Paper:

# Options for the Treatment of Uncertainty in Seismic Safety Assessment of Nuclear Power Plants

## Tamas Janos Katona

MVM Nuclear Power Plant Paks Ltd., 7133, FADD, TOKAJ u. 24, Hungary

This paper proposes options for improving seismic safety analysis for nuclear power plants. Cumulative absolute velocity (CAV) has been considered and analyzed for describing different load-cycle-dependent phenomena, e.g., fatigue failure and soil liquefaction. Fatigue damage estimation is based on load-cycle counting, which can be performed by counting zero or level crossings if power spectral density (PSD) of load time history is known. Correlation between CAV and moments of PSD of load time history is derived in this paper. A fatigue failure criterion is developed in terms of CAV. P-box theory is proposed for improving uncertainty modeling of probabilistic seismic safety assessment. P-boxes are represent upper and lower bounds of the distribution function specified by left side and right side distribution functions. The utilization of the p-box method has an advantage if the conditional probability of a particular failure mode of a component is known approximately only, and the sample size of damage histories is small or inconsistent or modeling of component failure is uncertain.

*J. Disaster Res.*, Vol.8, No.3, pp. 465-472, 2013.

- [1] J. Elter, “Insights from the seismic probabilistic safety analysis of Paks Nuclear Power Plant,” International Conference on Reliability, Safety and Hazard, Mumbai 2005 (ICRESH05), in P. V. Varde (Ed.), “Reliability, Safety and Hazard: Advances in Risk-informed Technology,” 2006, pp. 381-387, 2006.
- [2] “Preliminary Findings and Lessons Learned from the 16 July 2007 earthquake at Kashiwazaki-Kariwa NPP,” Mission Report, IAEA, Vienna, August 2007.
- [3] ASME, ASME/ANS RA-S-2008, “Standard for Level 1/Large Early Release Frequency Probabilistic Risk Assessment for Nuclear Power Plant Applications.”
- [4] B. Ellingwood, “Validation of Seismic Probabilistic Risk Assessments of Nuclear Power Plants,“ U.S. NRC NUREG/GR-0008, 1994.
- [5] R. J. Budnitz, et al., “An Approach to the Quantification of Seismic Margins in Nuclear Power Plants,” Lawrence Livermore National Laboratory, NUREG/CR-4334, 1985.
- [6] P. G. Prassinos, M. K. Ravindra, and J. D. Savay, “Recommendations to the Nuclear Regulatory Commission on Trial Guidelines for Seismic Margin Reviews of Nuclear Power Plants,” Lawrence Livermore National Laboratory, NUREG/CR-4482, 1986.
- [7] EPRI, “A Methodology for Assessment of Nuclear Power Plant Seismic Margin,” Electric Power Research Institute, NP-6041, 1988.
- [8] EPRI, “Criterion for determining accidence of the operating basis earthquake,” EPRI NP-5930, July 1988.
- [9] K. Minagawa, S. Fujita, S. Kitamura, and S. Okamura, “Fracture Prediction of Piping Using Energy Balance Method,” Transactions, SMiRT 19, Toronto, August 2007, Paper # K12/5, 2007.
- [10] L. Cabanas, B. Benito, and M. Herraiz, “An Approach To The Measurement Of The Potential Structural Damage Of Earthquake Ground Motions,” Earthquake Engineering And Structural Dynamics, Vol.26, pp. 79-92, 1997.
- [11] J. Nie, J. Xu, and C. Costantino, “P-CARES: Probabilistic Computer Analysis for Rapid Evaluation of Structures,” NUREG/CR-6922, BNL-NUREG-77338-2006, 2006.
- [12] Z. Qu and L. Ye, “Strength Deterioration Model Based on Effective Hysteretic Energy Dissipation for RC-members Under Cyclic Loading,” Joint Conference Proceedings, 7
^{th}International Conference on Urban Earthquake Engineering (7CUEE) &5^{th}International Conference on Earthquake Engineering (5ICEE), March 3-5, 2010, Tokyo Institute of Technology, Tokyo, Japan, 2010. - [13] I. M. Taflampas, C. C. Spyrakos, and A. Maniatakis Ch., “A New Definition of Strong Motion Duration and Related Parameters Affecting the Response of Medium-Long Period Structures,” The 14
^{th}World Conference on Earthquake Engineering, October 12-17, 2008, Beijing, China, 2008. - [14] K. Ochiai, K. Kobayashi, and A. Chigama, “Damage Indicating Parameters and Damage Modes of Mechanical Components,” 1st Kashiwazaki International Symposium on Seismic Safety of Nuclear Installations and Embedded Topical Meetings, November 2010.
- [15] T. J. Katona, “Options for the treatment of uncertainty in seismic probabilistic safety assessment of nuclear power plants,” Pollack Periodica, Vol.5, No.1, pp. 121-136, 2010.
- [16] T. J. Katona, “Interpretation of the physical meaning of the cumulative absolute velocity,” Pollack Periodica, Vol.6, No.1, pp. 9-106, 2011.
- [17] D. R. Karanki, H. S. Kushwaha, A. K. Verma, and S. Ajit, “Uncertainty Analysis Based on Probability Bounds (P-Box) Approach in Probabilistic Safety Assessment,” Risk Analysis, Vol.29, No.5, pp. 662-675, 2009, DOI: 10.1111/j.1539-6924.2009.01221, 2009.
- [18] J. H. Kim, I.-K. Choi, and J.-H. Park, “Uncertainty analysis of system fragility for seismic safety evaluation of NPP,” Nuclear Engineering and Design, 241, pp. 2570-2579, 2011.
- [19] EPRI, “Standardization of the Cumulative Absolute Velocity,” Report No. EPRI TR-100082-T2, EPRI, Palo Alto, California, 1991.
- [20] K. W. Campbell and Y. Bozorgnia, “Analysis of Cumulative Absolute Velocity (CAV) and JMA Instrumental Seismic Intensity (IJMA) Using the PEER-NGA Strong Motion Database,” PEER Report 2010/102, Pacific Earthquake Engineering Research Center, College of Engineering University of California, Berkeley, February 2010,

