Application of Analytic Hierarchy Process to Retaining wall maintenance prioritization

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 09 Issue: 11 | Nov 2022 www.irjet.net p-ISSN: 2395-0072

Application of Analytic Hierarchy Process to Retaining wall maintenance prioritization

Abstract – This paper proposes the application of the Analytic Hierarchy Process (AHP) in determining the relative weights of important maintenance decision-makingfactors in retaining wall management. Based on a pairwise comparison of the criteria (age, operating & maintenancecondition,safety consequence & mobility consequence), weights aregenerated, which are used in computing a priority index for ranking the maintenance importance of the walls. These weighted factors are applied to 29 retaining wall structures in Tennessee, with maintenance priority ranking as output.Thismethodprovides transportation agencies with a simple but effective method of selecting the retaining wall for maintenance, given a limited budget. Sensitivity analyses are conducted to identify the factors that most significantly affect a chosen outcome variable of estimated repair cost – in a bid to validate the AHP model. Overall, the case study clearly demonstrates the applicability and practicality of the AHP-based method for maintenance prioritization of retaining wall structures.

Key Words: Retaining Wall, Asset Management, AHP, MulticriteriaDecision-Making,Operations&Maintenance.

1. INTRODUCTION

In the United States, most transportation agencies do not observe specific maintenance or rehabilitation regime for their retaining wall structures (Anderson et al., 2009; Kimmerling & Thompson, 2015). While other “primary” transportationinfrastructuresuchaspavementandbridges havescheduledproactiveinspectiontimeframes,thisasset class is mostly ignored (Lawal, 2021). Without these inspection cycles, there is no way asset managers could identifydistressesatanearlystagetoavertfailure(Pettway &Sinkey,1980).Withthisbackground,afewDepartmentsof Transportationhavestartedextendingtheirrisk-basedasset management programs to include retaining walls (Tappenden&Skirrow,2020;Thompsonetal.,2016;Vessely etal.,2015).

However,withmoreassetclassestomanagecomesatthe competingcostofmaintenanceprioritization(Frangopol& Liu, 2019). The limited annual maintenance budget most transportationagencieshaveisbarelyenoughtocoverthe legacy assets in need of maintenance (Kulkarni & Miller, 2003).Yet,theseagenciesarecompelledtosimultaneously maintain other assets such as retaining walls which have beenfoundtobeequalcontributorstosafetyandmobility along transportation highways (NCHRP Report 903).

Therefore,itisanimportantissuefortheseagenciestofind the best possible waytheycanallocatetheirmaintenance budget,whilehavingthemostimpact.

Duetothelackofhistoricaldata,therehasnotbeenalotof researchonretainingwallmanagementasatransportation orgeotechnicalasset.Regardless,assetmanagersroutinely have to make maintenance decision-making on pavement and bridges at the network level, considering the performanceandothercharacteristicsoftheroadsections (O’Reily&Perry,2009;Wangetal.,2022).Theperformance of these assets and subsequent maintenance decisionmakingispremisedonseveralfactorsandcriteria(Niekamp et al., 2015; Lawal et al., 2017). Similarly, retaining walls alonghighwaycorridorscanbemodelledasamulti-factor and multi-criteria decision-making problem. Based on available literature, the factors worthy of consideration include structure age, condition rating, mobility consequence,etc.Thegoalsofmaintenancearetorestoreas manystructurestothebestpossibleconditions,andalsoto minimizeoverallagencymaintenancecostswhiledoingthis (Lawal, 2022). These two important, yet seemingly contradictory goals could be achieved using a scientific processthatcanrationallyrankthemaintenancepriorityof theassetsbasedonsetcriteria(Saaty,1988).

