## 6 Stability Analysis
### Stability Against Hydraulic Uplift Calculation  
For deep foundation pits involving confined aquifers beneath the excavation base, the results of stability against hydraulic uplift verification directly determine the water level in the dewatering wells of the confined aquifer, thereby indirectly influencing the development of ground settlement outside the pit. Consequently, stability against hydraulic uplift verification is critical not only for base safety but also for controlling ground settlement. Overly conservative stability calculations may lead to excessive ground settlement, potentially causing building tilt or cracking, which violates environmental protection requirements for surrounding areas. Conversely, overly risky calculations may compromise safety and are equally unacceptable. By analyzing the failure mechanisms derived from finite element simulations, this section introduces the standardized method for stability against hydraulic uplift analysis and proposes an improved approach that accounts for the shear strength of the overlying soil at peripheral interfaces.  
For foundation pits with confined aquifers underlying the base, current codes mandate stability verification using the pressure equilibrium method, as illustrated in Figure 20. The safety factor against hydraulic uplift (\(F_{\text{sl}}\)) is defined as the ratio of the overburden soil weight (resistance) to the confined aquifer's water pressure (load):  
\[F_{\text{sl}}=\frac{\gamma_{\text{sat}}H}{\rho_{\text{w}}} \tag{1}\]  
Figure 19: Failure zone localization map in foundation pit.  
Figure 18: Total horizontal strain distribution in foundation pit.  
In the formula:  
\(\gamma_{\text{sat}}\) is the saturated unit weight of the soil overlying the confined aquifer (kN/m\({}^{3}\)); \(H\) is the effective embedment depth of the retaining structure above the confined aquifer's upper boundary. If the retaining structure does not penetrate into the confined aquifer, this parameter is adjusted to include the vertical distance between the retaining structure's base and the confined aquifer's top surface. \(p_{\text{w}}\) is hydraulic pressure exerted by the confined aquifer (kPa), calculated as \(p_{\text{w}}=\gamma_{\text{w}}H_{\text{w}}\), where \(\gamma_{\text{w}}\) is the unit weight of water and \(H_{\text{w}}\) is the piezometric head. \(p_{\text{crl}}\) is the critical hydraulic pressure, representing the threshold for hydraulic uplift failure instability, which is derived as \(p_{\text{crl}}=\gamma_{\text{sat}}H\).  
To address the limitations of the code-prescribed method, this study proposes an improved calculation approach that incorporates the contribution of side shear resistance in the soil mass against hydraulic uplift, based on the standardized formula. A similar method for considering the contact shear strength between soil and support structures has been validated in [PERSON] [47]'s research. Based on this method, a global uplift stability analysis framework for foundation pits with confined aquifers is developed. The method treats the soil mass against hydraulic uplift as an integral body for force equilibrium analysis, assuming the pit reaches a critical state when forces balance:  
\[F+G-P=0 \tag{2}\]  
In the formula: \(F\) represents the shear strength contribution of the surrounding soil around the zone against hydraulic uplift; \(G\) represents the total weight of the overburden soil above the confined aquifer's top surface within the pit; \(P\) represents the confined water pressure.