An integrated framework for bridge infrastructure resilience analysis against seismic hazard

Figures & data

Figure 1. Flowchart of the bibliometric analysis by using VOSviewer.

Figure 2. The bibliographic map generated using VOSviewer on bridge infrastructure resilience.

Figure 3. The bibliographic map on bridge infrastructure resilience using decision-making tools.

Table 1. Different infrastructure resilience index.

Title	Type of Infrastructure	Hazards considered	Approach/Methodology	Ref
Resilience Index	Multimodal Transportation Facility	Natural, intentional, and technogenic disasters and failure due to poor design	Graph theory	Okine and Burden (2005)
Resilience Index	Urban highway Infrastructure network	Cascading and Escalating effect due to interdependencies, Common cause (natural disasters)	Belief function	Attoh-Okine et al. (2009)
Community Resilience Index	Road Network System	Natural hazards (Flooding & Earthquakes)	Graph theory	Gian Paolo Cimellaro et al. (2011)
Resilience Index	Urban Water Distribution Networks	Seismic hazards	Mathematical function considering three indices	Cimellaro et al. (2016)
Network Resilience Index	Road Network System	Hazards induced bridge damages	Scenario-based traffic modeling and GIS techniques	Twumasi-Boakye and Sobanjo (2018)
Resilience index	Infrastructure Asset Bridges and Road Network	Seismic Effect	Realistic fragility curves and the rapidity of the recovery and retrofitting	Nasiopoulos et al. (2019)
Resilience Index	Critical Infrastructure: Highway Bridges	Multiple Natural Hazards like Floods, Earthquake.	realistic fragility functions & realistic restoration functions	S. Argyroudis et al. (2019)
Robustness index	Structures: Truss & moment-resistant Frame	progressive collapse failure	damage evolution curve	Praxedes et al. (2020)
Evaluation Index	Road Network	Impact of failure probability bridges due to natural hazards on Road Network	Genetic Algorithm	Ishibashi et al. (2020)
Asset Resilience Index	Critical Infrastructure like Railway, Highway, Electric Power, Bridges, Airports, Ports, Gas.	Multiple Natural Hazards like Floods, Earthquake.	Development of realistic fragility and restoration functions for individual and combined hazards	Argyroudis et al. (2020)
Bridge Resilience Index	Bridge infrastructure	Floods	MCDM tools (AHP & TOPSIS)	Patel et al. (2020)
Bridge Damage Index	Highway Bridge Network	Natural Disaster (Earthquake)	Integer Program which is intervened by incorporating a Hybrid genetic algorithm coupled with an early termination test	Zhang and Wei (2021)
Cost-based Resilience Index	Bridge infrastructure	Seismic/Earthquake	realistic fragility functions & realistic restoration functions	Argyroudis et al. (2021)
Detour-Impact Index	Rural Road Network	Hazards due to a bridge collapse	traditional network-impact metrics in combination with a new algorithm	Pucci et al. (2021)

Figure 4. Infrastructure’s performance during its service life (modified after Sen et al., 2021bb).

Table 2. Key resilience factors of civil infrastructure against natural hazards (Khan et al., 2022).

Theme of the study	Factors of resilience	Reference
Framework for evaluating Resiliency of housing infrastructure against flood	Reliability Recovery	Sen et al., 2021
Resiliency analysis of Urban Transportation Systems using hierarchical Bayesian network model (BNM)	Resistance Re-stabilization of critical functionality Rebuilding of critical functionality Reconfiguration after recovery	Tang et al., 2020
Seismic resilience evaluation using fuzzy sets theory.	Residual Functionality Target Functionality Idle time interval Recovery time	Andrić & Lu, 2017
Structural resilience analysis against natural hazards	Preparedness Management Risk Analysis	Mebarki et al., 2016
Review paper on identifying the major factors of civil infrastructure resilience	Risk Assessment Disasters Risk Management Climate change Water resources Economic & Social resources Decision making Strategic Planning Sustainable development Water supply	Gay & Sinha, 2013
Framework for resilience assessment of single systems to interdependent systems	Disaster prevention Damage propagation Assessment & Recovery	Chang et al., 2012

Figure 5. Bridge infrastructure resilient hierarchy system against seismic hazard (Khan et al., 2022).

Table 3. Bridge infrastructure resilience parameters under reliability factor (Khan et al., 2022).

