A Strategic Move for Long-Term Bridge Performance Within a Game Theory Framework by a Data-Driven Co-Active Mechanism

infrastructures

Article A Strategic Move for Long-Term Bridge Performance within a Game Theory Framework by a Data-Driven Co-Active Mechanism

O. Brian Oyegbile and Mi G. Chorzepa *

College of Engineering, University of Georgia, Athens, GA 30602, USA; [email protected] * Correspondence: [email protected]

Received: 6 July 2020; Accepted: 27 September 2020; Published: 29 September 2020

Abstract: The Federal Highway Administration (FHWA) requires that states have less than 10% of the total deck area that is structurally deficient. It is a minimum risk benchmark for sustaining the National Highway System bridges. Yet, a decision-making framework is needed for obtaining the highest possible long-term return from investments on bridge maintenance, rehabilitation, and replacement (MRR). This study employs a data-driven coactive mechanism within a proposed game theory framework, which accounts for a strategic interaction between two players, the FHWA and a state Department of Transportation (DOT). The payoffs for the two players are quantified in terms of a change in service life. The proposed framework is used to investigate the element-level bridge inspection data from four US states (Georgia, Virginia, Pennsylvania, and New York). By reallocating 0.5% (from 10% to 10.5%) of the deck resources to expansion joints and joint seals, both federal and state transportation agencies (e.g., FHWA and state DOTs in the U.S.) will be able to improve the overall bridge performance. This strategic move in turn improves the deck condition by means of a co-active mechanism and yields a higher payoff for both players. It is concluded that the proposed game theory framework with a strategic move, which leverages element interactions for MRR, is most effective in New York where the average bridge service life is extended by 15 years. It is also concluded that the strategic move can lead to vastly different outcomes. Pennsylvania’s concrete bridge management strategy currently appears to leverage a co-active mechanism in its bridge MRR strategies. This is noteworthy because its bridges are exposed to similar environmental conditions to what is obtainable in Virginia and New York and are subjected to more aggressive weather conditions than those in Georgia. This study illustrates how a strategic move affects the payoffs of different players by numerically quantifying changes in service life from bridge time-dependent bridge performance relationships.

Keywords: asset management; coactive; depreciation; performance; element interactions; game theory; health indices; long term; strategic moves; payoﬀ; return; long-term bridge performance

1. Introduction Transportation asset management often requires a data-driven decision-making process to eﬀectively preserve the long-term performance of transportation assets. This data-driven decision-making process requires information obtainable from the quantitative analysis of transportation assets’ inspection records. Thus, there has been an increasing interest in the performance analysis of transportation assets among agencies around the world because each nation’s infrastructure is essential for supporting economic development and sustainability and boosting public health and safety [1]. Among transportation infrastructure, bridges constitute the most expensive assets, by mile, for transportation agencies across the United States [2] and around the world. Additionally, bridges

Infrastructures 2020, 5, 79; doi:10.3390/infrastructures5100079 www.mdpi.com/journal/infrastructures Infrastructures 2020, 5, 79 2 of 22 are a crucial component of the overall transportation system. A partial or full collapse of a bridge generally causes considerable damage and social loss to the users. Therefore, it is critical to preserve a certain level of bridge performance [3] and prevent rapid deterioration of bridges. Bridge preservation strategies include preventive maintenance, rehabilitation, and/or replacement (MRR). For an eﬀective application of these measures, bridge agencies need to implement a bridge management framework that eﬀectively prioritizes MRR actions, most especially for large inventories, which form a network of strategic highway systems within the United States, serving as a major pipeline for the national economy, well-being, and defense. FHWA’s Long-Term Bridge Performance (LTBP) program [4] has developed machine-learning models by mining the historical National Bridge Inventory (NBI) and climate data and employing a deep learning approach. This study provides that a co-active mechanism and a simple decision framework, similar to a decision tree method used for machine learning, can help state and federal transportation agencies (e.g., state DOTs and FHWA in the U.S.) to numerically quantify long-term returns on MRR investments.

1.1. Research Motivation Most in-service bridges in the United States were constructed between the 1950s and 1970s, with an average lifespan ranging from 50 to 100 years. Consequently, an increasing number of these bridges are in need of MRRs. Adversely, the MRR budget is constrained. Therefore, bridge owners are faced with a difficult task of balancing the condition of their bridges with the cost of maintaining them [2,3,5]. At the level of state transportation agencies, bridge managers are facing ever-increasing challenges in prioritizing investments to maintain the safety and functionality of deteriorating bridges [6–8]. Additionally, they are setting long-term performance goals by developing time-dependent bridge performance relationships in order to comply with the Moving Ahead for Progress in the 21st Century Act (MAP-21) [9]. The main goal of investing in bridge MRRs is to obtain the highest possible return while minimizing the risk associated with it [10–12]. Thus, much effort has been focused on the development of bridge prioritization strategies that optimize returns on MRR investments. Most recent studies have adopted a risk-based approach [1,3,6,13]. They often determine the risk associated with continuing the usage of a bridge based on its current and projected bridge performance. However, consideration for risk alone does not provide a comprehensive solution to bridge asset management. Therefore, tools that can accurately predict future conditions of bridges, as well as their remaining life, are essential for assessing the risk [2]. However, there are essential questions to answer in order to enhance the prediction accuracy: (1) How condition changes in each bridge element affect the overall bridge health; (2) how they affect the other elements; and (3) how element interactions impact the long-term bridge performance. Bridge element conditions can be assessed by computing their health indices from the recently mandated element-level inspection data [14]. They became available in the National Bridge Inventory (NBI). Once a bridge prioritization approach is developed, a return on investment (ROI) from the bridge maintenance, rehabilitation, and replacement (MRR) actions, is determined in terms of an associated average change in the bridge service life for a bridge inventory. To optimize ROIs, a strategic move is defined in this study as a purposeful step taken by transportation agencies in order to increase ROIs on bridge MRRs. This strategic move is implemented in a game theory framework. In computing a time-dependent bridge performance relationship, this study employs a co-active mechanism, which was developed in the previous study [15]. The mechanism accounts for time-dependent bridge element interactions in predicting time–bridge overall performance relationships. From such relationships, payoffs (or change in service life) for a threshold performance level can be determined. The advantage of employing a co-active mechanism includes more realistic, and thus less overly conservative, performance predictions [16]. In this study, an extensive research program was developed to formulate time-dependent bridge performance relationships for multiple states’ bridge inventories. Infrastructures 2020, 5, 79 3 of 22

