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  1. Probabilistic Assessment of Corrosion Risk due to Concrete Carbonation Frédéric Duprat Alain Sellier Materials and Durability of Constructions Laboratory INSA / UPS - Toulouse - France http://www-gci.insa-tlse.fr/lmdc/

  2. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results

  3. CO2 ingress: carbonation CO2 CO2 CO2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results CO2 pressure on external edges for most of concrete structures

  4. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results CO2 pressure on external edges for most of concrete structures CO2 ingress: carbonation Precipitation of calcite CO2 CO2 CO2

  5. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results CO2 pressure on external edges for most of concrete structures CO2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates CO2 CO2 CO2

  6. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results CO2 pressure on external edges for most of concrete structures CO2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates CO2 CO2 Decrease of pH in pore solution CO2

  7. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results CO2 pressure on external edges for most of concrete structures CO2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates CO2 CO2 Decrease of pH in pore solution Favourable conditions to initiation and development of corrosion CO2

  8. Mean values Given date: depassivation no depassivation c Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Physical parameters: - diffusion coefficient - concrete cover thickness Predicting model

  9. Laws of probability d(c) c Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Physical parameters: - diffusion coefficient - concrete cover thickness Random incertainties Mean values Predicting model Given date: depassivation no depassivation c

  10. Probabilistic approach Given date: probability of depassivation Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Physical parameters: - diffusion coefficient - concrete cover thickness Random incertainties Laws of probability Mean values Predicting model Given date: depassivation no depassivation e

  11. Concentration Porosity Saturation Diffusion Sink term : precipitation of calcite Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term

  12. Strongly non-linear term m g CO 2 Numerical instability around the carbonation front Change of variable Dissolved species CaS Agressive species CO2g Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term

  13. Dissolved species CaS Agressive species CO2g Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term Strongly non-linear term Numerical instability around the carbonation front Change of variable

  14. 10-3< (a) <10-2 negligible (Deq) non-linear All consumed CO2 reacts with CaS in hydrates Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term

  15. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term

  16. CaS * Deq Deq(CaS) Deqm CaSM Conservation of flow CaS(G) DeqM CaSm L G Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Deq

  17. Magnifying the diffusion coefficient Reference diffusion Tortuousity, connectivity of cracks Tension volumic strain Gazeous diffusion Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Influence of cracking

  18. Loading and mechanical properties Start Mechanical strain field Physical properties: CO2 diffusion coefficients tortuousity, saturation degree Magnified CO2 diffusion coefficient field Boundary condition: CaS=0 along the edges Initial condition: CaS=2500 mol/m3 Initial equivalent CaS diffusion coefficient field t=t0 Solid calcium field: CaS t=t +Dt no yes yes no Convergence for CaS field ? t=tf ? End Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Equivalent CaS diffusion coefficient field

  19. 5.2 kN/m Eb 35000 MPa 10-8 m2/s 55 cm 1.39.10-5 m2/s t0.5 25 cm 6 m j0.15 Carbonation profiles Sr 0.3 1month 5 years 20 years 35 years 50 years Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam

  20. 5.2 kN/m Eb 35000 MPa 10-8 m2/s 25 cm 6 m Carbonation depth 1.39.10-5 m2/s t0.5 j0.15 Non-carbonated CaS profiles between A and B Sr 0.3 A B B Non-carbonated zone CaS= 2500 mol/m3 A Carbonated zone CaS<< 2500 mol/m3 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam 55 cm

  21. Finite element analysis Carbonation depth dAB Concrete cover cAB u2 B Failure G(U) < 0 [ cAB < dAB ] B Performance G(U) > 0 [ cAB > dAB ] P* A A b G(U) = 0 u1 O Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results • Diffusion coefficient • Tortuousity / Connectivity • Concrete Young's modulus • Loading • Cover thickness

  22. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Direct approach Reliability index b = min(UTU)1/2 with G(U)=0 Rackwitz-Fiessler's algorithm • Significant computational cost Non-linear FEM • Very much time consuming 1 G(U) computation at T=60 years  12 minutes CPU time • Non-guaranteed convergence Gradient not accurately estimated

  23. Reliability index b = min(UTU)1/2 with Q(U)=0 1 "center point" 2N axial points star shape experimental design out-of-axes points Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Response surface approach Quadratic response surface with mixed terms • a0, ai, aii, aij determined by least square method • (N+1)(N+2)/2 numerical observations • Successive experimental designs are necessary

