## 2 Refined Numerical Modelling Approach
### Performance Degradation Simulation Approach
#### 2.5.5 Reinforcement Behavior  
Bridge A was reinforced with CFRP cloth and external prestress tendons in July 2006. Hence, reinforcement behaviors including external prestress and CFRP cloth are simulated within this model.  
The external prestressed tendons were modeled by virtual prestressed elements. Virtual prestressed element modeling primarily involves the connection between the virtual steel bundle and the actual steel bar through a spring mechanism. Specifically, a small section of the virtual steel bar is embedded within the concrete box girder bottom plate to establish contact with both the external prestressed steel bar and the real steel bar via spring connections. The stiffness of these springs is set to infinity, the purpose of which is to realize the linkage contact relationship between external prestressed steel bars and real steel bars.  
The thickness direction of the CFRP sheet was much smaller than the other two directions, and the stress change along its thickness direction was relatively small, so the shell element was selected for modeling. The CFRP sheet was affixed to the web of the box girder in order to impede crack development in the web section, which could be considered as an elastic material. Considering that reinforcement behavior of the CFRP sheet does not occur during initial operation, it remains necessary to record subsequent reinforcement locations' cooperative deformation for activating the shell-unit-simulating CFRP sheet at a later stage. To achieve this objective, this paper employed the virtual steel plate method for simulation. Specifically, a virtual steel shell element with a stiffness of 0 was arranged on the web of the box girder, enabling it to co-deform with the box girder. Once a predetermined deformation level had been reached, the activation of the CFRP sheet occurred at the position where the virtual steel plate was located and their contact relationship was set as \"Tie\" to accomplish structural constraint via the CFRP sheets. The above two methods are shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prestress Direction** & **Test Locations** & **Test Method** & \begin{tabular}{c} **AVG/SD 1 of Loss** \\ **Rate (\%)** \\ \end{tabular} & \begin{tabular}{c} **95\% Confidence Interval** \\ **of Prestress Loss Rate (\%)** \\ \end{tabular} \\ \hline \hline \begin{tabular}{c} Horizontal \\ Vertical \\ Longitudinal \\ \end{tabular} & \begin{tabular}{c} 1/4 span position \\ 1/4 span position \\ Whole-bridge range \\ \end{tabular} & \begin{tabular}{c} Transverse tension method \\ Stress release method \\ X-ray diffraction method \\ \end{tabular} & \
\begin{tabular}{c} 45.4/18.1 \\ 68.6/16.1 \\ 29.0/17.5 \\ \end{tabular} &
\begin{tabular}{c} [36.8, 53.9] \\ 62.7, 74.6] \\ \end{tabular} \\ \hline \hline \end{tabular}  
* AVG = Average value and SD = Standard deviation.  
\end{table}
Table 4: Field test results of prestress state.  
Figure 9: Three kinds of prestress test method: (**a**) transverse tension method; (**b**) stress release method; and (**c**) X-ray diffraction method.