Analysis of Collision Protection for Ocean and Offshore Structures

China Ocean Engineering , Vol.20 , No.3 ,pp.361 - 372◎2006 China Ocean Press , ISSN 0890-5487Analysis of Collision Protection for Ocean and Offshore StructuresZHU Bin(朱斌)，1 ,CHEN Yun-min( 陈云敏) and LEUNG A. Y. T.(梁以德少" Department of Cwvil Engineering , Zhejiang University , Hanghou 310027 ,Chinab Department of Building and Construction , Cily University of Hong Kong , Hong Kong , China( Received 21 August 2005 ; received revised form 28 March 2006 ; accepted 18 May 2006 )ABSTRACTAn elasto-plastic impact model based on the p-version finite element method is presented for the collision protectionof ocean and offshore structures. The impact force and responses of the impactor- absorber- structure system can be pre-dicted fficiently and automatically. A cost-effective Cellular Reinforced Concrele Absorber ( CRCA ) is designed tosmooth the impact force and absorb the impact energy. Quasi- static tests show that the concrete absorber has an excellentenergy absorbing characteristic. The impact experiment of a scaled offshore oil piping frame with the proposed concreteabsorber is carried out. The simulation results of the elasto- plastic model and the p-version finite element method are ingood agreement with the experimental ones. Owing to the plastic deformation of the absorber , the impact force during theimpact and responses of the structure are considerably reduced. Further , the proposed impact model and the concrete ab-sorber are applied to the design of ollision protection of the sheel-pile groin on the Qiantang River used to weaken the fa-mous Qiantang bore .Key words : ocean and offshore structure ; elasto- plastic ; impact ; p-version finite element method ; absorber1. IntroductionMany accidents of ocean and offshore structures involve impact loadings. Some famous ship colli-sion cases are the Tjorm Bridge ( Sweden ) , the West Bridge of the Great Belt Link ( Denmark ) and theMaracaibo Bridge ( Venezuela ). Most studies used the Hertzian contact law( Zukas et al. , 1982 ) tocalculate the impact force and analyze structures subjected to impact loadings. Other alternative meth-ods such as the spring- dashpot and momentum balance methods utilized the coefficient of restitution asan input for the dynamic analysis( Palas et al. , 1992 ). In some problems , the local deformation ab-sorbs a significant portion of the impact energy so that it must be modeled adequately. Some elasto-plastic impact models with mass-spring systems were proposed( Wu and Yu , 2001 ). The impact modelfor ice impact was presented by Zhang et al. ( 2002 ). There were also several other impact models at-tempted for civil and structural engineering( Chen et al. ,2002 ;Zhu et al. ,2003 ). Among these .methods some are restricted to the elastic impact and the others are effective only for the analysis ofsimple structures. Generally , the impact process中国煤化工entional plastic finite el-ements accurately( Liu and Gu ,2002 ;Hu et al.:MHC N M H Gnany numbers of degreesof freedom ( DOFs ) should be considered if satisfying solutions are to be obtained. To study the impactmechanism of ocean and offshore structures , some impact experiments of structural models were carriedout( Shi and Tong ,2001 ;Shi el al. ,2002 ). But existing impact experiments hardly studied on the1 Corresponting 持. E-mail : binzhu @ zju . edu.cn362ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372characteristic of the absorber during the collision. The safety of many important ocean and offshorestructures is drawing more and more attention. It should be carried out some structural impact experi-ments to show the impact mechanism and behavior of the absorber during the impact. Further , a simpleand efficient elasto-plastic impact model is needed for the analysis of the whole impactor- absorber-structure system in designing the absorber for structural collision protection .Some materials were used to smooth the impact force and absorb the impact energy. An overviewof rate effects in cellular material was presented in the monograph of Gibson and Ashby( 1997 ). Reidand Peng( 1997 ) studied the dynamic crushing of cylindrical specimens of five different kinds of woodsfor impact velocities up to 300 m/s. They showed that the substantial enhancement of the initial crush-ing stress for wood loaded along the grain was due to micro- inertia inhibiting cell wall buckling modes .Many interests focused on the analysis of high strain rate compressive honeycombs ( Zhao and Gary ,1998 ; Honig and Stronge , 2002a ; 2002b ) ,as well as the polyurethane foam and aluminum alloy foamsubjected to the impact loading( Deshpande and Felck ,2000 ;Shim et al. ,2000). Davalos et al.