## 3 Application
### Calculation of EMV  
When determining the optimal design flood frequency of the diversion structure, the individual risk should be quantified to make an optimal decision. The EMV is the total expected cost of the diversion structure with a 1-, 2-, 5- and 10-year flood frequency, including construction cost, re-construction cost, and delay LD (Liquidated Damage) with the failure probability and the recovery cost with the overflow probability.  
The EMV is thus calculated as  
EMV = Construction cost of diversion structure  
+ Failure probability of upstream cofferdam  
\(\times\) [(Reconstruction cost of upstream & downstream cofferdams) + Delay LD]  
+ Overflow probability of upstream cofferdam \(\times\) Recovery cost  
The costs of the diversion tunnel and upstream/downstream cofferdam are considered as the construction cost of the diversion structure.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Random Variable**} & **Probability** & \multirow{2}{*}{**Distribution Parameters**} \\  & **Distribution** & \\ \hline \multirow{2}{*}{Mass density of concrete} & \multirow{2}{*}{Normal} & \(\bullet\) & Mean: 2226 kg/m\({}^{3}\) \\  & & \(\bullet\) & Standard deviation: 226 kg/m\({}^{3}\) \\ \hline \multirow{2}{*}{Friction angle of soil} & \multirow{2}{*}{Normal} & \(\bullet\) & Mean: 45\({}^{\circ}\) \\  & & \(\bullet\) & Standard deviation: 7.2\({}^{\circ}\) \\ \hline \multirow{2}{*}{Adhesion force of soil} & \multirow{2}{*}{Log normal} & \(\bullet\) & Mean: 1.77 \(\times\) 10\({}^{6}\) Pa \\  & & \(\bullet\) & Standard deviation: 1.24 \(\times\) 10\({}^{6}\) Pa \\ \hline \multirow{2}{*}{Height of deposit soil} & \multirow{2}{*}{Uniform} & \(\bullet\) & El.480.4-494.4 m \\ \hline \multirow{2}{*}{Mass density of deposit soil} & \multirow{2}{*}{Normal} & \(\bullet\) & Mean: 2000 kg/m\({}^{3}\) \\  & & \(\bullet\) & Standard deviation: 200 kg/m\({}^{3}\) \\ \hline \multirow{2}{*}{Friction coefficient of deposit} & \multirow{2}{*}{Normal} & \(\bullet\) & Mean: 30\({}^{\circ}\) \\  & & \(\bullet\) & Standard deviation: 2.4\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Selected random variables.  
Figure 6: Failure probability.  
For failure probability, only the probability of destruction of the upstream cofferdam was considered because the downstream cofferdam is normally destroyed after destruction of the upstream cofferdam. For the re-construction cost, both the upstream and downstream cofferdam construction costs were considered.  
For delay LD, if the upstream cofferdam was destroyed, it should be restored to construct the main dam. Therefore, the total construction period inevitably increased. In this paper, the delayed period for the re-construction was set as two months based on the construction schedule, and Delay LD was set as 1.5% of the total EPC cost.  
The number of overflows during the construction period depends on the design flood frequency of the diversion structure. After overflow, the water stored in the working space for the main dam construction has to be pumped out and the sedimentation should be cleaned. In addition, some damages to the upstream/downstream cofferdam or on the equipment should be repaired. Accordingly, the costs for pumping out, cleaning, and repairing were considered as the recovery cost. Recovery cost varies according to construction condition, circumstances, and the proactive plan. In this paper, recovery cost was set as USD 0.5 mil., USD 1.0 mil., USD 2.0 mil., USD 3.0 mil., and USD 4.0 mil.