Penetration Equations

SAND97-2426DistributionCategoryUC-705UnlimitedReleasePrintedOctober1997PenetrationEquationsC.W.YoungAppliedResearchAssociates,Inc4300SanMateoBlvd.NE,SuiteA-220Albuquerque,NM87110SandiaContractNo.AN6295AbstractIn1967,SandiaNationalLaboratoriespublishedempiricalequationstopredictpenetrationintonaturalearthmaterialsandconcrete.Sincethattimetherehavebeenseveralsmallchangestothebasicequations,andseveralmoreadditionstotheoveralltechniqueforpredictingpenetrationintosoil,rock,concrete,ice,andfrozensoil.Themostrecentupdatetotheequationswaspublishedin1988,andsincethattimetherehavebeenchangesintheequationstobettermatchtheexpandingdatabase,especiallyinconcretepenetration.ThisisastandalonereportdocumentingthelatestversionoftheYoung/Sandiapenetrationequationsandrelatedanalyticaltechniquestopredictpenetrationintonaturalearthmaterialsandconcrete.iiIntentionallyLeftBlankiiiContentsSection1Introduction....................................................................................................................1Section2Background....................................................................................................................22.1JournalofSoilMechanicsandFoundations,1969(5)..........................................................22.2EquationsforComplexTargets,1972(6)..............................................................................22.3EquationsforPenetrationofIce,1974(7)..............................................................................22.4AnUpdateontheBasicPenetrationEquations,1988(8)......................................................32.5SAMPLLCode(9,10).............................................................................................................32.6RecentDevelopmentsinthePenetrationEquations............................................................3Section3PenetrationEquations.....................................................................................................43.1PenetrationEquationsforSoil,Rock,andConcreteTargets...............................................43.2PenetrationEquationsforIceandFrozenSoil.....................................................................53.3NosePerformanceCoefficient,N........................................................................................6Section4MethodsforSelectingorCalculatingS-NumbersforTargetMaterials........................................................................................................84.1S-numberforRock...............................................................................................................84.2S-numberforConcrete.........................................................................................................94.3S-numberforSoil...............................................................................................................104.4S-numberforIce/FrozenSoil.............................................................................................114.5S-numberforOtherMaterials............................................................................................11Section5AccuracyoftheYoungPenetrationEquations............................................................12Section6TechniquesforCalculatingPenetrationintoLayeredTargets.............................................................................................................136.1BasicSoilandRockLayeringTechnique..........................................................................136.2LayeringTechnique,ConcreteStructures..........................................................................14Section7ScalingLaws................................................................................................................177.1GeometricScalingLaws....................................................................................................177.2ModificationstoGeometricScaling..................................................................................18Section8Conclusion....................................................................................................................20References.....................................................................................................................................21APPENDIXAPenetrationEquationsinSIUnits......................................................................A-1APPENDIXBPenetrationEquationsSummarized...................................................................B-1Distribution...................................................................................................................................22TablesTable4-1.DescriptiveTermsforRockQuality,Q........................................................................9Table4-2.Penetrability(S-number)ofTypicalSoils..................................................................11Table7-1.PenetratorRelatedTerms............................................................................................17Table7-2.Conc