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    ICOSSAR PO et al ICOSSAR PO et al Presentation Transcript

    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasSapienza – University of RomePierluigi 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 eGeotecnicaBlast resistance assessment of a reinforced precastconcrete wall under uncertainty
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline2• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline3• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasIntroductionThe case of the Ronan Point apartments building4Reference:NISTIR 7396: Best practices for reducing the potentialfor 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 ofprecast concrete,-each floor was supported directly by the walls inthe lower stories (bearing walls system).
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas5Cause Damage Pr. CollapseDetails:-apartment building,-built between 1966 and 1968,-64 m tall with 22 story,-walls, floors, and staircases were made ofprecast concrete,-each floor was supported directly by the walls inthe lower stories (bearing walls system).The event:-May 16, 1968 a gas explosion blew out anouter panel of the 18th floor,-the loss of the bearing wall causes theprogressive collapse of the upper floors,-the impact of the upper floors’ debris caused theprogressive collapse of the lower floors.IntroductionThe case of the Ronan Point apartments building
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasCollapse probability6LOAD STRUCTURE RESPONSETruck bomb1.8 ton TNTA. P. M. BuildingBefore 19/05/95A. P. M. BuildingAfter 19/05/95HAZARD COLLAPSERESISTENCEP[●]: probabilityP[●|■]: conditional probabilityH: HazardLD: Local DamageC: CollapseNISTIR 7396UFC 4-023-03References:EXPOSUREVULNERABILITYROBUSTESS∑i = P[C]P[LD|Hi]P[Hi] P[C|LD]LOCAL EFFECTCAUSE GLOBAL EFFECT
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline7• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas8Component damage levels and responseparametersResponse parameters ΦelasticΦplasticMplasticδδel-r-relR = r ALLDuctility ratio Support rotation
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas9Component damage levels θ [degree] μ [-]Blowout >10° noneHazardous Failure ≤10° noneHeavy Damage ≤5° noneModerate Damage ≤2° noneSuperficial Damage none 1Blowout: component is overwhelmed by the blast load causingdebris with significant velocities.Hazardous Failure: component has failed, and debris velocities range frominsignificant to very significant.Heavy Damage: component has not failed, but it has significantpermanent deflections causing it to be un-repairable.Moderate Damage: component has some permanent deflection. It isgenerally repairable, if necessary, althoughreplacement 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
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline10• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas11Blast scenario and targetsBlast scenario – aerial viewStreetLevel 2Level 3Level 1TargetExplosiveweight
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas12Blast scenario and targetsBlast scenario – section view
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas13Blast scenario and targetsBlast scenario – section view: uncertaintiesFence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas14Panel 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
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas15Symbol Description Mean COV Distributionfc Concrete strength 28MPa 0.18 Lognormalfy Steel strength 495 MPa 0.12 LognormalL Panel length 3500 mm 0.001 LognormalH Panel height 150 mm 0.001 Lognormalb Panel width 1500 mm 0.001 Lognormalc Panel cover 75 mm 0.01 LognormalW Explosive weight 227 kgf 0.3 LognormalR Stand-off distance 15 m 20 m 25 m 0.05 LognormalBlast scenario and targetsInput data
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline16• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas17Fragility curvesFailure probabilityPf(X>x0|IM)Intensity Measure (IM)p(IM)
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas18Fragility curvesFlowchartCDL (j)Z=iMC analysisFC-CDL (i, j, k)FC-CDL (j,k)FC-CDL (k)i=N ?j=M ?i=i+1j=j+1YESNONOYES• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curvesof the Component Damage Level• i: the i-th point, of the j-th FC-CDLcorresponding 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, ornumber of the Z• M: number of the CDL• L: number of the stand-offdistance• Interpolated FC-CDL: lognormalinterpolated Fragility Curves of theComponent Damage LevelR=kk=L ?YESNOk=k+1FC-CDLLognormalInterpolationInterpolatedFC-CDLj=1 i=1 k=1INTENSITY MEASURE• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curveof the Component Damage Level• i: the i-th point, of the j-th FC-CDLcorresponding to the k-th R• j: the j-th CDL• k: the k-th stand-off distance• MC analysis: Monte Carloanalysis• N: number of FC-CDL points, ornumber of the Zs• M: number of the CDLs• L: number of the stand-offdistances• Interpolated FC-CDL: lognormalinterpolated Fragility Curve of theComponent Damage Level
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas19Fragility curvesIntensity measureta to t-oPsoP-soPoReflected pressureIncident pressurePrαP-rαPeak pressureImpulse density
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas20Fragility curvesIntensity measureScaled distanceSide-on pressureSide-on impulse densityShock durationShock waveReflected pressureINTENSITY MEASURE
