Open Pit Mine Planning UWA Course 2005_The Lerchs-Grossman Algorithm.ppt

1-Aug-05,1,OpenPitMinePlanningUWACourse2005Part2,TheLerchs-GrossmanAlgorithm,1-Aug-05,UWAPart2,2,,WorkswithblockvaluesWorkswithblockminingprecedences.Guaranteestofindthethree-dimensionaloutlinewiththehighestpossiblue.,ThreeDimensionalLerchs-Grossman,1-Aug-05,UWAPart2,3,,IfAistobemined,BmustbeminedtoexposeAThereverseisnottrueIfBistobemined,Amayormaynotbemined,A,B,ArcRelationships,1-Aug-05,UWAPart2,4,Allslopesaretranslatedintoalargenumberofblockrelationships.Itiswrongtoassumeweneedanarcfromeachblocktoeveryblockwhichis“above”it.Thisisbecausearcscanchain.,,A,B,C,,IfAisminedsoisC,,ArcChaining,1-Aug-05,UWAPart2,5,ChainingofThreeArcsperBlock,1-Aug-05,UWAPart2,6,MinimumArcsperBlock,1-Aug-05,UWAPart2,7,SlopeRegions,1-Aug-05,UWAPart2,8,DemonstrationofL-GAlgorithm,Asimpleexample45degreeslopes2-dimensionsBlocksarecubicPrinciplesarethesamefor3-dimensionsbuthardertoshow.,1-Aug-05,UWAPart2,9,Start,Startingwitha2-dimensionalcrosssectionalmodel.Only3blockscontainorehavuesasshown.Allotherblocksarewasteandhaveavalueof–1.0,1-Aug-05,UWAPart2,10,,Step1,Thefirstarcfromablockcontainingvaluethatwefindistoablockwhichisnotflaggedining,,,,,,,1-Aug-05,UWAPart2,11,,Step2,Welinkthetwoblockstogether.Thetotalvalueofthetwo-blockbranchis22.9,thereforebothblocksarenowflaggedtobemined.,22.9,,,,1-Aug-05,UWAPart2,12,,Step3,Wedealwiththeothertwoarcsfromthisblockinthesameway.Thetotalvalueofthefour-blockbranchis20.9,20.9,,,1-Aug-05,UWAPart2,13,,,Step4,Wecancontinuethesameprocesstotheendofthefirstbench,20.9,20.9,3.9,,,,,,,,,,,,,,1-Aug-05,UWAPart2,14,,,Step5,Wethenmovedalongthenextbench,andfindablockwhichhasnovalueitself,butispartofabranchwithvalue,17.9,20.9,3.9,,,,,,,,1-Aug-05,UWAPart2,15,,,Step6,Thenextflaggedblockhasanarctoablockwhichisalsoflagged.Wedonotcreatealinkforthisarcorfortheverticalonefromthesameblock,becausenothingnewhastoberesolved.,17.9,20.9,3.9,,,,,,1-Aug-05,UWAPart2,16,,,Step7,Thenextarcfromaflaggedtoanotherflaggedblockisbetweentwobranches.Theprocedureisunchanged–wedonotinsertalink,15.9,20.9,3.9,,,,,,,,,,,1-Aug-05,UWAPart2,17,,,Step8,Wecontinueaddinglinks.Thedottedlinkwhenaddedwillchangethueofthebranchto–0.1.Allblocksinthisbranchhavetheirflagsturnedoff.,15.9,20.9,0.9,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,18,,Step9,TheLerchs-Grossmanincludesaprocedureforcombiningthetwolinkedbranchesintoonebranch,withonlyonetotalvalue.Notethatthereisnorequirementtoalwaysbranchupwardsfromtheroot.,15.9,20.8,,,,,,,,,,,1-Aug-05,UWAPart2,19,Step10,Attheendofthesecondbenchwehavenowhaveonlytwobranches,15.9,16.8,,,,,,,,,,,,,1-Aug-05,UWAPart2,20,Step11,Lerchs-Grossmandetectsthattheextrawastewillremovetheabilityofthecentrebranchtoco-operatewiththerighthandbranchinpayingfortheminingofthecircledblock.,8.9,16.8,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,21,Step12,Lerchs-Grossmanincludesaprocedureforbreakingthesinglebranchintotwobranchesbyremovingalink,8.9,15.9,,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,22,Step13,Attheendofthisthirdbenchwehavedropthecentralsubbranchabovethelowgradeblock,8.9,8.9,,,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,23,,,Step14,Continueaddinglinksandeventuallythetotalvalueoftheleft-handbranchbecomesnegative.Thenextarcafterthisisagainbetweenapositiveandnegativebranch.,-0.1,8.9,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,24,Step15,Atthefourthbenchwehavejustonebranchandthecombinedvalueisnowonly0.8,0.8,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,25,Step16,TheL-Gprogramscansforarcsfromblockswhichareflaggedtoblockswhicharenotflagged.WecanseeThesearchhasreachthetopofthemodelandnotmoreblockhavetoberemoved.,0.8,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1-Aug-05,UWAPart2,26,,,,,,,,,,,OptimalPit,Theflaggedblocksconstitutetheoptimalpit.The‘W’-shapedpitisworth0.8.Thecentrebranchhasanegativuesononeofitsblocksareflaggedandnonearemined.,0.8,