## 5 Results
It should be noted that the earthquake events modeled here are extreme events, since the ground motion records are matched to a seismic spectrum with a 2% probability of exceedance in 50 years, as explained in Section 4, with the three perpendicular components of ground motion applied simultaneously at the bedrock surface. For such rare events, foundation tilting momentarily exceeding 0.25\({}^{\circ}\) can be tolerated, since the WT is shut down with no expectation of it to be functioning to produce power during the earthquake. A tower-strike can be prevented by implementing enough blade clearance in design. The relevant criterion in such events is the residual tilt, which is the tilting angle at the end of the seismic event. It is observed from Figures 14 and 15 that while the residual tilt of the 5 MW and 8 MW WTs is less than 0.25\({}^{\circ}\), it exceeds that limit with the 10 MW WT. This observation confirms that the foundation designed for the 5 MW WT can support a larger 8 MW WT in a shut-down event caused by an earthquake. However, any further increase in the WT capacity to 10 MW is not possible due to the exceedance of the residual tilt from the allowable 25\({}^{\circ}\). On the other hand, the width of the uplift area remains under 25% of the foundation width with the increased WT capacity of 8 MW. Based on these observations, it is deduced that while the zero-uplift rule under operational conditions can be relaxed without compromising the tilting limit, the 25% and 50% uplift limits for extreme conditions remain valid, since the residual tilt with the 10 MW WT exceeds the allowable 0.25\({}^{\circ}\) limit with only a 17% uplift area width, which is much smaller than 25%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**WT Capacity** & **Operation** & \
\begin{tabular}{c} **Shut-Down with** \\ **Saguenay EQ** \\ \end{tabular} &
\begin{tabular}{c} **Shut-Down with** \\ **Val des Bois EQ** \\ \end{tabular} \\ \hline
5 MW & 0.5 mm & 27.4 mm & 7.0 mm \\
8 MW & 1.5 mm & 31.5 mm & 7.1 mm \\
10 MW & 1.7 mm & 34.6 mm & 8.9 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Permanent settlements of the foundation. Figure 13: Tilting of the foundation under operational loads. Figure 16 shows the distribution of the degraded shear strength (\(S_{u,Degr}\)) in the soil around the foundation of the 8 MW WT at the end of the Val des Bois earthquake event, as calculated by the UMAT code explained in Section 2. It is observed that there is significant strength degradation (shown by orange and red colors) around the edges of the circular foundation. Figure 17 illustrates the distribution of the DCR as calculated by the UMAT, at the moment of peak maximum value of the DCR, under the same WT with the same earthquake shut-down event as of Figure 16. From the contour of the DCR shown in Figure 17, the point of the maximum DCR is determined, which is at the edge of the foundation in this case. Figure 18 shows the changes of the DCR at the most critical point of soil around the foundation of each WT under operational loads. It is observed that only the DCR curve of the 10 MW WT exceeds 1.0. Figures 19 and 20 display similar DCR curves for shut-down events with earthquakes. It should be noted that a DCR exceeding 1.0, as observed in Figures 18-20, indicates a localized shear failure. Figures 21 and 22 show that the region of soil where shear failure occurs (shown by red color) is limited to relatively small volumes of soil adjacent to edge of the foundation slab or pedestal. It should be noted that this type of localized shear failure is acceptable and even encouraged in the context of rocking foundations [14], since it dissipates energy in the soil and can reduce structural demand. Figure 14: Tilting of the foundation in shut-down with Saguenay earthquake. Figure 15: Tilting of the foundation in shut-down with Val des Bois earthquake. Figure 16: Degraded shear strength (Pa) under the 8 MW WT foundation, at the end of Val des Bois earthquake with WT shut-down.