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Nuclear Engineering and Design 247 (2012) 1– 10

Contents lists available at SciVerse ScienceDirect

Nuclear Engineering and Design

j ourna l ho me page: www.elsev ier .com/ locate /nucengdes

inite element analysis on the Meppen-II-4 Slab Test

liver Martina,∗, Vincent Centrob,1, Thierry Schwoertzigb,1

European Commission, Joint Research Centre (JRC), Institute for Energy and Transport (IET), Westerduinweg 3, NL-1755 LE Petten, The NetherlandsAltair Engineering France, 2, rue de la Renaissance, F-92184 Antony Cedex, France

r t i c l e i n f o

rticle history:eceived 16 August 2011ccepted 1 February 2012

eywords:inite elementissile impactuclear power plantoncrete containmenteppen Slab Tests

a b s t r a c t

In this paper finite element (FE) analyses on the Meppen-II-4 Slab Test are described. The Meppen SlabTests are a series of large scale missile impact tests performed in the 1970s and early 1980s to assessthe safety of containment buildings of German nuclear power plants against possible impacts of militaryaircrafts. In the second series of the Meppen Slab Tests different metallic pipes resembling the bodyof military aircrafts were impacted against reinforced concrete slabs of dimensions 6.5 m × 6 m × 0.7 m.The FE analyses that are subject of this article are part of the contribution of the Joint Research Centrein Petten, The Netherlands together with Altair Engineering France, Antony, France for the BenchmarkProject “Improving the Robustness of Assessment Methodologies for Structures impacted by Missiles(IRIS)” of the Subgroup on Concrete of the Working Groups on the Integrity and Ageing of Componentsand Structures (WGIAGE) of the Nuclear Energy Agency (NEA) of OECD. The FE analyses are performedwith the explicit solver RADIOSS and Lagrangian meshes are used for the missile and the concrete slab.The constitutive behaviour of the concrete is described by means of a Drucker-Prager/Cap model, thematerial model of Han and Chen. For the metallic parts, i.e. missile and steel reinforcement inside theconcrete slab, isotropic elastic–plastic deformation behaviour with partial strain-rate dependency is used.

Failure mode, crack pattern, shear cone inside the concrete slab and shape of the deformed missileemerging from the test are well resembled by the analysis. Comparisons between measured and calcu-lated time series for slab deflections, reaction forces in some of the slab mounting points and strains inthe slab reinforcements depict higher frequencies for the measured time series compared to the calcu-lated ones. The amplitudes of the calculated time series for all three properties have the tendency to belarger than the ones from the test, with small differences for slab deflections and reaction forces and

significant differences in reinforcement strains. In conclusion the analysis results show that with today’sexplicit FE solvers it is possible to predict the overall outcome of missile impact tests with flexural fail-ure quite accurately in terms of missile deformation and slab damage. Good agreement in time series ofphysical properties, like slab deflections, slab reaction forces and reinforcement strains, can be achieved,but remains challenging due to the stochastic nature of the tests and the limitations in FE modellingapproaches.

. Introduction

The safety of nuclear power plant (NPP) containments againsthe impact of aircrafts was considered since the design phase of

ost of today’s operating nuclear power reactors (Riera, 1968).mpirical formulas were and are still used to estimate the effects of

ircraft impacts on containment buildings of NPPs, mainly the pen-tration depth of an aircraft or other missile into the containmentsuilding (an overview on empirical formulas was provided by Li

∗ Corresponding author. Tel.: +31 224 56 5375; fax: +31 224 56 5637.E-mail addresses: oliver.martin@jrc.nl (O. Martin), vcentro@altair.com

V. Centro), schwoertzig@altair.com (T. Schwoertzig).1 Tel.: +33 1 41 33 09 92; fax: +33 1 41 33 09 91.

029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2012.02.001

© 2012 Elsevier B.V. All rights reserved.

et al. (2005)). In parallel, first numerical analyses were carried outusing finite difference or finite element (FE) approaches. The mod-els used for these numerical analyses were rather coarse comparedto today’s standards, because of the computational limitations atthat time. Also, simplifications had to be made in the modelling pro-cess, especially in the constitutive models and the geometry. Theeffects of aircraft impacts on NPP containment structures were alsoassessed experimentally in a number of impact tests, either smallscale tests on laboratory scale or large scale tests involving missilesand concrete slabs of considerable sizes and mass. The most notableof these large scale tests are the Meppen Slab Tests (Jonas et al.,

1979; Nachtsheim and Stangenberg, 1982, 1983; Rüdiger and Riech,1983) and the Tests at Sandia National Laboratory (Sugano et al.,1993). In both a series of missiles resembling the bodies and/orengine shafts of mostly military aircrafts were impacted on large

2 eering and Design 247 (2012) 1– 10

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2

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K1

K3

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550

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O. Martin et al. / Nuclear Engin

einforced concrete slabs resembling NPP containment buildings.n addition numerical analyses were performed on the two testeries with the aim of predicting their outcome.

