1

Impact loaded reinforced concrete structures,

numerical and experimental studies

Arja Saarenheimo *

*VTT Technical Research Centre of Finland

Co-authors: Kim Calonius*, Ilkka Hakola*, Ari Vepsä* and

Markku Tuomala (Tampere University of Technology)

BULATOM Conference, 5th – 7th June, 2013

Riviera Holiday Club, Varna, Bulgaria

2 28/05/2013

Osa 7: Luento 7.6, Arja Saarenheimo, VTT, 29.11.2011

Aircraft crashes considered in designing

modern nuclear power plants

Penetration of fuel tanks inside the building

• structural integrity of the impact loaded reinforced

concrete wall

• loading due to an aircraft crash

Fuel release and spreading from disintegrating tanks =>

• combustion of dispersed and vaporized fuel

• debris and missiles due to impact

Floor response spectra due to excited vibrations

Numerical methods need to be verified

against experimental data

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0 0.002 0.004 0.006 0.008 0.01 0.012

LOAD

Introduction

2

3 28/05/2013

Numerical analysis

The main aim is to validate, develop and take in use numerical

methods and models for predicting response of large scale reinforced

concrete structures to impacts of projectiles that may contain

combustible liquid (i.e. fuel).

Structural behavior, in terms of collapse mechanism type and

damage grade, is predicted both by simple analytical methods and by

more involved non-linear FE models.

Fuel spreading and fire risk associated with impacts are also

predicted by suitable analytical and numerical methods.

In order to obtain reliable numerical results, the methods and models

have to be verified against experimental data based smaller scale

tests

Medium scale impact tests carried out at VTT within IMPACT

projects are used for this purpose.

4 28/05/2013

Test apparatus

Concrete wall

Acceleration tube

v

Pressure

accumulator

p = 5 - 20 bar

L1 = 12 m L2 = 13.5 m

Missile

0.5 m m

Piston catcher

Back

pipes

Kickback

support

Bedrock

Piston

Steel frame

Capacity

Maximum impact velocity depends on the mass of the missile, e.g. 160 m/s

(~450 km/h) with a 50 kg missile.

Maximum dimensions of the wall to be tested: 2.1*2.1*0.25m.

32 measurement channels available for measurement as a function of time.

Plans are to increase both the dimensions of the walls (up to 3.5*3.5 m) and

the impact velocity with structural modifications made for the apparatus and

premises in 2013.

Testing capacity: ~30 walls/year.

3

5 28/05/2013

Measurements

Strains in reinforcement with

strain gauges

Horizontal support forces on the

support pipes

Velocity of the missile with lasers

Lasers

Additionally:

Tension forces are measured on some of the

tensioning bars in a case of pre-stressed walls.

The impact is documented with 3 high shutter

speed video cameras taking 1000 frames per

second.

Velocity of the missile after it has gone through

the wall is estimated.

Scabbing and spalling areas of concrete are

measured.

Impact forces

in force plate

tests

Force

transducers

Strains on the front surface of the wall

Displacements

Displacement

sensors

Strain gauges

6 28/05/2013

Aircraft parts divided on the basis of loading they cause

Fuselage (body of the aircraft)

• Much more deformable than the structure it

collides against (soft missile)

(Semi)hard parts: engines,

landing gear and turbine shaft

• Less deformable than the structure it

collides against (hard missile)

Fuel tank(s)

• Fires

Wings

• “Knife effect”

4

7 28/05/2013

Studies on reinforced concrete walls impacted by deformable and

hard missiles

Different types of collapse mechanisms are involved in

Bending

Punching

Combined bending and punching

Different kinds of analysis methods are needed

8 28/05/2013

Bending behavior test Soft missile, 250mm, m~50kg

150 mm thick wall, simply supported in 2

directions, impact velocity about 109 m/s

5

9 28/05/2013

Back surface of the wall

10 28/05/2013

Verification of numerical calculation models and methods for

deformable missile impacts

Nonlinear material behaviour: tensile cracking and compression crushing of

concrete, yielding of reinforcement

Two types of analyses:

1) Finite Element Method (FEM) with Abaqus/Explicit code

2) Simplified calculation methods with a two degrees of freedom model (TDOF)

Sensitivity studies on:

1) tensile cracking assumptions

2) shape of the loading function

6

11 28/05/2013

Deformable (soft) missile

The colliding object is considered to be much more deformable than the object it collides

against

In testing this loading type is simulated by using a thin walled steel or aluminium pipe