(2001 )and Qiao et al. ( 2004 ) designed and modeled the fiber- reinforced plastic honeycomb sand-wich panels and I-Lam sandwich system for the protection of highway bridges . A commercial finite ele-ment package was used for the analysis , and some applications were described .A simple elasto-plastic impact model based on the p-version finite element method( FEM ) is pre-sented. Since concrete is not easy to be rusted and aged ,it can be used in some tough environments .For engineering applications ,a new Cellular Reinforced Concrete Absorber( CRCA ) is designed as theimpact absorber for collision protection of structures including ocean and offshore ones. With the pro-posed elasto- plastic impact model , the structural impact process can be predicted efficiently and theoptimal CRCA can be designed for the collision protection without difficulty. To verify the proposed e-lasto-plastic impact model and investigate the energy absorbing characteristic of the CRCA , an experi-ment of a scaled offshore oil-piping frame subjected to impact loading is carried out by an impact facili-ty in laboratory. Additionally , with the elasto- plastic impact model and the p-version FEM , the ab-sorber for a sheet-pile groin on the Qiantang River is designed for its collision protection .2. Elasto- Plastic Impact Model2.1 p- Version Finite ElementsThe natural modes predicted by the p-version elements are , in general , more accurate than thoseof the low-order finite elements for the same number of DOFs ( Zienkiewica and Taylor , 2000 ; Zhu ,2005 ; Leung and Zhu , 2004a ; 2004b ). Since many iterations are involved in the impact simulation ,much computational time can be saved when using中国煤化工ts. The p-wverion thickbeam element THICK-1b used in this paper is st:MYHC N M H Gdevelopment of the ele-ments , refer to Zhu( 2005 ) and Leung and Zhu( 2004a ). The internal DOFs of the element are repre-sented by the additional hierarchical polynomial in the shape functions. With the enrichment of DOFsin the p-version element , the accuracy of vibration analysis is greatly improved. The convergence rateof the elenEe存黎振ery fast with respect to the additional terms in the shape functions. So it is a goodZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372363choice to use these p-version elements in the simulation of structural impact analysis.Wa4ww↑Wqprn↑wa↑。W' w,'w,'ww’WXor)>'WaFig. 1. Geometry and DOF system for p- version beam element THICK-1b.2.2 Impact ModelAs mentioned previously , the analysis will be complex and many DOFs should be involved in thecomputation to obtain satisfying solutions if the conventional plastic finite elements are used for the im-pact analysis. For the impact analysis of the structure with an absorber attached , usually , only the ab-sorber deforms plastically. Hence ,it is reasonable to linearly analyze the structure and just take intoaccount the plastic deformation of the absorber during the impact. With the following simple elasto-plastic impact model and the fast convergent p-version element , the analysis of this type of impact issatisfactorily accurate and the computation is efficient. The governing equations for the impactor-ab-sorber-structure system areMx( l)+ cx( l)+ KX( l)= F(l),( 1a)mi(t)+ jf(t)= 0,( 1b)where , K , M ,and C are the stiffness , mass and Rayleigh damping matrices of the structure , respec-tively ; F( t )is the force vector applied on the structure ;f t )is the impact force ; m is the mass ofthe impactor ; u( l )and X( l ) are the displacement of the impactor and the vector of displacements ofthe structure. The indentation of the absorber can be expressed as :a( l)= u( 1)- x(1 ).(2)Here x( t ) is the displacement at the point of the structure where the absorber is located. Before theiteration in each time step , it is assumed thatw°(l)= wn_(1)+ iwn_(1)O1 +wn (1)12 ,(3)x(1)= x(1)+ x_(1)1 +xn-(1)02 ,(4)where , superscript( n ) indicates the iteration in the n-th time step. Then the iteration starts to yieldthe impact force and responses of the impactor an中国煤化工Fig.2,in which△t isthe time step length. In this way , one can simulaMHCNMHGesystem when the massand the initial velocity of the impactor are given.3. Characteristic of CRCAThe死有数燕cA is made in laboratory as shown in Fig. 3( a ). The qusistatie test of the CRCA364ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372is performed with a Lloyd Instruments LR50K plus materials testing system. The force is chosen as thecontrol variable in tests . The tested result and the numerical simulation for a typical CRCA are plottedin Fig. 3( b). The simulated bilinear relationship between the load and the compressionis : F= Fox/Dζ0≤x≤Do)and F=ax+ F( x> Do), where F(N)and x( m ) are the applied load and thecompression of the absorber , respectively . Shown in Fig. 3(b) Fo=8000 N , Do=0.73377x 10-3m and a = 78533. In this study , for different strengths and sizes of the absorber , it is assumed thatthe simulated relationship between the load and the compression depends only on the valuesof Fo , Doand a. In the compressive test , cellular holes of the absorber are crushed layer by layer , and rein-forcements in the absorber constrain the development of vertical cracks. While the normal concretecube is shear failure when the load approaches its failure strength and then the load will decreaseabruptly. So the CRCA has much more excellent characteristic of plastic deformation than the normalconcrete cube does .Indentation ofabsorber a,"() fom Eq. (2)Impact force f{%"() from load-deformationrelationshio of absorberResponses ofstructure x"(1), (1)and X"()↓Fig.2. Elasto-plastic impact model.Acceleration of impactor的“(t) from Eq(lb)w")()=w.. ()+。(04+-的。,(02 +一.()M的”()-1 ()+ =l[_(0) +的2(0]Nolw"()-w"10[<10*?=i+1nn+1↓Yes中国煤化工Next time stepMYHCNM HGThe CRCA can vary in size , shape and strength with different proportions of cement , water , andaggregates. It is not easy to rust and age and is much cheaper than some other absorbers such as thefiber-reinfe片芳数搪For a real structure subjected to impact loading , the optimal size and strength ofZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -37236515 00012 000-9000-6 000一Experimental results3 000---- Numerical simulation0D。10204050Compression (mm)(a)Configuration(b)Typical load-compression relationshipFig.3. Configuration and load- compression relationship of CRCA.CRCA should be designed by means of some impact models , among which the present one is a good .choice.4. Experiment of A Scaled Frame Under ImpactAn impact facility is installed in the Heavy Structures Testing Laboratory of the City University ofHong Kong. The initial kinetic energy of the impact hammer can be changed by use of different combi-nations of steel plates and different initial heights . Four bearings are mounted on both sides of the ham-mer to reduce the friction between the hammer and the stainless steel rods.0.3 m_①日②③吉CRCA④⑥.P3⑦⑧2(a) Scaled model(b) FEMinental setup中国煤化工Fig. 4. Impact experiment:TYHCNM HGThe 1/10 scaled model of a steel frame structure used for oil-piping is presented in Fig. 4( a ).The present CRCA is used for its collision protection in the experiment. Its analytic model by the p-version elepdepicted in Fig. 4( b), and the setup of the experiment is shown in Fig. 4( c).月男数据ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372One Kistler 8774 and two Kistler 8776 accelerometers are , respectively , installed at positions P1 , P2and P3 on the structure( see Fig. 4( a)). After amplified by the coupler of Kistler 5134 , the accelera-tion data are collected by a data collector of National Instruments . The physical properties of the modelfor the computation are shown in Table 1. This experiment is used to examine the energy absorbingcharacteristic of the scaled CRCA and the prototypical CRCA can be used for the real structure. Alter-natively , the optimal strength and physical size can be designed by the proposed impact model based onthe p-version elements .Table 1Physical properties of the modelYoung' s modulusMaterial densityShear correctionPoisson' s ratio .ParameterSectional areaEfactor KValue200x 109 Pa7800 kg/m0.4 mx0.4 m0.3Totally eight p-version beam elements THICK-1b are used in the model. The first eight naturalmodes for transverse vibration of the model are listed in Table 2 with the increasing number of hierar-chical polynomial terms employed in shape functions . The results show that the convergence of the pre-sent element is very fast. The number of additional terms p =6 is selected in the following computa-tion. The first two modes' damping ratios 0.94% and 1.05% of the scaled model from the free vibra-tion test are used for the Rayleigh damping matrix involved in the famous Newmark linear accelerationmethod to compute the time-domain responses ( Clough and Penzien , 1993 ).Table 2Convergence study of p-version elements for the modelp-versionModeDOFsFEM14p=26018.35112.9116.1235.9404.0495.7627.9740.3p=390110.1113.6222.4303.7371.3620.6627.4p=4114110.0 .222.3303.4369.1584.6624.3p=5138110.0.222.2302.8367.8580. 9624.2p=6162110.0302.7580.1The weight and the initial velocity of the hammer are fixed at m = 139.4 kg and Uo= 1.4 m/s fordifferent CRCAs. Two CRCAs with different strengths are used in the tests , and their quasi-static test-ed results are plotted in Fig. 5. A common value of Dn= 0.73377x 10-3 m and different values of Fo .