## 5 Application  
### Target Structure and Ice Conditions  
This study focused on a semi-submersible drilling rig installed in an ice-covered area as shown in Figure 8. To prepare for long-term ice loads, a specially designed structure was applied in the ice belt zone to mitigate the impact of the ice loading. The detailed dimensions of the structure are presented in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Dimension** & \multicolumn{2}{c}{**Value**} \\ \cline{3-4}
**Steel** & **X-Z Plane** & **Y-Z Plane** \\ \hline Waterline width & **Angle T**[\({}^{\circ}\)] & 55 & 55 \\ Top/Bottom width & **Angle B**[\({}^{\circ}\)] & 50 & 50 \\ Height T & **Middle width [m]** & 29.18 & 30.46 \\
**Top/Bottom width [m]** & 17.66 & 18.56 \\
**Waterline width [m]** & 26.38 & 27.66 \\
**Height [m]** & 19.5 & 19.5 \\
**Height T [m]** & 3 & 3 \\
**Height B [m]** & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensions of the structure in ice belt zone. Figure 8: Finite element model of the semi-submergible drilling rig. The material properties of the ice applied in this study are presented in Table 3.  
Table 4 shows the ice thickness and velocity conditions. For the direct analysis, we selected 12 conditions (three thicknesses and four velocities) denoted in bold in Table 4, in order to minimize computational cost. The remaining conditions were covered through linear interpolation of calculated results. In the direct analysis and the semi-analytical methods applied in this study, the probability model was made based on the result of time series analysis. Assuming that the continuous ice load action by level ice breaking is a stationary process, the parameters derived from the short-term time series analysis can be equally applied to the long-term situation. However, valid statistical properties require time series calculations for a sufficient amount of time. On the other hand, time series analysis for too long a period of a time requires excessive analysis time. Therefore, in this study, the required analysis time to show statistical convergence was determined by calculating the parameters according to each analysis time. Using the analysis time as the criterion for convergence may lead to a large variation in the number of collisions depending on the applied speed of the ice. As a result, in this study, the moving distance of ice was used as the evaluation criterion instead of the analysis time. The subsequent paragraphs present an example of finding the effective length of level ice to obtain load data from statistical variables. For example, at velocity 9.18 cm/s, the parameters were calculated for the level ice moving as much as 25 m, 50 m, 100 m, 200 m, 400 m, and 1000 m. Figure 9a,b show the scale and shape parameters calculated by varying the moving distance of ice. The stability of statistical convergence was confirmed for ice movement conditions of 200 m or more, and the results of ice load calculation for 200 m movement were applied to the fatigue analysis. Similarly, the effective ice length was determined for the ice thickness-velocity combination indicated in bold in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case3** & **Case 4** & **Case 5** \\ \hline Thickness (cm) & 29.6 & 59.2 & 88.8 & 118.4 & 148 \\ \hline Velocity (cm/s) & 9.18, 18.36, 27.55, 36.73, 45.91, 55.09, 64.27, 73.45, 82.64, 91.82, 101 & & \\ \hline \end{tabular}
\end{table} 
Table 4: Velocity–thickness cases.