstand before it is considered unsafe or non-functional. Consequently, the key to bridge fragilities lies in the determination of
. Although spectral acceleration corresponding to the fundamental period of the bridge is more effective than other indicators, due to the need for modal analysis of the fundamental periods of regional bridges, the fundamental periods of different bridges are inconsistent. Additionally, regional bridges have a wide distribution, leading to significant differences in seismic intensity characteristics experienced by each bridge. This paper adopts the spectral acceleration corresponding to a period of 1.0 s (
Sa), which is commonly used in engineering [
34].
A data-driven seismic fragility surrogate method
is proposed in this study (
denote the ANN model). Furthermore, the regional highway bridge inventory should be first identified, including its geographical information, service environment, and structural properties. As illustrated in
Figure 2, this study focuses on the commonly used girder-type highway bridges; other types of bridges can be simulated following the same procedures. A typical girder-type highway bridge consists of superstructure (deck and girder), bearing, abutment, pier, and foundation. Subsequently, based on the mechanisms of bridge components, corresponding elements will be selected. By referring to the relative literature [
17,
35], the superstructure can be simulated by an elastic beam column element with distributed mass, representing the stiffness, strength, and mass of decks and girders [
33]. As for connection components, they can be modeled by zero-length elements with suitable materials. For example, the abutment, bearing, and foundation elements of girder-type highway bridges contain suitable hyperbolic–hysteretic–elastomeric bearing plasticity impact material [
36], hysteretic–elastomeric bearing plasticity [
33], and 6-DOF spring materials, respectively. Finally, a detailed three-dimensional FEM, including geometric nonlinearities like
P-
effects and Rayleigh damping, can be generated for bridge by integrating these elements.
Consequently, the influencing characteristics
of bridge
i are determined as the model parameters of critical components, as follows:
where
BN,
BL1, and
BW denote the span number, standard span, and deck width, respectively;
BST,
BA, and
BI represent the superstructure type, section area, and inertia moment, respectively;
BNb and
BKb are the number and stiffness of bearings, respectively;
BAT are the abutment type;
Bpn,
Bh,
BDc, and
Bpl denote the number of columns per pier, pier height, pier diameter, and longitudinal reinforcement ratio, respectively. Other parameters can be derived by (1) the above parameters, for example, the superstructure mass can be estimated as
Bpc ×
BL1 ×
BA (
Bpc is the concrete density); (2) MCS according to their engineering distribution, such as
Bpc following uniform distribution U(2250, 2750) kg/m
3, steel and concrete strength values following lognormal distribution LN(5.81, 0.1) MPa and normal distribution N(30, 4.5 MPa, respectively. For more details, please refer to [
21,
37].
3.2. Bridge Seismic Fragility Database Preparation
As mentioned above, the primary process of seismic damage analysis for bridges, which involves establishing a numerical model based on bridge characteristics , conducting incremental dynamic analysis (IDA) and probabilistic seismic demand (PSDA) for seismic responses and fragilities. To substitute for time-consuming numerical simulations, a data-driven surrogate seismic fragility model needs to be developed. For that purpose, a database with abundant bridge characteristics is crucial.
Figure 3 depicts the procedure for developing a seismic fragility database of bridges. A series of bridge characteristics were generated according to the potential engineering ranges of
. For example, the standard span length values of slab bridges and box-girder bridges are in the range of 5 m~15 m and 15 m~40 m, respectively. The potential span number is 2~7. The pier heights vary from 3.0 m to 9.0 m, with corresponding diameters ranging from 0.3 m to 2.0 m. The number of columns per pier is in the range of 1~5. They are paired with random parameters sampled according to their probability distributions, as outlined in
Table 1. Subsequently, these combinations undergo a checking step; anyone inconsistent with engineering reality would be rejected.