中国煤化工= 2850 N and 4760 N are taken into considerationbectively . Both simulatedand experimental acceleration responses at positiorMYHCNMH Gre shown in Figs.6(a)and( b ) , respectively. The two plots show that the simulated results are in good agreement with theexperimental ones . The hammer moves downward and the simulation ignores the influence of its weighton the impact force. Moreover , the used load-compression relationship of the absorber in the simulationis just the'ta smooth one and neglects the strain rate effect. As shown in Fig. 6 , these reasonsZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372367result in the little difference between the simulated and tested dynamic responses of the structure. Ifthe strength of the absorber is small , the long time duration of the impact smoothes the impact force aswell as the acceleration responses of the structure ; however , the indentation of the absorber is ratherlarge , the maximal indentation of the absorber during the impact determining the minimum size of theabsorber. So the optimal strength and size of the absorber need to be designed in practical engineeringapplication .0τ8一F- 2850NF 4760N6Fig.5. Quasi-static tested resuls of two CRCAs.10203040Compression (mm)300Simulated results400--- Experimentsul results"-Simulated reuts200--- - Experimental results200100o& -100-2000.000 0.0020.004 0.006 0.008 0.0100.000.010.02 0.030.04 0.05Time (@)Time (S)(a) F=2850 N(b) F.=4760 NFig.6. Acceleration responses at position P1 for CRCAs With diferent Fo.Fig. 7( a) gives the maximal w( m ) during the impact for different strengths of elastic absorbersand elasto-plastic absorbers , in which w1 is the displacement at the impacted position P1 , and ke is .the stifness of elastic absorbers. The corresponding maximal indentation of absorbers is shown in Fig.K b). The two plots show that the maximal indentatine af th. aInstn- nlostie absorber is smaller than中国煤化工。.that of the elastic absorber when they have sameFexample , with the samevalue of 0.014 m for the maximal w1 , the relatedJTYHiCNMH G” absorber and the elasto-plastic absorber are about 150 kN and 2.226 kN , respectively . The corresponding maximal indentationof the former is about 0.0387 m , which is larger than that of the latter ,0. 0325 m. That is to say ,theenergy absorbing characteristic of the present elasto-plastic absorber is better than the elastic one. Thiscan also be&r振d simply by the enclosed areas of curves in their load-compression plots.ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -3725. Analysis of Collision Protection for Sheet- Pile GroinSince the foundation of the conventional riprap groin is shallow , it tends to be destroyed by thebore. To solve this problem , the new simple sheet-pile groin was designed( Zhao et al. ,2001 ). Thispiled structure can weaken the bore and keep the relative stability of the bottomland in front of the riverdike ,and it is not easy to be destroyed by the bore due to its deep pile foundations . A sheet-pile groinused to weaken the famous Qiantang bore and protect the Qiantang River dike is shown in Fig. 8. Tworows of reinforced concrete piles with a length of 11 m are partly buried in the mucky soil , and they areconnected to each other( see Fig. 8( a))by cap beams and collar beams. The piles toward the up-stream of the river are numbered as P1-P22 .F。ofelasto-plastic absorbers (kN)F。ofelasto-plastic absorbers(kN)0.5 1.0 .2.5.00.51.0 1.5 2.03.0.0220.050 [Elastic absorbers0.020Elasto-plastic absortbers0.040 t0.0180.016 t0.030 I0.014 t0.012. Elastic absorbers0.010. - Elasto-plastic absorbers I2004006008000.0105- 200 400k, ofelastic absorbers (kN)k ofelastic absorbers (kN)(@) Maximal w,(b)Maximal indentationFig.7. Maximal w 1 and indentation during impact for different absorbers .15.35m一个Capbeam0m0.5p3.85mr z3.0.Thum Y2AZ227777489ColnrbeaenImx035元aDowostamUpsrem-o自能Maxeky soil只&中国煤化工MYHCNMHGAprofle(b) Side view(a) Plane viewFig.8. Sheet-pile groin on the Qiantang River .Since the教振ture is transversely extended into the river , the impact by moving ships on theZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372369Qiantang River is common. Some physical properties of the structure and the moving ship are shown inTable 3. only some parts of DOFs in the p-version element THICK-1b of the structure are taken intoaccount for the simplification of computation( see Fig. 9 ). There is one element for each cap beamand each collar beam respectively , but two elements for each pile. The element for the part of the pilein soil is also THICK-1b but resting on the two- parameter foundation( Zhu , 2005 ). The number of ad-ditional hierarchical polynomial terms in shape functions of the element p=4 is used in the followingcomputation .Capping beam1mx0.5mCollar beamFig.9. p-version finite element model of thesubstructure .surfaceofsoilConcrete pile0.5mx0.5mTable 3Physical propeties of impact analysis of sheet-pile groinParameterValueSheet-pile groinYoung' s modulus E30x 109 PaMaterial density ρ2500 kg/mShear correction factor KPoisson' s ratio 。