## 3 Parametric Analysis and Design Procedure  
### Parametric Analysis  
This part mainly discusses the influence of important parameters on the calculation results for two different failure mechanisms. The deep excavations for urban subway station in China are usually long rectangle excavation (\(L\gg B\)). The excavation depth of underground two-story station is 15-20 m and the width of the excavation in standard segment is 16-18 m. The regular size of a deep excavation of underground two-story station is considered in the calculation. The excavation width is set as 17.5 m. The homogeneous sandy soil is selected as the representative soil material for discussion. The unit weight of water, jet-grouted material and sandy soil is 10, 22 and 18.16 kN/m\({}^{3}\), respectively.  
Figure 5a,b display the relation curves of the dimensionless thickness \(h_{g}/B\) versus the dimensionless depth \(h_{s}/B\) of jet-grouted bottom sealing barriers when considering \"instability failure\" under the different water table and the unconfined compression strength. As can be seen from Figure 5a,b, when the dimensionless depth \(h_{s}/B\) is fixed, for meeting the requirement of the stability, the dimensionless thickness \(h_{g}/B\) should increase with the dimensionless water table \(h_{w}/B\), and vice versa. When the dimensionless depth \(h_{s}/B\) is fixed, the dimensionless thickness \(h_{g}/B\) decreases as the dimensionless term \(\delta q_{u}/\gamma_{w}B\) increases, and vice versa. This suggests that the unconfined compression strength \(q_{u}\) of the jet-grouted bottom sealing barriers play a crucial role in the design of the thickness of jet-grouted bottom sealing barriers. The greater the unconfined compression strength \(q_{u}\), the smaller the thickness \(h_{g}\) of jet-grouted bottom sealing barriers.  
Figure 6a-c display the relation curves of the dimensionless thickness \(h_{g}/B\) versus the dimensionless depth \(h_{s}/B\) of jet-grouted bottom sealing barriers when considering \"seepage failure\" under the different water table, the equivalent hydraulic conductivity of soils and the allowable seepage of jet-grouted  
Figure 4: Calculation procedure of jet-grouted bottom sealing barriers considering seepage failure.  
bottom sealing barriers per unit area, respectively. As can be seen from Figure 6a-c, when the dimensionless thickness \(h_{g}/B\) is fixed, to prevent from seepage failure the dimensionless depth \(h_{s}/B\) should increase with the dimensionless water table \(h_{u\!n}/B\), and vice versa. When the dimensionless thickness \(h_{g}/B\) is fixed, the dimensionless depth \(h_{s}/B\) should increase as the equivalent hydraulic conductivity of soils \(k_{u}\) becomes large, and vice versa. When the dimensionless depth \(h_{s}/B\) and the equivalent hydraulic conductivity of soils \(k_{u}\) are fixed, the dimensionless thickness \(h_{g}/B\) decreases as the allowable seepage of jet-grouted bottom sealing barriers per unit area [\(q\)] increases, but the allowable seepage of the jet-grouted bottom sealing barriers per unit area [\(q\)] varies between 0.01 and 0.3, the effect of which plays on the dimensionless thickness \(h_{g}/B\) or the dimensionless depth \(h_{s}/B\) is not significant.  
Figure 5: Relation curves of \(h_{g}/B\) versus \(h_{g}/B\) when considering “instability failure”: (**a**) water table; and, (**b**) unconfined compression strength.  
Figure 6: Relation curves of \(h_{g}/B\) versus \(h_{g}/B\) considering “seepage failure”: (**a**) water table; (**b**) equivalent hydraulic conductivity of soils; and, (**c**) allowable seepage of jet-grouted bottom sealing barriers per unit area.