1. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA Contents  Introduction  Modelling approach ongoing work  Summary

3. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA Introduction  Inspection data graphite moderator brick channel bore measurement/inspection unit magnified deformation of a graphite moderator brick height bore diameter N

6. INGSM-14, 16 th -18 th September 2013, Seattle, USA Introduction  Inspection data

7. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

9. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

10. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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 FE mesh of an AGR brick fluence temperature weight loss

11. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

12. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

13. INGSM-14, 16 th -18 th September 2013, Seattle, USA Metric  Measurement preferably available in simulator & calibration data sensitive to parameter(s) under investigation  insensitive to others  Two possibilities

14. INGSM-14, 16 th -18 th September 2013, Seattle, USA Metric  Stress not in calibration data compare against strength data and cracking observations

15. INGSM-14, 16 th -18 th September 2013, Seattle, USA Metric  Ovality

16. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

17. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

18. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

20. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix EmulatorCalibrated parameters Simulator Calibration data

21. INGSM-14, 16 th -18 th September 2013, Seattle, USA irradiation oxidation Calibration data

22. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix Calibration data EmulatorCalibrated parameters Simulator

23. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix EmulatorCalibrated parameters Simulator Calibration data

24. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix EmulatorCalibrated parameters Simulator Calibration data

26. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix EmulatorCalibrated parameters Simulator Calibration data

27. INGSM-14, 16 th -18 th September 2013, Seattle, USA Modelling approach Calibrated curves Metric Design matrix EmulatorCalibrated parameters Simulator Calibration data

28. INGSM-14, 16 th -18 th September 2013, Seattle, USA Calibrated curves Gilsocarbon

29. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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. INGSM-14, 16 th -18 th September 2013, Seattle, USA 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.ukmuhammad.fahad@manchester.ac.uk