Since a couple of years there is a re-emerging interest inside theuclear community for the issue of safety of nuclear power plantontainments against aircraft impacts. Also, the computational pos-ibilities to perform numerical missile impact analyses today areare greater compared to the 1970s and early 1980s, when thebove mentioned large scale impact tests were performed. In 2009he Nuclear Energy Agency (NEA) of the Organisation for Economicooperation and Development (OECD) together with the “Institute Radioprotection et de Sûreté Nucléaire (IRSN)”, France called for

benchmark project on computational missile impact analyses ononcrete containment structures. The benchmark project with theame “Improving the Robustness of Assessment Methodologies fortructures impacted by Missiles (IRIS)” was carried out within theSubgroup on Concrete” of the “Working Group on the Integritynd Ageing of Components and Structures (IAGE)” of the NEA andasted for the complete year of 2010. Its aim was to investigate to

hat extend today’s numerical methods are capable of predictinghe outcome of missile impact tests. Each participant was asked toerform numerical analyses on three different missile impact tests,n one of the Meppen Slab Tests (the 4th test of the 2nd series ofhe Meppen Slab Tests) and on two new missile impact tests per-ormed at the Technical Research Centre of Finland (VTT) during theenchmark project. The use of a wide range of different solvers andethodologies for the numerical analyses was envisaged. The Joint

esearch Centre (JRC) in Petten, the Netherlands participated in theenchmark project together with a contractor, Altair Engineeringrance, Antony, France. This paper describes the numerical analy-es on the Meppen Slab Test performed by JRC/Altair Engineeringsing the explicit solver RADIOSS (Altair Engineering, 2009), includ-

ng a detailed description of the modelling approach and in-depthomparison between numerical and experimental results.

. The Meppen Slab Tests

In order to assess the safety of containment buildings of GermanPP against possible impacts from military aircrafts the compa-ies HOCHTIEF (construction company) and SIEMENS performed

number of missile impact tests in the period from 1976 to 1982

able 1verview of 2nd series of Meppen Slab Tests (Rüdiger and Riech, 1983).

No. Missile Slab thickness [cm]

Mass [kg] Impact velocity [m/s]

II/1 1014 247.6 70

2 1016 172.2 ′′

3 992 217.9 70 (2nd shot on plate n4 1016 247.7 ′′

5 974 234.8 ′′

6 956 257.6 ′′

7 940 225.3 ′′

8 990 235.9 ′′

9 970 235.8 ′′

10 965 245.6 90

11 1000 222.5 70

12 980 241.5 ′′

13 996 244.8 ′′

14 960 247.9 ′′

15 1000 236.3 50

16 970 247.1 70

17 954 178.4 50

18 1060 237.4 70

19 980 240.3 ′′

20 972 197.7 50

21 1000 237.0 90

Fig. 1. Dimensions and mounting points of the reinforced concrete slab of the Mep-pen Slab Tests (GRS, 2010) (filled points indicate mounting points with devices tomeasure slab reaction forces).

near the town of Meppen, Germany known as the Meppen SlabTests (Jonas et al., 1979; Nachtsheim and Stangenberg, 1982, 1983;Rüdiger and Riech, 1983). Two series of tests were performed. Inthe first series deformable missiles were impacted against quasi-rigid targets in order to validate load curves that were generated inthe course of the tests (Nachtsheim and Stangenberg, 1982, 1983;Rüdiger and Riech, 1983). Load curves are curves displaying theimpact force of a missile on a target versus time (Riera, 1968). Theyare widely used in numerical analyses of missile impact problems,especially when large models with a high number of degrees of free-dom are involved. In the second series deformable missiles wereimpacted into reinforced concrete slabs of rectangular shape with

the dimensions 6.5 m × 6 m as shown in Fig. 1. The thickness of theconcrete slabs was 70 cm for most tests of the 2nd series, whereas in a limited number of cases slabs of 50 cm or 90 cm thicknesswere used. Table 1 lists all the tests of the 2nd series including the

