Economic risk assessment of concrete and asphaltic pavements in freeways and highways
ARTICLE INFO Articlehistory:
Received23July2019
Keywords:
Concretepavement Asphaltpavement Economicrisk MonteCarlosimulation
ABSTRACT
ThegreaterpartsofIranianroadsareoftheasphaltickind.Therealreasonbehindmaking thistypeofroadliesintheabundanceofbitumenandthecheaperpriceofthesubstancein pastyears.Theupwardspiralingpriceofoilatthegloballevelandtheliberalizationof subsidies were responsible for rocketing prices of asphalt pavement. As a result, a motivationwascreatedtoinvestigateanalternativemethodcalledconcretepavements.
Theconstructioncostofconcreteandasphaltpavementhingesonspecificationsofthe project,butoneofthemainconcernswasaboutthelikelihoodoffluctuationsinspending duringtheconstructionphase.Accordingtotheimportanceofpricechanges,thispaper intendstofindwhichtypeofconcreteandasphaltpavementshavelowerpricechangesin Iran.Toanswerthisquestion,theMonteCarlosimulationisapplied.SincetheMonteCarlo simulationneedsapredictionmodelandthedatausedfordevelopingthemodelhingeson historicaldata,theauthorsappliedregressionandtimeseriesmethods.Theresultsshow thatfirstly,theregressionmethodhasbetterperformancethanthetimeseriesmodeland thesecond,theimplementationofconcretepavementhaslesseconomicrisksinIranian freewaysandhighways.
©2020TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY license(http://creativecommons.org/licenses/by/4.0/).
1.Introduction
Roadsareaneffectivemeansofcommunicationbetweendifferentareas.Humanbeingshavebeenusingroadssince manyyearsago.Thelengthofroadnetworksismuchdiversifiedamongdifferentcountries,forexample,theUnitedStates hasthehighestlengthofroadsintheworldwhileIranranks26thwiththe214,006kmpavedandunpavedroadamongthe countries[1].Theimportanceoftheroadasaninfrastructureofcountriesisunavoidable.Severalcostparametersaffected thecostofconstructingthisinfrastructuresuchaslocation,typeofconstruction,numberoflanes,typeofpavements,etc.
One of thecostlyitemsin theconstruction ofroadsis thetype of pavement.The pavementis one ofthe important componentsofaroadwhichisdirectlycontactedwithvehicles.Thereareseveraloptionsforchoosingaspavementbutsome considerationssuchascostsofconstruction,maintenance,technology,etc.influencethedecision.Asanexample,most Iranianroadpavementsweremadeofasphalt.Oneofthemajorreasonsforusingasphaltaspavementisthewealthofoil resources,includingbitumenanditslowchargeinpastyears.ButaccordingtothepricereferenceofIran'sconstruction projects(pricelist),thepriceofbitumenMC250was0.14dollarsperkgin2006and0.2dollarsperkgin2016.Theratehas increasedover thepast tenyears.Therefore, withtheupsurgeinbitumenprices inthepast,otheroptionsshouldbe considered.Anothertype ofpavementtakingtheattentionof Iranianadministratorsintoaccountinrecent decadesis concretepavement.Concretepavementisaconcretelayerthatisreplacedbyasphaltandincontactwiththetrafficdirectly.
AnothermotivationistheupwardtrendintherateofcementproductioninIranleadstheuseofconcretepavementtobe economicallyjustified.
Theeconomic considerationsareoneofthemostimportantcriteriafor theselectionof thetype ofpavements.As explained,thedecisionfortheselectionofthetypeofpavementhasbeenchangedbecauseofeconomicsissues.Itseemsthat https://doi.org/10.1016/j.cscm.2020.e00346
2214-5095/©2020TheAuthors.PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/
4.0/).
ContentslistsavailableatScienceDirect
Case Studies in Construction Materials
j o u r n a lh o m e p ag e :w w w . e l s e v i e r . c o m / l o c a t e / c s c m
itisnotarealisticapproachtoselectthepavementonlybasedontheminimumcostbecauseitispossibletochangeduring thetime.Theactualcostisdependentondifferentcostvariablessochanginginthepriceofeachparameterleadstochange intheactualcostofpavement.Itisbettertoselectthetypeofpavementwiththelowesteconomicriskstoincreasethelevel ofconfidenceandminimizetheproject’scostdeviation.Ariskisanuncertaineventoroccasion.Itwillaffectatleastoneof theobjectivesoftheprojectsuchastime,costandqualitycanchange[2].
Thereareseveralrisksintheprocessofconstructingaroad.SharafandAbdelwahab[3]exploredtherisksinvolvedin implementinghighwayprojectsinEgypt.Theyidentified12riskgroups,whichincluded73threats.Then,theyevaluated theserisks,usingfuzzylogic.In2016[4],examinedtherisksinvolvedinconstructinghighways.Theytookrisksfromvarious sourcessuchasuncertaintyinfinancialmarkets,threatsfromprojectfailure,legaldebt,andcreditrisk.Theresultsoftheir researchshowedthattheprocessofeffectiveriskmanagementencouragesconstructioncompaniestoidentifyandreduce risks.Inlaterstages,theycouldmanagefinancialandinterestrebatesiftheriskswereeffectivelyhandled.
However,thenumberofeffectiverisksfortheselectionofpavementsisnumerousanddiversified,thispaperintendsto studytheeconomicrisksofconcreteandasphaltpavementinconstructingIranianhighwaysandfreeways.Thisstudynot onlyanswersthisquestionwhichtypeofpavements(asphaltorconcrete)hasthelowesteconomicrisksinIranbutalso presentsaframeworkforconductingthepurposeofthispaperinotherlocations.Thesubjectunderdiscussionspecifically triestomakeadecision onwhichtype ofconcreteorasphaltpavementonfreewaysandhighwayshastheminimum economicriskinIran.Tothisend,twopointsshouldbeconsidered.Thefirstoneisthedefinitionofeconomicrisksappliedin thisresearch.Theeconomicriskisdefinedastheprobabilityofpricechangesofdifferentcomponentsofthesepavements basedonthehistoryoftheirpricechanges.Forexample,ifthecostofoneofthecomponentsofasphaltpavementchanges verymuch,itseconomicriskwillbehigh.Inotherwords,thispaperconsiderstheeconomicriskstobeabletopredictthe futurebehaviorof pavementin termsof changingitsprice bystudyingthepricechangesof differentcomponentsof pavementsinthepast.Itisnoteworthythatotherparameters,suchascostofmaintenance,durationofprojects,etc.proneto influencethedecisiononapplyingconcreteorasphaltpavementshavenotbeentakenupinthecurrentresearchwork.