Parameters	Descriptions of Parameters	Reference
Foundation (Prel1)	Foundation, Abutment, Bearing, Piers, Girder & In-span joints are major structural components of bridges. The overall performance of bridge relies on these component’s condition jointly as well as separately.	Venkittaraman & Banerjee, 2014; Zheng et al., 2018; Nielson & Desroches, 2007; Khan, Etonyeaku et al., 2022
Abutment (Prel2)
Bearing (Prel3)
Piers (Prel4)
Girder (Prel5)
In-span joint (Prel6)
Age (Prel7)	Bridge structure is designed for certain design life. It is expected that newly constructed structures perform better than older structures	Dong & Frangopol, 2015; Vishwanath & Banerjee, 2019;
Design period (Prel8)	The seismic design provisions during the structural design changed over time. Like the Bridges, designed prior to 1970, did not have any seismic detailing. In 1970–1990 have some seismic consideration but no ductile mechanisms, post 2000 design were done with ductile mechanism.	Mitchell et al., 2010; Ramanathan et al., 2015; Shekhar et al., 2020
Bridge geometry (Prel9)	Bridge geometry is important for resilience. Curved and Skewed bridges are more susceptible to (seismic) damage than straight bridges.	Tavares et al., 2012; Kaviani et al., 2012

Table 4. Bridge infrastructure resilience parameters under-recovery factor (Khan et al., 2022).

Parameters	Descriptions	Reference
Structural Monitoring (Prec1)	Structural Monitoring is part of risk assessment. Regular monitoring of a bridge infrastructure can give the conditions of the bridges continuously and help to diagnose problems immediately after incidents that make the recovery process faster.	Gay & Sinha, 2013; Mebarki et al. 2014
Maintenance (Prec2)	Maintenance is part of management. If the bridge is maintained and managed in well and regular manner, the recovery would be faster.	Mebarkis et al. 2014
Degree of damage (Prec3)	Recovery depends upon the degree of damage, i.e., the higher the degree of damage, the lower the rate of recovery.	Ouyang & Wang, 2015
Importance of the structure (Prec4)	Structural importance is one of the most important factors for the decision makers whether and to what extent they will take actions to recover a damaged bridge or not	Gay & Sinha, 2013
Availability of Resource (Prec5)	Lack of construction material supplies decelerates the recovery process.	Sen et al., 2021aa & Sen et al., 2021b
Approachability (Prec6)	Bridge infrastructure reconstruction or repair works needs heavy and delicate equipment along with raw materials. Difficulties in accessibility to the bridge location affect the recovery process.	Sen et al., 2021aa & Sen et al., 2021b

Figure 6. Stages of framework for seismic resilience of bridge infrastructure.

Figure 7. Resilience Framework of a Generic HER model.

Table 5. Details of experts.

Experts	Profile	Experience	Roll of Work/Designation
Expert 1	PhD, P.Eng.	11 years	Assistant Professor, Structural Engineering Dept. & Ex-Bridge Design Engineer
Expert 2	M.Sc., P.Eng.	30+ years	Senior Principal Engineer (Transportation Structure)
Expert 3	M.Sc.	11 years	Bridge Design Engineer, Govt. Transportation Agency
Expert 4	M.Sc.	10 years	Project Manager, Govt. Transportation Agency
Expert 5	M.Sc.	10 years	Researcher, Bridge Engineering & Former Bridge Design Engineer, Govt. Transportation Agency

Table 6. The best and worst parameters according to different experts’ opinion (Khan et al., 2022).

Cluster	Name of Parameters	Best Parameter	Worst Parameter
Reliability	Foundation (Prel1)
	Abutment (Prel2)
	Bearing (Prel3)
	Piers (Prel4)	Ex-4
	Girder (Prel5)		Ex-1 &5
	In-span joint (Prel6)		Ex-2 & 3
	Age (Prel7)
	Design period (Prel8)	Ex-1, 2, 3 & 5
	Bridge geometry (Prel9)		Ex- 4
Recovery	Structural Monitoring (Prec1)
	Maintenance (Prec2)
	Importance of the structure (Prec3)	Ex-2
	Availability of Resource (Prec4)		Ex-4
	Approachability (Prec5)		Ex-1, 2, 3 & 5
	Degree of damage (Prec6)	Ex-1, 3, 4 & 5

Table 7. The rating of the best parameter over other parameters under reliability (Khan et al., 2022).