Results slab

Penetration depth front [cm] Plastic deformation on theback side [cm]

25 30 (spalling)2 No cracks

o. 2) Perforation4 5 (cellular cracks)Perforation5–15 15 (spalling)5 12 (cellular cracks)7 4 (cellular cracks)4 4 (cellular cracks)4 2 (no cracks)9 5 (cellular cracks)7 5 (cellular cracks)Perforation30 35 (spalling)Perforation20 16 (spalling)11 12 (spalling)13.5 11 (spalling)Perforation22 15 (spalling)8 Cracks, minor spalling

O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10 3

700

640

Back

Frontd = 20

d = 28

200

d = 20

R 70

s in the Meppen Tests (IRSN, 2010; GRS, 2010).

i(

ptvfnm14

sdatwof

cToaptsf

ibmmtt

c

Fig. 2. Reinforcement of the concrete slab

ndividual slab and missile characteristics and test resultsNachtsheim and Stangenberg, 1982; Rüdiger and Riech, 1983).

As indicated in Fig. 2 each concrete slab had two layers of per-endicular steel reinforcements, one at the front surface and one athe back surface. Both layers of reinforcements were “connected”ia transverse reinforcements (often also referred to as shear rein-orcements). The reinforcements were made of mild steel (Germanotation BSt 420/500 RK). The exact density of the slab reinforce-ents for each test can be found in (Nachtsheim and Stangenberg,

982; Rüdiger and Riech, 1983). Each concrete slab was mounted in8 points located on the backside of each slab as indicated in Fig. 1.

The missiles used in the Meppen Slab Tests were deformableteel cylinders with a total length of approximately 6 m, an outeriameter of 600 mm and varying wall thicknesses between 7 mmnd 20 mm (Rüdiger and Riech, 1983). Fig. 3 shows the geome-ry of a typical missile for the Meppen Slab Tests. Each missileas made of mild steel (German notation St37) and had a mass

f approximately 1 tonne. Initial velocities of the missiles variedrom 172.2 m/s to 257.6 m/s (see Table 1).

For the IRIS Benchmark Project the 4th test of the 2nd series washosen for numerical analyses, hereafter referred to as Meppen-II-4est. In this test a missile as displayed in Fig. 3 with an overall massf 1016 kg and an initial velocity of 247.7 m/s was impacted against

concrete slab of the above described design. Concerning its failureattern, the Meppen-II-4 Test can be regarded as a flexural failureest. In principal there are two failure modes for concrete reinforcedlabs impacted by a missile, flexural failure and punching shearailure. Both failure modes are displayed in Fig. 4.

At flexural failure the reinforced concrete slab bends follow-ng the impact of the missile, causing tension loading on theackside of the concrete slab. The tension loading leads to the for-ation of cracks in thickness direction of the concrete slab, whichight penetrate deeply into the reinforced concrete slab leading

o scabbing, i.e. falling off of concrete particles on the backside ofhe slab.

Punching shear failure is a failure mode where a so-called shearone is punched out of the concrete slab due to the impact of a

Stee l plate d = 580, t = 20

Steel plate d = 607, t = 40

Tube d = 580, t = 20

Tube d = 600, t = 10

3000300

5

Fig. 3. Missile used in the Meppen Slab Tests

Fig. 4. Basic failure modes: (a) flexural failure and (b) punching shear failure.

missile. A shear cone normally always develops inside a concreteslab that is impacted by a missile. The shear cone marks locations ofincreased shear stresses. If these reach a significant magnitude theshear cone may punch out of the concrete slab leading to punchingshear failure.

The likelihood for one of the failure modes to occur ratherthan the other depends upon the design characteristics of concreteslab and missile. Strong, dense reinforcements and the presenceof transverse reinforcements make flexural failure more likely.Weaker, less dense reinforcements and the absence of any trans-verse reinforcements make punching shear failure more likely.Deformable missiles, i.e. steel pipes, promote flexural failure, whereas hard missiles promote punching shear failure. Also the initialvelocity of the missile is of certain relevance. Lower initial veloc-ities increases the likelihood of flexural failure, where as higherinitial velocities make punching shear more likely.