The remaining qualified combinations are then used to generate FEMs that are paired with ground motions for seismic assessment. A total of 1548 urban highway bridge specimens, covering the common engineering range and combination of bridges, are designed herein. After conducting time-history analysis using ground motions, the seismic demands and damage states of these bridges can be quantified.
To consider the time-frequency characteristics of seismic motion, the 160 ground motion records for seismic analysis of transportation systems are adopted herein [
40]. They cover the influencing characteristics of broadband ground motions at various sites, with
Mw ranging from 4.3 to 7.9. Each ground motion consists of two orthogonal components in horizonal directions, which were employed in IDA for bridges. Typically, acceleration time histories rather than displacements were imposed to the base nodes of the FEM, effectively simulating the seismic forces and their impact on the structural response. This method ensures a realistic representation of seismic activity and its effects on the bridge. Specifically, each suite of ground motions was scaled to a peak ground acceleration (PGA) of 0.1 g, 0.3 g, 0.7 g, 1.0 g, and 1.3 g. This scaling allows the bridge database to cover a wide range of seismic intensities, ensuring the developed ANN model’s generation ability. The Open System for Earthquake Engineering Simulation (OpenSEES) software (version: 3.6.0) [
41] is adopted herein. It provides a versatile and robust platform for numerical simulation in earthquake engineering research and practice. The peak seismic responses of critical bridge components are selected as seismic demands, as illustrated in
Table 2. For example, the curvature ductility of pier columns is utilized herein. Finally, by comparing their seismic demands and capacities, the seismic fragility curves of bridges can be established.
3.3. Training and Validation
A data-driven seismic fragility model essentially means to directly relate
with
, bypassing the need using numerical analysis. Considering the significant difference in the ranges and units of both
and
(
ci = 1,2,3,…,6), they are first normalized within the range of [0,1] by
where
and
denote the minimum and maximum value of the
j-th feature of all bridge specimens, respectively;
and
are the minimum and maximum value of the
ci-th seismic demands of all bridge specimens, respectively.
Therefore, 14 input neurons (i.e., bridge characteristics and IM) and 6 output neurons are determined. While deep neural networks like convolutional neural networks (CNN) and recurrent neural networks (RNN) excel in nonlinear representation capabilities, they require substantial training samples. The scale of the model parameters to be determined can be extremely immense, even reaching tens of thousands or billions. Moreover, CNNs are suitable for mesh data, while RNNs are more adept at temporal feature data. A three-layer fully connected ANN is suitable for regression analysis, with few model parameters and strong controllability. According to Kolmogorov’s theorem, this network can approximate any continuous function.
Firstly, 80% and 20% of the bridge samples were randomly divided into training and testing sets. To avoid overfitting of the model and ensure generalization performance, the
K–fold cross validation method is adopted, which randomly divides the training set samples into
K equal parts and takes turns as the validation set to validate the model trained with the remaining
K–1 ones. Each data point is used for validation exactly once and for training
Kv1 times, ensuring that the model is tested against all available data while still being trained on a substantial subset of the data in each iteration. In this study, the choice of
K = 10 is adopted for the following reasons: (1) bias-variance trade-off: fewer folds, such as 5-fold, might result in higher variance, while more folds, such as 20-fold, can increase the bias, as each training set becomes smaller; (2) computational efficiency: 10-fold cross-validation is computationally efficient, allowing for a thorough evaluation of the model without excessively increasing the computational burden. Then, the data of each neuron are weighted and activated and passed to the next layer until the output layer. The weights of each connecting layer are adjusted based on the error between the predicted value and the actual value, and the process is repeated until the termination condition is met (loss less than 10
−3 or iteration number reaches 10
3). The performance of the established model is evaluated using root mean square error (
) and goodness of fittness (
), as follows:
where
denotes the total sample number;
is the average of all samples.