Force-time functions can be predicted by Riera method

Causes

large displacements with possible yielding of bending reinforcement

possible shear punching failure (shear cone formation)

vibrations of the structure, floor response spectra for further analyses of structures

Response prediction with numerical methods

Bending test with a soft missile

simulating the fuselage

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0 0.002 0.004 0.006 0.008 0.01 0.012

LOAD

Measured loading curve from one

soft missile test

Approximate

Riera curve

Simulated (FE) and estimated (Riera)

loading curve for one soft missile test

12 28/05/2013

Structural behaviour - FE simulations

Soft missile test

Soft missile impact simulation with impact force.

The missile after the test.

Above: FE simulation.

Below: Test.

Missile mass=50.12 kg

Missile material: stainless steel

Impact velocity=102.2 m/s

FP8

0,0E+00

5,0E+05

1,0E+06

0 0,005 0,01 0,015 0,02 0,025

Time (s)

Fo

rce (

N)

Meas

Riera

FEM

50 per. Mov. Avg. (FEM)

50 per. Mov. Avg. (Meas)

Simulated (FE), estimated (Riera method) and

measured impact force.

7

13 28/05/2013

Prediction of loading function due to missile impact

1) Finite element method

2) Riera method assuming folding visco-plastic crushing mechanism

3) Curved/straight folding model: stretching and bending energies of the cylindrical

shell are taken into account in computing the crushing force and rotationally

symmetric deformation mode is assumed. Strain hardening and strain rate

sensitivity are also taken into account.

Deformation at the end of folding cycle

(wall center line) Folding mechanism consisting of circular

arcs and straight elements

14 28/05/2013

Loading due to a deformable missile

by the Riera formula

When a deformable missile collides with a rigid target, the impact load can be thought to be composed of two different parts.

1) The main component is due to the mass flow

- mass distribution m(x) kg/m

2) An other part of the impact force is due to the crushing force of the missile.

In the case of an aircraft crash the mass flow contribution is the dominant part.

2

c mF(t)=P (x(t))-m(x(t))(v (t)) ,

8

15 28/05/2013

Bending wall test

•stainless steel missile

•t = 2mm, L = 2m

•Mass 50.5 kg

•v= 110 m/s

• 2m by 2 m slab, wall thickness 0.15 m,

•bending reinforcement 6c/c 55

•shear reinforcement 44 cm2/m2

16 28/05/2013

Load functions

The load functions calculated by the Riera method and with the curved/straight folding

model

Riera method: folding visco-plastic crushing mechanism

E=210 GPa, sy =410 MPa, r =7850 kg/m3

Cowper-Symonds 1-D visco-plastic model, D=1522 1/s and q=5.13.

0,00E+00

5,00E+04

1,00E+05

1,50E+05

2,00E+05

2,50E+05

3,00E+05

3,50E+05

4,00E+05

0 0,005 0,01 0,015 0,02 0,025

Time (s)

Fo

rce

(N

)

9

17 28/05/2013

Crushed missile

Crushed length

Test (2111-(970+940)/2=1156mm)

0

0,2

0,4

0,6

0,8

1

1,2

0 0,005 0,01 0,015 0,02

Time (s)

Cru

sh

ed

len

gth

(m

)

The predicted crushed length value agrees well with the test result

18 28/05/2013

Sensitivity studies on loading function alternatives

0,00E+00

1,00E+05

2,00E+05

3,00E+05

4,00E+05

5,00E+05

6,00E+05

7,00E+05

8,00E+05

9,00E+05

1,00E+06

0 0,005 0,01 0,015 0,02 0,025

Time (s)

Fo

rce

(N

)

F_fvp

FOLD_A

FOLD_B

•FOLD_A and FOLD_B are calculated with the

curved/straight folding model.

•The shape of folds is assumed to consist of

straight and circular parts.

•The stretching and bending energies of the

cylindrical shell are taken into account in

computing the crushing force and a

rotationally symmetric deformation mode is

assumed.

•Strain hardening and strain rate sensitivity

are taken into account.

•FOLD_B was tuned in order to obtain the

same duration for the loading pulse as was

obtained with the Riera method for the curve

F_fvp

10

19 28/05/2013

Final shape of the missile, FOLD_A

Number of the folds was 23-24.

