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＊Designmodelforshieldliningsegmentsanddistributionofload朱合华 崔茂玉 杨金松(,,200092) ,———-,,(),,,。 ,,, TU94 ,1962,,、。。ZhuHehua CuiMaoyu YangJinsong(DepartmentofGeotechnicalEngineering,TongjiUniversity,Shanghai,200092)Abstract Anewdesignmodelforshieldliningsegments,beam-discontinuousjointmodel,isdescribedinthispaper.Andbasedonthenewmodel,thedistributionmodeandvalueoftheloadingpressureontheliningsegmentsarebackanalyzedusingthemeasureddataofsegmentpiecessuchasaxialforceandbendingmomentetc.Inaddition,apartial-peripheralgroundspringmodeliscomparedwithawholeperipheraloneinthebackwardanalysis.Keywords shieldliningsegment,designmodel,loadingpressure,backwardanalysis1 ,()(),。-[3],,,-[1],。,-(Castigliano),、。-。,。,。,-,。,———-[2]。,(Goodman)[4],,。,,,。,。-,,,。,———。,,。2 2.1 ,。,,,1。-[1]。 ,2,1,2n,s:1999-06-17 22 2 Vol.22 No.2 2000 3ChineseJournalofGeotechnicalEngineeringMar., 2000 1901 -Fig.1 Beam-jointmodel2 Fig.2 Doublenodeofsegmentjoint Δu=u′1-u′2Δv=v′1-v′2Δθ=θ′1-θ′2 (1) :s,,ns,,2。,Δun,Δvs,Δθ;u′i,v′i,θ′i(i=1,2)i。。,-NQM=knkskθΔuΔvΔθ(2) {F}={N Q M}T,{Δd}=[Δu Δv Δθ]T,[K]=diag[kn ks kθ],{F}=[K]·{Δd}(3) N,Q,Mn,s、。,u′i,v′i,θ′i(i=1,2){δ}={u1,v1,θ1,u2,v2,θ2}T,{Δd}{Δd}=[E]·{δ}(4)[E]=[T -TT],[T]=sinφcosφ0-cosφsinφ0001(5) [E],[T],2φ90°。,[Kj][Kj]=[E]T·[K]·[E](6)[KG]=A1A30-A1-A30A20-A3-A20kθ00-kθA1A30A20sym.kθ(7) A1=knsin2γ+kscos2γ,A2=kncos2γ+kssin2γ,A3=(ks-kn)cosγsinγ,γ=α1+Χ-φ,α1(2),Χ。,-。Δθ,kθ=(kθ1-kθ2)e-βΔθ+kθ2(8)。2.2 ,2(),,3,:fnqfsq=knqksqΔu′Δv′(9) fnq,fsq;Δu,Δvfnq,fsq;knq,ksq。3 Fig.3 ShearingmodelofringjointΔu,Δv(1),u′i,v′i(i=1,2),3。,{Δdq}=[E]·{δq}(10)191 2. {Δdq}={Δu Δv}T,{δq}={u1 v1 u2 v2}T,[Eq]=[Tq -TqT],[Tq]=sinφcosφ-cosφsinφ,φ,3。[Kq]=[Kq]diag[Knq Ksq]·[Eq]T(11)(7)。3 [5],,4。,()x-yO,pi,qi(i=1,4)。p(x,y),q(x,y):p(x,y)=a0+a1x+a2x2+a3yq(x,y)=b0+b1y+b2y2+b3x(12) ai,bi(i=0,3)pi,qi。pi,qiai,bi,(10),(11)p(x,y)=p1+(2dx-1)dxp21+dxp31+4(1-dx)dxp41q(x,y)=q1+(2dy-1)dyq21+dyq31+4(1-dy)dyq41(13) dx=x/XL,dy=y/YL,pi1=pi-p1,qi1=qi-q1(i=2,4),XL,YLx,y。4 Fig.4 Loadingpressureonliningsegment4 。,。,,。,,,。-。,NM。5 ,,,。pi,qi(i=1,4),JJ(p,q)=w1·∑L1i=1(Ni-N＊i)2/∑L1i=1N2i+w2·∑L2i=1(Mi-M＊i)2/∑L2i=1M2i(14) L1,L2;Ni,Mi;N＊i,M＊i;w1,w2,w1=w2=1。pi,qi(i=1,4),。。6 1.2m(RC)1.0m。、、、,。30m,60,16.8m,G.L.-10m。。5,1,2。M-Δθ,N-ΔuQ-Δv。,。