Synthesis of National and International Methodologies Used for Bridge Health Indices

CHAPTER 3. Weighted Average Approaches

COMPUTATIONAL APPROACH OVERVIEW

BCIs calculated by weighted averaging of individual element conditions are the most common types identified in this report. Their development is based on structural element condition data, which captures the type, severity, and extent of deteriorations. Also, some indices rely on operational data such as traffic volume to capture the service provided by the bridge. The number of elements inspected and the type of rating systems adopted may be different from one country to the other.

UNITED KINGDOM’S BCI

Just like the California BHI, the United Kingdom’s BCI describes the condition of an element based on its condition state and the extent of deterioration. The key difference is that the value of the bridge elements’ conditions is based on its contribution to the overall bridge integrity and not the cost of the elements’ failure. Instead of calculating the remaining value of the bridge elements, a simple score based on engineering judgment is used to assign importance factors to each element. Also, the extent of damage is registered in qualitative terms. Table 4 and table 5 provide a description for different categories of damage severity and extent used for calculating the United Kingdom’s BCI.

Calculating British BCI

The BCI is calculated as follows.⁽¹¹⁾

Step 1

Assign an element condition score (ECS) for each element based on its severity and extent of deterioration (table 6). For example, an element with a severity of 3 and an extent of C receives a score of 3.2. In this approach, higher scores suggest worse conditions.

*Non-permissible severity-extent combinations.

Step 2

Assign an element importance factor (EIF) for each element. EIF accounts for the value of the element (table 7).

Step 3

Assign an element condition factor (ECF). ECF accounts for an element’s contribution to the overall bridge condition. Therefore, ECF of an element is calculated with respect to its importance (figure 5 through figure 7); an element with an importance of “very high” has an ECF of 0.⁽¹⁰⁾

Figure 5. Equation. ECF (“high” element importance).⁽¹⁰⁾

Figure 6. Equation. ECF (“medium” element importance).⁽¹⁰⁾

Figure 7. Equation. ECF (“low” element importance).⁽¹⁰⁾

Step 4

Calculate the element condition index (ECI) (figure 8).

Figure 8. Equation. ECI.

Step 5

Calculate the overall bridge condition score (BCS). BCS is calculated by a weighted combination of all the contributions of each bridge element. The weights are assigned based on the element’s importance (figure 9).

Figure 9. Equation. BCS.

Where:

N = Total number of bridge elements for structure.

Step 6

Calculate the BCI (figure 10). The condition of the bridge is based on the BCI value on a scale of 0 (worst) to 100(best) (table 8).

Figure 10. Equation. BCI.

SOUTH AFRICA’S BCI

The South African BMS allocates funds and prioritizes maintenance, repair, and rehabilitation needs by using an index similar to the British BCI. The BCI is calculated based on data obtained from routine structural condition assessments and a bridge importance factor, which is based on the average daily traffic (ADT) of the bridge.

Condition Ratings

Condition assessment of structures is performed based on the degree, extent, and relevancy (DER) of deterioration by assigning a DER score. The DER rating system identifies defects and prioritizes them by evaluating their relative importance to the structural integrity of the bridge.⁽¹²⁾ It is important to note that the ratings are not directly associated with the elements but with the distress or damage. Thus, with the DER rating system, an element is assigned a score greater than zero only if it has a distress on it.

Each distress identified is assigned a rating from 1 (minor) to 4 (severe) depending on the degree (how severe is the defect), extent (how widespread is the defect on the inspected element), and relevancy of the damage. The relevancy of the identified damage corresponds to the general impact of the defect with regards to structural integrity, serviceability, and safety of the bridge. Two defects may look the same and have the same extent, but their impact on the integrity of a bridge from a global point of view can be different. Therefore, the relevancy of the distress helps the inspectors capture information beyond ordinary visual ratings by assessing the impact of each distress on the overall structural integrity of the bridge.⁽¹³⁾ The DER rating system is summarized in table 9. An urgency category is also assigned based on the DER value, but it is not used to determine the BCI.

N/A = Not applicable.

Calculating South African BCI

Each defect on the element being inspected has a condition index (I_Cj) (figure 11).⁽¹²⁾

Figure 11. Equation. Defect condition index.

Where:

D = Degree of damage.

E = Extent of damage.

R = Relevancy of damage.

The bridge importance (figure 12) is based on how frequently the bridge is used or traveled in the network. Therefore, the overall BCI (figure 13) is computed as the sum of all defect condition values for all elements inspected weighted by a bridge importance factor.

Figure 12. Equation. Bridge importance factor.

Where:

ADT_i = ADT for structure i.

n = Number of bridges in the network being evaluated.

Figure 13. Equation. Final bridge condition.

Where:

BCI_i = BCI for structure i.

m = Number of inspected elements on structure i.

j = Individual element on structure i.