Thesecondpointishowtheeconomicriskofpavementscanbecalculated.Todothis,thecostpredictionmodelis developedbyusingtwowell-knowntechniques,includingtheregressionmodelandthetimeseriessince theauthors appliedthehistoricaldata.Differenttestswillbedonetofindwhichtypeofregressionortimeseriesmodelshasbetter results.Accordingtothedevelopedmodel,severaleffectiveparametersonthecostofeachpavementarediscovered.To examinewhichpavementhasmorecostfluctuation(ormoreeconomicrisk),theMonteCarlotechniqueisapplied.The MonteCarlomethodisacomputationalalgorithmthatusesrandomsamplingtocomputetheresults.Theresultswouldbe shownwhetherapplyingtheconcreteorasphaltpavementismorelogicalthantheotheroneintheIranianconstruction industrywithrespecttotheeconomicriskornot.Accordingtotheintroducedconcept,thestructureofthepaperisas follows:Theresearchbackgroundwasreviewedinthesection2.Inthefollowing,materialsandmethodsaredescribed.The resultsoftheresearcharepresentedinthenextsectionandfinally,theconclusionsareexplained.
2.Researchbackground
TheAmericanConcretePavementAssociation(ACPA) inits2002 reportreviewedfourinland stateroads(Western Tennesse,Utah,Eastern,OklahomaandGeorgia,NorthofAtlanta).Theassociation'sresearchresultsshowedthatconcrete sectionsinthisstudybetween1.6and2.6timesasphaltedsectionshaveservicelife;theaveragelifetimeofpavement concreteis2.2timesasphaltpavement.Also,theanalysisofthecostcyclesinthesestatesshowsthattheconcretepavement ismoreexpensivethan14–250%of theordinarypavement[5]. AreportreleasedbytheAmericanConcretePavement AssociationACPA,entitled"Greenwaysin2007,"states:"Tobuilda250mmThicknessofasphaltpavement,40,572litersof fuelperlane-kilometersisrequiredanda250mmThicknessconcretepavement7252litersoffuelperlane-kilometersis needed.Inotherwords,thefuelneededtopavetheasphaltis5.6timesthefuelneededtobuildaconcretepavement.
Bellow,aneconomicalcomparisonwasmadetoprovidelightingfortwotypesofpavements.Itwasarguedthatthecostof supplyinglightsforconcretepavementwasapproximately24%lessthantheasphaltpavement,resultinginmaintenance andenergycosts(electricityrequired)tobeapproximately24%lessthanasphaltpavement[6].Mack[7]criticizedthe previousapproachusedforpavementselection.HeprovedthatthediscountrateinLCCAanalysisisvariableforconcreteand asphaltpavement.Hesuggestedaprocedurebasedontheescalatedcostofmaterialtocalculatetherealdiscountrate.In 2014,SullivanandMossexaminedthecostofmakingMixAsphaltWarm(WMA)andMixAsphaltHot(HMA)withconcrete pavement.Asaresultoftheirwork,thefollowingconclusionwasdrawn:"Yes,WMAismorecost-effectivethanHMA,but stillnotcomparabletoconcretepavement"[8,9].reviewedtheusualprocedureforLCCAandLCAinColoradoandproposeda modifiedapproachforpavementselectionwithrespecttothegreenhousegasemission.Theyappliedthemodelforhighway reconstructionandrehabilitation.[10]exploredtheeconomicimpactofconcreteandasphaltpavements.Theirapproach wasbasedoninformalinterviewsandthecalculationofthebillofquantitiesforroads.Theresultsoftheirresearchshowthat concretepavement costs less in lifecycle coststhan asphalt pavement.Although theirresultsindicate that concrete pavementislesscostly,theydidnotpayattentiontorisks.MohodandK.N.Kadam(2016)investigatedrigidandflexible pavements.Theresultsoftheireffortsshowthatriggingpavementsaremoreconducivetoflexiblepavements.Asphalt pavementlifecyclecostis19%morethanthoseofconcretepavement[11,12].examinedthecostsofthelifecycleofconcrete pavementsandasphalticroads,takingintoaccountthecostoflightingintunnelsof750mto2000minlength.Theymade thecomparison basedonthestandardsusedin Italy.Theresultsoftheirresearchshowthat concretepavement,with
considerationoftherequiredlighting,hasalowerlifecyclecostthantheasphaltpavementinthetunnels.[13]proposeda frameworktoevaluatedifferenttypesofpavementbasedonLCAandLCCAanalysis.Theyassessedtheuncertaintyofthecost ofconstructionandmaintenanceactivities.Theyconcludedthattheflexibledesignhaslowercostandenvironmentalimpact intheircase study.AnintegratedframeworkcombinedwithLCCAandLCAwasdevelopedby[14].Theyappliedfuzzy compositeprogrammingtomodeltheuncertaintyinthedecision-makingprocessandrankingdifferenttypesofpavement [15].examinedfourscenariosintermsoftheselectionofpavementandlightingsystemsinItaly.Theirframeworkwas conductedbyLCAand theyconcludedthat theconcretepavementand LEDlampsarethemostenvironment-friendly scenario.[16]developedadecisionsupportsystembasedonthemulti-criteriadecision-makingapproachtorankseveral typesofasphaltmixtureforwearingcoursesintermsofthesustainabilityconcept.Theyappliedtheproposedmodelinareal casestudyandtheyshowedthatafoamedwarmmixasphaltmixturewithareclaimedasphaltpavementcontentof50%is themostsuitable.
