Embed Size (px)
Citation preview
Managing bridge infrastructure under budgetconstraints: a decision support methodology
Saleh Abu Dabous and Sabah Alkass
Abstract: Managing the deteriorating bridge infrastructure has become a major social and economic concern in NorthAmerica. The methodology developed in the present research consists of three methods: (1) ranking and prioritizing methodto evaluate and rank all bridge projects in a network, (2) ranking method to evaluate the available rehabilitation strategiesfor each project, and (3) recommended work program development method. The recommended work program specifies alist of projects to allocate the available budget to and what type of action to be implemented for each project. The developedmethodology allows engineers to use multiple and conflicting criteria and to incorporate their experience and judgment inthe decision making process. The methodology can assist bridge engineers and decision makers in selecting the most suit-able work program that can be performed with a limited budget. An example application is presented to demonstrate the useand capabilities of the developed methodology.
Key words: bridge, decision, budget, rehabilitation, multi-criteria, utility, AHP.
Résumé : La gestion de la détérioration de l’infrastructure des ponts est devenue un enjeu économique et social majeur enAmérique du Nord. La méthodologie développée dans la recherche présentée dans cet article comporte trois méthodes:(1) une méthode de classement et de détermination de l’ordre des priorités afin d’évaluer et de classer tous les projets deponts dans un réseau, (2) une méthode de classement pour évaluer les stratégies de remise en état disponibles pour chaqueprojet et (3) une méthode de développement d’un programme pour le travail recommandé. Ce programme de travail recom-mandé spécifie une liste de projets afin d’allouer le budget disponible ainsi que les actions à prendre pour chaque projet. Laméthodologie développée permet aux ingénieurs d’utiliser plusieurs critères incompatibles et d’incorporer leur expérience etleur jugement dans le processus de prise de décisions. Cette méthodologie peut aider les ingénieurs de ponts et les décideursà choisir le meilleur programme de travail qui peut être réalisé à l’intérieur d’un budget limité. Un exemple démontre l’utili-sation et les capacités de la méthodologie développée.
Mots‐clés : pont, décision, budget, remise en état, multicritères, utilité, MHM.
[Traduit par la Rédaction]
Introduction
Reports on the status of civil infrastructure in North Amer-ica demonstrate that the deteriorating bridge infrastructure re-quires immediate attention. In the 2009 report card forAmerica’s infrastructure, the American Society of Civil Engi-neers reported that more than 26% of bridges in the UnitedStates are either structurally deficient or functionally obsolete.The society estimated that a $17 billion annual investment isneeded to substantially improve current bridge conditions.The current yearly spending on the construction and mainte-nance of bridges in the United States is $10.5 billion (ASCE2009). In 2008, AASHTO estimated that it would cost about$48 billion to repair structurally deficient bridges and $91 bil-lion to improve functionally obsolete bridges that are no lon-ger adequate to serve traffic (AASHTO 2008).The Federation of Canadian Municipalities reported that
83% of Canadian bridges need some sort of repair (Mirza
and Haider 2003). Vanier (2000) concluded that managersand decision makers in the United States and Canada are re-quired to maintain the deteriorated bridge infrastructure underlimited budget considerations. Thus, these managers need de-cision support systems to help them to manage the existingdeteriorating bridge infrastructure.Many transportation agencies make bridge management
decisions based on a combination of analyzing availablequantitative data such as the inspection reports and usingsubjective judgments of the decision and policy makers (Kul-karni et al. 2004). This process aims toward distributing theavailable budget among bridges that need intervention anddefining what type of action to be taken for each bridge. Thesubjective nature of this decision making process could raisequestions about whether the investment decisions are beingmade in a fair, equitable and systematic manner or if theymore often reflect the intuitive judgments of the decisionmakers. Alternatively, bridge engineers and policy makers
Received 8 February 2011. Revision accepted 27 July 2011. Published at www.nrcresearchpress.com/cjce on 31 October 2011.
S. Abu Dabous. American University of Sharjah P.O. Box 26666, UAE.S. Alkass. Department of Building, Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve, Montreal, QCH3G 1M8, Canada.
Corresponding author: Saleh Abu Dabous (e-mail: [email protected]).
Written discussion of this article is welcomed and will be received by the Editor until 31 March 2012.
1227
Can. J. Civ. Eng. 38: 1227–1237 (2011) doi:10.1139/L11-082 Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
need rational decision support tools to help them in manag-ing bridge networks under budget constraints.This research develops a decision support methodology to
allocate limited budget to the most deserving projects in anetwork and to recommend the most effective rehabilitationstrategy for each project. The methodology integrates multi-ple criteria decision support methods within the developedframework to generate a recommended work program. Thefocus in the current research is directed at bridge decks. Fur-ther future research is recommended to study other elements.
Literature reviewThe main objective of a bridge management decision sup-
port system is to select the actions necessary to maintainbridge networks within acceptable limits of safety and serv-iceability. A review of existing literature on bridge manage-ment decision making is completed as a part of the research.The review divides the relevant available literature into threecategories: (1) Markov decision process to find optimal poli-cies describing what maintenance actions to take; (2) benefit–cost analysis to compare monetary values for benefits andcosts associated with individual projects or strategies; and(3) life cycle cost analysis procedures to design alternativeswith full recognition of the costs and benefits associatedwith each alternative life cycle.
