## 5 Stability
### Wave Forces  
Based on the maximum levels from Table 1, the wave input data are given in Tables 2-4. The resulting wave force for each seabed depth is represented by the horizontal force _Ph_, which acts at _hPh_ above the seabed. The width of the crest (Wc) and the caisson slope angle (\(\alpha\)) are adjusted in a spreadsheet, which gives a conservative minimum factor of safety (FoS) of 1.6 against sliding and overturning for the operational case and 1.4 for the storm case. Tables 5 and 6 include a vertical wave force component to balance the system of forces; it is taken as the horizontal force multiplied by the tangent of the slope angle. The estimate is excessive for shallow slopes, and the earth embankment as the horizontal force is based on waves impacting vertical walls. So, the vertical component is limited to the horizontal wave force. More work is required on modelling wave forces on sloping or stepped structures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operating Case** & \multicolumn{3}{c}{**Storm Condition**} \\ \hline MHWS (m OD) & 3.51 & HAT (m OD) & 4.70 \\ SLR (m) & 1.00 & SLR (m) & 1.00 \\  & & Storm surge (m) & 2.00 \\ Maximum static sea level (m OD) & 4.51 & Maximum static sea level (m OD) & 7.70 \\ Max operating head (m) & 5.79 & & \\ Impoundment water level (m OD) & \(-\)1.28 & & \\  & & MHWS—1.0 (m OD) & 2.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design static water levels for North Wales Coastal Lagoon. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Level of Seabed (m OD)** & \(\mathbf{-10.0}\) & \(\mathbf{-14.0}\) & \(\mathbf{-18.0}\) \\ \hline HMax, Design wave height (m) & 7.3 & 11.3 & 12.3 \\ T\({}_{1/3}\) wave period (s) & 8.8 & 8.8 & 8.8 \\ L, Wavelength from tables with water & & 93.0 & 101.0 & 108.0 \\ depth h and period T (m) & & & \\ \(\beta\), angle of incident waves \(\leq\) 15 degs & 15.0 & 15.0 & 15.0 \\ Level of bund crest (m OD) & 8.5 & 8.5 & 8.5 \\ level of top of rock armour (m OD) & \(-\)9.0 & \(-\)13.0 & \(-\)17.0 \\ Level of base of caisson (m OD) & \(-\)10.0 & \(-\)14.0 & \(-\)18.0 \\ MHWS (m OD) & 3.5 & 3.5 & 3.5 \\ Surge height, (m) & 2.0 & 2.0 & 2.0 \\ Sea Level Rise, (m) & 1.0 & 1.0 & 1.0 \\ g, gradient of Seabed, I in g & 100.0 & 100.0 & 100.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design wave input data. It is clear from Table 7 that the design of the vertical caissons is limited by high bearing pressures (note that 25\({}^{\circ}\) and 45\({}^{\circ}\) results are omitted for clarity). The design of the horizontal caissons in storm conditions is limited by the factor of safety against sliding, but the ground bearing pressures are less than those for vertical caissons. There is no risk of the embankment sliding, but circular slip analysis should be carried out for the final design. Overturning is a low risk for all cases in the relatively shallow waters along the west coast of GB. \begin{table}
\begin{tabular}{l c c c} \hline \hline Bund crest level (m OD) & 8.5 & Width of crest Wc (m) & 12.0 \\ Seabed level (m OD) & \(-\)14.0 & Slope angle \(\alpha\) (degs) & 45.0 \\ overall height of bund (m) & 22.5 & Bulk weight of bund (kN/m\({}^{3}\)) & 20.3 \\ Max static sea level (m OD) & 7.7 & Bulk weight of seawater (kN/m\({}^{3}\)) & 10.1 \\ Impoundment water level (m OD) & 2.5 & Angle of base friction (degs) & 26.0 \\ Total horizontal Wave Force Ph (kN) & 1310 & Height of total horizontal wave force above base, hPh. (m) & 11.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Example of stability calculation input.