RamezanianpourandAarabi[17]intheirbook(publishedinPersian)examinedconcreteandasphaltpavements.These twopavementswereexaminedin termsoftechnical,economicandenvironmentalconsiderations.Theresultsoftheir researchregardingthetwotypesofpavementsshowthatconcretepavementincomparisonwiththeasphalticpavement accordingtothecatalogsof2009,hasalowercostofconstructioninallways[17].Onecanfindtheproblemsofprevious researchthat wereobservedbystudying otherarticles,which are mentioned asfollows,is thelackof economicrisk assessment.Differentresearchhasbeencarriedoutinrelationtoeconomiccomparison,buttheydidnottakethissubject intoaccountbyconsideringthepricevariations.Noneoftheresearchersexaminedtheeconomicrisksofconcretepavement andasphaltpavement.
3.Materialsandmethods
Thisresearchtypeisbasedonanexperimentalstudy,becauseinthisstudytheindependentanddependentvariables affectedthecostofhighwaysandfreewayspavementsinIran,whicharebasedontheavailableinformationfromthepastto thepresent,havebeenconsidered.Basedontheproposedmodel,theeconomicriskevaluationoftheconcreteandasphalt pavementswasdoneusingMonteCarlosimulation.
Theresearchmethodisdividedintotwoparts:Thefirstpartpresentsthemodeltobeabletoforecastthepriceofconcrete andasphaltpavementbyexaminingtheindependentanddependentvariablesinthespecifiedperiod.
Thesecondpartisbasedontheobtainedmodelintheprevioussection.Sincethedefinitionoftheeconomicriskhasbeen setonthe probabilityofprice changesof pavements,bycombiningthedeveloped model forcalculating thepriceof pavementsandMonteCarlosimulationthelevelofpricechangesofpavementswillbecalculated.Thepavementwithahigh levelofchangehasahighereconomicriskthantheother.Differentstepstoreachthepaper’sgoalareshowninFig.1.
Theresearchmethodisdescribedindetailasfollows:
3.1.Presentingpricemodel
Todiscoverthecostpredictionmodel,twomethods,includingregressionandtimeseries,wereapplied.Thefollowing descriptionsexplainthesetwomethodindetail.
3.1.1.Theregressionmodel
Regressionanalysisstudiesthedependenceofavariable(Dependent-Variables)ononeormoreexplanatoryvariablesby estimatingorpredictingtheaveragevalueofthevariables.Thefirsttypeisdefinedinthecasewherethevaluesofthesecond typevariableareknownordetermined(inrepetitivesampling)[18].Toidentifythebestindependentvariables,Stepwise, Forward,andBackwardmethodsareused.IntheForwardmethod,someoftheindependentvariablesarerepresentedbythe leadingmethodinthelinearregressionmodel.IntheStepwisemethod,someindependentvariablesareincludedinthe linearregressionmodelinastep-by-stepmethod.IntheBackwardmethod,someindependentvariablesareincludedinthe linearregressionmodelinaregressiveway[19].Theresultoftheabove-mentionedmethodsistheregressionmodels.After determining theregression model,some methodswere usedtovalidate theobtainedmodelsby analysisofvariance (ANOVA)andStudentt-test.Themodelsrejectedforthesetestswereexcludedfromthesetofmodels.Afterconfirmationof themodelsbasedonthetestdata(2014–2016),theerrorrateðPEÞofeachyearwascalculatedbasedonEq.(1)andthemean errorpercentageðPEAÞcomputedaccordingtoEq.(2)foreachmodel.Tomakethefirstmodelwithaloweraverageerrorrate andresponses,linearregressionmodelwasselectedastheappropriatemodel.
P:E¼YcYf
Yc 100 ð1Þ
P:EA¼jP:E2014j þjP:E2015j þjP:E2016j
3 100 ð2Þ
whereYCisthepricecalculatedforpavementconstructioninarealsituation(Table1)andYfisthecostcalculatedforthe pavementaccordingtotheregressionmodel(equations4&5).
3.1.2.Timeseriesmodel
Giventhatthepricedataofeachyeararerelatedtothepreviousyear,theuseoftimeseriesmodelscanhaveproper function.Inthissection,anattemptismadetousethedatarelatedtothecostofpavementexecutionperyeartodetermine thetimeseriesassociatedwitheachofthepavements.
Thereareseveralmethodstodeterminethetimeseriesmodel.OneofthemostprolificmethodsistheBox-Jenkins method[18].Inthismethod,effortsaremadetopracticeasuitablemodelfortheexistingdatabasedonARIMA.Iftheprocess Table1
Averagecostperkilometer*.
Year 1998 1999 2000 2001 2002 2003 2004
Concrete 617,126,255 660,648,564 823,159,650 991,159,069 1,200,205,144 1,385,097,726 1,936,580,937 Asphalt 393,163,049 469,598,696 573,214,725 656,146,388 740,094,849 1,330,059,527 1,490,968,741
Year 2005 2006 2007 2008 2009 2010 2011
Concrete 2,161,546,247 2,372,591,140 2,543,655,838 2,858,380,514 3,277,999,343 3,412,894,145 3,953,798,137 Asphalt 1,950,972,823 2,109,593,492 2,216,130,647 3,530,218,925 3,866,575,061 4,027,186,253 5,147,826,421
Year 2012 2013 2014 2015 2016
Concrete 4,628,839,160 6,111,502,379 7,154,486,025 8,357,463,113 8,677,374,426 Asphalt 5,832,131,804 12,866,932,042 13,942,798,118 13,454,064,902 10,877,387,050
* AllamountsareinRials.