Markov decision process (MDP)Past research in infrastructure management utilized the
Markov decision process for decision making (Gopal andMajidzadeh 1991; Madanat and Ben-Akiva 1994; Abrahamand Wirahadikusumah 1999). The MDP is an extension ofMarkov chains. The MDP utilizes the state dependence as-sumption in Markov models and adds actions that can leadto improvements under specific certainties. The state depend-ence means that the probability of improvement is independ-ent of the history. When the process is in condition i and anaction A is taken, the process improves into condition j withprobability Pij.
½1� PijðAÞ ¼ PðXnþ1 ¼ jjXn ¼ iÞOptimization of maintenance policies using the Markov
decision process can be performed by applying recursivelythe following equation (Frangopol et al. 2004):
½2� VaðiÞ ¼ Cði;AÞ þ aXN
j¼1
PijðAÞVaðjÞ
where a is the discount factor for one year, estimated by a =(1 + r/100) – 1; r is the yearly discount rate; Va is the valuefunction using a; and C(i, A) is the costs that are incurredwhen the process is in condition i and action A is taken.Then a cost-optimal decision can be found by minimizingthe previous cost equation with respect to the action underconsideration through using one of the mathematical pro-gramming techniques such as linear programming or one ofits variations.The main shortcoming of the MDP is mainly due to the
state dependence assumption that overlooks the history of de-terioration process. Empirical research has confirmed that ageis a significant factor in the deterioration process (Jiang et al.
1988; Madanat et al. 1997). In addition, solution techniquesare intractable as the discrete set of condition states becomelarge. Thus, it is very difficult to manage large networks offacilities jointly or to consider complex relationships amongrelevant variables.
Benefit-to-cost ratio analysisThe benefit-to-cost ratio analysis evaluates all of the bene-
fits and costs associated with a project, including both directagency cost and indirect user cost using the dollar as the unitof measure. Priority is given to projects that provide morebenefits and incur less cost. The direct agency cost can beestimated from the available cost data. The indirect user costsor benefits are difficult to quantify and are usually estimatedusing certain parameters or simplifying assumptions.Kulkarni et al. (2004) reported that concerns arise when
the benefit concept is applied to evaluate a large number ofdiverse projects at many different locations, as opposed to asmall number of projects. Also, an excessive amount of effortis needed to apply the concept to a large number of projects.
Life cycle cost analysisCost is a major factor in the decision making process, es-
pecially within tight budgets considerations. The cost concepthas evolved over the years into life cycle cost, which impliesthat the preferred alternative is an alternative that would costless in the long run. Life cycle cost (LCC) analysis for bridgeengineering is defined by the National Cooperative HighwayResearch Program as a set of economic principles and com-putational procedures for comparing initial and future coststo arrive at the most economical strategy for ensuring that abridge will provide the services for which it was intended(Hawk 2003).Kong and Frangopol (2003) developed reliability-based life
cycle maintenance cost optimization of deteriorating bridges.Frangopol and Neves (2003) investigated uncertainty effectson the evaluation of condition and safety indices as well ason the LCC of deteriorating bridges under different mainte-nance strategies using Monte Carlo simulation. Huang et al.(2004) developed a project-level decision support tool torank maintenance scenarios for deteriorated concrete bridgedecks based on probabilistic LCC analysis.Applying the optimized life cycle cost methodology may
create practical difficulties especially when the availablebudget is larger or lower than the computed minimum lifecycle cost. If the available budget is larger than the computedminimum life cycle cost, the bridge performance can be im-proved to a higher level than the level achieved by the mini-mum life cycle cost solution. On the other hand, if theavailable budget is less than the computed minimum lifecycle cost, an alternative solution is needed since the mini-mum life cycle cost solution cannot be implemented (Frango-pol and Liu 2007).
Decision support methodologyInterviews with bridge experts from two private corpora-
tions in Montreal and with bridge engineers from the Minis-try of Transportation of Ontario concluded that decisionsupport systems are needed to assist in improving perform-ance of the bridge network and in distributing the limited
1228 Can. J. Civ. Eng. Vol. 38, 2011
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
budget effectively. One of the most critical challenges in thedecision making process is the evaluation of data and infor-mation especially when both subjective and objective data isincorporated in the process. The proposed decision supportmethodology in this paper integrates the Analytic HierarchyProcess (AHP) and the Multi-Attribute Utility Theory(MAUT) to extract experts’ knowledge and judgments whileincorporating quantitative and qualitative criteria in the deci-sion making process. The AHP is one of the most versatiledecision making tools due to its simplicity and ability tocope with complex decision making problems. The MAUTenables decision makers to include multiple and conflictingcriteria. In addition, the theory provides flexibility for the de-cision makers in expressing their degree of satisfaction withdecision attributes and captures the decision makers’ attitudetoward risk. The flow chart in Fig. 1 depicts the decisionsupport methodology.The following sections present in detail the different ele-
ments of the developed decision support methodology.
