Service life prediction models of concrete structures subjected to the initiation of reinforcing steel corrosion by chloride ions: contribution to the state of the art through systematic literature review – Part 1

Lopes, Rayane Campos; Oliveira, Andrielli Morais de; Cascudo, Oswaldo

Rayane Campos Lopes e-mail: rayaneclopes@discente.ufg.br, andriellimorais@ufg.br, ocascudo@ufg.br

Universidade Federal de Goiás, Escola de Engenharia Civil e Ambiental, Laboratório de Inovação Tecnológica em Construção Civil. Av. Universitária, nº 1488, Qd. 86, Lt. Área, 74.605-220, Setor Universitário, Goiânia, GO, Brasil.

Autor Responsável: Oswaldo Cascudo

https://orcid.org/0000-0002-1862-8854

Andrielli Morais de Oliveira e-mail: rayaneclopes@discente.ufg.br, andriellimorais@ufg.br, ocascudo@ufg.br

Universidade Federal de Goiás, Escola de Engenharia Civil e Ambiental, Laboratório de Inovação Tecnológica em Construção Civil. Av. Universitária, nº 1488, Qd. 86, Lt. Área, 74.605-220, Setor Universitário, Goiânia, GO, Brasil.

https://orcid.org/0000-0001-8977-785X

Oswaldo Cascudo e-mail: rayaneclopes@discente.ufg.br, andriellimorais@ufg.br, ocascudo@ufg.br

Universidade Federal de Goiás, Escola de Engenharia Civil e Ambiental, Laboratório de Inovação Tecnológica em Construção Civil. Av. Universitária, nº 1488, Qd. 86, Lt. Área, 74.605-220, Setor Universitário, Goiânia, GO, Brasil.

https://orcid.org/0000-0003-1879-6396

e-mail: rayaneclopes@discente.ufg.br, andriellimorais@ufg.br, ocascudo@ufg.br

Autor Responsável:

Oswaldo Cascudo

CATEGORIA	CRITÉRIOS DE EXCLUSÃO
Outros mecanismos de degradação	Reação álcali-agregado, corrosão induzida por carbonatação, ciclos de gelo-degelo e ataque combinado do cloreto com outro íon (sulfato, por exemplo).
Tipo de concreto ou de aço e formas de tratamento superficial	Concretos auto cicatrizante, com agregados reciclados ou sintéticos, leve, fibroso, modificados com polímeros ou com algum tipo de proteção superficial; e aço inoxi dável ou armadura com algum tipo de proteção (pintura, proteção catódica).
Tipo de estrutura ou elemento estrutural	Estrutura de concreto protendido, estruturas recuperadas, submersas ou enterradas, estrutura com carregamento externo e pilar circular.
Fonte de cloretos e meio ambiente	Fontes internas de contaminação (aditivo acelerador, agregados ou água de amassamento contaminados), sais de degelo, clima frio.
Outros	Penetração de cloretos em argamassa, modelos que considerem terremoto ou outros fenômenos conjuntos, aprimoramento de modelos, modelagem somente do ingresso de cloretos sem previsão do tempo, modelos que considerem a etapa de propagação da corrosão e artigos não disponíveis na íntegra.

ETAPA	QUANTIDADE
Resultado das buscas	1381
Artigos Duplicados	–656
Exclusão por título	–145
Exclusão por resumo	–329
Artigos não disponíveis	–55
Exclusão por leitura parcial ou completa	–146
Artigos aderidos	50

AUTORES	REPETIÇÕES	ÍNDICE h	AUTORES	REPETIÇÕES	ÍNDICE h
Ann, K.Y.	4	16	Li, Q.	2	15
Shekarchi, M.	3	24*	Pack, S.-W.	2	15
Alizadeh, R.	2	16	Smith, B. G.	2	3
Chini, M.	2	3	Song, H.-W.	2	22
Ghods, P.	2	16	Thomas, M.D.A.	2	38
Hooton, R.D.	2	39	Yu, Z.	2	22
Hoseini, M.	2	5