Fig.1.Theoverallprocessofresearchinthispaper.
ofautoregressiveiscontemplatedtotaketheformAR(p),themodelprocessofMovingAveragetakestheformofMA(q),the averagemotionprocessofself-regressiontaketheformofARMA(p,q)andthemovingaveragecumulativemotionprocessof self-regressiontakestheformofARIMA(p,d,q)inalloftheprecedingcasesPrepresentsthenumberofself-regression sentences, dstandsfor thenumberofthefirst-orderdifferentiationtechniquefor implantationof timeseriesmoving averages.Inthisresearch,theBox-Jenkinsmethodisusedtodeterminethetimeseries.Thismethodisappliedbytakingthe followingsteps:
Thefirststep,identification:
Atthisstage,thestatic(stationary)natureofdatashouldbeprimarilyprocessed.Thedataoftimeseriesarestaticwhen theirstatisticalcharacteristicsarefixedovertimesuchasvarianceandmedian.Tocheckthestationarynatureofthedata, theKwiatkowski-Philips-Schmidt-Shin(KPSS)testisused[18].Accordingtoreferenceinformation[18].TheamountofLM- Statshouldbesmallerthanthestatisticaldataat5%level.Ifthis amountis greaterthanthe5%level,thedifferential techniqueshouldbeusedtostabilizethedata.Thefirstorderdifferentiationiscarriedoutinsuchawayastodeductthedata oftheyeartfromthedataoftheirprevious(t-1)year.Theresultsrespectivelyshowthefirstorderdifferentiation.The subsequentdifferentiationisaccomplishedbyusingthedataobtainedfromthedifferentiationofthepreviousstageandthe differenceinthemannerdescribed[18].Thisprocessshouldpersistuntilthedataarrivesatthestationarystage.Tocontinue, theparametersofAutoCorrelationfunction(ACF)andPartialAutoCorrelationFunction(PACF)shouldbeusedsoasto identifyp andq.TheACFandPACFrevealcontradictorypatternsintheprocessesofAR(p)andMA(q).InAR(p),ACF decreasesingeometricformexponentially.ButPACFdecreasesgeometricallyorexponentiallyandeventuallyinterrupts afteracertainnumberofintervals[18].
Thesecondstepistoestimatethecoefficients:
Aftertheidentificationstage,themodelparametersareestimated.Toestimatetheparameters,theminimumsquares methodcanbeused.Butwhenthemodelisnonlineartowardstheparameters,thenonlinearapproachisappliedtoestimate theparameters.
Thirdstep,Verification:
Afterestimatingthemodel,theaccuracyandpertinenceofthemodelshouldbeconsidered.Amodelwillbesuitable whentheresidualsofthemodelbearthepropertiesofindependentnormalrandomvariablescommonlydistributedwith zeromedianandfixedvariance.Toverifytheaccuracyofthemodel,thestatisticalreportof(BOX-pierceQ)testisemployed [18].
Afterdevelopingtwomodelsincludingregressionandtimeseries,theirresultswillbecomparedtoeachothertofindthe bestcostpredictionmodel.
3.2.Evaluationofeconomicrisk
MonteCarlosimulationallowstheanalysttoallocateallpossibleuncertaincomponentstomathematicalmodelsofa probabilitystatementandthenuserandomsamplingfromthis.Thedistributionsidentifythedistributionofallthedifferent outcomesthatoccurasaresultoftheseuncertainties[20].ToapplytheMonteCarlosimulation,thefollowingstepsshould betakenintoaccount:
Identifyingthemodel:thefirststepistodevelopamodelfordependentvariablesbasedonsomeindependentparameters.
Thisstepwasdoneintheearliersectionforbothconcreteandasphaltpavements.
Determiningthedistributionofindependentparameters:Accordingtohistoricaldata,thedistributionofparameterscan becalculated.Checkingthenormalityofdataisagoodstartingpointtodeterminethetypeofdistribution.
Settingthenumberofiteration:TheMonteCarloisbasedonrandomsamplingfromthedistributionofindependent parameters.Bysetting theiterationand doingthesamplingprocess,thedistributionof dependentvariables canbe calculated.
4.Researchresults
AsshowninFig.1,fieldstudiesandliteraturereviewsweredonetodeterminethemethodofdesigningandrecognizing thetypesof pavementsystems.Afterselectingtheappropriate methodfordesigning ContinuousReinforcedConcrete Pavement(CRCP)andhotmixasphaltpavements,themostadaptedintheIranianenvironment,effortsweremadetousethe nationalpricingsystemofIranunderthenameofroadpricingtodeterminethepriceofconcreteandasphaltpavements.The pricesofthepartswereusedaswell.Forthispurpose,thepricelistswereconsideredbetweentheyears1998–2016.Inthe review,theauthorsencounteredthefactthatincertainyears,thepriceswerenotavailableduetothelackofpublicationof
thelistofpricesbythegovernment,sotosolvethisproblem,effortsweremadetoincreasethepricesbytherateofinflation declaredbyCentralBankoftheIslamicRepublicofIranannuallyinthepreviousyear.Theestimatedpricesfortheprevious yearhadtobeusedfortheyearinquestion.Afterthisprocess,theeffortwasmadetopresentamodelbasedondependent variables(thepriceofpavement)andindependentvariables.Usingtheproposedmodelinthepreviousstep,aquantitative economicriskwasassessed.Theresultsarepresentedasfollows:
4.1.Presentingpricemodel 4.1.1.Theregressionmodel
Accordingtothecollecteddatathestepsofregressionmodelwereimplemented.InTable1,theaveragecostofeach kilometerroadforconcreteandasphaltpavementsonfreewaysandhighwaysispresentedinIran.Themethodandthe processofcalculationandthelistofvariablesaffectingthepriceofconcreteandasphaltpavementsarepresentedinthe appendix.TheauthorsappliedthedatapresentedinTable1asrealdatafordevelopingtheregressionmodel.Thereaders shouldpayattentiontotwoconsiderationswhentheywanttointerprettheinformationprovidedinTable1.Thefirstoneis consideringthesourceofdata,whichisbasedonthenationalpricingsystemofIranunderthenameofroadpricing.Usually, this methodofcalculating prices isused bythegovernment topayin Iranian projects.It ispossible thatthecost of constructionisdifferentfromthepaymentbuttheauthorsappliedforthepaymentsincealloftheexpertsagreedtothis approach.Thesecondoneisthatthecalculatedpricesareforfreewaysandhighways.Inotherwords,theywoulddifferwhen othertypesofroadsareconsidered.
