## 3 3D Sliding Force Balance Analysis
### Calculation Results of Overall and Local Instability  
The determination of both the overall stability and local stability of the double-angled trench section of the circular ground connection wall is presented in Figure 10. It can be observed from the figure that with the increase in the depth, the slurry weight necessary to maintain the stability of the diaphragm wall exhibits an initial rise followed by stabilization. This entire process can be divided into three stages.  
In the initial stage (stage I), the required slurry weight to maintain the stability of the diaphragm wall gradually increases with depth. At shallower depths of less than 30 m, overall instability is found to be more likely to occur compared to local instability. This is due to the in uncence of external factors, such as site overloading, which may result in small-scale overall instability near the surface. Within the depth range of 10 to 30 m, the slurry weight required to ensure the stability of the diaphragm wall exhibits a linear increase. To prevent the diaphragm wall from becoming unstable due to suboptimal slurry quality, it is recommended to reinforce the wall to a depth of at least 30 m.  
As the depth increases, the stability of the diaphragm wall becomes a critical concern, particularly in stage II. Here, we observe that the slurry weight required to maintain the stability of the diaphragm wall remains nearly constant, except for a sharp shift at 60 m depth, where a layer of peat soil exists at the junction of rock and soil. This layer is susceptible to stress concentration, rendering it prone to instability. The physical and mechanical properties of peat soil, such as low natural density, high water content, a large pore ratio, high compressibility, poor uniformity, and a low bearing capacity, can signi can study affect the overall stability of the diaphragm wall. As a result, the diaphragm wall is vulnerable to destabilization in the presence of peat soil.  
In the stage III, which corresponds to the deeper regions beyond 60 m, the slurry weight required to ensure the stability of the diaphragm wall remains practically constant. The critical slurry weight is noticeably lower in comparison to stage II. This is primarily attributed to the fact that, upon entering the rock strata, the physical and mechanical properties of the surrounding geological material greatly improve, resulting in a higher stability threshold for the diaphragm wall. The superior properties of the rock strata, including their higher values of strength, stiffness, and cohesion, enable the diaphragm wall to better resist the destabilizing forces and thus maintain the overall stability.  
In stage III, the critical slurry weight required to maintain the overall stability of the double-angled trench wall remains essentially constant and is signi canty lower than in stage II. This is due to the better physical and mechanical properties of the underlying rock layer, resulting in a higher value and improved stability of the diaphragm wall. Therefore, the critical weight required to maintain the overall stability of the double-angled trench wall is determined to be 10.58 N/m 3, while the critical gravity needed to maintain the local stability of the trench wall is 11.14 kN/m 3.  
Based on the explanation above, the slurry must have a speci c density and consistency in order to provide wall protection. Many research studies have shown that when the density of the slurry increases, the hydrostatic pressure increases and the slurry wall trench becomes very stable [2]. In reality, the slurry density must be more than 10.3 kN/m 3. A slurry with a high density also has high shear strength, which increases the gelling action and improves the groove hole stability [24].  
Figure 10: Calculation results of overall stability and local instability.