1.2. Literature Review The application of the bridge management system is increasing due to the growing demand for an improvement in the long-term bridge performance. Consequently, various state departments of transportation (state DOTs) and other agencies are more interested in determining factors that influence the long-term bridge performance. These factors include traffic volume, level of vulnerability to natural hazards, susceptibility to long-term effects of climate, and the service environment [17–21]. For an effective bridge management, these factors are typically incorporated into the bridge long-term predictive models. Bridge predictive models, which indicate changes in the performance of bridges over a certain period of time, now constitute an essential component of the agency’s long-term bridge management plans. At present, cutting-edge bridge management systems classify bridge predictive models into two major categories: deterministic models and stochastic models [22–24]. For deterministic models, the measure of bridge condition is expressed without probabilistic considerations, whereas a stochastic approach reflects the uncertainties that each bridge condition represents. Over the years, bridge predictive models have enabled agencies to determine the level of funding required to sustain a certain level of bridge condition over a planning period [25,26]. However, as the bridges become older, other critical factors that affect long-term bridge performance include the types, frequency, and effectiveness of preservation, and maintenance, repair, or rehabilitation actions performed on bridges by the owner. Therefore, over the years, studies have focused on improving the efficiency of bridge maintenance strategies with the aim of enhancing long-term bridge performance [21,27]. A study conducted by Elbehairy et al. [28] investigated the application of two evolutionary-based optimization techniques that are capable of handling large-sized problems, namely genetic algorithms and shuffled frog leaping, to optimize bridge decks’ maintenance and repair decisions. A risk-based year-by-year optimization strategy, coupled with the use of a pre-processing function to allocate repair funds first to critical bridges, was recommended. Another approach by Zhang and Gao [8] proposed an optimization model and the search algorithm was consequently applied to three bridge decks maintenance scenarios. The optimization model was developed to determine the optimal length of the maintenance period based on the proposed maintenance policy, to minimize the system’s life cycle cost per unit time. Zhang and Wang [6] developed a decision model for bridge network management and project prioritization that enables the operational performance of a transportation system to be optimized, given the safety requirements mandated by the American Association of State Highway and Transportation Officials (AASHTO) and the inevitable budgetary constraints imposed by limited resources. The previous efforts relating to the prioritization of bridges for MRR are commendable because they attempted to maximize a return on investments in bridge MRR. In this study, the feasibility of implementing a proposed co-active mechanism within a game theory framework nationwide (specifically in the United States) was investigated. The co-active bridge prioritization model additionally accounts for the effects of time-dependent element interactions on the long-term bridge performance. Additionally, the model was implemented within a game theory framework and thus quantifies payoffs of the two players, FHWA and state DOTs. Finally, the model was used to investigate the performance of National Highway System (NHS) and non-NHS bridges.

1.3. Research Goals and Scope This study aimed to determine the feasibility of implementing a proposed co-active prioritization model nationwide in the United States. Speciﬁcally, this study aimed to answer the following three key questions by analyzing bridge inventories in four states (Georgia, Virginia, Pennsylvania, and New York):

1. Does the proposed co-active model have an application to other U.S. state agencies? Infrastructures 2020, 5, 79 4 of 22

2. Is there any diﬀerence in the performance of National Highway System (NHS) state-owned and non-NHS state-owned bridges? 3. How should one quantify payoﬀs for two players, the FHWA and a state DOT, using a game theory?

1.4. Background and Overall Approach Bridge inventories in four states, which are known to have proactive maintenance strategies, were investigated. Title 23 of the United States Code §150(c)(3), in compliance with the Moving Ahead for Progress in the 21st Century (MAP-21) legislation, requires state DOTs to establish, as part of their governance of performance measures, “minimum standards for States to use in developing and operating bridge and pavement management system”. For bridges on the National Highway System (NHS), Title 23 of the United States Code §119(f) stipulates that no more than 10% of the total NHS bridge deck area be structurally deﬁcient (SD) in a bridge network [29]. Equation (1) quantiﬁes the percentage of SD bridges:

PStructurally Deﬁcient [Length Width] SD=1 × Bridges SD % SD = 100 P . (1) × TOTAL[Length Width] SD=1 × Bridges A bridge is classiﬁed as SD when at least one of its National Bridge Inventory (NBI) items, 58 (deck), 59 (superstructure), 60 (substructure), or 62 (culverts), has a condition rating of 4 or less (out of the maximum rating of 9). Therefore, the Federal Highway Administration’s (FHWA’s) approach to the maintenance of NHS bridges can be described as the ‘worst case scenario’, where each bridge component is required to have a minimum condition rating of 4 in the preceding three years. However, other important factors for measuring bridge performance, such as the average life cycle, must be considered.

2. Methodology

2.1. Quantifying Depreciation of Bridge Assets, a Strategic Move, and Payoffs The process implemented in this study was divided into three main parts. Figure1 presents a flow chart showing the proposed approach for determining the three components shown in Parts I through III: (Part I) Long-term bridge performance (or depreciation of bridge assets) using the existing method [22]. In this step, it is assumed that health indices of bridge elements are mutually exclusive. The elements’ health indices are used as input to develop bridge performance predictions. (Part II) Long-term bridge performance by recognizing dependent and thus co-acting elements (i.e., a co-active approach [15]) with and without a strategic move—improving all joints or conducting joint MRRs. In this part, the depreciation models determined from Part I and the co-active coefficients determined by studying correlations among elements [15] are used to predict the bridge performance resulting from the strategic move. (Part III) Payoffs of the players (federal and state agencies) in terms of an associated service life extension from the strategic move. Infrastructures 2020, 5, 79 5 of 22 Infrastructures 2020, 5, x FOR PEER REVIEW 5 of 23

FigureFigure 1.1. AA ﬂowflow chart showing the the methodology. methodology.

2.2.2.2. Co-Active Co-Active Approach Approach PartPart II II identified identified and and computed computed thethe co-activeco-active para parametersmeters that that influence influence th thee overall overall bridge bridge health health indicesindices (BHIs). (BHIs). The The co-active co-active approachapproach waswas firstfirst introduced and and described described in in detail detail in inthe the previous previous studystudy [15 [15].]. In In brief, brief, the the co-active co-active modelmodel hypothesizeshypothesizes that that when when one one repairs repairs an an element, element, it itshould should reducereduce the the deterioration deterioration of of the the other other elements.elements. Su Subsequently,bsequently, the the improved improved element(s) element(s) reduce reduce the the deteriorationdeterioration of of itself itself and and other other co-active co-active elements. elemen Therefore,ts. Therefore, the the co-active co-active model model enables enables data-driven data- time-dependentdriven time-dependent element interactionselement interactions for preventive for preventive maintenance, maintenance, rehabilitation, rehabilitation, or replacement or (MRR)replacement decision-making. (MRR) decision-making. TheThe computation computation relevant relevant to to this this studystudy isis shownshown in Equation Equation (2). (2). For For each each element element deterioration deterioration model,model, there there are are year-to-year year-to-year depreciation depreciation factorsfactors (DFs) for for each each element’s element’s HIs HIs (i.e., (i.e., the the element’s element’s deteriorationdeterioration rates). rates). For For example, example, if if thethe reinforcedreinforced concrete deck’s deck’s HIs HIs are are 89.01 89.01 and and 88.12 88.12 in inthe the years years (Yrs)(Yrs) 2015 2015 and and 2016, 2016, respectively, respectively, the the DF DF isis 0.01,0.01, which is is computed computed by by (89.01–88.12)/89.01. (89.01–88.12)/89.01. Therefore, Therefore, whenwhen one one of of the the co-activeco-active elements is is maintained, maintained, rehabilitated, rehabilitated, or replaced or replaced (MRR), (MRR), it decreases it decreases the theDFs DFs for for the the other other co-active co-active elements elements as asshown shown in inEquation Equation (2) (2) and and becomes becomes an anacting acting element. element. Consequently, the decrease in the DF of each element affects the other elements’ HIs and the overall Consequently, the decrease in the DF of each element affects the other elements’ HIs and the overall BHI (see Figure 2a,b): BHI (see Figure2a,b): t h affected acting CAi t 1 HI e = DFe 1 AFeρe CA HIe− , (2) HI =DF 1 − AF ρ × × HI , (2) where: t where:HIe = Health index for an element in the year, t (e.g., 2018); t 1 HI − = Health index for an element in the preceding year, t 1 (e.g., 2017); e − Infrastructures 2020, 5, x FOR PEER REVIEW 6 of 23 Infrastructures 2020, 5, 79 6 of 22 HI = Health index for an element in the year, t (e.g., 2018); HI = Health index for an element in the preceding year, t − 1 (e.g., 2017); affected= DFDFe =Depreciation Depreciation factorfactor calculatedcalculated for an an element element (e.g., (e.g., column) column) not not being being maintained, maintained, repaired,repaired, and and rehabilitated; rehabilitated; acting AFAFe ==Appreciation Appreciation factor factor calculatedcalculated for an an element element (e.g., (e.g., expansion expansion joint) joint) being being maintained, maintained, repaired,repaired, and and rehabilitated; rehabilitated; and and CACA ρe ρ ==Co-active Co-active coecoefficientfficient between the the acting acting elemen elementt (e.g., (e.g., expansion expansion joint) joint) and and its its co-active co-active elementselements (e.g., (e.g., column). column). TheThe approach approach involved involved in in the the co-active co-active modelmodel [[15]15] is is not not repeated repeated here here in in detail, detail, and and the the process process belowbelow focuses focuses on on describing describing how how a a game game theorytheory approachapproach is used for for optimal optimal decision-making. decision-making.

