Profiling structurally deficient bridges in the United States: Sampling bridge performance data for qualitative trends

3.1 Parameters and definitions

3.1.4 Climate

Environmental conditions are a predominant factor for structural deterioration and this study has focused on how these conditions correlate to structural deficiency. The US Department of Energy Building America Program [10] has defined eight major climate zone designations in the United States climate zone designations used by the U.S. Department of Energy intended to help builders to identify the appropriate climate designation for the counties in which they are building. This study has chosen to use these zones shown in Fig. 1 as its climate criteria to achieve a diverse and complete panel of environmental conditions. For the purpose of data analysis, data from Cold and Very Cold climate zones are bundled into a single climate zone and the subarctic zone (Alaska) was not included in this study. Cold/Very Cold climates were combined because the sample size of the Very Cold is small compared to Cold. Also Cold/Very Cold can be assumed to be sufficiently alike inasmuch as building materials are concerned.

OPEN IN VIEWER

Fig.1

The seven climate regions in the Continental US as recognized by Building America and the US Department of Energy (USDOE) [11].

Therefore the following six climate zones are considered in this study: 1) Marine, 2) Hot-Humid, 3) Hot-Dry, 4) Mixed-Dry, 5) Cold and Very Cold, and 6) Mixed-Humid.

5.1 Discussion of structure’s age

The most readily available information offered by the data is the percentage of bridges in each primary parameter which are deficient. However, directly comparing these percentages is insensible. For example, the data reveals that 11.04% of state-owned steel bridges are structurally deficient while only 9.88% of federally-owned steel bridges are structurally deficient. The initial conclusion is that state-owned steel bridges should have a ‘more deficient’ index value than those with federal ownership. However, upon closer examination, it can be noted that deficient, state-owned steel bridges are, on average, 6 years older than those which are federally-owned, suggesting that state owned steel bridges take more time, on average, to reach the point of structural deficiency. Perhaps a better way to view this concept would be to consider that the percentages of deficient state-owned and federally-owned steel bridges are equal (for example, 10% of both state and federally-owned bridges are deficient), but the average age of state-owned steel bridges is 65 years and the average age of federally-owned steel bridges is 20 years. By common sense, the federally-owned bridges can be thought of as more critically deficient, as they seem to be reaching the point of structural deficiency much more rapidly than those owned by the state. Thus, before the deficiency percentages are converted into normalized index values, these percentages are first adjusted to account for different spreads in average age. The example in Table 1 illustrates the procedure for determining deficiency index values for a primary parameter (Material Y) and three secondary parameters or subdivisions A, B, and C while taking into consideration the average age spread. The data in Table 1 is obtained from LTBP Portal while the last row shows the calculated deficiency index values as demonstrated in the example that follows.

Example: bridge data for a primary parameter with 3 subdivisions

1. Determine a normalized weight (between 0-1) for the percent-deficient of A , B , and C by dividing the percent deficient of each by the sum of all percent-deficient values: Norm % A = 0.0704 0.0704 + 0.0347 + 0.0465 = 0.464 Norm % B = 0.0347 0.0704 + 0.0347 + 0.0465 = 0.229 Norm % C = 0.0465 0.0704 + 0.0347 + 0.0465 = 0.307

2. Determine the difference between deficient bridges and all bridges in each category and normalize that difference: Norm % Age % Spread % A = 55 - 45 10 + 15 + 7 = 10 32 = 0.3125 Norm % Age % Spread % B = 50 - 35 10 + 15 + 7 = 15 32 = 0.4688 Norm % Age % Spread % C = 49 - 42 10 + 15 + 7 = 7 32 = 0.2188

3. Determine the minimum difference between deficient bridges and all bridges in each category, and subtract that minimum difference from the average age of the deficient bridges in A , B , and C to arrive at a ‘base age’ by which the average ages of the deficient bridges in A , B , and C will be adjusted:

min(55 – 45, 50 – 35, 49 – 42) = min (10, 15, 7) = 7

Base Age A  = 55 – 7 = 48

Base Age B  = 50 – 7 = 43

Base Age C  = 49 – 7 = 42

4. Divide the normalized weight of the percent-deficient of A , B , and C by the natural logarithm of one plus the product of the respective ( A , B , and C ) age spreads and base ages to determine a raw, age-adjusted percent-deficient: RawAdj % A = 0.464 ln ( 0.3125 + 1 ) = 0.1674 RawAdj % B = 0.229 ln ( 0.4688 + 1 ) = 0.0751 RawAdj % C = 0.307 ln ( 0.2188 + 1 ) = 0.1321