(,)[6]:192 2000 1 Table1 Measureddataandcalculatedresultsofsegmentinternalforces/(kN·m)/(kN·m)1692.0697.2(653.0)693.1(650.0)1-18.0-69.4(-63.6)-53.0(-50.5)2499.0557.7(520.0)569.4(543.0)241.013.8(55.8)20.3(43.7)3458.0500.5(442.0)519.9(479.0)335.093.7(102.2)84.6(83.1)4571.0553.9(517.0)555.1(535.0)418.010.4(34.6)-19.9(29.1)5644.0646.9(657.0)664.5(656.0)5-9.0-71.6(-86.2)-71.2(-73.3)6746.0637.2(522.0)666.4(513.0)616.0-46.7(-103.0)-65.1(-82.2)7315.0636.7(522.0)649.6(513.0)7-12.026.2(3.3)16.2(85.7)8535.0545.3(697.0)513.1(681.0)847.058.9(139.0)79.1(106.8)9399.0562.4(645.0)556.4(618.0)912.028.3(82.3)34.7(60.8)10823.0629.8(574.0)665.0(563.0)10-21.0-39.1(-109.5)-60.8(-84.2) ( )。5 Fig.5 Thelayoutofmeasuringpointsforsegmentstressgaugesandearthpressurecells (1):E=3.5×107kPa,I=2.195×10-3m4,A=0.336m2,6.96kN/m;(2):k+θ1=34050kN·m/rad,k-θ1=37270kN·m/rad,k+θ2=6980kN·m/rad,k-θ2=4020kN·m/rad,β+=923rad-1,β-=2534rad-1,kn=104kN/m,ks=78600kN/m;(3):knq=ksq=39300kN/m;(4):K+n=2.4×104kN/m3,K-n=1.2×104kN/m3,pi,qi(i=1,4)2。,,—。、1,3()6,27pi,qi(i=1,4)。:,。,,65%。2 Table2 Theintitalandbackwardcalculatedpressurefordesign/(kN·m-2)/(kN·m-2)p1178.1223.4(147.3)207.0(164.2)p2178.1213.6(212.1)213.9(224.7)p3178.1248.7(236.3)268.8(271.7)p4178.1260.1(244.3)273.0(251.7)q198.0105.2(77.1)102.5(102.4)q2147.7179.4(158.7)130.3(151.4)q398.0117.4(101.6)161.9(154.1)q4120.0201.8(150.4)158.4(152.6)3 Table3 Themeasuredandcalcuatednormalpressureonliningsegment/(kN·m-2)/(kN·m-2)1286.7204.8(194.7)205.3(198.3)2280.0216.8(203.6)208.3(203.3)3360.0225.5(193.7)198.6(191.7)4240.0237.8(277.8)244.4(251.7) ,:(RE)N=1-∑iNi∑iN＊i,(RE)M=1-∑iMi∑iM＊i;(RE)N,(RE)M。1,(RE)N5.0%6.5%,,(RE)M100.0%240.0%,(RE)M(RE)M2,,193 2.6 Fig.6 Calculatedresultsusingpartialgroundspringmodel7 Fig.7 Backwardcalculatedloadingpressurefordesigning(RE)M。,(),。7 ,,:(1)———-()。-,-。(2),。,。(3),,。 1 MurakamiH,KoizumiA.Studyonloadbearingeapacityandme-chanicsofshieldsegmentring(inJapanese).ProcfortheJapanSocietyforCivilEngineers,1978,272(4):103～1152 HashimotoT,ZhuHH,NagayaJ.Anewmodelforsimulatingthebehaviorofsegmentsinsheildtunnel.Procofthe49thAnnualConferenceoftheJapanSocietyforCivilEngineers.September,1994.6263 ,..(),19964 GoodmanREetal.Amodelforthemechanicsofjointedrock.ProcASCEofJSM&FDn,1986,94(SM3)5 ,.シ-ルドトンネル.48,596 ZhuHH,HashimotoT.Studyonthetheoryandmethodofunder-groundstructureinsoftground(technicalreport).1995194 2000