After training, the optimal number of hidden layer neurons was ultimately selected as 50. The test results of this model are shown in
Figure 4. As can be seen, the
values of seismic demand prediction for the key components of bridges are between 0.03 and 0.08, and the
values are between 0.73 and 0.80. It can be seen that the ANN model can replace the IDA analysis method to accurately evaluate the seismic damage status of bridge structures. Moreover, once trained, the surrogate model no longer requires training. According to the predicted seismic demands, the damage states of components can be captured by comparing with limit states. As mentioned in
Section 3.1, the fragilities of the bridge, namely the probabilities of bridges being in a certain damage state, can then be determined,
. In this study, the damage states are divided into five groups: none (N), slight, moderate (M), extensive (E), and complete (C). The figures in
Figure 4 illustrate that the ANN-based fragilities compare well with their IDA-based counterparts.
Consequently, the ANN model for seismic demand assessment can provide bridge damage results within 1 s, achieving rapid seismic evaluation of regional bridges. In contrast, the IDA method requires several hours to analyze a single bridge, highlighting the superiority of ANN methods in terms of computational cost.
3.4. Normalized Recovery Process of Damaged Bridges
The functionality of bridges primarily revolves around their traffic capacity (TCB), maximum traffic speed (TSB), and other aspects, all of which are tied to the connectivity of the surrounding roads. In response to seismic damage on bridges, safety measures will be enacted to safeguard motorway users. These precautions might involve lane closures, partial or complete bridge shutdowns, and the imposition of speed limits. While these proactive measures are crucial for minimizing hazards and ensuring the safety of all motorists on the affected roadway, it is important to acknowledge that they will inevitably impact the traffic capacity of bridges. This can lead to traffic congestion and related issues.
The traffic restrictions (
TRB) are categorized into five categories: unrestricted (
TRB = 0), speed limit (
TRB = 1, limit free-flow speed), lane closure (
TRB = 2, only one lane is retained, allowing normal speed), speed limit and lane closure (
TRB = 3, one lane is retained, limiting free-flow speed), and complete closure (
TRB = 4). Based on these categories, the residual traffic capacity (
) and speed (
) of the damaged bridge can be determined as
where
and
represent residual rates of traffic capacity and free-flow speed at time
t, respectively;
r(
t) is the functional recovery process function that considers bridge damage states, emergency repair measures and resources;
and
are model parameters, which need to be adjusted according to the actual situation;
t0 is the time of earthquake occurrence, initiating the need for emergency response and recovery operations;
t represents the elapsed time since the earthquake occurred, i.e.,
t =
t −
t0, tracking the progression of response activities;
th is the duration of the emergency response phase, which can be determined based on the survival function
[
23] (probability of survival after a disaster). For instance, if
S(
t) drops below a certain threshold, emergency responses might be considered at the end, as this indicates a significant decline in the likelihood of finding survivors. This threshold-based approach ensures that critical rescue efforts are prioritized while effectively transitioning to recovery operations when the probability of survival becomes minimal. In this study, the threshold of 0.01% is established as the point at which large-scale emergency rescue and evacuation operations are discontinued. Beyond this threshold, the primary focus shifts towards recovery and reconstruction efforts. Notably, establishing this threshold using real-world observations and historical data would ensure that it is both practical and effective. By analyzing past emergency response outcomes and survival rates, a more accurate and justifiable threshold can be determined, which would enhance the decision-making process during large-scale emergencies. The model parameters
,
, and
are taken as 0.99, −0.005, and 2.17, respectively, with a
th of 32.0 h. Referring to the commonly used evaluation function of the Highway Capacity Manual [
42], the time required for traffic flow
TfB, defined as the number of vehicles passing through the bridge per unit time (pcu/h), is calculated as follows:
4. Intelligent Emergency Response Decision
Unlike losses resulting directly from earthquakes, sudden disasters exhibit localized characteristics, often occurring within one or a few specific regions [
43], and are characterized by their abrupt and stochastic nature, making them challenging to evaluate using traditional deterministic or probabilistic statistical methods.