Atfirst,theestimatedbasecostofthematerialsusedineachofthecalculations,forexample,theestimationofthebase costoftackcoatusedforasphaltpavementin2012havebeencalculatedasEq.(3):
y1¼ððVx150301Þ þðdaVx200201Þ þðdaVx200202Þ þðdaVx200203ÞÞ
1000 ð3Þ
Where,
y1=basecostofprimecoatperkilogram d=hypotheticaldistancefortransportation
a=theavailablecoefficientitemaffordingfineviewinthepricelist V=theamountofmaterialconsumedtocalculatetheprimerate x150301=priceforsupplyingandservingassurfacecoatings(kg) x200201=priceofcarryingbitumenfrom30to75km(ton/km) x200202=priceofcarryingbitumenfrom75to150km(ton/km) x200203=priceofcarryingbitumenfrom150to300km(ton/km)
Thenumbersshownbelowxpertaintotheirrownumberinthepricelist.
Finally,y1hasbeencalculatedasEq.(3):
y1¼ðð10007493Þþð451:051704Þþð751:051704Þþð1501:051454ÞÞ
1000 ¼7668Rial ð3Þ
ConsideringthedatainTable1andapplyingtheregressionmethods,threemodelsforconcretepavementandsixmodels forasphaltpavementwereobtained.AfterapplyingtheANOVAandt-test,onemodelofconcretepavementandonemodelof asphaltpavementwererejectedandconsequentlywereremovedfromthelist.Fortheremainingmodels,theprediction errorofeachmodelwasmeasuredand,finally,thefollowingregressionmodelswereapprovedwithameanerrorof8%for concretepavementsand7.1%forasphaltpavementforfreewaysandhighways.Below,themodelofregressionofconcrete andthentheasphaltpavementmodelsaredescribed.Itshouldbenoticedthatthemodelsweredevelopedbasedontheprice unitRial.
Themodelofregressionofconcretepavement
Forfreewaysandhighwayswithconcretepavement,themodelwascalculatedasEq.(4):
y¼11248:85839x1þ32732:57575x2þ92156734 ð4Þ
wherex1isthepriceofadumptruckwithacapacityofabout10tonswiththedriverandx2isthepriceofwashedgravel.The modeldepictsthatbypredictingthepriceoftwomentionedvariables,thecostofconcretepavementwouldbecalculated.
Themodelofregressionofasphalticpavement
Forfreewaysandhighwayswiththeasphaltpavement,themodelwascalculatedasEq.(5):
y¼68178:537x1þ24955:482891x2þ507892:791807x3þ29668:94969x45851:498718x5
3085:989966x610501:50597x7þ2236:485713x8þ80802486 ð5Þ
wherex1isthepriceofwashedsand,x2isthepriceofwashedgravel,x3isthepriceofbitumenMC250,x4isthepriceof asphaltworker,x5isthepriceofsprinklertank20,000literswithdriver,x6isthepriceofrubberwheelloaderwithapowerof about150horsepowerwiththedriver,x7isthepriceofgraderwith150horsepowerwithadriverandx8isthepriceofplay asphaltmachines-Fingerwheelchainsawwithdriver.Themodeldepictsthatbypredictingthepriceofeightmentioned variables,thecostofasphaltpavementwouldbecalculated.
TheEqs.4and5demonstratethatthecostofconstructingonekilometerofconcretepavementandasphaltpavementwill becalculatedbyinsertingsomeoftheparametersdepictedasxvalueintheequation.Inotherwords,theregressionmodel developedbyEqs.4and5issuitabletoestimatethecostpavement.Moreover,theauthorswillapplytheseequationsto evaluatetheeconomicriskofpavementsbyinsertingthepricefluctuationsofindependentparameters(xi).
Checkingthevalidityandcorrectnessofregressionmodels
Ineachlinearregressionmodel,thereareseveralassumptionsthatifthemodelsarecorrect,andregressionresultsare valid,otherwisetheyshouldbereplacedbyanothermodel.Thesestatementsinclude:1)Theaverageoferrorsiszero;2)The errorofvarianceisconstanteventhoughitisunknown;3)Thezeroisthecorrelationbetweenerrorsindifferentstages;4) Normaldistributionoferrors.Theseclaimsdonotnecessarilyapplytoremnants[19].Inthefollowing,regressionanalysis andverificationofthecorrectnessoftheregressionequationcalculatedforconcretepavementispresented.
1.Checkingthezeroofthemeanerrors:byapplyingthedatafrom1998–2013themeanerrorswerecalculatedasshown inTable2forconcreteandasphalticpavements.Theresultsshowedthatthemeanerrorsarezero.
InTable2thevalueofunstandardizedresidualisdefinedinthefollowingterms:
UnstandardizedResidual=ycalculation–yprediction
Where,
yprediction=constructioncostcalculatedinconformitywiththeregressionmodel ycalculation=constructioncostcalculatedinaccordancewithTable1.
2.Checkthenormaldistributionoferrors:ThiscontrolwasdonebasedontheShapiro-Wilktestwhichisforinvestigating thenormalityofdata[21].AccordingtoTable3andthesignificance leveloftheShapiro-Wilktestintheconcreteand asphalticpavement,beingequalto0.651and0.762,arerespectivelygreaterthan0.05.Onecanassumetheerrordistribution withhighnormalconfidence.
3.Checkingtheconstantofvarianceoferrors:ItmeansVð
e
iÞ¼s
2 : 8i.AscanbeseeninFig.2,thevarianceoferrorsis almostconstant.AsshowninFig.2,errorshavebeendistributedwithinaspecifiedrangeontheaxisy=0.Inotherwords,itcanbe concludedthaterrorshavenotsuddenlybeengreatlyreducedordecreased.Therefore,thevarianceoferrorsisalmost constant.
