Volume--Shape--and-Roundness-of-Rock-Particles

Volume,Shape,andRoundnessofRockParticlesAuthor(s):HakonWadellSource:TheJournalofGeology,Vol.40,No.5(Jul.-Aug.,1932),pp.443-451Publishedby:TheUniversityofChicagoPressStableURL::24/07/201320:27YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,[e-mail]..TheUniversityofChicagoPressiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoTheJournalofGeology.:27:56PMAllusesubjecttoJSTORTermsandConditionsVOLUME,SHAPE,ANDROUNDNESSOFROCKPARTICLESHAKONWADELLUniversityofChicagoABSTRACTThepresentpaperdealswiththefundamentalprinciples,conceptions,andideasuponwhichsomenewsedimentologicalresearchmethodsarebased.Sizeclassificationofparticlesiscommonlybasedoneitherthearithmeticorthegeometricmeanofthegreatest,intermediate,andleastdiameters.Thevaluesobtainedinbothcasesaredependentupontwofactors:theshapeandthevolumeoftheparticle.Twoparticles,onehavingdiametersofextremelydifferentvalues,theotherbeingaspherewiththethreediametersconsequentlyofthesamelength,maybothhavethesamesizevalueasaresultofthearithmeticorgeometricmeanoftheirdiameters,yettheymaydifferdistinctlyinrespecttobothshapeandvolume.Shapeandvolumearefactorsindependentofeachother,andadistinctionbetweenthetwoisofimportancefortheinterpretationofavastnumberofphenomena.Noagreementhaseverbeenreachedindefiningthethreediame-tersofaparticleofnon-sphericalshape.Someinvestigatorsrequirethatthethreediametersmeetatrightangles;othersstipulatethatthelinesofmeasurementbeatrightanglestoeachother,butdonotrequireacommonpointofcrossing.Inthelastcasethemeandiame-terisordinarilycomputedasthemeanoflength,breadth,andthicknessoftheparticle.Hereagainweenteruponambiguousconceptions(breadthandthicknessofanirregularsolid?)whichbecomestillmoreconfusingwhendealingwithparticleswithre-entrantangles.Ordinarilythelengthissynonymizedwiththedistancebetweenthetwomostdistantperiphericalpointssituatedoppositetoeachother.Maintainingthisviewandtherulethatthediametersshouldrunatrightanglestoeachother,themeandiameter,for443Thiscontentdownloadedfrom141.213.168.163onWed,24Jul201320:27:56PMAllusesubjecttoJSTORTermsandConditionsHAKONWADELLinstance,ofacubeof2mm.edge,equalsthediagonalofthecube,i.e.,3.46mm.Thediameterofasphereofthesamevolumeasthecubeamountsto2.48mm.Itisevidentthatthehighvalueofthemeandiameterofthecubeisduetotheshape.Themeandiameterhasnosignificancewhatsoever,exceptthatitgivesageneralideaofthesizeoftheparticle.Anattempttousethemeandiameterasabasisforcalculatingthevolumeoftheparticlegivesvaluesalloutofproportiontotheactualvalueofthevolume.Forinstance,inthegivenexample,3.463equals41.42cubicmillimeters,orfigur-ingonasphereofadiameterof3.46mm.thevolumeamountstoabout22cubicmillimeters;whereas,thetruevolumeofthecubeequals8cubicmillimeters.Itis,ofcourse,understoodthatthetruevolumeofaparticleofcubicshapemaybereadilyobtainedwhenthelengthofitsedgeisknown,but,sincerockparticles,ingeneral,donotattainsuchregularshape,theexampletendstoshowtheerroneousimpressionofthevolumeofaparticlewhenthemeandi-ameter,ascommonlydefined,isusedasanexpressionforsize.Thesizeofaparticleisbestexpressedbyitssimplevolumeval-ue,becausethisvalueremainsalwaysunaffectedbytheshape.Sometimesthesizemayadvantageouslybeexpressedbythevalueofthetruenominaldiameter,whichisthediameterofasphereofthesamevolumeastheparticle(nottobeconfusedwiththeequivalentdiameter[equivalentradius,Od6n,1915]whichisthediameterofaspherehavingthesamesettlingvelocityastheparticle).SHAPEOFPARTICLESAsolidmaybespherical,cylindrical,cubical,etc.Toexpressitsformitisnecessarytoadoptastandardshapeforcomparison.Transportationofsedimentaryparticleseitherbywindorwaterinvolvesrollingandsuspension,andbetweenthesetwoaninter-mediatemodeofdislodgment,saltation.Thesphericalformisadeterminantfactorinsortingtheparticlesintractionbyrolling,becausesphericalparticlesrollfasterthannon-spherical.Whendealingwithtractionalparticlesthespheremaythereforeappro-priatelybetakenasastandardofcomparison.Whendealingwithparticlesinsuspensiontheexpressionofshapemusttheoreticallybeseenfromanotherangle,viz.,theareaofthe444Thiscontentdownloadedfrom141.213.168.163onWed,24Jul201320:27:56PMAllusesubjecttoJSTORTermsandConditionsVOLUME,SHAPE,ANDROUNDNESSOFROCKPARTICLES445grainsurface.Aspherehasthegreatestrelativevolumewiththesmallestsurfaceareaand,therefore,hasagreatersettlingvelocitythananyothershapeofthesamevolumeanddensity.Progressivelygreaterdeparturefromsphericalshapemeansprogressiveincreaseofsurfacewithoutchangeofvolumeand,therefore,also,adecreaseofthesettlingvelocityofthesolid.Itisevidentthatthemostexactshapeexpression,approx