o ak r idge n ational l aboratory u. s. d epartment of e nergy 1 calculating nuclear power plant...
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Calculating Nuclear Power PlantVulnerability Using
Integrated Geometry and
Event/Fault Tree Models
ANS/EP&R Washington, DC November 20, 2002
Douglas E. Peplow, C. David Sulfredge,
Robert L. Sanders, and Robert H. Morris
Oak Ridge National Laboratory
Todd A. Hann
Defense Threat Reduction Agency
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Terrorist Attacks Against American Targets Using Car-Bomb Technology
Date Target/Location Delivery/Material TNT equiv (lbs)
Apr 1983 US Embassy Beirut, Lebanon
van
2000
Oct 1983 US Marine Barracks Beirut, Lebanon
truck, TNT with gas enhancement
12000
Feb 1993 World Trade Center New York, USA
van, urea nitrate and hydrogen gas
2000
Apr 1995 Murrah Federal Bldg Oklahoma City, USA
truck, ammonium nitrate fuel oil
5000
Jun 1996 Khobar Towers Dhahran, Saudi Arabia
tanker truck, plastic explosive
20000
Aug 1998 US Embassy Nairobi, Kenya
truck, TNT, possibly Semtex
1000
Aug 1998 US Embassy Dar es Salaam, Tanzania
truck 1000
Oct 2000 Destroyer USS Cole Aden Harbor, Yemen
small watercraft, possibly C-4
440
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Event/Fault Tree Models
and
Geometry Models
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Approaches to Blast Modeling
Hydrocode modeling Detailed, first-principles analysis Complex computer codes (CTH, DYNA-3D,
FLEX, etc.) Long computer run times
Correlation modeling Based on experimental test data Results given using scaled parameters Quick, with good general accuracy
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Early Nuclear Blast Testing
Nuclear tests at Nevada Test Site measured the blast resistance for many types of industrial and utility equipment
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Scaling Laws Allow Data Correlation
Hopkinson scaling parameters P = F1( R/w1/3)
I/w1/3 = F2( R/w1/3)
t/w1/3 = F3( R/w1/3)
Also known as “cube root” scaling
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Reflective Blast Enhancement
Correlations can account for effect of walls surrounding the charge
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
VISAC Concrete Breach Models NDRC experiments for air blast against concrete
walls
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Overpressure Fragility Curves
Critical components require fragility functions Plot of Pkill versus
peak overpressure Either linear or
logarithmic interpolation
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
For Independent Events…
P = P1P2…PJ
P = ΣPi – ΣPiPj + … ± P1P2…PJ
= 1 - (1-P1)(1-P2)…(1-PJ)
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Event/Fault Tree Evaluation
Brute Force Monte Carlo Minimal Cut Set Analysis
Rare Events Approximation Upper Bound Exact with Passes
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Minimal Cut Sets
• Sequence = E3E4 + E1E2E5 + E1E4E5 + …
= C1 + C2 + C3 + …
• P(Seq.) = ΣP(Ci) - ΣP(CiCj) + ΣP(CiCjCk) - …
~ ΣP(Ci)
< 1 – (1-P(C1))(1- P(C2))(1- P(C3))…
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
SAPHIRE Example Problemseq1 = /ecs = /epumpa /emova /ecva /tank /dga /emov1 + /tank /dga /ecvb /emov1 /emovb /dgb /epumpb
seq2 = ecs /ccs
= ecva emovb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + ecva epumpb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + epumpa emovb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + epumpa epumpb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + emova ecvb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + emova emovb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + emova emovb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + ecva ecvb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + emova epumpb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + ecva ecvb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + emov1 /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + epumpa epumpb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + epumpa ecvb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + ecva emovb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + ecva epumpb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + emova ecvb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + emov1 /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + epumpa emovb /cmov1 /tank /ccvb /cmovb /cpumpb /dgb + emova epumpb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + epumpa ecvb /cmov1 /tank /dga /cmova /ccva /cpumpa /dgb + dga /cmov1 /tank /ccvb /cmovb /cpumpb /dgb
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Example Problem – severe damage
Exact Cut Set Methods
Rare events
min cut upper bound
pass 1 pass 2 pass 3 pass 4 pass 5 pass 6
seq 1 0.379904 0.449060 0.399268 0.4490 0.3799 0.3799 0.3799 0.3799 0.3799
seq 2 0.209737 0.389429 0.327886 0.3894 0.0812 0.3198 0.1162 0.2813 0.1648
seq 3 0.410358 0.975697 0.631936 0.9757 -0.4369 2.0129 -3.0632 8.4509 -18.425
time 0.03 0.06 1.38 41.2 1013 19712
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Example Problem – severe damage
Brute Force Method Monte Carlo Method commons 17 3 errmax 0.01 0.001 histories 2500 245000
seq 1 0.379904 0.379904 0.3696 ± 0.0096 0.3800 ± 0.0010
seq 2 0.209737 0.209737 0.2024 ± 0.0080 0.2097 ± 0.0008
seq 3 0.410358 0.410358 0.4280 ± 0.0099 0.4103 ± 0.0010
time 2.2 0.0063 0.048 4.5
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Vulnerability Maps
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Geometry Fidelity
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Summary
Correlations using real data are faster than hydrocode calculations yet still accurate
Need fault/event tree calculator that handles large component failure probabilities
Geometric fidelity is important in obtaining useful results