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Salome-Meca Users Day 2018 Probabilistic description of concretes 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.

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SLIDE 1

Probabilistic description of concrete’s Thermo-Hydro-Mechanical behavior in Nuclear Containment Buildings – Application to the VeRCoRs mock-up

Salome-Meca Users’ Day 2018

20th March2018 – EDF Lab Paris-Saclay, France

http://fondation-grenoble-inp.fr/chaire/pereniti/

  • D. BOUHJITI, S. MICHEL-PONNELLE, B. MASSON, F. DUFOUR, J. BAROTH, M. BRIFFAUT
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SLIDE 2

Salome-Meca Users’ Day 2018

VeRCoRs mock-up, EDF LAB Les Renardières

CONTENT

  • Analysis framework
  • Uncertainties 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

20th March2018 – EDF Lab Paris-Saclay, France

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SLIDE 3

1

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • THM uncertainties
  • Modeling tools

& applications

  • Conclusion
  • Framework

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

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

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SLIDE 4

2

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • THM uncertainties
  • Modeling tools

& applications

  • Conclusion
  • Framework

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

How to answer such questions ?

Feed-back analysis and NDT Experimental studies Numerical tools

VERCORS (1/3 scale)

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SLIDE 5

3

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • THM uncertainties
  • Modeling tools

& applications

  • Conclusion
  • Framework

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

How to answer such questions ?

Engineering tools Feed-back analysis and NDT Experimental studies Numerical tools

z 

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SLIDE 6
  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • Modeling tools

& applications

  • THM uncertainties

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

THM uncertainties

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SLIDE 7

C-S-H molecular model

4

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Modeling tools

& applications

  • Conclusion
  • Framework
  • THM uncertainties

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Cement, aggregates, voids Cement, capillary voids CSH, gel pores

Concrete = heterogeneous + multiphasic material Variable mechanical + transfer properties Time t Space 𝑦 𝑧 𝑨

Molecular scale  Meso scale  Macro scale

Homogeneous Equivalent Material (HEM)

[VeRCoRs concrete]

Variable properties + Variable THM boundaries

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SLIDE 8

5

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Modeling tools

& applications

  • Conclusion
  • Framework
  • THM uncertainties

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Variable properties + Variable THM boundaries

[Inner temperature variation in a real NCB] [Design of a full scale NCB] [Prestressing losses variation in VeRCoRs]

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SLIDE 9

6

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Modeling tools

& applications

  • Conclusion
  • Framework
  • THM uncertainties

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

 There is a need for probabilistic coupling in order to account for uncertainties whilst modeling concrete’s behavior in NCBs ?

Variable structural response

[Early age cracks based on visual inspections]

  • Variable spacing values
  • Variable crack openings at early age
  • Variable crack openings during pressurization
  • Variable strain values
  • Variable ageing kinetic
  • Variable thermal behavior
  • Variable hydration kinetic

[VeRCoRs gusset thermo-hydration] [VeRCoRs gusset vertical strain]

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SLIDE 10
  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Modeling tools and applications (Deterministic modeling)

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SLIDE 11

7

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Deterministic modeling

DEFI_MATERIAU THER_HYDR U4.43.01 THER_NON_LINE U4.54.02

Thermo-hydration calculations Drying calculations Mechanical calculations Leakage calculations

Temperature Hydration rate Water content Saturation rate Relative Humidity

DEFI_MATERIAU SECH_GRANGER U4.43.01 THER_NON_LINE U4.54.02 DEFI_MATERIAU MFRONT* U2.10.02 U4.43.01 STAT_NON_LINE U4.51.03

THM-L scheme

Strain/Stress Damage Crack opening

DEFI_MATERIAU SECH_NAPPE* U4.43.01 THER_NON_LINE U4.51.03

Pressure Leakage *: Python-based developments [Bouhjiti et al. 2017]

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SLIDE 12

8

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Deterministic modeling Expected results

(c) (a) Crack initiation

Test 0 Test 1

[Bouhjiti et al. 2018]

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SLIDE 13
  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Modeling tools and applications (Spatial variability and random fields)

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SLIDE 14

9

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

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.

