## 4 Design of Jet Columns
\[CSR_{design}=CSR*S_{R} \tag{8}\]  
\[S_{R}=\frac{\tau_{s}}{\tau}=\frac{\tau_{s}}{\tau_{agg}}=\frac{\tau_{s}}{(1+(G _{r}-1)a_{r})}=\frac{1}{G_{r}}\frac{1}{\left(a_{r}+\frac{1}{G_{r}}(1-a_{r}) \right)} \tag{9}\]  
\[G_{r}=\frac{G_{sf}}{G_{s}} \tag{10}\]  
\[a_{r}=\frac{A_{jet}}{A_{imp}} \tag{11}\]  
where  
\(\mathrm{G_{r}}\): the shear modulus ratio,  
\(\mathrm{a_{r}}\): area replacement ratio,  
\(\mathrm{G_{sf}}\): shear modulus of jet-column,  
\(\mathrm{G_{s}}\): shear modulus of soil  
The lowest factor of safety against liquefaction was obtained as 1.01 from the Equation (8), and hence the necessary ground improvement was provided. After this stage, a total of 5 trial columns were constructed. Trial columns were constructed at different withdrawal speeds, injection pressures, and different locations, with a water/cement mixture of 1. \begin{table} \begin{tabular}{l c c c c} \hline \hline  & \multicolumn{3}{c}{**Unimproved**} & \multicolumn{3}{c}{**Improved**} \\ \cline{2-5}  & \multicolumn{2}{c}{**c\(\Phi\)**} & \multicolumn{2}{c}{**E (kN/m2)**} & \multicolumn{2}{c}{**c (kN/m2)**} & \multicolumn{2}{c}{**c(\(\circ\))**} \\ \cline{2-5}  & \multicolumn{2}{c}{**c(\(\circ\))**} & \multicolumn{2}{c}{**E (kN/m2)**} & \multicolumn{2}{c}{**c(\(\circ\))**} \\ \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. \[CSR_{design}=CSR*S_{R} \tag{8}\]  
\[S_{R}=\frac{\tau_{s}}{\tau}=\frac{\tau_{s}}{\tau_{agg}}=\frac{\tau_{s}}{(1+(G _{r}-1)a_{r})}=\frac{1}{G_{r}}\frac{1}{\left(a_{r}+\frac{1}{G_{r}}(1-a_{r}) \right)} \tag{9}\]  
\[G_{r}=\frac{G_{sf}}{G_{s}} \tag{10}\]  
\[a_{r}=\frac{A_{jet}}{A_{imp}} \tag{11}\]  
where  
\(\mathrm{G_{r}}\): the shear modulus ratio,  
\(\mathrm{a_{r}}\): area replacement ratio,  
\(\mathrm{G_{sf}}\): shear modulus of jet-column,  
\(\mathrm{G_{s}}\): shear modulus of soil  
The lowest factor of safety against liquefaction was obtained as 1.01 from the Equation (8), and hence the necessary ground improvement was provided. After this stage, a total of 5 trial columns were constructed. Trial columns were constructed at different withdrawal speeds, injection pressures, and different locations, with a water/cement mixture of 1. Figure 7: Method followed when calculating average of weighted areas. There are two nozzles with a diameter of 2.2 mm in the jet grout machine, and the trial works were carried out with a rotation speed of 15-17 rpm. Details of the trial columns are given in Table 4. In addition, Figure 8 shows the borehole works on the trial columns and cores obtained from the trial boreholes. As can be seen from Table 4, cores varying between 1.5 m and 10.10 m were obtained. When checking the jet grout performance, the total core recovery and the uniaxial compressive strength were considered. The total core recovery values were obtained as 85-100% from the trial columns. Therefore, the core quality is sufficient (Figure 8), and the performance of the trial columns is successful. In addition, core samples were obtained for laboratory experiments. Unit weight tests were carried out according to ISRM [60], sonic velocity testing according to ASTM C597 [61], and uniaxial compression testing according to ASTM C39 standards. The average unit weight values of the X64 and X71 series specimens were 16.94 kN/m\({}^{3}\) and 18.04 kN/m\({}^{3}\), respectively. This indicates that the cement injected into the natural sand seriously densified the material. This change is seriously reflected in the P-wave velocities, which were 1997 m/s and 2208 m/s for the X64 and X71 series specimens, respectively. The uniaxial compressive strength is the most critical parameter in jet grouting.