## 3 Test Results and Analysis
### Transverse Connectivity  
The transverse connections between the girders are weakened due to the deterioration of the joints. To make a comparison with the results in the load test, a three-dimensional FE model was established using the Midas software, as shown Figure 8. Beam element was used to model the single hollow slab girder. Virtual beams were simulated between girders to offer the transverse stiffness in the analysis. Element size was taken as 0.5 m, and there were a total of 847 elements in the grillage model. The mechanical properties of C50 grade concrete were used in the FE model. According to the Chinese code GB50010-2010 [22], the constitutive relationship of the concrete under uniaxial compression can be expressed by Equation (4):  
\[\frac{\sigma}{f_{c}}= \begin{cases}\frac{E_{c}\varepsilon}{f_{c}+(E_{c} \varepsilon_{c}-f_{c})(\frac{\varepsilon}{f_{c}})^{n}},&\varepsilon\leq \varepsilon_{c}\\ \frac{\varepsilon}{\alpha\frac{(E-\varepsilon_{c})^{2}}{\varepsilon_{c}}+ \varepsilon},&\varepsilon>\varepsilon_{c}\end{cases}  \tag{4}\]  
where \(\sigma\) is the axial stress; \(f_{c}\) is the peak stress; \(\varepsilon\) is the strain; \(\varepsilon_{c}\) is the strain at the peak; \(E_{c}\) is the elastic modulus of the concrete; and \(\alpha\) is the empirical parameter shaping the descending branch. For the C50 grade concrete, \(f_{c}\) = 50 Mpa, \(\varepsilon_{c}\) = 1.92 \(\times\) 10\({}^{-3}\), \(E_{c}\) = 34.5 GPa, and \(\alpha\) = 2.48. It is noted that the mechanical properties should be obtained by the uniaxial compression test of the cylinder concrete specimens of the real bridge. However, the test specimens were not fabricated before the demolition of the bridge, and specified values are used in the FE model. Moreover, the boundary condition is consistent with the simply supported bridge. The load of one truck is simplified as six concentrated forces which corresponds to six wheels. The mid-span deflection of each girder under the truck load is shown in Figure 9. The non-uniform distribution of the deflection results in the load test is obvious, which is inconsistent with the theoretical value in the FE simulation. The actual mid-span deflection of G4 girder is about twice of the theoretical value, and the deflections of G1, G2, and G3 girders are slightly smaller than the simulation results. It shows that the nearby joints of G4 girder were damaged to an extent, and the external load cannot be perfectly transferred to other girders. Similar condition occurs at the G6 girder. It can be inferred in Figure 9 that the hinge joints near the G4 and G6 girders may suffer severe damage after 25 years' service life. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Transverse Cracks on the Bottom Plates**} & \multicolumn{3}{c}{**Longitudinal Cracks on the Hinge Joints**} \\ \hline Length/cm & Number & Proportion (\%) & Length/cm & Number & Proportion (\%) \\ \hline
0–9 & 35 & 11.2 & 0–10 & 47 & 18.4 \\
10–19 & 117 & 37.4 & 10–50 & 30 & 11.7 \\
20–29 & 77 & 24.6 & 50–100 & 17 & 6.6 \\
30–39 & 48  
To evaluate the damage of the joint, a damage index \(\mu\) was proposed based on the theoretical and measured deflections. Given two adjacent girders \(G_{i}\) and \(G_{i+1}\), the hinge joint between the girders is defined as \(H_{i}\). Two measuring points with gauges, \(P_{i}\) and \(P_{i+1}\), are prepared on the left and right sides of the joint \(H_{i}\). The relative displacement of two points \(\gamma_{i}\) can be calculated by Equation (5):  
\[\gamma_{i}=d_{i+1}-d_{i}, \tag{5}\]  
where \(d_{i}\) is the theoretical or measured deflection at the measuring point \(P_{i}\). Based on the field test, the measured relative displacement for the joint \(H_{i}\) is defined as \(\gamma_{i}\), and the theoretical value is defined as \(\gamma_{i}\)'.