## 3 Test Results and Analysis
### Durability  
The evaluation indicators can be quantitative or qualitative. As multiple indicators are involved for the concrete hollow slab girders, their contributions may differ in the durability evaluation. Moreover, due to the inherent uncertainty in human perception, a fuzzy characteristic exists in human judgment and preference which will inevitably affect the decision making process [23]. Therefore, to determine the suitable weight of each indicator, as well as to reasonably transform the human judgment into ratio scales, AHP along with the fuzzy comprehensive evaluation (FCE) method was employed in this study to evaluate the durability of the hollow slab girder. The original AHP developed by [PERSON] [24] uses the scale of 1-9 with language labels in the pairwise comparisons, and the weights of various competing or conflicting criteria could be derived from comparison matrices [25]. When FCE is incorporated into the AHP, a fuzzy mapping is established between the indicators and appraisal grades. Fuzzy membership function was employed, and a qualitative evaluation was realized based on the qualitative indicators. The AHP generally includes four steps: (1) decompose the evaluation problem into a hierarchical structure including the goal, criteria, and alternatives; (2) establish the pairwise comparison matrix in each layer; (3) calculate the weights of the criteria and alternatives; (4) check the consistency. For the durability evaluation of the girders in this study, the hierarchical structure shown in Figure 12 was established considering the indicators in Section 2.4. There were four evaluation factors in the Criteria layer and one or two evaluation factors in the Alternatives layer. When the number of the evaluation factors was taken as \(k\), the evaluation vector \(U=[u_{1}\ u_{2}\ \dots\ u_{k}]\). The scale of 1-9 was used in the importance intensity in the pairwise comparisons. A value of '1' represents that two indicators are equally important while '9' represents that one indicator is extremely more important than the other. Given \(k\) factors considered in Figure 12, the certain pairwise comparison matrix \(M\) can be expressed by Equation (7):  
\[M= \begin{bmatrix}m_{11}\ m_{12}\dots\ m_{1k}\\ m_{21}\ m_{22}\dots\ m_{2k}\\.\.\.\.\.\\ m_{k1}\ m_{k2}\dots\ m_{1k}\end{bmatrix} , \tag{7}\]  
where \(m\) represents the importance intensity between two factors. The weight vector of \(k\) factors, \(W=[w_{1}\ w_{2}\ \dots\ w_{k}]^{T}\), was then obtained by normalizing the column vectors of the matrix, summing up the row vectors, and averaging the final column vector. In order to check if the human judgments were internally consistent, the consistency ratio \(CR\) was calculated by Equation (8):  
\[CR=\frac{\lambda_{\text{max}}-k}{(k-1)RI}, \tag{8}\]  
Figure 11: Surface damage of the joints. where \(\lambda_{\max}\) is the maximum eigenvalue of the matrix \(M\); \(R\) is the average random index which depends on the size of the matrix. The human judgment in the evaluation is acceptable when \(CR\) is smaller than 0.1. As such, the weights of the criteria (\(W_{C}\)) and alternatives (\(W_{A1}\), \(W_{A2}\), \(W_{A3}\), and \(W_{A4}\)) were obtained. The FCE is then conducted following the four steps: (1) determine the set of indicators; (2) define the set of appraisal grades; (3) form the fuzzy appraisal matrix; (4) obtain the evaluation result based on the weights and matrix. For the durability evaluation of the girders in this study, the set of indicators is consistent with the evaluation factors used in each layer in the AHP, as shown in Figure 12. Five appraisal grades shown in Table 4 are employed which range from 'Grade A-Intact' to 'Grade E-In danger', i.e., the grade vector \(V=[\)A B C D E\(]\). A membership function shown in Figure 13 is then used to represent the fuzzy mapping from a certain indicator to the grade vector \(V\).