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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