# Prediction of Ground Deformation during Pipe-Jacking Considering Multiple Factors
## 4 Application to Case Study
### Validation  
During the construction of Line 1 and Line 3, parameters for the calculation of ground movement have been listed in Table 1. The in situ soil stress in the tunnel face is about 0.4 MPa. The pressure in Table 1 is significant for the stability of the tunnel face. Based on the monitored ground settlements in different depths, the vertical strain can be determined. The average strain level is about 0.1\(\sim\)0.2%, which confirms to the small strain condition. Then, \(G\) is defined as the weighted average value of small strain stiffness. Compared to similar case studies, the adopted value is reasonable [72; 73]. Based on these parameters, the ground deformation can be calculated by the proposed method. The ground settlement is the result of ground deformation at the ground surface. As the ground movements in \(x\) axis direction and y direction are difficult to be monitored in the underground condition, the ground settlements at different depth are used to validate the effectiveness of the proposed method. The Atewell method [74] can compute the settlement along the tunnel path by using the cumulative curve on the results determined by the Peck method. The equation can be expressed as:  
\[S(y)=\frac{V}{\sqrt{2\pi i}}\bigg{[}\Phi\bigg{(}\frac{y-y_{i}}{i}\bigg{)}-\Phi \bigg{(}\frac{y-y_{f}}{i}\bigg{)}\bigg{]} \tag{44}\]  
where, \(i\) is the coefficient of width of ground settlement groove, \(\Phi\) is the integration of Gaussian distribution, \(y_{i}\) is the distance of pipe-jacking, \(y_{f}\) is the distance from tunnel face to the original point. [PERSON] et al. 's method [61] are used to compare the prediction effectiveness. [PERSON]'s method that is usually used in shield tunneling, only considered the effect of ground loss on the ground settlement. [PERSON] et al. 's  
Figure 8: Geotechnical profiles and soil properties of the construction site (based on [PERSON] et al. [71]). Figure 9: Location and vertical distribution of layered settlement gauges. method is a general empirical model based on [PERSON], [PERSON], [PERSON] and [PERSON]'s researches. However, the effect of grouting pressure is ignored in [PERSON] et al. 's method. Figure 10 shows the ground settlements of the monitoring points right above Line 1 and Line 3. Generally, the proposed method has a good consistency with the field results, as compared to the field data and the other two methods. In theoretical calculations, the jacking process will cause an upheaval of the ground surface before the jacking machine arrives at the monitoring point. However, the field data indicated that the upheaval is small in Line 1. For Line 3, the ground surface indicated evidence of settlement. The reason for this is that before the arrival of the jacking machine, the permeation of underground water had caused consolidation behavior. When the jacking machine arrives at the monitoring point, both the calculated results and field observations shows a sharp decrease in ground settlement. The final settlement calculated by the proposed method is the smallest among the calculated results as only the proposed method considers the effect of grouting process. The slurry grouting can apply pressure on the interface, expanding surrounding soils, then mitigating ground settlement. The difference between calculated settlements and field data may attribute to the mutual disturbance during the construction of Line 1 and Line 3. Figure 11 shows the proportions of the single factors as bulkhead thrust force, friction, grouting pressure and ground loss on the overall ground settlement. The main ground settlement is caused by the ground loss. The slurry grouting mitigates the ground settlement effectively after the jacking machine passing through the monitoring point. The ground movements induced by the bulkhead additive thrust and the friction on jacking machine were much smaller than that of ground loss.