4.Checkingthezerocorrelationbetweenerrors:ItmeansCOV
e
i :e
j¼0 : 8i:j.AccordingtoFig.2,itcanbeseenthat theresiduesarescatteredoveranx-axisbyaccidentsothatthenearregressionmodelisindependentofeachother.Giventhatalllinearregressionmodelsclaimthemodeliscorrect,thenthementionedmodelsareselectedasasuitable modelforfreewaysandhighwayswiththeconcreteandasphalticpavement.
Investigatingthecorrelationcoefficientofvariableswithoutputvalues:Findingthecorrelationcoefficientofvariableswith outputvalueswasdoneformoreconfidencewhetherthevariablespresentedinthemodelsarecorrelatedwithoutputsor not.
Table2
Mean,SkewnessandKurtosisoferrorsforfreewaysandhighways.
Pavement Model N Mean Skewness Kurtosis
Statistic Statistic Statistic Std.Error Statistic Std.Error Concrete UnstandardizedResidual-Model2StepwiseMethod 16 0.0000001 0.205 0.564 1.043 1.091
ValidN(list-wise) 16
Asphalt UnstandardizedResidual-Model6BackwardMethod 16 0.0000004 0.020 0.564 0.552 1.091
ValidN(list-wise) 16
Table3
Shapiro-Wilktestforerrorsforfreewaysandhighways.
Pavement Model Shapiro-Wilk
Statistic df Sig.
Concrete UnstandardizedResidual-Model2StepwiseMethod 0.959 16 0.651
Asphalt UnstandardizedResidual-Model6BackwardMethod 0.966 16 0.762
AsshowninTable4,therelatedvariablesinconcreteandasphalticpavementshaveahighcorrelationwiththeaverage costofconcreteandasphalticpavementsonfreewaysandhighways,beingpresentintheregressionequationgiven.
4.1.2.Timeseriesmodel
Theproceduretoobtainthetimeseriesoftheconcretepavementisdescribedasfollow:
Inthefirststep,towardtheexaminationof(stationary)data,thefollowingdiagram(theprocessofpricechanges)ofthe averageconstructioncostofconcretepavementwasdrawn.
AsshowninFig.3andbasedontheKPSStest,theamountofLM-Statisequalto0.634whichislargerthantheircritical level5%and10%.Therefore,thezerotheory(thedatabeingstationary)willberejected.Assuch,thedataarenotstationary overtime.Tostabilizethedata,thedifferentialtechniqueisemployed.TheamountofLM-Statisequalto0.304andbeing smallerthantheircriticallevel5%and10%byconductingdifferentialtechniquesonthreeoccasionsandbasedontheKPSS test.Therefore,thedatawillbecomestationarybytheemploymentofdifferentialtechniquesonthreeoccasions(d=3).The modeltypeandpositionofpandqwillbedeterminedbyusingACFandPACF.Here,thepositionofpisequalto1andqequal to0.Giventhefactthatpartialcorrelationwillloseitsmeaningfulnatureatlevel1;therefore,thetimeseriesmodelforthe concreteprocedurewillbeARIMA(1,3,0).
Afterthefirststepandidentifyingthemodel,theestimationofmodelcoefficientsisconductedasexplainedinEq.(6):
y3¼678331360:783177y3t1 ð6Þ
Where,y3isequaltothethirdorderofdifferentiationofthepriceofconcretepavements.
Inthethirdstep,theBOX-Piercetestwasusedtoverifytheaccuracyofthemodel.TheresultsoftheQstatisticsshowed thatithasnotbeenmeaningfulinstatisticaltermsandthatresidualsfromthemodelpracticepurelybychance.
Eventually,theEq.(7)isobtainedforconcretepavementbysimplifyingtheEq.(6),inwhichthebaseyearwouldbe2002.
yt¼67833136þ2:216823yt10:650469yt21:349531yt3þ0:783177yt4 ð7Þ Fig.2. Showsthedistributionoferrorsforfreewaysandhighways.
Table4
Coefficientofcorrelationofindependentvariableswithaverageconstructioncostinfreewaysandhighways.
Pavement Benchmark Coefficientofcorrelationwithaveragecostof
pavementonfreewaysandhighways Concrete dumptruckwithacapacityofabout10tonswiththedriver 0.993
Washedgravel 0.991
Asphalt Washedsand 0.978
Washedgravel 0.905
BitumenMC250 0.991
Asphaltworker 0.965
Sprinklertank(20000liters)withdriver 0.969
rubberwheelloaderwithapowerofabout150horsepowerwiththedriver 0.970
graderwith150horsepowerwithadriver 0.966
Playasphaltmachines-Fingerwheelchainsawwithdriver 0.946
Tocarryonwiththepresentattempt,theprocedureofachievingasphaltpavementaswellasthetimeseriesmodelis elucidated:
Inthefirststep,toinvestigatethe(stationary)natureofthedataagainsttheaveragecostofmakingasphaltpavementthe processofpricechangewaschartedinFig.4.
AsshowninFig.4andbasedontheKPSStest,theamountofLM-Statisequalto0.586whichisbiggerthantheircritical levelof5%and10%.Therefore,thezerotheory(ifdatabeingstationary)isrejected.So,thedataarenotstationaryovertime.
Tostabilizethedata,thedifferentialtechniqueisused.BydevelopingdifferentialontwooccasionsandbasedontheKPSS testtheamountofLM-Statisequalto0.288,beingsmallerthantheircriticallevel5%and10%.Hence,thedatawillbecome stationarybyconstitutingdifferentiationonthreeoccasions(d=2).Themodeltypeandpositionofpandqaredetermined byusingACFandPACF.Asaresult,pandqareequalto1and0respectively.Consideringthatpartialcorrelationlosesits meaningfulnatureatlevelone,sothetimeseriesmodelforconcretepavementisARIMA(1,2,0).
Afterthefirststepandidentifyingthemodel,theestimationofmodelcoefficientsismadebyEq.(8):
y2¼591427095þ1:24593803081y2t1 ð8Þ
Wherey2isequaltothesecondorderdifferentiationofthepriceofasphaltpavements.