AUSTRALIA’S BCN

Roads Corporation of Victoria (VicRoads), the roadway agency for Victoria, Australia, uses a BCN for relative comparison of the performance, integrity, and durability of bridge structures.⁽¹⁴⁾

Calculating Australian BCN

BCN is calculated based on a three-level hierarchical framework (figure 14). The first level (element level) calculates element-level condition ratings by aggregating condition state percentages for each element. At the second level (group level), structural group factors are assigned based on the group’s importance to the structure. A structural group consists of a number of elements which perform similar functions (e.g., bearings, piers, decks, etc.).

Figure 14. Illustration. Three-level hierarchy for calculating Australian BCN.

It is important to note that the level of importance is assigned at the structural group level and not at the element level. Combining all the average structural group ratings yields the overall BCN.

Element Level

Calculate the average condition rating (ACR) for each element (figure 15). Condition state numbers are subjective scores represtative of element condition, ranging from 1 to 4, with 1 being as-built and 4 being poor. Explicit definitions are provided in Rummey and Downling.⁽¹⁴⁾ Only critical elements are considered in this step.

Figure 15. Equation. ACR for each element.

Group Level (Piers, Decks, Bearings)

Calculate the average group rating (AGR) for each structural groups or categories (figure 16).

Figure 16. Equation. AGR for each structural group/category.

Where:

E = Exposure factor (environment).

Bridge Asset

BCN is calculated in this step (figure 17) using the AGR for bridge element groups.

Figure 17. Equation. BCN.

Where:

W_b = Structural group importance.

Table 10 shows how VicRoads uses the BCN for decisionmaking and prioritization.

AUSTRIA’S BCI

Austria’s BCI is calculated using inspection data from bridge elements. Each element is assigned five different ratings based on the following attributes:⁽¹⁵⁾

• Type of Damage—Rated between 1 and 5 for each of 32 types of damage that can be identified.
  
  
• Extent of Damage—Rated between 0 and1. The extent is not quantified in measured size of defects (e.g., length or area).
  
  
• Severity or Intensity of Damage—Rated between 0 and 1.
  
  
• Importance of the Structural Components—Rated between 0 and 1 and classified as primary, secondary, and other parts.
  
  
• Urgency of Intervention—Rated between 0 and 10 and is dependent on the risk of collapse of the structure or element. This attribute is not used in calculating the index.

Calculating Austrian BCI

The overall bridge condition rating (S) is calculated by weighting the type of distress by the square root of the sum of all the above mentioned attributes (figure 18).

Figure 18. Equation. Overall bridge condition rating.

Where:

G_i = Type of damage to element i.

k_1i = Extent of damage to element i.

k_2i = Severity of damage to element i.

k_3i = Importance of component to element i.

FINLAND’S BCI

The BMS used by the Finnish Road Administration (Finnra) uses a condition index based on weighted averaging of condition ratings of structural parts.⁽¹²⁾ The weights, assigned by structural part, are presented in table 11. Examples of inputs used to calculate the BCI includes damage cause, damage location, damage effect on bridge load capacity, and urgency of repair.

Calculating Finnish BCI

BCI, also known as the repair index, is computed for the set of identified defects on the bridge (see table 12). The bridge is divided into nine structural parts during inspection. The condition of each structural part is evaluated on a rating from 0 (very good) to 4 (very poor). Each instance of damage detected during inspection is also rated in terms of its severity and urgency of repair. Values for these ratings are shown in table 13 and table 14.

The repair index is computed for all identified defects (figure 19). The equation maximizes the worst defects and minimizes all other defects by a factor k, which has a default value of 0.2.

Figure 19. Equation. Repair index.

Where:

KTI = Repair index.

Wt = Weight assigned to structural part.

i = Index representing the worst defect on a given structural part.

C = Condition of structural part.

U = Urgency of the repair needed for structural part.

D = Severity of damage to structural part.

k = WF for other defects apart from the worst defect.

j = Indices representing the rest of the defects on a given structural part.

STRENGTHS AND LIMITATIONS

Strengths

The weighted averaging condition indices capture the degree, severity, and importance of every instance of damage identified during the inspection process, which helps provide a comprehensive picture of the condition of the bridge. Also, the approach is suitable for planning for bridge maintenance and rehabilitation activities because the overall index combines all defects identified at the element level. These indices provide a consistent framework within an agency, and engineering judgment has been incorporated by assigning categories rather than rigid numerical scores.

Limitations

The health index only captures conditions of structural elements of the bridge. Although the bridge’s functional adequacies (service provided by the bridge) such as capacity, traffic volume, and clearance issues are considered during maintenance prioritization and fund allocation, there is no index in the weighted average category integrating both structural condition and functional information. Finnra overcomes this challenge by using a rehabilitation index that combines structural condition information with some functional information.⁽¹²⁾

With the exception of the Australian BCN and Finnra’s repair index, most of the weighted combination health indices assign weights (significance level) at the element level. This is challenging because it is very difficult to assess the impact of the condition of an element on the overall bridge structure. Estimating the importance of a structural group (consisting of a number of elements with similar primary functions) is more practical.