5. Normalize the raw, age-adjusted percent-deficient figures: NormAdj % A = 0.1674 0.1674 + 0.0751 + 0.1321 = 0.447 NormAdj % B = 0.0.751 0.1674 + 0.0751 + 0.1321 = 0.200 NormAdj % C = 0.1321 0.1674 + 0.0751 + 0.1321 = 0.353

6. Subtract the maximum of the three normalized adjusted percent-deficient values from each individual normalized percent-deficient value and divide by the difference between the maximum and minimum normalized adjusted percent deficient values. Add 1 to each to reverse the scale (making 1 the proxy for ‘most deficient,’ rather than 0): Normalized % Deficiency % X = 1 + NormAdj % X - Max ( NormAdj % ) Max ( NormAdj % ) - Min ( NormAdj % )

Or Normalized % Deficiency % X = NormAdj % X - Min ( NormAdj % ) Max ( NormAdj % ) - Min ( NormAdj % )

Therefore for the above example, we obtain: Normalized % Deficiency % A = 0.447 - 0.200 0.247 = 1.00 Normalized % Deficiency % B = 0.200 - 0.200 0.247 = 0.00 Normalized % Deficiency % C = 0.353 - 0.200 0.247 = 0.618

7. Scale each of these values by a factor of 10 to obtain the final deficiency index value for subdivisions A, B, and C of the Primary Parameter X for the focus Material Y. The final deficiency index values of 10, 0, and 6.18 are shown in the last row of Table 1.

The key step in converting the data into the deficiency index is Step 4, in which a logarithmic scale is applied to age. More specifically, the “base age,” scaled by the normalized difference between the average age of deficient bridges and the average age of the total bridge population, is factored by an inverse natural logarithmic scale. This augments the effect of larger age spreads such that greater differences in deficient average age and total average age between subdivisions have heavier influences on determining the deficiency indexes. Because the natural log function crosses the x-axis at x = 1, an additional value of 1 is included in the argument of the function to ensure that the function always yields a raw, adjusted percent-deficient greater than (or equal to) zero in the event that average age statistics differ significantly from those sampled for this investigation. When viewing the results, it is important to recall the major aspects of the 0 to 10 deficiency index system created for this study. First, the system is designed such that, across all subdivisions of a primary parameter (i.e. climate), there will one subdivision with a most deficient value of 10 and one subdivision with a least deficient value of 0 for each material. All other subdivisions will fall between them. Second, because the index values of all subdivisions are interdependent; meaning that if the deficiency index value for “concrete, marine” was to change for some reason (i.e. new data), the index values for concrete in all other climates would change in course. Third, understanding that index numbers are purely relative, it follows that they attest to the relative deficiency of a parameter (or set of parameters) in comparison to each other and not at all to the degree of deficiency, explicitly. To reinforce these concepts, consider the index value results presented in Table 2, which is the simplest possible selection of parameters: material only. Of the subdivisions, there must be one with a value of 10 (most deficient, steel) and one with a value of 0 (least deficient, concrete). Hence, across all climates, owners, spans, and average daily traffic, steel bridges in the US are the most deficient, concrete bridges are the least deficient, and prestressed concrete bridges, with a deficiency index value of 0.18, can be thought of as being only slightly more deficient than the least deficient material, concrete.

Using the method described above, deficiency index values are obtained for all subdivisions of all primary parameters which includes each of the six designated climate zones, each maximum unsupported span range, each ownership category, and each range of average daily traffic. All of these deficiency index values are reported in the Results section of this report. The next step in data processing is the more unique aspect of this investigation. The end-goal of the process is to derive a system that will return a deficiency index value for any and every combination of material, climate region, span, ownership, and average daily traffic parameters. Using this system, one could obtain an index rating for a steel bridge structure, in a marine climate, with a maximum unsupported span of 40 meters, or for a concrete bridge structure, owned by a township, which experiences an average of 5,000–10,000 vehicle crossings per day, or for all prestressed concrete bridges of all climates, spans, ownerships, and daily traffic volume. Intersecting all subdivisions of all primary parameters for each material type yields about 70,200 possible combinations of bridge scenarios. However, there remains only one “most deficient” index value of 10 and “least deficient” index value of 0 within primary parameter subdivisions of every possible combination.

