A stochastic corrosion model for structural steels subject to sea waters

Document Type : Research Paper

Author

Abstract

In order to perform reliability analysis of steel structures subject to sea waters and thus to corroding marine environments, it is necessary to use: a) a model describing physical behavior of corrosion in structures placed in these circumstances and b) a stochastic model describing probabilistic behavior of corrosion phenomenon along time. In this study, Melchers' model is employed as a physical corrosion model. Furthermore, a probabilistic model is proposed in which the corrosion process is discretized into a few steps each of which representing a jump/an increment in corrosion quantity. Despite having a pre-defined deterministic small duration, each step is modeled with an independent random variable following a gamma distribution. In this paper, in contrast to the conventional gamma process, the shape and scale parameters of the involving gamma distributions are different for each step. This will result in an accumulating corrosion process which is a sum of n different gamma distributed random variables in any arbitrary point of time. Herein, in addition, a new application of "maximum likelihood method" for estimating of model parameters is proposed. Panama Canal data for carbon and low-alloyed steels is used for the purpose of parameter estimation. Reliability analysis of a structure subjected to an environment similar to that of Panama Canal is then investigated. Implementation of the model proposed herein to data available indicates that it could be sufficiently flexible to show the mean and variance of the marine corrosion processes. 

 





 





 

Keywords


[1] R. E. Melchers, "Modeling of marine immersion corrosion for mild and low-alloy steels—Part 1: Phenomenological model", Corrosion, Vol. 59, NO. 4, April 2003, pp. 363 – 367.
[2] R. E. Melchers, "Modeling of Marine Immersion Corrosion for Mild and Low-Alloy Steels—Part 2: Uncertainty Estimation", Corrosion, Vol. 59, NO. 4, April 2003, pp. 335-344.
[3] C. G. Soares, and Y. Garbatov, "Reliability of maintained, corrosion protected plates subjected to non-linear corrosion and compressive loads", Marine Structures, Vol. 12, NO. 6, July 1999, pp. 425-445.
[4] R. E. Melchers, "Long-term corrosion of cast irons and steel in marine and atmospheric environments", Corrosion Science, Vol. 68, March 2013, pp. 186-194.
[5] R. E. Melchers, "Microbiological and abiotic in modelling longer-term Marchine corrosion", Bioelectrochemistry, Vol. 97, June 2014, pp. 89-96.
[6] R. E. Melchers, "Long-term immersion corrosion of steels in seawaters with nutrient concentration", IEEE Transactions on Energy Conversion, Vol. 81, April 2014, pp. 110-116.
[7] S. Qin, and W. Cui, "Effect of corrosion models on the time-dependent reliability of steel plated elements", Marine Structures, Vol. 16, NO. 1, January 2003, pp. 15-34.
[8] M. D. Pandey, X. X. Yuan, and J. M. V. Noortwijk, "The influence of temporal uncertainty of deterioration on life-cycle management of structures", Structure and Infrastructure Engineering, Vol. 5, NO. 2, April 2009, pp. 145-156.
[9] J. M. Van Noortwijk, "A survey of the application of gamma processes in maintenance", Reliability Engineering & System Safety, Vol. 94, NO. 1, January 2009, pp. 2 – 21.
[10] M. Mahmoodian, and A. Alani, "Modeling deterioration in concrete pipes as a stochastic gamma process fortime-dependent reliability analysis", Journal of pipeline systems engineering and practice, Vol. 5, NO. 1, March 2013, pp. 1-5.
[11] M. Giorgio, M. Guida, and G. Pulcini, "A state-dependent wear model with an application to marine engine cylinder liners", Technometrics, Vol. 52, NO. 2, May 2010, pp. 172-187.
[12] M. R. Moarefzadeh, "Reliability of Marine Steel Structures Against Corrosion", Modares civil Engineering Journal, Vol. 16, NO. 3, 2016, pp. 203-215, (in Farsi).
[13] M. Guida, F. Postiglione, and G. Pulcini, "A time–discrete extended gamma process for time-dependent degradation phenomena", Reliability Engineering & System Safety, Vol. 105, September 2012, pp. 73-79.
[14] M. Giorgio, M. Guida, and G. Pulcini, "A new class of Markovian processes for deteriorating units with state dependent increments and covariates", IEEE Transactions on Reliability, Vol. 64, NO. 2, June 2015, pp. 562–578.
[15] M. Giorgio, M. Guida, and G. Pulcini, "Modeling a degradation process with dependent increaments in presence of random heterogeneity", InProceedings 6th International Conference on Accelerated Life Testing and Degradation Models–ALT’2016 2016, pp. 51-60.
[16] C. R. Southwell, and A. L. Alexander, "Corrosion of metals in tropical waters, structural ferrous metals", Materials Protection, Vol. 9, NO. 1, January 1970, pp. 14 – 23.
[17] R. E. Melchers, and R. Jeffrey, "The critical involvement of anaerobic bacterial activity in modeling the corrosion behavior of mild steel in marine environments", Electrochimica Acta, Vol. 54, NO. 1, December 2008, pp. 80-85.
[18] R. E. Melchers, and T. Wells, "Models for the anaerobic phases of marine immersion corrosion", Corrosion Science, Vol. 48, NO. 7, July 2006, pp. 1791-1811.
[19] J. N. Friend, "Deterioration of structures of timber, metal, and concrete exposed to the action of sea-water", eighteen report of the committee of the institution of civil engineers, ICE.
[20] P. G. Moschopoulos, "The distribution of the sum of independent gamma random variables", Annals of the Institute of Statistical Mathematics, Vol. 37, NO. 1, December 1985, pp. 541-544.
[21] P. L. Liu, and A. Der Kiureghian, "Multivariate distribution models with prescribed marginal and covariances", Probabilistic Engineering Mechanics, Vol. 1, NO. 2, June 1986, pp. 105-112.
[22] R. E. Melchers, "Structural reliability; analysis and prediction", John Wiley & Sons, 1999.
[23] T. A. Tran, and A. B. Sesay, "Sum of arbitrarily correlated Gamma variates and performance of wireless communication systems over Nakagami-m fading channels", IET communications, Vol. 1, NO. 6, December 2007, pp. 1133-1137.