(a) NHS Bridge Performance Prediction (b) NHS Bridge Performance Prediction (Georgia) without the Strategic Move (Georgia) with the Strategic Move (or joint MRR)

(c) Non-NHS Bridge Performance Prediction (d) Non-NHS Bridge Performance Prediction (Georgia) without the Strategic Move (Georgia) with the Strategic Move (or joint MRR)

FigureFigure 2. 2.National National Highway Highway SystemSystem (NHS) vs. non-NHS non-NHS bridge bridge in in Georgia. Georgia.

2.3.2.3. Determination Determination of of Service Service Life Life Using Using aa GameGame Theory Approach InIn Part Part III, III, the the proposed proposed co-active co-active modelmodel waswas implemented within within a agame game theory theory approach approach describeddescribed below below to determineto determine the the payo payoffsffs of 2 of player: 2 play federaler: federal and stateand state players, play specificallyers, specifically the Federal the HighwayFederal AdministrationHighway Administration (FHWA) and (FHWA) a state and Department a state Department of Transportation of Transp (stateortation DOT). (state The DOT). payo ffs areThe determined payoffs are by determined Equations by (3) Equations and (4). (3) Within and (4). this Within game this theory game approach,theory approach, the co-active the co-active model determinedmodel determined the NHS the and NHS non-NHS and non-NHS performance performance predictions predictions (i.e., depreciations) (i.e., depreciations) shown shown in Figure in 2, Figure 2, which were in turn used to calculate the bridge servicea yearsb (𝑌𝑟 , 𝑌𝑟a , and 𝑌𝑟 ) from two which were in turn used to calculate the bridge service years (Yr1, Yr1, and Yr2) from two moves using Equationsmoves using (3) and Equations (4). (3) and (4). The game theory approach modeled a strategic interaction between two players, the FHWA and The game theory approach modeled a strategic interaction between two players, the FHWA and a a state DOT. A sequential game with two FHWA’s strategic moves was conducted, one imposing the state DOT. A sequential game with two FHWA’s strategic moves was conducted, one imposing the 10% deck requirement and the other with a strategic change in deck requirement (10.5%) while requiring states to maintain all joints in superior conditions. Both NHS bridges and non-NHS bridges were Infrastructures 2020, 5, 79 7 of 22 investigated to review the effectiveness of FHWA’s strategic moves. For example, Figure3 shows the game tree illustrating a strategic move and payoffs of 2 players in Georgia. State DOT payoffs (1) and (2) shown in Table1 were calculated using Equations (3) and (4): h i a + a Nnhs Yr1 Ns Yr2 State DOT Payoff (1) = × × , (3) N h i b + a Nnhs Yr1 Ns Yr2 State DOT Payoff (2) = × × , (4) N where: State DOT payoff (1) = Payoff obtained from a move #1—the existing approach (<10% deck is structurally deficient); State DOT payoff (2) = Payoff obtained from a move #2—the proposed strategic move (<10.5% deck is structurally deficient); Nnhs = Number of bridges on the National Highway System; Ns = Number of bridges NOT on the National Highway System; N = Total number of bridges (Nnhs + Ns); a Yr1 = Bridge service year corresponding to the threshold BHI set at 70 (obtained from Figure2(a)); b Yr1 = Bridge service year corresponding to the threshold BHI set at 70 (obtained from Figure2b); and a Yr2 = Bridge service year corresponding to the threshold BHI set at 70 (obtained from Figure2(c)). Finally, the payoffs of the two players in prioritizing element MRR were quantified based on a service life extension of bridges when a threshold bridge health index (BHI) was set to be 70. In this study, a threshold BHI of 70 was selected because it is the dividing factor for determining whether a bridge needs preventive maintenance or rehabilitation [30–32]. For a fair comparison, the threshold BHI of 60 was used for New York because the observed bridge performance in the state appears to be relatively lower than the other states. The cost of reducing deck MRR by 0.5% was assumed to be equivalent to the cost of rehabilitating all expansion joints and joint seals in a bridge inventory. This reduction was substantiated by calculating the total quantity of deck areas and the total linear footage of joints.

3. Results The results are presented to review the eﬀect of the second move (or reallocate deck resources to improve all joints). Thus, this move is referred to as the “strategic move” in this section.

3.1. Analysis of Georgia DOT’s Element Data Figure2a shows the average service life of NHS bridges in Georgia when no joints are rehabilitated or replaced. Figure2b presents the NHS bridge performance when additional resources are allocated to expansion joints and joint sealant rehabilitation and/or replacements, the main strategic move (move #2 above) investigated herein. The average service life was extended by 10 years because the service life is 65 and 75 years in Figure2 a,b, respectively, for the BHI threshold of 70. Similarly, Figure2c,d show the non-NHS bridge performance. In Figure2a through to Figure2d, the proposed joint replacement a ffects the performance predictions at similar rates (overall BHI increases from 65 to 75 in NHS bridges, and 50 to 65 in non-NHS bridges). This observation can be attributed to the similar values of the co-active coefficients computed for NHS and non-NHS bridges in Georgia. The extent to which the maintenance, rehabilitation, or replacement (MRR) of an element affects the performance prediction of the other co-active elements largely depends on the degree of dependency that exists in the co-active elements. The higher the co-active coefficient is between two elements, the more likely the changes in the performance of one element affect the performance of the other Infrastructures 2020, 5, x FOR PEER REVIEW 8 of 23 Infrastructures 2020, 5, 79 8 of 22 the other dependent element. Thus, in addition to the previously identified factors in the literature dependent(e.g., present element. condition Thus, of bridges/elements, in addition to the depr previouslyeciation models, identified traffic factors volume, in the network literature priority, (e.g., presentetc.), transportation condition of bridgesagencies/elements, should consider depreciation the influence models, tra offfi interdependenciesc volume, network among priority, bridge etc.), transportationelements when agencies planning should MRR for consider a network the influenceof bridges. of That interdependencies is, the co-active among model bridgepresented elements in this whenstudy planning must be MRR implemented for a network in ofthe bridges. existing That br is,idge the management co-active model systems presented to inaccount this study for mustsuch beinterdependencies. implemented in the existing bridge management systems to account for such interdependencies. FigureFigure3 3 illustrates illustrates a a payo payoffff ofof thethe twotwo players,players, FederalFederal HighwayHighway AdministrationAdministration (FHWA)(FHWA) andand statestate Department of of Transportation Transportation (DOT). (DOT). Table Table 11 gives gives the the payoffs payo fffors forthe thefour four states states analyzed. analyzed. The Thetable table shows shows that that the thestrategic strategic move move in inthe the proposed proposed game game theory theory approach approach gives gives higher higher payoffs payoffs forfor FHWAFHWA andand statestate DOT.DOT. This This isis anan optimaloptimal outcomeoutcome forfor thethe twotwo players:players: thethe Nash equilibrium deduceddeduced fromfrom aa backwardbackward induction.induction.

