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1
BLAST RESISTANCE OF REINFORCED PRECAST CONCRETE WALLS UNDER UNCERTAINTY
Session 2D: Protective Construction
Paul F. Mlaker, Ph.D., U.S. Army Engineer Research and Development Center
Pierluigi Olmati 1
P.E., Ph.D. Student Email: [email protected]
Franco Bontempi 1
Full Professor, P.E., Ph.D. Email: [email protected]
Patrick Trasborg 2
Ph.D. Student Email: [email protected]
Clay J. Naito 2
Associate Professor and Chair, P.E., Ph.D. Email: [email protected]
1 Sapienza University of Rome 2 Lehigh University
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
2 Presentation outline
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1 Introduction
2 Component damage levels and response parameters
3 Blast scenario and target
4 Fragility curves
5 Conclusions
3
General view of Ronan Point prior to demolition/photo 1987/photographer
M Glendinning
Features: - apartment building, - built between 1966 and 1968, - 64 m tall with 22 story, - walls, floors, and staircases were made of precast
concrete, - each floor was supported directly by the walls in
the lower stories, (bearing walls system).
References: NISTIR 7396: Best practices for reducing the potential for progressive collapse in buildings. Washington DC: National Institute of Standards and Technology (NIST), 2007.
Ronan Point – May 16, 1968
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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References: NISTIR 7396: Best practices for reducing the potential for progressive collapse in buildings. Washington DC: National Institute of Standards and Technology (NIST), 2007.
Features: - apartment building, built between ‘66 and ‘68, - 64 m tall with 22 story, - walls, floors, and staircases were made of precast
concrete, - each floor was supported directly by the walls in
the lower stories, (bearing walls system).
The event: - May 16, 1968 a gas explosion blew out an outer
panel of the 18th floor, - the loss of the bearing wall causes the
progressive collapse of the upper floors, - the impact of the upper floors’ debris caused the
progressive collapse of the lower floors.
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Ronan Point – May 16, 1968
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Cause Damage Pr. Collapse
Features: - apartment building, built between ‘66 and ‘68, - 64 m tall with 22 story, - walls, floors, and staircases were made of precast
concrete, - each floor was supported directly by the walls in
the lower stories, (bearing walls system).
The event: - May 16, 1968 a gas explosion blew out an outer
panel of the 18th floor, - the loss of the bearing wall causes the
progressive collapse of the upper floors, - the impact of the upper floors’ debris caused the
progressive collapse of the lower floors.
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Ronan Point – May 16, 1968
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LOAD STRUCTURE RESPONSE
Truck bomb
1.8 ton TNT
A. P. M. Building
Before 19/05/95
A. P. M. Building
After 19/05/95
HAZARD COLLAPSE RESISTENCE
P[●]: probability
P[●|■]: conditional probability
H: Hazard
LD: Local Damage
C: Collapse NISTIR 7396
UFC 4-023-03
References:
EXPOSURE
VULNERABILITY
ROBUSTESS
∑i = P[C] P[LD|Hi] P[Hi] P[C|LD] LOCAL EFFECT CAUSE GLOBAL EFFECT
Collapse probability
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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7 Presentation outline
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1 Introduction
2 Component damage levels and response parameters
3 Blast scenario and target
4 Fragility curves
5 Conclusions
r
Φelastic
Φplastic
Mplasticδ
δel
-r
-rel
Rel = rel A
R = r A
L
L δtmδe
Tension membrane effect (tm)
PlasticElastic
δlim
8
θ = arctg2δmaxL
μ =δmaxδe
Response parameters
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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Component damage levels θ [degree] μ [-]
Blowout >10° none Hazardous Failure ≤10° none
Heavy Damage ≤5° none Moderate Damage ≤2° none Superficial Damage none 1
Blowout: component is overwhelmed by the blast load causing debris with
significant velocities. Hazardous Failure: component has failed, and debris velocities range from
insignificant to very significant. Heavy Damage: component has not failed, but it has significant permanent
deflections causing it to be un-repairable. Moderate Damage: component has some permanent deflection. It is generally
repairable, if necessary, although replacement may be more economical and aesthetic.
Superficial Damage: component has no visible permanent damage.
Component Damage Levels
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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10 Presentation outline
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1 Introduction
2 Component damage levels and response parameters
3 Blast scenario and target
4 Fragility curves
5 Conclusions
Stre
et
Level 2
Level 3
Level 1
Target
11 Blast scenario - Areal view
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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12 Blast scenario - Section view
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
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Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
Blast scenario - Section view
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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14 Precast cladding wall panel
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Panel dimensions: 3500x1500x150 mm (137x59x6 in.)
Panel reinforcement: 10 φ10 mm (0.4 in.) 100x100 mm (4x4 in.) φ6 mm (0.23 in.)