4.1. Historical Emergency Incident Database
There are a variety of potential sudden disasters following an earthquake, such as fires and explosions. Optimal emergency response strategies primarily rely on rapid organization and response. However, these incidents exhibit both universality and variability in spatial distribution, alongside randomness, disorderliness, and instability in temporal dimension. Currently, there is a deficiency in a mechanism for recording and disseminating information throughout the entire course of sudden disasters. The time constraints, communication challenges, and the complexity of post-disaster emergency scenarios often result in vague and challenging-to-quantify information. This entails determining the scope of impact based on the urgency and danger of these disasters, implementing measures to concentrate disaster management efforts, and preventing its spread.
According to the Emergency Response Law of the People’s Republic of China, “emergencies are categorized into four levels based on the post-disaster statistical losses, namely, extremely severe (I), severe (II), significant (III), and general (IV).” Different authorities will implement disposal measures accordingly. Nevertheless, it is impractical to calculate the induced losses or casualties in the post-earthquake emergency response stage. This will hinder real-time relief efforts to these events. To address that, abundant historical emergency events were investigated, and collected into a database. As illustrated in
Figure 5, the factors that may have an impact on the entire emergency response process are classified into three groups: pre-disaster, disaster occurrence, and emergency response. Since urgency demands immediate action, limiting the availability of extensive data, these factors are quantified based on types or levels rather than detailed values, as follows:
- (1)
Pre disaster: city level (city level of the disaster site, where I~IV represent first-tier cities, second-tier cities, third-tier cities, and other cities, respectively); distance from the hospital (distance between the disaster site and the nearest hospital, where I~IV represent >10 km, 5~10 km, 2~5 km, and 0~2 km, respectively); distance from rescue agencies (distance between the accident site and the nearest rescue department, where I~IV represent >10 km, 5~10 km, 2~5 km, and 0~2 km, respectively); attributes of the location (category of disaster location, I~V represent commercial/industrial areas, cultural and educational/residential areas, warehousing or development areas, comprehensive areas, and others, respectively); local road network density (road density at the location of the accident, where I~IV represent >6 km/km2, 5~6 km/km2, 4~5 km/km2, and <4 km/km2, respectively).
- (2)
Disaster occurrence: death toll (number of casualties directly caused by disasters in the first time, I~IV represent ≤3, 4~10, 10~30, and >30, respectively); number of injured individuals (number of injured/trapped people in the first instance of a disaster, I~IV represent <10, 10~50, 50~100, >100, respectively); number of people affected by the disaster (number of people affected by disasters, I~IV represent >105, 104~105, 103~104, <103, respectively); scope of impact (impact scope of the accident, I~IV respectively represent the entire city, a region/CBD, a community/park/multiple main roads, a building/a road, respectively).
- (3)
Emergency response: emergency response time (time elapsed from the occurrence of a disaster to the initiation of emergency rescue measures, where I~V represent within 3 min, 3~15 min, 15~30 min, 30 min~2 h, and >2 h, respectively); reserved material (reserved materials for responding to sudden disasters, where I~III represent “far exceeding demand”, “basically met”, and “lacking”); duration time (expected duration time from the commencement to the conclusion of emergency measures, where I~V represent within 30 min, 30 min~4 h, 4 h~12 h, 12 h~24 h, and >24 h, respectively); accident evolution (occurrence probability of derivative/secondary hazardous accidents, where I~V represent <0.1%, 0.1%~1%, 1%~10%, 10%~20%, and 20%~50%, respectively); environment condition (weather or driving conditions, I~IV represent good, average, poor, and severe, respectively).
