# Remedial Modelling of Steel Bridges through Application of Analytical Hierarchy Process (AHP)
## 7 Model Validation through a Case Study  
To ascertain the relevance of the proposed system in practical situations, a case study (courtesy of RMS) was used for testing. The chosen scenario involved severe pitting corrosion on the underside of the top chords of all steel truss spans, including the lift-span truss, on the Bateman's Bay Bridge as depicted in Figure 4. This iconic landmark, in service since 1956, plays a pivotal role for transportation on the South Coast of NSW, thus, efficient rehabilitation of the structure is paramount. Figure 4: Flow Chart of the Proposed Method for Strategy Selection at Project Level. After visual inspection of the bridge by the author, it was determined that the bridge has considerable corrosion on the surface of the steel, making up approximately 15% of the total area of the structure. The surface corrosion on the structure is therefore classed as severe. Other defects noted on the structure include pitting rust on the underside of the members on the truss span, breaking down of paint on the top and western edges on the plate girder spans. There was also some crevice corrosion occurring around joints. As a conclusion, deterioration mechanism and condition rating were specified, as corrosion and 3, respectively. For these constraints, four possible courses of action have been nominated. These included: splice plates; steel plate strengthening; fibre reinforced polymer strengthening; and partial member replacement. The dominant criteria proposed by the asset manager were Safety, Service life, Remediation Cost, Traffic Disruption, Environmental Impact and Heritage Significance/Aesthetic Appeal. Figure 5 illustrates the three level hierarchy structure constructed for remediation planning of the Bateman's Bay Bridge. The experts were then requested to compare the major criteria in pairs with respect to the overall goal. The AHP method has been applied to determine the vector of priority (VOP) for the introduced objectives based on the experts' judgments. The AHP matrix and the VOP (eigenvector of the AHP matrix) are presented in Figure 6 and Equation (2), respectively. \[\text{VOP}=\left[ \begin{array}{c}0.1376\\ 0.4581\\ 0.2627\\ 0.0453\\ 0.0663\\ 0.0299\end{array} \right]=\left[ \begin{array}{c}\text{Service Life}\\ \text{Safety}\\ \text{Cost}\\ \text{Environment}\\ \text{Traffic Disruption}\\ \text{Heritage/Aesthetic}\end{array} \right] \tag{2}\]  
Figure 5: Bateman’s Bay Bridge (Photo: Taken by the Author). Figures 7 and 8 illustrate the application of AHP and pairwise comparison of the identified criteria in the developed system. Figure 8: Pairwise Comparison of the Major Criteria in the Developed DSS. Figure 6: Three Level Hierarchy Structure for Remediation of Bateman’s Bay Bridge. Figure 7: AHP Matrix for Criteria Weighting. Since the decision makers may be unable to provide consistent pairwise comparisons, it is demanded that the comparison matrix should have an adequate level of consistency, which can be checked by using the following consistency ratio (\(CR\)):  
\[CR=\frac{(\lambda\text{max}-n)/(n-1)}{RI} \tag{3}\]  
where,  
\[\lambda_{\text{max}}=9.73(0.1376)+1.9(0.4581)+4.79(0.2627)+25.33(0.0453)+16.83 (0.0663)+29(0.0299)=6.59\]  
In order to calculate \(\lambda_{\text{max}}\), the values in front of brackets are the summations in AHP matrix in Figure 7, and the quantities inside the brackets are the corresponding VOPs. Random inconsistency index (\(RI\)) is extracted from Table 4 provided by [PERSON] (2004). The Consistency Ration (CR) has been estimated based on Equation (2). Since the value of CR is less than 1 (see Equation (4)), the accomplished judgement is consistent. \[CR=\frac{(\lambda\text{max}-n)/(n-1)}{RI}=0.095<0.1 \tag{4}\]  
As shown in Table 5, four different alternatives have been identified for rehabilitation of the affected area: \"Splice Plates\"; \"Steel Plate Strengthening\"; \"FRP Strengthening\"; and \"Partial Member Replacement\".