Considering the qualitative nature of the relationship between each factor, determining the weight of each criterion and sub-criteria then becomes difficult. Analytic HierarchyProcess(AHP)comesinhandyindemystifyingthe problems based on hierarchies and pairwise comparison (Saaty, 2008). This method has been widely adopted in several multicriteria decision-making problems with complicatedstructure,duetoitsrelativesimplicity(Ziaraet al., 2002). Its application has been found in several infrastructureclassfrombridges(Dabous&Alkass,2010) (Wakchaure et al., 2012) to pavements (Ramadhan et al., 1999)(Ahmedetal.,2017;Lietal.,2018),andhasbeenused inthisstudytodeterminetheweightofeachfactor,inabid to arrive at a comprehensive ranking index for the prioritizationofretainingwallmaintenance.

2. OBJECTIVE

The goal of this study is to develop an AHP-based maintenanceprioritizationrankingindexforretainingwalls. AcasestudyofretainingwalldatacollectedintheStateof Tennesseewasusedtodemonstratetheapplicabilityofthe

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AHP-theory.Certainpre-determinedimportantfactorswere used as decision-making factors. These factors include retaining wall age, operations & maintenance (O&M) condition, mobility consequence, safety consequence. Hierarchiesarethenconstructedbasedonthesefactorsto determinetheweightofeachofthedecision-makingfactors–cumulatively lending towards the prioritization ranking index. Sensitivity analysis is subsequently carried out in order to verify the accuracy and effectiveness of the weightingprocess.

3. MULTICRITERIA DECISION-MAKING

Thedecisionofwhichwalltomaintainataparticularpointin timeisbasedontheprioritizationrankingindexofthewall. Thisindexshouldreflecttherelativeimportanceofthewall, and why if required should be selected ahead of another. Therefore,thefactorsthathavegoneintothecomputationof this ranking should represent those that individually hold majorimportance.Whilethereareseveralprobablefactors thatcontributeinvaryingdegrees,itisimpracticaltoinclude all of it in the hierarchical process. Thus, key criteria that werefoundthroughliteraturereviewhavebeenshortlisted. TheNCHRPReport903whichprovidesanimplementation guidance for transportation agencies implementing geotechnical asset management (GAM) developed a GAM planner tool. These factors which were retaining wall age, O&M condition, mobility consequence, and safety consequence correlated with the variables in the asset inventoryoftheGAMplannertool.

3.1 Retaining wall age

Structure age represents one of the most significant influencingfactorsforretainingwallmaintenancedecisionmaking,justliketheother“primary”assets.Despitethelack of retaining wall historical data (construction and maintenance) in Tennessee, google earth pro historical imageryfunctionwasusedinestimatingtheapproximateage ofallofthewallssurveyed–whichrevealedthatmostofthe wallswerebuiltover20yearsago.Asastand-alonefactor,it followsthatbarringanymaintenance,theolderstructures wouldbeclosertotheirdesignlifeandwouldneedthemost urgent attention. However, since age is not the only contributingfactortodeterioration,thisapproachwouldnot hold.

3.2 Operations & Maintenance condition

BasedontheGAMplannertool,operatingandmaintenance condition, which in simple terms can be referred to as the condition rating of the structure is an important factor in maintenanceprioritization.AsdefinedinthetoolandNCHRP report 903, the conditions are categorized into “1-New or Good”, “2-Minor Loss”, “3-Fair”, “4-Poor”, “5-Critical to Failed”.Consideringthewallssurveyed,the1-4ratingscale hasbeenusedinstead.

Table 1:O&Mconditionleveldefinitions(NCHRPReport 903)

O&MCondition Definition 1 NeworGood 2 MinorLoss 3 Fair 4 Poor 5 CriticaltoFailed

3.3 Mobility consequence

Failureconsequencethatcouldaffectmobilityonadjourning highway is a very important factor to consider in maintenance decision-making. Those walls whose failure would seriously impact mobility would naturally be given priorityoverthosewithless.TheGAMplannertoolstipulates thedifferentcategoriesof“NoImpactpossible”,“Impactto shoulder possible”, “Impact to travel lane possible”, “Road closurepossible:1dayorless”,“Roadclosurepossible:>1 day”.