Figure 3. Game tree illustrating a strategic move and payoffs of two players in Georgia. Figure 3. Game tree illustrating a strategic move and payoffs of two players in Georgia. Table 1. Payoffs (years) of the strategic moves. Table 1. Payoffs (years) of the strategic moves. State FHWA payoff2 stateDOT payoff2 FHWA payoff1 stateDOT payoff1 FHWA stateDOT FHWA stateDOT GAState 75 65 65 59 VA 45payoff2 45payoff2 payoff1 35 payoff1 35 PA 55 52 50 48 GA 75 65 65 59 NY 50 39 35 31 VA 45 45 35 35

Figures4 and5 showPA changes55 in the health52 index (from50 2016 to 2018)48 with respect to health indices in 2016, for NHSNY and non-NHS50 bridges.39 In comparison35 with NHS31 bridges, non-NHS but state-owned bridge performance and performance predictions are investigated. In the absence of a strategicFigures incentive 4 and and 5 show resources, changes non-NHS in the bridges health areinde notx (from as well 2016 maintained to 2018) as with the NHSrespect bridges to health (see Figuresindices 4in and 2016,5). for This NHS may and be non-NHS attributed bridges. to the disparityIn comparison in the with available NHS bridges, funding non-NHS for the NHS but andstate- non-NHSowned bridge bridges. performance NHS bridges and receive performance federal funding, predictions while are the maintenanceinvestigated. of In non-NHS the absence bridges of isa mostlystrategic funded incentive by a and state resources, DOT. non-NHS bridges are not as well maintained as the NHS bridges (see Figures 4 and 5). This may be attributed to the disparity in the available funding for the NHS and non-NHS bridges. NHS bridges receive federal funding, while the maintenance of non-NHS bridges is mostly funded by a state DOT. Infrastructures 2020, 5, 79 9 of 22 InfrastructuresInfrastructures 2020 2020, ,5 5, ,x x FOR FOR PEER PEER REVIEW REVIEW 99 of of 23 23

(a)(a) OverallOverall Bridge Bridge (b) (b) DeckDeck

(c)(c) ExpansionExpansion Joint Joint (d) (d) BearingBearing

FigureFigureFigure 4. 4. NHS NHSNHS bridge bridgebridge performance performanceperformance in inin Georgia. Georgia.Georgia. ( (aa))) Overall OverallOverall Bridge; Bridge;Bridge; ( ((bbb))) Concrete ConcreteConcrete Deck; Deck;Deck; ( ((ccc))) Expansion ExpansionExpansion Joint;Joint;Joint; ( ((ddd))) Bearing. Bearing.Bearing.

(a) Overall Bridge (b) Deck (a) Overall Bridge (b) Deck Figure 5. Cont. Infrastructures 2020, 5, 79 10 of 22 Infrastructures 2020, 5, x FOR PEER REVIEW 10 of 23 Infrastructures 2020, 5, x FOR PEER REVIEW 10 of 23

FigureFigureFigure 5.5. Non-NHS 5.Non-NHS Non-NHS bridge bridge bridge performance performanceperformance in Georgia. inin Georgia.Georgia. (a) Overall( a()a )Overall Overall bridge; bridge; (bridge;b) concrete (b) (concreteb) deck;concrete (deck;c) expansion deck; (c) (c) joint;expansionexpansion (d) bearing. joint; joint; (d ()d bearing.) bearing.

Finally,Finally,Finally, FigureFigure Figure6 6 shows 6 showsshows that thatthat the the proposed proposedproposed co-active coco-active-active mechanism mechanism yields yields yields less less lessconservative conservative conservative deteriorationdeteriorationdeterioration predictions.predictions. predictions. Therefore, Therefore,Therefore, the the results resultsresults presented presentedpresented in Figure in inFigure 2 Figurewere 2 a morewere2 were realistica morea more comparison,realistic realistic whichcomparison,comparison, resulted which inwhich a 2–3-yearresulted resulted servicein in a a 2–3-year2–3-year life extension serviceservice life life for extension theextension bridges for for the in the Georgia.bridges bridges in Georgia. in Georgia.

(a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS) (a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS)

Figure 6. The eﬀect of an expansion joint replacement not including and including the co-active Figure 6. The effect of an expansion joint replacement not including and including the co-active mechanism:(c) Not Including (a) and Co-Activeness (b) in NHS bridges, (non-NHS (c) and) (d) in non-NHS (d) bridgesIncluding in Georgia.Co-Activeness (non-NHS) mechanism: (a) and (b) in NHS bridges, (c) and (d) in non-NHS bridges in Georgia.

Figure 6. The effect of an expansion joint replacement not including and including the co-active mechanism: (a) and (b) in NHS bridges, (c) and (d) in non-NHS bridges in Georgia.

3.2. Analysis of Virginia DOT’s Element Data Infrastructures 2020, 5, 79 11 of 22

Infrastructures 2020, 5, x FOR PEER REVIEW 11 of 23 3.2. Analysis of Virginia DOT’s Element Data 3.2. Analysis of Virginia DOT’s Element Data Figure7a shows the average service life of NHS bridges in Virginia when no joints are rehabilitated or replaced.Figure Figure 7a shows7b presents the average the bridge service performance life of NHS whenbridges additional in Virginia resources when no are joints allocated are to expansionrehabilitated joints or and replaced. jointsealant Figure 7b rehabilitation presents the bridge and/or performance replacements, when which additional is the resources strategic are move investigatedallocated into thisexpansion study. joints The co-activeand joint modelsealant isrehabilitation used in this and/or figure. replacements, The average which service is the life was strategic move investigated in this study. The co-active model is used in this figure. The average extended by 10 years because the service life is 35 and 45 years in Figure7a,b, respectively, for the health service life was extended by 10 years because the service life is 35 and 45 years in Figure 7a,b, indexrespectively, threshold offor 70.the Tablehealth1 indexsummarizes threshold the of payo70. Tableff of 1 thesummarizes players forthe existingpayoff of andthe players new strategies. for Figureexisting7a,c show and new that strategies. NHS and Figure non-NHS 7a,c bridgesshow that in NHS Virginia and arenon-NHS depreciating bridges fasterin Virginia than are similar bridgesdepreciating in Georgia faster (see than Figure similar2a,c). bridges However, in Georgia the co-active (see Figure model 2a,c). yields However, a similar the service co-active life model extension of 10yields years a forsimilar Virginia service and life Georgia. extension This of 10 is years due tofor the Virginia differences and Georgia. in the valuesThis is ofdue the to co-activethe coeffidifferencescients computed in the values for the of twothe co-active states. They coefficients are data-driven computed factors.for the two Although states. They bridges are indata- Virginia are depreciatingdriven factors. faster Although than thosebridges in Georgia,in Virginia the are elements’ depreciating co-active faster coethanffi cientsthose in are Georgia, relatively the lower. Stateselements’ with relatively co-active lowercoefficients health are indices relatively are lower. more States likely with to benefit relatively from lower the health co-active indices mechanism are identifiedmore likely from itsto benefit element-based from the inspectionco-active mechanism database. identified from its element-based inspection database. Similarly, non-NHS but state-owned bridge performance and performance predictions were Similarly, non-NHS but state-owned bridge performance and performance predictions were investigated,investigated, in comparison in comparison with with NHS NHS bridges. bridges. In In the the absence absence of ofa strategic a strategic incentive incentive and resources, and resources, non-NHSnon-NHS bridges bridges are are not not as wellas well maintained maintained as as the the NHS NHS bridgesbridges (see Figures Figures 88 and and 9).9). Finally, Finally, Figure Figure 10 shows10 thatshows the that proposed the proposed co-active co-active mechanism mechanism yields yields less conservative less conservative (and (and possibly possibly more more realistic) deteriorationrealistic) deterioration predictions. predictions.