MODELO	ARTIGOS ADERIDOS	DESCRIÇÃO	SOMA DE CITAÇÕES DOS ARTIGOS ADERIDOS	EQUAÇÕES
Segunda Lei de Fick*^R	[³⁰[30] SONG, H.W., ANN, K.Y., PACK, S.W., et al., “Factors influencing chloride transport and chloride threshold level for the prediction of service life of concrete structures”, In: Proceedings of the International Conference on Durability of Concrete Structures. Hangzhou, 2008. pp.131–144., ³⁶[36] ZHANG, J., LOUNIS, Z., “Nonlinear relationships between parameters of simplified diffusion-based model for service life design of concrete structures exposed to chlorides”, Cement and Concrete Composites, v. 31, pp. 591–600, 2009., ⁴⁸[48] NILSSON, L.-O., “On the uncertainty of service-life models for reinforced marine concrete structures”, In: Proceedings of the International Rilem Workshop on Life Prediction and Aging Management of Concrete Structure. Paris, 2000., ⁵⁰[50] DO, J., SONG, H., SO, S., et al., “Comparison of deterministic calculation and fuzzy arithmetic for two prediction model equations of corrosion initiation”, Journal of Asian Architecture and Building Engineering, v. 4, n. 2, pp. 447–454, 2005., ⁵⁴[54] ARYA, C., VASSIE, P., BIOUBAKHSH, S., “Chloride penetration in concrete subject to wet–dry cycling: influence of pore structure”, Proceedings of the Institution of Civil Engineers – Structures and Buildings, v. 167, n. 6, pp. 343–354, 2014.–⁵⁸[58] ANN, K.Y., AHN, J.H., RYOU, J.S., “The importance of chloride content at the concrete surface in assessing the time to corrosion of steel in concrete structures”, Construction and Building Materials, v. 23, n. 1, pp. 239–245, 2009.]	Fick – solução de Crank – D e Cs constantes	233	$\begin{matrix} C_{x} = C_{s} (1 - e r f (\frac{x}{2 \sqrt{D t}})) \end{matrix}$
RILEM (1996)	[⁵⁰[50] DO, J., SONG, H., SO, S., et al., “Comparison of deterministic calculation and fuzzy arithmetic for two prediction model equations of corrosion initiation”, Journal of Asian Architecture and Building Engineering, v. 4, n. 2, pp. 447–454, 2005.]	Fick – solução simplificada	6	$\begin{matrix} t_{i} = \frac{d^{2}}{12 D} (\frac{1}{1 - \sqrt{\frac{C c r}{C s}}}) \end{matrix}$
Ann et al. (2009)	[⁵⁸[58] ANN, K.Y., AHN, J.H., RYOU, J.S., “The importance of chloride content at the concrete surface in assessing the time to corrosion of steel in concrete structures”, Construction and Building Materials, v. 23, n. 1, pp. 239–245, 2009.]	Fick + C_s (t)	138	$\begin{matrix} C_{s} (t) = k t / C_{s} (t) = k \sqrt{t} \\ C_{s} (t) = C_{0} + k \sqrt{t} \end{matrix}$
Software CIKS	[⁵⁹[59] DOMINGUEZ, J.G., MENDOZA, C.G., “Durability of reinforced concrete applying some expert systems from the world wide web”, In: Proceedings of the International Conference Achieving Sustainability in Construction. Scotland, 2005. pp. 299–306.]	Fick + C_s cíclico + fixação	1	$\begin{matrix} \frac{C_{c r}}{C_{s}} = \erf \frac{d}{2 \sqrt{{D t}_{i}}} \end{matrix}$
Amey et al. (1998)	[⁵¹[51] MEDEIROS-JUNIOR, R.A., LIMA, M.G., MEDEIROS, M.H.F., “Service life of concrete structures considering the effects of temperature and relative humidity on chloride transport”, Environment development and sustainability, v. 17, pp. 1103–1119, 2015.]	Fick + D (T)	14	$\begin{matrix} D (T) = D_{0} \frac{T}{T_{0}} \exp [k (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$
Kristiawan et al. (2017)	[⁶⁰[60] KRISTIAWAN, S., GAN, B.S., NURROHMAH, S., “Estimating corrosion initiation period due to chloride ingress into reinforced self-compacting concrete incorporating high volume fly ash”, In: Proceedings of the International Symposium on Civil and Environmental Engineering, ISCEE 2016. Shenzhen, 2017.]	Fick + D (T)	3	$\begin{matrix} D_{f a} (T) = D_{0} F A \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \\ F A = 0.00014 {f a}^{3} - 0.0242 {f a}^{2} \\ + 1.351 f a - 23.8 \end{matrix}$
