Chia 0ean Engieing, Vol.16, No.3, p.369- 382◎2002 China Ovean Press. ISSN 0890-5487Simulation of the Whole Process of Ship Bridge CollisionLIU Jiancheng (劉建成) and GU Yongning (顧永寧)School of Naxal Archicxure und 0cean Fngineing, Shanghui JuTong UnitersityShanghai 200030，China(Received 23 March 2002; acxptel 22 May 2002)ABSTRACTelement method. Based on the simple desripion of the theory, a scenario of a 4000 DWT oil lunker olliding with abridge axms the Yangte River is designed for similation. The tchnology of stnucture mudeling and the delemination ofrelated paramelers are introduxced. The deformation of the bullb bow, the histony of ollision fore change, the exchange ofollision enerey and the stres dstibutionin o[ the bridge pier are deacibed in delail, which are of greal valuc to bnidge de-sign and bridge pier damage estimation. Some mechanical characters in the proces of ship-bridge cllisi are describred.More accurale resals can be prduced by finite element method than thal bhy empirical fomulas and simplifed analyticalmethods.Key words: ship- bridge cllision ; structwral dumage; nonlinear finite element mehod; dymamio plsticit1. IntroductionShip-bridge ollision often happens in river lransportation these years. Although not every ship-bridge ollision accident nessrly causes calanities, more or less damage l bridges uccus eachtime, decreasing the reliability and seismic resistance capability of bridges to some extent. For irn-provement of the safety of bridges against ship collision and decrease of the construction and mainte-nance cost of bridges, it is necessary tn acuralely calculale the ollision force and the damage ofbridges.The striking ship and the bridge undergo a complicaled dynamic process under the impetuousloads within a very short time of collision. There are many nonlinear problems including material non-linearity, gometrie nonlinearity, contacl nonlineariy, and so on. The deformation, ruplure and fail-ure of structural components of the ship and rigid motion of the ship hull are coupled. In addition, thefluid around the ship absorbs collision energy and affects the collision process.The ship-bridge ollision problem involves both ship engineering and bridge engineering in whichthe deformalion and motion of the ship and the bridge should be both considered. Several methds havebeen used for ship-bridge collision analysis, such as the Minorsky Thoery ( Minorsky, 1959), theHeins-Denucher Theory (Derucher, 1982) , numerical apprach (Liang et al . ,2000), sinplified ana-lytical methods ( Pedersen et al., 1993)，experimental methods ( Reckling，1983)， finite elemenlmethods (Msc/Dytran, 1997)， and so on.To display the basic phenonena of ollision and the resporuse stres distibution of the bridge pier,a scenario of a 40000 DWT oil tanker colliding with a bridge across the Yangtze River is designed forsimulation, by use of the dynamic nonlinear finite element program, see Fig. 1. The history of colli-中國煤化工MYHCNMHG370LU Jiancheng arnd GU Yongningsion frce, the exchange of eny, the srucural delomation and danmage of the ship and bridge aedescribeal in delal and the mechanical chararters of the clsinin process are aleo descnibed. Some gen-eral conclusions on ship-bridge ollisin are drawn.Roadway, Upper structures. Pier capPier colun( The striking ship-Pile capFig. 1. Shipbridge ollision.2. Dynamic Nonlinear Finite Element Technology2.1 Motion EquationThe motion equation for the clision problem may be witen as follows:[M]{a} +[C]{卟+[K]}d| = {F"}(1)where [M] is the mass matix of the structure; [ C] is the damnping malrix of the structure; [K] isthe sifness matix of the structure; }a{ is the vetor of acceleration; {v{ is the vector of velocity;osqwwom0 is the vector of displacement; and |F* I is the veclor of extemally applied loads.The explicit time integration scheme is suitable for the transient dynamic problem. The schemedoes not need to operate on the whole model matrices, and it can be performned rapidly since theequations are solved at the element level. Every time step is autoatically calculated for stable solut-ions and the accunacy of time integrity . When the explicit central diference scheme is used to solve theollision problem, the time step should be smaller than the crtical time step, which is approximatelythe characteristic length of the nininum elenent of the finite element model L' divided by stress wavevelocity C in general (Msc/Dytran, 1997):Ot≤Ot。