Development of a stress-based emulator for AGR moderator bricks

1. Development of a stress-based emulator for AGR moderator bricks M Fahad†, K McNally‡, G Hall†, BJ Marsden†, P Mummery†, and N Warren‡ †Nuclear Graphite Research Group, School of MACE, The University of Manchester, Manchester, England M13 9PL ‡Statistical Modelling Team, Mathematical Sciences Unit, Health and Safety Laboratory, Harpur Hill, Buxton, England SK17 9JN

2. Contents • Introduction • Modelling approach • ongoing work • Summary

3. Introduction • Why? • AGR safety requirements • safe shutdown • continued fuel cooling • AGR lifetime • structural integrity of graphite core • number and behaviour of cracked graphite components • assessments and predictions of graphite and core behaviour • uncertainty in predictions • internal stresses require understanding of • dimensional changes • irradiation creep (a.k.a. stress-dependent dimensional change)

4. Introduction • Irradiation creep data • many data on inert behaviour • limited for Gilsocarbon • no data on combined behaviour • fast neutron irradiation + radiolytic oxidation • some pre-oxidised data • new MTR programme(ACCENT) • empirical relationships • informed behaviour Gilsocarbon

5. Introduction bore diameter • Inspection data bore diameter N graphite moderator brick height channel bore measurement/inspection unit magnified deformation of a graphite moderator brick

6. Introduction • Inspection data

7. Introduction • Emulator approach • presented at INGSM-11 & INGSM-12 • applied successfully for dimensional change behaviour • inspection data • constitutive equations • calibrated dimensional changes • inert similar to baseline • reduced effect of oxidation

8. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

9. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

10. Simulator • Representative model of physical process(es) • Finite element model of AGR brick • finite element mesh • loadings & boundary conditions • constitutive relationships • irradiation creep • UK • EDF Energy • ... • Many parameter inputs • uncertainties & unknowns • effect of oxidation on irradiation creep weight loss temperature fluence FE mesh of an AGR brick

11. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

12. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

13. Metric • Measurement • preferably available in simulator & calibration data • sensitive to parameter(s) under investigation • insensitive to others • Two possibilities

14. Metric • Stress • not in calibration data • compare against strength data and cracking observations

15. Metric • Ovality

16. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

17. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

18. Design matrix • Experimental design • Variation in parameter inputs • adequately cover parameter space • encompass parameter limits • Maximin Latin Hypercube sampling • Irradiation creep • e.g. 200 design points/FE models

19. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

20. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

21. Calibration data irradiation oxidation

22. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

23. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

24. Emulator • Statistical approximation of simulator • built using runs of simulator • design matrix/points • based upon Gaussian processes • in a Bayesian framework • Advantages • fast • computationally efficient cf. FE models • easy to modify

25. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

26. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

27. Modelling approach Simulator Calibrated parameters Metric Emulator Design matrix Calibrated curves Calibration data

28. Calibrated curves Gilsocarbon

29. Summary • Bayesian emulator • FE model of AGR brick • Reverse engineer irradiation creep behaviour • inspection data • constitutive equations • Initial procedure outlined • Next stage • run design points • calibrate and compare • re-iterate

30. Acknowledgement The authors wish to thank the Office for Nuclear Regulation (Health & Safety Executive) for sponsoring this work. Disclaimer Any views or opinions presented are those of the authors and do not necessarily represent those of the sponsor.

31. Development of a stress-based emulator for AGR moderator bricks M Fahad†, K McNally, G Hall, BJ Marsden, P Mummery, and N Warren †Nuclear Graphite Research Group, School of MACE, The University of Manchester, Manchester, England M13 9PL email: muhammad.fahad@manchester.ac.uk