In the test the number of the folds was 22

20 28/05/2013

1) Finite element model

•One quarter model

•Four noded shell elements with reduced integration

•Loaded area determined by assuming a load spreading

angle of 45o in the slab thickness direction

•Reinforcement is modelled as layers

•Shear reinforcement is not taken into consideration

11

21 28/05/2013

Concrete damage material model

wt = 0 corresponds to no recovery as load changes

from compression to tension and

wt = 1 corresponds to complete recovery

as the load changes from compression to tension,

the default value is wt = 0

wc = 0 corresponds to no recovery as load changes

from tension to compression and

wc = 1 corresponds to complete recovery

as the load changes from tension to compression,

default value is wc = 1

22 28/05/2013

Stress-strain curve for steel

Strain rate sensitivity is taken into consideration by the Cowper-Symonds

equation

where D=40 1/s and q=5 for mild steel.

0

100

200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1

Strain (mm/mm)

Str

es

s (

MP

a)

q

yydD

/1

1

ss

12

23 28/05/2013

Tensile cracking

0

1000000

2000000

3000000

4000000

5000000

6000000

0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 0,004

Cracking strain (-)

Str

es

s (

Pa

)

lin_static

bilin_static

bilin_rate=1

Hordijk_static

Hordijk_rate=1

•The assumed tensile cracking behaviour dominates the analysis results

•Static fracture energy 200 J/m2

•Dynamic increase factor 1.37

•Linear, bilinear and exponential (alternative) assumptions

24 28/05/2013

Concrete tension damage

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,0005 0,001 0,0015 0,002 0,0025

Cracking strain (-)

Da

ma

ge

T

lin_DT95

lin_DT99

DT_v1

DT_v20

500000

1000000

1500000

2000000

2500000

3000000

3500000

4000000

0 0,0005 0,001 0,0015 0,002 0,0025

Cracking strain (-)

Str

es

s (

Pa

)

lin_static

DT1

DT2

DT3

DT4

Tensile damage assumptions Recovery stiffness after tensile cracking

in the linear tensile damage assumption

DT99

13

25 28/05/2013

Sensitivity studies on the tensile cracking assumptions

with linear decrease of tensile strength

-0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

ft_lin_DT95

ft_lin_DT99

-0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

ft_lin_DT99

ft_lin_DT99_v1

ft_lin_DT99_v2Linear increase of DT

Nonlinear assumptions for DT, v1 and v2

compared with the linear assumption DT99

26 28/05/2013

Sensitivity studies on dynamic tensile strength Static: ft= 3.7 MPa

Dynamic: ft= 5.1 MPa

-0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

ft_bilin_st_DT95

ft_bilin_r1_DT95

ft_bilin_r1_DT99 -0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

ft_H_st_DT95

ft_H_r1_DT95

ft_H_r1_DT99

Bilinear assumption for tensile cracking Exponential assumption for tensile cracking

14

27 28/05/2013

TDOF model (2 d.o.f)

Shear strength due to concrete,

stirrups and bending reinforcement

TDOF model (modified CEB model) describing bending and shear cone formation.

Spring 1 and mass 1 are connected

to the global bending deformation

Spring 2 and mass 2 are used in describing

the local shear behaviour at the impact area

Constitutive law for rebar: elastic-plastic; concrete: elastic plastic with tensile cracking

Bending stiffness

28 28/05/2013

Sensitivity studies on the shape of the loading function

-0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

F_fvp

FOLD_A

FOLD_B -0,04

-0,035

-0,03

-0,025

-0,02

-0,015

-0,01

-0,005

0

0 0,02 0,04 0,06 0,08 0,1

Time (s)

Dis

pla

ce

me

nt

(m)

Test

F_fvp

FOLD_A

FOLD_B

FE results,

exponential assumption for tensile cracking

TDOF model results

15

29 28/05/2013

Collapse by punching

The punching capacity of a concrete slab can be obtained from the formula

where rp is the average percentage of reinforcement on the tensioned face, [%], fc is the compression strength of

concrete [Pa], de is the distance between the front face and reinforcement, [m], dload is the diameter of loaded

area, [m], [Jowett, 1989].

According to Reference [Jowett, 1989] the punching shear resistance formula can be applied for dynamic soft

impact cases by checking the condition

where is the average value of the time dependent force resultant of the missile and it can be calculated by

where t0.9I is the time when 90% of the total impulse (0.9I) is reached during the dynamic loading transient. This

means in practice that the possible long tail of the loading function F(t) is discarded.