Panel materials: Concrete fcm=35 MPa (5000 psi) Steel B450C (≈GR60)
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Mean COV Distribution
Concrete 28 MPa 0.18 Lognormal Reinforcing steel 495 MPa 0.12 Lognormal
Panel length 3500 mm 0.001 Lognormal Panel height 150 mm 0.001 Lognormal Panel width 1500 mm 0.001 Lognormal Panel cover 75 mm 0.01 Lognormal
Explosive 227 kg 0.3 Lognormal Stand-off 20 m 0.05 Lognormal
Input data
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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16 Presentation outline
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1 Introduction
2 Component damage levels and response parameters
3 Blast scenario and target
4 Fragility curves
5 Conclusions
17 Fragility curves – Failure probability
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Pf (X
> x 0
|IM
)
Intensity Measure (IM)
Pf X > x0 = Pf X > x0|IM p IM dIM
+∞
−∞
p(I
M)
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2
3
4
5
CDL (j)
Z=i
MC analysis
FC-CDL (i, j, k)
FC-CDL (j,k)
FC-CDL (k)
i=N ?
j=M ?
i=i+
1
j=j+
1 YES
NO
NO
YES
• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curves
of the Component Damage Level• i: the i-th point, of the j-th FC-CDL
corresponding to the k-th R• j: the j-th CDL• k: the k-th stand-off distance• MC analysis: Monte Carlo analysis• N: number of FC-CDL points, or
number of the Z• M: number of the CDL• L: number of the stand-off
distance• Interpolated FC-CDL: lognormal
interpolated Fragility Curves of the Component Damage Level
R=k
k=L ?
YES
NO
k=k+
1
FC-CDL
Lognormal Interpolation
Interpolated FC-CDL
j=1 i=1 k=1
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INTENSITY MEASURE
Fragility curves – Flowchart
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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• CDL: Component Damage Level • R: Stand-off distance • Z: Scaled distance • FC-CDL: numerical Fragility Curve
of the Component Damage Level • i: the i-th point, of the j-th FC-
CDL corresponding to the k-th R • j: the j-th CDL • k: the k-th stand-off distance • MC analysis: Monte Carlo
analysis • N: number of FC-CDL points, or
number of the Zs • M: number of the CDLs • L: number of the stand-off
distances • Interpolated FC-CDL: lognormal
interpolated Fragility Curve of the Component Damage Level
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ta to t-o
Pso
P-so
Po
Reflected pressure
Incident pressure
Prα
P-rα
P t = Pr 1 −t
tde−βttd ta≤ t ≤ td
Intensity measure
Peak pressure
Impulse density
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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0
20
40
60
80
100
0 0.004 0.008 0.012 0.016P
ress
ure
[kP
a]Time [sec]
R=15 m - W=20 kgp
R=30 m - W=20 kgp
R=10 m - W=20 kgp
R=20 m - W=50 kgp
20
Ps0 = 1.7721
Z3− 0.114
1
Z2+ 0.108
1
Z
i0 = 3001
Z𝑊3
Z =R
W3 Scaled distance
Side-on pressure
Side-on impulse density
Pr = 2Ps07Patm + 4Ps07Patm + Ps0
td =2is0Ps0
P t = Pr 1 −t
tde−βttd ta≤ t ≤ td
Shock duration
Shock wave
Reflected pressure
INTENSITY MEASURE
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Intensity measure
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1
10
100
1000
100 1000 10000 100000
P [
kP
a]
i [kPa ms]
θ=2
θ=5
θ=10
I
D
P
I: impulsive region
D: dynamic region
P: pressure region
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Intensity measure
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2
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CDL (j)
Z=i
MC analysis
FC-CDL (i, j, k)
FC-CDL (j,k)
FC-CDL (k)
i=N ?
j=M ?
i=i+
1
j=j+
1 YES
NO
NO
YES
• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curves
of the Component Damage Level• i: the i-th point, of the j-th FC-CDL
corresponding to the k-th R• j: the j-th CDL• k: the k-th stand-off distance• MC analysis: Monte Carlo analysis• N: number of FC-CDL points, or
number of the Z• M: number of the CDL• L: number of the stand-off
distance• Interpolated FC-CDL: lognormal
interpolated Fragility Curves of the Component Damage Level
R=k
k=L ?
