Probabilistic Assessment of Corrosion Risk due to Concrete Carbonation Frédéric Duprat Alain Sellier Materials and Durability of Constructions Laboratory INSA / UPS - Toulouse - France

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results CO 2 CO 2 pressure on external edges for most of concrete structures CO 2 ingress: carbonation

CO 2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results CO 2 pressure on external edges for most of concrete structures CO 2 ingress: carbonation Precipitation of calcite

CO 2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results CO 2 pressure on external edges for most of concrete structures CO 2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates

CO 2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results CO 2 pressure on external edges for most of concrete structures CO 2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates Decrease of pH in pore solution

CO 2 pressure on external edges for most of concrete structures CO 2 ingress: carbonation Precipitation of calcite Dissolution of calcium fixed by cement hydrates Decrease of pH in pore solution Favourable conditions to initiation and development of corrosion CO 2 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results

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

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

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

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

g CO 2  Strongly non-linear term Numerical instability around the carbonation front Change of variable Agressive species CO 2g Dissolved species Ca S Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Diffusion term Capacity term Introduction Carbonation modeling Probabilistic approach Results

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Strongly non-linear term Numerical instability around the carbonation front Change of variable Diffusion term Capacity term Introduction Carbonation modeling Probabilistic approach Results Agressive species CO 2g Dissolved species Ca S

All consumed CO 2 reacts with Ca S in hydrates < (a) <10 -2 negligible (D eq ) non-linear Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Diffusion term Capacity term Introduction Carbonation modeling Probabilistic approach Results

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Diffusion term Capacity term Introduction Carbonation modeling Probabilistic approach Results

G Ca Sm Ca SM D eqm D eqM D eq Ca S D eq (Ca S ) L Conservation of flow Ca S(G) D eq * Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Diffusion term Introduction Carbonation modeling Probabilistic approach Results

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

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Equivalent Ca S diffusion coefficient field Mechanical strain field Loading and mechanical properties Magnified CO 2 diffusion coefficient field Physical properties: CO 2 diffusion coefficients tortuousity, saturation degree Initial condition: Ca S =2500 mol/m 3 Initial equivalent Ca S diffusion coefficient field Boundary condition: Ca S =0 along the edges t=t 0 Solid calcium field: Ca S Convergence for Ca S field ? no t=t f ? yes t=t +  t no Start End yes

Practical application: reinforced concrete beam 6 m 25 cm 5.2 kN/m 55 cm E b MPa m 2 /s m 2 /s  0.5  0.15 S r 0.3 Carbonation profiles 1month5 years20 years35 years 50 years Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results

Carbonation depth Carbonated zone Ca S << 2500 mol/m 3 Non-carbonated zone Ca S = 2500 mol/m 3 A B AB Non-carbonated Ca S profiles between A and B E b MPa m 2 /s m 2 /s  0.5  0.15 S r 0.3 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Practical application: reinforced concrete beam Introduction Carbonation modeling Probabilistic approach Results 6 m 5.2 kN/m 25 cm 55 cm

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Diffusion coefficient Tortuousity / Connectivity Concrete Young's modulus Loading Cover thickness G(U) = 0 u1u1 u2u2 Concrete cover c AB P*  O Carbonation depth d AB Finite element analysis Failure G(U) < 0 [ c AB < d AB ] A B A B Performance G(U) > 0 [ c AB > d AB ]

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

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Response surface approach Reliability index  = min(U T U) 1/2 with Q(U)=0 Quadratic response surface with mixed terms a 0, a i, a ii, a ij determined by least square method (N+1)(N+2)/2 numerical observations 1 "center point" 2N axial points out-of-axes points star shape experimental design Successive experimental designs are necessary

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Reliability index  = min(U T U) 1/2 with Q(U)=0 Response surface approach u1u1 u2u2 ED (1) Q(U) (1) =0 P* G(U)=0 P* (1)

P* G(U)=0 Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Reliability index  = min(U T U) 1/2 with Q(U)=0 Response surface approach u1u1 u2u2 ED (2) Q(U) (2) =0 P* (2)

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results P* (m) #1 Previous P* (m) outside the ED (m) ED (m+1) "recentered" on P* (m) ED (m) P0P0 u1u1 u2u2 Building the experimental design P* G(U)=0

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design ED (m+1) |1||1| |2||2| ED (m+1) "recentered" on P* (m) #1 Previous P* (m) outside the ED (m) +  i |  0.25  0 = N ½ + U* (m) P* G(U)=0

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design Q(U) (m) =0 Q(U) (m) <0 Q(U) (m) >0 ED (m+1) "recentered" on P* (m) #1 Previous P* (m) outside the ED (m) +  i |  0.25  0 = N ½ + ED (m+1) 22 U (m) P* G(U)=0

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design #2 Previous P* (m) inside the ED (m) ED (m) P* (m) P0P0 P1P1 P2P2 P0P0 P* G(U)=0 Retained points: cos(P 0 P i,P 0 P* (m) ) > 0

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design Retained points: cos(P 0 P i,P 0 P* (m) ) > 0 #2 Previous P* (m) inside the ED (m) ED (m+1) P* (m) P2P2 Complementary points: symmetrical transformed / P* (m) P* G(U)=0

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design Retained points: cos(P 0 P i,P 0 P* (m) ) > 0 #2 Previous P* (m) inside the ED (m) ED (m+1) P* (m) Complementary points: symmetrical transformed / P* (m) P* G(U)=0 Bringing the transformed points closer to P* (m) P2P2

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design Retained points: cos(P 0 P i,P 0 P* (m) ) > 0 #2 Previous P* (m) inside the ED (m) ED (m+1) P* (m) Complementary points: symmetrical transformed / P* (m) P* G(U)=0 Bringing the transformed points closer to P* (m)

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results u1u1 u2u2 Building the experimental design Retained points: cos(P 0 P i,P 0 P* (m) ) > 0 #2 Previous P* (m) inside the ED (m) ED (m+1) Complementary points: symmetrical transformed / P* (m) P* G(U)=0 Bringing the transformed points closer to P* (m) P0P0 ED (m+1) "recentered" on P* (m)

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

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

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

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January Introduction Carbonation modeling Probabilistic approach Results Practical application: reinforced concrete beam Material properties: Concrete strength Reference diffusion coefficient Turtuousity factor Distribution Mean CoV Lognormal 35 MPa 0.1 Lognormal m 2 /s 0.8 Uniform [0.1 to 0.9]

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

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

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

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