1/38170( ) ( 2.5 ),p p c e load eF f d d dr

pFF

0.9

0.9,

I

IF

t

F

30 28/05/2013

Water filled missile

The deformable missile is made of stainless steel pipe with a diameter of

0.25 m and thickness of 2 mm.

The impact velocity is about 110 m/s.

The total mass of the missile 50 kg, some equipped with a water tank

containing 25 l of water.

TF11

TF13

16

31 28/05/2013

Bending tests t = 150 mm

Geometry and supporting Reinforcement: Bending: F6 mm c/c=50 mm in both directions and

both faces~5.65 cm2/m

Shear: F6 mm stirrups ~53.5 cm2/m2

32 28/05/2013

TF13 v=111 m/s water filled missile

front back

17

33 28/05/2013

Deflections, v=111 m/s, water filled missile

34 28/05/2013

Conclusions on bending studies

In the studied case the bending reinforcement ratio of the slab is relatively low

rs = 0.4% and the tensile cracking occurs almost through the slab thickness.

Calculation results are sensitive for the assumed tensile cracking behaviour while the tensile crack energy was kept constant.

High strain rate in concrete increases the tensile strength value. This phenomenon was studied by increasing the tensile strength value by 40%.

The maximum displacement was well predicted using this dynamic tensile

strength.

The steeper increase of the tensile damage parameter DT decreases the

permanent displacement which was somewhat overestimated in all the cases.

As the impulse is constant the assumed shape of the loading function does not

affect the results as much as the difference in the duration on the loading pulse.

18

35 28/05/2013

Verification of numerical calculation models and methods for hard

missile impacts

36 28/05/2013

Pre-stressed concrete wall impacted by a hard

missile M = 47 kg and v = 100 m/s

250 mm thick wall, simply supported in 2 directions

front back

19

37 28/05/2013

Punching behavior test- The wall after the test

Scabbing area

Penetration

depth (how deep

the missile goes

inside the walll)

Spalling area

Front side

Main parameters to be measured:

•Residual velocity of the missile after the impact

in case it goes through the wall or

•Penetration depth of the missile

•Area of scabbed concrete

•Area of spalled concrete

Backside

Vertical cross section Horizontal cross section

38 28/05/2013

38

The ACE penetration formula (in SI units)

,5.0103506.0785.2

5.1

03

cfd

Mv

d

x

M is the projectile mass,

vo is the impact velocity,

d is the diameter of projectile,

fc is the compressive strength of concrete and

x is the penetration depth.

20

39 28/05/2013

39

The penetration depth according to the modified

NDRC formulation

Gd

x2 1G

1 Gd

x1G

,1081.38.2

8.1

05

df

NMvG

c

if

N is a nose shape factor, for flat nose N=0.72.

if

40 28/05/2013

40

The U.K. Atomic Energy Authority formulae

for penetration depth, Barr (1990)

Gd

x 0756.0275.0 0726.0G

242.04 Gd

x0605.10726.0 G

9395.0 Gd

x0605.1G

8.2

8.1

051081.3df

NMvG

c

if

if

if

Application limits: < 36 MPacf

21

41 28/05/2013

41

Reinhardt and Meyer

Normalized stress-displacement curve based on static penetration

tests is used in calculating the penetration depth. The normalized

displacement and contact stress are

yielding an initial incremental contact force - penetration relation

is the initial stiffness of the normalized stress-displacement

curve and Am is the cross-sectional area of round projectile. The

normalised penetration depth is now

40

cf

d

x

2/1

40

c

c

f

f

sand

dxd

ffAkdF cc

m

2/1

040

0k

2/1

3

2

00583.24

d

Mv

d

x

42 28/05/2013

42

Dimensionless penetration depth of the model by

Forrestal et al. (2003) in the form by Li et al. (2003)

cfd

Mv

SI

3

2

01

3

~

dN

MN

cr

kI

NI

Nk

d

x 4

)~

/1(

)~

4/1(

k

d

x

kNk

NIN

d

x

~

4/1

~/1

ln~2

k

d

x

,

if

if

22

43 28/05/2013

43

Shallow penetration

786.2

628.1

d

x

d

x a

Li et al. (2003) proposed a modified formula

where xa is penetration by normal formula (*)

(in Li et al. (2003) the factor 1.628 is outside brackets

in a corresponding formula)

44 28/05/2013

UMIST formula

3

2

0

72.0

2

d

mvN

d

p

ts

0

66 )1045.0014.0(101352.4 vff cct s

0v

6000 d 250035 m 5.2/0 dp

2.663 0 v

Within a research program by UK Nuclear Electric the following penetration depth formula has been developed at

University of Manchester, Institute of Technology (UMIST), Li (2005)

where the nose shape factor is 0.72 for a flat nose, 0.84 for a hemispherical nose, 1.0 for a blunt nose and 1.13 for a sharp nose and

is the rate dependent characteristic strength of concrete, in which the strength values are in Pa and in m/s.