Table 2:Mobilityconsequencedefinitions(NCHRPReport 903)

Mobility consequence Definition

1 Noimpactpossible 2 Impacttoshoulderpossible 3 Impacttotravellanepossible 4 Roadclosurepossible,1day orless 5 Roadclosurepossible,>1 day

3.4 Safety consequence

Failure consequences of retaining walls that have safety implicationstowardsthetravelingpublicisaverysignificant metric that contributes to the maintenance prioritization decision-makingoftheassets.Thecategoriesofthisfactoras includedintheGAMplannertoolare:“Noimpactpossible”, “Impacttoshoulderpossible”,“Impacttotravellanepossible butavoidable”,“Vehicledamagepossible”,“Fatalityorinjury possible”

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Table 5: Scaleofrelativeimportance(Saaty,1980)

Intensityof importance Definition

4. THE ANALYTIC HIERARCHY PROCESS

AHPwasfirstdevelopedandexploredbySaaty(1980)asan objective mathematical and psychological weighting technique. Over the years, the technique has found its application in different transportation infrastructure multicriteria decision-making. However, specifically for retainingwallmaintenance,ithasnotbeenreallyexplored TherangeofproblemsthatcouldbesolvedusingAHPspans across both objective and subjective evaluations. This is achieved through a systematic process including: a) developmentofahierarchicalstructure;b)methodologyfor establishment of priorities, and c) ranking and overall consistencyassessment.

4.1 Hierarchical structure

ThefirststageintheAnalyticHierarchyProcessisthedesign of the hierarchies itself. This involves breaking down the wholeproblemstructureintoindividualclusters–thatforms a hierarchy. Each hierarchical level comprises of elements thatinturnfeedoffintoothersub-elementsuntiltheentire structure is decomposed completely. The goal of this approachwouldbetopresentthelogicalandmathematical interactionofthefunctionalcomponentsthatmakeupthe problem.Theflexibilityandreliabilityofferedbyhierarchies make it difficult for the entire system to be affected by outsideinfluence(Saaty,1977).Inthehierarchymodel,the goal of the AHP is placed on the uppermost layer. This is followed by the criteria layer. In the case where there are sub-criteria,thisrepresentsthethirdlayer.Thealternatives arethenplacedatthebottomlayer.AtypicalAHPhierarchy structureisshowninFig.1

4.2 Methodology for establishment of priorities

ThesecondstageintheAnalyticHierarchyProcessinvolves theestablishmentofanacceptablebasisforprioritysettings. Through a pairwise comparison of each criterion, relative importanceisdetermined.Thisisachievedusinga1-9scale showninTable1.

1

Equalimportance 3

Weakormoderate importanceofoneoverthe other 5

Essentialorstrong importance 7

VerystrongorDemonstrated importance 9

AbsoluteorExtreme importance 2,4,6,8

Intermediatevaluesbetween twoadjacentjudgement values

Theassignmentsandcomparisonsaredonebasedonexpert judgementandexperience.

4.3

Ranking and overall consistency assessment

Based on the hierarchical structure and pairwise comparison,theimportanceofeachcriterionrelativetothe otherisobtained.Consideringthedifferentindicesused,the judgementmatrixisnormalizedinordertogivetherelative importance.Duetotheprocessofthepairwisecomparison, itispossibleforinconsistenciestobeintroduced,i.e.,inthe caseof3criteriaA,B,C,criterionAismoreimportantthan B,criterionBismoreimportantthanC,ifcriterionCismore importantthanA,thisismathematicallyimpossibleandthus aninconsistencyarises.

Therefore,itisnecessarytocarryoutaconsistencycheck attheendofthepairwisecomparisonprocessinorderto avoidcontradictoryresults.Whileitisunlikelytoobtaina perfectconsistency,thesmallertheconsistencyratio(CR) is to 10%, the better. In order to obtain the consistency ratio(CR),aconsistencyindex(CI)iscalculatedusingEq. 1basedonthemaximumeigenvalue

CI= ,n=1,2,….,9 (1)

Consistencyratioisobtainedbydividingtheconsistency index(CI)bytherandomconsistencyindex(RI).RIis showninTable2.

