Application of Performance Parameter

The four-level performance parameter was developed with the intention of transforming the performance of any given level to Level 4, so that the state of the bridge fleet or any

individual bridge may more accurately be reflected. If one could determine how bridge performance scores change between Level 4 and other levels for a smaller number of bridges, then the performance of all bridges at each Level 4 may be determined.

For all bridges within a certain level performance scores were determined. Then the difference in scores between Level 4 and each level was determined and plotted against the age of the bridge to identify trends in score differences. Identification of trends enables one to

effectively transform the score of a bridge in Level 1 to that of another level. Figure 35 through Figure 37 show the change in performance with respect to age between Level 1 and Level 4, Level 2 and Level 4, and Level 3 and Level 4, respectively.

-10.0 0.0 10.0 20.0 30.0 40.0 50.0

0 10 20 30 40 50 60 70 80

Age

Change in Performance Parameter

Figure 35. Change in Performance between Levels 1 and 4

-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

0 10 20 30 40 50 60 70 80

Age

Change in Performance Parameter

Figure 36. Change in Performance between Levels 2 and 4

0.0

Change in Performance Parameter

Figure 37. Change in Performance between Levels 3 and 4

Stated below are Equation 3 through Equation 5 which were the results from the trend lines shown in the above figures.

Equation 3. Level 4 Fleet Performance Derived from Level 1

)

Equation 4. Level 4 Fleet Performance Derived from Level 2

)

Equation 5. Level 4 Fleet Performance Derived from Level 3

)

where,

60 . 8 257

. 0 ) 3 4

( L − L = × Age −

f

If one applies the respective transforming function to the Levels 1, 2, and 3 results, the plots shown in Figure 38 through Figure 40 are obtained.

0 20 40 60 80 100 120 140

0 10 20 30 40 50 60 70 80

Age

Level 4 Performance

Figure 38. Level 4 Performance from Level 1

0 20 40 60 80 100 120 140

0 10 20 30 40 50 60 70 80

Age

Level 4 Performance

Figure 39. Level 4 Performance from Level 2

0 20 40 60 80 100 120 140

0 10 20 30 40 50 60 70 80

Age

Level 4 Performance

Figure 40. Level 4 Performance from Level 3

One would expect for the Level 4 values for a particular bridge to be nearly equal regardless of the level from which the Level 4 scores were obtained. That is, Level 4 scores are nearly the same no matter which level the score for Level 4 score was determined. Figure 41 illustrates this idea by overlaying the Level 4 performance scores of the previous figures.

0 20 40 60 80 100 120 140

0 10 20 30 40 50 60 70 80

Age

Level 4 Performance

L4 from L1 L4 from L2 L4 from L3 Linear (L4 from L1) Linear (L4 from L2) Linear (L4 from L3)

Figure 41. Level 4 Performance from Each Level

Engineering judgment says that performance should not increase over time, yet Figure 38 through Figure 41 shows exactly that phenomenon. It is necessary to determine if confounding variables are actually affecting the bridge performance. Looking closely at Figure 41, it appears that two separate groups of data are present along the trend lines. These groups are shown below in Figure 42. A confounding variable and common factor found within each group is the moment of inertia of the girders, or more simply put, the size of the girders. When the moment of inertia of the girders was plotted against the bridge age a pattern was revealed. Coincidentally, the older bridges of group number 2 had girders of a greater moment of inertia than the younger bridges of group number 1 (see Figure 43) even though age and girder size are independent parameters.

That is, the moment of inertia of the girders of bridges in group number 1 tends to be smaller than that of group number 2.

0 20 40 60 80 100 120 140

0 10 20 30 40 50 60 70 80

Age

Level 4 Performance

L4 from L1 L4 from L2 L4 from L3

Group #1

Group #2

Figure 42. Data Groups within Level 4 Performance

0 500 1000 1500 2000 2500 3000 3500

0 10 20 30 40 50 60 70 80

Age Moment of Inertia (in4 )

Figure 43. Relationship between Moment of Inertia and Age

Figure 44 shows the Level 4 performance plotted against the moment of inertia of the girders for each respective bridge. It appears that the overall bridge performance may be better in bridges with girders of greater moment of inertia.

0 20 40 60 80 100 120 140

0 500 1000 1500 2000 2500 3000 3500

Moment of Inertia (in⁴)

Level 4 Performance

L4 from L1 L4 from L2 L4 from L3 Linear (L4 from L1) Linear (L4 from L2) Linear (L4 from L3)

Figure 44. Level 4 Performance vs. Girder Moment of Inertia

Another confounding variable and common factor found between groups 1 and 2 of Figure 42 was the average superstructure moisture content. When the average superstructure moisture content was plotted against the age of the bridges a trend was identified (see Figure 45).

Seemingly, as the age the bridge increases the moisture content decreases, even though these parameters are independent of each other. As a result, the Level 4 performance was plotted against the average moisture content of the superstructure and another trend was identified (see Figure 46). The Level 4 performance may increase with decreasing average superstructure moisture content. One should note that there was a strong correlation between moisture content and geographic location, as would be expected. This fact could prove useful in management practices as it is much less difficult to determine the geographic location of a bridge than the average superstructure moisture content.

0 5 10 15 20 25 30 35

0 10 20 30 40 50 60 70 80

Age

Moisture Content (%)

Figure 45. Average Superstructure Moisture Content vs. Age

0 20 40 60 80 100 120 140

0 5 10 15 20 25 30 35

Moisture Content (%)

Level 4 Performance

L4 from L1 L4 from L2 L4 from L3 Linear (L4 from L1) Linear (L4 from L2) Linear (L4 from L3)

Figure 46. Level 4 Performance vs. Average Superstructure Moisture Content

The girder size and moisture content appear to be two factors governing the Level 4 performance. Even though a good correlation was found between the Level 4 performance and the age of the bridges, it did not seem correct that the performance of a bridge would increase with increasing age. However, it does seem correct to say that the performance should increase with a greater moment of inertia and lesser moisture as shown in Figure 44 and Figure 46. The aging of a bridge most certainly is still a factor among bridges with very similar girder sizes and moisture contents, so age should not be discarded as a governing factor.

One could conclude from the above figures that bridges with girders of a lesser moment of inertia will perform lower than bridges with girders of a higher moment of inertia and bridges with greater average superstructure moisture content will perform lower than bridges with lesser moisture content. Preventive maintenance could be administered more frequently to bridges with higher superstructure moisture contents and lower girder moments of inertia to equalize the effects of lower performance. For preventive maintenance practices, one should conform to the methods outlined previously. One should note that moisture contents are not readily available as are the girder dimensions for each bridge; therefore the bridge owner may have to predict the average moisture content through climatology reports.