= min(L'/C).(2)2.2 Contact SurfacesThe interaction between contaet structural components is modeled by definition of contact surfac-es. Two surfaces that may come into contact must be defined respectively as one master surface and one中國煤化工MYHCNMHGSinulation of the Whole Poe of Ship- Bridpe Cllisin371slave suface, see Fig. 2. At each timne step, each gid point on the slare surface is checked, and lhenearest masler segment is located there. If the gid point has not penetated the master segment, thecaleulation continues. Otherwise, contact forces are applied in a direction nomal t0 the masler sufaceto prevent further penelration hrough the segment. The magnitude of the force depends on the amountof penetraion and the properties of the elements on each side of the contact surface.Slave surfuce. Master surfaceFig. 2. Materslave contart surfaces.3. Stress .Strain Relationship of Material3.1 ConcreteThe bridge pier is made of reinforced concrete. Considering the hardening of concrete materialduring ollision, the Colorado cap malerial model is adoped (Simo el al., 1988; Chen, 1982). Thismaterial model is a plastic model whose failure surface consists of the failure envelope, the hardeningcap surface and the fixed lension cutofT surface, see Fig. 3. The cap surface is useud to describe thenonelastic volume expansion of the conc.rete before its collapse which is indicated in wncrete: materialtest. The stress-strain relation of concrete material is given in terms of lensors as:jde = de'+ de"(3)ldo = E(de - de'")↑| Fai lure envelopef2HardeningBlastic regionFixed tensioncap surfacecutoff surfaceT0Fg. 3. Conxrete materidl cap model.中國煤化工MYHCNMHG372uU Jiancdeng and (GU Yongningwhere de, de' , and de" are the total easic and plastic tensor, E is the easicit matrix and do isthe stress lensor. The low rule is given bhy:de' =上o。.da。(4)The coneree material parmeters are lsted in Table 1.Table 1Paramcters of concrete materialCKa0r[W27001.IEI0 1.4E10| 2.7F70.11 8.0E6 1.4E-7 4.43 4.6E-10 0.42 1.1E8In Table 1, ρ is density (kg/m' );G is shear modulus (N/m?); K is bulk modulus (N/m);ais failure envelope;日is linear coficient of failure envelope; Y is exponential coffcient of failure en-velope; β is exponent of failure envelope; R is cap surface axis ratio; D is exponent of hardeninglaw; W is eoficeient of hardening law; and Xo is exponent of hardening law.3.2 Steel BarThe stress strain relationship of sleel bar is usually assumned to be the same under tension andcompression. This relationship can be described as bilinear or curilinear (Ye and Diao, 1995). Anelastic perectly plastic yield model is adopted in this paper. The parameters of the material ane densityρ=7.85x 10' kg/m', elastie module E=2.03x 10" N/m', yield stress σσ =3.15x 10' Nm',and Poisson's ratio v=0.3..3 Mild Stee Material of Ship HullFor the bulb bow of the striking ship linearly hardening elastic plastic material is adopted, andthe hardening stress is considered ater the material itially yields (Paik and Petersen, 1996). Its pa-ramneters are: density ρ=7.8x 10 kg/m' , elastic module E =2.1 x l0'" N/m2，hardening moduleE,=1.18x 10° N/m2，initial yield stress on =2.35x 10 N/m2，and Poison' s matio v= 0.3.The yield stress o, can be oblained by the fllwing fommula:EE,0，=90+ E-吧(5)where Ep is the equivalent plastic strain.4. Failure-Fracture Criteria of Material4.1 Mild Steel Material of Ship HullIn high energy cllision, some structural cornponents of the ship may rupture due to large strain.Pevious research resuls show that the maximum plastic strain of material is related 1o both the physicalproperties of the material and the mesh size of the finite element model (Glykas et al., 2001). Thematerial failure-fracture criterion based on strain is taken as 34% as long as all mesh sizes of finite ele-ment models of the ship and bridge pier are larger than 50 mm.