Ranking and prioritizing projectsAt the network level, a large number of projects (can be up
to 5000 bridges) need to be ranked and prioritized while in-corporating experts’ inputs. The MAUT is utilized to performthis task. The basic principle of the MAUT is based on esti-mating performance using attributes that are concrete, meas-urable, and representative of the degree of satisfaction withthe various aspects of each alternative. The foundation ofMAUT is the use of utility functions, which are utilized toquantify the preference of the decision maker by depictingthe degree of satisfaction, as the attribute under considerationtakes values between the most and least desirable limits.Figure 2 presents a flow chart for the ranking method
based on the MAUT. The method uses a default hierarchystructure and a defined set of criteria. At the same time themethod allows the decision maker to modify these elements.The default hierarchy is four levels. The first level of the hier-archy is the overall goal of the ranking exercise that is the ef-fective allocation of available funds. The second levelcontains the three objectives necessary to achieve the overallgoal. The third level of the hierarchy holds the criteria to beused for evaluating the objectives. These criteria are conditionrating, live load carrying capacity and seismic risk to measurethe objective of maximizing bridge preservation and safety,average daily traffic and supporting road type to measure theobjective of maximizing effectiveness of investment, and ver-tical clearance, approach and drainage system conditions tomeasure the objective of minimizing bridges deficiencies.The alternatives are added at the bottom level. Each objectiveor criterion has a specific weight reflecting its importance.The weights of the different criteria and objectives are devel-oped using the Eigenvector approach. Abu Dabous (2008)discusses this hierarchy structure development in detail.Figure 3 presents the utility functions developed to be in-
corporated within the proposed decision support methodol-ogy. These functions are developed based on data andjudgments extracted during the previously mentioned inter-views with bridge engineers and managers.A utility model can be used to aggregate the utility values
for the various attributes. Since the elements in each level ofthe hierarchy structure are considered to be independent, theadditive utility model can be used as a simple and practical ap-proach to aggregate utilities. In such a model, the overall ex-pected utility is expressed as follows (Keeney and Raiffa 1993):
½3� UðxÞ ¼Xn
i¼1
kiuiðxÞ
where ki is the weight for attribute i, ui is utility value for at-tribute i, and x1 to xn are the available alternatives.The utility scores obtained from the utility functions are
aggregated using eq. [3] to estimate the utility associatedwith each objective. Then, the utilities of the various objec-tives are aggregated using the same equation to evaluate theoverall utility of the bridge. All bridges in the network orsub-network can be ranked based on the overall utility val-ues. For example, the attribute values for bridge number 10are given in Table 1. The expected utility value for thisbridge is as follows:
½4� Uð10Þ ¼ ð78:66� 0:4þ 28:89� 0:45þ 28:89� 0:15Þ � 0:60� �þ ð33:33� 0:55þ 11:11� 0:45Þ � 0:20
� �
þ ð24:44� 0:4þ 77:77� 0:35þ 62:95� 0:25Þ � 0:20 ¼ 44:49
Fig. 1. Flow chart for the decision support methodology.
Abu Dabous and Alkass 1229
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
The overall expected utility for each bridge can be esti-mated and used to rank all bridges in the network.
Ranking rehabilitation strategies
At the project level, a number of alternative maintenanceand rehabilitation strategies are available for each project.Decision makers are required to evaluate these strategiesbased on multiple criteria. The AHP is a multi-criteria deci-sion process that utilizes both actual measurements and ex-pert judgment. Using the AHP for this task can enableproviding preferences between the different maintenance andrehabilitation strategies that are specific to each project.Two fundamental steps are required to use the AHP meth-
odology. First, a complex system is broken down into a hier-
archic structure to represent the problem. Second, pairwisecomparisons are performed to measure the relative impact ofdifferent elements in the hierarchy and to establish relationswithin the structure. The pairwise comparisons are performedusing a fundamental scale of absolute values that representsthe strength of judgments (Saaty 1980). The pairwise com-parisons lead to dominance matrices from which ratio scalesare derived in the form of principal eigenvectors.To demonstrate the applicability of the AHP, a case study
is discussed to rank rehabilitation strategies for a deteriorat-ing bridge deck. The assessment and pairwise comparisonsin this case study are performed by an expert from the indus-try who is involved in bridge management decision making.The available strategies are major rehabilitation, minor reha-bilitation or increased routine maintenance. These three alter-natives should be evaluated using the following criteria:
Fig. 2. Flow chart for the project ranking method.
1230 Can. J. Civ. Eng. Vol. 38, 2011
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
agency cost, user cost, bridge safety, bridge deck useful life,and environmental impact.Figure 4 presents the decomposition of the problem into a
hierarchy. The first level is the overall goal of choosing a re-habilitation strategy. The second level represents the five cri-teria that contribute to the overall goal, and the third levelrepresents the three candidate rehabilitation strategies.The judgments provided by the expert are provided in
Figs. 5 and 6. The judgements are solicited by asking the ex-pert to compare the decision elements in pairs and select lin-guistic expressions to define the intensity of relativeimportance as defined above in the second step of the AHPmethodology. The matrix in Fig. 5 is obtained by comparingthe set of criteria in pairs with respect to the overall goal.The matrices in Fig. 6 are obtained by comparing the alterna-tive rehabilitation strategies in pairs with respect to each cri-terion.