  24. u2 P*(1) P* Q(U)(1)=0 G(U)=0 u1 ED(1) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Response surface approach Reliability index b = min(UTU)1/2 with Q(U)=0

  25. u2 P*(2) P* ED(2) Q(U)(2)=0 G(U)=0 u1 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Response surface approach Reliability index b = min(UTU)1/2 with Q(U)=0

  26. Building the experimental design u2 ED(m+1) "recentered" on P*(m) P* G(U)=0 P*(m) ED(m) u1 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results #1 Previous P*(m) outside the ED(m) P0

  27. + |D2| |D1| + ED(m+1) |Di|  0.25 D0 = N½ U*(m) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #1 Previous P*(m) outside the ED(m) u2 ED(m+1) "recentered" on P*(m) P* G(U)=0 u1

  28. Q(U)(m)<0 Q(U)(m)>0 + ED(m+1) Q(U)(m)=0 |Di|  0.25 D0 = N½ U(m) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #1 Previous P*(m) outside the ED(m) u2 ED(m+1) "recentered" on P*(m) + P* D2 G(U)=0 u1

  29. Retained points: cos(P0Pi,P0P*(m)) > 0 P1 P*(m) P0 P0 P2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #2 Previous P*(m) inside the ED(m) u2 P* G(U)=0 ED(m) u1

  30. Complementary points: symmetrical transformed / P*(m) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #2 Previous P*(m) inside the ED(m) u2 Retained points: cos(P0Pi,P0P*(m)) > 0 P* P*(m) G(U)=0 P2 ED(m+1) u1

  31. Bringing the transformed points closer to P*(m) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #2 Previous P*(m) inside the ED(m) u2 Retained points: cos(P0Pi,P0P*(m)) > 0 Complementary points: symmetrical transformed / P*(m) P2 P* P*(m) G(U)=0 ED(m+1) u1

  32. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #2 Previous P*(m) inside the ED(m) u2 Retained points: cos(P0Pi,P0P*(m)) > 0 Complementary points: symmetrical transformed / P*(m) P* P*(m) G(U)=0 Bringing the transformed points closer to P*(m) ED(m+1) u1

  33. ED(m+1) "recentered" on P*(m) Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Building the experimental design #2 Previous P*(m) inside the ED(m) u2 Retained points: cos(P0Pi,P0P*(m)) > 0 Complementary points: symmetrical transformed / P*(m) P* P0 ED(m+1) G(U)=0 Bringing the transformed points closer to P*(m) u1

  34. Start End First experimental design ED(0) RF algorithm: P*(0) ED(m)ED(0) ; P*(m)P*(0) no yes P*(m) inside the ED(m) ? Building the ED(m+1) with procedure #2 Building the ED(m+1) with procedure #1 Finite element anlysis ED(m)ED(m+1) P*(m)P*(m+1) yes no | P*(m+1) P*(m) | < 0.15 Reliability index b Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results RF algorithm: P*(m+1)

  35. Concrete probes of similar scale Concrete probes of low scale No change Variance reduction Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam • Material properties: • Concrete strength • Reference diffusion coefficient • Turtuousity factor

  36. Distribution Mean CoV Lognormal 35 MPa 0.1 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam • Material properties: • Concrete strength • Reference diffusion coefficient • Turtuousity factor Concrete probes of similar scale No change

  37. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam Distribution Mean CoV • Material properties: • Concrete strength • Reference diffusion coefficient • Turtuousity factor Lognormal 35 MPa 0.1 Lognormal 10-8 m2/s 0.8 Uniform 0.5 0.46 [0.1 to 0.9]

  38. Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam Distribution Mean CoV • Material properties: • Concrete strength • Reference diffusion coefficient • Turtuousity factor Lognormal 35 MPa 0.1 Lognormal 10-8 m2/s 0.8 Uniform 0.5 0.46 [0.1 to 0.9] • Loading parameter: • Live load E1max 1.04 kN/m2 0.38 • Geometrical parameter: • Concrete cover thickness Lognormal 2 cm 0.2

  39. Efficiency of the adaptative RSM T=2 years T=30 years Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam

  40. Variation of the reliability with time bSLS Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam • Significant decrease of the reliability index • Reliability index lower than threshold value • recommended by Eurocodes after T=30 years

  41. Variation of the sensitivity factors with time Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam • Diffusion coefficient and cover thickness for T < 35 years • Tortuousity factor and loading play a role for T > 35 years