## 4 Design of Jet Columns  
As described in the previous section, the foundation soils of the infills to be constructed in the offshore environment are highly susceptible to liquefaction. For this reason, ground improvement is mandatory. In ground improvement practice, jet grout, dynamic compaction, and deep-soil mixing, stone column methods are used to eliminate liquefaction problems. The improvement works must be applied on the offshore platform. Among the methods mentioned, jet grouting is the most suitable method due to operational reasons. The design of the jet columns was carried out by a Unitek-Vemak Joint Venture [58]. The lowest uniaxial compressive strength and modulus of elasticity values were accepted as \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & 0.4 & 2 & SM & 18 & 0 & 3.1 & 3.1 & 0.04 & liq, expected. & 10.93 & 11.38 \\  & 1.9 & 4 & SM & 18 & 2 & 6.1 & 6.1 & 0.06 & liq, expected. & 13.29 & 14.14 \\  & 3.4 & 12 & SP-SM & 18 & 2 & 20.8 & 20.8 & 0.15 & liq, expected. & 11.06 & 13.01 \\ \(\text{c}_{\text{s}}^{\text{s}}\) & 4.9 & 16 & SW- & 18 & 1 & 28.2 & 28.2 & 0.24 & liq, expected. & 9.03 & 11.86 \\  & 6.4 & 15 & SW- & 18 & 1 & 23.1 & 23.1 & 0.17 & liq, expected. & 9.23 & 11.12 \\  & & & SM & & & & & & & \(\text{L}=54\) & Very High & L = 62 & Moderate \\ \hline  & 0.5 & 4 & SW & 18 & 0 & 6.1 & 6.1 & 0.05 & liq, expected. & 10.32 & 10.86 \\  & 1.7 & 4 & SW & 18 & 7 & 6.1 & 6.1 & 0.06 & liq, expected. & 11.99 & 12.76 \\  & 3.2 & 8 & SW & 18 & 0 & 13.9 & 13.9 & 0.10 & liq, expected. & 11.85 & 13.16 \\  & 4.7 & 12 & SM & 18 & 1 & 21.6 & 21.6 & 0.15 & liq, expected. & 10.23 & 12.03 \\  & 6.2 & 19 & SM & 18 & 1 & 29.7 & 29.7 & 0.29 & liq, expected. & 7.75 & 10.86 \\  & 7.7 & 21 & SM & 18 & 1 & 29.5 & 29.5 & 0.29 & liq, expected. & 6.72 & 9.42 \\  & 9.1 & R & SM & 18 & 1 & – & – & – & – & – & – \\ \hline  & 1.9 & 6 & ML & 18 & 59 & 9.2 & 9.2 & 0.11 & liq, expected. & 21.62 & 24.29 \\  & 3.2 & 5 & ML & 18 & 8.7 & 8.7 & 0.07 & liq, expected. & 11.36 & 12.21 \\  & 4.7 & 9 & ML & 18 & 53 & 16.2 & 24.4 & 0.18 & liq, expected. & 8.23 & 10.03 \\  & & & & & & & & \(\text{L}=41\) & Very High & L = 47 & Moderate \\ \hline  & 0.7 & 1 & SM & 18 & – & 1.5 & 1.5 & 0.04 & liq, expected. & 13.68 & 14.25 \\  & 2.2 & 10 & SM & 18 & 13 & 15.3 & 17.9 & 0.12 & liq, expected. & 12.24 & 13.91 \\  & 3.7 & 9 & SM-SC & 18 & – & 15.6 & 15.6 & 0.11 & liq, expected. & 11.38 & 12.79 \\  & 5.2 & 9 & SM-SC & 18 & 24 & 15.4 & 21.3 & 0.15 & liq, expected. & 12.23 & 14.38 \\  & & & & & & & & \(\text{L}=50\) & Very High & L = 55 & Moderate \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Liquefaction analysis input parameters and the results for some boreholes. 3 MPa and 920 MPa, respectively. The planned jet ground pattern is 2 m \(\times\) 2 m, while the diameter of those is 80 cm. Considering these design parameters, the ground conditions of the improved soil were calculated by employing the average of weighted areas as shown in Figure 7. Accordingly, the improved and natural shear strength parameters of loose sand and moderately dense sand layers are given in Table 3.  
\begin{table} \begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Unimproved**} & \multicolumn{3}{c}{**Improved**} \\ \cline{2-7}  & \multicolumn{2}{c}{**c\(\Phi\)**} & \multicolumn{2}{c}{**c(\(\circ\))**} & \multicolumn{2}{c}{**E (kN/m2)**} & \multicolumn{2}{c}{**c(\(\circ\))**} & \multicolumn{2}{c}{**c(kN/m2)**} \\ \cline{2-7}  & \multicolumn{2}{c}{**c(\(\circ\))**} & \multicolumn{2}{c}{**E (kN/m2)**} & \multicolumn{2}{c}{**c(\(\circ\))**} & \multicolumn{2}{c}{**E (kN/m2)**} \\ \hline Loose sand layer & 0 & 25 & 4750 & 38 & 26 & 41,852 \\ Moderately dense sand layer & 0 & 30 & 8250 & 38 & 31 & 44,912 \\ \hline \hline \end{tabular}  [PERSON] and [PERSON] [59] proposed a method for the seismically safe design of jet grout columns. In this method, the cyclic stress ratio (CSR) is reduced by a CSR reduction factor (SR) that is determined by using Equations (8) and (9). The SR is calculated as 0.0396 for the study site.