Maage et al. (1995) *^R	[³⁴[34] ANGST, U.M., “Predicting the time to corrosion initiation in reinforced concrete structures exposed to chlorides”, Cement and Concrete Research, v. 115, pp. 559–567, 2019., ⁴⁸[48] NILSSON, L.-O., “On the uncertainty of service-life models for reinforced marine concrete structures”, In: Proceedings of the International Rilem Workshop on Life Prediction and Aging Management of Concrete Structure. Paris, 2000., ⁶¹[61] KHATRI, R.P., SIRIVIVATNANON, V., “Characteristic service life for concrete exposed to marine environments”, Cement and Concrete Research, v. 34, n. 5, pp. 745–752, 2004., ⁶²[62] MAAGE, M., HELLAND, S., POULSEN, E., et al., “Service life prediction of existing concrete structures exposed to marine environment”, ACI Materials Journal, v. 93, n. 6, 1996.]	Fick + D (t)	240	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} \end{matrix}$
UCT (2001)	[⁶³[63] HEATH, K. “Marinas in the Arabian Gulf region”. In: ALEXANDER, M. (org) Marine Concrete Structures. 1 ed. United Kingdom: Woodhead Publishing, 2016. pp. 215–240,]	Fick + D (t)	0	$\begin{matrix} C_{x} = C_{s} (1 - e r f (\frac{x}{2 \sqrt{D_{0} t^{(1 - n)}}})) \end{matrix}$
HZM (2015)	[²⁵[25] LI, Q., LI, K., ZHOU, X., et al., “Model-based durability design of concrete structures in Hong Kong–Zhuhai–Macau Sea link Project”, Structural Safety, v. 53, pp.1–12, 2015.]	Fick + D (t)	32	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} / C_{s} = A (w / b)^{} \end{matrix}$ ver [²²[22] PANESAR, D.K., CHING, G.H., “Implications of coupled degradation mechanisms of cement-based materials exposed to cold climates”, Internat. Journal of Mechanical Sciences, v. 144, pp. 865–76, 2018.]
Kwon et al. (2009)	[⁶⁴[64] KWON, S.J., NA, UJ., PARK, S.S., et al., “Service life prediction of concrete wharves with early-aged crack: Probabilistic approach for chloride diffusion”, Structural Safety, v. 31, n. 1, pp. 75–83, 2009.]	Fick + D (t) + fissuras	167	$\begin{matrix} D_{m} (t) = \frac{D_{0}}{1 - n} {(\frac{t_{0}}{t})}^{n} (t < t_{c t e}) \\ D_{m} (t) = D_{0} [1 + \frac{t_{c t e}}{t} (\frac{n}{1 - n})] {(\frac{t_{0}}{t_{c t e}})}^{n} (t \geq t_{c t e}) \\ D (w) = (31.61 w^{2} + 4.73 w + 1) \\ D_{m} (w \geq 0.1 m m) \end{matrix}$
Leung, Hou (2015)	[⁶⁵[65] LEUNG, C.K., HOU, D., “Numerical simulation of chloride-induced corrosion initiation in reinforced concrete structures with cracks”, Journal of Materials in Civil Engineering, v. 27, n. 3, 04014122, 2015.]	Fick + D (t) + fissura	8	$\begin{matrix} D_{e q} = \frac{D_{c r} + D_{u n c} A 1 {(D_{u n c} t / x^{2})}^{A 2}}{1 + A 1 {(D_{u n c} t / x^{2})}^{A 2}} \end{matrix}$
CHLODIF (1995)	[²⁶[26] OSLAKOVIC, I.S., BJEGOVIC, D., MIKULIC, D., “Evaluation of service life design models on concrete structures exposed to marine environment”, Materials and Structures, v. 43, n. 10, pp. 1397–1412, 2010.]	Fick + D (t) + C_s (t)	29	$\begin{matrix} D (t) = D_{w / c} D_{c} t^{- 0.1} \\ C_{x} = [C_{0} + k (t - 1)] (1 - e r f (\frac{x}{2 \sqrt{D t}})) \\ + [\dots]^{} \end{matrix}$ consultar [²⁶[26] OSLAKOVIC, I.S., BJEGOVIC, D., MIKULIC, D., “Evaluation of service life design models on concrete structures exposed to marine environment”, Materials and Structures, v. 43, n. 10, pp. 1397–1412, 2010.]
CTDRC/ BHRC (2007)	[⁵²[52] SAFEHIAN, M., RAMEZANIANPOUR, A.A., “Assessment of service life models for determination of chloride penetration into silica fume concrete in the severe marine environmental condition”, Construction and Building Materials, v. 48, pp. 287–294, 2013.]	Fick + D (t) + C_s (t)	53	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} / C_{s} (t) = C_{0} {(\frac{t_{0}}{t})}^{m} \end{matrix}$ Consultar equação empírica em [⁶⁶[66] ASHRAFI, H.R., RAMEZANIANPOUR, A.A., “Service life prediction of silica fume concretes”, Internacional Journal of Civil Engineering, v. 5, n. 3, pp. 182–197, 2007.]
Pack et al. (2010)	[⁵⁶[56] PACK, S.W., JUNG, M.S., SONG, H.W., et al., “Prediction of time dependent chloride transport in concrete structures exposed to a marine environment”, Cement and Concrete Research, v. 40, pp. 302–312, 2010.]	Fick + D (t) + C_s (t)	136	$\begin{matrix} D_{m} (t) = \frac{D_{0}}{1 - n} {(\frac{t_{0}}{t})}^{n} + \\ C_{s} (t) = k 1 [\ln (k 2 t + 1)] + k 3 \end{matrix}$
Duan et al. (2015)	[⁶⁷[67] DUAN, A., DAI, J.G., JIN, W.L., “Probabilistic approach for durability design of concrete structures in marine environments”, Journal of Materials in Civil Engineering, v. 27, n. 2, A4014007, 2015.]	Fick + D (t) + C_s (t)	22	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} \\ C_{s} (t) = C_{0} + k (1 - e^{- m (t - t_{0})}) \end{matrix}$
