## 5 A Case Study
### Project Overview  
The Mingyuan Forest Urban Green Underground Smart Garage Project is located at the southeast corner of Guangyan Road and Yonghe Road in Jingan District, Shanghai. The project comprised two circular shafts with an inner diameter of 21.0 m, constructed by mechanical excavation. In mechanical shaft construction, the segmental lining was installed by a top-down, ring-by-ring assembly synchronized with the shaft's progressive sinking. The first ring was pre-assembled on the ground or in a shallow shaft. As excavation proceeded in stages and the shaft subsided, subsequent rings were installed sequentially within the sinking space. Each ring was bolted and sealed to ensure structural integrity and watertightness. Each shaft support structure consisted of three components: a 2.0 m thick cast-in-place bladed footing at the base, 22 rings of precast segmental linings totaling 44.0 m in height, and a 4.2 m high cast-in-place top section. For convenience in the following analysis, the blade foot was designated as Ring 0, and the precast segments were consecutively numbered from Ring 1 to Ring 22 in ascending order from bottom to top. The shaft excavation diameter was 23.0 m, with a segment thickness of 1.0 m. Each ring comprised 10 segments. The total excavation depth was approximately 50.2 m. The relevant geological parameters are listed in Table 1.  
The circular shaft case study aligns well with the calculation model proposed herein, and the comparative validation based on this case is both appropriate and robust. In addition, to verify the reliability of the analytical results, vibrating wire earth pressure gauges and steel reinforcement bar axial force gauges were installed to monitor the earth pressure on the Ring 3 and Ring 6 segments, as well as the axial forces in the inner and outer reinforcement bars, respectively. The locations of the monitoring points are shown in Figure 10.  
To facilitate subsequent analysis, based on the on-site construction plan and the stress characteristics of the support structure, the shaft construction process was divided into three stages.  
Stage I: Excavation to the bottom under the condition that the outer wall was in contact with slurry and the inner wall was in contact with silty water. The unit weight of silty water on the inner wall was 12.5 kN/m\({}^{3}\), and the unit weight of slurry on the outer wall was 11.0 kN/m\({}^{3}\).  
Stage II: Replacement of the slurry on the outer wall with plain concrete.  
Stage III: Extraction of water from inside the shaft.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Soil** & **Thickness/(m)** & **Unit Weight/(kN-m\({}^{-3}\))** & **Internal Friction Angle/(\({}^{\circ}\))** & **Cohesion/(kPa)** \\ \hline Clayey silt & 3.5 & 18.7 & 25 & 10 \\ Soft plastic silty clay & 10.3 & 17.8 & 14 & 14 \\ Plastic silty clay & 6.1 & 18.1 & 16 & 17 \\ Hard plastic silty clay & 3.2 & 19.9 & 18 & 18 \\ Silty clay interbedded with sandy silt & 6.6 & 19 & 19 & 24 \\ \hline Hard plastic silty clay & 16.3 & 18.3 & 18 & 19 \\ Silty clay interbedded with sandy silt & 7.3 & 18.5 & 23 & 14 \\ \hline \end{tabular} Since the physical and mechanical parameters of each soil layer varied slightly, the subsequent earth pressure analysis used the weighted average method based on soil layer thickness, treating the multi-layer soil as a single homogeneous layer.  
\end{table}
Table 1: Geological parameters.  
Since both the inner and outer sides of the segments were surrounded by fluid in Stage I, and therefore not subjected to earth pressure, the earth pressure analysis was conducted only for Stages II and III.