## Example 3617

A local Department of Transportation (DOT) management policy is to replace its concrete bridge decks when there is active corrosion in 50% of the deck. A serviceability failure in concrete decks is often determined by the amount of active corrosion in the steel reinforcing. The expansion due to corrosion causes concrete to spall, which reduces driving speeds, increases accident hazards, and eventually requires replacement of the deck. The half-cell potential test is used to detect active corrosion in concrete slab reinforcement by measuring the electric potential difference between a standard portable copper-copper sulfate half-cell placed on the surface of the concrete and the embedded reinforcing steel. According to ASTM (1987), if the potential difference reading is more positive than —200 mV, there is a greater than 90% probability that corrosion activity is not taking place in that area. Similarly, if the potentials of an area are more negative than —350 mV, there is a greater than 90% probability that corrosion activity is taking place. For electric potential readings that fall in between those ranges, corrosion activity is more uncertain.

In an effort to better quantify the uncertainty, Marshall (1996) compiled the half-cell potential data from 89 different bridges. The PDF of half-cell potentials in areas where the deck was known to be undamaged (i.e., there was no reinforcement corrosion) was a normal distribution with a mean value of —207 mV and a standard deviation of 80.4 mV. Similarly, the PDF for half-cell readings in damaged areas of deck was found to be N[—354 mV, 69.7 mV] as shown in Figure 36.10. The overlap of the two PDFs indicates a significant risk of misinterpretation of actual readings based on half-cell potential mapping.

Half-cell potential, -mV

FIGURE 36.10 Probability density functions (PDFs) of half-cell potentials in areas where the deck is known to be damaged and undamaged.

Half-cell potential, -mV

FIGURE 36.10 Probability density functions (PDFs) of half-cell potentials in areas where the deck is known to be damaged and undamaged.

In a half-cell potential test for a bridge deck, readings were taken at eight locations evenly spread throughout the deck. The potential difference readings in (mV) were —200, —225, —297, —300, —305, —310, —197, and —330. What is the probability of active corrosion at each of these locations? Estimate the percentage of damage to the deck. Does it need to be replaced at this time?

### Answer

The probability of damage (pdam) at one of the readings can be determined as p = pdfbad-x am pdfbad-x + pdfgood-x where pdfbad-x and pdfgood-x are the values of the density distributions in Figure 36.10 for the damaged and undamaged decks for a half-cell reading of x, respectively. Because the distributions in Figure 36.10 are both normal, the probability of damage when the half-cell reading is —200 mV is obtained as follows:

pdfgood-(—200mV) = ^pffi e—(1/2)((x—m)/s)2 = e—(1/2)((200—207)/80-4)2 = 0.004943

pdfbad-(—200mV) = ^^ffi e—(1/2)((200—354)/697)2 = 0.00 0 4 32 0 000432

The results for the other seven readings are computed in a similar manner and are shown in Table 36.4. The assessed percentage of damage over the deck (pdamdeck) would be the weighted average of the probabilities of damage:

_ En=1 pdam i _ (0 .080 + 0 .156 + 0 .573 + 0 .591 + 0 . 621 + 0 . 651 + 0 .074 + 0 . 752) _

where i is an individual half-cell reading and n is the total number of readings taken. According to the repair policy, the deck does need to be replaced until pdamdeck = 0.50, but at pdamdeck = 0.437, it is getting close.

There are three main sources of uncertainty that need to be quantified with an NDE inspection: (a) the quality of the inspection equipment and its ability to accurately read whatever measurement is being taken, (b) the correlation between whatever the equipment is measuring and the presence of an actual defect, and (c) the ability to assess the condition of an entire structure based on a finite number of readings. In Example 36.17, the accuracy of the equipment and whether eight evenly spaced readings were sufficient to assess the condition of the entire deck were not addressed. For a probabilistic analysis and an update of a structure's reliability, these uncertainties should all be quantified and considered. Such data are not readily available for most NDE techniques, are often difficult to obtain, and remain a bountiful area for continued research. Estes and Frangopol (2001c) used these half-cell results to optimize maintenance planning for an existing concrete deck.

TABLE 36.4 Probability of Damage for Various Half-Cell Potential Readings on a Reinforced Concrete Deck Half-cell Probability density Probability density reading distribution for undamaged distribution for damaged Probability of

(—mV) deck, pdfgood-x deck, pdfbad-x damage, Pdam

TABLE 36.4 Probability of Damage for Various Half-Cell Potential Readings on a Reinforced Concrete Deck Half-cell Probability density Probability density reading distribution for undamaged distribution for damaged Probability of

(—mV) deck, pdfgood-x deck, pdfbad-x damage, Pdam

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