Pang e Li (2016)	[⁶⁸[68] PANG, L., LI, Q., “Service life prediction of RC structures in marine environment using long term chloride ingress data: Comparison between exposure trials and real structure surveys”, Construction and Building Materials, v. 113, pp. 979–987, 2016.]	Fick + D (t) + C_s (t)	43	$\begin{matrix} D_{app} (t) = D_{app, 0} {(\frac{t_{0}}{t})}^{n^{}} \\ C_{s} (t) = C_{s, 1} t^{m} \end{matrix}$ fórmulas empíricas em [⁶⁸[68] PANG, L., LI, Q., “Service life prediction of RC structures in marine environment using long term chloride ingress data: Comparison between exposure trials and real structure surveys”, Construction and Building Materials, v. 113, pp. 979–987, 2016.]
DuraCrete (2000)*^R	[²⁶[26] OSLAKOVIC, I.S., BJEGOVIC, D., MIKULIC, D., “Evaluation of service life design models on concrete structures exposed to marine environment”, Materials and Structures, v. 43, n. 10, pp. 1397–1412, 2010., ⁵³[53] WU, L., LI, W., YU, X., “Time-dependent chloride penetration in concrete in marine environments”, Construction and Building Materials, v. 152, pp. 406–413, 2017., ⁶⁹[69] VAN BREUGEL, K., POLDER, R.B., DE ROOIJ, M.R., “Long-term performance of marine structures in the Netherlands – validation of predictive models for chloride ingress”. In: Proceedings of 5th International Symposium on Life-Cycle Engineering. Netherlands, 2016. pp. 1285–1294.; ⁷⁰[70] YU, B., NING, C.L., LI, B., “Probabilistic durability assessment of concrete structures in marine environments: Reliability and sensitivity analysis”, China Ocean Engineering, v. 31, n. 1, pp.63–73, 2017.]	Fick + D (t) + fatores k	62	$\begin{matrix} D_{app} (t) = K_{c} K_{e} K_{tm} D_{0} {(\frac{t_{0}}{t})}^{n} \end{matrix}$
LNEC E465 (2007)	[⁵³[53] WU, L., LI, W., YU, X., “Time-dependent chloride penetration in concrete in marine environments”, Construction and Building Materials, v. 152, pp. 406–413, 2017.]	Fick + D (t) + fatores k	22	$\begin{matrix} D_{a p p} (t) = K_{c} K_{h} K_{T} D_{0} {(\frac{t_{0}}{t})}^{n} \end{matrix}$
Smith (2001)	[⁴⁹[49] SMITH, B.G., CREVELING, M., TEIG, J.W. “Sustainable concrete mix designs for 100-year service life for bridges in san diego county coastal environments”, In: Proceedings of Conference on Coastal Engineering Practice. Florida, 2011. pp. 184–197., ⁷¹[71] SMITH, B.G., “Durability of silica fume concrete exposed to chloride in hot climates”, Journal of materials in civil engineering, v. 13, n. 1, pp. 41–48, 2001.]	Fick + D (t, T)	21	$\begin{matrix} D_{eff} = D_{0} f (t) f (T) {(\frac{t_{0}}{t})}^{n} \\ f (t) = 1 /_{[1 + 2 \log (t + 1)]} para OPC \\ f (t) = 1 /_{11 + (2 + 0.01 sf \log (t + 1)]} \\ para concreto com silica ativa \\ f (T) = \frac{T}{T_{0}} \exp [k (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$
Ferreira (2010)	[⁷²[72] FARAHANI, A., TAGHADDOS, H., SHEKARCHI, M., “Prediction of long-term chloride diffusion in silica fume concrete in a marine environment”, Cement and Concrete Composites, v. 59, pp.10–17, 2015.]	Fick + D (t, T)	74	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} \\ f (T) = \frac{T}{294} \exp [\frac{U}{R} (\frac{1}{294} - \frac{1}{T})] unid: K \end{matrix}$
Life-365*^R	[²⁶[26] OSLAKOVIC, I.S., BJEGOVIC, D., MIKULIC, D., “Evaluation of service life design models on concrete structures exposed to marine environment”, Materials and Structures, v. 43, n. 10, pp. 1397–1412, 2010., ⁵²[52] SAFEHIAN, M., RAMEZANIANPOUR, A.A., “Assessment of service life models for determination of chloride penetration into silica fume concrete in the severe marine environmental condition”, Construction and Building Materials, v. 48, pp. 287–294, 2013., ⁵³[53] WU, L., LI, W., YU, X., “Time-dependent chloride penetration in concrete in marine environments”, Construction and Building Materials, v. 152, pp. 406–413, 2017., ⁵⁶[56] PACK, S.W., JUNG, M.S., SONG, H.W., et al., “Prediction of time dependent chloride transport in concrete structures exposed to a marine environment”, Cement and Concrete Research, v. 40, pp. 302–312, 2010., ⁷³[73] BURRIS, L.E., RIDING, K.A., “Diffusivity of binary and ternary concrete mixture blends”, ACI Materials Journal, v. 111, n. 4, pp. 373–382, 2014., ⁷⁴[74] JACIR, U., NAGI, M., “Evaluation of service life of reinforced concrete in the middle east – five year testing”, In: Proceedings of European Corrosion Congress, EUROCORR 2016. Paris, 2016.]	Fick + D (t, T) + Cs (t)	249	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} / f (T) = \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$
