Keywords: reliability, aging material, life prediction, Monte Carlo method, reinforced concrete, corrosion, carbonation, painting.

Structural reliability is defined as "the measurable capability of a system to perform its intended function in the required time under specified conditions". The intended service life is the period during which the structural system is expected to maintain an adequate level of safety and serviceability without requiring unforeseen excessive charges for maintenance and repair. Failure is the total or partial loss of the capability of a system. Let us consider three possible groups of failure (see Bolotin [2]).

Materials of engineering structures (e.g. reinforced concrete) in service may be affected by aging, which may include changes in strength and stiffness beyond the baseline conditions that are assumed in structural design. Some of these effects may cause component or system strengths to degrade over time, particularly when the concrete is exposed to an aggressive environment and may accelerate the risk of the structural failure.

In the present work, we first mention the principal definitions of the theory of probabilities that are employed in the study of structure reliability (see Milton [1], Melchers [3], Frankel [4]).

We then address the question of the determination of the service life of reinforced concrete structures in relation to the aggressiveness of the surrounding environment. The issue has previously been addressed by, for example, Moskvin et al. [5]. To exemplify, we examine one of the most complete laws proposed for the determination of the service life of reinforced concrete structures (see Siemens et al. [6]) and point out that due to its noteworthy complexity, it is impossible to perform the analysis of probability in a closed form. The analysis is thus carried out using the classic Monte Carlo method of simulation. To apply this method we prepared a specific calculation program.

We examine the case of a reinforced concrete structure considering as an example both the hypothesis of a structure with no surface protection and that of a structure with a protective coat of paint and a twenty-year maintenance interval.

It can be seen that the method is simple to apply, quick and extremely efficient. The results obtained are illustrated in graphic form to facilitate comprehension and the relative comment. The results obtained show the great influence of maintenance on the lifetime of the structure. The number of simulations used in the different cases was the same and no significant differences were found as concerning the rapidity of convergence.

1

E.H. Milton, "Reliability Based-Design in Civil Engineering", Mc Graw Hill Book Company, New York, N.Y., 1987.

2

V.V. Bolotin, "Life prediction of engineering systems", Proceedings of 4th Int. Conf. Application of Statistics and Probability in Soil and Structural Engineering, G. Augusti, A. Borri, G. Vannucchi (Eds), Vol. 2, Pitagora Editrice, Firenze (Italy), 851-866, 1983.

3

R.E. Melchers, "Structural Reliability. Analysis and prediction", Ellis Horwood Limited, Chichester, U.K., 1987.

4

E.G. Frankel, "Systems Reliability and Risk Analysis", Kluver Academic Publisher, Dordrecht, ND, 1988.

5

V. Moskvin, F. Ivanov, S. Alexeyev, E. Guzeyev, "Concrete and Reinforced Concrete Deterioration and Protection", (English translation), MIR Publishers, Moscow, USSR, 1983.

6

A.J.M. Siemens, A.C.W.M. Wrouvenvelder, A. Van Den Beukel, "Durability of buildings: a reliability analysis", HERON, 30, 1985.

7

S. Gowripalan, J. Shakil, G. Singh, "Life-cycle studies of a concrete structure using simulation on a microcomputer", Computer and Structures 41(6), 1225-1230, 1991. doi:10.1016/0045-7949(91)90258-N

8

Y. Mori, B.R. Ellingwood, "Reliability-Based Service-Life Assessment of Aging Concrete Structures", Journal of Structural Engineering, 119(5), 1600-1621, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:5(1600)

9

W.H. Press, S.A. Teukolsky, W.T. Wetterling, B.P. Flannery, "Numerical Recipes in Fortran. The Art of Scientific Computing", Second Edition, Cambridge University Press, New York, N.Y., 1992.

10

C. Alexopoulos, K. Seong-Hee, "Output data analysis for simulations", Proceedings of the 2002 Winter Simulation Conference, 85-96, 2002. doi:10.1109/WSC.2002.1172872

11

A.M. Law, W.D. Kelton, "Simulation Modeling and Analysis", Second Edition, McGraw-Hill, New York, 1991.

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