The outcomes of the Meppen-II-4 Test, i.e. damage pattern andoverall behaviour of the slab, make it a flexural failure test. Whatmakes the test remarkable is that the values for the mass and initialvelocity of the missile are among the highest of all tests of the 2nd

series, which might induce high shear stresses in the concrete slaband thus promote punching shear failure. These considerations andthe actual outcomes of the Meppen-II-4 Test lead to the decision toinclude it in the IRIS Benchmark Project.

Tube d = 600, t = 7

Nose t = 5

2500 130

990

(Rüdiger and Riech, 1983; IRSN, 2010).

4 O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10

conc

3

3

ustmcrtspect

tisbst7ct

rasiatt

Fig. 5. FE mesh of reinforced

. Finite element modelling approach

.1. FE meshes

The explicit FE solver RADIOSS (Altair Engineering, 2009) wassed for all the analyses. The reinforced concrete slab and the mis-ile are modelled using Lagrangian meshes. The concrete part ofhe slab is modelled with three dimensional (3D) linear brick ele-

ents with reduced integration. Full geometric non-linearities ando-rotational formulation are activated in order to ensure accurateesponse of the FE model towards the expected large deforma-ions and rotations. The artificial bulk viscosity is set to zero. Theteel reinforcements are modelled with linear beam elements withroper inertia and cross section definitions. The nodes of the beamlements are merged with the nodes of the brick elements of theoncrete. Fig. 5 shows the model of the reinforced concrete slab andhe beam elements of the steel reinforcements.

The average element size of the brick elements is 35 mm. Aroundhe beam elements the hexahedron mesh for the concrete is refinedn order to enable uniform distance between the rebars (elementize: 22 mm). The hexahedron mesh for the concrete contains 22rick elements in thickness direction of the slab, which providesufficient accuracy. In total the FE model of the concrete slab con-ains 727,584 brick elements and 61,440 beam elements giving69,143 nodes. It is simply supported on its backside at nodes whichorrespond to the mounting points of the concrete slab in the realest (see Fig. 1).

The missile is modelled with four noded shell elements ofeduced integration. Hourglass physical stabilisation is enabled tovoid unnecessary build-up of hourglass energy during the analy-es. Fig. 6 shows the mesh of the missile. The average element size

s 20 mm. In total the mesh of the missile contains 30,132 elementsnd 30,038 nodes. The mass densities of the different sections ofhe mesh of the missile are adjusted so that the mass of each sec-ion agrees to the corresponding section of the real missile used in

Fig. 6. FE mesh of

rete slab and reinforcement.

the test. In preliminary FE analyses the FE model of the missile isimpacted against a rigid surface in order to validate the quality ofthe mesh, the failure modes and to receive a rough estimate for theduration of the analyses.

3.2. Constitutive models

The constitutive behaviour of the concrete is described withthe material model of Han and Chen (1985). It is non-uniformhardening plasticity model and can be regarded as a Drucker-Prager/Cap model (Chen, 2007). The material model of Han andChan was designed to model the constitutive behaviour of rein-forced concrete under high impact loading. It is the standardmaterial model for pre-stressed concrete in the FE solver RADIOSS(Altair Engineering, 2009).

The material model of Han and Chen is characterised by a tri-axial open failure envelope with a closed yield envelope (cap)inside. Fig. 7a shows failure and yield envelope. The constitutivemodel allows for anisotropic plasticity and hardening, where asthe underlying hardening rule is non-uniform. Behaviour in ten-sion and compression are different and failure is achieved either bytensile cracking (brittle fracture) or compressive crushing. Fig. 7bshows the stress–displacement curve. The material model of Hanand Chen accounts for opening and closure of cracks, volumet-ric dilatation under compression and sensitivity of shear stressestowards different states of compression (pressure sensitivity).

The material model of Han and Chen contains in total 24 mate-rial parameters, but normally only the basic material properties areknown, e.g. Young’s modulus, Poisson ratio, etc. These are normallydetermined from standard uni-axial material tests or other rathersimple material characterisation tests invloving cubic or cylindrical

test specimen. In RADIOSS the material model of Han and Chan isimplemented in such a way that with five basic material parame-ters the constitutive behaviour of concrete can be fully described.These five material parameters are the initial mass density, Young’s

the missile.

