1. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 1 Calculating Nuclear Power Plant Vulnerability 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

2. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 2 Terrorist Attacks Against American Targets Using Car-Bomb Technology

3. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 3 Event/Fault Tree Models and Geometry Models

4. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 4 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

5. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 5 Early Nuclear Blast Testing  Nuclear tests at Nevada Test Site measured the blast resistance for many types of industrial and utility equipment

6. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 6 Scaling Laws Allow Data Correlation  Hopkinson scaling parameters  P = F 1 ( R/w 1/3 )  I/w 1/3 = F 2 ( R/w 1/3 )  t/w 1/3 = F 3 ( R/w 1/3 )  Also known as “cube root” scaling

7. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 7 Reflective Blast Enhancement  Correlations can account for effect of walls surrounding the charge

8. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 8 VISAC Concrete Breach Models  NDRC experiments for air blast against concrete walls

9. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 9 Overpressure Fragility Curves  Critical components require fragility functions  Plot of P kill versus peak overpressure  Either linear or logarithmic interpolation

10. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 10 For Independent Events…  P = P 1 P 2 …P J  P = Σ P i – Σ P i P j + … ± P 1 P 2 …P J = 1 - (1-P 1 )(1-P 2 )…(1-P J )

11. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 11 Event/Fault Tree Evaluation  Brute Force  Monte Carlo  Minimal Cut Set Analysis  Rare Events Approximation  Upper Bound  Exact with Passes

12. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 12 Minimal Cut Sets Sequence = E 3 E 4 + E 1 E 2 E 5 + E 1 E 4 E 5 + … = C 1 + C 2 + C 3 + … P(Seq.) = Σ P(C i ) - Σ P(C i C j ) + Σ P(C i C j C k ) - … ~ Σ P(C i ) < 1 – ( 1-P(C 1 ) )( 1- P(C 2 ) )( 1- P(C 3 ) ) …

13. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 13 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

14. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 14 Example Problem – severe damage

15. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 15 Example Problem – severe damage

16. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 16 Vulnerability Maps

17. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 17 Geometry Fidelity

18. O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 18 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