Calculating Nuclear Power Plant Vulnerability Using Integrated Geometry and Event/Fault Tree Models

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Calculating Nuclear Power PlantVulnerability
Using Integrated Geometry andEvent/Fault Tree
Models

• ANS/EPR 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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Terrorist Attacks Against American Targets Using
Car-Bomb Technology
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Event/Fault Tree Models and Geometry Models
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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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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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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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Reflective Blast Enhancement

• Correlations can account for effect of walls
  surrounding the charge

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VISAC Concrete Breach Models

• NDRC experiments for air blast against concrete
  walls

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Overpressure Fragility Curves

• Critical components require fragility functions
• Plot of Pkill versus peak overpressure
• Either linear or logarithmic interpolation

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For Independent Events

• P P1P2PJ
• P SPi SPiPj P1P2PJ
• 1 - (1-P1)(1-P2)(1-PJ)

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Event/Fault Tree Evaluation

• Brute Force
• Monte Carlo
• Minimal Cut Set Analysis
• Rare Events Approximation
• Upper Bound
• Exact with Passes

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Minimal Cut Sets

• Sequence E3E4 E1E2E5 E1E4E5
• C1 C2
  C3
• P(Seq.) SP(Ci) - SP(CiCj) SP(CiCjCk) -
• SP(Ci)
• lt 1 (1-P(C1))(1- P(C2))(1-
  P(C3))

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SAPHIRE Example Problem

• seq1 /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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Example Problem severe damage
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Example Problem severe damage
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Vulnerability Maps
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Geometry Fidelity
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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