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
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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, [email protected], +358 20 722 6685
Ari Vepsä, [email protected] +358 20 722 6838
For more information regarding liquid dispersal study:
Ari Silde, [email protected], +358 20 722 5039
For more information regarding FEM computation:
Arja Saarenheimo, [email protected], +358 20 722 4156
Kim Calonius, [email protected], +358 20 722 5853
For more information regarding fire simulation:
Simo Hostikka, [email protected], +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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