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas21Fragility curvesIntensity measure1101001000100 1000 10000 100000P[kPa]i [kPa ms]θ=2ƒθ=5ƒθ=10ƒIDPI: impulsive regionD: dynamic regionP: pressure region
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas22Fragility curvesIntensity measure0204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failure
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas23Fragility curvesFlowchartCDL (j)Z=iMC analysisFC-CDL (i, j, k)FC-CDL (j,k)FC-CDL (k)i=N ?j=M ?i=i+1j=j+1YESNONOYES• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curvesof the Component Damage Level• i: the i-th point, of the j-th FC-CDLcorresponding 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, ornumber of the Z• M: number of the CDL• L: number of the stand-offdistance• Interpolated FC-CDL: lognormalinterpolated Fragility Curves of theComponent Damage LevelR=kk=L ?YESNOk=k+1FC-CDLLognormalInterpolationInterpolatedFC-CDLj=1 i=1 k=1Fragility curves forn° M CDLs and thek-th stand-offdistance (R)Fragility curves forn°M CDLs and n°Lstand-off distances(R)Fragility curve forthe j-th CDL and thek-th stand-offdistance (R)• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curveof the Component Damage Level• i: the i-th point, of the j-th FC-CDLcorresponding to the k-th R• j: the j-th CDL• k: the k-th stand-off distance• MC analysis: Monte Carloanalysis• N: number of FC-CDL points, ornumber of the Zs• M: number of the CDLs• L: number of the stand-offdistances• Interpolated FC-CDL: lognormalinterpolated Fragility Curve of theComponent Damage Level
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas24Fragility curvesComputing the fragility curveFence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [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=ZNZ123NP(X>x|Z)Fragility curve for the j-th CDL and the k-thstand-off distance (R)Monte CarloSimulation
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas250204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failure j-th CDLk-thRi-th ZFragility curvesResults
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas26Fragility curvesResultsComponent damage levels θ [degree] μ [-]Blowout >10° noneHazardous Failure ≤10° noneHeavy Damage ≤5° noneModerate Damage ≤2° noneSuperficial Damage none 10204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failure0204060801002.8 3.0 3.2 3.4 3.6 3.8 4.0Heavy DamagePf(X>x0|Z) Z0204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate Damage0204060801005 6 7 8 9 10 11Pf(X>x0|Z)ZSuperficial DamageCDLR
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas27Blast scenarioBlast scenario – section viewFence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas28Fragility curvesResults0204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate DamageSafeUnsafeExample
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas29Fence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]Scaled distancep[Z]ZBlast scenarioBlast scenario – section view
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas30Fragility curvesFailure Probability0204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failurep(Z)[-]
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas31Fragility curvesFailure ProbabilityCDLMean W=227 kgf COV=0.3 lognormal distributionR, COV=0.05 lognormal distributionFC analysis MC analysis Difference Δ%R = 20 mSD 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 mSD 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 mSD 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 %
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasPresentation outline32• Introduction• Component damage levels and responseparameters• Blast scenario and targets• Blast scenario• Precast cladding wall panel• Input data• Fragility curves• Calculation procedure• Results• Conclusions
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas33Conclusions0204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate DamageSafeUnsafeExample• Fragility curves can be helpful in the design of precastconcrete wall panels, or cladding panels in general.
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas34Conclusions (2)• It is important to define a appropriate thresholds for theprobability of failure.• The probability of failure computed by means offragility curve analysis and Monte Carlo analysisshows a maximum difference of 11 % for the casestudy wall panel. The question is, is this acceptable?• In a future study, it could be useful to implementfragility surfaces instead of fragility curves.• Furthermore, it could be useful to account for thestructural deterioration of the wall panel on computingthe fragility curves.
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos GkoumasThank you for your attention35Pierluigi Olmati, Francesco Petrini, Konstantinos GkoumasSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e GeotecnicaThis study is partially supported by StroNGER s.r.l. from the fund “FILAS - POR FESR LAZIO2007/2013 - Support for the research spin-off”.
    • BlastresistanceassessmentofareinforcedprecastconcretewallunderuncertaintyICOSSAR 201311thInternational Conference on Structural Safety & ReliabilityJune 16-20, Columbia University, New York, NYPierluigi OlmatiFrancesco PetriniKonstantinos Gkoumas36Pierluigi Olmati, Francesco Petrini, Konstantinos GkoumasSapienza - University of Rome, Dipartimento di Ingegneria Strutturale e GeotecnicaFence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]0204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate Damage