Best to others	Prel1	Prel2	Prel3	Prel4	Prel5	Prel6	Prel7	Prel8	Prel9
Expert −1	8	5	4	2	9	7	3	1	6
Expert −2	3	3	4	2	3	7	3	1	3
Expert −3	7	6	4	2	8	9	3	1	5
Expert −4	5	7	6	1	2	8	3	4	9
Expert −5	8	5	4	3	9	7	2	1	6

Table 8. The rating of the best parameter over other parameters under recovery (Khan et al., 2022).

Best to others	Prec1	Prec2	Prec3	Prec4	Prec5	Prec6
Expert −1	5	4	2	3	6	1
Expert −2	2	2	1	4	9	2
Expert −3	5	4	2	3	6	1
Expert −4	6	4	2	5	3	1
Expert −5	4	2	5	3	6	1

Table 9. The other parameters’ priority over the worst parameter under reliability (Khan et al., 2022).

Others to the Worst	Prel1	Prel2	Prel3	Prel4	Prel5	Prel6	Prel7	Prel8	Prel9
Expert −1	3	5	6	8	1	2	7	9	4
Expert −2	7	7	7	8	7	1	7	9	8
Expert −3	3	4	6	8	2	1	7	9	5
Expert −4	5	3	4	9	8	2	7	6	1
Expert −5	2	4	5	7	1	2	8	9	3

Table 10. The other parameters’ priority over the worst parameter under recovery (Khan et al., 2022).

Others to the Worst	Prec1	Prec2	Prec3	Prec4	Prec5	Prec6
Expert −1	2	3	5	4	1	6
Expert −2	2	3	9	6	1	7
Expert −3	2	3	5	4	1	6
Expert −4	1	3	5	2	4	6
Expert −5	3	5	2	3	1	6

Table 11. The weights of the parameters as per each expert under reliability.

Parameters	Prel1	Prel2	Prel3	Prel4	Prel5	Prel6	Prel7	Prel8	Prel9	C.R.
Expert −1	0.048	0.077	0.096	0.192	0.027	0.055	0.128	0.315	0.064	0.068
Expert −2	0.103	0.103	0.077	0.154	0.103	0.022	0.103	0.232	0.103	0.077
Expert −3	0.055	0.064	0.096	0.192	0.048	0.027	0.128	0.315	0.077	0.068
Expert −4	0.077	0.055	0.064	0.315	0.192	0.048	0.128	0.096	0.027	0.068
Expert −5	0.048	0.076	0.096	0.127	0.028	0.055	0.191	0.316	0.064	0.066
Geometric Mean	0.067	0.078	0.091	0.200	0.063	0.041	0.143	0.251	0.066

Table 12. The weights of the parameters as per each expert under recovery.

Parameters	Prec1	Prec2	Prec3	Prec4	Prec5	Prec6	C.R.
Expert −1	0.089	0.111	0.221	0.148	0.053	0.379	0.063
Expert −2	0.136	0.167	0.348	0.106	0.030	0.212	0.076
Expert −3	0.089	0.111	0.221	0.148	0.053	0.379	0.063
Expert −4	0.053	0.111	0.221	0.089	0.148	0.379	0.063
Expert −5	0.109	0.219	0.088	0.146	0.055	0.383	0.055
Geometric Mean	0.095	0.145	0.212	0.131	0.061	0.356

Table 13. Resilience, reliability and recovery and all the parameters’ frame of discernment.