The penetration equation is verified for the ranges: mm kg

and m/s.

.

23

45 28/05/2013

Prestressed wall penetration depth

for M = 47 kg and v = 100 m/s

RM Reinhardt and Meyer

FL Forrestal et al. and Li et al,

FLS for shallow penetration,

UMIST University of Manchester

Institute of Technology

Test results

A: no pre-stress

B: pre-stress 5MPa,

C: pre-stress 10 MPa

T: with T-bars

46 28/05/2013

Pre-stressed concrete wall impacted by a hard missile M = 47 kg

and v = 135 m/s

250 mm thick wall, simply supported in 2 directions

24

47 28/05/2013

48 28/05/2013

Prediction of residual velocity

The punching test is simple enough to allow concentration on the essential phenomena.

The local compression strength of concrete will be exceeded

The missile penetrates into the target slab through spalling and possibly in tunnel phase.

The velocity of the missile is so large that at some stage the contact force surpasses the remaining shear capacity of the slab.

Scabbing is also involved, concrete cover on the rear side.

This leads into a formation of a punching cone or more generally into concrete fracture on the rear side of the slab.

This ultimately will lead to perforation with the missile possessing a residual velocity.

Sensitivity studies were carried out in in order to predict the effect of shear reinforcement and liner

Analyses were carried out with a one-dimensional penetration perforation model and with Abaqus/Explicit Finite element program

25

49 28/05/2013

One-dimensional penetration-perforation (Forrestal, 1994)

Prediction of penetration depth, contact force,

possible perforation and residual velocity

Assumptions:

Punching cone angle as data (~60o)

Simply supported plate

Constitutive law for rebar and concrete: plastic

Strain rate effect not explicitly included

Missile assumed as rigid

1) Spalling or crater formation phase

2) Tunneling phase

3) Shear punching

50 28/05/2013

1) Spalling phase

cuF when 1uu spalling phase

Li nosehdu 707.01 (shallow penetration)

Even smaller spalling phase would be obtained by Hill’s type mechanism

26

51 28/05/2013

2) Tunneling phase

)( 2vNSfAF ccm r when 1uu tunnel phase

mA area of projectile, cr density of concrete

544.06.82 cfS , cf compressive strength of concrete

for flat nose 1N

for blunt/spherical nose

28

11

N

dr / , r is the radius of sphere and d is the diameter of projectile

095.1168/184/ dr (in the present case)

8958.08

11

2

N

139.002.0168.0707.01 u m

52 28/05/2013

Equation of motion

02

2

Fdt

udm

with initial conditions

0)0( u and 0)0( vu

m mass of projectile

solution by central difference (CD) method, or analytical solution

27

53 28/05/2013

Spalling phase

222

0 )( cuvvm , 1uu

Tunnel phase

cc

cc

mc SfvN

SfvN

AN

muu

2

2

1

1 ln2 r

r

r, 1uu

1v is the velocity at the time 1tt when the projectile goes into the tunnelling phase

Continuity conditions at 1uu

mcc AvNSfcu 2

11 r

2

1

2

1

2

0 )( cuvvm

determine at t=t1

1

1

2

02

1uANm

uASfmvv

mc

mc

r

2

1

2

1

2

0 )(

u

vvmc

54 28/05/2013

3) Shear punching

Shear capacity of the cone with a height

, where

Shear surface

( tan )

/ 3 , is missile diameter, is the cone angle

Bending reinforcement

( tan ) sin

is

p

s sc sb ss

sc c p p

c c

sb p s y

s

h h u

F F F F

F h d h

f d

F d h A f

A

the area of reinforcement per unit width

Shear reinforcement

( tan ) tan

is the area of shear reinforcement per unit area

Perforation is initiated when

ss p p ss ys

ss

s

F h d h A f

A

F F

28

55 28/05/2013

Perforation velocity (Barr)

2

3

1 1 126 2 2

6 2

1.3 0.3 ,

is reinforcement ratio and is plate thickness.