Concrete Works	[⁷³[73] BURRIS, L.E., RIDING, K.A., “Diffusivity of binary and ternary concrete mixture blends”, ACI Materials Journal, v. 111, n. 4, pp. 373–382, 2014.]	Fick + D (t, T) + Cs (t)	9	$\begin{matrix} D (t) = D_{0} {(\frac{t_{0}}{t})}^{n} / D_{ult} [1 - {(\frac{t_{0}}{t})}^{n}] t_{0} = 28 d \\ f (T) = \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \\ C_{s} (t) = C_{s, max} \frac{k t}{1 + k t} \end{matrix}$
ClinConc	[⁴⁸[48] NILSSON, L.-O., “On the uncertainty of service-life models for reinforced marine concrete structures”, In: Proceedings of the International Rilem Workshop on Life Prediction and Aging Management of Concrete Structure. Paris, 2000.]	Fick + D (t,T,x) + Cs (t) – senoidal	1	$\begin{matrix} C_{s} (t) = \frac{C_{s, max} + C_{s, min}}{2} + \frac{C_{s, max} - C_{s, min}}{2} \\ \sin k (t + t_{\exp}) \\ D (x, t) = \frac{D_{0}}{N} f (x) f (t) f (T) \end{matrix}$ $\begin{matrix} f (x) = \{φ + (1 - φ) {(\frac{x}{x_{s}})}^{k}; x < x_{s} 1; x \geq x_{s} \\ f (t) = \{{(\frac{t_{cte}}{t + t_{\exp}})}^{n}; t < t_{cte} - t_{\exp} 1; t \geq t_{cte} - t_{\exp} \end{matrix}$ Equação de Arrhenius: $\begin{matrix} f (T) = \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$
DuraPGulf (2008)	[⁵²[52] SAFEHIAN, M., RAMEZANIANPOUR, A.A., “Assessment of service life models for determination of chloride penetration into silica fume concrete in the severe marine environmental condition”, Construction and Building Materials, v. 48, pp. 287–294, 2013., ⁷⁵[75] ALIZADEH, R., GHODS, P., CHINI, M., et al., “Effect of curing conditions on the service life design of RC structures in the Persian Gulf region”, Journal of Materials in Civil Engineering, v. 20, n. 1, pp. 2–8, 2008.;⁷⁶[76] SHEKARCHI, M., GHODS, P., ALIZADEH, R., et al., “Durapgulf, a local service life model for the durability of concrete structures in the south of Iran”, The Arabian Journal for Science and Engineering, v. 33, pp.78–88, 2008.]	Fick + D (t, T, h)	100	f(t) igual Maage et al. (1995) f(T): Equação de Arrhenius (ver ClinConc) f(h) = [1 + 256 (1 − h)⁴]⁻¹
Farahani et al. (2015)	[⁷²[72] FARAHANI, A., TAGHADDOS, H., SHEKARCHI, M., “Prediction of long-term chloride diffusion in silica fume concrete in a marine environment”, Cement and Concrete Composites, v. 59, pp.10–17, 2015.]	Fick + D (t, T, h)	74	f(t) igual Maage et al. (1995) f(T): Equação de Arrhenius $\begin{matrix} f (h) = {[1 + {(\frac{100 - h}{100 - h_{c}})}^{4}]}^{- 1} \\ D_{0} = (- 4.002 + 18.09 w / b + 1.8129 (w / b)^{2} \\ - 0.09937 s f + 0.01861 {s f}^{2} \\ - 0.8558 w / b s f) 10^{- 12} \end{matrix}$
Yu et al. (2015)	[⁷⁷[77] YU, Z., CHEN, Y., LIU, P., WANG, W., “Accelerated simulation of chloride ingress into concrete under drying–wetting alternation condition chloride environment”, Construction and Building Materials, v. 93, pp. 205–213, 2015.]	Fick + D (t, T, h)	50	$\begin{matrix} D_{eq} = D_{app} f (t) f (T) f (h) \\ f (t) = \{\begin{cases} {(t_{0} / t)}^{n}; t \leq 30 anos \\ {(t_{0} / t_{c t e})}^{n}; t > 30 a n o s \end{cases} \\ f (T) = \frac{T}{T_{0}} \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$ f(h) igual Farahani et al. (2015)
Shi et al. (2012)	[⁷⁸[78] SHI, W., YU, Z., KUANG, Y., et al., “Probability-based durability analysis of structural concrete under chloride salt environment”, Applied Mechanics and Materials, v. 166, pp. 1843–1847, 2012.]	Fick + D (t, T, h, fixação, fissura)	0	$\begin{matrix} D = f (T) f (h) f (C_{b}) f (w) D_{app} \\ D_{app} = D_{0} f (t)^{} \\ f (T) = \exp [\frac{U}{R} (\frac{1}{T_{0} + 273} - \frac{1}{T + 273})] \end{matrix}$ f(h) igual Farahani et al.(2015) $\begin{matrix} f (C_{b}) = 1 + \frac{\partial C_{b}}{\partial C_{f}} \\ f (w) = 31.61 w^{2} + 4.73 w + 1 \end{matrix}$ consultar [⁷⁸[78] SHI, W., YU, Z., KUANG, Y., et al., “Probability-based durability analysis of structural concrete under chloride salt environment”, Applied Mechanics and Materials, v. 166, pp. 1843–1847, 2012.]