http://www.eqsafetysys.com/cav_paper.htm [accessed Sep. 12, 2012] - [21] S. Kramer and R. A. Mitchell, “Ground Motion Intensity Measures for Liquefaction Hazard Evaluation, Earthquake Spectra,” Vol.22, No.2, pp. 413-438, Earthquake Engineering Research Institute, 2006.
- [22] A. Papoulis, “Probability, Random Variables, and Stochastic Processes,” McGraw-Hill, 1965, 1985.
- [23] J. S. Bendat, “Probability Functions for Random Responses,” NASA report on Contract NAS-5-4590, 1964.
- [24] T. Dirlik, “Application of computers in Fatigue Analysis,” University of Warwick Thesis, 1985.
- [25] V. A. Passipoularidis and P. Brøndsted, “Fatigue Evaluation Algorithms: Review,” Risø-R-1740(EN) November 2009, ISBN 978-87-550-3835-6, 2009.
- [26] T. J. Katona, “Modeling of Fatigue Type Seismic Damage for Nuclear Power Plants,” to be published in Computational Material Science, Vol.64, pp. 22-24, 2012.
- [27] P. H. Wirsching, H. P. Nguyen, and K.-T. Ma, “Fatigue reliability as a first passage problem,” in: Proceedings of 8
^{th}ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, University of Notre Dame, 2000. - [28] K. W. Campbell and Y. Bozorgnia, “A Ground Motion Prediction Equation for the Horizontal Component of Cumulative Absolute Velocity (CAV) Based on the PEER-NGA Strong Motion Database, Earthquake Spectra,” Vol.26, No.3, pp. 635-650, © 2010, Earthquake Engineering Research Institute, 2010.
- [29] K. W. Campbell and Y. Bozorgnia, “Prediction equations for the standardized version of cumulative absolute velocity as adapted for use in the shutdown of U.S. nuclear power plants,” Nuclear Engineering and Design, Vol.241, pp. 2558-2569, 2011.
- [30] G. Wang and W. Du, “Empirical correlations between cumulative absolute velocity and spectral accelerations from NGA ground motion database,” Soil Dynamics and Earthquake Engineering, Vol.43, pp. 229-236, 2012.
- [31] P. E. J. Varpasuo, et al., “Seismic Hazard Evaluation For Simo and Pyhajoki NPP Sites Using PGA and CAV as Scaling Parameter,” Proceedings of the International Youth Nuclear Congress 2010, 12-18 July 2010, Cape Town, South Africa, Paper No.138, 2010.
- [32] M. Kostov, “Site Specific Estimation of Cumulative Absolute Velocity,” 18
^{th}International Conference on Structural Mechanics in Reactor Technology (SMiRT 18), Beijing, China, August 7-12, 2005, paper SMiRT18- K03-4, 2005. - [33] D. A. Heacock and E. S. Grecheck, “Dominion North Anna Power Station Restart Readiness,” October 21, 2011 Briefing, 2011.
- [34] J. Hancock and J. J. Bommer, J “Predicting the Number of Cycles of Ground Motion,” 13
^{th}World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004, Paper No.1989, 2004. - [35] J. Hancock and J. J. Bommer, “Predicting the Number of Cycles of Ground Motion,” Earthquake Engineering and Structural Dynamics, Vol.34, pp. 637-664, 2005.
- [36] S. Kramer and S. B. Upsall, “Instrumental Intensity Scales for Geohazards,” 2006 ECI Conference on Geohazards, 2006,

http://services.bepress.com/eci/geohazards/11 [accessed May 21, 2011] - [37] R. P. Kennedy and M. K. Ravindra, “Seismic fragilities for nuclear power plant risk studies, Nuclear Engineering and Design,” Vol.79, pp. 47-68, 1984.
- [38] R. C.Williamson and T. Downs, “Probabilistic arithmetic I: Numerical methods for calculating convolutions and dependency bounds,” International Journal of Approximate Reasoning, Vol.4, pp. 89-158, 1990.
- [39] W. T. Troy and S. Ferson, “Probability bounds analysis in environmental risk assessments,” Applied Biomathematics, 100 North Country Road, Setauket, New York, 2003,

www.ramas.com/pbawhite.pdf [accessed Feb. 11, 2010]

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