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- 1. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos 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 Rome Dipartimento di Ingegneria Strutturale e Geotecnica Blast resistance assessment of a reinforced precast concrete wall under uncertainty
- 2. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 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. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Presentation outline 3 • 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
- 4. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Introduction The case of the Ronan Point apartments building 4 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).
- 5. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 5 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. Introduction The case of the Ronan Point apartments building
- 6. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Collapse probability 6 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 EFFECTCAUSE GLOBAL EFFECT
- 7. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Presentation outline 7 • 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
- 8. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 8 Component damage levels and response parameters Response parameters Φelastic Φplastic Mplasticδ δel -r -rel R = r A L L Ductility ratio Support rotation
- 9. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 9 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
- 10. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Presentation outline 10 • 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
- 11. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 11 Blast scenario and targets Blast scenario – aerial view Street Level 2 Level 3 Level 1 Target Explosive weight
- 12. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 12 Blast scenario and targets Blast scenario – section view
- 13. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 13 Blast scenario and targets Blast scenario – section view: uncertainties Fence barrier Vehicle bomb w [kgp] p [W] Stand-off distance r [m] p [R] Cladding wall θi p [Θi]
- 14. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 14 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 targets Precast cladding wall panel
- 15. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 15 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 Blast scenario and targets Input data
- 16. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Presentation outline 16 • 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
- 17. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 17 Fragility curves Failure probability Pf(X>x0|IM) Intensity Measure (IM) p(IM)
- 18. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 18 Fragility curves Flowchart 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 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
- 19. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 19 Fragility curves Intensity measure ta to t - o Pso P - so Po Reflected pressure Incident pressure Prα P - rα Peak pressure Impulse density
- 20. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 20 Fragility curves Intensity measure Scaled distance Side-on pressure Side-on impulse density Shock duration Shock wave Reflected pressure INTENSITY MEASURE
- 21. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 21 Fragility curves Intensity measure 1 10 100 1000 100 1000 10000 100000 P[kPa] i [kPa ms] θ=2ƒ θ=5ƒ θ=10ƒ I D P I: impulsive region D: dynamic region P: pressure region
- 22. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 22 Fragility curves Intensity measure 0 20 40 60 80 100 2.4 2.6 2.8 3.0 3.2 3.4 Pf(X>x0|Z) Z Hazardous Failure
- 23. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 23 Fragility curves Flowchart 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 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 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
- 24. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 24 Fragility curves Computing 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. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 25 0 20 40 60 80 100 2.4 2.6 2.8 3.0 3.2 3.4 Pf(X>x0|Z) Z Hazardous Failure j-th CDL k-th R i-th Z Fragility curves Results
- 26. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 26 Fragility curves Results 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>x0|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>x0|Z) Z 0 20 40 60 80 100 3.0 3.5 4.0 4.5 5.0 Pf(X>x0|Z) Z Moderate Damage 0 20 40 60 80 100 5 6 7 8 9 10 11 Pf(X>x0|Z) Z Superficial Damage CDL R
- 27. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 27 Blast scenario Blast scenario – section view Fence barrier Vehicle bomb w [kgp] p [W] Stand-off distance r [m] p [R] Cladding wall θi p [Θi]
- 28. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 28 Fragility curves Results 0 20 40 60 80 100 3.0 3.5 4.0 4.5 5.0 Pf(X>x0|Z) Z Moderate Damage Safe Unsafe Example
- 29. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 29 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 scenario Blast scenario – section view
- 30. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 30 Fragility curves Failure Probability 0 20 40 60 80 100 2.4 2.6 2.8 3.0 3.2 3.4 Pf(X>x0|Z) Z Hazardous Failure p(Z)[-]
- 31. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 31 Fragility curves Failure 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 %
- 32. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Presentation outline 32 • 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
- 33. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 33 Conclusions 0 20 40 60 80 100 3.0 3.5 4.0 4.5 5.0 Pf(X>x0|Z) Z Moderate Damage Safe Unsafe Example • Fragility curves can be helpful in the design of precast concrete wall panels, or cladding panels in general.
- 34. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 34 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.
- 35. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas Thank you for your attention 35 Pierluigi Olmati, Francesco Petrini, Konstantinos Gkoumas Sapienza - 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”.
- 36. Blastresistanceassessmentofareinforcedprecastconcretewallunderuncertainty ICOSSAR 2013 11th International Conference on Structural Safety & Reliability June 16-20, Columbia University, New York, NY Pierluigi Olmati Francesco Petrini Konstantinos Gkoumas 36 Pierluigi Olmati, Francesco Petrini, Konstantinos Gkoumas Sapienza - 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 Pf(X>x0|Z) Z Moderate Damage