## 4 Numerical Simulation and Analysis
### Soil Impact Zoning  
A surface settlement envelope was established on the basis of the numerical simulation results and actual measured data and compared with previous research [36], as shown in Figure 12. The horizontal axis represents the ratio of the distance (\(d\)) from a point behind the support structure to the sinking depth (\(H\)) of the shaft, whereas the vertical axis represents the nondimensional surface settlement. During the sinking of the VSM, the surface settlement around the shaft exhibits a concave shape. The settlement envelope obtained from the numerical simulation results is similar in shape and trend to the measured data, indicating that the HSS constitutive model can accurately reflect the disturbance of the surrounding soil during the VSM sinking process. However, owing to the time-dependent characteristics of soft soil, slight discrepancies exist in the results. Figure 11: Validation of the calculated results: (**a**) horizontal displacement comparison and (**b**) ground settlement comparison. Figure 12: Comparison with the ground surface settlement envelope of excavation cases in Shanghai. A comparison of the surface settlement envelope from the Shanghai engineering case reveals that the simulated settlement values and settlement range are significantly smaller than those reported in the Shanghai case and fall within Zone I, as defined by [PERSON] [37]. This is because settlement deformation is influenced by the regional soil layers and the form of the support structure, as well as by the new VSM construction method, which controls the deformation of the surrounding environment effectively. Figure 13a shows the vertical displacement deformation distribution curves of different soil layers at various depths. The horizontal axis represents the ratio of the horizontal distance (\(L\)) from the shaft to the maximum sinking depth of the shaft (\(H_{\text{m}}\)), whereas the displacement values are represented numerically, with positive values indicating settlement and negative values indicating heave. At the maximum excavation depth of \(H_{\text{m}}\) = 40.14 m, the influence range of displacement decreases as the depth of the soil layer increases. On the basis of the pattern of the settlement trough in the soil layers, the soil outside the shaft is divided into three zones: the groove-shaped settlement zone, the heave influence zone, and the heave zone, as shown in Figure 13b. The soil layers within the depth range of 0 to 0.7 \(H_{\text{m}}\) constitute the groove-shaped settlement zone, and their deformation pattern is similar to that of the surface. Shear deformation occurs in the soil due to the shearing effect of the shaft wall during shaft sinking, resulting in groove-shaped settlement. The maximum settlement occurs at a depth of 2-6 m rather than at the surface. Additionally, the shallow soil layers (0-12 m) are influenced by the reinforcement of jet grouting piles and the load from the upper ring beam, which restricts the deformation of the soil near the shaft. The soil layers within the depth range of 0.7 to 0.9 \(H_{\text{m}}\) form the heave influence zone, where the deformation is more complex, showing both indistinct concave settlement and some heave. This occurs because, during shaft sinking, the telescopic arm inside the shaft cuts into the soil, and the unloading of the bottom soil causes heave in deeper layers. Furthermore, changes in the lateral stress cause the external soil to gradually displace towards the inner side of the shaft. When the shaft sinks to a depth of 0.4 \(H_{\text{m}}\) to 0.9 \(H_{\text{m}}\), the corresponding soil layer is primarily soft clay. With an increasing excavation depth, the pore water pressure in the soil inside the pit rises, generating excess pore water pressure, reducing effective stress, and increasing the soil volume, making it more prone to heave deformation.