In addition, it is necessary to collect post-disaster statistical results:
(number of injuries),
(number of deaths), and
(economic losses), in order to determine the emergency level (
EL) of the disaster. Based on the above analysis, containing 63 emergency events, including the “6.21 Yinchuan Barbecue Shop Explosion”, “4.18 Beijing Changfeng Hospital Fire”, and “8.31 Shanghai Liquid Ammonia Leakage”, have been collected. Due to space limitations, the established databases were uploaded at the website (
https://github.com/liuzhenliangstd/EmergencyEventCollection 1 June 2024). And more information can be found by referring to the source website (
https://www.ccdi.gov.cn/, accessed on 1 June 2024).
4.2. Decision Tree Based Traffic Demand Generation
The primary purpose of an HBN is to fulfill transportation demands. such as the circulation of personnel and materials among regions. This means meeting the traffic demand (vi and vj are region nodes). Therefore, the specific emergency response measures and means are out of the investigated scope herein. This study explores the feasibility of utilizing a DT methodology to assess the emergency level. By employing this approach, the relevant authorities can be identified, as well as the potential increase in traffic demand (traffic attraction and generation ).
The analysis of the emergency level of sudden disasters is essentially a classification problem. The DT algorithm was applied to learn from the emergency event database data. DT is a non-parametric machine learning algorithm similar to tree decision making (consisting of a root node, several internal nodes, and leaf nodes), with strong interpretability and insensitivity to outliers. 50 and 13 of the emergency data were first randomly divided for training and testing, respectively. Each observation consists of a vector
x of inputs (the influencing factors) and an output
y (emergency level), as follows:
where
and
represent the predicted emergency level and actual level of the event, respectively.
Training a DT model to predict the emergency level is a classification problem. It begins with creating a root node
Droot. Subsequently, the training data are grouped based on the Gini coefficient and trained to form a root node. And by gradually segmenting the dataset, a series of internal nodes output binary classification results, up to the leaf nodes, to obtain
. Corresponding to the prediction, the cost function is used to measure the error. The change in prediction error due to the split is measured by assessing the reduction in cost achieved by splitting the root node. As shown in
Figure 6a, the established DT model quickly and accurately identifies the emergency level of the events. The predicted results of the 42 events of the 50 ones in the training set and 4 events in the test set are consistent with the actual results, with an accuracy rate of about 80%. The inconsistencies in predictions may be attributed to variability in rescue efforts, data limitations, unpredictable random factors such as weather conditions, human errors, model simplification, and the dynamic nature of the emergencies. To address these issues, more detailed rescue data of high accuracy and quality are required to enhance the model’s capabilities. Additionally, implementing models that continuously learn and adapt to real-time updated data and situations can capture the emergencies better. Despite these limitations, the developed DT model can still provide a reasonable evaluation of the level of disaster accidents at the first moment of a disaster.
In addition, the specific allocation plan varies depending on the needs and situations of different regions and institutions. The response speed of emergencies is divided into three categories: i (fast), ii (fast), and iii (general), which will lead to varying degrees of traffic generation increase
and attraction increase
. Consequently, based on pre-earthquake traffic generation and attraction
, as well as the speed of rescue work in each region, the post-earthquake traffic demand
of the HBN can be adjusted. As illustrated in
Figure 6b, post-earthquake traffic demand typically increases due to emergency responses, evacuation needs, and recovery operations, which is a realistic assumption reflecting real-world scenarios. The traffic demand increment depends on the severity of the emergency level, with higher levels indicating more critical situations requiring greater traffic flow. This relationship shows that traffic demand surges from baseline pre-earthquake levels to peak demand at the highest emergency levels. While the figure provides a reasonable assumption of this increment, actual traffic demand levels are typically specified by stakeholders based on local conditions and specific emergency plans. This understanding is crucial for effective resource allocation, emergency response planning, and ensuring infrastructure resilience to manage increased traffic demand during and after an earthquake.
4.3. HBN Emergency Response Model
The pre-disaster traffic demand can be evaluated according to the transportation gravity model, (where and represent traffic generation and attraction, respectively; and are equilibrium coefficients; is the traffic impedance coefficient between vi and vj). For simplicity, the following assumptions are utilized regarding the post-disaster emergency response scenarios:
- (1)
Inventory information access: the decision-making department can acquire inventory information of emergency material points, meaning the relevant authorities have comprehensive data on available emergency supplies and resources.
