blast resistance of reinforced precast concrete walls under uncertainty

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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



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



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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



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.




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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



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.




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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



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1 Introduction



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



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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



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1 Introduction



4 Fragility curves

5 Conclusions

Stre

et

Level 2

Level 3

Level 1

Target

11 Blast scenario - Areal view



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12 Blast 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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4

5

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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



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14 Precast cladding wall panel



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



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1 Introduction



4 Fragility curves

5 Conclusions

17 Fragility curves – Failure probability



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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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



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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



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0

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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



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



Intensity measure

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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

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)



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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



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0

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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



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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




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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

Pf(X

> x 0

|Z)

Z

Moderate Damage




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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




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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



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 %



Fragility curves – Failure probability

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1 Introduction



4 Fragility curves

5 Conclusions

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

Conclusions

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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

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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

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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 5.0P

f(X

> x 0

|Z)

Z

Moderate Damage

BLAST RESISTANCE OF REINFORCED PRECAST CONCRETE WALLS UNDER UNCERTAINTY

blast resistance of reinforced precast concrete walls under uncertainty

Engineering