Finally, global priorities of the different rehabilitation strat-egies are estimated by multiplying the weights of the strategywith respect to each criterion by the criterion weight andfinding the overall sum as follows:
• Major rehabilitation = 0.093 × 0.121 + 0.089 × 0.088 +0.571 × 0.548 + 0.571 × 0.121 + 0.669 × 0.121 = 0.483
• Minor rehabilitation = 0.221 × 0.121 + 0.323 × 0.088 +0.286 × 0.548 + 0.286 × 0.121 + 0.257 × 0.121 = 0.278
• Routine maintenance = 0.685 × 0.121 + 0.587 × 0.088 +0.143 × 0.548 + 0.143 × 0.121 + 0.074 × 0.121 = 0.239
• The analysis prefers bridge deck replacement and gives ap-proximately the same weight for minor rehabilitation androutine maintenance.
Work program developmentOne of the most challenging tasks for bridge managers and
decision makers is to select a work program to be performedwhen the available budget is limited. The purpose of thiswork program is to recommend a list of projects for improve-ment and to specify a rehabilitation strategy to be performedfor each project. These recommended strategies maximizebenefits to the agency and the users and can be implementedwithin the available budget. The recommended work programis developed by evaluating the various combinations of thedifferent projects and the available rehabilitation actions. Theproblem under consideration is difficult to analyze manuallysince a large number of possible combinations can be devel-oped and included for consideration. Simulation can be usedto develop and evaluate the various possible work programs.The following is a description of the first three iterations ofthe simulation process. These iterations are intended to ex-plain how work programs can be developed and evaluated.
0102030405060708090
100
35 40 45 50 55 60 65 70 75 80 85 90 95 100
Utilit
y
Deck condition index
0
10
20
30
40
50
60
70
80
90
100
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9
Utilit
y
Live load capacity factor
Utility function for load carrying capacity
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Utilit
y
Seismic vulnerability index
Utility function for seismic risk
60708090
100
Utility function for average daily traffic
60708090
100Utility function for vertical clearance
60
80
100Utility function for supporting road type
0102030405060708090
100
35 40 45 50 55 60 65 70 75 80 85 90 95 100 0
10
20
30
40
50
60
70
80
90
100
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.90
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
0102030405060708090
100
0 20 40 60 80 100 120 140 160 180 200
Utilit
y
Average daily traffic (Thousands of vehicles)
0102030405060708090
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Utilit
y
Vertical clearance index
102030405060708090
100
Utilit
y
Utility function for approach condition
0102030405060708090
100Drainage system
0
20
40
60
80
100
Utilit
y
Highway National Regional Local
0102030405060708090
100
35 40 45 50 55 60 65 70 75 80 85 90 95 100
Utility function for condition rating
0
10
20
30
40
50
60
70
80
90
100
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.90
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
0102030405060708090
100
0 20 40 60 80 100 120 140 160 180 2000
102030405060708090
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0102030405060708090
100
0 1 2 3 4 5Approach condition rating
0102030405060708090
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Utilit
y
Drainage system index
0
20
40
60
80
100
Fig. 3. Utility functions for the bridge attributes.
Table 1. Attributes and utility values of projects (Bridge 10).
Criterion
Bridge 10
Attributevalue
Utilityvalue
Condition rating 64 78.66Load carrying capacity 1.6 28.89Seismic risk 2.6 28.89Average daily traffic (thousands) 40 33.33Supporting road type Local 11.11Vertical clearance 0.25 24.44Approach condition Fair 77.77Drainage system 0.60 62.95Expected utility value 44.49
Abu Dabous and Alkass 1231
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
• In the first iteration of the simulation, one project is con-sidered. The selected project is the one with the highestpriority. For this single project, the candidate work pro-grams are the available rehabilitation actions: replace-ment, repair or maintenance of the deck. If the availablebudget is sufficient to perform any of these three alterna-tives, the one that has the highest weight is selected asthe current best work program. For example, if theweight for replacement is 0.45, the weight for repair is0.35, and the weight for maintenance is 0.2, the current
recommended work program will be to replace the bridgedeck since it has the highest weight.
• The second iteration of the simulation considers two pro-jects, which have the highest and the second highest uti-lity. One of the available three maintenance, replace, andrepair (MR&R) options can be selected for each projectas the project is included in a possible work program. Inthis case, nine candidate work programs can be developedfor evaluation. These work programs are: (replace1 andreplace2), (replace1 and repair2), (replace1 and main-
Fig. 4. Hierarchy structure for choosing bridge rehabilitation strategy.
Fig. 5. Comparison of criteria with respect to the overall goal.
Fig. 6. Comparison of alternatives with respect to each criterion.
1232 Can. J. Civ. Eng. Vol. 38, 2011
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
tain2), (repair1 and replace2), (repair1 and repair2), (re-pair1 and maintain2), (maintain1 and replace2), (main-tain1 and repair2), or (maintain1 and maintain2). Thesimulation develops these combinations and estimates thetotal weights and the total cost for the rehabilitation stra-tegies associated with each of the developed programs.The work program with the highest total weight and totalcost less than or equal to the available budget will be-come the current best replacing the one from the previousiteration.
