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基于分数阶微积分的岩石非线性黏弹性应力松弛模型研究.docx

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基于分数阶微积分的岩石非线性黏弹性应力松弛模型研究 Abstract: Thestudyofnonlinearviscoelasticstressrelaxationmodelsforrocksbasedonfractionalcalculusisofgreatsignificancetounderstandthemechanicalbehaviorofrocks.Thispaperaimstoinvestigatetheapplicationoffractionalcalculusinmodelingthestressrelaxationbehaviorofrockswithnonlinearity. 1.Introduction: Rockmechanicsisabranchofgeotechnicalengineeringthatfocusesonthebehaviorofrocksunderdifferentloadconditions.Theunderstandingofrockmechanicsisessentialinvariousengineeringprojects,suchasmining,tunneling,andslopestability.Thestressrelaxationbehaviorofrocksplaysacrucialroleintheseapplications,asitisrelatedtothestabilityandlongevityofengineeringstructures. 2.Background: Traditionallinearviscoelasticmodels,suchasMaxwellandKelvinmodels,havebeenwidelyusedtodescribethestressrelaxationbehaviorofrocks.However,thesemodelsoftenfailtocapturethenonlinearcharacteristicsofrocks,leadingtosignificantdiscrepanciesbetweenthemodelpredictionsandexperimentalresults.Toaddressthisissue,theapplicationoffractionalcalculushasgainedincreasingattentioninrecentyears. 3.FractionalCalculus: Fractionalcalculusisamathematicalframeworkthatextendsthetraditionalcalculustonon-integerorders.Itprovidesamoreaccuratedescriptionofthestressrelaxationbehaviorofrocks,whichoftenhavecomplexandnonlinearcharacteristics.Thefractionalorderderivativeandintegraloperatorsareusedtomodeltherockbehavior,takingintoaccountboththelong-termmemoryeffectsandtheinstantaneousresponse. 4.NonlinearViscoelasticStressRelaxationModel: Inthisstudy,anovelnonlinearviscoelasticstressrelaxationmodelbasedonfractionalcalculusisproposed.Themodelcombinestheadvantagesoffractionalcalculusandbasicviscoelasticconstitutiveequationstoaccuratelydescribethestressrelaxationbehaviorofrocks.Thefractionalorderderivativeisusedtocapturethenonlinearstress-strainrelationship,whilethefractionalorderintegralisusedtoaccountforthelong-termmemoryeffects. 5.ExperimentalVerification: Tovalidatetheproposedstressrelaxationmodel,aseriesoflaboratorytestsare