Van Dinh (2017)	[⁷⁹[79] VAN DINH, D., “Initiation time of corrosion in reinforced concrete structures exposed to chloride in marine environment”, International Journal of Civil Engineering and Technology, v. 8, n. 9, pp. 564–571, 2017.]	Fick + D (t, T, h, fissuras) + Cs (t)	0	D_app = D₀[exp(−0.165 sf)]f(t)f(T)f(h) + ^w/_{s_cr} D_Cr f(t): Maage et al. (1995) / f(T): Equação de Arrhenius / f(h): Farahani et al. (2015) $\begin{matrix} n = 0, 2 + 0, 4 (f a / 50 + s g / 70) \\ C_{s} (t) = \{\begin{cases} k t; t \leq t_{cte} \\ C_{s, m a x}; t \geq t_{cte} \end{cases} \end{matrix}$
Dominicini (2016)	[³⁵[35] VIEIRA, D.R., MOREIRA, A.L.R., CALMON, J.L., et al., “Service life modeling of a bridge in a tropical marine environment for durable design”, Construction and Building Materials, v. 163, pp. 315–325, 2018.]	Fick + D (t, T, h) + diferentes Cs (t) + efeito radiação solar	6	D = D₀f(t)f(T)f(h) f(t) igual Maage et al. (1995) f(T): Equação de Arrhenius f(h) igual Farahani et al. (2015) Ver efeito radiação solar em [³⁵[35] VIEIRA, D.R., MOREIRA, A.L.R., CALMON, J.L., et al., “Service life modeling of a bridge in a tropical marine environment for durable design”, Construction and Building Materials, v. 163, pp. 315–325, 2018.]
Zhang et al. (2019)	[⁸⁰[80] ZHANG, Y., ZHOU, X., ZHANG, Y., et al., “Randomness of bidirectional chloride corrosion of sluice gate and time to corrosion initiation of reinforcement in a strong tidal environment”, Construction and Building Materials, v. 227, 116707, 2019.]	Fick + D (t) + Convecção*	1	$\begin{matrix} C_{s, Δ x} = C_{i} + k \sqrt{t} / Δ x = k 1 + k 2 \ln t \end{matrix}$ Equação empírica em [⁸⁰[80] ZHANG, Y., ZHOU, X., ZHANG, Y., et al., “Randomness of bidirectional chloride corrosion of sluice gate and time to corrosion initiation of reinforcement in a strong tidal environment”, Construction and Building Materials, v. 227, 116707, 2019.]
fib (2006) *^R	[⁵²[52] SAFEHIAN, M., RAMEZANIANPOUR, A.A., “Assessment of service life models for determination of chloride penetration into silica fume concrete in the severe marine environmental condition”, Construction and Building Materials, v. 48, pp. 287–294, 2013., ⁸¹[81] NIELSEN, C.V. “Service life modelling for chloride ingress in reinforced concrete”, In: Proceedings of the 2017 fib Symposium. Netherlands, 2017. pp. 2234–2243., ⁸²[82] YOGALAKSHMI, N.J., RAO, K.B., ANOOP, M.B., “Durability-based service life design of RC structures – chloride-induced corrosion”. In: Proceedings of the International Conference on Reliability, Safety and Hazard, ICRESH 2019. Chennai, 2020. pp. 580–590.]	Fick + D (t, T) + Convecção*	54	$\begin{matrix} C_{x} = C_{i} + (C_{s, Δ x} - C_{i}) (1 - e r f (\frac{x - Δ x}{2 \sqrt{D_{a p p} t})}) \\ D_{a p p} = D_{R C M} f (t) f (T) K_{t m} \\ f (t) = {(\frac{t_{0}}{t})}^{n} / f (T) = \exp [K (\frac{1}{T_{0}} - \frac{1}{T})] \end{matrix}$
Da Costa et al. (2013)	[⁸³[83] DA COSTA, A., FENAUX, M., FERNÁNDEZ, J., SÁNCHEZ, E., MORAGUES, A., “Modelling of chloride penetration into non-saturated concrete: Case study application for real marine offshore structures”, Construction and Building Materials, v. 43, pp. 217–224, 2013.]	Fick + Convecção	27	$\begin{matrix} \frac{\partial C (t, x)}{\partial t} + u \frac{\partial C (t, x)}{\partial x} - D \frac{\partial^{2} C (t, x)}{\partial x^{2}} = 0 \end{matrix}$
Hong e Ann (2018)	[⁸⁴[84] HONG, S.I., ANN, K.Y., “Numerical prediction of chloride penetration in concrete exposed to a marine environment at tide”, Advances in Materials Science and Engineering, v. 2018, 7591576, 2018.]	Fick + Convecção + Transporte de umidade	0	$\begin{matrix} (\frac{\partial C_{b}}{\partial C_{f}} + S Φ) \frac{\partial C_{f}}{\partial t} = \nabla (S Φ D_{e f f} \nabla C_{f} \\ + S Φ C_{f} D_{h} \nabla h \\ \frac{\partial h}{\partial t} = \nabla (- K_{1}^{'} \nabla P_{c} + K_{v}^{'} \nabla P_{v}) \end{matrix}$
