## Example 3623

A bridge manager is responsible for maintaining a group of highway bridges. One of these bridges is currently 15 years old and is deteriorating fast. The manager feels that the bridge might become unsafe (b < 3.0) before reaching its prescribed service life (i.e., 75 years). Analyzing the existing records on the performance of the bridge during the past 15 years the manager realizes that there were no visual defects in the first 3 years of service, after which small cracks were visible. The first signs of corrosion appeared when the bridge was 10 years old. Measuring the loss of reinforcement at the present time (at year 15) the manager estimated that a loss of bending resistance of 4% had occurred. The most economical maintenance action available is the replacement of the concrete cover. This will correct visual defects and delay deterioration. The bending load effect and the bending resistance (both in kN m) at the beginning of service life are characterized by normal distributions N[85, 12] and N[180, 9], respectively.

It is assumed that the replacement of concrete cover improves the condition index C to its initial value (at time t = 0). After this concrete replacement, the condition index does not deteriorate for a period of 3 years, as is the case of a new structure. The replacement of the concrete cover does not improve the reliability index but delays any further deterioration until the condition index reaches the level corresponding to initiation of corrosion. Using the above assumptions, estimate the effect of concrete cover replacement on condition and reliability and find the time of application of maintenance such that the target reliability index is not violated during the entire service life.

### Answer

The visual deterioration of a bridge can be assessed by the condition index. This index is defined in discrete terms as 0 — no chloride contamination; 1 — onset of corrosion; 2 — onset of cracking; and 3 — loose concrete/significant delamination. According to existing records, the initiation time of condition deterioration is 3 years. Assuming that the coefficient of variation of the resistance is constant over time, the mean resistance reduction of 4% results in a bending resistance after 15 years that is characterized by a normal distribution with a mean and standard deviation as follows:

mR5years = 180 x 0.96 = 172.8 kN m and ffR5years = 9 x 0.96 = 8.64 kN m

The initial (at time t = 0) reliability index and the reliability index at 15 years are

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