rock - Stress-strain relationships - Encyclopedia Britannica

The deformation of materials is characterized by stress-strain relations. For elastic-behaviour materials, the strain is proportional to the load (i.e., ... rock TableofContents rock Introduction&TopQuestionsGeneralconsiderationsRocktypesRockcycleTextureClassificationbygrainorcrystalsizePorosityPhysicalpropertiesDensityMechanicalpropertiesStressandstrainElasticconstantsRockmechanicsStress-strainrelationshipsEffectofenvironmentalconditionsThermalpropertiesThermalconductivityThermalexpansionRadioactiveheatgenerationElectricalpropertiesMagneticpropertiesApplicationsofthestudyofrockmagnetizationBasictypesofmagnetizationTypesofremanentmagnetizationHysteresisandmagneticsusceptibilityMagneticmineralsandmagneticpropertiesofrocks FastFacts 2-MinSummary RelatedContent Media Videos Images More MoreArticlesOnThisTopic AdditionalReading Contributors ArticleHistory Stress-strainrelationshipsThedeformationofmaterialsischaracterizedbystress-strainrelations.Forelastic-behaviourmaterials,thestrainisproportionaltotheload(i.e.,theappliedstress).Thestrainisimmediatewithstressandisreversible(recoverable)uptotheyieldpointstress,beyondwhichpermanentstrainresults.Forviscousmaterial,thereislaminar(slow,smooth,parallel)flow;onemustexertaforcetomaintainmotionbecauseofinternalfrictionalresistancetoflow,calledtheviscosity.Viscosityvarieswiththeappliedstress,strainrate,andtemperature.Inplasticbehaviour,thematerialstrainscontinuously(butstillhasstrength)aftertheyieldpointstressisreached;however,beyondthispointthereissomepermanentdeformation.Inelasticoviscousdeformation,thereiscombinedelasticandviscousbehaviour.Thematerialyieldscontinuously(viscously)foraconstantappliedload.Anexampleofsuchbehaviouriscreep,aslow,permanent,andcontinuousdeformationoccurringunderconstantloadoveralongtimeinsuchmaterialsascrystals,ice,soilandsediment,androcksatdepth.Infirmoviscousbehaviour,thematerialisessentiallysolidbutthestrainisnotimmediatewithapplicationofstress;rather,itistakenupandreleasedexponentially.Aplasticoviscousmaterialexhibitselasticbehaviourforinitialstress(asinplasticbehaviour),butaftertheyieldpointstressisreached,itflowslikeaviscousfluid.SomerepresentativevaluesofelasticconstantsandpropertiesarelistedinTable36.Thecoefficientofviscosity(η)istheratioofappliedstresstotherateofstraining(changeofstrainwithtime).Itismeasuredinunitsofpoise;onepoiseequalsonedyne-secondpersquarecentimetre. ReadMoreonThisTopic tunnelsandundergroundexcavations:Modernrocktunneling Itisimportanttodistinguishbetweenthehighstrengthofablockofsolidorintactrockandthemuchlowerstrength... Sometypicalvaluesofelasticconstantsandproperties elasticconstants(atroomtemperatureandpressure) material Young'smodulus(in106bars) shearmodulus(in106bars) ice 0.1 0.03 shale 0.2–0.3 0.15 limestone 0.4–0.7 0.22–0.26 granite 0.3–0.6 0.2 basalt 0.7–0.9 0.3 steel 2.1 0.83 material temperature(degreesCelsius) coefficientofviscosity(poises) lava(MountVesuvius) 1,100 1,400 28,300 250 lava(Oshima,Japan) 1,038 1,125 230,000 5,600 andesitelava 1,400 150–1,500 material compressivestrength(atroomtemperatureandpressure,inkilobars) shale 0.8–1.8 sandstone 0.5–2 limestone 1–2 granite 1.7–2.5 basalt 1–3.4 Rheologyisthestudyoftheflowdeformationofmaterials.Theconceptofrheidityreferstothecapacityofamaterialtoflow,arbitrarilydefinedasthetimerequiredwithashearstressappliedfortheviscousstraintobe1,000timesgreaterthantheelasticstrain.Itisthusameasureofthethresholdoffluidlikebehaviour.Althoughsuchbehaviourdependsontemperature,relativecomparisonscanbemade.SomerepresentativevaluesofrheiditytimesaregivenintheTable. Rheiditythresholdoffluidlikedeformation material approximatetime ice(e.g.,glacier) 2weeks gypsum 1year rocksalt(e.g.,saltdome) 10–20years serpentine(amaficsilicatemineral) 10,000years