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**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/**Probabilistic Assessment of Corrosion Risk due to**Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results**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**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**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**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**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**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**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**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**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**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**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**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**Probabilistic Assessment of Corrosion Risk due to**Carbonation Baltimore January 5-7 2005 Introduction Carbonation modeling Probabilistic approach Results Diffusion term Capacity term**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**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**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**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**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**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**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**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**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**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**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**+**|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**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**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**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**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**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**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**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)**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**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**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]**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**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**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**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