RMTC	[⁸⁵[85] BOULFIZA, M., SAKAI, K., BANTHIA, N., et al., “Prediction of chloride ions ingress in uncracked and cracked concrete”, ACI Materials Journal, v. 100, n. 1, pp. 38–48, 2003.]	Fick + Convecção + transporte de umidade + fissura	77	$\begin{matrix} \frac{\partial θ C}{\partial t} + u \frac{\partial C}{\partial x} - D \frac{\partial^{2} θ C}{\partial x^{2}} = 0 \end{matrix}$ Alterna entre o transporte na fissura e na matriz Fórmulas do transporte de umidade: [⁸⁵[85] BOULFIZA, M., SAKAI, K., BANTHIA, N., et al., “Prediction of chloride ions ingress in uncracked and cracked concrete”, ACI Materials Journal, v. 100, n. 1, pp. 38–48, 2003.]
Saetta et al. (1993)	[⁵¹[51] MEDEIROS-JUNIOR, R.A., LIMA, M.G., MEDEIROS, M.H.F., “Service life of concrete structures considering the effects of temperature and relative humidity on chloride transport”, Environment development and sustainability, v. 17, pp. 1103–1119, 2015., ⁷²[72] FARAHANI, A., TAGHADDOS, H., SHEKARCHI, M., “Prediction of long-term chloride diffusion in silica fume concrete in a marine environment”, Cement and Concrete Composites, v. 59, pp.10–17, 2015.]	Fick + D (t, T, h) + Convecção + Transfer. decalor + Transporte de umidade	88	$\begin{matrix} D = D_{0} f (t) f (T) f (h) \\ f (t) = ς + (1 - ς) {(\frac{28}{t})}^{1 / 2} \\ f (T) = \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \\ f (h) = {[1 + {(\frac{1 - h}{1 - h_{c}})}^{4}]}^{- 1} \end{matrix}$ *Demais equações ver em [⁸⁶[86] SAETTA, A.V., SCOTTA, R.V., VITALIANI, R.V. “Analysis of chloride diffusion into partially saturated concrete”, ACI Materials Journal, v. 90, n. 5, pp. 441–451, 1993.]
Lin, et al. (2010) *^R	[⁸⁷[87] LIN, G., LIU, Y., XIANG, Z., “Numerical modeling for predicting service life of reinforced concrete structures exposed to chloride environments”, Cement and Concrete Composites, v. 32, pp. 571–579, 2010.]	Fick + D (t, T, h, de) + Convecção + Transf. de calor + Transporte de umidade	72	D = D₀f(t)f(T)f(h)f(de) f(t) igual Maage et al. (1995) f(T): Equação de Arrhenius f(h) = h^k / k – Power index $\begin{matrix} f (de) = 1 + \frac{D_{max}}{D_{0}} \{1 - {[1 + {(\frac{de}{K_{1}})}^{K_{2}}]}^{- 1}\} \end{matrix}$
Universidade de Toronto (1999)*^R	[⁸⁸[88] BODDY, A., BENTZ, E., THOMAS, M.D.A., et al., “An overview and sensitivity study of a multimechanistic chloride transport model”, Cement and Concrete Research, v. 29, pp. 827–837, 1999., ⁸⁹[89] THOMAS, M.D.A., BAMFORTH, P.B., “Modelling chloride diffusion in concrete: Effect of fly ash and slag”, Cement and Concrete Research, v. 29, n. 4, pp. 487–495, 1999.]	Fick + D (t, T) + Convecção + Permeabilidade + Wicking	578	$\begin{matrix} D (t, T) = D_{0} {(\frac{t_{0}}{t})}^{n} \exp [\frac{U}{R} (\frac{1}{T_{0}} - \frac{1}{T})] \\ \frac{\partial C_{f}}{\partial t} = D \frac{\partial^{2} C_{f}}{\partial x^{2}} - v \frac{\partial C_{f}}{\partial x} + \frac{ρ}{N} \frac{\partial C_{b}}{\partial t} \end{matrix}$
Sub-difusão	[⁸²[82] YOGALAKSHMI, N.J., RAO, K.B., ANOOP, M.B., “Durability-based service life design of RC structures – chloride-induced corrosion”. In: Proceedings of the International Conference on Reliability, Safety and Hazard, ICRESH 2019. Chennai, 2020. pp. 580–590.]	investigações teóricas de Janett (2010)¹ 1 P. Janett, Diffusion on fractals and space-fractional diffusion equations. Technische Universitat Chemnitz, Fakultat fur Naturwissenschaften, Dissertation (2010).	0	$\begin{matrix} \frac{\partial C}{\partial t} = D \propto D_{t}^{1 - \propto} \frac{\partial^{2} C}{\partial x^{2}} \end{matrix}$
Bob (1996)	[⁵¹[51] MEDEIROS-JUNIOR, R.A., LIMA, M.G., MEDEIROS, M.H.F., “Service life of concrete structures considering the effects of temperature and relative humidity on chloride transport”, Environment development and sustainability, v. 17, pp. 1103–1119, 2015.]	–	14	$\begin{matrix} d = 150 (\frac{{c K}_{T} K_{h} K_{c_{c r} /_{c s}}}{f_{c}}) \sqrt{T_{i}} \end{matrix}$
Frente de ingresso de cloretos	[⁹⁰[90] CHEEWAKET, T., JATURAPITAKKUL, C., CHALEE, W., “Initial corrosion presented by chloride threshold penetration of concrete up to 10 year-results under marine site”, Construction and Building Materials, v. 37, pp. 693–698, 2012.]	–	49	Sem equações / graficamente se faz a frente de penetração de cloreto ao longo do tempo para cada tipo de concreto – únicos parâmetros são teor crítico obtido experimentalmente e cálculo da frente de ingresso de cloretos