By this process, a vector is constructed which describes the intersection (combination) of data for parameters, the magnitude of which is the value of the ultimate deficiency index for a selection of parameters. Each of the four primary parameters “k,” filtered by the material parameter, is considered as one dimension (k _i , i = 1, 2, 3, 4) of an ultimate deficiency vector. Each primary parameter dimension, ki, may assume n distinct values, with n being the number of subdivisions of that primary parameter. The magnitude of the k _i dimension is the deficiency index value, previously determined as explained in the preceding section. The values for each of the four dimensions are normalized to obtain an ultimate deficiency vector for that combination.

5.4 Example: Step-by-step

Select the primary parameters of interest k 1, k 2, k 3, and k 4 filtered by prestressed Concrete

•Material: Prestressed Concrete

k 1 = Climate: Mixed-Humid, k 2 = Maximum Unsupported Span: 50–75 meters

k 3 = Ownership: City/Municipal, k 4 = Average Daily Traffic: 500–5,000 vehicles/day

2. Reference the magnitude of each dimension. This is the index value determined for that subdivided primary parameter for prestressed concrete following the example in the previous section, in this case:

k 1 = 4.15, k 2 = 1.73, k 3 = 10.0, and k 4 = 5.19

3. Determine the magnitude of the four-dimensional “raw deficiency vector” D: | D | = k 1 2 + k 2 2 + k 3 2 + k 4 2 = 4 . 15 2 + 1 . 73 2 + 10 . 0 2 + 5 . 19 2 = 12 . 13

4. The maximum value for each k _i is 10. Therefore the maximum magnitude of D given i-chosen parameters is: D max = i ( 10 2 )

Which in this four-parameter example is: D max = 4 ( 10 2 ) = 20

5. Adjust the magnitude of D by D_max to obtain a ultimate deficiency D_u index vector for the selected parameters: D u = | D | D max = 12.13 20 = 6.07

Therefore, a prestressed concrete bridge, in a mixed-humid climate, with a maximum unsupported span of 60 meters, owned by a city/municipality, and with an average daily traffic of 1,500 vehicles per day has a deficiency index rating of 6.07, with 10 being the most deficient, and 0 being the least. This system is programed with all collected data in spreadsheet software and includes dropdown selection menus for the user to quickly obtain deficiency index values for any desired combination of parameters.

5.5 Observations on deficiency index values for one versus multiple primary parameters

The deficiency index values that this approach derives are based on the primary parameter data collected from the LTBP Portal database. It is worth mentioning that using this method to determine index values for intersections of multiple primary parameters is not the same as filtering the Portal database with the selected criteria. Rather, it vectorizes the individual primary parameter data to, essentially, generate a synthetic value which is informed by, but may not necessarily match, the actual data. An index value for a single primary parameter, within each material, is closely represented by the data as seen in Table 2. In Table 2, the construction material type was the only considered parameter (single primary parameter). Table 2 shows that prestressed concrete bridges have the lowest deficiency index (0) compared to concrete and steel bridges. When all materials together are considered, the deficiency index is 3.24. Concrete bridges have slightly higher deficiency index while steel bridges have the highest. This is primarily due to the fact that percent-deficient of steel bridges (over 17%) is significantly higher than concrete and prestressed concrete bridges (approximately 6.34% and 3.45% respectively). This 17% deficient figure is notably high.

However, as more primary parameters are considered for a single index value, the index value will become less likely to closely represent the data. In other words, considering fewer primary parameters returns a more accurate depiction of the current condition of bridge deficiency (in the sense that it more closely matches the primary data). On the other hand, the more primary parameters that are considered for a single index value, the more theoretical the result will become a depiction of how deficient a bridge with the selected criteria would be if it were to exist. The value of this approach is that the theory is entirely rooted in the data, and it produces reliable results that are characteristically informative of the state of the US bridge infrastructure.