Inthethirdstep,toverifytheaccuracyofthemodel,thestatisticalBOX-Piercetestwasemployed.Thestatisticalresultsof Qshowedthatthemodelisnotmeaningfulinstatisticaltermsandthattheremainderresultsfromthemodelpracticepurely bychance.
Eventually,bysimplifyingEq.(8),Eq.(9)isobtainedfortheasphaltpavement,inwhichthebaseyearwouldbe2002.
yt¼591427095þ0:754619692yt1þ1:491876062yt21:24593803081yt3 ð9Þ
4.2.Comparisonofregressionandtimeseriesmodels
Inthissection,thecomparisonofregressionandtimeseriesmodelsismadeandthesuitablemodelwillbechosenfrom amongthesemodels.Tocarryonwiththepresentattempt,theresultsofTable5areachievedbyusingmodels1,2,3,4,6,8 andTable1.
AsshowninTable5theaverageerrorpercentageofthetimeseriesmodelsandtheregressionofconcretepavementare equal,butconsideringthatthetimeseriesmodelsareverysensitivetothedataofitspreviousyearsandsince2013withthe riseofbitumenpriceaswellastheliberalizationofthesubsidies(consequentlysuddenincrementalriseintheconstruction
Fig.3.Trendofpricechangeofconcretepavementduringthetime.
Fig.4.Trendofpricechangeofasphaltpavementduringthetime.
costofasphaltpavement)thismodeldoesnotprovideagoodestimationforasphaltpavement.Therefore,errorsinthetime seriesmodeloftheasphaltpavementareverylarge.Hence,theauthorsintendtousetheregressionmodelsofasphaltand concretepavementsforperformingtheMonteCarlosimulationtoassesseconomicrisks.
4.3.Evaluationofeconomicrisk
Now,toevaluatetheeconomicrisksofconcreteandasphaltpavements,theMonteCarlosimulationwasapplied.To determinethepricefluctuationsofindependentvariables,thehistoricaldatawouldbeapplied.Sincethepriceofthelast threeyearsofindependentvariables(2014,2015and2016)wasduetopricefluctuations,theywereoutoftheordinary.The dataintheyears1998–2013wereselectedtofindtheirdistribution.Sincethecostpredictionmodelforbothofpavementsis clear,thesecondstep,whichisdeterminingthedistributionofindependentvariables,wastaken.Theauthorsexamined theirnormalityand,inthenormalcase,thestandarddeviationsoftheindependentvariableswerediscussed.Byexamining thetenindependentvariables,thenormalityofdatawasprovedandtheirstandarddeviationsdemonstratedinTable6.The parametersdepictedin Table6 are thesameas those existingin thecost prediction modelfor concreteand asphalt pavement.
TheresultsoftheMonteCarlosimulationand10,000timesoftherepetitionareasFigs.5and6.,andTable7;calculations werecarriedoutinthe@RISKsoftware:
Table5
Percenterrorofestimationpriceofpavementforregressionandtimeseriesmodel.
Pavement Model P.E P.EA
2014 2015 2016 Average
Concrete Regression 7 8 10 8
Timeseries 11 5 7 8
Asphalt Regression 0 10 11 7.1
Timeseries 10 71 46 42
Table6
Standarddeviationofindependentvariables.
Pavement Benchmark StandardDeviation
Concrete dumptruckwithacapacityofabout10tonswiththedriver 74,051.307
Washedgravel 22,398.139
Asphalt Washedsand 19102.972
Washedgravel 22398.139
BitumenMC250 2027.136
Asphaltworker 10913.199
Sprinklertank(20000liters)withdriver 92683.248
rubberwheelloaderwithapowerofabout150horsepowerwiththedriver 119353.338
graderwith150horsepowerwithadriver 118394.338
Playasphaltmachines-Fingerwheelchainsawwithdriver 153284.769
Fig.5.Estimatedhistogramforpricechangesforpavementonfreewaysandhighways.
AsshowninFigs.5&6,alsoinTable7withmoredetails,itisrevealedthatthestandarddeviationofasphaltpavementsis greaterthanconcretepavement.Inotherwords,theeconomicriskorcostfluctuationofasphaltpavementsinIranwillbe higherthanconcreteones.ByreferringtoTable1,thecostofconcretepavementincomparisonwithasphaltpavementhas beendecreasedfrom2008to2016.Thisimpliesthatthechoiceofconcretepavementismorelogicalthanitscostand economicrisksonfreewaysandhighways.
Formoreinvestigationsonresults,asensitivityanalysiswasdone.Fig.7presentstornadographsforeachpavement.
AsshowninFig.7,thesensitivityofvariablesineachpavementisdifferent.Thecostofperhourforadumptruckwitha capacityofabout10tonswiththedriverismoresensitivethanwashedsandonthecostofconcretepavementbutthis differenceisnotconsiderable.Inthesameway,thecostofasphaltpavementismoresensitivetowashedsand.Thisanalysis isusefulwhenthechangeinthepriceofindependentvariablesoccurs.Thedecision-makercantracetheamountofchange inthecostofeachpavement.Inotherwords,thedecision-makershouldpayattentiontothosevariableswithhighsensitivity duringtheexecutionphasetodecreaseitseconomicriskduringtheconstruction.
Fig.6.Predictivecurveofpricechangesforpavementonfreewaysandhighways.
Table7
Informationonthepredictionofpricechangesonpavementsinfreewaysandhighways.
Name Minimum Mean Maximum StdDev Variance Skewness Kurtosis Mode LeftX LeftP
Asphalt 3.51E+09 1.18E+10 1.97E+10 2.32E+09 5.38E+18 3.14E-02 2.932057 8.71E+09 7.90E+09 5%
Concrete 5.17E+09 9.52E+09 1.42E+10 1.11E+09 1.22E+18 2.19E-02 2.976211 8.58E+09 7.67E+09 5%
Name RightX RightP Diff.X Diff.P 5thPerc. 95thPerc.
