Reliability Analysis of the Ductile Fracture of Overpacks for High-Level Radioactive Waste in Repository Conditions
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 2
Abstract
In France, a deep geological repository project is under development for radioactive waste management. The lack of knowledge from similar facilities and the large time scales involved result in uncertainties about the repository environment in operating conditions. The reliability methods are dedicated to dealing with such problematics and are used in this work to study the behavior of the overpack containing high-level radioactive waste. Its function is to isolate the waste from the environment for the first . The analysis is based on a finite-element model of the system integrating the time-related degradation of the system and considers a ductile fracture criterion. The stochastic structural model includes uncertain and time dependent corrosion rates and mechanical loading. A Kriging metamodel is calibrated in order to predict the behavior of the finite-element model with a much smaller computation time. The failure probability of the system is estimated using Monte Carlo simulations based on the results of both the finite-element model and the Kriging metamodel. The behavior of the system and the parameters having a first order influence on its performances are investigated through a sensitivity analysis.
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Data Availability Statement
The data (Monte Carlo simulations, AK-MCS iterations, finite-element model, and corrosion analytical models) is proprietary in nature, and its availability will be handled by Andra. Requests should be addressed to Dr. Bumbieler ([email protected]).
Acknowledgments
This work is founded by Andra, which is gratefully acknowledged for technical and financial support. The authors would like to gratefully thank Didier Crusset, Valerie Deydier, and Sophia Necib for the helpful discussions on corrosion modes expected in repository conditions.
References
Ahammed, M., and R. E. Melchers. 1997. “Probabilistic analysis of underground pipelines subject to combined stresses and corrosion.” Eng. Struct. 19 (12): 988–994. https://doi.org/10.1016/S0141-0296(97)00043-6.
Amirat, A., A. Mohamed-Chateauneuf, and K. Chaoui. 2006. “Reliability assessment of underground pipelines under the combined effect of active corrosion and residual stress.” Int. J. Press. Vessels Pip. 83 (2): 107–117. https://doi.org/10.1016/j.ijpvp.2005.11.004.
ANDRA (Agence Nationale pour la gestion des Déchets Radioactifs). 2005. Dossier 2005 synthesis Argile: Tome phenomenological evolution of a geological repository. Paris: ANDRA.
Ayyub, B. M. 2001. Elicitation of expert opinions for uncertainty and risks. Boca Raton, FL: CRC Press.
Beaurepaire, P., C. Mattrand, N. Gayton, and J. Y. Dantan. 2018. “Tolerance analysis of a deformable component using the probabilistic approach and Kriging-based surrogate models.” J. Risk Uncertainty Eng. Syst. 4 (3): 04018028. https://doi.org/10.1061/AJRUA6.0000979.
Beer, M., S. Ferson, and V. Kreinovich. 2013. “Imprecise probabilities in engineering analyses.” Mech. Syst. Sig. Process. 37 (1–2): 4–29. https://doi.org/10.1016/j.ymssp.2013.01.024.
Bumbieler, F., S. Necib, J. Morel, D. Crusset, and G. Armand. 2015. “Mechanical and SCC behavior of an API5L steel casing within the context of deep geological repositories for radioactive waste.” In Vol. 56963 of Proc., ASME 2015 Pressure Vessels and Piping Conf. New York: ASME. https://doi.org/10.1115/PVP2015-45234.
Chen, N., D. Yu, B. Xia, and M. Beer. 2016. “Uncertainty analysis of a structural—Acoustic problem using imprecise probabilities based on P-Box representations.” Mech. Syst. Sig. Process. 80 (Dec): 45–57. https://doi.org/10.1016/j.ymssp.2016.04.009.
Ciampoli, M. 1999. “A probabilistic methodology to assess the reliability of deteriorating structural elements.” Comput. Methods Appl. Mech. Eng. 168 (1–4): 207–220. https://doi.org/10.1016/S0045-7825(98)00141-8.
Croisé, J., G. Mayer, J. Talandier, and J. Wendling. 2011. “Impact of water consumption and saturation-dependent corrosion rate on hydrogen generation and migration from an intermediate-level radioactive waste repository.” Transp. Porous Media 90 (1): 59–75. https://doi.org/10.1007/s11242-011-9803-0.
de Angelis, M., E. Patelli, and M. Beer. 2015. “Advanced line sampling for efficient robust reliability analysis.” Struct. Saf. 52 (Jan): 170–182. https://doi.org/10.1016/j.strusafe.2014.10.002.
Dunn, W. L., and J. K. Shultis. 2012. Exploring Monte Carlo methods. Boston: Elsevier.
Durrenberger, L., D. Even, A. Molinari, and A. Rusinek. 2006. “Influence of the strain path on crash properties of a crash-box structure by experimental and numerical approaches.” J. de Physique IV (Proceedings) 134 (Aug): 1287–1293. https://doi.org/10.1051/jp4:2006134195.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
Goller, B., M. Broggi, A. Calvi, and G. I. Schueller. 2011. “A stochastic model updating technique for complex aerospace structures.” Finite Elem. Anal. Des. 47 (7): 739–752. https://doi.org/10.1016/j.finel.2011.02.005.
Gurson, A. L. 1975. “Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media.” J. Eng. Mater. Technol. 99 (1): 2–15. https://doi.org/10.1115/1.3443401.