Factors	Frame of Discernment	Narration
Resilience	Poor	0 to 33% probability that the bridge can withstand seismic hazard and can return to its former state prior to the disaster.
	Moderate	34 to 66% probability that the bridge can withstand against seismic hazard and can to its former state prior to disaster.
	Excellent	67 to 100% probability that the bridge can withstand seismic hazard and can return to its former state prior to the disaster.
Reliability	Poor	The bridge is fully damaged (0 to 33%).
	Moderate	Moderate damage done requires some maintenance work (34 to 66%).
	Excellent	Minor damage, no or slight maintenance is required (67 to 100%).
Recovery	Poor	0 to 25% of full recovery
	Moderate	26 to 75% of full recovery
	Excellent	76 to 100% percent of full recovery
Reliability Parameters
Parameters	Frame of Discernment	Narration
Foundation	Poor	Foundation collapse
	Moderate	Moderate damage
	Excellent	Slight or no damage
Abutment	Poor	Abutment collapse
	Moderate	Moderate damage
	Excellent	Slight or no damage
Bearing	Poor	Complete damage bearing
	Moderate	Moderate damage
	Excellent	Slight or no damage
Piers	Poor	Pier collapse
	Moderate	Moderate damage
	Excellent	Slight or no damage
Girder	Poor	Girder Collapse
	Moderate	Moderate damage
	Excellent	Slight or no damage
In-span joint	Poor	Complete Damaged In-span joint
	Moderate	Moderate damage
	Excellent	Slight or no damage
Age	Poor	>50 years
	Moderate	>25 years to 50 years
	Excellent	<25 years
Design period	Poor	Designed prior to 1990
	Moderate	Designed from 1990 to 2000
	Excellent	Designed after 2000
Bridge geometry	Poor	Skewed
	Moderate	Curved
	Excellent	Straight
Recovery Parameters
Parameters	Frame of Discernment	Narration
Monitoring	Poor	Lack of Monitoring
	Moderate	Monitoring every five years
	Excellent	Continuous Monitoring
Maintenance	Poor	No Maintenance
	Moderate	Reactive Maintenance
	Excellent	Pro-active maintenance
Importance of Structure	Poor	Bridge located in a remote place
	Moderate	Bridge located in the major route
	Excellent	Bridge located in the lifeline
Resource Availability	Poor	Resource is not available
	Moderate	Resource is not available in a nearby place
	Excellent	Resource is available
Approachability	Poor	Difficult to access the bridge location
	Moderate	Slightly difficult to access the bridge location
	Excellent	Easy access to the bridge location
Degree of Damage	Poor	Collapsed and requires bridge replacement
	Moderate	Moderately damaged bridge and repairable
	Excellent	No damage or repair work is needed

Figure 8. (a) Plan and elevation of the bridge, (b) Typical cross section at pier location, (c) Cross section of the pier cap beam, and (d) Cross section of the concrete pier.

Table 14. Evaluation grade of the parameters of bridge resilience.

Major Factor	Degree of Belief (ß)	Data set 1			Data set 2
		Evaluation Grade			Evaluation Grade
		Poor	Moderate	Excellent	Poor	Moderate	Excellent
Reliability	Foundation	0.00	0.75	0.25	0.10	0.75	0.10
	Abutment	0.20	0.60	0.20	0.15	0.70	0.10
	Bearing	0.50	0.35	0.15	0.20	0.50	0.20
	Pier	0.20	0.50	0.20	0.30	0.50	0.20
	Girder	0.10	0.60	0.30	0.10	0.60	0.25
	In-span joint	0.65	0.25	0.10	0.65	0.25	0.10
	Age	0.50	0.30	0.10	0.50	0.30	0.10
	Design period	0.50	0.30	0.10	0.50	0.30	0.10
	Bridge geometry	0.00	0.10	0.80	0.00	0.15	0.85
Recovery	Monitoring	0.00	0.90	0.00	0.00	0.90	0.00
	Maintenance	0.10	0.70	0.00	0.10	0.70	0.00
	Importance of Structure	0.00	0.70	0.30	0.00	0.70	0.30
	Resource Availability	0.00	0.30	0.70	0.00	0.30	0.70
	Approachability	0.00	0.30	0.70	0.00	0.30	0.70
	Degree of Damage	0.00	0.40	0.60	0.20	0.70	0.10

Table

BPA of basic parameters of Recovery factor	P	M	E	H
$m_{1,1}=\left\{m_{1,1}^{H_n},m_{1,1}^H\right\}$=	{0.000,	0.086,	0.000,	0.009}
$m_{1,2}=\left\{m_{1,2}^{H_n},m_{1,2}^H\right\}$=	{0.015,	0.102,	0.000,	0.029}
$m_{1,3}=\left\{m_{1,3}^{H_n},m_{1,3}^H\right\}$=	{0.000,	0.148,	0.064,	0.000}
$m_{1,4}=\left\{m_{1,4}^{H_n},m_{1,4}^H\right\}$=	{0.000,	0.039,	0.092,	0.000}
$m_{1,5}=\left\{m_{1,5}^{H_n},m_{1,5}^H\right\}$=	{0.000,	0.018,	0.043,	0.000}
$m_{1,6}=\left\{m_{1,6}^{H_n},m_{1,6}^H\right\}$=	{0.000,	0.142,	0.214,	0.000}

Table 15. Bridge resilience against seismic hazard.

Bridge Data Set	Bridge Resilience (BR)
	BR (Poor)	BR (Moderate)	BR (Excellent)	BR (Unpredictable)
1 (Physical inspection)	15.1%	51.9%	29.4%	3.6%
2 (FE Analysis)	15.0%	58.3%	24.0%	2.7%

Figure 9. Bridge resilience distribution grade from two different sources of data.

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Data availability statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.