## Example 3611

A structural engineer is designing a retaining wall where the main structural members are exposed, unpainted steel I-beams located in the downtown area. In performing a life cycle cost analysis of the structure, the designer needs to predict the degree of section loss in the beams over time due to corrosion. Corrosion is a common deterioration mechanism that is difficult to predict since it is dependent on the type of steel, the local environment, the presence of moisture, and even the location of the steel member in the structure. Ideally, the designer would prefer to allow samples of the same type of steel that is used in the project to corrode over time under the same conditions as the proposed structure and use those data to develop a deterioration model. However, it is costly and time consuming to obtain this information. A literature search reveals that Albrecht and Naeemi (1984) developed a commonly referenced corrosion propagation model that predicts the average corrosion penetration C(t) (mm) at any time t (years) as follows:

where A and B are regression parameters based on the environment and type of steel. For carbon steel in an urban environment, A has a mean value of mA = 80.2 and a standard deviation of sA = 33.68, while mB = 0.593 and aB = 0.24. The correlation coefficient between A and B is pA>B = 0.68. What is the estimated section loss after 10 years? After 20 years?

### Answer

A probabilistic analysis using Monte Carlo simulation with @RISK software (Palisade 2003) (100,000 simulations) reveals a distribution for C(t) that looks lognormal in shape and has the parameters shown in Table 36.1. In all cases, the uncertainty in the result, as indicated by the extremely large standard deviation, is quite high and increases with time. Column (1) represents the values if the correlation between A and B is not included in the analysis. Column (2) includes the correlation, and Column (3) truncates the distribution for A at 0.0 on the lower end to prevent any results that show a thickness increase due to corrosion. Such results can be quite different depending on the tools that the analyst chooses to use. The information derived from these tools is not exact, and there is no guarantee that the model from the literature matches how the retaining wall will actually behave. Still, the model provides a reasonable predictive tool to make an estimate, but in each case, the analyst needs to understand its limitations.

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