Possible pre-stress steel and liner are included in

For higher velocities (correction)

(1 4 10 )

p c c p

p

p

ph p p

d

hv fm

h

v v v

r r

r

r

56 28/05/2013

FE simulations Test P1

Solving numerically the structural behaviour of the wall

and projectile (Abaqus/Explicit code)

Highly nonlinear and dynamic cases

Hard missile impact

Local punching behaviour, possible perforation,

29

57 28/05/2013

Residual velocity as a function of impact velocity

(T bars => smaller => curve to the left)

-10

0

10

20

30

40

50

60

70

80

110 120 130 140 150 160 170

vo [m/s]

vr

[m/s

]

B

BL

BT

C

AT2

P1_test

P2_test

P3_test

Case 1 (B)

Case 2 (BT)

Case 3 (BL)

Case 4 (BLT)

B basic case

BL with liner

BT with T-bars

C penetration by Teland

BLT liner and T-bars

Test results:

AT2 fc=59.5 MPa,T-bars

P1 fc=60.5 MPa

P2 fc=56 MPa

P3 fc=58 MPa

58 28/05/2013

Perforation thickness

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0 40 80 120 160

vo [m]

e [

m]

fc40

fc50

fc60

fc70

shallow penetration model with bending reinforcement contribution, effect of fc

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Conclusions on punching studies

Simplified methods are easy to use and parametric studies can be made very effectively with them.

An increase of 5o in the cone angle assumption decreases the predicted residual velocity by more than 10 m/s.

The increase of concrete compressive strength from 40 MPa to 70 MPa will change the residual velocity from 81 m/s to 8.1 m/s. This is probably more than would be obtained from tests.

According to FE simulations, the T-headed bars decrease considerably the residual velocity of the missile. They also decrease scabbing to some degree.

The liner decreases slightly them both.

The T-bars together with the liner decrease them dramatically and make the slab more resistant to hard missile impacts.

This sensitivity study shows that the FE model is highly sensitive to the erosion criteria by which the elements are removed from the model.

The strain criterion value approximately in the range from 20% to 30% seems to be the most adequate choice.

It should to noted, that this study is very limited and the impact velocity lies in a region where slight variations of parameter values and model characteristics change the dominating damage modes.

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Combined bending and punching

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Combined bending and punching test X1

Geometry and supporting Reinforcement and strain gauges Bending:F10 mm c/c=90 mm in both directions and on

both sides→ ~8.73 cm2/m,

Shear:F6 mm closed stirrups ~17.22 cm2/m2

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X1 – high speed video footage Soft missile,

m=50.04 kg,

v=165.9m/s

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Prediction of loading function due to missile impact

Predicted load functions for test X1

with an impact velocity of 166 m/s.

Stainless steel pipe

=256mm, t=3mm

m=50.04 kg

Observed and predicted missile shapes at the end of test

X1.

The missile

shape before

and after the

test.

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Inherent FEM program

16 DOF plate element based on Kirchhoff plate

theory (FEKR) (no transverse shear)

12 DOF plate element based on Reissner-Mindlin

theory with transverse shear (FE-RMR)

models use moment-curvature relationships for

reinforced plate sections

10 by 10 element model for symmetric quarter

(484 d.o.f)

impact load given as in Abaqus models

no prominent shear deformation at impact area

FE-RMR model can detect shear cone formation

(as well as the TDOF model can)

t=250 mm

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Solid finite element model (520 000 d.o.f)

520 000 degrees of freedom

Quarter model includes missile

and all reinforcements

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Displacements as a functions of time

At the centre sensor 5

Structural models

Abaqus = Abaqus shell element model

Abaqus_3D = Abaqus solid element

model

FEKR = Bogner-Fox-Schmit plate

element model

TDOF = simple 2 degree of freedom

model

Loading models

fvp=Riera method with folding taken into

account in an averaged sense

fold=Riera method with true folding

mechanism model

Abaqus_3D=missile included in the

model

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Cross-sections sawn through the centre-lines of the X1 slab

Vertical cross-

section

Horizontal cross-

section

Shear strains indicated by colour contours

Missile impact radius

at 4 ms (middle of impact)

3D solid FE model

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Deflection behaviour

Deflection contours by Reissner-Mindlin element Deflection at the symmetry line

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Results calculated by TDOF model

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Strains in shear reinforcement

21 ms

8 ms

4 ms

Axial strain in steel

rebars (front rebars

removed)

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Back surface of the X1 slab

3D solid FE model

Cracking of concrete

Tensile damage of

FE model

21 ms

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Conclusions on combined bending and punching studies

Simplified models (due to simple data generation and short execution

time) are valuable in making parametric studies in preliminary design

phase and when checking the reliability of both the test results and the

more extensive numerical simulations.