Typicalstress-strain(deformation)curvesforrockmaterialsareshowninFigure8.Thestressσ,compressioninthefigure,isforceperunitarea.Thestrainεisfractionalshorteningofthespecimenparalleltotheappliedcompression;itisgivenhereinpercent.Thebrittlematerialbehaveselasticallynearlyuntilthepointoffracture(denotedX),whereastheductile(plasticallydeformable)materialiselasticuptotheyieldpointbutthenhasarangeofplasticdeformationbeforefracturing.Theabilitytoundergolargepermanentdeformationbeforefractureiscalledductility.Forplasticdeformation,theflowmechanismsareintracrystalline(slipandtwinningwithincrystalgrains),intercrystallinemotionbycrushingandfracture(cataclasis),andrecrystallizationbysolutioningorsoliddiffusion.stress-straincurvesFigure8:Typicalstress-straincurvesforrockmaterials.EachXrepresentsthepointoffractureforthecorrespondingmaterial.EncyclopædiaBritannica,Inc.Iftheappliedstressisremovedwhileaductilematerialisintheplasticrange,partofthestrainisrecoverable(elastically),butthereispermanentdeformation.Theultimatestrengthisthehighestpoint(stress)onastress-straincurve,oftenoccurringatfracture(whichisthecompletelossofcohesion).Thestrengthofamaterialisitsresistancetofailure(destructionofstructure)byfloworfracture;itisameasureofthestressrequiredtodeformabody.Typicalcompressivestrengths(thestressrequiredtocausefailureundercompression)aregivenintheTable.EffectofenvironmentalconditionsThebehaviourandmechanicalpropertiesofrocksdependonanumberofenvironmentalconditions.(1)Confiningpressureincreasestheelasticity,strength(e.g.,yieldpointandultimatefracturestress),andductility.(2)Internalpore-fluidpressurereducestheeffectivestressactingonthesample,thusreducingthestrengthandductility.Theeffective,ornet,confiningpressureistheexternalhydrostaticpressureminustheinternalpore-fluidpressure.(3)Temperaturelowersthestrength,enhancesductility,andmayenhancerecrystallization.(4)Fluidsolutionscanenhancedeformation,creep,andrecrystallization.(5)Timeisaninfluentialfactoraswell.(6)Therateofloading(i.e.,therateatwhichstressisapplied)influencesmechanicalproperties.(7)Compaction,aswouldoccurwithburialtodepth,reducesthevolumeofporespaceforsedimentaryrocksandthecrackporosityforcrystallinerocks.Rocks,whicharetypicallybrittleattheEarth’ssurface,canundergoductiledeformationwhenburiedandsubjectedtoincreasedconfiningpressureandtemperatureforlongperiodsoftime.Ifstressexceedstheirstrengthoriftheyarenotsufficientlyductile,theywillfailbyfracture—asacrystal,withinabedorrock,onanearthquakefaultzone,andsoon—whereaswithductilitytheycanflowandfold.SomestrengthsforvariousrocktypesunderdifferenttemperaturesandconfiningpressuresarelistedintheTable.Theplasticyieldstrengthhereisthestressata2percentstrain;theultimatestrength,asstatedabove,isthehighestpoint(stress)onthestress-straincurve. Rockstrengths,withvaryingtemperatureandpressure rocktype temperature(°C) confiningpressure(kilobars) plasticyieldstrength(kilobars) ultimatestrength(kilobars) granite 500 5 10 11.5 800 5 5 6 gabbro 500 5 4 8 peridotite 500 5 8 9 800 5 5.5 8 basalt 500 5 8 10 800 5 2 2.5 marble 24 2 2.5 5.5 500 3 1 2 limestone 24 2 4.5 5.5 500 3 2.5 3 dolomite 24 2 6 7 500 5 4 6.5 shale 24 2 1.5 2.5 rocksalt 24 1 0.5 1 Anincreaseinconfiningpressurecausesbrittlefracturetobecomeshearslippageandeventuallycausesflow(ductile)behaviour.Thistransitionisalsoaidedbyhighertemperature,decreasedinternalpore-fluidpressure,andslowerstrainrate.TheTablegivesthevaluesofsomeelasticconstants—bulkmodulus(k),Young’smodulus(E),shearmodulus(μ),andPoisson’sratio(σp)—atroompressure(1bar)andhighconfiningpressure(3,000bars).Thevaluesforclasticsedimentaryrockswouldbeparticularlyvariable. Variationofsomeelasticconstants(in106bars)withrocktypeandconfiningpressure atpressure=1bar rocktype bulkmodulus Young'smodulus shearmodulus Poisson'sratio granite 0.1 0.3 0.2 0.05 gabbro 0.3 0.9 0.6 0.1 dunite 1.1 1.5 0.5 0.3 obsidian 0.4 0.7 0.3 0.08 basalt 0.5 0.8 0.3 0.23 gneiss 0.1 0.2 0.1 0.05 marble 0.1 0.4 0.2 0.1 quartzite sandstone 0.07 0.2 0.08 0.1 shale 0.04 0.1 0.05 0.04 limestone 0.8 0.6 0.2 0.3 atpressure=3,000bars rocktype bulkmodulus Young'smodulus shearmodulus Poisson'sratio granite 0.5 0.6 0.4 0.25 gabbro 0.9 0.8 0.5 0.2 dunite 1.2 1.7 0.7 0.27 obsidian basalt 0.8 1.2 0.4 0.25 gneiss 0.5 0.7 0.3 marble 0.8 0.7 0.3 0.3 quartzite 0.5 1.0 0.4 0.07 sandstone shale limestone LoadNextPage