- (2)
Emergency report: responsible persons in each region can promptly report information as per the actual situation; this suggests that there is efficient communication and reporting mechanisms in place to relay information about the emergency status.
- (3)
Emergency response in HBNs: the focus of the emergency response scenario is solely on traffic-related aspects that depend on the Highway Bridge Network (HBN) transportation; other aspects such as material transportation decrease, and social organization capacity are not considered in this scenario.
- (4)
Material allocation: material allocation decisions prioritize fairness (maximizing demand rate) and efficiency (minimizing time), rather than economy and environmental protection, etc.
- (5)
Travel path selection: all vehicles opt for the shortest available path on the primary transportation routes provided by the HBN.
These assumptions help define the scope and context of the emergency response scenario, providing clarity on the factors considered and the limitations of the model. Based on these factors, the post-earthquake emergency response within an HBN can be simulated.
As shown in
Figure 7a, for a hypothetical area connected by an HBN, the research area can be divided into several sub-areas according to the administrative division criteria. Each one is represented by a node
vi. Then the area can be formed into a node set
V = {
vi}. Additionally, the main road connecting region
vi and
vj is represented by the connecting edge
eij. All of the road segments can be formed into an edge set
E = {
eij}. A graph model
G = {
V,
E} of the HBN can be established. The weights of the edges are the traffic capacity
TC(
eij) and time
Tt(
eij), which will be updated in the recovery process according to Equation (4). Subsequently, for each node
vi, as the starting point (O) and destination point (D), the incremental traffic allocation method is used to select the minimum travel time route for the traffic demand between each OD set, as shown in
Figure 7b. The OD traffic demand is divided into
Nq subsets, each of which will be assigned to the fastest path step by step. Each subset represents a fraction of the total traffic demand among OD. During that process, the travel time of the roads will be continuously updated according to Equation (5), such as to account for the additional traffic time caused by the newly assigned traffic load. By continuously updating the travel times, the model ensures that each subsequent subset of traffic is routed based on the most current conditions, thereby optimizing the overall traffic distribution across the network. The travel time
T1(
eij) of the link
eij can be updated based on traffic flow
and capacity
(
and
are the number of lanes and capacity per lane, respectively).
Finally, the travel time and operational status of HBNs can be simulated, such as to evaluate their functionalities as follows:
6. Application to HBN Case Studies
6.1. Regional Seismic Hazard and Bridge Damage State
The seismic emergency resilience of the Sioux Falls network is analyzed to verify the proposed methodologies. This HBN includes a variety of road types and intersections. To align with its scale and complexity, its location is assumed to be a second-tier city. Second-tier cities usually have a population and traffic volume that is significant but not overwhelming, enabling detailed analysis without the computational intensity required for larger metropolitan areas. As shown in
Figure 9, the HBN connects 24 regions through 38 highway segments. The network is composed of various types of regions as follows:
- (1)
Nodes 1, 2, 3, 7, 8, 12, and 18 are industrial areas;
- (2)
Nodes 4, 5, 6, 9, 14, and 16 are commercial areas;
- (3)
Nodes 13, 21, and 24 are storage/development areas;
- (4)
Nodes 15, 17, 20, and 22 are comprehensive areas;
- (5)
Nodes 11 and 19 are schools and sports fields (used as emergency evacuation points in emergency stages);
- (6)
Node 10 is the location of the hospital;
- (7)
Node 23 is the location of the fire brigade.