(a) NHS Bridge Performance Prediction (Virginia) (b) NHS Bridge Performance Prediction (Virginia) without the Strategic Move with the Strategic Move (or joint MRR)

Infrastructures 2020, Figure5, x FigureFOR 7. PEER National7. National REVIEW Highway Highway SystemSystem (NHS) (NHS) vs vs.. non-NHS non-NHS bridge bridge in Virginia. in Virginia. 12 of 23

(a) Overall Bridge (b) Deck

Figure 8. Cont.

Figure 8. NHS bridge performance in Virginia. (a) Overall bridge; (b) concrete deck; (c) expansion joint; (d) bearing.

Infrastructures 2020, 5, x FOR PEER REVIEW 12 of 23

Infrastructures 2020, 5, 79 12 of 22 (a) Overall Bridge (b) Deck

FigureFigure 8. 8. NHSNHS bridgebridge performance in in Virginia. Virginia. (a ()a Overall) Overall bridge; bridge; (b) ( bconcrete) concrete deck; deck; (c) (expansionc) expansion Infrastructuresjoint;joint; ( d(d)) bearing. 2020bearing., 5, x FOR PEER REVIEW 13 of 23

(a) Overall Bridge (b) Deck

FigureFigure 9. Non-NHS9. Non-NHS bridge bridge performance performance in Virginia. in Virginia. (a) Overall (a) Overall bridge; bridge; (b) concrete (b) concrete deck; ( c)deck; expansion (c) joint;expansion (d) bearing. joint; (d) bearing.

(a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS) Infrastructures 2020, 5, x FOR PEER REVIEW 13 of 23

(a) Overall Bridge (b) Deck

InfrastructuresFigure2020 ,9.5, 79Non-NHS bridge performance in Virginia. (a) Overall bridge; (b) concrete deck; (c) 13 of 22 expansion joint; (d) bearing.

Infrastructures 2020, 5, x FOR PEER REVIEW 14 of 23 (a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS)

FigureFigure 10. 10.The The eﬀ effectect of of an an expansion expansion jointjoint replacement not not including including and and including including the theco-active co-active mechanism:mechanism: (a )(a and) and (b ()b in) in NHS NHS Bridges, Bridges, ((c) and ( (dd)) in in Non-NHS Non-NHS bridges bridges in inVirginia. Virginia.

3.3.3.3. Analysis Analysis of Pennsylvaniaof Pennsylvania DOT’s DOT’s Element Element Data FigureFigure 11 a11a shows shows the the average average serviceservice life of NHS NHS bridges bridges in in Pennsylvania Pennsylvania when when no joints no joints are are rehabilitatedrehabilitated or replaced.or replaced. Figure Figure 11b presents11b presents the NHSthe NHS bridge bridge performance performance when when additional additional resources areresources allocated are to expansionallocated to jointsexpansion and jointjoints sealantand join rehabilitationt sealant rehabilitation and/or replacements.and/or replacements. The co-active The modelco-active is used model in this is figure.used in Thethis averagefigure. The service average life service was extended life was byextended 5 years by because 5 years the because service the life is service life is 50 and 55 years in Figure 11a,b, respectively, for the HI threshold of 70. Table 1 50 and 55 years in Figure 11a,b, respectively, for the HI threshold of 70. Table1 summarizes the payo ff summarizes the payoff of the players for existing and new strategies. of the players for existing and new strategies. In Figures 12 and 13, the performances of NHS bridges are compared with the non-NHS but state-ownedIn Figures bridge12 and performance. 13, the performances In the absence of NHS of a bridgesstrategic areincentive compared and resources, with the non-NHSnon-NHS but state-ownedbridges are bridge not as well performance. maintained Inas the the NHS absence bridges. of aHowever, strategic the incentive disparities and in resources,the performances non-NHS bridgesof the are NHS not and as wellnon-NHS maintained bridges as in thePennsylvania NHS bridges. (Figures However, 12 and the13) disparitiesare relatively in less the significant performances of thethan NHS in the and state non-NHS of Georgia bridges (see Figures in Pennsylvania 4 and 5). Factors, (Figures such 12 and as traffic 13) are volume relatively (ADDT), less significantbridge thangeographical in the state location, of Georgia bridge (see design, Figures and4 andbridge5). construction Factors, such materials, as tra ffimightc volume also be (ADDT), responsible bridge geographicalfor the disparities location, in bridge the performances design, and of bridge the NH constructionS and non-NHS materials, bridges. might Future also research be responsible should for thetherefore disparities investigate in the performances how these offactors the NHS affect and NHS non-NHS and non-NHS bridges. bridge Future performances, research should and therefore the investigatepossible howvariation these in factors the effe actsffect across NHS the and United non-NHS States. bridge performances, and the possible variation in the effects across the United States.

(a) NHS Bridge Performance Prediction (b) NHS Bridge Performance Prediction (Pennsylvania) (Pennsylvania) without the Strategic Move with the Strategic Move (or joint MRR) Infrastructures 2020, 5, x FOR PEER REVIEW 14 of 23

Figure 10. The effect of an expansion joint replacement not including and including the co-active mechanism: (a) and (b) in NHS Bridges, (c) and (d) in Non-NHS bridges in Virginia.

3.3. Analysis of Pennsylvania DOT’s Element Data Figure 11a shows the average service life of NHS bridges in Pennsylvania when no joints are rehabilitated or replaced. Figure 11b presents the NHS bridge performance when additional resources are allocated to expansion joints and joint sealant rehabilitation and/or replacements. The co-active model is used in this figure. The average service life was extended by 5 years because the service life is 50 and 55 years in Figure 11a,b, respectively, for the HI threshold of 70. Table 1 summarizes the payoff of the players for existing and new strategies. In Figures 12 and 13, the performances of NHS bridges are compared with the non-NHS but state-owned bridge performance. In the absence of a strategic incentive and resources, non-NHS bridges are not as well maintained as the NHS bridges. However, the disparities in the performances of the NHS and non-NHS bridges in Pennsylvania (Figures 12 and 13) are relatively less significant than in the state of Georgia (see Figures 4 and 5). Factors, such as traffic volume (ADDT), bridge geographical location, bridge design, and bridge construction materials, might also be responsible for the disparities in the performances of the NHS and non-NHS bridges. Future research should therefore investigate how these factors affect NHS and non-NHS bridge performances, and the Infrastructures 2020, 5, 79 14 of 22 possible variation in the effects across the United States.

Infrastructures(a) NHS 2020 Bridge, 5, x FOR Performance PEER REVIEW Prediction (b) NHS Bridge Performance Prediction (Pennsylvania)15 of 23 Infrastructures 2020, 5, x FOR PEER REVIEW 15 of 23 (Pennsylvania) without the Strategic Move with the Strategic Move (or joint MRR)

(c)(c) Non-NHSNon-NHS BridgeBridge PerformancePerformance Prediction (d)(d) Non-NHS Non-NHS Bridge Bridge Performance Performance Prediction Prediction (Pennsylvania)(Pennsylvania) withoutwithout the Strategic Move (Pennsylvania)(Pennsylvania) with the with Strategic the Strategic Move Move(or joint (or MRR)joint MRR)

FigureFigureFigure 11. 11.11.National National Highway Highway SystemSystem (NHS)(NHS) vs.vs. vs. non-NHSnon-NHS non-NHS bridge bridge bridge in in Pennsylvania. Pennsylvania. in Pennsylvania.

(a)(a) Overall Bridge (b)(b) DeckDeck

Figure 12. Cont.

Figure 12. NHS bridge performance in Pennsylvania. (a) Overall bridge; (b) concrete deck; (c) Figureexpansion 12. joint;NHS (dbridge) bearing. performance in Pennsylvania. (a) Overall bridge; (b) concrete deck; (c) expansion joint; (d) bearing. Infrastructures 2020, 5, x FOR PEER REVIEW 15 of 23

(c) Non-NHS Bridge Performance Prediction (d) Non-NHS Bridge Performance Prediction (Pennsylvania) without the Strategic Move (Pennsylvania) with the Strategic Move (or joint MRR)

Figure 11. National Highway System (NHS) vs. non-NHS bridge in Pennsylvania.

