probabilistic description of concrete’s thermo-hydro ...€¦ · 1 d. bouhjiti et al. –...

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








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

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

o THM uncertainties

o Modeling tools & applications

o 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


o THM uncertainties


o Conclusion

● Framework


How to answer such questions ?

Feed-back analysis and

NDT

Experimental studies

Numerical tools

VERCORS (1/3 scale)


o THM uncertainties


o Conclusion

● Framework


How to answer such questions ?

Engineering tools

Feed-back analysis and

NDT

Experimental studies

Numerical tools

z

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

o Conclusion

o Framework


● THM uncertainties


THM uncertainties

C-S-H molecular model 4 D. BOUHJITI et al. – Probabilistic description of concrete’s THM behavior in NCBs


o Conclusion

o Framework



Cement, aggregates, voids

Cement, capillary voids

CSH, gel pores

Concrete = heterogeneous + multiphasic material

Variable mechanical + transfer properties

Time t

Space 𝑥𝑦𝑧

Mo

lecu

lar

scal

e

Mes

o s

cale

M

acro

sca

le

Homogeneous Equivalent Material (HEM)

[Ve

RC

oR

s co

ncr

ete

]

Variable properties + Variable THM boundaries



o Conclusion

o Framework



Variable properties + Variable THM boundaries

[Inner temperature variation in a real NCB]

[Design of a full scale NCB]

[Prestressing losses variation in VeRCoRs]



o Conclusion

o Framework



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]


o Conclusion

o Framework

o THM uncertainties

● Modeling tools & applications


Modeling tools and applications (Deterministic modeling)


o Conclusion

o Framework

o THM uncertainties



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


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


Pressure Leakage

*: Python-based developments

[Bouhjiti et al. 2017]


o Conclusion

o Framework

o THM uncertainties



Deterministic modeling Expected results

(c) (d)

(a) (b)

Crack initiation Crack initiation

(e) (f) (g) (h)

Test 0 Test 0 Test 1 Test 1

(c) (d)

(a) (b)

Crack initiation Crack initiation

(e) (f) (g) (h)

Test 0 Test 0 Test 1 Test 1



o Conclusion

o Framework

o THM uncertainties



Modeling tools and applications (Spatial variability and random fields)


o Conclusion

o Framework

o THM uncertainties



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

𝐱 = 𝛍 + λi 𝛗𝐢 𝐱 𝛏𝐢

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, 𝑦 = σ2 ρac x, 𝑦 , lac

Autocorrelation function

[Ghanem et al. 1991]


o Conclusion

o Framework

o THM uncertainties



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 !

𝐥𝐚𝐜 𝐥𝐚𝐜

𝐥𝐚𝐜 𝐥𝐚𝐜

[Der Kiureghian A. 1988]


o Conclusion

o Framework

o THM uncertainties



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


o Conclusion

o Framework

o THM uncertainties



1/Stochastic modeling of cracking

Random cracking patterns at early-age

Spatial scattering of Young’s modulus property !



o Conclusion

o Framework

o THM uncertainties



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


o Conclusion

o Framework

o THM uncertainties



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: dSrdt

− div A e𝐁𝐂𝟎grad(Sr) = 0

B*C0 considered as a random input

Aiming at an explicit: Srmoy

= function B ∗ C0 ? MC at low cost • CDF of Sr

moy

• Pf = P(Srmoy

≤ Srlim)

After a limited number of model evaluations for a limited number of values

Carefully select the integration points to obtain a representative response surface


o Conclusion

o Framework

o THM uncertainties



Water content

What B*C0 value ? Quadrature method

Hyp: B*C0 follows a Lognormal distribution

𝑵𝒑𝒈 ↗ : 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 =Hen𝑛! 𝑛≥1

= 1, 𝑥,𝑥2 − 1

2,𝑥3 − 3𝑥

6,…

𝐒𝐫,𝐧=𝟑𝐦𝐨𝐲

𝛇, 𝐭 = 𝐚𝟎 𝐭 + 𝐚𝟏 𝐭 𝛇 + 𝐚𝟐 𝐭𝛇𝟐 − 𝟏

𝟐+ 𝐚𝟑 𝐭

𝛇𝟑 − 𝟑𝛇

𝟔

𝜁 =log 𝐵∗𝐶0 −𝜇𝐵𝐶0

𝜎𝐵𝐶0 gaussian

[Sudret et al. 2000]

2/Stochastic modeling of drying

[Baldeweck 1999]


o Conclusion

o Framework

o THM uncertainties



Water content

Exact Response Surface

𝑁𝑝𝑔 ≥ 4 ‼

𝑅2 ≥ 99,96 % 1 − 𝑄2 ≤ 3. 10−3

PC-based Response surface



o Conclusion

o Framework

o THM uncertainties



Water content

𝐒𝐫,𝐧=𝟑𝐦𝐨𝐲

𝛇, 𝐭 = 𝐚𝟎 𝐭 + 𝐚𝟏 𝐭 𝛇 + 𝐚𝟐 𝐭𝛇𝟐 − 𝟏

𝟐+ 𝐚𝟑 𝐭

𝛇𝟑 − 𝟑𝛇

𝟔

MC

Metamodel (based on 4 calculations)

Accessible quantities • Mean • Statistical moments • Failure probabilities

Drying



o Conclusion

o Framework

o THM uncertainties



3/Stochastic modeling of leakage rates


o Framework

o THM uncertainties


● Conclusion


• 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]


Contact: [email protected] / [email protected]

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 ‘’


o Framework

o THM uncertainties


o Conclusion


• References:

o VeRCoRs project: Corbin M., Garcia M. Benchmark VERCORS report 2015 (https://www.conference-service.com/EDF-VeRCoRs-Benchmark-2018/welcome.cgi)

o 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

o 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

o 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

o Sudret B., DER KIUREGHIAN A. Stochastic Finite Element Methods and Reliability. A State-of-the-Art Report. Report UCB/SEMM-2000/08.

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

de doctorat 1999. o …

https://www.conference-service.com/EDF-VeRCoRs-Benchmark-2018/welcome.cgi










probabilistic description of concrete’s thermo-hydro ...€¦ · 1 d. bouhjiti et al. –...

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