The pre-earthquake traffic generation and traffic attraction of each regional node range from 1280 pcu/h to 5740 pcu/h. To reflect the diversity of road segment characteristics in the bridge network, appropriate adjustments have been made to the basic road features. The number of lanes is 2–6, the width is 3.75 m per lane, the basic free flow capacity is 2200 pcu/h, and the free-flow speed is 80 km/h. Based on this, the HBN node set V, connection matrix E, traffic demand Q among different regions, traffic capacity TCB of each section, and maximum traffic speed TSB can be determined. By combining the network topology structure, the functionalities of the HBN can be simulated using the previous method. As can be seen, the majority of the highway sections had a congestion rate smaller than 1.0 and an average speed of larger than 75 km/h before the earthquake. All of the traffic demands can be met.
In addition, the HBN includes 23 bridges with a designed service life of 100 years, currently ranging in age from 10 to 60 years, as illustrated in
Table 3. This analysis does not account for the impact of maintenance measures on each bridge during its service life. The atmospheric chloride ion concentration and chloride ion diffusion coefficient in the service area are 2.95 kg/m
3 and 129 mm
2/year, respectively. The site category in this area is Class B, with an average shear wave velocity of 450 m/s within 30 m, mainly threatened by the northeast reverse fault in the area. This study simplifies it as an earthquake caused by seismic motion at the epicenter of the region, with an average rupture angle of 75° and a depth of 10 km. The Richter scale is 7.0 (
Mw = 7.0).
6.2. Seismic Damage Distribution of Regional Bridges
According to the seismic source characteristics, the potential seismic sources can be identified. The likelihood of seismic motion intensities is then quantified using the Probability Seismic Hazard Analysis (PSHA) method. The distance from the epicenter to each bridge site is calculated to reflect the seismic wave amplitude propagation. Subsequently, the Ground Motion Prediction Equation (GMPE) is used to estimate the expected
IM at each bridge location under seismic motion. Combining the contributions from all seismic sources, the probability of exceeding various levels of
IM at each bridge site can be estimated. Given the necessity for a micro-level analysis of the seismic performance of regional bridges, this paper chooses the GMPE model proposed by Kumar et al. [
46]. This model is based on a large number of shallow seismic records, with good fitting results, and is suitable for the area where the bridge network is located, as shown below:
where
Mw is the magnitude,
RJB is the epicenter distance, and
is the total standard deviation of the prediction model, taken as 0.281. In order to consider the uncertainty of seismic motion, 10
3 sets of seismic motion
Sa values were generated through MCS to simulate earthquake scenarios for regional bridge seismic damage analysis.
To obtain the evolution process of the seismic emergency resilience of the HBN during its service life, the earthquake occurrence time
t0 is taken as five time points: 0 years, 10 years, 20 years, 30 years, and 40 years later. For each time point, the time-varying performance of each bridge during its service life is determined based on the performance degradation model. This article mainly considers the mechanical attenuation mechanism of bridge pier columns caused by environmental corrosion. According to the degradation mechanisms proposed by Ghosh et al. [
47], the model parameters of bridges can be updated. In this model, when chloride ions permeate the concrete cover, namely
t >
Tini, the steel bars start to corrode, leading to a decreasing longitudinal reinforcement ratio
. This approach enables the prediction of the evolving seismic fragilities of the bridges, highlighting the impact of long-term environmental exposure on their structural performance.