Infrastructures 2020, 5, 79 15 of 22 (a) Overall Bridge (b) Deck

Figure 12. NHS bridge performance in Pennsylvania. (a) Overall bridge; (b) concrete deck; (c) expansion Figure 12. NHS bridge performance in Pennsylvania. (a) Overall bridge; (b) concrete deck; (c) Infrastructuresjoint; (d) bearing.2020, 5, x FOR PEER REVIEW 16 of 23 expansion joint; (d) bearing.

(a) Overall Bridge (b) Deck

FigureFigure 13. 13.Non-NHS Non-NHS bridge performance performance in inPennsylvania. Pennsylvania. (a) Overall (a) Overall bridge; bridge; (b) concrete (b) concrete deck; (c) deck; (c)expansion expansion joint; joint; (d ()d bearing.) bearing.

Finally,Finally, Figure Figure 14 14 showsshows thatthat the proposed proposed co-active co-active mechanism mechanism yields yields less lessconservative conservative deteriorationdeterioration predictions. predictions.

(a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS) Infrastructures 2020, 5, x FOR PEER REVIEW 16 of 23

(a) Overall Bridge (b) Deck

Figure 13. Non-NHS bridge performance in Pennsylvania. (a) Overall bridge; (b) concrete deck; (c) expansion joint; (d) bearing.

InfrastructuresFinally,2020, 5Figure, 79 14 shows that the proposed co-active mechanism yields less conservative16 of 22 deterioration predictions.

Infrastructures 2020, 5, x FOR PEER REVIEW 17 of 23

Infrastructures 2020, 5, x FOR PEER REVIEW 17 of 23 (a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS)

Figure 14. The effect of an expansion joint replacement not including and including the co-active (c)mechanism: Not including (a) andCo-Activeness (b) in NHS (non-NHS Bridges, (c) ) and (d) in non-NHS (d) Including bridges in Co-Activeness Pennsylvania. (non-NHS)

3.4.Figure FigureAnalysis 14. 14.The of The New eff effectect York of of anDOT’s an expansion expansion Element joint joint Data replacement replacement notnot includingincluding and and including including the the co-active co-active mechanism:mechanism: (a) (a and) and (b ()b in) in NHS NHS Bridges, Bridges, ( c()c) and and ( d(d)) inin non-NHSnon-NHS bridgesbridges in in Pennsylvania. Pennsylvania. Figure 15a shows the average service life of NHS bridges in New York when no joints are 3.4.3.4. Analysisrehabilitated Analysis of Newof Newor Yorkreplaced. York DOT’s DOT’s Figure Element Element 15b Data Data presents the NHS bridge performance when additional resources are allocated to expansion joints and joint sealant rehabilitation and/or replacements. The co-activeFigureFigure 15 model a15a shows shows is used the the in average thisaverage figure. service service The averaglifelife ofofe NHS NHSservice bridges life was in in extendedNew New York York by when15 when years no no becausejoints joints are the are rehabilitatedrehabilitatedservice life or is replaced.or 35 replaced.and 50 Figure years Figure in15 bFigure presents15b 15a,b,presents the respectively, NHS the bridgeNHS for performancebridge the health performance index when threshold additional when additionalof resources60. Table areresources allocated1 summarizes are to expansionallocated the payoff to joints expansionof the and player joint jointss for sealant and existing join rehabilitationt andsealant new rehabilitation strategies. and/or replacements. and/or replacements. The co-active The modelco-active is usedIn Figuresmodel in this is 16 used figure. and in 17, Thethis in averagefigure. comparison The service averag with lifee service wasNHS extended bridges, life was bynon-NHSextended 15 years bybut because 15 state-owned years the because service bridge the life is 35serviceperformance and 50 life years is 35 and in and Figure performance 50 years 15a,b, in respectively, Figurepredicti 15a,b,ons are forrespectively, investigated. the health for index In the the thresholdhealth absence index of of a 60.threshold strategic Table1 incentive ofsummarizes 60. Table and the1 payo resources,summarizesff of the non-NHS playersthe payoff bridges for of existing the are player not and ass for newwell existing strategies.maintained and new as the strategies. NHS bridges. In Figures 16 and 17, in comparison with NHS bridges, non-NHS but state-owned bridge performance and performance predictions are investigated. In the absence of a strategic incentive and resources, non-NHS bridges are not as well maintained as the NHS bridges.

(a) NHS Bridge Performance Prediction (b) NHS Bridge Performance Prediction (New (New York) without the Strategic Move York) with the Strategic Move (or joint MRR)

(a) (a) NHS Bridge Performance PredictionFigure 15. Cont(b). NHS Bridge Performance Prediction (New (New York) without the Strategic Move York) with the Strategic Move (or joint MRR)

Infrastructures 2020, 5, 79 17 of 22 Infrastructures 2020, 5, x FOR PEER REVIEW 18 of 23

Infrastructures 2020, 5, x FOR PEER REVIEW 18 of 23

(c) Non-NHS Bridge Performance Prediction (New (d) Non-NHS Bridge Performance Prediction (New York) without the Strategic Move York) with the Strategic Move (or joint MRR)

FigureFigure 15. 15.National National Highway Highway SystemSystem (NHS) vs. vs. non-NHS non-NHS bridge bridge in in New New York. York. (a) Non-NHS Bridge Performance Prediction (New (b) Non-NHS Bridge Performance Prediction (New In Figures 16 and 17, in comparison with NHS bridges, non-NHS but state-owned bridge performanceYork) and performance without the Strategic predictions Move are investigated. InYork) the with absence the Strategic of a strategic Move incentive(or joint MRR) and resources, non-NHSFigure bridges 15. National are notHighway as well System maintained (NHS) vs. as thenon-NHS NHS bridge bridges. in New York.

(a) Overall Bridge (b) Deck

Figure 16. NHS bridge performance in New York. (a) Overall bridge; (b) concrete deck; (c) expansion joint; (d) bearing.

Figure 16. NHS bridge performance in New York. (a) Overall bridge; (b) concrete deck; (c) expansion Figure 16. NHS bridge performance in New York. (a) Overall bridge; (b) concrete deck; (c) expansion joint; (d) bearing. joint; (d) bearing. Infrastructures 2020, 5, 79 18 of 22 Infrastructures 2020, 5, x FOR PEER REVIEW 19 of 23 Infrastructures 2020, 5, x FOR PEER REVIEW 19 of 23

(a) Overall Bridge (b) Deck (a) Overall Bridge (b) Deck

(c) Expansion Joint (d) Bearing (c) Expansion Joint (d) Bearing FigureFigure 17. 17.Non-NHS Non-NHS bridge performance performance in inNew New York. York. (a) Overall (a) Overall bridge; bridge; (b) concrete (b) concrete deck; (c) deck; Figure 17. Non-NHS bridge performance in New York. (a) Overall bridge; (b) concrete deck; (c) (c) expansionexpansion joint; joint; (d (d) )bearing. bearing. expansion joint; (d) bearing. Finally,Finally, Figure Figure 18 18 shows shows thatthat thethe proposedproposed co-active co-active mechanism mechanism yields yields less less conservative conservative Finally, Figure 18 shows that the proposed co-active mechanism yields less conservative deterioration predictions. deteriorationdeterioration predictions. predictions.