中國煤化工MYHCNMHGSimulation of the Whole Process of Ship Bridge ollision3734.2 ConcreteThe research on the way to delemine the filure crtera for concrete materials under complicatedload conditins has been caried on for many years, but m perfet strength theory for all kinds ol loedconditions has been dereloped yet. The filure crteion for concrete alerial is usually obained hasedon concrele strengh tests under sorme specified load condition. The concrete strength with stress σq canbe defined as:f(o,，k，后，...的)=0(6)where k，k2，.，h。 are the parameters of concrete material, which are detemined based on con-crete strength tests. The strength criterion whose definition function consists of n parameters is calledn-paraneter strength criteria (Bazant et al., 1982). One-parameter strength criterion, which is alsocalled maximun tension stress theory, is adopted in this paper. According to the specifications for con-crele structure design, the slandard lension strength of concrete C30 is 2.0x 10^(N/mm2 ).5. Influence of Strain-Rate SensitivityFor consideration of the influence of strain-rale sensitivity of ship mild steel malerial in collision,the dynamic yield stress σn' should be adoptedo'/o。= 1+ (e/D)"*(7)where a' is the dynanic yield stress with plastic strain-rate E; σσ is the static yield stress;D=40.4s" ' and q =5 for the ship mild steel (Wang and Gu, 2000).6. Influence of WaterWhen the striking ship ollides with the bridge pier in the nomal direction, it only moves in thelongitudinal direction. The influence of water on the ship motion is relatively small and can be depictedwith an added mass 0.04 times of the total ship mass. The added mass is realized by increasing thedensity of elenents of the rear part of the ship in this paper ( Petersen, 1982).7. Finite Element ModelBased on a 40000 1 oil lanker and a bridge across the Yangtze River, finite element models arebuilt up. The principal dimensions of the striking ship and the struck bridge pier are listed in Table 2and Table3. It is assumed that the head velocity of the oil tanker is 6 m/s at the initial moment of col-lision.Table 2Principal dimensions of te striking shipLongitudinalBreaduhDeptDraughtDWTDisplacementShip(m)x 10'(t)0il tanker16019.540.050.5中國煤化工MYHCNMHG374LU Jiacheng and GU YongningTable 3Principel dimensions of struck pierunit: mPile eanp(Lx Bx H)Pier(LxBxH)Waler depch20x 18x9.56x3x217.1 The Finite Element Model of the ShipThe finite elenent model of the striking ship is composed of the colliding zone of the ship bow andthe afer-part. The bow part is modeled precisely with elastic-plastic material including the shell,decks, bulkheads and girders. In order to shurten the calculation time, the afer-part of the hull issimplifed as a model composed of shell and major bulkheads of rigid material. The minimal mesh sizeof the finite element model is 15 cm. The mass of the ship is added to the finite elements and the cen-ter of gravity is located on the central longitudinal plan. The finite element models of the ship bow andthe ship are shown in Fig. 4 and Fig. 5.Fg.4. Finite enent model of ship bow (par).7.2 Finite Element Model of Bridge PierThe finite element model of the bridge pier consists of the pile, pile cap, pier column, pier cap,and upper slnuctures.Pile: The itesecion betwen the pile and soil can be prfecly rlcted by the dynanic nonlin-ear pile soil rlaionship, but that will need l000 much work and time. Therefore the equivalent piermethod is adopted in this paper. The length of equivalent pile is 8 times the pile dianeter and is lowerend is fixed.Pile cap, pier column and pier cap: 'The pile cap, pier column and pier cap are made o[ rein-fored conerele and their scanting are depicted in detail in the firite element model. Slim steel barswithin the range of 1 m are silifidf as one equivalent seel bar by adding an aditional sectionl areafor the pupose of reducing computing time. The equivalent seel har is depicled as a beam in the finiteelement model (Yu and lai, 1999).Upper structures: During clisin, the initial force from the roadway and skew cabless are中國煤化工MYHCNMHGSimulation o the Whale Proces of Ship- Bridge Cllisin375transfered to the bridge pier through the pier cap. The influene of upper stctures is given by meansof a mass blok, which is estimated to be 7.32 x 10* kg in this paper including jackets, skew cable,reinfored concrete and pitch of the bridge surface, and obher upper stnuclures.The finite element model of ship-bridge ollison is shown in Fig. 5.Fig.5. Finite element mouel of shipbridge ollisin.8. Results of Numerical Simulation8.1 Collision ProcessStructural components of the ship bow contacting the pier are gradually crashed into the hull dur-ing ollision. The length of pressed structures is called penetration. The moment when 99% of the ki-netic enengy of the ship is consumed is defined as the end of ollision. The simulation results show thatthe penetration is 10.2 m and collision lasts 2. 8 seconds.. Kinetic energyEnergy (N-四---- Distortional energy Penetration(m)1. 05+0099. 0+008010.0}7. 50+008 t8.006.00+008 |4.50+0083. 00+0081. 50+008 I2.00|0.50 1.001.502.00 2.50 3.0000.50 1.00 1.50 2.00 2.50 3.00 3.50Time(s)Fig. 6. Energy-ime curve of striking ship.Fig. 7. Penetration- time curve.中國煤化工MYHCNMHGuU jiancheng and CU Yongming8.2 Analysis of Collision ForceFig. 5 shows that there are two contact areas between the ship bow and the bridge pier. One isbetween the bow and the pile cap and the other between the upper bulb and the pier colunn. The con-tact beltween the bow and the pile cap P: ocurs before the contact between the upper bulb and the piercolum Pz, see Fig. 8. The cllision forcee curve is nonlinear and fuctuant. Fach peak represents thefailure of one structural component of the ship bow. The collision force increases with the increase ofpenetration as a whole. The maximum collision force occurs at point A at the moment of 2.68 secondsin the present study .0n pile colunForce (N)一On pile cap1. 5X103母1.25 X10叫1.0X107. 5X1015. 0X10|-2. 5X1070 0.50 1.00 1.502.002.503.00Time(s)Fig. 8. ollision force timne curve.The maximum ollision forceisPm = P + P2 = 1.63x 10*(N).(8)The average cllisio fore is defined as energy divided by penetration:p。_導(dǎo)= 9.09x10= 8.8x 10'(N).(9)10.3The ratio of the maximum ollision force to the avernge cllision force is1.63x 10%= 1.85.(10)8.8x 10That is in agreement with the conclusion from ship ollision test by Woison in Germany in 1976.The maximum cllision force is compared with the resut of empirical formulas. The maximum col-lision foree by Woison' s formula (Saul and Svensson, 1983) isPm =0.88xVDWTx(1+50%) =0.88x√4.0x10 x(1士50%) = 176士 88(MN)(11)The maximum cllisinin force by the formula given in Chinese Seifictions for Highuay BridgeDesign published in 1989 isPm=2. Pm= 2.V6”= 2.0x 10*(N),(12)中國煤化工MYHCNMHGSimularion of the Whole Proce6e of Ship Bridge ollision377where W is the weight of the ship and V initial velocity of the striking ship.The maximum ollisin force by the fonmula given in ASSHO (Knott etal, 1990) isPm = 0.98/DWT長= 0.147 x 10'(N).(13) .It is indicated that the resuls by empirial formulas are slighly higher than the result by the finiteelement method. The collision force is related nol only with the structural components of the bow andkinetic energy of the striking ship, but also with the sizes of the striking ship and the bridge pier, theshape of the bridge pier, collision diection, and so on. Those characters that can not be considered byempirical formulas can be perfecly depicted by the finite element method. .8.3 Energy ExchangeDuring collision, the kinetic energy of the striking ship, including the kinetic energy of addedwater mass is changed into the elastic-plastic distortional energy and residual kinetic energy of thestriking ship, the elatic-plastie distortional enerngy and kinetic energy o[ the bridge pier, heat energydue to friction between structural components, and energy loss due to hourglassing.Numerical calculation results show that the energy absorbed by the bridge pier is only 10% N.mand the total energy is 10° N'm. That means most of the ollision energy is absorbed by the elastic-plastic deformed structural components of the striking ship and the energy absorbed by the bridge is solttle that it can be neglected.The enengy curves in Fig. 6 and Fig. 9 indicate the energy absorbed by individual struchural com-ponents .