ICOSSAR PO et al

Blast resistance assessm

ent of a reinforced precast concrete wall under uncertainty

ICOSSAR 201311th International Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NY

Pierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas

Sapienza – University of Rome

Pierluigi Olmati, Ph.D. student, P.E.Francesco Petrini, Ph.D., P.E.Konstantinos Gkoumas, Ph.D., P.E.

Sapienza - University of RomeDipartimento di Ingegneria Strutturale e Geotecnica

Blast resistance assessment of a reinforced precast concrete wall under uncertainty





Presentation outline

2

• Introduction• Component damage levels and response

parameters• Blast scenario and targets

• Blast scenario• Precast cladding wall panel• Input data

• Fragility curves• Calculation procedure• Results

• Conclusions






3





• Conclusions





IntroductionThe case of the Ronan Point apartments building

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Reference: NISTIR 7396: Best practices for reducing the potential for progressive collapse in buildings. Washington DC: National Institute of Standards and Technology (NIST), 2007.

Details:-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).





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Cause Damage Pr. Collapse

Details:-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).

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.

IntroductionThe case of the Ronan Point apartments building





Collapse probability

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LOAD STRUCTURE RESPONSETruck bomb1.8 ton TNT

A. P. M. BuildingBefore 19/05/95

A. P. M. BuildingAfter 19/05/95

HAZARD COLLAPSE RESISTENCE

P[●]: probabilityP[●|■]: conditional probabilityH: HazardLD: Local DamageC: Collapse

NISTIR 7396UFC 4-023-03

References:

EXPOSURE

VULNERABILITY

ROBUSTESS

∑i = P[C] P[LD|Hi]P[Hi] P[C|LD]LOCAL EFFECTCAUSE GLOBAL EFFECT






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• Conclusions





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Component damage levels and response parameters Response parameters

r

Φelastic

Φplastic

Mplasticδ

δel

-r

-rel

Rel = rel A

R = r A

L

L δtmδe

Tension membrane effect (tm)

PlasticElastic

δlim

Ductility ratio Support rotation





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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 (CDL’s)

Source: US Army Corps of Engineers






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• Conclusions





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Blast scenario and targetsBlast scenario – aerial view

Stre

et

Level 2

Level 3

Level 1

Target

Explosive

weight





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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 and targetsBlast scenario – section view





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Blast scenario and targetsBlast scenario – section view: uncertainties

Fence barrier

Vehicle bomb

w [kgp]

p [W]

Stand-off distance

r [m]

p [R]

Cladding wall

θi

p [Θi]





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Panel dimensions:3500x1500x150 mm(137x59x6 in.)

Panel reinforcement:12 φ10 mm (0.4 in.)

Panel materials:Concrete fcm=35 MPa (5000 psi)Steel B450C (≈GR60)

Blast scenario and targetsPrecast cladding wall panel





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Symbol Description Mean COV Distribution fc Concrete strength 28MPa 0.18 Lognormal fy Steel strength 495 MPa 0.12 Lognormal L Panel length 3500 mm 0.001 Lognormal H Panel height 150 mm 0.001 Lognormal b Panel width 1500 mm 0.001 Lognormal c Panel cover 75 mm 0.01 Lognormal

W Explosive weight 227 kgf 0.3 Lognormal R Stand-off distance 15 m 20 m 25 m 0.05 Lognormal

1

Blast scenario and targetsInput data






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• Conclusions





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Fragility curvesFailure probability

Pf (X

> x

0|IM

)

Intensity Measure (IM)

p(I

M)





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Fragility curvesFlowchart

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

INTENSITY MEASURE

• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curve


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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Fragility curvesIntensity measure

ta to t-o

Pso

P-so

Po

Reflected pressure

Incident pressure

Prα

P-rα

Peak pressure

Impulse density





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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

Scaled distance

Side-on pressure

Side-on impulse density

Shock duration

Shock wave

Reflected pressure

INTENSITY MEASURE





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1

10

100

1000

100 1000 10000 100000

P [

kPa]

i [kPa ms]

θ=2 �θ=5 �θ=10 �

I

D

P

I: impulsive regionD: dynamic regionP: pressure region





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0

20

40

60

80

100

2.4 2.6 2.8 3.0 3.2 3.4

P f(X

> x 0

|Z)

Z

Hazardous Failure





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Fragility curvesFlowchart

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


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

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)

• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curve


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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Fragility curvesComputing the fragility curve

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





25

0

20

40

60

80

100

2.4 2.6 2.8 3.0 3.2 3.4

P f(X

> x 0

|Z)

Z

Hazardous Failure j-th CDL

k-th R

i-th Z

Fragility curvesResults





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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

P f(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

P f(X

> x 0

|Z)

Z

0

20

40

60

80

100

3.0 3.5 4.0 4.5 5.0

P f(X

> x 0

|Z)

Z

Moderate Damage

0

20

40

60

80

100

5 6 7 8 9 10 11

P f(X

> x 0

|Z)

Z

Superficial Damage

CDL

R





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Blast scenarioBlast scenario – section view

Fence barrier

Vehicle bomb

w [kgp]

p [W]

Stand-off distance

r [m]

p [R]

Cladding wall

θi

p [Θi]





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0

20

40

60

80

100

3.0 3.5 4.0 4.5 5.0

P f(X

> x 0

|Z)

Z

Moderate Damage

Safe

UnsafeExample





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Fence barrier

Vehicle bomb

w [kgp]

p [W]

Stand-off distance

r [m]

p [R]

Cladding wall

θi

p [Θi]

Scaled distance

p [Z

]

Z

Blast scenarioBlast scenario – section view





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Fragility curvesFailure Probability

0

20

40

60

80

100

2.4 2.6 2.8 3.0 3.2 3.4

P f(X

> x 0

|Z)

Z

Hazardous Failure

p(Z

) [-

]





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Fragility curvesFailure Probability

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 %






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• Conclusions





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Conclusions

0

20

40

60

80

100

3.0 3.5 4.0 4.5 5.0

P f(X

> x 0

|Z)

Z

Moderate Damage

Safe

UnsafeExample

• Fragility curves can be helpful in the design of precast concrete wall panels, or cladding panels in general.





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Conclusions (2)

• It is important to define a appropriate thresholds for the probability of failure.

• 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?

• In a future study, it could be useful to implement fragility surfaces instead of fragility curves.

• Furthermore, it could be useful to account for the structural deterioration of the wall panel on computing the fragility curves.





Thank you for your attention

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Pierluigi Olmati, Francesco Petrini, Konstantinos GkoumasSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica

This study is partially supported by StroNGER s.r.l. from the fund “FILAS - POR FESR LAZIO 2007/2013 - Support for the research spin-off”.





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Pierluigi Olmati, Francesco Petrini, Konstantinos GkoumasSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica

Fence barrier

Vehicle bomb

w [kgp]

p [W]

Stand-off distance

r [m]

p [R]

Cladding wall

θi

p [Θi]

0

20

40

60

80

100

3.0 3.5 4.0 4.5 5.0

P f(X

> x 0

|Z)

Z

Moderate Damage

ICOSSAR PO et al

Technology

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