## 5 Case Study Implementation of the Decision-Support Framework
### Calculation of Effect and Life Extension
#### 5.3.4 Calculation of Time to Reach the Lowest Acceptable Level  
From the predicted results in the table, it can be seen that the time when IRI reaches the lowest acceptable level is later than PCI, so as long as the time when PCI reaches the lowest acceptable level is calculated, it is the time when this plan reaches the lowest acceptable level. The years for each plan to reach the lowest acceptable level of preventive maintenance and the calculation of their respective life extensions are shown in Table 19: \begin{table}
\begin{tabular}{c c} \hline \hline
**Indicators** & **The Lowest Acceptable Level** \\ \hline PCI & \(\geq\)70 \\ IRI & \(\leq\)6 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Minimum Acceptable Levels of pavement Condition Indicators. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Road Age** & **Decay Curve** & **PCI** & **IRI** \\ \hline
4 & \(\text{y}=100\times\text{e}^{-0.058\text{x}}\) & \(\text{y}=1.71\times\text{e}^{0.063\text{x}}\) \\
5 & \(\text{y}=100\times\text{e}^{-0.0456\text{x}}\) & \(\text{y}=1.75\times\text{e}^{0.058\text{x}}\) \\
6 & \(\text{y}=100\times\text{e}^{-0.0483\text{x}}\) & \(\text{y}=1.81\times\text{e}^{0.058\text{x}}\) \\
7 & \(\text{y}=100\times\text{e}^{-0.0556\text{x}}\) & \(\text{y}=1.83\times\text{e}^{0.063\text{x}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Decay curve after Preventive maintenance measures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Decay Curve** & **X Value at the Lowest** & **Road Age at the Lowest** & **Life Extension** \\  & **Acceptable Level** & **Acceptable Level** & **Acceptable Level** & **Life Extension** \\ \hline \(\text{y}=100\times\text{e}^{-0.047\text{x}}\) & 7.5 & 7.5 & 0 \\ \(\text{y}=100\times\text{e}^{-0.0583\text{x}}\) & 6.1 & 10.1 & 2.6 \\ \(\text{y}=100\times\text{e}^{-0.0456\text{x}}\) & 7.8 & 12.8 & 5.3 \\ \(\text{y}=100\times\text{e}^{-0.0483\text{x}}\) & 7.4 & 13.4 & 5.9 \\ \(\text{y}=100\times\text{e}^{-0.0556\text{x}}\) & 6.4 & 13.4 & 5.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: The road age for PCI to reach the lowest acceptable level for each plan. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicators** & **Decay Curve** & \\ \hline PCI & \(\text{y}=100\times\text{e}^{-0.047\text{x}}\) & \(\text{y}=1.73\times\text{e}^{0.06\text{x}}\) \\ IRI & \(\text{y}=1.73\times\text{e}^{0.06\text{x}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Decay curve without preventive maintenance measures. According to Table 19, the analysis period is the road service life of the plan that first reaches the lowest acceptable level of preventive maintenance measures, so the analysis period of LCCA is 10 years. 5.3.5. Calculation of the Effectiveness of Each Plan  
Calculate the area A1 between PCI and the lowest acceptable level when no maintenance measures are taken, as follows:  
\[\text{AREA}_{0}=\int_{0}^{7.5}\Big{(}100\times\text{e}^{-0.047\text{x}}-70 \Big{)}\text{dx}=106.4\]  
The absolute values of the area increase enclosed by PCI and the lowest acceptable level after maintenance are: Plan 1: 64.34, Plan 2: 85.97, Plan 3: 79.7, and Plan 4: 65.82, indicating that the improvement effect of road performance is 60.47%, 80.80%, 74.91%, and 61.86%. 5.4. Cost Calculation for Different Plans  
5.4.1. Agency Cost Calculation  
(1) Routine maintenance costs  
Based on the daily maintenance costs of 1.1, 1.27, and 1.41 \(\text{yuan}/(\text{m}^{2}\cdot\text{year})\), traffic volume, and PCI data invested by the local maintenance department on this road from 2017 to 2019, the coefficients of Formula (1) were calibrated using the least squares method, and a = 0.72 and b = 3.44 \(\times\) 10\({}^{-6}\) were obtained, indicating that the daily maintenance cost model is:  
\[\text{MC}_{\text{i}}=0.72+3.44\times 10^{-6}\cdot(100-\text{PCI}_{\text{i}}) \text{AADT}_{\text{i}}\]  
(2) Preventive maintenance costs  
Since we are conducting a life cycle cost analysis on the maintenance project on this road, the initial construction cost is the same.