Comparative Analysis of Engineering Carbonation Model Extensions to Account for Pre-Existing Cracks
Abstract
:1. Introduction
2. Carbonation Models for Concrete
2.1. Model for Uncracked Concrete
2.2. Models for Cracked Concrete
2.2.1. CIF Approach
2.2.2. Diffusion-Based Model
2.2.3. Crack Depth Adaption
2.3. Probabilistic Analyses for Concrete with Pre-Existing Cracks
3. Experimental Studies
3.1. Validation Data from Literature
3.2. Experimental Study
4. Deterministic Evaluation of Models against Experimental Datasets
4.1. Uncracked Concrete
4.2. Cracked Concrete
5. Case Study for Service Life Predictions
5.1. Deterministic Results
5.2. Probabilistic Results
6. Limitations of the Extensions for Carbonation-Induced Depassivation of Cracked Concrete
7. Conclusions
- Both CIF approaches had a similar good prediction accuracy. The carbonation depth for concrete with natural cracks was predicted well. However, the models tend to underestimate the carbonation depth with increasing exposure time.
- The diffusion-based model significantly underestimated carbonation depths for experiments with low concentrations.
- The crack depth adaption overestimated the carbonation depth in (nearly) all cases. For natural cracks, the carbonation depth was even overestimated by up to a factor 3.5. However, the prediction accuracy increased with increasing exposure time.
- 0% for the uncracked concrete structure.
- Significantly below 1% for the whole structure, which includes the 0.65% cracked surface. However, the probability of depassivation could be underestimated because the carbonation from the crack surface and from the crack along the steel–concrete interface is not accounted for. Additionally, while such reliability assessments predict low depassivation probabilities, cracks can speed up local corrosion with potential consequences for the entire structure.
- Between 1% and 70% in the cracked area depending on the modeling approach. Structural investigations indicate that the depassivation probability of about 1% predicted by the CIF approaches is unrealistically low. In contrast, the 70% probability of depassivation of the other approaches highlights the risk of potential damage at the location of a crack. However, preventing this higher probability of depassivation could make reinforced concrete structures cost-inefficient. An alternative approach is to change the limit state for the reliability assessment from the very conservative depassivation limit (initiation period) to the corrosion propagation state.
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Unit | Van Mullem et al. [13] | De Schutter [14] | Zhang et al. [10] | Guo et al. [37] | ||
---|---|---|---|---|---|---|---|
mix | mortar | mortar | mortar | mortar | concrete | paste | |
binder | 50 w.% CEM I 52.2 N, 50 w.% fly ash | 50 w.% CEM I 52.2 N, 50 w.% fly ash | CEM I 42.5 R | 85 w.% CEM I, 15 w.% fly ash | OPC | OPC 42.5 | |
crack type | notch | natural | notch | notch | notch | notch | |
uncracked concrete tested | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ | |
w | [mm] | 0.1, 0.2, 0.3 | 0.1, 0.2, 0.3 | 0.5 | 0.5 | 0.1, 0.2, 0.3, 0.5, 0.62 | 0.1, 0.2,0.3 |
d | [mm] | 30 | 50 | 10 | 10 | 20 | 10, 15, 20, 25, 30 |
[Vol.%] | 1 | 1 | 10 | 10 | 20 | 20 | |
[days] | 14–63 | 14–31 | 56–196 | 56–196 | 7–56 | 7–21 | |
[−] | 1.11 | 1.11 | 1 | 1 | 0.86 | 0.86 | |
[−] | 0.32 | 0.32 | 0.45 | 0.45 | 0.46 | 0.46 |
Binder | CaO | SiO2 | Al2O3 | Fe2O3 | MgO | K2O | Na2O | TiO2 | P2O5 | MnO | LIO | Na2Oeq | Others |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CEM I 42.5 R | 57.90 | 18.85 | 5.43 | 3.33 | 2.30 | 1.64 | 0.06 | 0.24 | 0.12 | 0.08 | 3.44 | 1.14 | |
Fly ash | 3.14 | 48.09 | 29.66 | 9.16 | 0.07 | 1.27 | 0.43 | 3.4 | 0.31 | 1.27 | 1.75 | 1.45 |
Parameter | Unit | Van Mullem et al. [13] | De Schutter [14] | Zhang et al. [10] | Guo et al. [37] | |||
---|---|---|---|---|---|---|---|---|
[] | 127,166 | 234 | 451 | 1676 | 3015 | 6308 | 16,994 | |
[%] | 60 | 65 | 65 | 70 | 70 | 70 | 70 | |
[days] | 51 | 28 | 28 | 28 | 28 | 28 | 28 | |
[−] | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
[−] | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
[] | 0.018 | 0.182 | 0.182 | 0.367 | 0.367 | 0.367 | 0.367 | |
C | [] | 486 1 | 499 1 | 499 1 | 400 | 1590 1 | 1742 1 | 1371 1 |
[−] | 30.52 2 | 57.90 2 | 49.69 2 | 66.60 | 62.24 | 62.24 | 62.24 | |
[−] | 0.55 | 0.5 | 0.5 | 0.5 | 0.3 | 0.35 | 0.4 | |
[−] | 0.93 3 | 0.91 3 | 0.91 3 | 0.80 3 | 0.71 3 | 0.78 3 | 0.83 3 |
Parameter | Unit | OPC | OPC + FA |
---|---|---|---|
[] | 1024 | 3407 | |
[%] | 65 | 65 | |
[days] | 7 | 7 | |
[−] | 0 | 0 | |
[−] | 0 | 0 | |
[] | 0.036 | 0.036 | |
C | [] | 499 1 | 499 1 |
[−] | 57.90 | 46.95 | |
[−] | 0.5 | 0.5 | |
[−] | 0.91 2 | 0.91 2 |
Parameter | Unit | Distribution | Mean | Std | Boundaries |
---|---|---|---|---|---|
[] | Normal distribution | 2144 1 | 273.6 1 | ||
[%] | Beta distribution | 71.96 | 20.92 | [0, 100] | |
[days] | 7 | ||||
[−] | 77/365 | ||||
[−] | Beta distribution | 0.3 | 0.1 | [0, 1] | |
[] | Normal distribution | 0.00082 1 | 0.0001 1 | ||
C | [] | 280 | |||
[−] | 0.579 | ||||
[−] | 0.91 | ||||
[mm] | Beta distribution | 35 | 6 1 | [0, 175] 1 | |
w | [mm] | Normal distribution | 0.25 | 0.015 | |
d | [mm] | Beta distribution | 35 | 5 | [0, 175] |
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Schultheiß, A.L.; Patel, R.A.; Vogel, M.; Dehn, F. Comparative Analysis of Engineering Carbonation Model Extensions to Account for Pre-Existing Cracks. Materials 2023, 16, 6177. https://doi.org/10.3390/ma16186177
Schultheiß AL, Patel RA, Vogel M, Dehn F. Comparative Analysis of Engineering Carbonation Model Extensions to Account for Pre-Existing Cracks. Materials. 2023; 16(18):6177. https://doi.org/10.3390/ma16186177
Chicago/Turabian StyleSchultheiß, Annika Lidwina, Ravi Ajitbhai Patel, Michael Vogel, and Frank Dehn. 2023. "Comparative Analysis of Engineering Carbonation Model Extensions to Account for Pre-Existing Cracks" Materials 16, no. 18: 6177. https://doi.org/10.3390/ma16186177