Trans. Tianjin Univ. 2012, 18: 057-061 DOI 10.1007/s12209-012-1623-y Accepted date: 2011-06-09. *Supported by National Natural Science Foundation of China (No. 10902073). ZHOU Haiying, born in 1979, male, Dr. Correspondence to CHEN Tingguo, E-mail: chentg@dlut.edu.cn. Test and Numerical Analysis on Performance of Reinforced Concrete Segment in Subway Tunnel* ZHOU Haiying()1CHEN Tingguo()1LI Lixin()2 (1. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China 2. School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China) Tianjin University and Springer-Verlag Berlin Heidelberg 2012 AbstractToinvestigatethemechanicalbehaviorofsegmentallining,athree-dimensionalnumericalanalysisand test using three actual segments were used to analyze the effects of axial force and reinforcement ratio on the failuremechanismandultimatebearingcapacityofsegmentallining.Bothnumericalandtestresultsconfirmedthatthe cracking load, yield and ultimate load were strongly influenced by axial force, and it was also proved that the yield and ultimateloadwouldincreasewiththeincreaseofreinforcementratio,butthecrackingloadwasalmostnotaffected. The cracking load, yield and ultimate load are about 28.7%, 500% and 460% larger due to the effect of axial force re-spectively. The comparison between numerical calculation and test results showed that the finite element analysis re-sults were in good agreement with the test results. Keywords shield tunnel; segmental lining; numerical analysis; finite element model The majority of segments used in subway tunnel are made of reinforced concrete. Due to the brittle character-isticsandlowtensilestrength,thereinforcedconcrete segmentsarepronetobedamagedinapplications.The segmental lining must sustain all the loads transmitted by thesurroundingground.Therefore,themechanicalbe-haviorofsegmentalliningmustmeettherequirementof design.Inrecentyears,anumberofresearchesonthe performance of segmental lining have been conducted[1-5]. Whilemostoftheresearchesfocusedonpureflexure, therewasfewmodelingonthebehaviorofsegmental lining[3]. To investigate the distribution of stress, bearing capacity and cracking behavior of segmental lining, a 3D numerical analysis and test were conducted in this paper. Thereliabilityandreasonabilityofnumericalanalysis were also verified.1Test Testswereconductedusingthreeactualseg-ments(Pzw1, Pzw2 and Jzw3) in the tunnel construction. Theloadingreactionsystem,including anchorrod, bear-ingplatformandreactionbeam,wasrigid-framedstruc-ture with large size. The test segments were subjected to threeconcentratedloadsthatwereappliedbymeansof three hydraulic jacks connected to a testing machine. The axial load was applied by means of rigid-framed reaction structure.ForPzw2andJzw3,hingedconnectionthat wasintroducedattheends ofsegmentcouldresistverti-cal and horizontal loads and allow a relative rotation. For Pzw1, it was assumed that the characteristic of the struc-tureissimilartothatofasimplysupportedbeamstruc-ture. The steel plate should be introduced in order to pro-videadequateprotectiontotheendsofsegment.Thein-teractingsurfacesofsteelplatewerelubricatedwithmineral oil to reduce the effect of friction at the ends for Pzw1.Therefore,theycanmoverelativelyfreelyduring testing. In the present analysis, they are idealized as fric-tionlesssurfacesattheendsforPzw1.Alotofstrain gaugeswereinstalledinsegmentbody.Tomeasurethe deflection,electrictransducerswerealsoused.Andthe occurrenceanddevelopmentofcrackswererecorded. The test arrangements are shown in Fig.1 and Fig.2. Theinternaldiameterandwidthoftestsegments