Spatial variability of parameters Theory: Karhunen-Loève decomposition 𝐲 = 𝛎 + λi 𝛘𝐣 𝐲 𝛐𝐣

N i=1

Centered reduced normal vector of random realizations Spatially correlated random realizations Vector of mean values (spatially constant or not)

Covariance matrix: C x, 𝑧 = σ2 ρac x, 𝑧 , lac

Autocorrelation function [Ghanem et al. 1991]

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SLIDE 15

10

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

1/Stochastic modeling of cracking Spatially Discretized Random Field - MidPoint

A given mesh Considered spatial discretization for RF generation Geometrical boundaries

  • Wider domain to prevent boudary

effects associated with correlation

  • Discretization: 4 elements per lac

(3 at least for representativeness)

Linear Projection Random values assigned per element

  • Non-intrusive
  • Within a given element all Gauss

points have the same random value !

𝐦𝐛𝐝 𝐦𝐛𝐝 𝐦𝐛𝐝 𝐦𝐛𝐝

[Der Kiureghian A. 1988]

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11

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

1/Stochastic modeling of cracking

User-defined inputs

  • Coefficient of variation or variance
  • Fluctuation length (related to auto-correlated length)
  • Auto-correlation function
  • RF nature: Gaussian or Lognormal

Preprocessing Generate centroids table containing Elements’ Ids & coordinates  coor.libr TAB=POST_ELEM() IMPR_TABLE(TABLE=TAB, FORMAT=’ASTER’, NOM_PARA=(‘Lieu’, ‘CDG_X’, ‘CDG_Y’, ‘CDG_Z’)

Mesh.med

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

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SLIDE 17

12

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

1/Stochastic modeling of cracking

Random cracking patterns at early-age

Spatial scattering of Young’s modulus property !

[Bouhjiti et al. 2018]

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SLIDE 18
  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Uncertainties propagation using alternative stochastic approaches to MCM (Non-intrusive strategies)

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SLIDE 19

13

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

2/Stochastic modeling of drying Water content

The variation of concrete’s behavior at the structural scale is modeled using non-intrusive stochastic approaches: Quadrature-Polynomial Chaos method

Descriptive equation of drying: dSr dt − div A e𝐂𝐃𝟏grad(Sr) = 0

B*C0 considered as a random input

Aiming at an explicit: Sr

moy = function B ∗ C0 ?

MC at low cost •

CDF of Sr

moy

  • Pf = P(Sr

moy ≤ Sr lim)

After a limited number of model evaluations for a limited number of values Carefully select the integration points to

  • btain a representative response surface
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  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Water content

What B*C0 value ? Quadrature method

Hyp: B*C0 follows a Lognormal distribution

𝑶𝒒𝒉 ↗ : Computational cost ↗ Accuracy↗

What projection basis? Hermite Polynomials He−1 = He0 = 1 Hen≥1 x = x Hen−1 x − n Hen−2 x n!

Orthonormal functions with respect to Gaussian distribution

Hnor = Hen 𝑜!

𝑜≥1

= 1, 𝑦, 𝑦2 − 1 2 , 𝑦3 − 3𝑦 6 , …

𝐓𝐬,𝐨=𝟒

𝐧𝐩𝐳

𝛈, 𝐮 = 𝐛𝟏 𝐮 + 𝐛𝟐 𝐮 𝛈 + 𝐛𝟑 𝐮 𝛈𝟑 − 𝟐 𝟑 + 𝐛𝟒 𝐮 𝛈𝟒 − 𝟒𝛈 𝟕 𝜂 =

log 𝐶∗𝐷0 −𝜈𝐶𝐷0 𝜏𝐶𝐷0

 gaussian [Sudret et al. 2000]

