## 5 Model Validation  
Based on previous research [20; 30], ground deformation is mainly related to the key construction characteristics of shield tunneling, such as the support pressure at the excavation face, the friction between the shield skin and soil, and the quantity of synchronous pouring. In the first phase of the model validation process, nondimensional processing key elements are considered.  
The support pressure ratio expresses the support pressure level, and its calculation correlation is:  
\[P_{s}^{*}=p_{s}/\sigma_{h} \tag{4}\]  
where \(p_{s}\) is the support pressure at the center of the excavation face; \(\sigma_{h}\) is the total horizontal stress at the center of the excavation face.  
The friction coefficient expresses the friction level between the shield skin and soil, and its calculation correlation is:  
\[F_{f}^{*}=4F_{f}/\big{[}\pi D_{e}L_{e}\big{(}p_{e1}+p_{e2}+q_{e1}+q_{e2}+p_{g} \big{)}\big{]} \tag{5}\]  
where \(F_{f}\) is the friction between the shield skin and soil; \(p_{e1}\) is the vertical earth pressure at the top of the shield; \(p_{e2}\) is the vertical earth pressure at the bottom of the shield; \(q_{e1}\) is the horizontal earth pressure at the top of the shield; \(q_{e2}\) is the horizontal earth pressure at the bottom of the shield; \(p_{m}\) is the earth counterforce.  
The synchronous grouting ratio expresses the synchronous grouting quantity level, and its calculation correlation is:  
\[V_{g}^{*}=V_{g}/V_{void} \tag{6}\]  
where \(V_{g}\) is the synchronous grouting quantity within the length of one segment ring; \(V_{void}\) is the ground loss caused within the length of one segment ring.  
To clarify the evolution characteristics of the ground settlement and excess pore water pressure during shield tunneling, the calculation condition (\(P_{s}^{*}=0.90\), \(F_{f}^{*}=0.38\), \(V_{g}^{*}=1.27\)) is chosen to perform the simulation.  
Figure 11 depicts the vertical displacement development curves of the monitoring points. According to the calculation results, the settlement value of point B was greater than that of point A before the shield passed through, which indicated that the soil in the monitoring zone was in a state of vertical expansion. When the shield passed, the uplifting of point B became evident due to the synchronous grouting impact. In addition, the changing trend of the vertical displacement of points C and B was basically the same; however, the direction was opposite.  
Figure 11: Settlement development curves at monitoring points.  
The excess pore water pressure development curves at the monitoring points are shown in Figure 12. According to the findings, it can be concluded that the excess pore water pressure of the monitoring points was closely related to the shield tunneling, and the variations were consistent with the monitoring results in Shanghai [32] and Hangzhou [33].  
The ground settlement and pore water pressure responses caused by shield tunneling in water-rich soft stratum can be categorized into four phases. Stage 1: When the shield machine approaches, small ground deformation is observed. Stage 2: Sensible ground deformation and positive pore water pressure are induced by the arrival of the cutterhead. Stage 3: During the shield passage, the conical shield shell leads to ground loss and the pore water pressure at the measurement point decreases to a negative value. Stage 4: Pour water pressure increases from negative to positive values, and ground deformation rebounds, caused by tail void grouting. As the shield machine drives away, excess pore water pressure dissipates, and the ground settlement increases slightly.  
In summation, the refined shield tunneling model developed in the current study can accurately simulate the vertical ground displacement variation law and excess pore water pressure induced by shield tunneling disturbance in water-rich soft stratum. Therefore, in the next section, the refined model was utilized to investigate the impact of shield tunneling parameters.