高压水射流作用下岩石破碎机理及过程的数值模拟研究

:1000-0887(2005)12-1445-08X1,1,2(1.(),257061;2.,100022)():,,,,,,,,,:;;;;:TE248:A,,,,,,[1],,1,:1),;2),5441,2612(200512)AppliedMathematicsandMechanicsX:2004-11-19;:2005-08-17:(50574062;50234030);(2004035692):(1972),,,(.Tel:[phone];Fax:[phone];E-mail:[e-mail])©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[2]:=0,(1)55t+€v22+P=f(t),(2),;€vP:P=0;5/5z=v0(t);5/5n=0(n),Galerkin:Kee=0,(3)Ke=VNTNdV-S255nNTNdS,,N;eCrank-Nicolson:e=12((e)tn+1+(e)tn),(4):Ke((e)tn+1+(e)tn)=0(5),,,,(5),,:(Ke)tn+1(e)tn+1=-(Ke)tn(e)tn(6)1.21.2.1,Lagrange[3,4]:ij,j+fi=xi,(7)=J0,(8)ÛH=VSijÛij-(p+q)V,(9),xi;xi;ijÛijSijCauchy,Sij=ij+(p+q)ij;fi;VH;0,J;pq,p=-kk/3-q,S1,ijnj=ti(t),njS1,ti,;S2,xi(Xj,t)=Ki(t),Ki(t),:=VxixidV+Vxi,jdV-VfixidV-S1tixidS,(10)6441©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(,,)[2,3]:j(,,)=18(1+j)+(1+j)(1+j),j=1,2,,8,(11)(j,j,j)j:x(,,,t)=NXe,(12),Xe(7):=6wm=1(xe)TVmNTNdVxe+VmBTdV-VmNTfdV-S1mNTtdS=0,(13)B;wm=VmNTNdV,,(10)Mx(t)=P(x,t)-F(x,Ûx),(14),M;x(t);P,,;F,F=6wm=1VmBTdV[3,5]1.2.3,,Jaumann[3,5]:ij(tn+1)=ij(tn)+CijklÛkl(tn+1/2)tn+[ik(tn)kj(tn+1/2)+jk(tn)ki(tn+1/2)]tn,(15),ij=0.5(5Ûxj/5xi-5Ûxi/5xj);Ûkl=0.5(5Ûxk/5xl-5Ûxl/5xk);Cijkl1.2.4,,,,,,,,[4,5]q=l(C0l|Ûkk|2-C1a|Ûkk|),Ûkk0,0,Ûkk0,(16),l=3V,V;a;;|Ûkk|7441©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1.5)C1(0.06)1.2.5,[35]:x(tn)=M-1[P(x,tn)-F(x,Ûx,tn)],Ûx(tn+1/2)=Ûx(tn-1/2)+12(tn-1+tn)x(tn),x(tn+1)=x(tn)+tnÛx(tn+1/2)(17),tCourant,tl/C,l(8l=Ve/Aemax,Ve,Aemax),C,C=E(1-)/[(1+)(1-)],E,,1.3:1),,,;2),,;3)1)3)2,,2.12.1.1[6],,Lemaitre[7],,ÛD=2eq2ESRvÛp,H0,D=1,H0,maxf,(18),E,S;Ûp;eqvonMises;Rv,Rv=(2/3)(1+)+3(1-2)(H/eq)2,,H,H=kk/3,fLemaitre,,,RDA[7,8],:ÛD=ÛWp1-D,H0,D=1,H0,maxf,(19),,ÛWP,D8441©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[7,8]:s=0,H0,maxf,[0(1+C1lnÛp)+C2P](1-D),H0,maxf,(20),0,C1,Ûp,D,C22.1.2:ij=3K(1-D)ij+2G(1-D)eij,(21),KG,D,eij,ij2.2,[9]:1);2),;3),;4)au,(22),[9](23)max=cr=KC4a,(22)l=b,(23),cr;a;KC;b,b=l+au,=1-cos(H/(2u)),u2.3,Lemaitre[9]D=1-0,(24),0,,,Lemaitre:D=1-1-1-0,(25)=1-(1-D)(1-0),(26),0=f(N)a3u,(27)9441©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(N)auN(23)(27):=,(28),,=1/cos3(H/(2u))(26)(28)(25),:D=D+-11-0[1-(1-D)(1-0)](29)2.4,,,,3,,0.003m,250m/s,0.012m1[8,10]1(C1=0.3,C2=0.05)/(kgm-3)E/GPa0/MPaf/MPaS/MPaKC/(MNm)-3/2/(kgJ)235216.7878.411.90.2655.010-60.22.210-60.1312()2,,25m/s250m/s,0.10.98,,,,,,,45,,,,,,,,,,0541©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(,d,t),,,,34,,,,,,,,,,,,,,,,,,,,,,,,,,,,[11]4,,,,,,,Vd41.,,,2.,,1541©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[][1],.[J].(),2002,26(4):118122.[2].[M].:,1986.[3],.[M].:,1997.[4].[J].,1993,12(1):296304.[5].[M].:,1995.[6],.[M].:,641.[7]FurlongJR,DavisJF,AlmeML.Modelthedynamicload/unloadbehaviorofceramicsunderim2pactloading[R].RDA-TR-00.0-0001,Arlington,VA:R&DAssociates,Arlington,1990.[8],,.[M].:,1999.[9],.[M].:,1997.[10]LemaitreJ.[M].,.:,1996.[11],.[M].:,1984.NumericalSimulationStudyonRockBreakingMechanismandProcessUnderHighPressureWaterJetNIHong-jian1,WANGRui-he1,ZHANGYan-qing2(1.CollegeofPetroleumEngineering,ChinaUniversityofPetroleum(EastChina),DongyingShandong257061,P.R.China;2.CollegeofBuildingEngineering,BeijingUniversityofTechnology,Beijing100022,P.R.China)Abstract:ThenumericalsimulationmethodtostudyrockbreakingprocessandmechanismunderhighpressurewaterjetwasdevelopedwiththecontinuousmechanicsandtheFEMtheory.Therockdamagemodelandthedamage-couplingmodelsuitedtoanalyzethewholeprocessofwaterjetbreak2ingrockwereestablishedwithcontinuumdamagemechanicsandmicrodamagemechanics.Thenu2mericalresultsshowthedynamicresponseofrockunderwaterjetandtheevolvementofhydrodynam2iccharacteristicofjetduringrockbreakingisclosetoreality,andindicatesthatthebodyofrockdamageandbreakageunderthegeneralcontinualjetoccurswithinseveralmilliseconds,themaindamageformistensiledamagecausedbyrockunloadandjetimpact,andtheevolvementofrockdamageshowsastep-changetrend.Onthewhole,thenumericalresultscanagreewithexperimentalconclusions,whichmanifestthattheanalyticalmethodisfeasibleandcanbeappliedtoguidethere2searchandapplicationofjetbreakingrocktheory.Keywords:waterjet;rockbreakage;rockdamagemodel;fluid-wallinteraction;finiteelementmethod2541©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.