O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10 5

and y

msmstiEuupcFTw

edmFwt

TM

The Johnson–Cook parameters (a, b, and c) were extracted fromstress–strain curves of tensile tests that were distributed to the

Fig. 7. Constitutive model for concrete: (a) failure

odulus, Poisson ratio, uni-axial compression strength and tensiletrength. The remaining material parameters are then either esti-ated out of these five basic parameters inside the FE code via

tandard default ratios or other relationships or default values areaken (Altair Engineering, 2009). This is also the approach whichs adopted for all the numerical analyses performed by JRC/Altairngineering within the IRIS Benchmark project, because only val-es for the initial mass density, Young’s modulus, Poisson ratio,ni-axial compression strength and tensile splitting strength wererovided to the benchmark participants. The tensile strength can bealculated from the latter and the tensile tangent modulus Ht (seeig. 7b), for which a default value of Ht = −3000 MPa is assumed.able 2 lists the main material properties for the concrete as theyere taken for the FE analysis presented in this paper.

For the brick elements that are directly attached to the beamlements representing the reinforcements a tensile strength valueifferent to the one in Table 2 is chosen. The steel reinforce-

ents inside the real concrete slab occupy a certain volume. In the

E model the reinforcements are modelled with beam elements,hich do not take away volume of the brick elements resembling

he concrete. The consequence is an overestimation of concrete

able 2ain material properties of the concrete.

Material property Value

Initial density � [kg/m3] 2400Young’s modulus E [MPa] 29,053Poisson coefficient � 0.2Uniaxial compressive strength fC [MPa] 37.2Tensile strength fT [MPa] 4.8

ield envelopes and (b) stress–displacement curve.

volume in the FE model that could lead to an unrealistic build-upof crack energy in the FE model for the concrete slab. To avoid this,the tensile strength for the brick elements directly attached to thebeam elements is raised by a factor of 4 compared to the normalvalue. Experience has shown this factor to be adequate.

For the steel reinforcements isotropic elastic–plastic deforma-tion behaviour with strain hardening is assumed. A Johnson–Cookmodel is used to model the constitutive behaviour of the steelreinforcement with identical hardening curves for tension andcompression. The Johnson–Cook model assumes a power type rela-tionship between true stress and plastic strain (Johnson and Cook,1985):

� = (a + bεnp)

(1 + c ln

ε̇

ε̇0

)(1)

benchmark participants (IRSN, 2010). Table 3 lists the extracted

Table 3Main material properties of the steel reinforcements.

Material Property Value

Initial density � [kg/m3] 7800Young Modulus E [MPa] 210,000Poisson coefficient � 0.3Yield coefficient a [MPa] 430Yield coefficient b [MPa] 560Yield exponent n 0.4Strain rate coefficient c 0.01Reference strain rate [1/s] 0.001

6 O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10

Table 4Tabular function for the stress–strain curve of the mild steel of the missile.

Plastic Strain [×10−3] Stress [MPa]

0.000 286.00.313 295.00.946 308.41.716 322.02.838 340.64.203 360.35.658 378.16.764 390.18.136 400.09.254 407.4

10.475 411.8

Fd

Jvori

bcstaciipbsf

3

fb

TM

Table 6Scale factors to account for strain-rate effects in the deformation of the missile.

Strain rate [1/s] Scale factor

0.001 1.0001 1.311

10 1.414

results.The prediction of test results related to the concrete slab by

the analysis was expected to be more difficult. Fig. 12 shows thedamage pattern on the back side of the reinforced concrete slab

35Strain energy Kinetic energy Hourglass energy

ig. 8. Assumed stress–strain curve for the mild steel of the missile with linearamage function in the tensile regime.

ohnson–Cook parameters. Because the Johnson–Cook model pro-ides no maximum stress for the material involved, necking canccur during the FE analyses if a sufficiently high strain level iseached. To avoid any uncontrolled rise in stresses related to neck-ng during the analyses a maximum stress level is set.

Also, for the missile isotropic elastic–plastic deformationehaviour with strain hardening is assumed. The stress–strainurve is defined as a tabular function containing pairs of associatedtress and strain values, which have been extracted from curves dis-ributed to the benchmark participants (IRSN, 2010). Table 4 list thessociated stress and strain values for the tabular function. Identi-al stress–strain curves are used for tension and compression, butn the tensile regime a linear damage model is included as indicatedn Fig. 8. Table 5 lists the basic material properties together with thearameters of the damage model. Strain-rate effects are consideredy applying scale factors to the basic stress–strain curve (= curve attrain-rate 0.001 s−1). Table 6 lists the used scale factors to accountor strain-rate effects.