were5.4mand1.2m,respectively.Thesegmenthada thicknessof0.3m.Andthesegmenthadacentralangle of67.5.ThesegmentalliningwasconstructedbyC50 concrete. The details of geometry, reinforcement and ma-terialpropertiesofreinforcedconcretesegmentusedin this paper can be found in Refs. [4] and [5]. Transactions of Tianjin University Vol.18 No.12012 58 Fig.1Test arrangement of segments Pzw2 and Jzw3 Fig.2Test arrangement of segment Pzw1 2Three-dimensional numerical model 2.1Constitutive model of material 2.1.1Constitutive model of steel Inthispaper,steelwasassumedtobeperfectlyelas-tic-plastic. The bilinear kinematic (BKIN) hardening was adopted to simulate the behavior of steel. 2.1.2Constitutive model of concrete Theelastic-plasticincrementconstitutivemodel[6-9] forconcretewasadoptedthevonMisesyieldfunction can be written as follows p p3( , ) ( )( ) 02ij a ij ij ij ij sf H c c o = = s s o c c (1)where soisthestressofconcretewhenthenonlinear stress-strainrelationshipoccurs aHisinternalvari-able; cisthescalarquantityrelatedto aH pijcisthe plastic strain tensor; sij is the deviatoric stress tensor; ijois the stress tensor. Based on the theory of plasticity[10], the elastic-plastic increment constitutive model for concrete is given by e pd d dij ij ij= + c c c(2)where eijcistheelasticstraintensor,whoseincrement meets general Hookes law: ed3d d2ijij ijG Evo = oc o (3)where v is Poissons ratio; E is modulus of elasticity; G is shear modulus; and oij is the Kronecker delta. p1d d , 1, 2, ,nkij kk ijfk n =c= = cco (4)where fk is yield surface of stress space. 0 ( 0 or 0, d 0)d0 ( 0, d 0)k k kkk kf f ff f= < = < = = (5)wheredkis a scaling factorand it is defined by ( / )dd( / )( / )k ij ijkk k kl k klfc f fc c=c c c cs ss s (6)Substituting Eq.(6) into Eq.(4), we can obtain p1( / )d1d( / )( / )nk ij ijkijk k k kl k kl ijffc f f=c cc=c c c c cs ss sco (7)where p3/ ( ) /2k ij ij ij kf c f c c = s s c . Asasimplifiedconstitutivemodelforreinforced concrete,multilinearkinematichardeningmodelwas adopted in this paper, as shown in Fig.3. Fig.3Multilinear kinematic hardening model 2.1.3Failure criterion of concrete The William-Warnke five-parameter failure criterion for concrete[8-11] was used. The failure surface of concrete strength, tensile and compressive meridian are defined as follows 2 22 2 2 2( ) [2 ( ) cos(2 ) 4( ) cos 5 4 ]c c tc t c c t t c t u u u = + + 2 2 2 2 1[4( ) cos (2 ) ]c t t c u + (8) 1 2 32 2 21 2 2 3 3 12cos2[( ) ( ) ( ) ]o o ouo o o o o o = + + (9) 2 m m m0 1 2( ) at 0tc c ca a af f ft o ou= + + = (10) 2 m m m0 1 2( ) at 60cc c cb b bf f ft o ou= + + = (11) whereuistheangleofsimilaritylyingindeviatoric planetisuniaxialtensilestrengthforconcrete; cis uniaxial compressive strength for concretem 13 I o =is meannormalstress; m 2(2 5)J t =ismeanshearstress; 1Iisthefirststressinvariant;2Jisthesecondinvariant ZHOU Haiyinget al: Test and Numerical Analysis on Performance of Reinforced Concrete Segment in Subway Tunnel 59ofdeviatoricstresstensor; 0 1 2 0 1, , , , a a a b band 2bdepend onthefiveparametersofthemodelobtainedfromthe test of the uniaxial, biaxial and high hydrostatic pressure ofconcreteduetothefactthatthetensileandcompres-sive meridians and hydrostatic stress axis converge at one point. 