## 5 Case Study
### Validation of Model-I: Life Cycle Lifespan Evaluation Model
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Facility**} \\ \hline
**Period No.** & **1 sup** & **1 sub** & **2 sup** & **2 sub** & **3 sup** & **3 sub** & **4 sup** & **4 sub** \\ \hline
1 st period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 3 \\ \hline
2 nd period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
3 rd period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
4 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
5 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
6 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
7 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
8 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \multicolumn{6}{c}{**Facility**} \\ \hline
**Period No.** & **5 sup** & **5 sub** & **6 sup** & **6 sub** & **7 sup** & **7 sub** & **8 sup** & **8 sub** \\ \hline
1 st period plan & 1 & 3 & 3 & 3 & 2 & 3 & 1 & 1 \\ \hline
2 nd period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
3 rd period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 3 \\ \hline
4 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
5 th period plan & 1 & 3 & 1 & 1 & 1 & 3 & 1 & 3 \\ \hline
6 th period plan & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline
7 th period plan & 1 & 3 & 1 & 1 & 1 & 3 & 1 & 3 \\ \hline
8 th period plan & 1 & 3 & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Calculation results of Model-I. Figure 9: Simulation result of practical maintenance decisions. When the budget is abundant, the most common choice of maintenance plan for bridges will be plan one (early maintenance), as this has the greatest benefit, i.e., the plan with the highest number of effect years, and will repeat it until the end of the plan cycle. In the results of Model-I, most bridges repeat the same plan until the end of the plan cycle, except for the first cycle. Such results show that, at the beginning of the plan cycle, because of the influence of the current situation data, Model-I will first choose the best plan to suit the current situation to obtain the maximum overall benefit. In addition, by comparing Table 9 with Table 10, it can be found that for the last cycle of the majority of bridges in the model, even if the same plan is selected, the maintenance period may be still different because all other cycles--except the last cycle--have subsequent operations. If there are no subsequent operations, then the effect period will not be reduced, owing to the selection of the subsequent plans. From Table 9, it can be observed that the selection of plans for some facilities is constantly changing, except at the initial stage of the plan cycle. There are several possible reasons for this situation. First, taking the substructure of bridge eight as an example, after selecting maintenance plan one at the initial stage of the plan cycle, although the plans selected in the subsequent maintenance cycles have changed, regularity can be seen, proving that in addition to the maximum benefits obtained by single plan selection, the combination of plans may also create greater benefits. Another possible reason is that, like the substructures of bridge five and bridge seven in their respective life cycles, they seem to change maintenance plans irregularly and continuously, which means that when calculating different plan combinations, Model-I may have some combinations with the same sum, but they can all be selected; therefore, irregular plan combinations may occur. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Facility** & **1 sup** & **1 sub** & **2 sup** & **2 sub** & **3 sup** & **3 sub** & **4 sup** & **4 sub** \\ \hline Effect period(year) & 1 & 2 & 0 & 1 & 6 & 3 & 5 & 0 \\ \hline  
\hline \end{tabular}
\end{table} 
Table 10: Calculation results of effect period.