• The third iteration will include the three highest utility pro-jects and can have 27 candidate work programs. The simu-lation develops these programs and evaluates the total costand total weight for each program. The program with thehighest total weight for its rehabilitation strategies and totalcost less than or equal to the available budget becomes thecurrent best.The process continues adding new projects based on their
utilities until the point when adding an additional project willproduce work programs with total costs that cannot be imple-mented with the available budget, such that the cost of eachwork program exceeds the available budget. At this point thesimulation stops and eliminates the programs that exceed theavailable budget. The program that has the highest total
weight and can be performed with the available budget isflagged as the recommended work program. Figure 7 showsthe sequence of steps to develop the different candidate workprograms and to select a recommended one.The cost of each MR&R action must be estimated since
that will be needed to estimate an overall cost for the devel-oped work program. This is important to ensure that theoverall cost of the recommended work program does not ex-ceed the available budget. The following section discussesthe development of cost models for the MR&R actions.
Cost estimating models for rehabilitationactions
A number of maintenance and rehabilitation strategies areavailable for the bridge deck once it reaches the interventionlevel. These strategies can range from do-nothing to completereplacement. Cost estimating models to evaluate the cost ofbridge rehabilitation actions are essential elements of the pro-posed methodology. One cost model for bridge deck replace-ment and one for deck major repair are developed here basedon data and reports collected during the above mentioned in-terviews. The unit costs of the different items are extractedfrom winning bid proposals submitted by specialized contrac-
Send a request to develop a recommended work
program
Cost < Budget
Retrieve the project with the highest overall utility
No
Yes
Develop the possible work programs
Evaluate the total weights of the rehabilitation strategies
associated with each program
Estimate the cost of each program
Select a current best program
Add the next highest utility project
The current best with total cost less or equal the available budget is
the recommended work program
Fig. 7. Work program development using simulation.
Abu Dabous and Alkass 1233
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
tors to Canadian ministries of transportation. The unit cost ofeach item includes the direct cost, indirect cost and the markupadded to cover the contractor’s profit and contingency. A thirdmodel for maintenance cost is developed based on a modelfrom the literature. The following sections discuss the develop-ment of cost models for bridge improvement projects.
Bridge deck replacementBridge deck replacement provides a brand new deck with
the longest useful life. This option is normally performed byreplacing the superstructure of the bridge. In concretebridges, a bridge deck is integral with the girders whichmakes it difficult to remove the deck slab while keeping thegirders in place. Hence, deck replacement typically includesreplacing the girders which provides a new superstructure forthe bridge. This is a major improvement with a relativelyhigh cost. The cost of replacing the bridge deck depends onthe type of the new superstructure to be constructed and thearea of the deck. Saito et al. (1988) reported that the unitsuperstructure cost can be estimated in terms of dollars persquare unit of deck area.The superstructure type is defined according to the slab
and girders configuration. The most common arrangement ispre-stressed girders with a composite concrete slab on top.During the interviews with the bridge engineers, the develop-ment of a work breakdown structure for this type of arrange-ment was discussed and cost data for all the elementsincluded in the structure was collected. Table 2 presents thework breakdown structure and the cost elements for bridgedeck replacement. The total deck area is 930 m2 and thesuperstructure arrangement is 150 mm thickness concreteslab on pre-stressed concrete girders. The cost data presentedin the table includes both direct and indirect cost elements inaddition to the markup for profit and contingency. The costdata is in Canadian dollars, adjusted for inflation and basedon the 2008 dollar value.
Analysis of the cost estimate for 17 bridge deck replace-ment projects showed that the unit cost can be between $837and $1115 with a mean value equal to $917.50 per squaremetre. The replacement unit cost for each project is estimatedby dividing the total project cost by the deck area.
Bridge deck major repairMajor repair can improve the deck to an excellent condi-
tion state. This option is performed by repairing the deck sur-face and installing a cathodic protection system. It involvesthe removal of the delaminated concrete from the deck sur-face and soffit and patch repair of the removal areas. A tita-nium mesh anode embedded in a normal concrete overlaywill be installed to ensure cathodic protection of the reinforc-ing steel in the deck. This system is recommended since theoverlay will allow the placing of waterproofing to prevent theingress of water and deicing salts into the concrete.In this research, the total cost is estimated and linked to
the bridge deck area to evaluate the cost per square metre forthe major repair option. Table 3 presents a work breakdownstructure for the major repair and the cost associated witheach item. The cost includes both direct and indirect cost el-ements. As before, the cost data are in Canadian dollarsbased on the 2008 value.Analysis of the cost estimate for 19 bridge deck major re-
pair projects showed that the unit cost can be between $669and $792 with a mean value of $701 per square metre. Themajor repair unit cost for each project is estimated by divid-ing the total project cost by the deck area.
Bridge deck maintenance costThe maintenance option does not involve any improve-
ments to the condition or the structural aspects of the bridgedeck. The maintenance activities include patching, sealingcracks or eliminating visible distresses that can accelerate the
Table 2. Cost elements for bridge deck replacement.