.3. Contact definitions

A general contact algorithm based on the penalty method is usedor the interaction between missile and concrete slab. The contactetween concrete slab and missile is defined as a nodes-to-surface

able 5ain material properties for the missile.

Material property Value

Initial density � [kg/m3] 7780Young modulus E [MPa] 210,000Poisson coefficient � 0.3Yield stress [MPa] 286.0Maximum plastic strain 0.72Tension failure strain 1 0.70Tension failure strain 2 0.71

100 1.5181000 1.622

contact. The contact domain covers all exterior element faces of theslab (master surface) and the nodes of the missile (slave nodes).A possible interaction between beam elements for the reinforce-ments is considered via edge-to-edge contact.

Self-contact of missile is included in the model. Severely rup-tured elements at the interfaces are removed during the analysis toprevent high velocity impacts of their nodes into other elements.Another self-contact includes the first layers of solid elements onthe front side of the slab in order to limit large compressive distor-tions of elements in the impact zone. All contacts are assumed tobe friction free.

4. Results

Fig. 9 shows the energy balance of the analysis. The initial kineticenergy of the missile is entirely transformed into strain energyof concrete slab and missile, which is a realistic result for flexu-ral failure tests. The hourglass energy is negligible compared tothe physical energies (kinetic + strain energy) indicating that theanalysis ran numerically smooth and that the analysis results arephysically meaningful.

Fig. 10 displays the deformed missile according to the analy-sis. The front section of the missile is totally compressed together.The analysis gives a length of 1500 mm for the undeformed partof the missile, which is in good agreement with the test resultswhere the undeformed part laid in the range between 1450 mmand 1540 mm (IRSN, 2010). Fig. 11 shows the velocity of the rearpart of the missile versus time for test and analysis. Until 15 msboth curves are in perfect agreement. For the time afterwards theanalysis slightly underestimates the missile velocity compared tothe real test. According to the analysis, the duration of the impactprocess is 26 ms compared to 33 ms in the real test (= time to bringthe missile down to zero velocity). In summary the analysis resultsrelated to the missile are in very good agreement with the test

0

5

10

15

20

25

30

0.00 20.00 40.00 60.00 80.00 100.00 120.00Time [ms]

Ener

gy [M

J]

Fig. 9. Energy balance of the analysis.

O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10 7

Fig. 10. Deformed missile according t

-50

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

Time [ms]

Velo

city

[m/s

]

Test FE Analysis

ftrtacic

W8 lies on the edge of the deformed zone on the backside of the

Fig. 11. Missile velocity versus time.

ollowing the impact of the missile, both for the analysis and theest (GRS, 2010). Red areas in the pattern for the analysis indicateegions of high damage (cracked material). When comparing thewo crack patterns one can see that analysis and test are in goodgreement. The crack pattern of the concrete slab from the test with

racks starting at the centre of the slab proceeding to the slab edgess clearly resembled by the FE model. Also, the shear cone inside theoncrete slab is visible in the analysis results as Fig. 13 shows.

Fig. 12. Damage pattern of the reinforced concret

Fig. 13. Damage pattern inside the reinforced concrete slab: (top) analysis, (

o analysis (left) and test (right).

During the test the deflection of the slab at various positionson the slab’s backside was measured. Fig. 14 shows these posi-tions (GRS, 2010). Fig. 15 displays the measured (taken from GRS(2010)) and calculated deflections versus time for position W6. Theamplitude of the calculated deflection is higher than the one forthe measured deflection, but the residual deflections of the slab(remaining permanent deflection after the impact) both calculatedand measured are relatively close to each other. The frequency ofthe time serial of the measured deflection is slightly higher thanthe one of the analysis, but complete agreement in frequency isdifficult to achieve, due to the stochastic nature of the test results.Considering this one can conclude that there is good agreementconcerning slab deflection at position W6.