Hamby, D. M. 1994. “A review of techniques for parameter sensitivity analysis of environmental models.” Environ. Monit. Assess. 32 (2): 135–154. https://doi.org/10.1007/BF00547132.
Hoorelbeke, J. M. 2009. Conteneurs pour le stockage des déchets HA et MAVL. Paris: Techniques de l'ingénieur.
Jones, D. R., and M. Schonlau. 1998. “Efficient global optimization of expensive black-box functions.” J. Global Optim. 13 (4): 455–492. https://doi.org/10.1023/A:1008306431147.
Krige, D. G. 1951. “A statistical approach to some basic mine valuation problems on the Witwatersrand.” J. Chem. Metall. Min. Soc. S. Afr. 52 (6): 119–139.
Lelièvre, N., P. Beaurepaire, C. Mattrand, and N. Gayton. 2018. “AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models.” Struct. Saf. 73 (Jul): 1–11. https://doi.org/10.1016/j.strusafe.2018.01.002.
Lemaire, M. 2013. Structural reliability. Hoboken, NJ: Wiley.
Ling, C., and Z. Lu. 2020. “Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis.” Appl. Math. Modell. 77 (Jan): 1820–1841. https://doi.org/10.1016/j.apm.2019.08.025.
Martin, J. D., and T. W. Simpson. 2004. “On using Kriging models as probabilistic models in design.” J. Mater. Manuf. 113: 129–139.
Matheron, G. 1973. “The intrinsic random functions and their applications.” Adv. Appl. Probab. 5 (3): 439–468. https://doi.org/10.2307/1425829.
Meng, Z., Z. Zhang, D. Zhang, and D. Yang. 2019. “An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization.” Comput. Methods Appl. Mech. Eng. 357 (Dec): 112570. https://doi.org/10.1016/j.cma.2019.112570.
Moustapha, M., B. Sudret, J. M. Bourinet, and B. Guillaume. 2016. “Quantile-based optimization under uncertainties using adaptive Kriging surrogate models.” Struct. Multidiscip. Optim. 54 (6): 1403–1421. https://doi.org/10.1007/s00158-016-1504-4.
Necib, S., F. Bumbieler, C. Duret-Thual, N. Bulidon, D. Crusset, and P. Combrade. 2017. “Assessment of the resistance to environmentally assisted cracking (EAC) of C-steel casing and over pack in the Claystone.” Corros. Eng. Sci. Technol. 52 (1): 95–100. https://doi.org/10.1080/1478422X.2017.1336003.
Nguyen, T. 2017. “Flambage sous contact d'une coque cylindrique soumise à pression externe.” [In French.] Doctoral dissertation, Dept. of Civil Engineering Soils, Materials, Structures, Building Physics, The Institut National des Sciences Appliquées de Lyon.
O’Hagan, A. 2006. Uncertain judgments: Eliciting experts’ probabilities. Hoboken, NJ: Wiley.
Patelli, E., M. Broggi, Y. Govers, and J. E. Mottershead. 2017. “Model updating strategy of the DLR-AIRMOD test structure.” Procedia Eng. 199 (Jan): 978–983. https://doi.org/10.1016/j.proeng.2017.09.221.
Persoons, A., P. Beaurepaire, A. Chateauneuf, and F. Bumbieler. 2019. “Time-dependent reliability analysis of over packs for high-level radioactive waste.” Nucl. Eng. Des. 352 (Oct): 110156. https://doi.org/10.1016/j.nucengdes.2019.110156.
Petryna, Y. S., and W. B. Krätzig. 2005. “Computational framework for long-term reliability analysis of RC structures.” Comput. Methods Appl. Mech. Eng. 194 (12–16): 1619–1639. https://doi.org/10.1016/j.cma.2004.09.002.
Rubinstein, R. Y., and D. P. Kroese. 2008. “Simulation and the Monte Carlo method, Wiley series.” In Probability and statistics. 2nd ed. Hoboken, NJ: Wiley.
Ryberg, A. B., R. Domeij Bäckryd, and L. Nilsson. 2012. Metamodel-based multidisciplinary design optimization for automotive applications. Linköping, Sweden: Linköping University Electronic Press.
Saltelli, A. 2008. Global sensitivity analysis: The primer. Hoboken, NJ: Wiley.
Schlegel, M. L., C. Bataillon, F. Brucker, C. Blanc, D. Prêt, E. Foy, and M. Chorro. 2014. “Corrosion of metal iron in contact with anoxic clay at 90°C: Characterization of the corrosion products after two years of interaction.” Appl. Geochem. 51 (Dec): 1–14. https://doi.org/10.1016/j.apgeochem.2014.09.002.
Sobol’, I. M. 1993. “Sensitivity estimates for nonlinear mathematical models.” Math. Modell. Comput. Exp. 1 (4): 407–414.
Yu, W. 2009. “Corrosion effects on the ductile fracture, strength and reliability of membranes, plates and shells.” Doctoral dissertation, Dept. of Naval Architecture and Marine Engineering, Univ. of Michigan.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 2 • June 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 2, 2020
Accepted: Nov 18, 2020
Published online: Feb 19, 2021
Published in print: Jun 1, 2021
Discussion open until: Jul 19, 2021
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