Item Item description Unit Quantity Unit cost ($)A.1 Removal of asphalt wearing surface m2 830 6A.2 Removal railing LS 1 3 000A.3 Removal of concrete end posts LS 1 7 500A.4 Removal of existing deck including curbs m3 270 525A.5 Removal of top of pier m3 6 1 500A.6 Removal of existing approach slab m3 51 150B.1 Granular backfill m3 75 60B.2 Concrete in new top of existing piers m3 10 750B.3 Prestressed members (fabrication and erection) m 505 900B.4 Concrete in barrier wall m3 12 1 275B.5 Concrete in deck (150 mm topping) m3 100 675B.6 Concrete in new deck extensions m3 12 900B.7 Concrete in approach slabs m3 50 375B.8 Stainless steel rebar in barrier wall tonne 1.6 15 000B.9 Coated rebars in deck topping tonne 9 2 250B.10 Rebars in deck extensions tonne 0.6 1 500B.11 Rebars in approach slabs tonne 1 1 500B.12 Bearings each 84 165B.13 Abutment repairs m3 2 6 000B.14 Bridge deck waterproofing m2 650 18B.15 Asphalt tonne 180 90
Note: The cost data is in Canadian dollars, adjusted for inflation and based on the 2008 dollar value. LS, allowance or lot.
1234 Can. J. Civ. Eng. Vol. 38, 2011
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
Table 3. Cost elements for bridge deck major repair.
Item Item description Unit Quantity Unit cost ($)
C.1 Removal of asphalt wearing surface m2 830 6C.2 Removal of railings LS 1 3 000C.3 Removal of concrete end posts LS 1 7 500C.4 Removal of concrete curbs m3 20 525C.5 Type A removals from top of deck (delaminations only) m2 300 285C.6 Access to work area LS 1 7 500C.7 Type B removals from deck soffit m3 2 6 000C.8 Type C removals from fascia m3 5 4 500C.9 Type C removals from deck ends (tendon anchors) m3 1 15 000C.10 Removal of existing approach slab m3 51 150D.1 Granular backfill m3 75 60D.2 Scarify deck surface m2 625 17D.3 Cathodic protection m2 625 300D.4 Abrasive blast cleaning of rebar m2 300 82D.5 Abrasive blast cleaning for overlays m2 325 26D.6 Concrete overlay (includes padding for new crown) m3 100 638D.7 Finish and cure overlay m2 625 38D.8 Concrete barrier wall m3 12 1 275D.9 Concrete in new deck extensions m3 12 900D.10 Concrete in approach slabs m3 50 375D.11 Stainless steel rebar (barrier wall & deck extensions) tonne 2.2 15 000D.12 Coated rebar for overlay padding area tonne 4 2 250D.13 Rebars in deck extensions tonne 0.6 1 500D.14 Rebars in approach slabs tonne 1 1 500D.15 Abutment repairs m3 2 6 000D.16 Deck soffit repairs m3 4 6 000D.17 Bridge deck waterproofing m2 650 18D.18 Asphalt tonne 180 90
Note: The cost data is in Canadian dollars, adjusted for inflation and based on the 2008 dollar value. LS, allowance or lot.
Fig. 8. Bridge deck maintenance cost.
Table 4. Rehabilitation stratey costs for the three top ranked bridges.
BridgeDeckarea (m2)
Replacementcost ($)
Repaircost ($)
Maintenancecost ($)
Bridge 70 1 250 1 146 875 876 250 61 806Bridge 40 1 100 1 009 250 771 100 52 556Bridge 30 950 871 625 665 920 39 583
Note: The cost data is in Canadian dollars, adjusted for inflation andbased on the 2008 dollar value.
Table 5. Weighted priorities for the rehabilitation strategies.
Bridge Replacement Repair MaintenanceBridge 70 0.45 0.30 0.25Bridge 40 0.35 0.35 0.30Bridge 30 0.60 0.32 0.08
Abu Dabous and Alkass 1235
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
corrosion of the deck reinforcement. The maintenance costdepends on the condition of the bridge. The available studiesreport that annual maintenance costs range from 1% to 2% ofthe reconstruction cost (Branco and de Brito 2004). De Britoand Branco (1998) developed a graphical representation formaintenance cost in relation to the bridge deck area. Theydescribed a linear relationship between the deck area and themaintenance cost. In addition, they specified that the mainte-nance cost for a 4000 m2 deck is double the maintenance costfor a 400 m2 deck and that the maintenance cost for a 400 m2
deck is double the maintenance cost for a 100 m2 deck.Increased maintenance cost for a bridge deck is estimated to
be 5% of the reconstruction cost. Applying the linear relationsuggested by Branco and de Brito (2004), the graph for themaintenance cost is developed as shown in Fig. 8. From thisrepresentation, the unit cost for a 400 m2 deck is $40 per squaremetre and for a 4000 m2 deck it is $80 per square metre.Using this graphical representation, the maintenance cost
for any bridge deck can be estimated by multiplying the cor-responding unit cost for the area by the bridge deck area.