一Shell---- Kinetic energyDecksEnergy(N.m)一一Di atortional energyEnergy (N.m)----- Bulkhead5.70+006r4. 40+008r4. 75+0063. 85+008-3. 30+0083. 80+0062. 75+0082. 85+006-2. 20+0081. 90+006-1. 65+001. 10+0089.50+005-5. 50+007° 0.501.00 1.50~2.002.50 3.0000.501.001.502.002.503.00Time (s)Fig. 9. Energy in concrele of struck pier.Fig. 10. Disorional energy of components.8.4 Deformnation of Ship and Bridge PierIt is indicated that the defomation of the pier is far smaller than that of the ship. For instance, atmoment A when the ollision force is maximal, the penetration of the ship is 10.2 m while the defor-mation of the pier is only 0.175 m, soe Fig. 11.中國煤化工MYHCNMHG378uU Jancheng and (GU YongpingFIg.11. Deformation of ship and bride pier.The deforned and damaged structures of the striking ship are concenlrated in the contact region ofthe ship bow, and damnages include folding, 1earing and bending of plates, frames and stringers. Thplastie yielding of structural components happens al the begining of ollision. During ollision, thecrushing of decks begins with buckling, then the parts near the contacl region bend plastically, foldand fail with the incerease of penetration, see Fig. 12. Under further crushing, the shell plating of thebulb bow is prgresively folded together. 'The crnushing configuration is nearly uniform in the circum-ferential direction, as indicated both by the mumerical calculation and the ship cllision testl carried outin Gerany (Lehman and Yu, 1998) see Fig. 13 and Fig. 14.T=0.5s .r=1.0sr=1.5sτ=2.8sFig.12. Crushing of deeks and bulks.8.5 Damage to Bridge PierNumerical resuts show that high stress regions of the bridge pier are concentrated in: (A) thecontact region of the ship and the pile cap and its vicinity, (B) the connection of the pile cap and thepier column and its vicinity, and (C) the connection of the pile and the pile cap and is vicinity, seeFig. 15.The high stress in region (A) is caused by local concentrated loads，which dange a small zone中國煤化工MYHCNMHGSimulation of the Whole Proces of Stip-Bride Cllision379Flg. 13. Cnusting of hir abdl ty rimml. sion.Fy.14. Danugod brw alher edlin ly ksl.7. 45+206 68102066.68+06 24.02001.88-557.0-XK4月.5 r5TD 1.*4002 7001ea6061. 4Fig. 15. Streas dsribution in pier for T=1.7s.of the bridge pier and only leads to the failure of local concrele. The most dangerous moment for region(A)is T=1.42s.The high stress in region (B) is caused by the global bending of the pier column. Numercal cal-culation shows that the horizontal displacement of upper parts of the bridge pier lags behind that of thepile cap during the initial ollision phase , causing the bending of the pile column. The most dangerousmoment for region (B) is 1.72 s when the horizontal displacement of the upper parts of the bridge pierlags nost behind that of the pile cap. The failure area accounts for one third of the whole sectional areaof the pile column acording to the mximum tension stress eriteria.The high stress in region (C) is caused by the bending of piles and reaches the peak value whenthe piles bend most. It is indicated thal the displacement of he pile cap fluctuates and the most dan-gernous moment for region (C) is a lttle later than the rmoment when the maximum collision force takesplace. The mosl dangerous moment for region (C) is 2.7 s and the failure area accounts for half of中國煤化工MYHCNMHG380uU Jancheng and CU Yungingeach pile sectional area according to the maximum tension slress criteria.8.6 Effect of Bridge Pier Displacement on Collision ForceSince the displacement and energy absorption of the bridge pier are 80 small that they can be ne-glected compared with that of the striking ship, may the efeet of displacement of the bridge pier oncollision force be neglecled? In order l0 answer the question, numerical calculation is perfomned of col-lision o[ the same ship finite element model with a rigid wall of the same shape as the bridge pier, withthe same parameters . Comparisons between lwo results of ollision force are showm in Fig. 16 and Fig.17. It is indicated that the two results are nearly the same, meaning that the efct of bridge pier dis-placement on the cllision force is very small. In addition, the consideration of the bridge pier as beingrigid may simplify the problem, reduce the work load and shorten the calculation time.