Fig. 16 displays the measured (taken from GRS (2010)) and cal-culated deflections versus time for position W8. The amplitude ofthe calculated deflection is significantly higher than for the mea-sured one compared to W6. The fact that the amplitudes of themeasured deflections are smaller than the ones from the analysiscan be explained by the neglected damping of the concrete in theFE model. Also, the difference in residual deflections is more sig-nificant for deflection W8. From Fig. 12b it is visible that position

concrete slab (“Grenze der aufgebauchten Zone”, dashed line), andtherefore experiences limited deflection in the test. However, theanalysis delivers a smooth distribution of the slab deflection along

e slab: (a) analysis and (b) test (GRS, 2010).

bottom) test (GRS, 2010), (left) horizontal cut, and (right) vertical cut.

8 O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10

2550 2550 700 70012

0060

060

012

0012

0012

00

W6

W4

W2

W8

W1

W3

W5

W7

Fig. 14. Deflection measurement positions on backside of slab (GRS, 2010).

-20

-10

0

10

20

30

40

50

60

70

0 20 40 60 80 10 0 12 0

Dis

plac

emen

t [m

m]

Test FE Ana lys is

-20

-10

0

10

20

30

40

50

60

70

0 20 40 60 80 10 0 12 0

Dis

plac

emen

t [m

m]

Test FE Ana lys is

ifd

osss

Test FE Ana lys is

-60 0

-40 0

-20 0

0

200

400

600

800

1000

1200

0 20 40 60 80 10 0 12 0

Time [ms]

Forc

e [k

N]

Time [ms]Time [ms]

Fig. 15. Slab deflection at position W6.

ts height and width and thus overestimates the residual deflectionor W8. Like for W6 the frequency of the time series of the measuredeflection is higher than the one for the analysis.

In addition to the slab deflections the reaction forces at some

f the slab mounting points were measured during the test. Fig. 1hows the mounting points for which the reaction force was mea-ured (GRS, 2010). Fig. 17 shows the measured and calculated timeeries of the reaction force K4 (measured values taken from GRS

Test FE Ana lys is

-5

0

5

10

15

20

25

30

35

0 20 40 60 80 10 0 12 0

Time [ms]

Disp

lace

men

t [m

m]

Fig. 16. Slab deflection at position W8.

Fig. 17. Reaction force at mounting point K4.

(2010)). Until 35 ms during the impact process measured and cal-culated reaction force are in very good agreement. Afterwards thecalculated amplitudes are higher than the measured ones. The fre-quency of the measured time serial is higher than the one for thecalculated time serial following the trend that has been observedalready for the slab displacements.

The relation between measured and calculated time series forthe reaction force at mounting point K6 is similar, as Fig. 18shows. Until 37 ms both curves are in very good agreement.Afterwards the curves deviate with the calculated one havinga larger amplitude and lower frequency compared to the mea-surement curve. After 90 ms both curves seem to be in perfectagreement.

During the Meppen-II-4 Test the strains at various locations ofthe front and back reinforcements were measured. For this purposea number of strain gauges were attached to the reinforcements atthe front and back of the concrete slab as indicated in Fig. 19 (GRS,2010). Fig. 20 displays the measured and calculated strains versustime at Gauge D6. Both curves have a similar shape, but the calcu-lated strains are higher than the measured one for the whole lengthof the time series. The same trend could be observed for the strainsof all the other gauges at the front reinforcement. The reason for thehigher calculated strains is that the beam elements resembling thereinforcements are only connected in their nodes to the surround-ing brick elements for the concrete allowing them to move more

freely compared to reality. In the real concrete slab the reinforce-ments are embedded into the concrete reducing the movementof the reinforcements. Also friction between reinforcements and

-400

-300

-200

-100

0

100

200

300

400

500

600

700

0 20 40 60 80 100 120

Time [ms]

Forc

e [k

N]

Test FE Analysis

Fig. 18. Reaction force at mounting point K6.

O. Martin et al. / Nuclear Engineering and Design 247 (2012) 1– 10 9

Fig. 19. Position of strain gauges to measure

sav

fshom

Fig. 20. Strain in front reinforcement at Gauge 6.

urrounding concrete is likely to occur in real slab tests. This is notccounted for in the FE model resulting in larger calculated strainalues in the reinforcements compared to the test.

Fig. 21 shows the measured and calculated strains versus timeor Gauge D18 on the reinforcement of the backside of the concretelab. Also here the magnitude of the strains from the analysis is

igher than the one of the measurements. This trend could also bebserved for all the other strain gauges on the backside reinforce-ent of the slab.

Fig. 21. Strain in rear reinforcement at Gauge 18.

strains in reinforcements (GRS, 2010).