Case exampleTo illustrate the development of a recommended work pro-
gram, the following case example is presented. The case ex-ample is based on a case study discussed in Abu Dabous(2008). The three bridges with the highest rank from thecase study are considered since they have the highest utilityand must be prioritized for intervention. The cost of the threerehabilitation strategies for each project is estimated from the
cost models developed earlier. The cost estimates are shownin Table 4.The decision maker provides specific judgments for each
bridge to evaluate the different rehabilitation actions and todevelop a weight for each option. The weights for the reha-bilitation actions are provided in the Table 5.The 27 candidate work programs are developed as all pos-
sible combinations of high priority projects and the availablerehabilitation strategies as shown in Table 6. The total cost inTable 6 is estimated by finding the sum for the cost of all therehabilitation actions associated with each program. The costof each action is provided in Table 4. Similarly, the totalweight is estimated by finding the sum for the weights of allthe rehabilitation strategies involved in the program. The pri-ority for each action is given in Table 5.Assuming that the available budget is $2.10 million, work
programs that cost more than the available budget are notpossible, which means that work programs 2, 3, 5, 6, 11, 12,14, and 15 must be eliminated. Work program 9 has thehighest total weight of 1.35 and a total cost of $2 071 056,and work program 18 has the second highest weight of 1.20and a total cost of $1 800 431. The decision makers cancompare these two efficient work programs to select themore attractive one for the agency.Analysis of the above case study has shown that 27 possible
work programs are available for three projects with three pos-sible actions. The number of possible work programs will in-crease significantly as the number of bridges and availablerehabilitation actions increases. For instance, 20 projects with
Table 6. Candidate work programs.
Program Action 1 Action 2 Action 3 Total cost ($) Total weightProgram 1 Replace 70 Repair 40 Maintain 30 1 957 558 0.88Program 2 Replace 70 Repair 40 Repair 30 2 583 895 1.12Program 3 Replace 70 Repair 40 Replace 30 2 789 600 1.4Program 4 Replace 70 Replace 40 Maintain 30 2 195 708 0.88Program 5 Replace 70 Replace 40 Repair 30 2 822 045 1.12Program 6 Replace 70 Replace 40 Replace 30 3 027 750 1.4Program 7 Replace 70 Maintain 40 Maintain 30 1 239 014 0.83Program 8 Replace 70 Maintain 40 Repair 30 1 865 351 1.07Program 9 Replace 70 Maintain 40 Replace 30 2 071 056 1.35Program 10 Repair 70 Repair 40 Maintain 30 1 686 933 0.73Program 11 Repair 70 Repair 40 Repair 30 2 313 270 0.97Program 12 Repair 70 Repair 40 Replace 30 2 518 975 1.25Program 13 Repair 70 Replace 40 Maintain 30 1 925 083 0.73Program 14 Repair 70 Replace 40 Repair 30 2 551 420 0.97Program 15 Repair 70 Replace 40 Replace 30 2 757 125 1.25Program 16 Repair 70 Maintain 40 Maintain 30 968 389 0.68Program 17 Repair 70 Maintain 40 Repair 30 1 594 726 0.92Program 18 Repair 70 Maintain 40 Replace 30 1 800 431 1.2Program 19 Maintain 70 Repair 40 Maintain 30 872 489 0.68Program 20 Maintain 70 Repair 40 Repair 30 1 498 826 0.92Program 21 Maintain 70 Repair 40 Replace 30 1 704 531 1.2Program 22 Maintain 70 Replace 40 Maintain 30 1 110 639 0.68Program 23 Maintain 70 Replace 40 Repair 30 1 736 976 0.92Program 24 Maintain 70 Replace 40 Replace 30 1 942 681 1.2Program 25 Maintain 70 Maintain 40 Maintain 30 153 945 0.63Program 26 Maintain 70 Maintain 40 Repair 30 780 282 0.87Program 27 Maintain 70 Maintain 40 Replace 30 985 987 1.15
Note: The cost data is in Canadian dollars, adjusted for inflation and based on the 2008 dollar value.
1236 Can. J. Civ. Eng. Vol. 38, 2011
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
three possible rehabilitation actions will yield 3 486 784 401work programs. Developing this large number of work pro-grams and evaluating them will require relatively long process-ing time. This limitation of the proposed methodology needsto be further evaluated to study options to eliminate its impact.
ConclusionsAllocating limited available budget to maintain bridge net-
works and selecting effective MR&R strategies for each proj-ect are among the most challenging tasks for managers anddecision makers. The research investigated the current deci-sion making process used for managing bridge infrastructure.Based on that, a decision support methodology is developedthat integrates multi-criteria decision making methods to rankand prioritize project for intervention and evaluate the avail-able rehabilitation strategies. The methodology enables thedecision makers to include their judgments and inputs intothe decision making process and modify the decision makingattributes and criteria based on their requirements. The re-search proposes a technique to develop a recommendedwork program that can be implemented under budget con-straints. The technique uses the simulation to develop all thepossible work programs and to evaluate effectiveness of therehabilitation strategies associated with each program.During the course of this work, future research directions
arose. First, data and cost estimating models for bridge reha-bilitation actions are scarce or inaccessible as compared tobuilding cost data. More data needs to be collected to extendthe cost estimating models for bridge deck rehabilitation andto refine the proposed models accuracy. In addition, moremodels are needed for the different bridge elements includingjoints, girders, abutments, and piers. Second, methods toquantify enhancements from implementing rehabilitation strat-egies and work programs need to be further investigated anddeveloped. Third, multi-year programming for budget alloca-tion is another essential and complex issue. Further researchis needed to develop a sequence of recommended work pro-grams over an extended planning period that can ensure themost efficient use of resources over the life cycle of bridgenetworks. Fourth, the proposed methodology needs to be ex-tended to other bridge components and can be implementedinto a full-scale computerized bridge management system.
AcknowledgementThe partial financial support from the Natural Sciences and
Engineering Research Council of Canada is appreciated.