Considering bridges of all three materials (steel, concrete, and prestressed concrete), the cold/very cold climate is currently the most deficient as shown in Table 3. One possible explanation (or partial explanation) for this could be the frequent presence of de-icing salt on and about the roadways, which could accelerate the oxidation of steel, causing steel corrosion and deterioration in steel beams and spalling in reinforced concrete. Steel and prestressed concrete are currently the most deficient materials in these cold/very cold climates. Standard concrete is currently the least deficient material. A relevant statistic is that the deficient concrete bridges in the cold/very cold climate are approximately ten to twenty years older than their steel and prestressed concrete counterparts, respectively. To compare, the second-most structurally deficient climate is mixed-humid, in which steel is the most deficient and concrete is the least deficient, and the least deficient climate is hot-humid.

For all climate data in Table 3, the following results could be reasonably expected, given the general nature of material deterioration:

Marine climates are quite deficient, in general — index value of 6.76 for all three materials, inclusive. Marine is currently the most deficient climate for all concrete bridges, which could be presumed for the ionic/salt conditions in marine environments which are caustic to reinforced concrete, causing corrosion, spalling, and other deteriorations. Prestressed concrete is second-most deficient in marine climates, and steel is the least deficient. Still, with a value of 6.71, steel bridges are considerably deficient in marine climates. For all climate data, the following results might not be expected, given the general nature of material deterioration:

6.2 Maximum unsupported span

As can be observed in Table 4, structural deficiency generally increases as the maximum unsupported span grows. This, of course, could be reasonably expected. Accordingly, the more deficient bridges are mostly those with super-long spans. However, observing the trends for each individual material reveals more interesting trends. Concrete follows a mostly logical trend, with deficiency being the lowest at shorter spans and increasing with increasing span lengths. Super-long spans are the most deficient for concrete. However, for both prestressed concrete and steel, the shortest-span bridges (less than 10 meters) are the most deficient. From a purely structural perspective, one could find this result surprising. Another interesting result is that the least deficient spans, including all three materials, are mid-length spans from 30 to 50 meters. For both steel and prestressed concrete, this span range is the least deficient of all studied spans. Conversely, though, this same span range is the second-most deficient range for concrete.

6.3 Average daily traffic

The average daily traffic deficiency index values indicate a surprising trend. While one might expect significantly heavier volumes of daily traffic to be associated with greater degrees of structural deficiency, Table 5 reveals that the opposite is true. Across all construction materials, lower volumes of traffic are associated with more deficient structures, and heavier volumes are associated with healthier, more structurally-fit bridges. The least deficient bridges experience an average of more than 5,000 to 25,000 vehicles, each day. The most deficient bridges experience fewer than 500.

6.4 Ownership

The deficiency index values in shown in Table 6 indicate that the structural deficiency of a given bridge significantly depends on the agency that owns and operates the structure. The table indicates that state-owned bridges are the least deficient and that county-owned are the most deficient bridges. Further, it suggests that bridges owned by smaller agencies (such as townships and counties) tend to be more deficient than those owned by larger agencies, in general. As the size of the owning agency increases, the relative degree of structural deficiency decreases. The most deficient bridges for each of the three materials are those owned by a city/municipality (prestressed concrete), a township (steel), and a county (concrete).

The major goal of the data processing method developed for this study is to assign deficiency index values based on the percent deficient in each category while accounting for the age of those deficient bridges compared to the age of all bridges in that category. Consider the raw data in Appendix A and the results in Table 7 for concrete bridges within the primary parameter of climate. More specifically, consider the hot-dry and cold/very cold climates.

The raw data reveals that the percentage of structurally deficient concrete bridges in cold/very cold climates is significantly greater than the percent-deficient in hot-dry climates (8.28% and 4.65% for cold/very cold and hot-dry, respectively). One might conclude that cold/very cold would have the “more deficient” index value. However, the data also indicates that the average age of deficient concrete bridges in hot-dry climates is 50.31 years, whereas the average age of deficient concrete bridges in cold/very cold climates is 68.51 years. Compare this to the average age of all hot-dry concrete bridges (42.22 years) and the average age of all cold/very cold concrete bridges (39.54 years). While there are a larger percentage of structurally deficient concrete bridges in cold/very cold climates than in hot-dry climates, all concrete bridges in hot-dry climates are older, appear to reach the point of structural deficiency more rapidly, and/or remain as such for less time before remediation is considered necessary in comparison to those in a cold/very cold climate. The data processing method takes this into consideration, and consequently determines a “more deficient” index value of 4.90 for hot-dry climates and a “less deficient” index value of 3.93 for cold/very cold.