Asphalt 1.56E+10 95% 7.67E+09 90% 7.90E+09 1.56E+10
Concrete 1.13E+10 95% 3.63E+09 90% 7.67E+09 1.13E+10
Fig.7.TornadoGraphAnalysisofsensitivitytopavementpricesonfreewaysandhighways.
5.Conclusion
Thepavementisoneofthemostimportantcomponentsofroadssinceitdirectlycontactswiththevehicles.Thestructure ofpavementsisrelatedtotheirtypes.TherearetwomostfrequentlyusedpavementsinIran,concreteandasphalt.Sincethe considerableamountofroadbuildingcostisdependentonthecostofpavements,itisnecessarytoanswerthisquestion whethertheconcreteorasphaltpavementsarethesuitableselection.Thispaperintendstoanswerthisquestionintermsof theeconomicrisks.Theprobabilityofpricechangesinconstructingconcreteorasphaltpavementshasbeenappliedasa definitionoftheeconomicrisksinthispaper.SincetheIraniangovernmentisresponsibleformostinfrastructuressuchas freewaysandhighways,theproblemofpricechangesisveryimportant.Asanexample,thegovernmentbudgettocomplete thefreewaysprojectshasbeenchallengedwhenthepriceofbitumenhasbeendoubledinIran.Basedonunofficialreports, about40%oftheIranianbudgetinthefreewaysprojectshasbeenconsumedtoprovidebitumen.Thereisthesamechallenge forconcretepavementssuchastheprobabilityofpricechangesofcement.Thefindingsofthispapercanhelpadministrators todecidetoimplementwhichtypeofpavementintheirprojectswithrespecttotheeconomicriskofconstruction.
TodeterminewhichtypeofconcreteorasphaltpavementshaslowerpricechangesinIran,twosectionsweredeveloped.
Inthefirstsection,developingamodeltopredictthecostofthesepavementswasconsideredandinthesecondsection,the bestchoicewasselectedintermsofeconomicrisksforconstructingIranianhighwaysandfreeways.Inmoredetail,basedon thecollecteddatafortheyears1998–2016,twomodelsincludingtheregressionmodelandtimeseriesweredevelopedto predictthecostofconcreteandasphalticpavement.Tofindasuitablemodel,theregressionandtimeseriesoneswere comparedbasedontheiraverageerrorswhen theyestimatethefuturecostand theirabilitytoworkin anabnormal situation.Theresultsshowed thatalthough thetwomodelsgivethesame averageerrorin thenormalsituation,the regressionmodelismoreappropriatethanthetimeseriesmodelwhentheyareappliedinanabnormalsituation.Theresults oftheregressionmodelshowedthatthecostofconcretepavementwouldbeestimatedbytwoindependentvariableswith 8%meanerrorandeightindependentvariableswith7.1%meanerrorforasphalticpavement.Afterfinalizingtheprediction model,byapplyingtheMonteCarlosimulation,theeconomicrisksofthesepavementswereassessed.Theresultsshowed thatthecostofconcretepavementduringtheconstructionphaseischeaperthanasphaltpavementsince2008inIran.Thisis becauseoftheincreaseofbitumenpricesandtheriseofcementproductioninthecountrybutthemainquestioniswhich typeofpavementhasthelowesteconomicrisk.Fortheyear2016,usingthesimulationofMonteCarloand10,000times,90% ofthepricerangeforthecostofconcretepavementrangedfrom7.67to11.31billionRials.Forasphaltpavement,thisamount stoodbetween7.90and15.57billionRials.Meanwhile,theresultsoftheMonteCarlosimulationindicatedthattheconcrete pavementhaslessstandard deviationthantheasphaltpavement.Itmeansthattheprobabilityofpricechangesinthe concretepavementislessthanasphaltpavement.
However,theauthorstriedtodotheirbesttherearesomeshortcomingsinthisresearch.Thefirstoneisthatthefindings ofthispaperincludingthepriceoftwopavementsandtheresultofeconomicriskassessmentarestronglyrelatedtothe Iranianprojectspecificationsbutthepresentedmethodologycanbeappliedineverysituation.Theothershortcomingisthat thispaperdidnotconsiderothercriteriasuchasmaintenancecostsandthedurationofprojects.Theauthorslimitedtheir researchtochangesofthesepavements’ingredientsandtheywantedtoconcludethebehaviorofthesepavementsinterms oftheircostbasedonthehistoricaldatatheiringredients.Anotherlimitationwastoignoreenvironmentalissues.Theresults maybealteredwhentheenvironmentalissueswereconsidered.
According tothe stated shortcomings, researchers in theirfuture studycan develop their works in solving these shortcomings.Moreover,thefutureworkscanuseMontenegro'sneuralnetworksandsimulationstoevaluatetheeconomic risksofthesetwotypesofpavementsandcomparetheresultsoftheirworkwiththepresentattempttoanswerthequestion astowhichmethodwillbepreferable.Also,itispossibletoevaluatetheeconomicriskofthesetwopavementsusingother riskassessmentmethodssuchasRealOptionandcomparetheresultswiththeresultsofthepresentresearchwork.The othersuggestioniscomparingtheriskofconcreteandasphalticpavementsinthelifecycleofpavements.
DeclarationofCompetingInterest
Thereisnoconflictofinterest.
AppendixA.Supplementarydata
Supplementarymaterial related tothis article can befound, in theonline version, at doi:https://doi.org/10.1016/j.
cscm.2020.e00346.
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HamidrezaAbbasianjahromia,* ShahryarAghevlib MehdiRavanshadniac
aCivilEngineeringDepartment,K.N.ToosiUniversityofTechnology,No.1346,ValiAsrStreet,MirdamadIntersection,Tehran,Iran
bIslamicAzadUniversity,ScienceandResearchBranch,DaneshgahBlvd,SimonBulivarBlvd,Tehran,Iran
cFacultyofCivilEngineering,IslamicAzadUniversity,ScienceandResearchBranch,DaneshgahBlvd,SimonBulivarBlvd,Tehran, Iran
* Correspondingauthor.
E-mailaddress:[email protected](H.Abbasianjahromi).
Received23July2019