2.2Finite element model Inthispaper,Solid65elementwasusedtomodel concrete, and Link8 element was used to model steel. The steelelementswereconnectedtotheconcretemesh nodes.Fig.4showsthethree-dimensionalfiniteelement meshofreinforcedconcretesegmentusedinnumerical analysis. Fig.4Three-dimensional finite element mesh of numerical model 3Results and analyses The load-deflection relation curves for both test and simulation are shown in Fig.5, and they match each other well.Thereisalinearrelationshipforload-deflection beforetheconcretecracking.Thereafter,theslopede-creasesslightly,andthecurveshowsalinearvariation. However, the curve exhibits obvious nonlinear character-istics from yield to compression failure of concrete. It can be seen that the smaller the load, the better the agreement between numerical and test results. For a higher load, the discrepancy between the numerical and test results is lar-ger, which may be due to that the elastic-plastic constitu-tivemodelforconcretecannotfullydescribe thecharac-teristicsofconcretematerial.Anotherpossiblereasonis thatthenumericalmodelusedinthispaperisbasedon simplificationsthatdoesnottakeintoaccountofhand holes, bolt holes or grouting holes. Fig.5Load-deflection curves Tab.1showsacomparisonbetweenthenumerical andtestresults.Bothnumericalandtestresultsindicate thatthecrackingload,yieldandultimateloadincreased obviouslybecauseoftheeffectofaxialforce.Itwas found that the cracking load, yield and ultimate load were about28.7%,500%and460%largerduetotheeffectof axialforcerespectively.Thenumericalandtestresults alsoprovethattheyieldandultimateloadincreasewith the increase of reinforcement ratio, but the cracking load isnotaffectedbyreinforcementratio.Ingeneral,the elastic-plasticmodelresultsshowgoodaccuracyinpre-dictingthedistributionofstressandstrain,thebearing capacity and cracking behavior of segmental lining. Fig.6showsthetypicaldistributionanddevelop-mentofcracks,thefailurecharacteristicsofsegment Jzw3 from test. The first transverse crack was observed at midspan of the segment with a load of 79 kN. The cracks wereobservedin tensilestresszone,developingtowards theexteriorsurfacewithincreasingload.Itcanbeseen fromFig.6thatthecrackspacingisrelativelyuniform. The yielding of segment occurred when the load reached 1 021 kN. The crushing failure of concrete occurred in a zone close to the exterior surface of segment between the left and right loading points when the load reached 1 226 kN. Figs.710showthetypicaldistributionofstress andstrain,thedeformationandcrackingbehaviorof segmentJzw3fromnumericalanalysis.Itcanbeseen thatthecrushingfailureofconcreteoccursinazone closetotheexteriorsurfacebetweentheleftandrightTab.1Comparison between numerical and test results Cracking load /kNYield load /kNUltimate load /kN Segment TestNumerical analysis DiscrepancyTest Numerical analysis Discrepancy Test Numerical analysisDiscrepancyPzw157593.3%160 1716.4%191 1931.0% Pzw280822.5%960 1 08011.1%1071 1 20511.2% Jzw379845.9%1 021 1 1309.6%1226 1 2995.6% Transactions of Tianjin University Vol.18 No.12012 60loading points. It is obvious that the crushing failure zone isthesameasthemaximumcompressionstresszone. Thereinforcedconcretesegmentistypicallycharacter-izedbythedominanceofcompressionstresscombined with relatively small tensile stress under loads. There is a tensile stress zone near the inner surface between the left and right load points. The cracks are observed in the ten-silestresszone,developingtowardstheexteriorsurface withincreasingload.Andthecrackspacingisrelatively uniform.Thelargestdeflectionofreinforcedconcrete segment occurs at the midspan. Fig.8 shows the variation ofdeflectionforreinforcedconcretesegmentalongthe horizontaldirection.Itcanbeobservedthatcomputed deflection for reinforced concrete segment decreases with theincreaseofdistancefromthemidspan.Thetotalde-formation of reinforced concrete segment is small at fail-ure.