YES
NOk=
k+1
FC-CDL
Lognormal Interpolation
Interpolated FC-CDL
j=1 i=1 k=1
22 Fragility curves – Flowchart
Fragility curves for n° M CDLs and the k-th
stand-off distance (R)
Fragility curves for n° M CDLs and n° L stand-off
distances (R)
Fragility curve for the j-th CDL and the k-th stand-off
distance (R)
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1
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• CDL: Component Damage Level • R: Stand-off distance • Z: Scaled distance • FC-CDL: numerical Fragility Curve of the
Component Damage Level • i: the i-th point, of the j-th FC-CDL
corresponding to the k-th R • j: the j-th CDL • k: the k-th stand-off distance • MC analysis: Monte Carlo analysis • N: number of FC-CDL points, or number
of the Zs • M: number of the CDLs • L: number of the stand-off distances • Interpolated FC-CDL: lognormal
interpolated Fragility Curve of the Component Damage Level
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Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
(1) R=R0 W=W1 Z=Z1
(2) R=R0 W=W2 Z=Z2
(3) R=R0 W=W3 Z=Z3
…….. (N) R=R0 W=WN Z=ZN
Z
1 2
3
N P(X
>x|Z
)
Fragility curve for the j-th CDL and the k-th stand-off distance (R)
Monte Carlo Simulation
Fragility curves – Computing the fragility curve
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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0
20
40
60
80
100
2.4 2.6 2.8 3.0 3.2 3.4
Pf(X
> x 0
|Z)
Z
Hazardous Failure j-th CDL
k-th R
i-th Z
Fragility curves – Results
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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Component damage levels θ [degree] μ [-]
Blowout >10° none Hazardous Failure ≤10° none
Heavy Damage ≤5° none Moderate Damage ≤2° none Superficial Damage none 1
0
20
40
60
80
100
2.4 2.6 2.8 3.0 3.2 3.4
Pf(X
> x 0
|Z)
Z
Hazardous Failure
0
20
40
60
80
100
2.8 3.0 3.2 3.4 3.6 3.8 4.0
Heavy Damage
Pf(X
> x 0
|Z)
Z
0
20
40
60
80
100
3.0 3.5 4.0 4.5 5.0
Pf(X
> x 0
|Z)
Z
Moderate Damage
0
20
40
60
80
100
5 6 7 8 9 10 11
Pf(X
> x 0
|Z)
Z
Superficial Damage
CDL
R
Fragility curves – Results
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
Blast scenario - Section view
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
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0
20
40
60
80
100
3.0 3.5 4.0 4.5 5.0
Pf(X
> x 0
|Z)
Z
Moderate Damage
Fragility curves – Results
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1
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Safe
Unsafe Example
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Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
𝐙 =𝐑
𝐖𝟑
Scaled distance
p [
Z]
Z
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Blast scenario - Section view
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3
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0
20
40
60
80
100
2.4 2.6 2.8 3.0 3.2 3.4
Pf(X
> x 0
|Z)
Z
Hazardous Failure
p(Z
) [-
]
P X > x0 = Pf X > x0|Z p Z dz ≅ Pf X > x0|Z i
∞
i=0
p Z i∆Zi
+∞
−∞
R = Zm Wm3 = Rm
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Fragility curves – Failure probability
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CDL
Mean W=227 kgf COV=0.3 lognormal distribution R, COV=0.05 lognormal distribution
FC analysis MC analysis Difference Δ%
R = 20 m
SD 100.0 % 100.0 % 0.0 % MD 96.6 % 97.5 % 0.9 % HD 55.7 % 55.5 % 0.3 % HF 13.6 % 12.1 % 11.0 %
R = 25 m
SD 100.0 % 100.0 % 0.0 % MD 74.6 % 77.3 % 3.5 % HD 14.2 % 12.6 % 11.2 % HF 1.02 % 1.02 % 0.0 %
R = 15 m
SD 100.0 % 100.0 % 0.0 % MD 97.9 % 99.9 % 2.0 % HD 93.6 % 96.9 % 3.4 % HF 67.8 % 72.6 % 6.6 %
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
Fragility curves – Failure probability
1
2
3
4
5
31 Presentation outline
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1 Introduction
2 Component damage levels and response parameters
3 Blast scenario and target
4 Fragility curves
5 Conclusions
32
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
1- Fragility curves can be helpful in the design of precast concrete wall panels, or cladding panels in general.
Conclusions
1
2
3
4
5 0
20
40
60
80
100
3.0 3.5 4.0 4.5 5.0
Pf(X
> x 0
|Z)
Z
Moderate Damage
Safe
Unsafe Example
33
2- It is important to define a appropriate thresholds for the probability of failure. 3- The probability of failure computed by means of fragility curve analysis and Monte Carlo analysis shows a maximum difference of 11 % for the case study wall panel. The question is, is this acceptable? 4- In a future study, it could be useful to implement fragility surfaces instead of fragility curves. 5- Also, it could be useful to account for the structural deterioration of the wall panel on computing the fragility curves.
Conclusions
1
2
3
4
5
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
34
Fence barrier
Vehicle bomb
w [kgp]
p [W]
Stand-off distance
r [m]
p [R]
Cladding wall
θi
p [Θi]
P Olmati, P Trasborg, CJ Naito, F Bontempi Sapienza University of Rome & Lehigh University
[email protected] www.francobontempi.org
0
20
40
60
80
100
3.0 3.5 4.0 4.5 5.0P
f(X
> x 0
|Z)
Z
Moderate Damage
BLAST RESISTANCE OF REINFORCED PRECAST CONCRETE WALLS UNDER UNCERTAINTY