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Compdyn po

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    Compdyn po Compdyn po Presentation Transcript

    • 1MONTE CARLO ANALYSIS FOR THE BLAST RESISTANCE DESIGN ANDASSESSMENT OF A REINFORCED CONCRETE WALLAdvances in computational methods for resilient structural systemsunder extreme hazardsMinisymposium Organizers: J. Ricles, T. KaravasilisChair: J. RiclesPierluigi OlmatiP.E., Ph.D. StudentSapienza University of RomeEmail: pierluigi.olmati@uniroma1.itPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 2 Presentation outline1 Introduction2 Component damage levels and response parameters3 Blast scenario and target4 Fragility curves5 ConclusionsPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 3General view of Ronan Point prior todemolition/photo 1987/photographerM GlendinningFeatures:- apartment building,- built between 1966 and 1968,- 64 m tall with 22 story,- walls, floors, and staircases were made of precastconcrete,- each floor was supported directly by the walls inthe lower stories, (bearing walls system).References:NISTIR 7396: Best practices for reducing the potential forprogressive collapse in buildings. Washington DC: NationalInstitute of Standards and Technology (NIST), 2007.Ronan Point – May 16, 196812345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 4Cause Damage Pr. CollapseFeatures:- apartment building, built between ‘66 and ‘68,- 64 m tall with 22 story,- walls, floors, and staircases were made of precastconcrete,- each floor was supported directly by the walls inthe lower stories, (bearing walls system).The event:- May 16, 1968 a gas explosion blew out an outerpanel 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.Ronan Point – May 16, 196812345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 5LOAD STRUCTURE RESPONSETruck bomb1.8 ton TNTA. P. M. BuildingBefore 19/05/95A. P. M. BuildingAfter 19/05/95HAZARD COLLAPSE RESISTENCEP[ ]: 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 EFFECTCollapse probability12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 6 Presentation outline1 Introduction2 Component damage levels and response parameters3 Blast scenario and target4 Fragility curves5 ConclusionsPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • ΦelasticΦplasticMplasticδδel-r-relR = r ALL7 Response parameters12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 8Component 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 causing debris withsignificant velocities.Hazardous Failure: component has failed, and debris velocities range frominsignificant to very significant.Heavy Damage: component has not failed, but it has significant permanentdeflections causing it to be un-repairable.Moderate Damage: component has some permanent deflection. It is generallyrepairable, if necessary, although replacement may be moreeconomical and aesthetic.Superficial Damage: component has no visible permanent damage.Component Damage Levels12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 9 Presentation outline1 Introduction2 Component damage levels and response parameters3 Blast scenario and target4 Fragility curves5 ConclusionsPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • StreetLevel 2Level 3Level 1Target10 Blast scenario - Areal view12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 11 Blast scenario - Section viewFence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 12Fence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]Blast scenario - Section view12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 13 Precast cladding wall panelPanel dimensions:3500x1500x150 mm(137x59x6 in.)Panel reinforcement:12 φ10 mm (0.4 in.)Panel materials:Concrete fcm=35 MPa (5000 psi)Steel B450C (≈GR60)12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 14 Input data12345Symbol 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 LognormalPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 15 Presentation outline1 Introduction2 Component damage levels and response parameters3 Blast scenario and target4 Fragility curves5 ConclusionsPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 16 Fragility curves – Failure probabilityPf(X>x0|IM)Intensity Measure (IM)p(IM)12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • CDL (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=117INTENSITY MEASUREFragility curves – Flowchart12345• 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-CDL corresponding 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 ofthe Component Damage LevelPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 18ta to t-oPsoP-soPoReflected pressureIncident pressurePrαP-rαIntensity measurePeak pressureImpulse density12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 0204060801000 0.004 0.008 0.012 0.016Pressure[kPa] Time [sec]R=15 m - W=20 kgpR=30 m - W=20 kgpR=10 m - W=20 kgpR=20 m - W=50 kgp19Scaled distanceSide-on pressureSide-on impulse densityShock durationShock waveReflected pressureINTENSITY MEASUREIntensity measure12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 201101001000100 1000 10000 100000P[kPa]i [kPa ms]θ=2θ=5θ=10IDPI: impulsive regionD: dynamic regionP: pressure regionIntensity measure12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 210204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failure12345Intensity measurePierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • CDL (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=122 Fragility curves – FlowchartFragility curves for n° MCDLs and the k-thstand-off distance (R)Fragility curves for n° MCDLs and n° L stand-offdistances (R)Fragility curve for the j-thCDL and the k-th stand-offdistance (R)12345• CDL: Component Damage Level• R: Stand-off distance• Z: Scaled distance• FC-CDL: numerical Fragility Curve of theComponent 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, or numberof the Zs• M: number of the CDLs• L: number of the stand-off distances• Interpolated FC-CDL: lognormalinterpolated Fragility Curve of theComponent Damage LevelPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 23Fence 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=ZNZ1 23NP(X>x|Z)Fragility curve for the j-th CDL andthe k-th stand-off distance (R)Monte CarloSimulationFragility curves – Computing the fragility curve12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 240204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failure j-th CDLk-th Ri-th ZFragility curves – Results12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 25Component 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 DamageCDLRFragility curves – Results12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 26Fence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]Blast scenario - Section view12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 270204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate DamageFragility curves – Results12345SafeUnsafeExamplePierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 28Fence barrierVehicle bombw [kgp]p [W]Stand-off distancer [m]p [R]Cladding wallθip [Θi]Scaled distancep[Z]ZBlast scenario - Section view12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 290204060801002.4 2.6 2.8 3.0 3.2 3.4Pf(X>x0|Z)ZHazardous Failurep(Z)[-]Fragility curves – Failure probability12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 30CDLMean 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 %Fragility curves – Failure probability12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 31 Presentation outline1 Introduction2 Component damage levels and response parameters3 Blast scenario and target4 Fragility curves5 ConclusionsPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 321- Fragility curves can be helpful in the design of precastconcrete wall panels, or cladding panels in general.Conclusions123450204060801003.0 3.5 4.0 4.5 5.0Pf(X>x0|Z)ZModerate DamageSafeUnsafeExamplePierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 332- It is important to define a appropriate thresholds for theprobability of failure.3- The probability of failure computed by means of fragilitycurve analysis and Monte Carlo analysis shows a maximumdifference of 11 % for the case study wall panel. Thequestion is, is this acceptable?4- In a future study, it could be useful to implement fragilitysurfaces instead of fragility curves.5- Also, it could be useful to account for the structuraldeterioration of the wall panel on computing the fragilitycurves.Conclusions12345Pierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -
    • 34Advances in computational methods for resilient structural systemsunder extreme hazardsMinisymposium Organizers: J. Ricles, T. KaravasilisChair: J. RiclesPierluigi OlmatiSapienza University of Romepierluigi.olmati@uniroma1.itwww.francobontempi.org- June 12, 2013 -Fence 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