## 4 Application
### Design of Jet-Grouted Bottom Sealing Barriers  
Table 2 lists the calculating parameters that have been known for the design of jet-grorted bottom sealing barriers. Considering such factors for importance of the excavation, uncertainty of jet grouting and safety allowance, safety factor \(F_{s}\) is set as 1.2 for the design of jet-grorted bottom sealing barriers. Figure 8 presents the relation curves of \(h_{g}\) versus \(h_{s}\) under the condition of both instability failure and seepage failure. The intersection of the two curves of \(h_{g}\) versus \(h_{s}\) plotted in Figure 8 should be a set of optimum solutions for the design of jet-grorted bottom sealing barriers, namely, \(h_{s}\) is 14 m and \(h_{g}\) is 1.8 m. On the one hand, it can prevent \"instability failure\" and \"seepage failure\" of jet-grorted bottom sealing barriers, so as to avoid the occurrence of, and on the other hand, the thickness of jet-grorted bottom sealing barriers is not very large, so that the excavation cost is not expensive.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{\(B\) **(m)**} & \(\gamma_{s}\) & \(\gamma_{w}\) & \(\gamma_{g}\) & \(k_{u}\) & \multirow{2}{*}{\(h_{uv}\) (m)} & \multirow{2}{*}{\(h_{exc}\) (m)} & \([q]\) & \multirow{2}{*}{\(c_{g}\) (kPa)} \\  & & **(kN/m3)** & (kN/m3)** & (kN/m3)** & (m/d) & & & & & (m/d) \\ \hline Value & 18.1 & 19 & 10 & 22 & 11.5 & 13 & 16 & 0.25 & 200 \\ \hline \hline \end{tabular} Note that unit weight of natural soil \(\gamma_{s}\) and the hydraulic conductivity of multi-layer soils \(k_{u}\) are taken a weighted value.  
\end{table}
Table 2: Calculating parameter.  
Figure 7: Typical geology profile at site.  
However, when considering the safety allowance and uncertainty factors during construction, the thickness of jet-grouted bottom sealing barriers is conservatively designed as 5 m (larger than the calculated thickness 1.8 m). Finally, the depth of untreated soils and thickness of jet-grouted bottom sealing barriers are determined to be 14 m and 5 m, respectively, as shown in Figure 9. The designed diameter and center spacing of the jet grouting columns is 1.1 m and 0.75 m, respectively.  
The double high-pressure jet grouting technique that develops on the traditional triple-rod method is used for the construction due to the deep depth of jet-grouted bottom sealing barriers that are below the ground surface. Table 3 lists the construction parameters of the jet grouting columns.  
Figure 8: Relation curve of depth \(h_{s}\) versus thickness \(h_{g}\) of jet-grouted bottom sealing barriers.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Properties**} & \multicolumn{3}{c}{**Grout**} & \multicolumn{3}{c}{**Water**} & \multicolumn{3}{c}{**Air**} & \multicolumn{3}{c}{**Rod**} & \multicolumn{1}{c}{**Rod**} \\  & \multirow{2}{*}{\begin{tabular}{c} **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Flow** \\ **Rate** \\ **(L/min)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Water-Cement** \\ **Ratio** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Flow** \\ **Rate** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Flow Rate** \\ **(m\({}^{3}\)/min)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Life** \\ **Rate** \\ **(cm/min)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Rotation** \\ **Rate** \\ **(ppm)** \\ \end{tabular} } \\ \hline \hline
**Range** & \multirow{2}{*}{35} & \multirow{2}{*}{100} & \multirow{2}{*}{1:1} & \multirow{2}{*}{25–35} & \multirow{2}{*}{70} & \multirow{2}{*}{0.8} & \multirow{2}{*}{6} & \multirow{2}{*}{12} & \multirow{2}{*}{10} \\  & & & & & & & & \\ \end{tabular}
\end{table}
Table 3: Construction parameters of jet grouting columns.  
Figure 9: Design of jet-grouted bottom sealing barriers.