(a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS) (a) Not Including Co-Activeness (NHS) (b) Including Co-Activeness (NHS)

Figure 18. Cont. Infrastructures 2020, 5, 79 19 of 22 Infrastructures 2020, 5, x FOR PEER REVIEW 20 of 23

Figure 18. The effect of an expansion joint replacement not including and including the co-active Figure 18. The effect of an expansion joint replacement not including and including the co-active mechanism: (a) and (b) in NHS bridges, (c) and (d) in non-NHS bridges in New York. mechanism: (a) and (b) in NHS bridges, (c) and (d) in non-NHS bridges in New York. 4. Discussion of Results 4. Discussion of Results The bridge performance analysis presented in this study integrates a co-active model and a game The bridge performance analysis presented in this study integrates a co-active model and a game theory approach to optimize a return on investment (ROI) from the bridge maintenance, rehabilitation, theory approach to optimize a return on investment (ROI) from the bridge maintenance, andrehabilitation, replacement and (MRR) replacement actions. (MRR) Joint MRRs actions. were Joint selected MRRs were to illustrate selected the to illustrate proposed the approach, proposed which is notapproach, currently which being is not considered currently bybeing transportation considered by agencies. transportation The game agencies. theory The approach game theory models a strategicapproach interaction models a betweenstrategic interaction two players, between the federal two players, and state the federal transportation and state agencies transportation (or FHWA andagencies a state (or DOT). FHWA The and game a state theory DOT). utilizes The game a sequential theory utilizes game awith sequential two FHWA’s game with strategic two FHWA’s moves, one imposingstrategic the moves, 10% one deck imposing requirement the 10% (which deck requir is theement current (which requirement) is the current and requirement) the other with and a the strategic changeother inwith deck a strategic requirement change (10.5%) in deck whilerequirement requiring (10.5%) states while to maintain requiring all states joints to maintain in superior all joints conditions. in superiorIn each ofconditions. the four states investigated, the co-active model leverages on element interactions and givesIn each a realistic of the four long-term states investigated, bridge performance the co-active prediction. model leverages The on proposed element co-activeinteractions model and and thegives game a realistic theory approachlong-term arebridge most performance effective in prediction. prioritizing The bridge proposed actions co-active in New model York, and where the the game theory approach are most effective in prioritizing bridge actions in New York, where the bridge bridge average service life is extended by 15 years. This may be attributed to the relatively lower average service life is extended by 15 years. This may be attributed to the relatively lower bridge bridge health indices and high co-activeness among the elements in the New York bridge inventory. health indices and high co-activeness among the elements in the New York bridge inventory. The The effectiveness of the co-active model in the Georgia and Virginia bridge inventories is similar. In both effectiveness of the co-active model in the Georgia and Virginia bridge inventories is similar. In both states,states, the the bridge bridge average average serviceservice life life is is extended extended by by 10 10 years. years. The The proposed proposed co-active co-active model model and the and the gamegame theory theory approach approach resultedresulted in in a a bridge bridge average average service service life life extension extension of 5 ofyears 5 years in Pennsylvania. in Pennsylvania. ThisThis lower lower value value of of service service life life extensionextension in Pennsylvania, compared compared to to the the other other states states investigated investigated in thisinstudy, this study, may bemay attributed be attributed to Pennsylvania’s to Pennsylvania’s bridge bridge management management strategy, strategy, which which currently currently leverages theleverages proposed the co-activeness proposed co-activeness mechanism mechanism in their bridge in their MRR, bridge even thoughMRR, even bridges though in Pennsylvania bridges in are exposedPennsylvania to aggressively are exposed deteriorating to aggressively environment deteriorati conditionsng environment similar conditions to what is similar obtainable to what in Virginiais andobtainable New York. in Virginia and New York. ThisThis study study serves serves to highlightto highlight (1) the(1) needthe need for maintaining for maintaining bridges bridges worldwide worldwide and (2)and the (2) prevalence the ofprevalence depreciating of transportationdepreciating transportation assets without asse accountingts without for accounting bridge elements’ for bridge interdependencies. elements’ interdependencies. The proposed co-active scheme, on the other hand, yields less conservative and The proposed co-active scheme, on the other hand, yields less conservative and thus more realistic thus more realistic performance predictions, which account for element interactions. Furthermore, a performance predictions, which account for element interactions. Furthermore, a strategic move that strategic move that involves leveraging the co-active mechanism and quantifying payoffs can result involvesin significant leveraging service the life co-active extension mechanism and cost andsavings. quantifying In the absence payoff sof can a strategic result in incentive significant and service liferesources, extension some and bridges cost savings. (e.g., state- In the and absence county-owned of a strategic bridges) incentive may be andleft out resources, of maintenance, some bridges (e.g.,repair, state- and and rehabilitation. county-owned For example, bridges) in maythis st beudy, left non-NHS out of maintenance,bridges are not repair,as well maintained and rehabilitation. as Forthe example, NHS bridges. in this With study, the non-NHSstrategic move bridges invested are not in this as wellstudy, maintained both state and asthe federal NHS transportation bridges. With the strategicagencies move were investedable to achieve in this positive study, outcomes. both state and federal transportation agencies were able to achieve positive outcomes. 5. Conclusions Infrastructures 2020, 5, 79 20 of 22

5. Conclusions The bridge element-based inspection data from four U.S. states (Georgia, Virginia, Pennsylvania, and New York) were investigated to determine the feasibility of implementing a proposed co-active mechanism nationwide in the United States. It is concluded that co-activeness exists in the element data, and the extent of co-activeness among elements aﬀects the long-term bridge performance. Based on the ﬁndings of this study, the following conclusions are made:

The Federal Highway Administration (FHWA) requires that states have less than 10% of the total • deck area that is structurally deficient. Therefore, the FHWA has a minimum risk benchmark, which can be described as a “worst-case scenario”, for its investments on the nation’s NHS bridges. However, criteria for obtaining the highest return on investment on bridge maintenance, rehabilitation, and replacement (MRR) are lacking. Long-term bridge performance predictions reflecting a co-active mechanism that is present in a • bridge inventory are effective in prioritizing elements for MRR decisions. Investments on the bridge MRR are optimized when the co-active mechanism that exists in a • bridge network is determined and considered in the long-term bridge performance predictions. By applying a game theory approach, it is possible to identify an inherent and particular payoff • structure between FHWA and a state DOT. The 10% limit on deck maintenance in the current requirements may not be the most cost beneficial for extending the service life in the long term. By changing this requirement to 10.5%, both FHWA and state DOTs will be able to allocate additional resources to expansion joints and joint seals. The outcome of such a strategic move yields a higher payoff for the players. State agencies with relatively lower bridge health indices are more likely to benefit from using the • proposed method that accounts for the co-active mechanism because condition changes in one element are more likely to significantly influence the bridge health indices.

6. Future Work The results presented in this paper are limited to NHS and non-NHS bridge inspection and asset management in the United States. Future work should consider applying the proposed co-active mechanism to locally owned bridges, which are known to have much-limited resources for MRR. The cause of the diﬀerences between the performances of NHS and non-NHS bridges should be investigated in detail. Finally, additional pairs/groups of players and strategic moves should be identiﬁed for a broader implementation of the proposed approach.

Author Contributions: The authors confirm contribution to the paper as follows: methodology, O.B.O., M.G.C.; development of co-active model, O.B.O., M.G.C.; data analysis and paper writing, O.B.O., M.G.C. All authors have read and agreed to the published version of the manuscript. Funding: The study presented in this paper was conducted by the University of Georgia and was partially completed under the auspices of the Georgia Department of Transportation (GDOT) RP 17-28. Acknowledgments: The authors extend our sincere appreciation to GDOT staff and engineers that supported this research. The funding sponsors had no role in the design, analyzes, or interpretation of data. The opinions, findings, and conclusions may not reflect the views of the funding agency or other individuals. All authors have read and agreed to the published version of the manuscript. Conflicts of Interest: The authors have no implicit or explicit conflict of interest of any kind in this study.