2/Stochastic modeling of drying

[Baldeweck 1999]

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SLIDE 21

15

  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Water content Exact Response Surface 𝑂𝑞𝑕 ≥ 4 ‼ 𝑆2 ≥ 99,96 % 1 − 𝑅2 ≤ 3. 10−3 PC-based Response surface 2/Stochastic modeling of drying

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  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

Water content

𝐓𝐬,𝐨=𝟒

𝐧𝐩𝐳

𝛈, 𝐮 = 𝐛𝟏 𝐮 + 𝐛𝟐 𝐮 𝛈 + 𝐛𝟑 𝐮 𝛈𝟑 − 𝟐 𝟑 + 𝐛𝟒 𝐮 𝛈𝟒 − 𝟒𝛈 𝟕

MC

Metamodel (based on 4 calculations)

Accessible quantities

  • Mean
  • Statistical moments
  • Failure probabilities

Drying 2/Stochastic modeling of drying

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SLIDE 23

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  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Conclusion
  • Framework
  • THM uncertainties
  • Modeling tools

& applications Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

3/Stochastic modeling of leakage rates

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SLIDE 24

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  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Framework
  • THM uncertainties
  • Modeling tools

& applications

  • Conclusion

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

  • Non-intrusive methods used to:

 Generate RFs representative of the spatial scattering of a given material property  Stochastically describe concrete THM-L behavior (early age + delayed ageing)

  • Tools/Methodology used and validated based on the VeRCoRs mock-up

Thermo-hydration calculations Drying calculations Mechanical calculations Leakage calculations

0,5 hr – 225 steps 0,5 hr –179 steps 2 dy –634 steps 0,5 hr – 160 steps

Number of calls to describe probabilistically the leakage rate: 768 (using 30 14-core nodes //)

Parametric analysis [U2.08.07] – Uncertainties propagation [OpenTurns]

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SLIDE 25

Salome-Meca Users’ Day 2018

Contact: david.bouhjiti@3sr-grenoble.fr / david.elmahdi.bouhjiti@gmail.com

Thank you for listening!

‘’ The probabilistic modeling of concrete’s behavior allows better assessment of NCBs ageing and aims at improving the prediction of their lifespan and the planning of maintenance and repair operations ‘’

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  • D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs
  • Framework
  • THM uncertainties
  • Modeling tools

& applications

  • Conclusion

Salome-Meca Users’ Day 2018 20th March2018 – EDF Lab Paris-Saclay, France

  • References:
  • VeRCoRs project: Corbin M., Garcia M. Benchmark VERCORS report 2015 (https://www.conference-

service.com/EDF-VeRCoRs-Benchmark-2018/welcome.cgi)

  • Bouhjiti D. E-M., Baroth J., Dufour F., Masson B. Sensitivity analysis of cracking in large reinforced concrete

structures: Case of the VeRCoRs mock-up. CFM 2017

  • Bouhjiti D. E-M., Boucher M., Briffaut M., Dufour F., Baroth J., Masson B. Accounting for realistic Thermo-

Hydro-Mechanical Boundary Conditions whilst modeling the ageing of concrete in Nuclear Containment Buildings: Model validation and sensitivity analysis. Eng. Struct 2018

  • Bouhjiti D. E-M., Baroth J., Dufour F., Masson B. Prediction of air permeability in large RC structures using a

stochastic FE THM modeling strategy. Euro-C 2018

  • Sudret B., DER KIUREGHIAN A. Stochastic Finite Element Methods and Reliability. A State-of-the-Art Report.

Report UCB/SEMM-2000/08.

  • Der Kiureghian A., Ke. Second order reliability approximations. Eng. Mech. 1988.
  • Baldeweck H. Methodes aux elements finis stochastiques - Application a la geotechnique. These

de doctorat 1999.

  • …