Salome-Meca Users’ Day 2018 Probabilistic description of concrete’s Thermo -Hydro-Mechanical behavior in Nuclear Containment Buildings – Application to the VeRCoRs mock-up D. BOUHJITI , S. MICHEL-PONNELLE , B. MASSON, F. DUFOUR, J. BAROTH, M. BRIFFAUT http://fondation-grenoble-inp.fr/chaire/pereniti/ 20 th March2018 – EDF Lab Paris-Saclay, France
Salome-Meca Users’ Day 2018 CONTENT • Analysis framework • U ncertainties and variability of concrete’s THM properties • Tools to account for uncertainties in FE analysis of NCBs • Examples – VeRCoRs gusset: Probabilistic modeling of early-age cracking Probabilistic modeling of saturation rate • Conclusions VeRCoRs mock-up, EDF LAB Les Renardières 20 th March2018 – EDF Lab Paris-Saclay, France
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o ● Framework THM uncertainties Conclusion & applications The double-wall containment buildings (1300-1450 MWe NPP reactors) [22 reactors] • A reinforced and pre-stressed concrete inner wall tightness • an outer reinforced concrete wall protection against external effects Ambitions for EDF : • to demonstrate the good behavior of inner wall in situation of severe accident ; • to have a better comprehension of the leakage and its evolution with the ageing of the structure 1 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o ● Framework THM uncertainties Conclusion & applications How to answer such questions ? Feed-back Numerical Experimental analysis and tools studies NDT VERCORS (1/3 scale) 2 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o ● Framework THM uncertainties Conclusion & applications How to answer such questions ? Feed-back Numerical Experimental analysis and tools studies NDT Engineering z tools 3 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o Framework ● THM uncertainties Conclusion & applications THM uncertainties D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o Framework ● THM uncertainties Conclusion & applications Homogeneous Equivalent Material (HEM) Variable properties + Variable THM boundaries Molecular scale Meso scale Macro scale Concrete = heterogeneous + multiphasic material Time t 𝑦 Variable mechanical + transfer properties Cement, aggregates, voids 𝑧 Space 𝑨 Cement, capillary voids [VeRCoRs concrete] CSH, gel pores 4 C-S-H molecular model D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o Framework ● THM uncertainties Conclusion & applications Variable properties + Variable THM boundaries [Prestressing losses variation in VeRCoRs] [Inner temperature variation in a real NCB] [Design of a full scale NCB] 5 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France o Modeling tools o o Framework ● THM uncertainties Conclusion & applications Variable structural response • Variable thermal behavior • Variable hydration kinetic [VeRCoRs gusset thermo-hydration] [Early age cracks based on visual inspections] • Variable strain values • • Variable spacing values Variable ageing kinetic • Variable crack openings at early age • Variable crack openings during pressurization [VeRCoRs gusset vertical strain] There is a need for probabilistic coupling in order to account for uncertainties whilst modeling 6 concrete’s behavior in NCBs ? D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Modeling tools and applications (Deterministic modeling) D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Deterministic modeling [Bouhjiti et al. 2017] THM-L scheme Thermo-hydration DEFI_MATERIAU U4.43.01 Temperature THER_HYDR calculations Hydration rate THER_NON_LINE U4.54.02 Water content DEFI_MATERIAU U4.43.01 Drying calculations Saturation rate SECH_GRANGER THER_NON_LINE U4.54.02 Relative Humidity Strain/Stress DEFI_MATERIAU U4.43.01 MFRONT* Mechanical calculations Damage U2.10.02 STAT_NON_LINE U4.51.03 Crack opening DEFI_MATERIAU U4.43.01 Pressure Leakage calculations SECH_NAPPE* Leakage THER_NON_LINE U4.51.03 *: Python-based developments 7 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Deterministic modeling [Bouhjiti et al. 2018] Expected results (a) Test 0 Test 1 (c) Crack initiation 8 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Modeling tools and applications (Spatial variability and random fields) D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Spatial variability of parameters 1/Stochastic modeling of cracking The heterogeneousness of concrete and its effect on the spatial scattering of the mechanical properties is modeled by spatially correlated Random Fields . Theory: Karhunen-Loève decomposition [Ghanem et al. 1991] Centered reduced normal vector of random realizations N Spatially correlated random realizations 𝐲 = 𝛎 + λ i 𝛘 𝐣 𝐲 𝛐 𝐣 i=1 Vector of mean values (spatially constant or not) Covariance matrix: = σ 2 ρ ac x, 𝑧 C x, 𝑧 , l ac Autocorrelation 9 function D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications Spatially Discretized Random Field - MidPoint 1/Stochastic modeling of cracking [Der Kiureghian A. 1988] Linear Projection Geometrical boundaries 𝐦 𝐛𝐝 𝐦 𝐛𝐝 𝐦 𝐛𝐝 𝐦 𝐛𝐝 A given mesh Considered spatial discretization Random values assigned per element for RF generation • Non-intrusive • Wider domain to prevent boudary • Within a given element all Gauss effects associated with correlation points have the same random value ! Discretization: 4 elements per l ac • (3 at least for representativeness) 10 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications User-defined inputs 1/Stochastic modeling of cracking - Coefficient of variation or variance - Fluctuation length (related to auto-correlated length) Preprocessing - Auto-correlation function Generate centroids table containing Elements’ Ids & - RF nature: Gaussian or Lognormal coordinates coor.libr Mesh.med TAB=POST_ELEM() IMPR_TABLE(TABLE=TAB, FORMAT=’ASTER’, NOM_PARA=(‘Lieu’, ‘CDG_X’, ‘CDG_Y’, ‘CDG_Z’) Processing 0/ In file.comm call libraries: Import math;Import random;Import numpy as np; Import time;From scipy.interpolate import griddata 1/ Read coor.libr and define the extended domain for RF generation 2/ Generate the centered and reduced random values on the extended domain 3/ Define the covariance matrix and derive its Eigen values and vectors 4/ Calculate the autoccoraletd RF values on the extended domain 5/ Linearly project the RF on the considered mesh.rmed using coor.libr 11 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Salome-Meca Users’ Day 2018 20 th March2018 – EDF Lab Paris-Saclay, France ● Modeling tools o o o Framework THM uncertainties Conclusion & applications 1/Stochastic modeling of cracking [Bouhjiti et al. 2018] Random cracking patterns at early-age Spatial scattering of Young’s modulus property ! 12 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
Recommend
More recommend