ReferencesAASHTO. 2008. Bridging the Gap [online]. Available from http://
www.transportation1.org/bridgereport/scarce.html,Abraham, D., and Wirahadikusumah, R. 1999. Development of
prediction model for sewer deterioration. In Proceedings of 8thConference on Durability of Building Materials and Components,National Research Council (Canada), Ottawa, pp. 1257–1267.
Abu Dabous, S. 2008. A decision support methodology forrehabilitation management of concrete bridges. Ph.D. thesis,Department of Building, Civil and Environmental Engineering,Concordia University, Montreal, Que.
ASCE. 2009. Report card for America’s infrastructure [online].Available from: http://www.infrastructurereportcard.org/ [cited 7February 2011].
Branco, F., and de Brito, J. 2004. Handbook of concrete bridgemanagement. American Society of Civil Engineers, U.S.
De Brito, J., and Branco, F. 1998. Computer aided lifecycle costsprediction in concrete bridges. Engineering Modeling, 11(3–4):97–106.
Frangopol, D., and Liu, M. 2007. Maintenance and management ofcivil infrastructure based on condition, safety, optimization, andlife-cycle cost. Structure and Infrastructure Engineering, 3(1): 29–41. doi:10.1080/15732470500253164.
Frangopol, D., and Neves, L. 2003. Life-cycle maintenance strategiesfor deteriorating structures based on multiple probabilisticperformance indicators. Edited by F. Bontempi, System-BasedVision for Strategic and Reactive Design, Vol. 1. Sweets andZeitlinger, Lisse.
Frangopol, D., Kallen, M., and Noortwijk, J. 2004. Probabilisticmodels for life-cycle performance of deteriorating structures:review and future directions. Progress in Structural Engineeringand Materials, 6(4): 197–212. doi:10.1002/pse.180.
Gopal, S., and Majidzadeh, K. 1991. Application of markov decisionprocess to level-of service-based maintenance system. Transporta-tion Research Record, No. 1304, Transportation Research Board,Washington, D.C., pp. 12–17.
Hawk, H. 2003. Bridge life-cycle cost analysis. NCHRP ReportNo. 483, Transportation Research Board, National ResearchCouncil, Washington, D.C.
Huang, Y., Adams, T., and Pincheira, J. 2004. Analysis of life-cyclemaintenance strategies for concrete bridge decks. Journal ofBridge Engineering, 9(3): 250–258. doi:10.1061/(ASCE)1084-0702(2004)9:3(250).
Jiang, Y., Satio, M., and Sinha, K. 1988. Bridge performanceprediction model using the Markov chain. Transportation ResearchRecord, No. 1180, Transportation Research Board, Washington,D.C., pp. 25–32.
Keeney, R., and Raiffa, H. 1993 Decision with multiple objectivespreferences and value tradeoffs. Cambridge University Press, NewYork, N.Y.
Kong, J., and Frangopol, D. 2003. Life-cycle reliability-basedmaintenance cost optimization of deteriorating structures withemphasis on bridges. Journal of Structural Engineering, 129(6):818–828. doi:10.1061/(ASCE)0733-9445(2003)129:6(818).
Kulkarni, R.B., Miller, D., Ingram, R.M., Wong, C., and Lorenz, J.2004. Need-based project prioritization: alternative to cost-benefitanalysis. Journal of Transportation Engineering, 130(2): 150–158.doi:10.1061/(ASCE)0733-947X(2004)130:2(150).
Madanat, S., and Ben-Akiva, M. 1994. Optimal inspection and repairpolicies for infrastructure facilities. Transportation Science, 28(1):55–62. doi:10.1287/trsc.28.1.55.
Madanat, S., Karlaftis, M., and McCarthy, P. 1997. Probabilisticinfrastructure deterioration models with pannel data. Journal ofInfrastructure Systems, 3(1): 4–9. doi:10.1061/(ASCE)1076-0342(1997)3:1(4).
Mirza, S., and Haider, M. (2003) The state of infrastructure inCanada: implications for infrastructure planning and policy, AReport Prepared for Infrastructure Canada, McGill University,Montreal, Que.
Saaty, T.L. 1980. The analytic hierarchy process. McGraw-Hill, NewYork, N.Y.
Saito, M., Sinha, K., and Anderson, V. 1988. Bridge replacement costanalysis. Transportation Research Record, No. 1180, Transporta-tion Research Board, Washington, D.C., pp. 19–24.
Vanier, D. 2000. Advanced asset management: tools and techniques,innovations in urban infrastructure. Seminar of the APWAInternational Public Work Congress, Louisville, KY, pp. 39–57.
Abu Dabous and Alkass 1237
Published by NRC Research Press
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
This article has been cited by:
1. Mohamed Marzouk, Ehab Awad, Moheeb El-Said. 2012. An integrated tool for optimizing rehabilitation programs of highwayspavement. The Baltic Journal of Road and Bridge Engineering 7:4, 297-304. [CrossRef]
Can
. J. C
iv. E
ng. D
ownl
oade
d fr
om w
ww
.nrc
rese
arch
pres
s.co
m b
y C
alif
Dig
Lib
- D
avis
on
05/0
9/14
For
pers
onal
use
onl
y.