*Obs: essa é a soma do número de citações que os artigos que aplicaram o modelo tiveram na base Scopus ou na base Web of Science, quando não tinha esse levantamento na primeira base.

PARÂMETROS DAS EQUAÇÕES: A – coeficiente com equação / c – capacidade de fixação de cloretos em função do tipo de cimento / C₀ – concentração superficial inicial de cloreto / C_b – concentração de cloretos fixos / C_cr – teor crítico de cloretos / C_en – concentração de cloretos livres no ambiente / C_f – concentração de cloretos livres / C_i – concentração de cloretos inicial no concreto / C_s – concentração superficial de cloretos/ C_s,max – concentração superficial máxima / C_s,min – concentração superficial mínima / C_s,1 – concentração superficial depois de um ano de exposição / C_s,Δx – concentração de cloretos na profundidade Δx em um tempo específico / C_x = concentração de cloretos na profundidade x e tempo t / d – cobrimento (m) / de – decaimento do desempenho da estrutura de concreto / D – coeficiente de difusão (m²/s) / D₀ – D referência ou inicial / D_app – D aparente / D_c – D que leva em conta o tipo de cimento / D_cr – D na fissura / D_eff – D efetivo / D_eq – D equivalente / D_fa– D de concreto auto adensáveis com alta substituição de cinza volante / D_h – D da umidade / D_m – D médio / D_max – D máximo devido decaimento estrutural / D_RMC – coeficiente de migração obtido pelo ensaio / D_unc – Do do concreto não fissurado / D_w/c – D que leva em conta a influência da relação a/c / Dα – coeficiente de sub-difusão do cloreto/ Dt (1-α) – termo derivado da fração / erf = equação/ função de erro de Gauss / fa – teor de substituição de cinza volante / fc – resistência à compressão do concreto / h – umidade relativa do concreto / h_c – umidade relativa crítica (geralmente 0.75) / k – constante / K – parâmetro do modelo / Kc – tipo de cura / Ke – ambiental / Ktm – test method para medição do D / K’l – permeabilidade do concreto à água líquida (kg/m.s.Pa) / K’v – permeabilidade do concreto ao vapor da água (kg/m.s.Pa) / m – age factor do C_s / n – age factor, ageing factor, fator de envelhecimento do D / N – porosidade do concreto / P_c – pressão capilar (Pa) / P_v– pressão do vapor d’água (Pa) / R = constante universal dos gases (8,314472 J/mol. K) / s_cr – distância entre fissuras / sf – teor de substituição do cimento por sílica ativa / sg – teor de substituição do cimento de escória / t – tempo / t₀ – tempo referência ou inicial / t_cte – tempo a partir do qual certa variável é admitida constante / t_exp – idade do concreto quando começou a exposição / t_i = tempo de início de corrosão / T – temperatura / T₀ – temperatura referência / U = energia de ativação do processo de difusão (J/mol) / v – velocidade média linear / w – abertura de fissuras / w/b – relação água cimento / x – profundidade (m) / xs – profundidade da zona superficial / Δx – profundidade da zona de convecção / ∇ – nabla – operador diferencial parcial / ρ – densidade do concreto / Φ – razão entre D da superfície e D da zona interior do concreto.

*^R – Modelos citados pelos artigos de revisão aderidos / convecção* de forma simplificada / D (t, T, h, de) – coeficiente de difusão variando conforme tempo, temperatura, umidade e decaimento estrutural, respectivamente / C_s (t) – concentração superficial variando com o tempo.

MODELO	QUANTIDADE DE REPETIÇÕES
Segunda Lei de Fick	9
Life-365	6
Maage et al. (1995)	4
DuraCrete (2000)	4
DuraPGulf (2008)	3
fib (2006)	3
Smith (2001)	2
Saetta et al. (1993)	2
Universidade de Toronto (1999)	2

[1] e-mail: rayaneclopes@discente.ufg.br, andriellimorais@ufg.br, ocascudo@ufg.br

Brasil

Brasil

Service life prediction models of concrete structures subjected to the initiation of reinforcing steel corrosion by chloride ions: contribution to the state of the art through systematic literature review – Part 1

ABSTRACT