CR= (2)

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Table 4:TheRIvalues

Elements 1 2 3 4 5 6 7 8 9 RI 0 0 0.58 0.9 1.12 1.26 1.36 1.41 1.45

5. RESEARCH CASE STUDY

Twenty-nineretainingwallstructuresacrossthethreemaincities(Chattanooga,Knoxville,andNashville)inTennesseewere selected from the Tennessee DOT report on rating and inventory of retaining walls. The four important factors earlier establishedwereusedincollectingandsynthesizingthedata,andaggregatedasshown.

Table 6: Retainingwalldataforcasestudy

Wall Retainingwall locations Age

1

Weighted Overall Rating

O&M condition level Safety Consequence Mobility consequence

7244-7544E Brainerd Chattanooga,TN 14 3.74 1 3 3

2

308Ashland Terrace, Chattanooga,TN 22 2.45 2 2 2

TN-153,OffBonny OaksDr., Chattanooga,TN 21 2.1 3 3 2 3

4

Northpoint Boulevard, Chattanooga,TN 13 2.91 2 3 2

5 RiversideDr, Chattanooga,TN 27 2.21 3 3 3

6

SignalMountain Rd,Chattanooga, TN 18 3.49 1 5 5

7 1727DaytonBlvd, Chattanooga,TN 16 2.95 2 3 3 8 222BakerStreet, Chattanooga,TN 24 2.95 2 4 5 9

918-998Cherokee Blvd,Chattanooga, TN 22 2.84 2 4 5

10 I-75N, Chattanooga,TN 35 2.66 2 4 3

11

1201-1261Dayton Blvd,Chattanooga, TN 27 2.97 2 4 4

12 I-75S, Chattanooga,TN 36 2.43 2 4 3

13

US-11,Birmingham HwyCrossRailway, Chattanooga,TN 38 1.85 3 2 2

14 6401LeeHwy 47 2.41 2 2 2 15 4177WillardDr 48 2.77 2 5 5

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16 6828NorthsideDr 17 3.74 1 4 4

17

US-27N/Exitto SignalMountain, Chattanooga,TN 6 3.9 1 4 4

18

19

US-27S/Dayton BlvdEntrance, Chattanooga,TN 6 3.78 1 4 4

US-27S/Near Manufacturers RoadExit, Chattanooga,TN 6 3.93 1 4 5

20 9303EBrainerdRd 15 3.75 1 3 3

21 6312FiskAve, ChattanoogaTN 16 3.32 1 4 3

22 1701-1899 MeharryDr 45 2.4 2 2 2 23

US-27N/Between RedBankExitand R.R.OlgiatiBridge, Chattanooga,TN 6 3.88 1 3 3 24

1301Washington Avenue,Knoxville, TN 21 3.62 1 3 2

25 HallofFameDr, Knoxville,TN 19 3.1 2 4 3 26 JamesWhitePkwy, Knoxville,TN 31 2.59 2 4 5

27

NBroadwayRamp toI40,Knoxville, TN 15 2.16 3 4 5

BrileyPkwy, Nashville,TN 35 2.03 3 3 2 29 ElmHillPike, Nashville,TN 24 3.01 2 3 2

28

5.1 AHP weighting factor determination

In the hierarchical structure, the ultimate goal at the objectivelevelistocomputeapriorityrankingindexthat would guide in retaining wall maintenance decisionmaking. The four important factors that are believed to affectthisdecision-makingprocess,i.e.,age,operatingand maintenancecondition,safetyconsequence,andmobility consequence form the criteria level. While the different retaining wall options available to be considered for maintenancearethealternatives.Thehierarchicalstructure modelisshowninFig.