References

1. Contreras-Nieto, C.; Shan, Y.; Lewis, P.; Hartell, J.A. Bridge maintenance prioritization using analytic hierarchy process and fusion tables. Autom. Constr. 2019, 101, 99–110. [CrossRef] 2. Lu, P.; Phares, B. Integration of Structural Health Monitoring (SHM) into Multilayer Statewide Bridge Maintenance and Management Practices–SHM-Facilitated Condition-Based Maintenance (SHM-CBM) Prioritization System; Iowa State University: Ames, IA, USA, 2018. Infrastructures 2020, 5, 79 21 of 22

3. Kim, D.; Lee, Y.; Lee, M.J. Development of Risk-Based Bridge Maintenance Prioritization Methodology. KSCE J. Civ. Eng. 2018, 22, 3718–3725. [CrossRef] 4. Parvardeh, H.; Babanajad, S.; Ghasemi, H.; Maher, A.; Gucunski, N.; Zobel, R. The Long-Term Bridge Performance (LTBP) Program Bridge Portal. In Proceedings of the 4th International Conference on Road and Rail Infrastructure, Šibenik, Croatia, 23–25 May 2016; pp. 389–395. 5. Sarhosis, V.; De Santis, S.; de Felice, G. A review of experimental investigations and assessment methods for masonry arch bridges. Struct. Infrastruct. Eng. 2016, 12, 1439–1464. 6. Zhang, W.; Wang, N. Bridge network maintenance prioritization under budget constraint. Struct. Saf. 2017, 67, 96–104. [CrossRef] 7. Van Erp, H.N.; Orcesi, A.D. The use of nested sampling for prediction of infrastructure degradation under uncertainty. Struct. Infrastruct. Eng. 2018, 14, 1025–1035. [CrossRef] 8. Zhang, X.; Gao, H. Determining an optimal maintenance period for infrastructure systems. Comput. Aided Civ. Infrastruct. Eng. 2012, 27, 543–554. [CrossRef] 9. FHWA. Moving Ahead for Progress in the 21st Century Act (MAP-21): A Summary of Highway Provisions. Available online: https://www.fhwa.dot.gov/map21/summaryinfo.cfm (accessed on 1 July 2020). 10. Agdas, D.; Rice, J.A.; Martinez, J.R.; Lasa, I.R. Comparison of visual inspection and structural-health monitoring as bridge condition assessment methods. J. Perform. Constr. Facil. 2016, 30, 04015049. [CrossRef] 11. Andrijcic, E.; Haimes, Y.Y. Metamodeling of interdependent systems: Application to bridge infrastructure management. J. Infrastruct. Syst. 2017, 23, 04016028. [CrossRef] 12. Sabatino, S.; Frangopol, D.M. Decision support system for optimum lifetime sustainability-based maintenance planning of highway bridges. In Proceedings of the International Conference on Sustainable Infrastructure, New York, NY, USA, 26–28 October 2017; pp. 65–72. 13. Puls, E.; Hueste, M.B.D.; Hurlebaus, S.; Damnjanovic, I.; Policy. Prioritization of a bridge inventory for historic preservation: A case study for Tarrant County, Texas. Public Work. Manag. Policy 2018, 23, 205–220. [CrossRef] 14. AASHTO. The AASHTO Manual for Bridge Element Inspection, 2nd ed.; American Association of State Highway and Transportation Officials: Washington, DC, USA, 2019. 15. Oyegbile, O.B.; Chorzepa, M.G. Co-Active Prioritization by Means of Contingency Tables for Analyzing Element-level Bridge Inspection Results and Optimizing Returns. Infrastructures 2020, 5, 13. [CrossRef] 16. Oyegbile, O.B. Novel Element-Data Driven Coactive Prioritization for Bridge Asset Management. Ph.D. Thesis, University of Georgia, Athens, GA, USA, 2020. 17. MandićIvanković,A.; Skokandić,D.; Žnidariˇc,A.; Kreslin, M. Bridge performance indicators based on traffic load monitoring. Struct. Infrastruct. Eng. 2019, 15, 899–911. [CrossRef] 18. Hooks, J.M.; Frangopol, D.M. LTBP Bridge Performance Primer; Federal Highway Administration: McLean, VA, USA, 2013. 19. Zanini, M.A.; Faleschini, F.; Casas, J.R. State-of-research on performance indicators for bridge quality control and management. Front. Built Environ. 2019, 5, 1–22. [CrossRef] 20. Strauss, A.; MandićIvanković,A.; Matos, J.; Casas, J.R. Performance indicators for road bridges—Overview of findings and future progress. In Proceedings of the Value of Structural Health Monitoring for the Reliable Bridge Management, Zagreb, Croatia, 2–3 March 2017; pp. 1–6. 21. Frangopol, D.M.; Dong, Y.; Sabatino, S. Bridge life-cycle performance and cost: Analysis, prediction, optimisation and decision-making. Struct. Infrastruct. Eng. 2017, 13, 1239–1257. [CrossRef] 22. Agrawal, A.K.; Kawaguchi, A.; Chen, Z. Deterioration rates of typical bridge elements in New York. J. Bridge Eng. 2010, 15, 419–429. [CrossRef] 23. Li, L.; Sun, L.; Ning, G. Deterioration prediction of urban bridges on network level using Markov-chain model. Math. Probl. Eng. 2014, 2014, 1–10. [CrossRef] 24. Chang, M.; Maguire, M.; Sun, Y. Framework for mitigating human bias in selection of explanatory variables for bridge deterioration modeling. J. Infrastruct. Syst. 2017, 23, 04017002. [CrossRef] 25. Zanini, M.A.; Faleschini, F.; Pellegrino, C. Cost analysis for maintenance and seismic retrofit of existing bridges. Struct. Infrastruct. Eng. 2016, 12, 1411–1427. [CrossRef] 26. Ghodoosi, F.; Abu-Samra, S.; Zeynalian, M.; Zayed, T. Maintenance cost optimization for bridge structures using system reliability analysis and genetic algorithms. J. Constr. Eng. Manag. 2018, 144, 04017116. [CrossRef] Infrastructures 2020, 5, 79 22 of 22

27. Fang, Y.; Sun, L. How do funds allocation and maintenance intervention aﬀect the deterioration process of urban bridges in Shanghai. In Proceedings of the International Symposium on Pavement. Roadway, and Bridge Life Cycle Assessment, Sacramento, CA, USA, 3–6 June 2020; p. 72. 28. Elbehairy,H.; Elbeltagi, E.; Hegazy,T.; Soudki, K. Comparison of two evolutionary algorithms for optimization of bridge deck repairs. Comput. Aided Civ. Infrastruct. Eng. 2006, 21, 561–572. [CrossRef] 29. USC. Title 23—Highways, Chapter 1: Federal-Aid Highways. Available online: https://uscode.house.gov/ view.xhtml?path=/prelim@title23&edition=prelim (accessed on 15 June 2019). 30. FHWA. Bridge Preservation Guide: Maintaining a Resilient Infrastructure to Preserve Mobility. Available online: https://www.fhwa.dot.gov/bridge/preservation/guide/guide.pdf (accessed on 14 August 2020). 31. Robert, W.E.; Marshall, A.R.; Lin, S.S.; Shepard, R.W.; Aldayuz, J. Integration of agency rules with the preservation optimization model in the Pontis bridge management system. Transp. Res. Rec. 2002, 1795, 74–81. [CrossRef] 32. Roberts, J.E.; Shepard, R. Bridge management for the 21st century. In Proceedings of the Structures Congress, Washington, DC, USA, 21–23 May 2001; pp. 1–12.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).