## 2 Methodology
### Calculation of Jet-Grouted Bottom sealing Barriers Considering Seepage Failure  
Ideally, jet-grouted bottom sealing barriers are considered to be almost impermeable materials that have a very low hydraulic conductivity, but in fact jet-grouted materials in the field still have permeability. The hydraulic conductivity of jet grouting in the field is far larger than that obtained by the laboratory test under an ideal condition. When the hydraulic conductivity of the jet-grouted bottom sealing barriers in the field exceeds a certain value, groundwater with high head can induce seepage failure. Therefore, it is necessary to propose a calculation method of the jet-grouted bottom sealing barriers when considering seepage failure. For the seepage failure mechanism, the following assumptions are considered:  
Figure 3: Calculation procedure of jet-grouted bottom sealing barriers considering instability failure. (1) The water table is horizontal without considering the fluctuation of groundwater level during pumping inside the excavation. (2) Groundwater seepage follows [PERSON]'s law, and it is based on the principle of flow balance; the flow of any cross-section is equal. (3) The equivalent hydraulic conductivity of multi-layer soils can be expressed as the weighted hydraulic conductivity \(k=\sum\limits_{i}\frac{k_{i}M_{i}}{M_{i}}\), where \(k_{i}\) and \(M_{i}\) are the hydraulic conductivity and average thickness of each soil layer, respectively. Followed [PERSON]'s law, the flow rate \(Q\) of any cross-section can be expressed as:  
\[Q=kLB\frac{dH}{dz} \tag{11}\]  
Because of the effect of vertical waterproof curtains (underground enclosures), groundwater outside the excavation needs to flow over the underground enclosures and flow towards the excavation through the jet-grouted bottom sealing barriers. By introducing hydraulic boundary conditions of multi-layer soils outside the enclosures: \(z=h_{g}+h_{s}-h_{u}\), \(H=h_{w}\); \(z=h_{g}+h_{s}\), \(H=h_{2}\); the flow rate \(Q\) of groundwater outside that flows into the jet-grouted bottom sealing barriers can be calculated based on Equation (11) as  
\[Q=k_{u}LB\frac{h_{w}-h_{2}}{h_{u}} \tag{12}\]  
where \(k_{u}\) is the equivalent hydraulic conductivity of multi-layer soils outside the enclosures and \(h_{2}\) is the hydraulic head of groundwater below the jet-grouted bottom sealing barriers. By introducing hydraulic boundary conditions of jet-grouted bottom sealing barriers: \(z=h_{g}+h_{s}\), \(H=h_{2}\); \(z=h_{s}\), \(H=h_{1}\), the flow rate \(Q\) of groundwater flows from the jet-grouted bottom sealing barriers (\(h_{g}\)) can be computed based on Equation (11), as  
\[Q=k_{g}LB\frac{h_{2}-h_{1}}{h_{g}} \tag{13}\]  
where \(k_{g}\) is the effective hydraulic conductivity of jet-grouted bottom sealing barriers and \(h_{1}\) is the hydraulic head of groundwater at the top of the jet-grouted bottom sealing barriers. By introducing hydraulic boundary conditions of untreated soils below the excavation bottom: \(z=h_{s}\), \(H=h_{1}\); \(z=0\), \(H=h_{0}\), the flow rate \(Q\) of untreated soils (\(h_{s}\)) below the excavation bottom based on Equation (11) as  
\[Q=k_{s}LB\frac{h_{1}-h_{0}}{h_{s}} \tag{14}\]  
where \(k_{s}\) is the effective hydraulic conductivity of untreated soils below the excavation bottom and \(h_{0}\) is the hydraulic head of the excavation bottom. Generally, the water level inside the excavation should be lowered below the excavation bottom, so as to provide dry working space for the excavation.