Itisknownthattheliningsegmentsinsubwaytun-nel are joined with bolts, and the number and orientation of joints in the lining have significant effects on the mo-mentinducedinthelining.However,inthedesignof segmentallining, the influence ofjoints betweenthelin-ingsegmentsonthemomentisoftenignored.Asthe numberofjointsincreases,themomentdecreases.The mostfavourabledistributionof6jointscanreducethe moment in the lining. Fig.6Failure characteristics of segment Jzw3 Fig.7Mises stress distribution of segment Jzw3 Fig.8Deformation of segment Jzw3 Fig.9Strain distribution of segment Jzw3 Fig.10Cracking and crushing distribution of segment Jzw3 4Conclusions (1)Thethree-dimensionalfiniteelementanalysis can be an effective measure to analyze the crack propaga-tion,bearingcapacity,distributionofstressandstrainof segmental lining.(2) Both numerical and test results indicate that the crackingload,yieldandultimateloadincreasedobvi-ouslybecauseofaxialforceeffect.Thecrackingload, yieldandultimateloadwereabout28.7%,500%and 460%largerduetotheeffectofaxialforcerespectively. Itwasalsofoundthattheyieldandultimateloadsin-creasedwithincreaseofreinforcementratio,butthe crackingloadwasalmostnotaffectedbyreinforcement ratio. (3)Thesegmentalliningistypicallycharacterized bythedominanceofcompressionstresscombinedwith relatively small tensile stress under the action of loads. It isobviousthatcrushingfailurezoneisthesameasthe maximumcompressionstresszone.Thereisatensile stresszoneneartheinnersurfacebetweentheleftand rightloadpoints.Thenumericalandtestresultssupport the above conclusions. (4)Bothnumericalandtestresultsshowthatthe ZHOU Haiyinget al: Test and Numerical Analysis on Performance of Reinforced Concrete Segment in Subway Tunnel 61segmentalliningiscapableofbearinglow-tensile strength. Therefore, it is suggested that the cracking resis-tanceofsegmentalliningshouldbereinforcedwhile safety and reliability are still satisfied. References 1YinLchao,ZhuZhenhong,LiYuzhen.JapaneseNew Technology in Tunnel Shielding[M]. Huazhong University ofScienceandTechnologyPress,Wuhan,1999(inChi-nese).2NasriAWunfah,MichaelPDellaPosta.Fullscaletesting of tunnel liner[C]. In: Towards New Worlds in Tunnelling. Balkema, Rotterdam, 1992.3LiJingshuang,WangZhe.Testresearchonthebending resistance of segment for subway shield tunnel[J]. Journal ofNorthernJiaotongUniversity,2004,28(1):60-64(in Chinese).4ZhouHaiying,LiLixin,ChenTingguo.Experimentsand calculationmethodforbearingcapacityoftheliningseg-mentofmetroshieldtunneling[J].JournalofShandong University(EngineeringScience),2010,40(4):84-87(in Chinese).5ZhouHaiying,LiLixin,ChenTingguo.Experimentsand calculatingmethodforcrackingstrengthandcrackwidth ofthemetrosegment[J].JournalofShandongUniversity (EngineeringScience),2010,40(3):124-127(inChi-nese).6SaenzLP.Discussionofequationforthestress-strain curveofconcretebyDesayiandKrishnan[J].Journalof ACI, 1964, 61(9): 1229-1236.7Willam K J, Warnke E P. Constitutive model for the triax-ialbehaviorofconcrete[C].In:IABSESeminaronCon-creteStructures Subjectedto TriaxialStresses.Paper-1. Bergamo, Italy, 1974.8JiangJianjing.TheNonlinearFEMAnalysisofRCStruc-tures[M].ShaanxiScience&TechnologyPress,Xian, 1994 (in Chinese).9WangRen,XiongZhuhua,HuangWenbin.Fundamentals of Plastic Mechanics[M]. Science Press, Beijing, 1982 (in Chinese).10 ZhangHoumei,ZhangZhenglin,WangJianhua.3-DFEM Analysisonprefabricatedsegmentjointsofshieldtun-nel[J].JournalofShanghaiJiaotongUniversity,2003, 37(4): 566-569(in Chinese).11 ErnstGC,MarletteRR,BergGV.Ultimateloadtheory and tests of cylindrical long shell roofs[J]. Journal of ACI, 1954, 26(3): 257-272.