0.3Moving shipMoving speed3 m/sFoundationWinkler foundation modulus k2x10*PaShear foundation modulus hc2.5x 107 NIn view of large impact energy of the moving shin .CRCA is a good choice to protect this structurefrom ship collision. With the bilinear load-deformYH中国煤化工orber and the p-vesion .FEM , the optimal strength and size of the absorbeCN MH Gs.Various Fo , Do= 7.3377x 10-3 m and a = 78533 are used in the simulation to study the effectof the strength of the absorber. Shown in Fig. 8a the right part of the structure tends to be impactedmore than the left one , and it is clear that the responses of the structure will be the largest if the top ofpile P1 is p教插Thus , only the transverse impact at the top of pile P1 is analyzed herein , and the370ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372appropriate concrete absorber can be selected for the protection of this location. Actually , the strengthof the absorber determines the impact force. Hence , for the given mass( m = 200 t )of the ship and itsattached water , with the increasing strength of the absorber , the responses of the structure increase , asshown in Fig. 10 , but the maximal deformation of the absorber decreases , as shown in Fig. 11. Theabsorber with a small strength can smooth to a large extent the impact force as well as the responses ofthe structure , but the deformation of the absorber during the impact will be large. Consequently ,for agiven mass and moving speed of a ship , the strength of the structure should be checked against the re-sponses of the structure during the impact and related design codes ; then the appropriate strength andsize of the absorber can be selected based on the simulated results. For example , for the case of m =200 t and maximal(a )=1.0 m ,the valueof Fo will be about 750 kN( see Fig. 11 ),if the strengthof the sheet-pile groin during the impact is satisfied. In this way , the optimal strength and size of theabsorber are determined .0.04.1.5-F。=800kN0.03-F_=800kN.0-F=1600kN--- F-=1600kN....F=2500kN...置。0.02-0.5卡0.01 .0.0+0.00--0.0.0020.40.60.8Time (S)Time (s)(a) Displaccment response(b) Velocity responseFig. 10. Reponses at impacted position on structure for impactor with mass of 200 t.2.0-1.6-m=100tm=200tm=300t1.2-Fig.11. Maximal indentation of the absorber0.8-with different strength.0.4-中国煤化工0.0↓500 10001500 20002500MHCNM HGF。(kN)6. Conclusions and DiscussionAn elpimpact model is presented in this paper. The simulated responses of the struc-方方数据ZHU Bin et al./ China Ocean Enginering ,20(3), 2006 , 361 -372371ture are analyzed by use of p-version elements developed previously by the authors. One can obtain ac-curate solutions with the elements using a less number of DOFs than with the conventional finite ele-ments. For a structure subjected to an impact loading in engineering application , the method is effi-cient for designing an appropriate small elasto plastic absorber generating acceptable responses of theimpactor-structure system .A cellular reinforced concrete absorber with an excellent characteristic of plastic deformation ispresented. Owing to the reinforcement of the composite material of the absorber , it has a much moreexcellent energy absorbing characteristic than the normal concrete cube. The strength and compressioncharacteristic of the absorber can vary with the water cement ratio and proportion of aggregates. By useof the load-compression relationship from the quasi-static test and the elasto-plastic impact model basedon the p-version FEM，the responses of the impactor- absorber- structure system can be computed eff -ciently.An impact experiment of a scaled oil-piping frame is carried out , and the tested results show thatan appropriate absorber can largely smooth the impact force and responses of the structure. For the softimpact , the CRCA has a relatively small strength , and the long time duration of the impact smoothesthe impact force as well as the acceleration responses of the structure , but the deformation of the ab-sorber is larger than that induced by the hard impact. With the proposed elasto-plastic impact modelbased on the p-version FEM , the appropriate CRCA is selected for the sheet-pile groin on the QiantangRiver to resist the impact by moving ships .The analysis will be complex and many DOFs should be involved in the computation if the con-ventional plastic finite elements are used for the impact analysis. For the impact analysis of the struc-ture with an absorber attached , usually , only the absorber will deform plastically. With the presentsimple impact model and fast convergence p-version elements , the analysis of this type of impact isreasonable and much computational time can be saved. The model assumes that there is no deformationfor the impactor. If its deformation cannot be neglected in the real situation , finite element analysisshould also be considered for the impactor. 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