The TDOF model is, however, sensitive to the assumed angle (needs to

be conservative) of shear failure cone and 3D finite element solutions are

needed for comparison and more detailed studies.

Displacements calculated with three different methods applying two

different loading functions were compared with the experimental

recordings in the bending cases.

Transverse nonlinear shear behaviour to be considered.

As the impulse and the duration of loading are the same, the assumed

shape of the loading function did not significantly affect the results.

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Conclusions

Collapsing mode is dependent on the type of the loading and the

calculation method and modelling technique should be chosen

accordingly.

Simplified models (due to simple data generation and short execution

time) are valuable in making parametric studies in preliminary design

phase and when judging the reliability of both the test results and the

more extensive numerical simulations.

It should be noted that these results are sensitive to the material property

assumptions e.g. high strain rate in concrete increases the tensile strength

value.

Bending vibration behaviour is dependent on the recovery stiffness

assumption after tensile cracking.

The applied damping value affects the bending vibration behaviour.

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Conclusions

In order to simulate realistically dynamic behaviour of an impact loaded reinforced concrete slab, all the material behaviour should be modelled strain rate dependent.

However, in a real scale case, considering a passenger aircraft crashing to a containment building, the strain rates in reinforced concrete wall are probably lower than those observed during the impact tests.

Experimental research is needed to obtain relevant data for numerical analyses.

Also numerical methods and models need further development.

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References NUMERICAL COMPUTATION

Journal articles: Saarenheimo A., Tuomala M., Välikangas P. and Vepsä A.,

Sensitivity studies on a bending wall of IRIS_2010

benchmark exercise. Journal of Disaster Research Vol.7

No.5.

Tuomala M., Calonius, K., Kuutti, J., Saarenheimo A. and

Välikangas, P. Sensitivity studies on a punching wall of

IRIS_2010 benchmark exercise. Journal of Disaster

Research, Vol 7 No.6, 2012

Saarenheimo, A., Tuomala, M., Calonius, K., Hakola, I.,

Hostikka, S. and Silde, A. (2009). ”Experimental and

numerical studies on projectile impacts”. Journal of

Structural Mechanics. Vol. 42 No 1.

Numerous SMiRT-conference papers such as: Saarenheimo, A. et al. “Sensitivity studies on IRIS_2010

bending wall.”, Transactions, SMiRT 21, 6-11 November,

2011, New Delhi, India. Div-V: Paper ID# 518

Tuomala M. et al. “Sensitivity studies on IRIS_2010

punching wall.”, Transactions, SMiRT 21, 6-11 November,

2011, New Delhi, India. Div-V: Paper ID# 832

For more information regarding testing:

Ilkka Hakola, ilkka.hakola@vtt.fi, +358 20 722 6685

Ari Vepsä, ari.vepsa@vtt.fi +358 20 722 6838

For more information regarding liquid dispersal study:

Ari Silde, ari.silde@vtt.fi, +358 20 722 5039

For more information regarding FEM computation:

Arja Saarenheimo, arja.saarenheimo@vtt.fi, +358 20 722 4156

Kim Calonius, kim.calonius@vtt.fi, +358 20 722 5853

For more information regarding fire simulation:

Simo Hostikka, simo.hostikka@vtt.fi, +358 20 722 4838

TESTING

63 tests with concrete walls carried out in

different international projects between 2006-

2012 (IMPACT I, IMPACT II, IMPACT III)

10 participating organizations in IMPACT II

project from around the world

Benchmark data (5 tests) for OECD/NEA

exercise IRIS_2010) Related SMiRT-conference paper: Vepsä; A. et al.

“IRIS_2010 - PART II: EXPERIMENTAL DATA”

Transactions, SMiRT 21, 6-11 November, 2011, New

Delhi, India. Div-V: Paper ID# 520

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