In order to account for the inherent uncertainties, MCS is used to sample each bridge and simulate the degradation process of each bridge’s characteristics, thereby establishing 10
3 bridge samples. Combined with seismic intensity samples, 10
6 bridge seismic samples were obtained. This process requires creating finite element models and conducting extensive seismic time history analyses using the conventional IDA method, rendering long-term seismic performance analysis of regional bridges nearly impractical. Alternatively, the established ANN model for seismic analysis was then used to predict the seismic damage states and probability of key components of regional bridges in the HBN. The figures in
Figure 10 depict the time-varying seismic damage probabilities of bridge piers. It can be observed that environmental corrosion increases the probability of damage to bridges. For example, during the 0–40 year service life, the probabilities of slight and severe damage to the piers of bridge B1 action increased from 0.105 and 0.027 to 0.110 and 0.028, respectively, while the probabilities of slight and severe damage to the piers of bridge B6 increase from 0.102 and 0.017 to 0.114 and 0.024, respectively. Notably, there is a decrease observed in the probability of certain damage levels in some cases, such as the probabilities of B5 and B8 in moderate damage state. This can be attributed to changes in specific structural characteristics of the bridge over its service life. For example, corrosion-induced degradation will lead to a decrease in the reinforcement ratio of bridge piers, which can significantly affect the bridge’s response to seismic excitations. If the bridge’s response undergoes a sharp increase, surpassing the limit states for moderate damage, and tends to increase dramatically, exceeding the limit states of moderate damage, the probabilities of moderate state will decrease. However, this may cause the bridge to experience severe or complete damage, leading to an increase in the probabilities of extensive or complete damage. In summary, the developed ANN surrogates can capture complex effects of various factors, providing the evolving seismic behaviors of bridges.
Based on the damage to key components of bridges and the resulting traffic restrictions, the traffic capacity of the highway segment where the bridge is located can be evaluated. This helps determine the process of restoring the traffic function of the damaged bridge.
6.3. Seismic Emergency Resilience during Service Life
Using the previous methods, the post-earthquake emergency level and functionality recovery process of the HBN were investigated. And the satisfaction of different traffic emergency needs under earthquake action at different time points was analyzed. The seismic emergency resilience of the HBN was obtained, which took about 107 min (with an average simulation time of about 0.07 s). It can be seen that the intelligent analysis model can achieve rapid evaluation of seismic resilience of HBNs, which is crucial for timely and effective emergency response and recovery planning.
Figure 11 shows the analysis results and distribution of emergency resilience indicators
R1 and
R2 of the HBN, which predominantly range between 0.68 and 1.0. It can be seen that under the assumed earthquake scenario, the HBN is highly likely to meet the traffic demand, with a 67.8% probability of
R1 exceeding 0.9 at the current stage. However, special attention should still be paid to some special situations, such as when bridge B1 and B11 are completely destroyed simultaneously. This will cause zone 1 (node 1 in the HBN) to be isolated from other areas, reducing the resilience value to less than 0.5, and greatly hindering seismic rescue efforts. This highlights the need to prioritize the maintenance and retrofitting of critical bridges, such as B1 and B11, whose failure would severely disrupt network connectivity. Ensuring these key structures are resilient can prevent the isolation of critical zones.
In addition, for overextended service periods, the emergency performance of the HBN will deteriorate, and the discreteness will gradually increase. For example, R1 mean μ decreases from 0.911 to 0.853, while standard deviation σ increases from 0.099 to 0.134. This is because during long-term service, the degradation process and mechanical performance of different bridges have significant discreteness, which has an increasing impact on the seismic performance of bridges, leading to an increase in the discreteness of toughness analysis. The degradation patterns of different seismic emergency resilience indicators also differ. Notably, the mean (μ) and standard deviation (σ) of R2 changed from 0.906 to 0.846 and from 0.105 to 0.142, respectively. The results suggest the need for long-term planning and investment in bridge maintenance. Incorporating resilience criteria into these standards can ensure that future infrastructure is better equipped to withstand seismic events. Therefore, regular inspections and upgrades should be scheduled to address the gradual degradation of bridge performance and ensure sustained resilience over time.
Overall, the intelligent evaluation method established in this article can quickly and accurately assess the seismic emergency resilience of HBNs throughout their service life. In practical engineering applications, this method allows for the analysis of emergency resilience under various seismic conditions (such as magnitude, site, epicenter distance, and source depth) and service environments. It comprehensively deduces the process of emergency resilience changes and studies the impact of different emergency strategies on resilience. This approach provides a robust decision-making basis for formulating emergency plans and strategies for disaster prevention and mitigation.