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Králik Juraj

A RSM Method for Nonlinear Probabilistic Analysis of NPP Reinforced Concrete Structures. Králik Juraj. Outline.  Brief look at the principal problems of PSA 3 level analysis.  Scenario of possible accidents.  Monitoring of NPP and definition of the investigation tasks.

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Králik Juraj

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  1. A RSM Method for Nonlinear Probabilistic Analysis of NPP Reinforced Concrete Structures Králik Juraj

  2. Outline Brief look atthe principal problems of PSA 3 level analysis Scenario of possible accidents Monitoring of NPP and definition of the investigation tasks FE - model of the NPP structures Nonlinear analysis of the concrete containment Probability analysis of the concrete containment failure using RSM method Conclusions 2

  3. NPP Accident in Cernobil Chernobyl power plant in 2003 with the sarcophagus containmentstructure Aerial view of the damaged core on May 3, 1986. Roof of the turbine hall is damaged (image center). Roof of the adjacent reactor 3 (image lower left) shows minor fire damage. Thebattle to contain the contamination and avert agreater catastrophe ultimately involved over500,000 workers and cost an estimated 18 billionrubles. A 2006 report predicted 30,000 to60,000 cancer deaths as a result of Chernobyl fallout. 3 26 April 1986

  4. The Fukushima Daiichi Incident 2. Accident progression • Unit 1 und 3 • Hydrogen burn inside the reactor service floor • Destruction of the steel-frame roof • Reinforced concrete reactor building seems undamaged • Spectacular but minor safety relevant 4

  5. Experimental testing of NPP Contaiment ISP48 The design pressure is 0.39 MPa. *** Failure pressure is 1.42 MPa PCCV Model after the Structural Failure Mode Test 5

  6. Problems  Definition fothescenariofor LOCAloads  Consideration of the long-term influence of the temperature, creep and shrinkageof concrete after 20 years  Consideration of the soil-structure interaction, the influence of the soil consolidation after 20 years   Investigation of the concrete cracking and crushing Checking of calculation model and its accuracy Calculation means  Program ANSYS and own programs CREEP, SHRINK and CRACK 6

  7. PSA 3 level Analysis of Containment failure 7

  8. Probabilistic safety assessment Definition PSA 3 level Systematic study of the possibilities of the penetration hermetic zone due to accident of the various technology segments considering the uncertainties of the structures and accident posibilities. Aim of the PSA 3 level Definition of failure pressionpuand its probability distribution in dependency of all posibility uncertainties (action effects and structure resistance) Three sourses of uncertainties for PSA 3 level 1. Definition of plant damage states (PDS) 2. Simulation of the problem, including eventtree construction and models 3. Input data used to feed models 8

  9. Plant damage states Each PDS consists of a collection of core damage sequences, which are expected to behave similarly following the onset of core damage. The PDS set includes 69 possible combinations of PDS parameter values. It should be noted that not all of the possible combinations of PDS parameter values need to be considered. The grouping diagram for core damage sequences in the full power state is shown in follow scheme 9

  10. LOCA Loss of Collant Accident Scenario 10

  11. Accident progression • Four main source of Accident progression • Large LOCA (2x  500mm) • Transients or small LOCA (13mm, 32mm, 71mm ) • Interfacing LOCA • Open reactor (or fuel pool) 11

  12. LOCA Dp= 87kPa pmax= 135,5kPa pmax= 222,7kPa 12

  13. LOCA DT= 60oC Tmax = 149oC Tmax = 156oC 13

  14. Monitoring of Power Plant State 14

  15. Box PG and emergency basin of NPP V1 EWST 15

  16. Look into Space below EWST 16

  17. Nuclear Power Plant FE - model 17

  18. Calculation model of the main building of NPP V1 JaslovskéBohunice 26 923 elements 325 036 DOF 18

  19. Calculation model of the main building of NPP V1 JaslovskéBohunice 19

  20. Corrosion model Sommer’s law Faraday’s law 20

  21. Experimental testing and numerical analysis of NPP 21

  22. Nonlinear model of Reinforced Concrete Shell Structures 22

  23. Concrete cracking model 23

  24. fc Tensil Failure fc Compressive Failure Fig.6 Bidimensional conrete model Concrete cracking model 24

  25. Layered model of concrete shell Shell91 25

  26. 9 2x23,5 65 9 Comparison Numerical Solution with Experiment 26

  27. Nonlinear Analysis of Reinforced Concrete Containment 27

  28. Linear solution for LOCA 28

  29. Nonlinear Solution for LOCA 29

  30. Tension strength in Plate at level +10,5m 30

  31. 260kPa 210kPa Non-linear Containment Analysis 31

  32. Probability Analysis of Containment Resistance 32

  33. Probability Analysis of Containment  The reliability condition is defined in the form SF = R - E ≥ 0, various in the form relative SF = R / Ed -1 ≥ 0 where R is the capacity of structure, E - the load action.  The total strain vector forlth loadlevel gvar , Tvar , pvarand evar are the variable defined by histograms • The reliability of the shell structure is defined depending on concrete failure condition for layered shell as follow • R = Fui(epvar(t,) ;eup; x) + eup , • where epvar(t,) is the variable strain vector 33

  34. Uncertainty of Random Quantity 34

  35. Response Surface Method - RSM Probability of failure where fE(x), fR(x) are the density functions and FE(x),FR(x) are the distribution functions of action E and resistance R Aproximation and simulation Number of variability input : 4 Number of simulations CCD : 25 35

  36. Input Response Black Boxed System DOE and Experiments RS Model 1 0 x2 -1 0 1 -1 x1 Concept of Response Surface Method Original System RSM : Response Surface Method : Response Surface Model Intelligent System Design Lab. 36

  37. Scheme of Aproximation Methods CentralCompositeDesign Box-BehnkenMatrix Number of variability input : 4 Number of simulations BBM : 25 Number of variability input : 4 Number of simulations CCD : 25 37

  38. Advantages and Disadvantages Aproximation methods - RSM :  Advantages • reduction of simulation quantities • posibilities to use the „designexperiments“ or „regresion analysis” • independence of simulations Disadvantages • Number of simulation increase with the number of input simples • Non acceptable for non continuous problems 38

  39. Probability of containment failure Pm=320kPa Model without deqradation SF=83,4% Model with deqradation SF=94,8% 39

  40. Probability of containment failure Pressure pm=260 kPa Pressure pm=320 kPa 40

  41. CONCLUSIONS ÜProbability of the containment failure is less as 10-6 for overpressure 320kPa and the original model without degradation effects. Ü Probability of the containment failure is equal to 1,375.10-4 for overpressure 320 kPa consideringdegradation effects. ÜThe degradation - the bottom EWST plate and wall vertical microcracks – decrease the safety of CTMT structure, but not significant (about 15%) ÜThe RSM method is very effective method for nonlinear problems on robust FE- models. 41

  42. Thanks

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