一ith rigid pierForce (N)---- With reinforced concrete pierrred1. 60+0082. 40+0071.40+008-2. 10071. 20+0081. 80+001.00+008-1. 50+0078. 001. 20+076. 009. 0064. 00706. 00+0062. 003.00+00600. 2.004.006.008.0010.012.00.00 7.00 8.00 9.00 10.0 TL.oPenetration (m)Penetration(m)Fig. 16. Bow colisin force compare.Fg.17. Bulb ollision force comnpare.9. ConclusionsBased on the present study, the fllowing conclusions can be drawn.-The sip-bridge cllisinin proces can be pfeetly sinulated by expliei transient nonliner fi-nite element tcholoy . The interaction between defomed stuclural components can be considered bydefining master-slave contact surfaces and slf-contact surfaces in the finite element method. For caleu-lation of cllision between such complicated stuctures as ship hulls, the finite element method has odb-vious advantages corpered with other methods. The structurl intemal stres distribution, ollisionforce change, energy exchange , and structural deformation, which can not be depicted by other meth-ods, can be perfectly done by the fnite elermnent method.-The damaged stuctures of the ship hull are concentated near the contact regions with thebridge pier. That means only the stuctural components around the contact regos need to be modeledin delail and the snucural components far away from the contact regions can be modeled roughly as nig.id bdies.中國煤化工MYHCNMHGSimulation of the Whole Poxems of Ship Bride Cllision381一Ihe curve of cllisin force is nonlinear and fluctuant, indicaing continuous unloading due tostruetural failure and nuptures of the ship hull during ollision. 'The collision force increases with in-creasing penetration as a whole, and it is dependent on the structure ' s profile and scanling of compo-nents.一The damage to the bridge pier depends on the maximu ollision force. Based on the stressdistribution in the bridge pier, the damage to it can be estimated in accordance with some concretestrength theory. The high stress region of the bridge pier can be lasifed into two groups acording tocaluses .)ne is caused by the concentrated impact loads which mainly distributes near the contact re-gions between the ship and the bridge pier and the other is caused by the global bending of the bridgepier which mainly distibutes near the connections of the pile and the pile cap, and the pile cap andthe pier colunn. The distribution scope of the second kind of high stress regions is relatively large,and that high stress greatly damages the bridge pier. The estimation of damage to the bridge pier is acomplicated dynamie problem closely related with the ollision force, ollision position, the lower endboundary condition of the bridge pier, and so on.一'The kinetic energy of the striking ship is mainly absobed by the bow struchures and changed todefornation energy. Because the sifness of the bridge pier is much higher than that of the ship bow,the displacement and defomation of the bridge pier are much smaller than that of the striking ship.Their efcts on the cllisioni force, the displacement of the striking ship and the disotional energy ofthe striking ship are so small that they can be neglected. Therefore, except for the displacenent of anddamage to the bridge pier, which need 10 be taken into account, the bridge pier can be regarded asrigid in ship-bridge collision calculation.ReferencesBaan,2. P. eal, 1982. Slate of the un repaont on firite element urul/ys ofR. C.. Chapter 2, ASCE, Special Pubr-lication.Chen, w. F., 1982. 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