23 Mass diagram

1CE453Lecture23EarthworkandMassDiagrams2TheBasicsDon’tcallitdirtBorrowisnotreturnedWasteisexcessFrequentlybigvolumesAtlowunitpricesAddinguptobig$$$3TerrainEffectsonRouteLocationDon’tforgetyourdesigncriteria(grades,etc)AttempttominimizeamountofearthworknecessarySetgradelineascloseaspossibletonaturalgroundlevelSetgradelinesothereisabalancebetweenexcavatedvolumeandvolumeofembankmentTakecross-sections(typically50feet)PlotnaturalgroundlevelPlotproposedgradeprofileIndicateareasofcutandfillCalculatevolumebetweencross-sections5AverageEndAreaMethodAssumesvolumebetweentwoconsecutivecrosssectionsistheaverageoftheirareasmultipliedbythedistancebetweenthemV=L(A1+A2)÷(2*27)V=volume(yd3)A1andA2=endareasofcross-sections1&2(ft2)L=distancebetweencross-sections(feet)6Source:GarberandHoel,20027ShrinkageMaterialvolumeincreasesduringexcavationDecreasesduringcompactionVarieswithsoiltypefillheightcutdepth8SwellExcavatedrockusedinembankmentoccupiesmorespaceMayamountto30%ormore9ComputingVolume(Example)Shrinkage=10%,L=100ftStation1:GroundlineCutFillCutArea=6ft2FillArea=29ft210ComputingVolume(Example)Shrinkage=10%Station2:GroundlineCutArea=29ft2FillArea=5ft2CutFill11Vcut=L(A1cut+A2cut)=100ft(6ft2+29ft2)=64.8yd3*5454Vfill=L(A1fill+A2fill)=100ft(29ft2+5ft2)=63.0yd35454Fillforshrinkage=63.0*0.1=6.3yd3Totalfill=63.0ft3+6.3ft3=69.3yd3Totalcutandfillbetweenstations1and2=69.3yd3fill–64.8yd3cut=4.5yd3borrow*note:noallowancemadeforexpansion1213EstimatingEndAreaStation1:GroundlineCutFill14EstimatingEndAreaStation1:GroundlineCutFillFillArea=∑Shapes15MassDiagramSeriesoflinesthatshowsnetaccumulationofcutorfillbetweenany2stationsOrdinateisthenetaccumulationofvolumefromanarbitrarystartingpointFirststationisthestartingpoint16CalculateMassDiagramAssumingShrinkage=25%17CalculateMassDiagramAssumingShrinkage=25%Volumefill=100ft(20ft2+0ft2)=37.0yd3fill54Volumecut=100ft(40ft2+140ft2)=333.3yd3cut5418CalculateMassDiagramAssumingShrinkage=25%Volumefill=adjustedforshrinkage=37.0yd*1.25=46.3yd319CalculateMassDiagramAssumingShrinkage=25%Totalcut=333.3yd3-46.3yd3=287.0yd320CalculateMassDiagramAssumingShrinkage=25%Totalcut1to2=555.6yd3–104.2yd3=451.4yd3Volumefill=100ft(20ft2+25ft2)=83.3yd3fill54Volumecut=100ft(140ft2+160ft2)=555.6yd3cut54Volumefill=adjustedforshrinkage=83.3yd*1.25=104.2yd321CalculateMassDiagramAssumingShrinkage=25%Totalcut=451.4yd3+287=738.4yd322CalculateMassDiagramAssumingShrinkage=25%FinalStation23MassDiagram-400-2000200400600800100001234567StationNetCumulativeVolume(C.Y.)Series124-400-2000200400600800100001234567NetCumulativeVolume(C.Y.)StationMassDiagramSeries1Station1:netvolume=287cy25MassDiagram-400-2000200400600800100001234567StationNetCumulativeVolume(C.Y.)Series1Station1:netvolume=287.04ft3Station2:netvolume=738cy26MassDiagram-400-2000200400600800100001234567StationNetCumulativeVolume(C.Y.)Series1Station1:netvolume=287.04ft3Station2:netvolume=738.43ft3Station3:netvolume=819cy27Balancepoint:balanceofcutandfillA’andD’D’andE’NandMEtc.note:ahorizontallinedefineslocationswherenetaccumulationbetweenthesetwobalancepointsiszero28LocationsofbalancedcutandfillJKandSTSTis5stationslong[16+20]–[11+20]29SpecialTermsFreehauldistance(FHD)-distanceearthismovedwithoutadditionalcompensationLimitofProfitableHaul(LPH)-distancebeyondwhichitismoreeconomicaltoborroworwastethantohaulfromtheprojectOverhaul–volumeofmaterial(Y)movedXStationsbeyondFreehaul,measuredinsta–yd3orsta-m3Borrow–materialtakenfromoutsideofprojectWaste–excavatedmaterialnotusedinproject30MassDiagramDevelopment1)CalculateLPHdistance(LPH=FHD+(borrow$÷overhaul$))2)PlaceFHDandLPHdistancesinalllargeloops3)PlaceotherBalancelinestominimizecostofmovementTheoretical;contractormaymovedirtdifferently4)Calculateborrow,waste,andoverhaulinallloops5)Identifystationswhereeachoftheaboveoccur31MassDiagramExampleFHD=200mLPH=725m32Source:Wright1996BetweenStations0+00and0+132,cutandfillequaleachother,distanceislessthanFHDof200mNote:definitelyNOTtoscale!33Source:Wright,1996BetweenStations0+132and0+907,cutandfillequaleachother,butdistanceisgreaterthaneitherFHDof200morLPHof725mDistance=[0+907]–[0+132]=775m34Source:Wright,1996BetweenStations0+179and0+379,cutandfillequaleachother,distance=FHDof200mTreatedasfreehaul35Source:Wright,1996BetweenStations0+142and0+867,cutandfillequaleachother,distance=LPHof725m36Source:Wright,1996MaterialbetweenStations0+132and0+142becomeswasteandmaterialbetweenstations0+867and0+907becomesborrow37Source:Wright,1996BetweenStations0+970and1+170,cutandfillequaleachother,distance=FHDof200m38Source:Wright,1996BetweenStations0+960and1+250,cutandfillequaleachother,distanceislessthanLPHof725m39Source:Wright,1996ProjectendsatStation1+250,anadditional1200m3ofborrowisrequired40VolumeErrorsUseofAverageEndAreatechniqueleadstovolumeerrorswhencross-sectionstaperbetweencutandfillsections(prisms)ConsiderPrismoidalformula41PrismoidalFormulaVolume=(A1+4Am+A2)/6*LWhereA1andA2areendareasatendsofsectionAm=crosssectionalareainmiddl