Basedonexpertjudgementonretainingwallmanagement, a comparison matrix of the criteria was formed. The pairwisecomparisonmatrix,CisshowninEq.3

C= (3)

Wethecomputethenormalizedpairwisematrix, as showninEq. = (4)

Theaverageofthenormalizedpairwisematrixthen givesthefactorweightsrepresentedbythevector, W W = (5)

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Thisistheweightsofthefactorsage,O&Mconditionlevel, safety consequence, and mobility consequence, respectively. The maximum principal eigenvalue, isobtainedasanaverageoftheratiooftheweighted sumvalueandcriteriaweight.Theweightedsumvalueis showninequationbelow.

isobtainedas4.1449.Consistencyindex,CIisgivenby Eq.1.Therefore,usingTable2ofRIvalues,withn=4,and given , CIis0.0483.ConsistencyRatio,CR,fromEq.2 isthenobtainedas0.0537.i.e.,0.0483/0.9.

Since 0.0537 < 0.1, the overall ranking is consistent and passesthislogicaltest.

5.2 Weighting Application to Ranking

Based on the weights of the four factors, and the synthesizeddata,apriorityrankingindexisgeneratedfor allthetwenty-nineretainingwalls.Usingtheprinciplesof normalization on the synthesized data, older retaining walls,retainingwallswiththeworstO&Mcondition,

retaining walls with worst safety consequence, and retainingwallswithworstmobilityconsequencearegiven highest preference. In Table, the summary of weighting together with the other factors computed in assessing consistencyareshown.Overall,Tableoutputsthepriority ranking index based on normalized data values from all fourconsideredfactors.

Table 7:Factorweightsandconsistencycheck

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Theweightsofeachfactormultipliedbytheassignedvalue(normalized)isthensummedforeachretainingwall,andthisgives arelativeindex(0-1)ofthemaintenanceneedsoftheretainingwalls,andwhichshouldbeprioritized.Thehigherthepriority index,thegreatertheneedformaintenancerelativetotheotherstructures,andvice-versa.Finally,ranksareassignedtogivea numericalimportancetothepriorityofthewallsformaintenance.ThisisfurtherpresentedinTable.

Table 8: Priorityindexandrankingbasedonnormalizationofdata

Wall Age O&M condition level

Safety consequence Mobility consequence Priority index Priority Ranking

1 0.291667 0.333333333 0.6 0.6 0.436998012 27 2 0.4375 1 0.6 0.4 0.766379702 5 3 0.458333 0.666666667 0.4 0.4 0.545853091 20 4 0.270833 0.666666667 0.6 0.4 0.577632502 19 5 0.5625 1 0.6 0.6 0.810205187 3 6 0.375 0.333333333 1 1 0.602498553 15 7 0.333333 0.666666667 0.6 0.6 0.617170763 14 8 0.5 0.666666667 0.8 1 0.743746519 8 9 0.458333 0.666666667 0.8 1 0.740888369 9 10 0.729167 0.666666667 0.8 0.6 0.688964269 12 11 0.5625 0.666666667 0.8 0.8 0.712782707 10 12 0.75 0.666666667 0.8 0.6 0.690393343 11 13 0.791667 1 0.4 0.4 0.746032889 7 14 0.979167 0.666666667 0.4 0.4 0.581579961 17 15 1 0.666666667 1 1 0.822685398 2 16 0.354167 0.333333333 0.8 0.8 0.521177357 22 17 0.125 0.333333333 0.8 0.8 0.505457534 23 18 0.125 0.333333333 0.8 0.8 0.505457534 23 19 0.125 0.333333333 0.8 1 0.540708571 21 20 0.3125 0.333333333 0.6 0.6 0.438427086 26 21 0.333333 0.333333333 0.8 0.6 0.484497246 25 22 0.9375 0.666666667 0.4 0.4 0.578721811 18 23 0.125 0.333333333 0.6 0.6 0.425565413 28 24 0.4375 0.333333333 0.6 0.4 0.411750499 29 25 0.395833 0.666666667 0.8 0.6 0.666099072 13 26 0.645833 0.666666667 0.8 1 0.753750042 6 27 0.3125 1 0.8 1 0.908199447 1 28 0.729167 1 0.6 0.4 0.786386749 4 29 0.5 0.666666667 0.6 0.4 0.593352325 16

value:

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6. BENEFIT OF THE METHOD

MaintenancebudgetforDepartmentofTransportationis greatlylimited,despitethedifferenttransportationassets undertheirmanagementjurisdiction.Theattendanteffect ofthisissomeimportantassetsnotmaintainedatthemost optimal time, leading to increased life-cycle cost. In recognitionofthisconstraint,thisAHP-basedmaintenance prioritizationmethodforretainingwallsoffermanagersa data-driven, yet, simple approach of timely prioritizing theirmaintenanceandrehabilitation.Withthissystemin place,availablebudgetcanbeallocatedtothestructures basedonpriorityindexandoverallrelativerank.

7. STUDY LIMITATIONS

AHP operates on a subjective evaluation and pairwise comparison of criteria. Despite that this is mitigated through expert judgements and assessment, it’s still an imperfectsystembasedonthesubjectivity.Two experts alsoarenotlikelytohavethesameexactassessment.This is a great limitation for the method. Nevertheless, it is greatly encouraged in future studies to incorporate multiple expert judgements in the process and compare the final outcomes. If the individual comparisons are consistent(whichconfirms thelogicofthecomparison), thefinalpriorityindexandrankingshouldnotbesuchthat awallranked1st throughoneexpert’scomparisonisthen ranked15th throughanother’s.

8. SENSITIVITY ANALYSIS

Inthissection,theresultsoftheAHP-basedmaintenance prioritizationarevalidatedusingsensitivityanalysis.The goalofsensitivityanalysisistoidentifywhichcontributing factor(s) has significant effect on the decision-making pertaining to retaining wall maintenance. This is tested againstatargetvariableofestimatedrepaircost,whichis providedintheTennesseeDOTreport.

For the analysis, retaining wall age was set to 10 years, O&Mconditionto3,safetyconsequenceto3andmobility consequenceto3.Theinfluenceofeachofthefactorsare testedontheestimatedrepaircostandisillustratedbythe changingvalueofthecost.Thetimevalueofmoneyisused inestimatingthepresentvalueofthewallsaftertyears

Original cost of wall * , where y is the 30 years averageinflationrate.The y valueadoptedfortheproject is3.5%(Zarenski,2021) TheO&Mconditionlevelchange had the most significant impact on the estimated repair cost. The O&M condition level were substituted with residualpercentageandusedinestimatingtherepaircost. Similarly,thesafetyandmobilityconsequencewerevaried toseetheirimpactontheestimatedcostofrepair.Overall, theO&Mconditionlevelresultedinthemostvariationin the repair cost which validates the outcome of the weightingfromtheAnalyticHierarchyProcessmodel.

Table 9:AssumptionofResidualPercentageBasedon RatingScore(NCMA,2004)

CurrentRatingScore ResidualPercentage

9. CONCLUSIONS

This method has been widely applied to different multicriteria decision-making problems across different fields,includingtransportationinfrastructuremanagement like pavement and bridges. Given that retaining wall management is relatively new to most Transportation agencies, they typically do not have to plan for their maintenance, and thus there had not been a need for prioritization. As more highway agencies are moving to improved proactive management techniques, this approachforprioritizingretainingwallmaintenancecould notbetimelier

TheAHP-basedtechniqueincorporatedcertainimportant potentialmaintenancerelatedfactorsthatcouldhelpgivea quantitativerelativeimportanceofthewalls–througha priorityindexandrankingforalloftheconsideredwalls. With the case-study validation using a total of four maintenance decision-making factors including age, operatingandmaintenancecondition,safetyconsequence, and mobility consequence considered. A hierarchical structure model consisting of the goal, criteria, and retaining wall alternatives was developed followed by pairwise comparison and weighting of the important factors.Withthefactorweights,andthedatanormalized, the result is a retaining wall maintenance priority index andpriorityranking.

ACKNOWLEDGEMENT

Theauthor(s) would liketo acknowledgethe Tennessee DepartmentofTransportationforfundingtheprojecton Rating and Inventory of TDOT retaining walls, which providedinpart,thedatausedforthispaper.

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