5. Summary and conclusions

In this paper the numerical analyses on the Meppen-II-4 Testby JRC/Altair Engineering using the explicit solver RADIOSS (AltairEngineering, 2009) were described, including a detailed descrip-tion of the modelling approach and an in-depth comparisonbetween numerical and experimental results. The described anal-yses were part of the JRC contribution to the Benchmark Project“Improving the Robustness of Assessment Methodologies for Struc-tures impacted by Missiles (IRIS)” organised within the “Subgroupon Concrete” of the “Working Group on the Integrity and Age-ing of Components and Structures (IAGE)” of the “Nuclear EnergyAgency (NEA)” of OECD. A modelling approach with complete 3DLagrangian meshes for missile and concrete slab, without use ofsymmetry conditions, was chosen. The concrete was modelledwith linear brick elements of reduced integration and the steelreinforcements inside the concrete slab was modelled with beamelements with proper cross section definitions. The missile wasmodelled with four noded shell elements of reduced integration.Special emphasis was put on the constitutive modelling of all thematerials involved. A special Drucker-Prager/Cap model, the mate-rial model of Han and Chen, was used to model the constitutivebehaviour of the concrete. Isotropic elastic–plastic hardening withpartial strain-rate dependencies, where appropriate, was assumedfor steel reinforcements and the missile. The description of the con-stitutive behaviour of the metallic parts in the used FE code was inthe form of Johnson–Cook models or tabular functions.

The energy balance of the analysis is physically sound for a flex-ural failure test like the Meppen-II-4 Test. The deformation of themissile in real test is resembled correctly by the analysis. The crackpattern of the impacted slab provided by the FE model resem-bles the crack pattern of the test. The shear cone that is typicallyinduced in a concrete slab impacted by a missile is clearly visiblein the FE mesh of the concrete slab and its dimensions agree wellwith the dimensions of the shear cone from the real test. Morein-depth comparison between analysis and test were performedby comparing measured and calculated time series for slab deflec-tions, reaction forces in the slab mounting points and strains ofthe slab reinforcements. The frequencies of the time series fromtest are higher than the ones for the analyses for all three proper-ties. The amplitudes of the calculated slab deflections are in generalhigher than the amplitudes of measured slab deflections, because

of the neglected damping of the concrete in the analysis. Never-theless, good agreement between measured and calculated slabdeflections could be achieved for most locations inside the sig-nificantly deformed zone of slab in the test. The time series for

1 eering

tcptsonbc

Fibttcti

A

tMStttCI

impact of deformable missiles onto reinforced concrete slabs. In: Transactionsof the 7th SMiRT Conference, Chicago, Paper No. J8/3.

Sugano, T., et al., 1993. Local damage to reinforced concrete structures caused

0 O. Martin et al. / Nuclear Engin

he reaction forces are generally in very good agreement, espe-ially until the 35 ms, counting from the beginning of the impactrocess. There was a slight tendency of the calculated amplitudeso be higher than the measured ones for the rest of the timeeries. Concerning the strains in the reinforcements the analysisverestimates the measured strains from the tests, because of theeglect of embedding of the reinforcements into the concrete andecause of the neglect of friction between reinforcement and con-rete.

In conclusion, the analysis results show that with today’s explicitE solvers it is possible to predict the overall outcome of missilempact tests with flexural failure quite accurately in terms of energyalance, missile deformation and slab damage. Good agreement inime series of physical properties, like slab deflections, slab reac-ion forces and reinforcement strains, can be achieved, but remainshallenging due to the stochastic nature of the tests and the limi-ations in FE modelling approaches (embedding of reinforcementsn concrete, etc.).

cknowledgements

The authors would like to thank the organising committee ofhe IRIS Benchmark Project, i.e. Mr. Jean-Mathieu Rambach (IRSN),

r. Francois Tarallo (IRSN), Mr. Nebojsa Orbovic (Canadian Nuclearafety Commission) and Mr. Alejandro Huerta (OECD-NEA), for allheir efforts in organising the benchmark project and providing

he basic test data. The authors would also like to thank Mr. Chris-ian Heckötter from “Gesellschaft für Reaktorsysteme (GRS) mbH”,ologne, Germany for providing a detailed report on the Meppen-

I-4/5 Tests for the benchmark participants.

and Design 247 (2012) 1– 10

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