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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

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

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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)

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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

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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

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

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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

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

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

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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

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

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

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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

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

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

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

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

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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

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

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

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

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

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

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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

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

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

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

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

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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

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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.

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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